<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD with MathML3 v1.3 20210610//EN"  "JATS-archivearticle1-3-mathml3.dtd"><article xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.3"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn publication-format="electronic" pub-type="epub">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">95992</article-id><article-id pub-id-type="doi">10.7554/eLife.95992</article-id><article-id pub-id-type="doi" specific-use="version">10.7554/eLife.95992.3</article-id><article-version article-version-type="publication-state">version of record</article-version><article-categories><subj-group subj-group-type="display-channel"><subject>Research Article</subject></subj-group><subj-group subj-group-type="heading"><subject>Structural Biology and Molecular Biophysics</subject></subj-group></article-categories><title-group><article-title>Activation of polycystin-1 signaling by binding of stalk-derived peptide agonists</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Pawnikar</surname><given-names>Shristi</given-names></name><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>Magenheimer</surname><given-names>Brenda S</given-names></name><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="aff" rid="aff3">3</xref><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>Joshi</surname><given-names>Keya</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0009-0001-8139-478X</contrib-id><xref ref-type="aff" rid="aff4">4</xref><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>Nevarez-Munoz</surname><given-names>Ericka</given-names></name><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>Haldane</surname><given-names>Allan</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0002-8343-1994</contrib-id><xref ref-type="aff" rid="aff5">5</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund7"/><xref ref-type="other" rid="fund8"/><xref ref-type="other" rid="fund9"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Maser</surname><given-names>Robin L</given-names></name><email>rmaser@kumc.edu</email><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="aff" rid="aff3">3</xref><xref ref-type="aff" rid="aff6">6</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund3"/><xref ref-type="other" rid="fund5"/><xref ref-type="fn" rid="con6"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Miao</surname><given-names>Yinglong</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0003-3714-1395</contrib-id><email>Yinglong_Miao@med.unc.edu</email><xref ref-type="aff" rid="aff4">4</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="fn" rid="con7"/><xref ref-type="fn" rid="conf1"/></contrib><aff id="aff1"><label>1</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/001tmjg57</institution-id><institution>Center for Computational Biology and Department of Molecular Biosciences, University of Kansas</institution></institution-wrap><addr-line><named-content content-type="city">Lawrence</named-content></addr-line><country>United States</country></aff><aff id="aff2"><label>2</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/036c9yv20</institution-id><institution>Clinical Laboratory Sciences, University of Kansas Medical Center</institution></institution-wrap><addr-line><named-content content-type="city">Kansas City</named-content></addr-line><country>United States</country></aff><aff id="aff3"><label>3</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/036c9yv20</institution-id><institution>The Jared Grantham Kidney Institute, University of Kansas Medical Center</institution></institution-wrap><addr-line><named-content content-type="city">Kansas City</named-content></addr-line><country>United States</country></aff><aff id="aff4"><label>4</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/0130frc33</institution-id><institution>Department of Pharmacology and Computational Medicine Program, University of North Carolina</institution></institution-wrap><addr-line><named-content content-type="city">Chapel Hill</named-content></addr-line><country>United States</country></aff><aff id="aff5"><label>5</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/00kx1jb78</institution-id><institution>Department of Physics, and Center for Biophysics and Computational Biology, Temple University</institution></institution-wrap><addr-line><named-content content-type="city">Philadelphia</named-content></addr-line><country>United States</country></aff><aff id="aff6"><label>6</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/036c9yv20</institution-id><institution>Department of Biochemistry and Molecular Biology, University of Kansas Medical Center</institution></institution-wrap><addr-line><named-content content-type="city">Kansas City</named-content></addr-line><country>United States</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Cui</surname><given-names>Qiang</given-names></name><role>Reviewing Editor</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/05qwgg493</institution-id><institution>Boston University</institution></institution-wrap><country>United States</country></aff></contrib><contrib contrib-type="senior_editor"><name><surname>Cui</surname><given-names>Qiang</given-names></name><role>Senior Editor</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/05qwgg493</institution-id><institution>Boston University</institution></institution-wrap><country>United States</country></aff></contrib></contrib-group><pub-date publication-format="electronic" date-type="publication"><day>07</day><month>10</month><year>2024</year></pub-date><volume>13</volume><elocation-id>RP95992</elocation-id><history><date date-type="sent-for-review" iso-8601-date="2024-01-28"><day>28</day><month>01</month><year>2024</year></date></history><pub-history><event><event-desc>This manuscript was published as a preprint.</event-desc><date date-type="preprint" iso-8601-date="2024-01-06"><day>06</day><month>01</month><year>2024</year></date><self-uri content-type="preprint" xlink:href="https://doi.org/10.1101/2024.01.06.574465"/></event><event><event-desc>This manuscript was published as a reviewed preprint.</event-desc><date date-type="reviewed-preprint" iso-8601-date="2024-03-04"><day>04</day><month>03</month><year>2024</year></date><self-uri content-type="reviewed-preprint" xlink:href="https://doi.org/10.7554/eLife.95992.1"/></event><event><event-desc>The reviewed preprint was revised.</event-desc><date date-type="reviewed-preprint" iso-8601-date="2024-08-14"><day>14</day><month>08</month><year>2024</year></date><self-uri content-type="reviewed-preprint" xlink:href="https://doi.org/10.7554/eLife.95992.2"/></event></pub-history><permissions><copyright-statement>© 2024, Pawnikar et al</copyright-statement><copyright-year>2024</copyright-year><copyright-holder>Pawnikar et al</copyright-holder><ali:free_to_read/><license xlink:href="http://creativecommons.org/licenses/by/4.0/"><ali:license_ref>http://creativecommons.org/licenses/by/4.0/</ali:license_ref><license-p>This article is distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use and redistribution provided that the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife-95992-v1.pdf"/><self-uri content-type="figures-pdf" xlink:href="elife-95992-figures-v1.pdf"/><abstract><p>Polycystin-1 (PC1) is the protein product of the <italic>PKD1</italic> gene whose mutation causes autosomal dominant Polycystic Kidney Disease (ADPKD). PC1 is an atypical G protein-coupled receptor (GPCR) with an autocatalytic GAIN domain that cleaves PC1 into extracellular N-terminal and membrane-embedded C-terminal (CTF) fragments. Recently, activation of PC1 CTF signaling was shown to be regulated by a stalk tethered agonist (TA), resembling the mechanism observed for adhesion GPCRs. Here, synthetic peptides of the first 9- (p9), 17- (p17), and 21-residues (p21) of the PC1 stalk TA were shown to re-activate signaling by a stalkless CTF mutant in human cell culture assays. Novel Peptide Gaussian accelerated molecular dynamics (Pep-GaMD) simulations elucidated binding conformations of p9, p17, and p21 and revealed multiple specific binding regions to the stalkless CTF. Peptide agonists binding to the TOP domain of PC1 induced close TOP-putative pore loop interactions, a characteristic feature of stalk TA-mediated PC1 CTF activation. Additional sequence coevolution analyses showed the peptide binding regions were consistent with covarying residue pairs identified between the TOP domain and the stalk TA. These insights into the structural dynamic mechanism of PC1 activation by TA peptide agonists provide an in-depth understanding that will facilitate the development of therapeutics targeting PC1 for ADPKD treatment.</p></abstract><kwd-group kwd-group-type="author-keywords"><kwd>PC1</kwd><kwd>ADPKD</kwd><kwd>stalk-derived peptide agonists</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd>Mouse</kwd></kwd-group><funding-group><award-group id="fund1"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R56DK135824</award-id><principal-award-recipient><name><surname>Haldane</surname><given-names>Allan</given-names></name><name><surname>Maser</surname><given-names>Robin L</given-names></name><name><surname>Miao</surname><given-names>Yinglong</given-names></name></principal-award-recipient></award-group><award-group id="fund2"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100017223</institution-id><institution>National Energy Research Scientific Computing Center</institution></institution-wrap></funding-source><award-id>Project M2874</award-id><principal-award-recipient><name><surname>Miao</surname><given-names>Yinglong</given-names></name></principal-award-recipient></award-group><award-group id="fund3"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R01DK123590</award-id><principal-award-recipient><name><surname>Maser</surname><given-names>Robin L</given-names></name></principal-award-recipient></award-group><award-group id="fund4"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000005</institution-id><institution>Department of Defense Education Activity</institution></institution-wrap></funding-source><award-id>CDMRP PRMRP Discovery Award (PR160710/W81XWH-17-1-0301)</award-id><principal-award-recipient><name><surname>Maser</surname><given-names>Robin L</given-names></name></principal-award-recipient></award-group><award-group id="fund5"><funding-source><institution-wrap><institution>Jared Grantham Kidney Institute, KU Medical Center</institution></institution-wrap></funding-source><award-id>Pilot award 1004015</award-id><principal-award-recipient><name><surname>Maser</surname><given-names>Robin L</given-names></name></principal-award-recipient></award-group><award-group id="fund6"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100007890</institution-id><institution>University of North Carolina - Chapel Hill</institution></institution-wrap></funding-source><award-id>Startup project 27110</award-id><principal-award-recipient><name><surname>Miao</surname><given-names>Yinglong</given-names></name></principal-award-recipient></award-group><award-group id="fund7"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R35-GM132090 and OD020095</award-id><principal-award-recipient><name><surname>Haldane</surname><given-names>Allan</given-names></name></principal-award-recipient></award-group><award-group id="fund8"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000001</institution-id><institution>National Science Foundation</institution></institution-wrap></funding-source><award-id>MRI1625061</award-id><principal-award-recipient><name><surname>Haldane</surname><given-names>Allan</given-names></name></principal-award-recipient></award-group><award-group id="fund9"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100006754</institution-id><institution>US Army Research Laboratory</institution></institution-wrap></funding-source><award-id>W911NF-16-2-0189</award-id><principal-award-recipient><name><surname>Haldane</surname><given-names>Allan</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>Structural dynamic insights revealed the mechanisms of PC1 activation by stalk-derived peptide agonists which can form a foundation for development of PC1 as a therapeutic target for ADPKD treatment.</meta-value></custom-meta><custom-meta specific-use="meta-only"><meta-name>publishing-route</meta-name><meta-value>prc</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>PC1 is the protein product of the <italic>PKD1</italic> gene that is mutated in the majority of cases (~85%) of ADPKD (<xref ref-type="bibr" rid="bib12">Harris and Torres, 2014</xref>). ADPKD is a potentially lethal disease, affecting &gt;0.6 million individuals in the US. It causes renal cyst formation that could consequently lead to kidney failure. Currently, the only approved treatment for ADPKD is Jynarque, a small-molecule antagonist of the arginine vasopressin receptor 2, V2R, whose signaling, and production of cAMP has been shown to be increased in PKD. This drug targets one of the aberrant pathways downstream from the PKD gene mutation but is inadequate due to its limitations in only slowing disease progression and causing adverse side effects (<xref ref-type="bibr" rid="bib19">Ingelfinger, 2017</xref>). ADPKD severity is dependent on the functional level of PC1, and as such, therapies designed to increase the level of PC1 protein, and its functionality are currently being pursued (<xref ref-type="bibr" rid="bib15">Hopp et al., 2012</xref>; <xref ref-type="bibr" rid="bib4">Cai et al., 2014</xref>; <xref ref-type="bibr" rid="bib14">Hofherr et al., 2016</xref>; <xref ref-type="bibr" rid="bib22">Krappitz et al., 2016</xref>; <xref ref-type="bibr" rid="bib24">Lakhia et al., 2022</xref>). Approximately one-third of <italic>PKD1</italic> mutations are non-truncating and could encode partially functional PC1 protein (<xref ref-type="bibr" rid="bib15">Hopp et al., 2012</xref>; <xref ref-type="bibr" rid="bib58">Tan et al., 2011</xref>; <xref ref-type="bibr" rid="bib50">Rossetti et al., 2009</xref>; <xref ref-type="bibr" rid="bib13">Heyer et al., 2016</xref>). As such, therapeutic treatments that directly target and activate PC1 may represent a promising approach for the treatment of ADPKD. However, this approach remains difficult due to incomplete knowledge of the proximal-most functions of PC1.</p><p>PC1 shares characteristics with the Adhesion class of GPCRs (ADGRs), including a conserved GPCR autoproteolysis inducing (GAIN) domain that directs autocatalytic cleavage at an embedded GPCR proteolysis site (GPS) motif (<xref ref-type="bibr" rid="bib2">Araç et al., 2012</xref>). Intramolecular cleavage at the GPS motif generates two non-covalently attached fragments - the extracellular N-terminal fragment (NTF) and the membrane-embedded C-terminal fragment (CTF) (<xref ref-type="bibr" rid="bib46">Qian et al., 2002</xref>; <xref ref-type="bibr" rid="bib23">Kurbegovic et al., 2014</xref>). Similar to ADGRs, the PC1 NTF consists of multiple adhesive domains that promote interactions between cells and with the extracellular matrix (<xref ref-type="bibr" rid="bib21">Kim et al., 2016</xref>; <xref ref-type="bibr" rid="bib65">Weston et al., 2001</xref>; <xref ref-type="bibr" rid="bib51">Sandford et al., 1997</xref>; <xref ref-type="bibr" rid="bib18">Ibraghimov-Beskrovnaya et al., 2000</xref>; <xref ref-type="bibr" rid="bib66">Weston et al., 2003</xref>), while the PC1 CTF is composed of 11 transmembrane (TM) helices and a short C-terminal tail (C-tail) (<xref ref-type="bibr" rid="bib38">Nims et al., 2003</xref>) that has been shown to interact with G proteins for signaling activation or regulation (<xref ref-type="bibr" rid="bib30">Maser and Calvet, 2020</xref>; <xref ref-type="bibr" rid="bib31">Maser et al., 2022</xref>) and has thus led to description of PC1 as an atypical GPCR. Previous studies demonstrated the critical importance of cleavage at the PC1 GPS site to prevent renal cystogenesis in mouse models (<xref ref-type="bibr" rid="bib4">Cai et al., 2014</xref>; <xref ref-type="bibr" rid="bib68">Yu et al., 2007</xref>). For the ADGRs, a TA model has been proposed for activation of G protein signaling. After dissociation of the NTF, the N-terminal stalk of the ADGR CTF interacts with its membrane-embedded TM domains to induce conformational rearrangements that mediate activation of G protein signaling (<xref ref-type="bibr" rid="bib27">Liebscher et al., 2014</xref>; <xref ref-type="bibr" rid="bib52">Schöneberg et al., 2015</xref>; <xref ref-type="bibr" rid="bib8">Demberg et al., 2015</xref>; <xref ref-type="bibr" rid="bib55">Stoveken et al., 2015</xref>). Exogenous synthetic peptides consisting of various lengths of the N-terminal sequence of the stalk have been shown to function as soluble agonists in the activation of signaling by full-length and CTF mutants for numerous ADGRs (<xref ref-type="bibr" rid="bib30">Maser and Calvet, 2020</xref>; <xref ref-type="bibr" rid="bib67">Xiao et al., 2022</xref>).</p><p>In previous studies of the PC1 CTF, we revealed a stalk TA-dependent molecular mechanism underlying CTF-mediated activation of an NFAT promoter luciferase reporter through complementary <italic>in vitro</italic> cell signaling experiments and all-atom Gaussian accelerated Molecular Dynamics (GaMD) simulations (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>). GaMD is an unconstrained enhanced sampling method that works by adding a harmonic boost potential to reduce large biomolecular energy barriers (<xref ref-type="bibr" rid="bib32">Miao et al., 2014</xref>) and has been used successfully to capture multiple complex biological processes (<xref ref-type="bibr" rid="bib33">Miao et al., 2015</xref>; <xref ref-type="bibr" rid="bib34">Miao and McCammon, 2016</xref>; <xref ref-type="bibr" rid="bib40">Pang et al., 2017</xref>; <xref ref-type="bibr" rid="bib35">Miao and McCammon, 2017</xref>; <xref ref-type="bibr" rid="bib62">Wang and Chan, 2017</xref>; <xref ref-type="bibr" rid="bib26">Liao and Wang, 2019</xref>; <xref ref-type="bibr" rid="bib36">Miao et al., 2018</xref>; <xref ref-type="bibr" rid="bib5">Chuang et al., 2018</xref>; <xref ref-type="bibr" rid="bib53">Sibener et al., 2018</xref>; <xref ref-type="bibr" rid="bib41">Park et al., 2018</xref>; <xref ref-type="bibr" rid="bib37">Miao and McCammon, 2018</xref>; <xref ref-type="bibr" rid="bib48">Ricci et al., 2019</xref>; <xref ref-type="bibr" rid="bib39">Palermo et al., 2017</xref>; <xref ref-type="bibr" rid="bib3">Bhattarai et al., 2020</xref>; <xref ref-type="bibr" rid="bib43">Pawnikar and Miao, 2020</xref>) including GPCR activation (<xref ref-type="bibr" rid="bib34">Miao and McCammon, 2016</xref>). Expression constructs encoding a stalkless PC1 CTF (a nonbiological mutant with deletion of the first 21 N-terminal residues of CTF) and three ADPKD-associated missense mutants within the stalk region (G3052R, R3063C, and R3063P) were shown to be defective in reporter activation as compared to wild-type PC1 CTF. GaMD simulations revealed a novel allosteric transduction pathway for activation of PC1 CTF signaling that involves initiation by the Stalk interacting with a large extracellular loop between TM segments S1/TM6 and S2/TM7, called the TOP domain, followed by close interactions between the TOP and a putative pore loop (PL) domain between the final 2 TM domains. GaMD simulations of the wild-type PC1 CTF also identified a ‘Closed/Active’ low-energy state related to the large number of Stalk-TOP contacts and the R3848-E4078 ionic interaction between the TOP and PL domains that was not present in the stalkless CTF (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>).</p><p>Here, we have utilized <italic>in vitro</italic> cell signaling assays to identify peptide agonists targeting PC1 in combination with <italic>in silico</italic> studies to investigate their binding mechanisms for activation of PC1 signaling. Synthetic peptides of 7–21 residues in length derived from the N-terminus of the PC1 CTF stalk sequence were tested for their ability to re-activate signaling of the stalkless CTF expression construct. Peptide docking and simulations with the recently developed Peptide GaMD (Pep-GaMD), which is able to characterize peptide-protein binding processes more efficiently (<xref ref-type="bibr" rid="bib64">Wang and Miao, 2020</xref>), were combined for selected peptide agonists p9, p17, and p21 to gain insight into their binding mechanism to the stalkless PC1 CTF. Pep-GaMD was able to successfully refine the docking conformations of the peptides bound to the extracellular TOP domain of PC1. In further Pep-GaMD simulations, the key salt bridge interaction between R3848 and E4078 from the TOP domain and PL, respectively, was observed upon binding of the peptides to stalkless PC1 CTF. Using Potts covariation analysis, in which a protein fitness model is inferred based on observed mutational covariation patterns in multiple sequence alignments (MSAs) of homologous proteins (<xref ref-type="bibr" rid="bib25">Levy et al., 2017</xref>), we identified residues in the PC1 stalk with direct mutational covariation with residues in the TOP domain, which were strikingly consistent with the binding interfaces identified in docking and simulation studies. Overall, these analyses yielded mechanistic insights underlying the stalk peptide agonist-mediated signal re-activation of stalkless PC1 CTF. Such insights provide significant contributions toward the future design and development of peptide modulators targeting PC1 for an effective ADPKD therapeutic treatment.</p></sec><sec id="s2" sec-type="results"><title>Results</title><sec id="s2-1"><title>Synthetic, stalk-derived peptides re-activate NFAT reporter by CTF<sup>∆st</sup> <italic>in trans</italic></title><p>Our previous study utilized expression constructs of human PC1 CTF. However, in order to prepare for eventual <italic>in vivo</italic> experiments in mouse models, we generated expression constructs of mouse (m) PC1 consisting of the signal peptide sequence of the T cell surface glycoprotein CD5 (MPMGSLQPLATLYLLGMLVASVLG) fused in frame with the stalk sequence of wild-type mCTF beginning with residue T3041, or with a ‘stalkless’ CTF lacking the first 21 residues of the stalk (mCTF<sup>∆st</sup>) beginning with residue S3062 (<xref ref-type="fig" rid="fig1">Figure 1A</xref>). The CD5 signal peptide coding sequence was added to the wild-type mCTF and stalkless mCTF<sup>∆st</sup> expression constructs in order to ensure their translation at the endoplasmic reticulum for plasma membrane localization.</p><fig-group><fig id="fig1" position="float"><label>Figure 1.</label><caption><title>Synthetic peptides derived from the stalk sequence of polycystin-1 (PC1) can stimulate the signaling of stalkless PC1 C-terminal fragment (CTF).</title><p>(<bold>A</bold>) Alignment of CTF stalk sequences from human (<bold>h</bold>) and mouse (<bold>m</bold>) PC1. CTF<sup>∆st</sup> has a 21-residue deletion from the N-terminal end of the stalk region. Arrow, GPCR proteolysis site (GPS) cleavage site. Non-identical residues are shown in bolded blue. (<bold>B</bold>) Activation of the NFAT-luc reporter by transfected mCTF or mCTF<sup>∆st</sup> expression constructs shown relative to empty expression vector (ev) as means (+ standard deviation, SD) of three wells/construct from each of seven independent experiments. (<bold>C</bold>) Representative Western blot of total cell lysates from one of the experiments in (<bold>B</bold>), probed with antisera A19 against mouse PC1 C-tail. ns, non-specific. (<bold>D</bold>) Summary of the total expression levels (means + SD) of CTF<sup>∆st</sup> relative to CTF from the experiments in (<bold>B</bold>). (<bold>E</bold>) Stalk peptide treatment of expression vector (ev)- or mCTF<sup>∆st</sup>-transfected cells. Sequences of stalk-derived peptides p7-p21 are shown. Graph represents the fold NFAT-luc activation for both ev- (gray bars) and CTF<sup>∆st</sup>- (blue bars) transfected cells relative to the CTF<sup>∆st</sup> control after 24 hr treatment with or without peptide. Results are the means (+ SD) of three separate experiments, each with three wells/conditions. *p&lt;0.05; ***p=0.0001; ****p&lt;0.0001. Analysis by one-way ANOVA with Tukey-Kramer post-test.</p><p><supplementary-material id="fig1sdata1"><label>Figure 1—source data 1.</label><caption><title>Uncropped and labeled Western blot data for <xref ref-type="fig" rid="fig1">Figure 1C</xref>.</title></caption><media mimetype="application" mime-subtype="zip" xlink:href="elife-95992-fig1-data1-v1.zip"/></supplementary-material></p><p><supplementary-material id="fig1sdata2"><label>Figure 1—source data 2.</label><caption><title>Raw unedited Western blot data for <xref ref-type="fig" rid="fig1">Figure 1C</xref>.</title></caption><media mimetype="application" mime-subtype="zip" xlink:href="elife-95992-fig1-data2-v1.zip"/></supplementary-material></p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig1-v1.tif"/></fig><fig id="fig1s1" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 1.</label><caption><title>Cell surface expression of mouse polycystin-1 (PC1) C-terminal fragment (CTF), and mCTF<sup>∆stk</sup>.</title><p>Representative Western blot of a surface biotinylation experiment with mCTF and mCTF<sup>∆stk</sup>. (<bold>A</bold>) ‘- biotin’ control was included using CTF-transfected cells for which the NHS-biotin reagent was omitted from the procedure. Aliquots of the total cell lysate (input; after biotinylation and before neutravidin pulldown), supernatant (sup; following neutravidin bead removal), and biotinylated cell surface proteins bound to neutravidin beads (beads) representing 10%, 10%, and 70% of each sample, respectively, were analyzed. Blots were probed with A19 and then stripped and reprobed for NaKATPase or the resident ER protein, TRAM2. (<bold>B</bold>) Summary of cell surface expression levels of CTF<sup>∆stk</sup> relative to CTF (means + SD) from two separate experiments.</p><p><supplementary-material id="fig1s1sdata1"><label>Figure 1—figure supplement 1—source data 1.</label><caption><title>Uncropped and labeled Western blot data for <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplements 1</xref> and <xref ref-type="fig" rid="fig1s2">2</xref>.</title></caption><media mimetype="application" mime-subtype="zip" xlink:href="elife-95992-fig1-figsupp1-data1-v1.zip"/></supplementary-material></p><p><supplementary-material id="fig1s1sdata2"><label>Figure 1—figure supplement 1—source data 2.</label><caption><title>Raw unedited Western blot data for <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplements 1</xref> and <xref ref-type="fig" rid="fig1s2">2</xref>.</title></caption><media mimetype="application" mime-subtype="zip" xlink:href="elife-95992-fig1-figsupp1-data2-v1.zip"/></supplementary-material></p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig1-figsupp1-v1.tif"/></fig><fig id="fig1s2" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 2.</label><caption><title>Solubility tag peptide treatment of ev- or CTF<sup>∆st</sup>-transfected cells.</title><p>(<bold>A</bold>) Sequences of the p17 stalk peptide derived from human polycystin-1 (PC1) and the solubility tag peptide (sol tag). Residues differing from the mouse PC1 stalk sequence are shown in blue. (<bold>B–D</bold>) HEK293T cells were transfected with an empty expression vector (ev) or the CTF<sup>∆st</sup> expression construct from either mouse (<bold>B</bold>) or mouse PC1, and transfected cells were treated either without (negative control; culture medium only) or with human p17 peptide (positive control) or sol tag peptide. Graphs show the NFAT-luc activity for ev- (gray bars) and CTF<sup>∆st</sup>- (blue bars) transfected cells after 24 hr treatment with or without peptide for each experiment. Results are the means (+ SD) of reporter activity from three wells/conditions in each experiment. *p&lt;0.05, **p&lt;0.01, ***p&lt;0.001; ****p&lt;0.0001; ns = not significant. Analysis by one-way ANOVA with Tukey-Kramer post-test. In each of the experimental replicates, treatment with the sol tag peptide led to a nominal ~2 fold increase in reporter activity with CTF<sup>∆st</sup>- versus ev-transfected cells (2.24-, 1.60-, and 2.02-fold for B-D, respectively). Although the level of NFAT reporter activity stimulated by the positive control p17 in CTF<sup>∆st</sup>-transfected cells varied between the three experiments, the effect of the sol tag peptide on CTF<sup>∆st</sup>- (and ev-) transfected cells was consistent and differed significantly in comparison to CTF<sup>∆st</sup>-transfected cells with p17 treatment in all three experiments (regardless of PC1 origin). Furthermore, the NFAT-luc activity of CTF<sup>∆st</sup>+ sol tag-treated cells did not differ from ev + p17-treated cells for each experiment, suggesting that the ‘background’ reporter activation observed with ev + stalk peptide versus ev + no peptide control may be due to the solubility tag. Altogether, these results support the rescue of CTF<sup>∆st</sup> signaling by certain stalk-derived peptides is specific to the stalk sequence itself.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig1-figsupp2-v1.tif"/></fig></fig-group><p>Transient transfection of HEK293T cells with either empty expression vector (ev), CTF or CTF<sup>∆st</sup> showed that the CTF<sup>∆st</sup> mutant exhibited a dramatic loss of NFAT reporter activation that was essentially reduced to ev control levels (<xref ref-type="fig" rid="fig1">Figure 1B</xref>). Both total (<xref ref-type="fig" rid="fig1">Figure 1C–D</xref>) and cell surface (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A–B</xref>) expression levels of CTF<sup>∆st</sup> were comparable to CTF, which suggests that neither protein stability nor membrane trafficking was responsible for the inability of CTF<sup>∆st</sup> to activate the NFAT reporter. These results are consistent with those obtained using expression constructs of human PC1 that demonstrated the stalk region of PC1 CTF acts as a tethered peptide agonist (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>).</p><p>To further investigate the agonistic property of the CTF stalk, we synthesized peptides (p) consisting of the N-terminal 7, 9, 11, 13, 15, 17, 19, or 21 residues from the stalk sequence of mPC1. All peptides were appended with a C-terminal, 7-residue hydrophilic sequence (GGKKKKK) to increase solubility. HEK293T cells were transiently transfected with empty expression vector or mCTF<sup>∆st</sup> plasmids along with the NFAT luciferase reporter and then treated with stalk peptides p7 through p21 or with the addition of culture medium only (‘no peptide’ control). The NFAT reporter was significantly activated in CTF<sup>∆st</sup>-transfected cells by treatment with p7, p9 or p17 as compared to their corresponding ev + peptide treatment controls. These stalk peptides also significantly increased reporter activity in comparison to the CTF<sup>∆st</sup> with no peptide treatment control (<xref ref-type="fig" rid="fig1">Figure 1E</xref>). Treatment of CTF<sup>∆st</sup>-transfected cells with p19 or p21 also significantly increased reporter activation in comparison to the CTF<sup>∆st</sup> + no peptide control; however, reporter activation occurred in both ev- and CTF<sup>∆st</sup>-transfected cells treated with either p19 or p21, suggesting that p19- and p21-mediated activation was not dependent on exogenous expression of mouse CTF<sup>∆st</sup> and could be activating the endogenous human PC1 protein. Treatment of ev- and CTF<sup>∆st</sup>-transfected cells with a peptide consisting of the hydrophilic sequence alone (i.e., solubility peptide) showed that the solubility tag was not responsible for the rescue of CTF<sup>∆st</sup>-mediated reporter activation by stalk peptides such as p17 (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2</xref>). Altogether, these results were consistent with soluble stalk-derived peptides acting as PC1 CTF agonists <italic>in trans</italic>, and provided additional support for the PC1 CTF stalk region harboring TA activity (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>). We hypothesized that the soluble, activating peptides bind to the TOP domain of PC1 in a manner mimicking the tethered stalk in order to reactivate the signaling of the stalkless CTF<sup>∆st</sup> mutant. From among the active stalk-derived peptides, we selected p9, p17, and p21 that exhibited the highest agonist activity in CTF<sup>∆st</sup> reporter activation (<xref ref-type="fig" rid="fig1">Figure 1E</xref>) for <italic>in silico</italic> simulation studies.</p></sec><sec id="s2-2"><title>Docking and Pep-GaMD simulations of peptide agonist binding to stalkless PC1 CTF</title><p>We chose to use the stalkless CTF (∆Stalk CTF) as representing the least complex system in which the binding of exogenous peptides could be studied. ∆Stalk CTF is not a biological form or a mutant protein of PC1 observed in ADPKD. However, in our previous study, it mimicked the ADPKD-associated stalk mutants by being defective in cell signaling assays and rarely formed the R3848-E4078 salt bridge that was frequently seen in GaMD simulations with wild-type CTF (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>). Therefore ∆Stalk CTF served as the negative control for the following studies.</p><p>The cryo-EM structure of the human PC1-PC2 complex (PDB: 6A70) (<xref ref-type="bibr" rid="bib56">Su et al., 2018</xref>) was used to build the computational model for ΔStalk PC1 CTF after deleting the first 21 residues (3049–3069) from the CTF (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>). We successfully docked the p9, p17, and p21 stalk peptides to the ∆Stalk CTF model with HPEPDOCK (<xref ref-type="bibr" rid="bib69">Zhou et al., 2018</xref>) (See Materials and Methods). The peptides are all bound to the TOP domain and the interface between the TOP domain and extracellular loop 1 (ECL1) of CTF (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1A–B</xref>). In particular, peptide p21 occupied a closely similar binding region as the stalk in wild-type CTF as observed in the previous study (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>). We then performed five independent 500 ns Pep-GaMD simulations on each of the three stalk peptide agonists p9, p17 and p21 bound to ΔStalk CTF to refine their HPEPDOCK docking conformations (See Materials and Methods).</p><p>With the Pep-GaMD simulation frames, we performed structural clustering of each peptide using the hierarchical agglomerative algorithm in CPPTRAJ (<xref ref-type="bibr" rid="bib49">Roe and Cheatham, 2013</xref>). The top-ranked conformations of each peptide bound to ΔStalk CTF were compared to their initial docking conformations. Next, we calculated 2D free energy profiles of the peptides-bound ΔStalk CTF by reweighting the Pep-GaMD simulations. The R3848-E4078 residue distance and the number of contacts between the peptides (p9, p17, and p21) and the TOP domain were selected as the reaction coordinates. The number of contacts was calculated between any atom pairs within 4 Å distance of the peptide and extracellular domains of the PC1 protein. In the subsequent analyses, stalk and peptide residues are numbered relative to the N terminus of the stalk as starting from 1, while residues of the ∆stalk CTF are numbered according to the human PC1 protein sequence.</p></sec><sec id="s2-3"><title>Active conformation of peptide p9-bound PC1 CTF</title><p>From the free energy profile of the p9-bound ΔStalk CTF, we identified ‘Unbound’ and ‘Bound’ low-energy states (<xref ref-type="fig" rid="fig2">Figure 2A</xref>). In the docking conformation, peptide p9 bound to the interface between the TOP and ECL1 of ΔStalk CTF (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1A–B</xref>). In Pep-GaMD simulations, the p9 peptide dissociated from the TOP-ECL1 binding pocket and rebound to the TOP domain in a slightly different region (<xref ref-type="fig" rid="fig2">Figure 2B–C</xref>). The p9 peptide sequence is mostly composed of hydrophobic residues. Polar interactions between the main chain atoms of peptide-protein residues were observed in the top-ranked representative conformation of the p9-bound ΔStalk CTF. Protein residues R3892 and H3864 formed hydrogen bonds with p9 residues A2 and A5, respectively (<xref ref-type="fig" rid="fig2">Figure 2D</xref>). These interactions were also highlighted in the protein contact map between peptide p9 and the extracellular domains of CTF in the representative ‘Bound’ state (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2</xref>). The distance between the TOP domain residue R3848 and PL residue E4078 was 3.9 Å (<xref ref-type="fig" rid="fig2">Figure 2E</xref>), suggesting that the top-ranked representative conformation of the p9-bound ΔStalk CTF was in the ‘Closed/Active’ low-energy state. In addition, the 2D free energy profile of each individual simulation was calculated and the ‘Bound’ low-energy state was consistently identified in the 2D free energy profiles of peptide p9 (<xref ref-type="fig" rid="fig2s3">Figure 2—figure supplement 3</xref>).</p><fig-group><fig id="fig2" position="float"><label>Figure 2.</label><caption><title>Free energy profile and low-energy conformations of the p9-bound ΔStalk CTF obtained from Pep-GaMD simulations.</title><p>(<bold>A</bold>) Free energy profile of the p9-bound ΔStalk CTF regarding the number of atom contacts between p9 and extracellular domains of CTF and the distance between the CZ atom of R3848 and the CD atom of R4078 in CTF. (<bold>B–C</bold>) Comparison of HPEPDOCK docking (cyan) and Pep-GaMD refined (magenta) conformations of peptide p9 in ΔStalk CTF. (<bold>D</bold>) Polar interactions between peptide-protein residues were observed in the top-ranked representative conformations of p9. Peptide residues are numbered relative to the N terminus of the stalk with the peptide starting from 1, while residues within ∆Stalk CTF are numbered according to the standard polycystin-1 (PC1) residue number. (<bold>E</bold>) Distance between the TOP domain residue R3848 and pore loop (PL) residue E4078 observed in p9-bound ΔStalk CTF.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig2-v1.tif"/></fig><fig id="fig2s1" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 1.</label><caption><title>Peptide docking conformations and computational model for Peptide GaMD (Pep-GaMD) simulations.</title><p>(<bold>A–B</bold>) Docking conformations of p9, p17, and p21 to ΔStalk CTF. (<bold>C</bold>) Pep-GaMD simulation system of ΔStalk polycystin-1 (PC1) C-terminal fragment (CTF) (blue cartoon) embedded in a palmitoyl-oleoyl-phosphatidyl-choline (POPC) lipid bilayer (orange sticks) solvated in 0.15 M NaCl solution.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig2-figsupp1-v1.tif"/></fig><fig id="fig2s2" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 2.</label><caption><title>Contact maps showing residue-pairs in contact (black squares) between the peptide (y-axis) and the extracellular domains of C-terminal fragment (CTF) (x-axis), in the representative ‘Bound’ state for p21 (top), p17 (middle), and p9 (bottom).</title><p>Contacts were defined by a distance less than 4 Å between any atom in each residue pair. The secondary structure annotation is colored as in <xref ref-type="fig" rid="fig5">Figure 5</xref>, and the sequence is annotated with amino acids in ‘Taylor’ color scheme. For p9, an additional cluster of contacts with residues in helix S3 are not shown.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig2-figsupp2-v1.tif"/></fig><fig id="fig2s3" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 3.</label><caption><title>2D free energy profiles of the p9 system regarding the number of atom contacts between the p9 and protein extracellular domains and the R3848-E4078 distance (the CZ atom in R3848 and the CD atom in E4078) calculated from (<bold>A</bold>) Sim1, (<bold>B</bold>) Sim2, (<bold>C</bold>) Sim3, (<bold>D</bold>) Sim4, and (<bold>E</bold>) Sim5 of the Peptide GaMD (Pep-GaMD) simulations.</title><p>Important low-energy conformational states are identified, including the ‘Unbound’ and ‘Bound’.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig2-figsupp3-v1.tif"/></fig></fig-group></sec><sec id="s2-4"><title>Active and intermediate conformational states of peptide p17-bound PC1 CTF</title><p>The free energy profile of the p17-bound ΔStalk system allowed us to identify three low-energy states - ‘Unbound,’ ‘Intermediate,’ and ‘Bound’ (<xref ref-type="fig" rid="fig3">Figure 3A</xref>). In the docking conformation, peptide p17 bound to the interface between the TOP and ECL1 of ΔStalk CTF (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1A–B</xref>). In the Pep-GaMD refined ‘Bound’ state, a folded antiparallel ß-strand conformation was observed for the peptide p17 at the interface of ECL1 and the TOP domain (<xref ref-type="fig" rid="fig3">Figure 3B–C</xref>). Peptide residues T1, F3, A5, F8, F16, and V17 formed hydrophobic interactions with the protein residues H3311, R3314 and Y3307 from ECL1, and E3708, S3711, Q3707, A3704, R3700, and L3701 from the TOP domain (<xref ref-type="fig" rid="fig3">Figure 3D</xref>). These interactions were also highlighted in the protein contact map between peptide p17 and the extracellular domains of CTF in the representative ‘Bound’ state (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2</xref>). The distance between the TOP domain residue R3848 and PL residue E4078 was 4.1 Å (<xref ref-type="fig" rid="fig3">Figure 3E</xref>), suggesting that the top-ranked representative conformation of the p17 bound ΔStalk CTF was in the ‘Closed/Active’ low-energy state.</p><fig-group><fig id="fig3" position="float"><label>Figure 3.</label><caption><title>Free energy profile and low-energy conformations of the p17-bound ΔStalk CTF obtained from Pep-GaMD simulations.</title><p>(<bold>A</bold>) Free energy profile of the p17-bound ΔStalk CTF regarding the number of atom contacts between p17 and extracellular domains of CTF and the distance between the CZ atom of R3848 and the CD atom of R4078 in CTF. (<bold>B–C</bold>) Comparison of HPEPDOCK docking (cyan) and Pep-GaMD refined (magenta) conformations of peptide p17 in ΔStalk CTF. Hydrophobic interactions (red dashed lines) between peptide-protein residues were observed in the (<bold>D</bold>) 'Bound’ and (<bold>F</bold>) 'Intermediate’ low-energy conformations of p17-bound ΔStalk CTF. Distance between the TOP domain residue R3848 and pore loop (PL) residue E4078 observed in the (<bold>E</bold>) ‘Bound’ and (<bold>G</bold>) ‘Intermediate’ low-energy conformations of p17-bound ΔStalk CTF.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig3-v1.tif"/></fig><fig id="fig3s1" position="float" specific-use="child-fig"><label>Figure 3—figure supplement 1.</label><caption><title>2D free energy profiles of the p17 system regarding the number of atom contacts between the p17 and protein extracellular domains and the R3848-E4078 distance (the CZ atom in R3848 and the CD atom in E4078) calculated from (<bold>A</bold>) Sim1, (<bold>B</bold>) Sim2, (<bold>C</bold>) Sim3, (<bold>D</bold>) Sim4, and (<bold>E</bold>) Sim5 of the Peptide GaMD (Pep-GaMD) simulations.</title><p>Important low-energy conformational states are identified, including the ‘Unbound’ ‘Intermediate,’ and ‘Bound’.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig3-figsupp1-v1.tif"/></fig></fig-group><p>In the ‘Intermediate’ state, p17 with a short helical turn was also observed to bind the TOP domain of ΔStalk CTF (<xref ref-type="fig" rid="fig3">Figure 3B–C</xref>). Hydrophobic residue interactions were also formed between the peptide and protein. In particular, peptide residues T1, F3, P10, P11, H13, R15, F16, and V17 formed hydrophobic interactions with the protein residues P3859, A3704, S3741, Q3739, Y3734, P3733, H3729, W3726, R3712, and R3856 from the TOP domain (<xref ref-type="fig" rid="fig3">Figure 3F</xref>). The distance between the TOP domain residue R3848 and PL residue E4078 was 14.6 Å (<xref ref-type="fig" rid="fig3">Figure 3G</xref>), suggesting that this representative conformation (ranked the second among the Pep-GaMD structural clusters) of the p17-bound ΔStalk CTF was in the ‘Intermediate’ low-energy state. In addition, the 2D free energy profile of each individual simulation was calculated. Pep-GaMD simulations were able to refine the peptide conformation from the ‘Unbound’ to ‘Intermediate,’ and ‘Bound’ states in Sim1 and Sim5, while the peptide reached only the ‘Intermediate’ state in the other three simulations (<xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref>). The free energy values of 2D PMF minima shown in <xref ref-type="fig" rid="fig3">Figure 3A</xref> could differ from those in the 1D PMF minima of peptide structural clusters, especially with the usage of distinct reaction coordinates.</p></sec><sec id="s2-5"><title>Active conformational state of peptide p21-bound PC1 CTF</title><p>Finally, the free energy profile of the p21-bound ΔStalk CTF allowed us to identify only a broad low-energy well corresponding to the ‘Bound’ state (<xref ref-type="fig" rid="fig4">Figure 4A</xref>). The docking conformation of p21-bound ΔStalk CTF was refined through Pep-GaMD simulations, where folding of the peptide was observed on the protein surface of the TOP domain (<xref ref-type="fig" rid="fig4">Figure 4B–C</xref>). The p21 peptide occupied a similar binding region as the stalk in wild-type CTF as observed in the previous study (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>). Hydrophobic contacts were observed between peptide residues L7, F8, P10, S12, H13, V14, V17, P19, E20, and P21 and protein residues L3863, L3701, I3705, L3709, E3708, R3712, F3714, H3729, W3726, V3730, L3732, P3733, N3738, R3856, and S3741 (<xref ref-type="fig" rid="fig4">Figure 4D</xref>). These interactions were also highlighted in the protein contact map between peptide p21 and the extracellular domains of CTF in the representative ‘Bound’ state (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2</xref>). The distance calculated from the top-ranked structural cluster of the system between the TOP domain residue R3848 and PL residue E4078 was 3.8 Å, corresponding to the ‘Closed/Active’ low-energy state (<xref ref-type="fig" rid="fig4">Figure 4E</xref>). Furthermore, time courses of the radius of gyration (<italic>Rg</italic>) and root-mean-square deviation (RMSD) of p21 relative to the starting HPEPDOCK conformation showed large conformational changes of the peptide during Pep-GaMD simulations (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1A–C</xref>). In addition, the 2D free energy profile of each individual simulation showed that Pep-GaMD was able to refine the peptide docking conformation to the ‘Bound’ state in all the five simulations (<xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2</xref>).</p><fig-group><fig id="fig4" position="float"><label>Figure 4.</label><caption><title>Free energy profile and low-energy conformations of the p21-bound ΔStalk CTF obtained from Pep-GaMD simulations.</title><p>(<bold>A</bold>) Free energy profile of the p21-bound ΔStalk CTF regarding the number of atom contacts between p21 and extracellular domains of CTF and the distance between the CZ atom of R3848 and the CD atom of R4078 in CTF. (<bold>B–C</bold>) Comparison of HPEPDOCK docking (cyan) and Pep-GaMD refined (magenta) conformations of peptide p21 in ΔStalk CTF. (<bold>D</bold>) Polar interactions between peptide-protein residues were observed in the top-ranked representative conformations of p21. (<bold>E</bold>) Distance between the TOP domain residue R3848 and pore loop (PL) residue E4078 observed in p21-bound ΔStalk CTF.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig4-v1.tif"/></fig><fig id="fig4s1" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 1.</label><caption><title>Time courses of the p21 system obtained from the five Peptide GaMD (Pep-GaMD) simulations.</title><p>(<bold>A</bold>) Time courses of the p21 system regarding the TOP-pore loop (PL) interaction distance between the CZ atom in R3848 and the CD atom in E4078. (<bold>B</bold>) Time courses of the root-mean-square deviation (RMSD) of p21 relative to the starting HPEPDOCK conformation of the peptide. (<bold>C</bold>) Time courses of the radius of gyration (<italic>Rg</italic>) of p21.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig4-figsupp1-v1.tif"/></fig><fig id="fig4s2" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 2.</label><caption><title>2D free energy profiles of the p21 system regarding the number of atom contacts between the p21 and protein extracellular domains and the R3848-E4078 distance (the CZ atom in R3848 and the CD atom in E4078) calculated from (<bold>A</bold>) Sim1, (<bold>B</bold>) Sim2, (<bold>C</bold>) Sim3, (<bold>D</bold>) Sim4, and (<bold>E</bold>) Sim5 of the Peptide GaMD (Pep-GaMD) simulations.</title><p>Important low-energy conformational state is identified, including the ‘Bound’.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig4-figsupp2-v1.tif"/></fig></fig-group></sec><sec id="s2-6"><title>Peptide binding regions correlated with covarying residue pairs identified between the TOP domain and stalk TA</title><p>To provide an independent basis of evidence supporting the observation of ‘Bound’ and ‘Intermediate’ states of agonist peptide binding, we constructed a multiple sequence alignment (MSA) with an effective count of 1022 evolutionarily diverged PC1 homologs (illustrated in <xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>) from which we inferred a Potts statistical model (<xref ref-type="fig" rid="fig5">Figure 5</xref>). Columns of the MSA with ‘direct’ statistical interactions, as detected using the Potts inference method, reflect compensatory mutation pairs maintained through evolution supporting a conserved function. We limited our MSA to 394 residues on the extracellular side of PC1 because of the computational challenge of fitting the entire PC1 sequence (<xref ref-type="fig" rid="fig5">Figure 5B</xref> and <xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>).</p><fig-group><fig id="fig5" position="float"><label>Figure 5.</label><caption><title>Potts covariation analysis of residue interactions in polycystin-1 (PC1).</title><p>(<bold>A</bold>) Potts interaction map based on the Polycystic Kidney Disease 1 (<italic>PKD1)</italic> multiple-sequence-alignment illustrated in <xref ref-type="fig" rid="fig5s2">Figure 5—figure supplement 2</xref>, showing interactions with the stalk. Gray dots are shown for residue position-pairs with Potts covariation scores above a threshold, colored darker for higher scores, and selected interacting pairs are annotated with the stalk residue (horizontal, numbered from the stalk N-terminus) and other residue (vertical, standard PC1 numbering) with the PC1 residue at each position. The secondary structure as a function of position is annotated along the axes. (<bold>B</bold>) Cartoon showing the subset of PC1 included in the Potts covariation analysis colored as in the secondary structure in panel A, using a structure predicted by AlphaFold. Gray regions were excluded from the Potts model. (<bold>C</bold>) Residue Covariation scores for selected position-pairs. The scores reflect the percentage excess frequency of the residue-pair relative to the null expected frequency if the multiple sequence alignment (MSA) columns were uncorrelated, with blue values reflecting excess and red dearth. Only the most common residue types are shown.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig5-v1.tif"/></fig><fig id="fig5s1" position="float" specific-use="child-fig"><label>Figure 5—figure supplement 1.</label><caption><title>Sequence alignment of Polycystic Kidney Disease 1 (<italic>PKD1)</italic> homologs showing the 394-residue extracellular region included in the Potts model.</title><p>The full alignment includes 4383 sequences, and only six diverse homologs are shown for illustration. The polycystin-1 (PC1) sequence is shown including inserts relative to the alignment (lower case with a gray background, matched with ‘.’ in homologs), inserts are not shown for the six homologs. Gaps characters are indicated as ‘-,’ representing positions included in the alignment which were missing in that sequence. The human PC1 protein sequence residue numbering is indicated at the bottom ends of each aligned region.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig5-figsupp1-v1.tif"/></fig><fig id="fig5s2" position="float" specific-use="child-fig"><label>Figure 5—figure supplement 2.</label><caption><title>Comparison of residue-residue interactions within the end of the polycystin-1 (PC1) GPCR autoproteolysis inducing (GAIN) domain.</title><p>(<bold>A</bold>) Interactions predicted using the Potts model, shaded by interaction strength. Secondary structure elements predicted using an Alphafold structure is annotated along the axes. (<bold>B</bold>) Contacts observed in the rat latrophilin-1 GAIN domain crystal structure (PDB: 4DLQ <xref ref-type="bibr" rid="bib2">Araç et al., 2012</xref>), showing contacts where the nearest side-chain heavy atom distance was under 8 Å. (<bold>C</bold>) Contacts observed in the structure of the Polycystic Kidney Disease 1 (<italic>PKD1)</italic> GAIN domain were predicted using Alphafold with the same distance criteria. The contacts predicted using the Potts model show correspondence with the structure-based contacts, detecting two antiparallel beta-sheet interactions extending from the diagonal (upper right and middle), plus a possible third antiparallel beta-sheet interface (lower left) not observed in the latrophilin structure as this region may have low similarity.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-fig5-figsupp2-v1.tif"/></fig></fig-group><p><xref ref-type="fig" rid="fig5">Figure 5A</xref> shows the pairs of positions with strong Potts interaction scores where one position is either in the stalk, the nearby GAIN domain, or the TM1 helix. Some predicted interaction pairs recapitulated beta-sheet contacts within the GAIN domain observed in the homolog rat latrophilin-1 (<xref ref-type="bibr" rid="bib2">Araç et al., 2012</xref>) as well as predicted by Alphafold (<xref ref-type="bibr" rid="bib20">Jumper et al., 2021</xref>, <xref ref-type="fig" rid="fig5s2">Figure 5—figure supplement 2</xref>) or between the extracellular ends of the TM2/3 and TM4/5 alpha helices known from cryo-EM structures (<xref ref-type="bibr" rid="bib56">Su et al., 2018</xref>) or predicted by Alphafold, validating that our model detected biologically functional interactions.</p><p>We identified strong interactions between the stalk and other residues from the Potts model. They were not observed in the cryo-EM structure, in which the flexible stalk is missing. For interactions with the TOP domain, out of the 4875 possible pairs (25 stalk residues by 195 TOP domain residues in our Potts model), this analysis detected a stringent set of 6 strongly interacting pairs. Remarkably, multiple positions in this small set were among those relevant to the ‘Intermediate’ binding conformation of p17 and ‘Bound’ conformation of p21 as identified from the Pep-GaMD simulations. These were W3726 and S3741 in the TOP domain, both interacting with T1 of the stalk, and P3859 interacting with N25 at the end of the stalk (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). Additionally, we identified E3743 to be strongly interacting with F16 in the stalk, and it was also near the observed binding region in the TOP domain for the peptide p17 in the ‘Intermediate’ state near S3741 (<xref ref-type="fig" rid="fig3">Figure 3F</xref>). The remaining two strong interactions between the stalk and the TOP domain involved Q3821 with T1 and L3893 with G4. L3893 is adjacent to R3892 that was identified to interact with the peptide p9 in the ‘Bound’ state (<xref ref-type="fig" rid="fig2">Figure 2D</xref>) and mutating it may affect its neighbor’s positioning. Besides the interactions between the TOP domain and the stalk TA, we also found a set of interactions between the stalk and the extracellular ends of TM2-TM3 helices and TM4-TM5 helices, in which stalk residues G4, P10, F16, and E20 interact with W3298, A3296, and S3579, respectively, as well as a strong interaction between V3077, three residues past the end of the stalk, and T3856 in the TOP domain. TOP domain residue T3856 was also identified as relevant to the binding region of peptide p17 in the ‘Intermediate’ state (<xref ref-type="fig" rid="fig3">Figure 3F</xref>) and peptide p21 in the ‘Bound’ state (<xref ref-type="fig" rid="fig4">Figure 4D</xref>). These interactions could additionally play a role in stalk-TA activation or could be related to other functionality such as cleavage in the GPS motif.</p><p>To gain further insight and to validate that these detected ‘direct’ interactions reflect biologically meaningful functional interactions and are not artifacts of the data, we examined the residue-specific covariation observed in the MSA (<xref ref-type="fig" rid="fig5">Figure 5C</xref>), which measures the difference between the observed pairwise residue frequency and its null expectation under the assumption of independent variation. Values greater than ~1% are commonly found to be indications of a statistically reliable mutational covariation (see Materials and Methods), and many of the covarying pairs discovered involving the stalk were significantly above this value. We validated that the covarying residue pairings were consistent with biophysical interaction. For example, for the position-pair 20–3579, here annotated such that the first index is the stalk residue numbered relative to the N terminus of the stalk and the second index is the TOP domain residue numbered according to the human PC1 protein sequence, there were excess residue-pair counts in the MSA consistent with opposite-charge or polar pairing such as K20-E3579, N20-Q3579, and others, and a dearth of repulsive like-charge pairs such as E20-E3579. Similarly, position-pair 1–3741 favored certain combinations of polar residues such as T1-S3741. Other position-pairs appeared consistent with hydrophobic packing interactions, such as F16-A3296, G4-W3298, and T1-W3726. A large residue F or W at position 3298 in the extracellular end of TM2 was commonly paired with a G at stalk position 4, while a smaller I or L residue at position 3298 was more commonly paired with a T at stalk position 4.</p><p>Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) (<xref ref-type="bibr" rid="bib47">Rastelli et al., 2010</xref>) analysis was further performed to calculate the binding free energies of peptides p9, p17, and p21 to PC1 CTF and decompose the residue-wise energy contributions using the gmx_MMPBSA software (<xref ref-type="bibr" rid="bib59">Valdés-Tresanco et al., 2021</xref>). The relative rank of the overall peptide binding free energies (<xref ref-type="table" rid="table1">Table 1</xref>) was consistent with the experimental signaling data, i.e., p21 &gt; p9 &gt; p17, for which p21 showed the largest free energy value of binding (–40.29±6.94 kcal/mol). Furthermore, we performed residue-wise energy decomposition analysis with MM/PBSA using gmx_MMPBSA software (<xref ref-type="bibr" rid="bib59">Valdés-Tresanco et al., 2021</xref>), which allowed us to identify key residues that contributed the most to the peptide binding energies. These included residues T1 and V9 in p9 (<xref ref-type="table" rid="table2">Table 2</xref>), residues T1, R15 and V17 in p17 (<xref ref-type="table" rid="table3">Table 3</xref>), and residues P10, P11, P19, and P21 in p21 and residue W3726 in the PC1 CTF (<xref ref-type="table" rid="table4">Table 4</xref>). The energetic contributions of these residues apparently correlated to the sequence coevolution predicted from the Potts model.</p><table-wrap id="table1" position="float"><label>Table 1.</label><caption><title>Summary of MM/PBSA binding free energy analysis for the peptides p9, p17 and p21 and polycystin-1 (PC1) C-terminal fragment (CTF) in the bound state sampled during Peptide GaMD (Pep-GaMD) simulations.</title></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="bottom">System</th><th align="left" valign="bottom">ΔG (kcal/mol)</th></tr></thead><tbody><tr><td align="left" valign="bottom">p21</td><td align="char" char="plusmn" valign="bottom">–40.29±6.94</td></tr><tr><td align="left" valign="bottom">p9</td><td align="char" char="plusmn" valign="bottom">–17.30±4.50</td></tr><tr><td align="left" valign="bottom">p17</td><td align="char" char="plusmn" valign="bottom">–12.74±5.62</td></tr></tbody></table></table-wrap><table-wrap id="table2" position="float"><label>Table 2.</label><caption><title>Summary of residue-wise energy decomposition analysis between the peptide p9 and polycystin-1 (PC1) C-terminal fragment (CTF) in the bound state sampled during Peptide GaMD (Pep-GaMD) simulations.</title></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="top">Residue</th><th align="left" valign="top">ΔG (kcal/mol)</th></tr></thead><tbody><tr><td align="left" valign="top"><bold>T1</bold></td><td align="char" char="plusmn" valign="top"><bold>–10.47</bold>±<bold>6.92</bold></td></tr><tr><td align="left" valign="top">A2</td><td align="char" char="plusmn" valign="top">–3.28±2.18</td></tr><tr><td align="left" valign="top">F3</td><td align="char" char="plusmn" valign="top">–2.62±2.62</td></tr><tr><td align="left" valign="top">G4</td><td align="char" char="plusmn" valign="top">–0.30±2.38</td></tr><tr><td align="left" valign="top">A5</td><td align="char" char="plusmn" valign="top">–1.61±2.67</td></tr><tr><td align="left" valign="top">S6</td><td align="char" char="plusmn" valign="top">–0.59±4.49</td></tr><tr><td align="left" valign="top">L7</td><td align="char" char="plusmn" valign="top">–0.28±2.96</td></tr><tr><td align="left" valign="top">F8</td><td align="char" char="plusmn" valign="top">–1.51±1.84</td></tr><tr><td align="left" valign="top"><bold>V9</bold></td><td align="char" char="plusmn" valign="top"><bold>–10.14</bold>±<bold>5.68</bold></td></tr><tr><td align="left" valign="top">R3891</td><td align="char" char="plusmn" valign="top">–0.14±7.26</td></tr><tr><td align="left" valign="top">R3892</td><td align="char" char="plusmn" valign="top">–0.31±7.85</td></tr><tr><td align="left" valign="top"><bold>F3888</bold></td><td align="char" char="plusmn" valign="top"><bold>–3.24</bold>±<bold>2.95</bold></td></tr><tr><td align="left" valign="top">H3864</td><td align="char" char="plusmn" valign="top">–0.03±3.86</td></tr><tr><td align="left" valign="top">R3970</td><td align="char" char="plusmn" valign="top">–0.94±2.62</td></tr><tr><td align="left" valign="top">R3968</td><td align="char" char="plusmn" valign="top">–0.27±1.67</td></tr></tbody></table></table-wrap><table-wrap id="table3" position="float"><label>Table 3.</label><caption><title>Summary of residue-wise energy decomposition analysis between the peptide p17 and polycystin-1 (PC1) C-terminal fragment (CTF) in the bound state sampled during Peptide GaMD (Pep-GaMD) simulations.</title></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="top">Residue</th><th align="left" valign="top">ΔG (kcal/mol)</th></tr></thead><tbody><tr><td align="left" valign="top"><bold>T1</bold></td><td align="left" valign="top"><bold>–10.98±2.32</bold></td></tr><tr><td align="left" valign="top">A2</td><td align="left" valign="top">–0.36±2.34</td></tr><tr><td align="left" valign="top">F3</td><td align="left" valign="top">–0.23±3.82</td></tr><tr><td align="left" valign="top">G4</td><td align="left" valign="top">–0.03±3.83</td></tr><tr><td align="left" valign="top">A5</td><td align="left" valign="top">–0.86±3.08</td></tr><tr><td align="left" valign="top">S6</td><td align="left" valign="top">–0.48±4.06</td></tr><tr><td align="left" valign="top">L7</td><td align="left" valign="top">–0.05±2.90</td></tr><tr><td align="left" valign="top">F8</td><td align="left" valign="top">–0.21±4.42</td></tr><tr><td align="left" valign="top">V9</td><td align="left" valign="top">–0.19±3.41</td></tr><tr><td align="left" valign="top">P10</td><td align="left" valign="top">–0.72±2.64</td></tr><tr><td align="left" valign="top">P11</td><td align="left" valign="top">–0.09±3.23</td></tr><tr><td align="left" valign="top">S12</td><td align="left" valign="top">–0.29±4.92</td></tr><tr><td align="left" valign="top">H13</td><td align="left" valign="top">–1.19±7.37</td></tr><tr><td align="left" valign="top">V14</td><td align="left" valign="top">–1.25±3.08</td></tr><tr><td align="left" valign="top"><bold>R15</bold></td><td align="left" valign="top"><bold>–10.63±3.76</bold></td></tr><tr><td align="left" valign="top">F16</td><td align="left" valign="top">–0.93±5.52</td></tr><tr><td align="left" valign="top"><bold>V17</bold></td><td align="left" valign="top"><bold>–10.20±3.83</bold></td></tr><tr><td align="left" valign="top">Y3307</td><td align="left" valign="top">–0.11±2.68</td></tr><tr><td align="left" valign="top">H3311</td><td align="left" valign="top">–0.04±3.25</td></tr><tr><td align="left" valign="top"><bold>R3314</bold></td><td align="left" valign="top"><bold>–8.90±1.65</bold></td></tr><tr><td align="left" valign="top"><bold>R3700</bold></td><td align="left" valign="top"><bold>–14.63±7.8</bold></td></tr><tr><td align="left" valign="top">Q3707</td><td align="left" valign="top">–0.27±4.96</td></tr><tr><td align="left" valign="top">S3711</td><td align="left" valign="top">–0.08±4.06</td></tr><tr><td align="left" valign="top"><bold>E3708</bold></td><td align="left" valign="top"><bold>–10.14±4.15</bold></td></tr></tbody></table></table-wrap><table-wrap id="table4" position="float"><label>Table 4.</label><caption><title>Summary of residue-wise energy decomposition analysis between the peptide p21 and polycystin-1 (PC1) C-terminal fragment (CTF) in the bound state sampled during Peptide GaMD (Pep-GaMD) simulations.</title></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="top">Residue</th><th align="left" valign="top">ΔG (kcal/mol)</th></tr></thead><tbody><tr><td align="left" valign="top">T1</td><td align="left" valign="top">–0.25±1.66</td></tr><tr><td align="left" valign="top">A2</td><td align="left" valign="top">–1.02±2.90</td></tr><tr><td align="left" valign="top">F3</td><td align="left" valign="top">–0.08±0.10</td></tr><tr><td align="left" valign="top">G4</td><td align="left" valign="top">–2.42±2.65</td></tr><tr><td align="left" valign="top">A5</td><td align="left" valign="top">–0.11±2.15</td></tr><tr><td align="left" valign="top">S6</td><td align="left" valign="top">–0.09±1.31</td></tr><tr><td align="left" valign="top">L7</td><td align="left" valign="top">–0.83±1.43</td></tr><tr><td align="left" valign="top">F8</td><td align="left" valign="top">–0.68±1.10</td></tr><tr><td align="left" valign="top">V9</td><td align="left" valign="top">–8.17±2.10</td></tr><tr><td align="left" valign="top"><bold>P10</bold></td><td align="left" valign="top"><bold>–6.16±1.79</bold></td></tr><tr><td align="left" valign="top"><bold>P11</bold></td><td align="left" valign="top"><bold>–1.22±2.83</bold></td></tr><tr><td align="left" valign="top">S12</td><td align="left" valign="top">–0.05±2.56</td></tr><tr><td align="left" valign="top">H13</td><td align="left" valign="top">–1.13±3.74</td></tr><tr><td align="left" valign="top">V14</td><td align="left" valign="top">–1.16±1.78</td></tr><tr><td align="left" valign="top">R15</td><td align="left" valign="top">–0.59±1.02</td></tr><tr><td align="left" valign="top">F16</td><td align="left" valign="top">–0.59±1.02</td></tr><tr><td align="left" valign="top">V17</td><td align="left" valign="top">–1.59±1.13</td></tr><tr><td align="left" valign="top">F18</td><td align="left" valign="top">–0.20±1.37</td></tr><tr><td align="left" valign="top"><bold>P19</bold></td><td align="left" valign="top"><bold>–7.09±1.51</bold></td></tr><tr><td align="left" valign="top">E20</td><td align="left" valign="top">–3.76±2.24</td></tr><tr><td align="left" valign="top"><bold>P21</bold></td><td align="left" valign="top"><bold>–8.43±2.01</bold></td></tr><tr><td align="left" valign="top">L3863</td><td align="left" valign="top">–0.33±2.28</td></tr><tr><td align="left" valign="top">L3701</td><td align="left" valign="top">–0.04±2.39</td></tr><tr><td align="left" valign="top">I3705</td><td align="left" valign="top">–0.51±2.16</td></tr><tr><td align="left" valign="top"><bold>E3708</bold></td><td align="left" valign="top"><bold>–1.68±3.11</bold></td></tr><tr><td align="left" valign="top"><bold>R3712</bold></td><td align="left" valign="top"><bold>–3.85±1.56</bold></td></tr><tr><td align="left" valign="top">F3714</td><td align="left" valign="top">–0.01±2.28</td></tr><tr><td align="left" valign="top"><bold>W3726</bold></td><td align="left" valign="top"><bold>–2.93±2.11</bold></td></tr><tr><td align="left" valign="top">H3729</td><td align="left" valign="top">–0.56±2.00</td></tr><tr><td align="left" valign="top">L3732</td><td align="left" valign="top">–0.26±2.49</td></tr><tr><td align="left" valign="top">P3733</td><td align="left" valign="top">–0.61±2.33</td></tr><tr><td align="left" valign="top">N3738</td><td align="left" valign="top">–0.07±4.91</td></tr><tr><td align="left" valign="top">S3741</td><td align="left" valign="top">–0.03±4.27</td></tr></tbody></table></table-wrap></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>In <italic>in vitro</italic>, cell-based signaling assays, PC1 CTF-mediated activation of the NFAT reporter is dependent on its N-terminal, extracellular stalk, as shown by the loss of reporter activity with the CTF stalk-deletion expression construct, CTF<sup>∆st</sup> (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>, <xref ref-type="fig" rid="fig1">Figure 1B</xref>) and by the ability of synthetic, stalk sequence-derived peptides to reactivate signaling by CTF<sup>∆st</sup> <italic>in trans</italic> (<xref ref-type="fig" rid="fig1">Figure 1E</xref>). A series of synthetic peptides derived from the N-terminal sequence of the mouse PC1 CTF stalk were used to determine their agonistic activity in PC1 CTF<sup>∆st</sup>-transfected cells. Notably, treatment with stalk peptides p7, p9, p17, p19, and p21 resulted in significant NFAT reporter activity over CTF<sup>∆st</sup> control (no peptide treatment), wherein the effects of p7, p9, and p17 were specific to mouse CTF<sup>∆st</sup>-expressing cells. These data are consistent with the stalk peptides acting as soluble TA peptide agonists for PC1 and provide further evidence for the activation of PC1 signaling via an ADGR-like TA mechanism.</p><p>In ADPKD, numerous missense mutations reported within the GAIN domain that have been shown to prevent or inhibit cleavage at the GPS (<xref ref-type="bibr" rid="bib2">Araç et al., 2012</xref>). Loss of PC1 GPS cleavage, which is known to cause ADPKD, would likely sequester the stalk tethered agonist within the interior of the GAIN domain, which would presumably interfere with interactions between stalk tethered agonist residues and the remainder of the CTF and thus loss of the stalk-mediated signaling mechanism. Furthermore, there are 10 single nucleotide polymorphisms reported within the stalk sequence (ADPKD Variant Database; <ext-link ext-link-type="uri" xlink:href="https://pkdb.mayo.edu/welcome">https://pkdb.mayo.edu/welcome</ext-link>), most of which were found to significantly reduce CTF-mediated activation of the NFAT reporter (<xref ref-type="bibr" rid="bib28">Magenheimer et al., 2021</xref>). In particular, the ADPKD-associated G3052R stalk mutation that was previously analyzed along with the stalkless CTF by GaMD simulations (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>) has the same reduction in activity as the stalkless CTF in the cellular signaling reporter assays and the same loss of active/closed conformation interactions in GaMD analyses. Therefore, the stalkless CTF was used in our docking and simulation studies as representative of a biologically relevant mutant form of PC1.</p><p>To reveal the molecular mechanisms of the soluble stalk-derived peptides, we chose to perform HPEPDOCK docking and novel Pep-GaMD simulations to sample the peptide interactions with the ΔStalk PC1 CTF. Pep-GaMD simulations were able to refine the docking conformations of peptide agonists bound to the ∆Stalk PC1 CTF. It is important to note that the free energy profiles calculated from GaMD simulations of PC1 CTF were not fully converged since certain variations were observed among the individual simulations. Nevertheless, these calculations allowed us to identify representative low-energy binding conformations of the peptides. Pep-GaMD simulations sampled an antiparallel ß-strand and a short helical secondary structure of peptide p17 bound to the ΔStalk CTF. Furthermore, peptides p9 and p21 adopted a more folded structure as compared to their disordered loop conformations in the docking poses. We also observed TOP-PL interactions, particularly the salt bridge between residues R3848-E4078 that is a key feature of the stalk TA-mediated activation of signaling for PC1 CTF (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>). Signal transduction was initiated upon binding of the stalk (TA) to the TOP domain, which was transmitted to the PL via a salt bridge formation between residue R3848 in the TOP domain and residue E4078 in the PL. The bound peptide agonists p9, p17, and p21 maintained the ΔStalk CTF in its ‘Closed/Active’ conformation as observed in the wild-type PC1 CTF simulations (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>).</p><p>The interacting pairs identified using sequence-based covariation analysis matched the pairs identified by Pep-GaMD simulations, providing complementary evidence of the importance of these interactions and of the existence of the ‘Bound’ and ‘Intermediate’ binding states of the stalk TA and stalk-derived peptide agonist. This suggests that such stalk TA binding states are evolutionarily conserved across PC1 orthologs. Covariation analysis identifies interactions important during any part of the protein lifecycle, and alone cannot be used to distinguish which conformational state an interaction arises in. By comparison to the conformations found in the Pep-GaMD simulations, we found that most of the identified interactions between the stalk TA and the TOP domain were consistent with either the ‘Intermediate’ or ‘Bound’ binding states of the stalk-derived peptides, which are related to CTF inactive and active signaling states, however, it remained possible that other interactions, such as between the start of the stalk-TA and TM2/TM3, may be related to conformational states necessary for cleavage of the GAIN/GPS domain. Additionally, structural contacts may be incompletely detected at some positions when the statistical signal of covariation is masked by high conservation, subfamily specialization, or misalignment. This can explain why some interactions identified in the binding interface through docking are not detected using covariation analysis. Despite this, the specific subset of interactions detected using covariation analysis suggest broader peptide binding interfaces, and we found these to be consistent with the peptide binding interactions observed in the Pep-GaMD simulations and the MM/PBSA binding free energy analysis, and the covarying residue pairings were consistent with functional biophysical interactions.</p><p>The proposed binding interactions of the PC1 stalk peptides share some similarities with those observed for the ADGRs. Specifically, <xref ref-type="bibr" rid="bib67">Xiao et al., 2022</xref> resolved cryo-EM structures of active ADGRG2 and ADGRG4 in complex with tethered Stachel sequences. The structures showed that the 15 residue Stachel sequence inserts into the TM bundle to form intense hydrophobic interactions. A hydrophobic F/Y/LXφφφXφ motif identified in the ADGR tethered sequences formed five finger-like projections in the hydrophobic pits of the TM bundle (<xref ref-type="bibr" rid="bib67">Xiao et al., 2022</xref>). In our study, we observed a similar pattern of intense hydrophobic interactions between the peptide agonists p9, p17, and p21 and the hydrophobic pockets in the TOP domain of PC1 CTF. Notably, a closely similar TOP binding pocket was identified for interaction of the tethered agonist (Stalk) in our previous study (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>) and for binding of peptide agonist p21 in this study. The TOP domain hydrophobic pocket may serve as a significant candidate binding site for designing new synthetic peptides or small molecules to aid in the rescue of PC1 function levels. Moreover, the shorter peptide agonists’ (p9 and p17) binding sites also serve as novel pockets for the design and development of therapeutic approaches for treating ADPKD. While the present study is focused on the identification of initial peptides that are able to activate the PC1 CTF, we shall include further mutation experiments and simulations, peptide SAR, and optimization of the lead peptides in future studies. It is also important to note that we have not tested the selectivity of the peptides for PC1 versus PC2 in the present study primarily because transfection of PC2 does not activate the NFAT reporter. However, it is possible that co-transfection of PC2 with the PC1 CTF could alter the stalk peptide binding. This will be important to consider in future studies.</p></sec><sec id="s4" sec-type="materials|methods"><title>Materials and methods</title><sec id="s4-1"><title>Experimental procedures</title><sec id="s4-1-1"><title>Antibodies and peptide synthesis</title><p>Primary antibodies used included A19, for detection of mouse PC1 CTF (<xref ref-type="bibr" rid="bib57">Sutters et al., 2001</xref>), and TRAM2 (Epitomics, 3685–1). Secondary antibodies conjugated to HRP were purchased from Sigma or Jackson ImmunoResearch. Stalk-derived peptides were synthesized by GenScript using the Fmoc method and verified by HPLC-MS analysis.</p></sec><sec id="s4-1-2"><title>DNA expression constructs and cloning</title><p>To produce CTF expression construct of mouse (m) PC1, sequences starting at T3041 and proceeding past the first TM domain were amplified by PCR from PC1-11TM (<xref ref-type="bibr" rid="bib45">Puri et al., 2004</xref>), respectively, using 5’-mCleavStalkBsm-For and 3’-TMI-EcoRV primers to produce mCleavStk, which was joined via the BsmBI site to a PCR product encoding the signal peptide sequence (MPMGSLQPLATLYLLGMLVASVLG) from the T cell surface glycoprotein CD5 (<xref ref-type="bibr" rid="bib38">Nims et al., 2003</xref>) in pBlueScript (pBS) to generate pBS-mCD5-cleaved stalk. The EcoRI-EagI fragment containing mCD5-cleaved stalk was joined to a 3.2 kb EagI-NotI fragment from PC1-11TM encoding TM2 through the C-tail to produce the final pCIneo-mCTF expression construct. The stalkless CTF mutant expression construct, pCIneo-mCTF<sup>∆st</sup>, starting with S3062 of the mouse PC1 stalk was generated by the same scheme except for using the 5’-m∆StalkBsmFor primer for the initial PCR. PCR and mutagenesis primers were synthesized by IDT and sequences are as follows:</p><p>5’-CD5 Eco: 5’- <named-content content-type="sequence">TTCTAGAATTCCCTCGACCTCG</named-content> –3’; 3’-CD5-BsmBI: 5’- <named-content content-type="sequence">GACTAGCGTCTCATGCCTAGCACGGAAGC</named-content> –3’; mCleavStalkBsm-For: 5’- <named-content content-type="sequence">GACTAGCGTCTCAGGCACTGCCTTCGGTGCC</named-content>-3’; m∆StalkBsmFor: 5'- <named-content content-type="sequence">GACTAGCGTCTCAGGCAGTGCAAGCATCAACTACATTGTCC</named-content> –3'; TMI-EcoRV: 5’-<named-content content-type="sequence">GACTAGGATATCCCTCTGGACTCTAGTAAAGCG</named-content>-3’; BsrGIstalk-Rev: 5’- <named-content content-type="sequence">AGGGTCTGGGTAGAGTGCTT</named-content> –3’.</p><p>PCR and mutagenesis products and their final constructs were confirmed by Sanger sequencing (GeneWiz). Expression constructs of CTF and CTF<sup>∆st</sup> from human PC1 were made in the pCI vector as described previously (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>). In the conduct of research utilizing recombinant DNA, the investigator adhered to NIH Guidelines for research involving recombinant DNA molecules.</p></sec><sec id="s4-1-3"><title>Cell culture and transient transfection</title><p>HEK293T cells (ATCC) were maintained and transiently transfected as described previously (<xref ref-type="bibr" rid="bib29">Maser et al., 2003</xref>). Cells were passaged into 6-well plates (6×10<sup>5</sup> cells/well; 3 wells/transfection condition) and transfected with a DNA mixture containing either the 4xNFAT or the 7xAP-1 promoter-Firefly luciferase reporter (100 ng; Stratagene), along with Renilla luciferase (50 ng of pGL4.70[<italic>hRluc</italic>] or 1 ng of pRL-null; Promega), and pCI expression vector encoding either CTF or CTF<sup>∆st</sup> (75 ng for signaling; 600 ng for surface biotinylation) or an equimolar amount of empty pCI vector as control. pBlueScript (Stratagene) was used to bring the total DNA amount to 8 ug. After 2.5 hr, the DNA mixture was replaced with serum-free culture medium, and after 20–24 hr, cells were lysed in 1 X Passive Lysis buffer (PLB; Promega) supplemented with protease and phosphatase inhibitors. Firefly (Fluc)- and Renilla (Rluc)-luciferase activity in each cell lysate was determined using the Dual Luciferase Assay Kit (Promega) and a Berthold tube luminometer. NFAT-Fluc luminescence was normalized to Rluc for each well within a transfection condition, and then averaged for each condition (n=3 wells/condition). Means of normalized NFAT-Fluc with standard deviation (<xref ref-type="bibr" rid="bib6">Dalagiorgou et al., 2013</xref>) were graphed. Signaling-transfection experiments were performed a minimum of three times (i.e., &gt;3 biological replicates) each with three technical replicates/condition except where noted.</p></sec><sec id="s4-1-4"><title>Stalk peptide treatment</title><p>Cells were plated into 24-well plates (1.5×10<sup>5</sup> cells/well) and transfected with CTF<sup>∆st</sup> or empty pCI expression vectors, along with NFAT-Fluc and Rluc plasmids. Two hours following medium exchange, one-half of the culture medium volume was replaced with an equal volume of either serum-free medium (no peptide control), or stalk-derived or solubility tag peptide (2 mM in serum-free medium) and incubated overnight. In some experiments, an additional 50–100 ul of peptide (1 mM) was added the following morning. Cells were lysed at 24 hr following the initial peptide or control medium addition.</p></sec><sec id="s4-1-5"><title>Cell surface biotinylation analyses</title><p>Surface labeling (<xref ref-type="bibr" rid="bib42">Pavel et al., 2014</xref>) was performed on intact cells 22–24 hr post-transfection using 1.5 mg/ml PBS of the membrane-impermeable, cleavable biotin cross-linking reagent (Sulfo-NHS-SS-Biotin; Pierce) for 30 min on ice. Crosslinking was inactivated by the addition of 50 mM Tris, pH 8.0. Cells were washed and then lysed in 1 X PLB with protease inhibitors. A 10% aliquot of the total cell lysate was removed and saved as the input sample. NeutraAvidin-agarose beads (Pierce) were added to remove biotinylated surface proteins. The supernatant was removed and saved as the unbound cytosolic fraction (sup). A representative amount of each fraction, i.e., the total lysate (input), cytosolic (sup), and biotinylated surface proteins (beads) was analyzed by SDS-PAGE/Western blot. TRAM2 (ER-resident protein) was used as a cell fractionation marker.</p></sec><sec id="s4-1-6"><title>Western blot analyses</title><p>Gel loading volumes of signaling cell lysates were calculated based on normalization to relative Rluc activity within a condition. Lysate samples were electrophoresed through 7.5% denaturing polyacrylamide gels and transferred to nitrocellulose membrane using the TransBlot Turbo and ReadyBlot transfer buffer (BioRad). Blots were incubated with primary antibody (1:1000 dilution for A19; 1:10,000 for anti-TRAM2) in Tris-buffered saline (TBS; 10 mM Tris pH 7.4, 150 mM NaCl) with 0.1% Tween-20 (TBST) and 5% powdered dry milk for 14–16 hr at 4 °C. Secondary antibodies conjugated to HRP were incubated at 1:5,000 dilution in TBST/5% milk for 1 hr at room temperature. Blots were developed using a chemiluminescent substrate (Clarity; BioRad), and multiple exposures were captured for each blot with the Amersham Imager 600 with the band saturation detection mode enabled. Volume density (minus background) of immunoreactive bands was determined using ImageQuant TL (GE Healthcare). In most cases, duplicate blots were prepared and quantified to obtain an average band density relative to wild-type CTF.</p></sec><sec id="s4-1-7"><title>Statistical analyses</title><p>Statistical analysis was performed using GraphPad Prism 9 (GraphPad Software, San Diego, CA, USA). Data are presented as means + standard deviation (<xref ref-type="bibr" rid="bib6">Dalagiorgou et al., 2013</xref>) for bar graphs. Multiple comparisons used one-way ANOVA and Tukey’s post-hoc analysis. p≤0.05 was considered statistically significant.</p></sec></sec><sec id="s4-2"><title>Computational Methods</title><sec id="s4-2-1"><title>Gaussian accelerated molecular dynamics (GaMD)</title><p>GaMD is an unconstrained enhanced sampling approach that works by adding a harmonic boost potential to smooth the potential energy surface of biomolecules to reduce energy barriers (<xref ref-type="bibr" rid="bib33">Miao et al., 2015</xref>). Brief description of the method is provided here.</p><p>Consider a system with <italic>N</italic> atoms at positions <inline-formula><mml:math id="inf1"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>. When potential energy of the system <inline-formula><mml:math id="inf2"><mml:mi>V</mml:mi><mml:mo>(</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>⃑</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:math></inline-formula> is less than a threshold energy <italic>E</italic>, a boost potential <inline-formula><mml:math id="inf3"><mml:mo>∆</mml:mo><mml:mi>V</mml:mi><mml:mo>(</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>⃑</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:math></inline-formula> is added to the system as follows:<disp-formula id="equ1"><label>(1)</label><mml:math id="m1"><mml:mrow><mml:msup><mml:mi>V</mml:mi><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:mi>E</mml:mi></mml:mrow></mml:math></disp-formula><disp-formula id="equ2"><label>(2)</label><mml:math id="m2"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mi>k</mml:mi><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>E</mml:mi><mml:mo>−</mml:mo><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:mi>E</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula></p><p>where <italic>k</italic> is the harmonic force constant. The two adjustable parameters <italic>E</italic> and <italic>k</italic> can be determined by the application of three enhanced sampling principles. First, for any two arbitrary potential values <inline-formula><mml:math id="inf4"><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mfenced separators="|"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>⃑</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:math></inline-formula> and <inline-formula><mml:math id="inf5"><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mfenced separators="|"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>⃑</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:math></inline-formula> found on the original energy surface, if <inline-formula><mml:math id="inf6"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>, <inline-formula><mml:math id="inf7"><mml:mo>∆</mml:mo><mml:mi>V</mml:mi></mml:math></inline-formula> should be a monotonic function that does not change the relative order of the biased potential values, i.e., <inline-formula><mml:math id="inf8"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>. Second, if <inline-formula><mml:math id="inf9"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>, the potential difference observed on the smoothed energy surface should be smaller than that of the original, i.e., <inline-formula><mml:math id="inf10"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>r</mml:mi><mml:mo stretchy="false">→</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>. By combining the first two criteria and plugging in the formula of <inline-formula><mml:math id="inf11"><mml:msup><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup><mml:mo>(</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>⃑</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:math></inline-formula> and <inline-formula><mml:math id="inf12"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>V</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula>, we obtain:<disp-formula id="equ3"> ,<label> (3)</label><mml:math id="m3"><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mi>E</mml:mi><mml:mo>≤</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mfrac></mml:math></disp-formula></p><p>where <inline-formula><mml:math id="inf13"><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="inf14"><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are the system’s minimum and maximum potential energies. To ensure that <xref ref-type="disp-formula" rid="equ3">Equation 3</xref> is valid, <italic>k</italic> has to satisfy: <inline-formula><mml:math id="inf15"><mml:mi>k</mml:mi><mml:mo>≤</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></inline-formula>. Let us define <inline-formula><mml:math id="inf16"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>k</mml:mi><mml:mo>≡</mml:mo><mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math></inline-formula>, then <inline-formula><mml:math id="inf17"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>0</mml:mn><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mstyle></mml:math></inline-formula>. Third, the standard deviation (SD) of <italic>∆V</italic> needs to be small enough (i.e., narrow distribution) to ensure accurate reweighting using cumulant expansion to the second order: <inline-formula><mml:math id="inf18"><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mo>∆</mml:mo><mml:mi>V</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>v</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mi>V</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>, where <inline-formula><mml:math id="inf19"><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>v</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="inf20"><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mi>V</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are the average and SD of ∆V with <inline-formula><mml:math id="inf21"><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> as a user-specified upper limit (e.g. <inline-formula><mml:math id="inf22"><mml:mn>10</mml:mn><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mi>T</mml:mi></mml:math></inline-formula>) for accurate reweighting. When <italic>E</italic> is set to the lower bound <inline-formula><mml:math id="inf23"><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> according to <xref ref-type="disp-formula" rid="equ3">Equation 3</xref>, <inline-formula><mml:math id="inf24"><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> can be calculated as:<disp-formula id="equ4"><label>(4)</label><mml:math id="m4"><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">min</mml:mi></mml:mrow><mml:mo>⁡</mml:mo><mml:mrow><mml:mfenced separators="|"><mml:mrow><mml:mn>1.0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>`</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mn>1.0</mml:mn><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mi>V</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>v</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced></mml:math></disp-formula></p><p>Alternatively, when the threshold energy <italic>E</italic> is set to its upper bound <inline-formula><mml:math id="inf25"><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mfrac></mml:math></inline-formula>, <inline-formula><mml:math id="inf26"><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is set to:<disp-formula id="equ5"><label>(5)</label><mml:math id="m5"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mtext>”</mml:mtext></mml:mrow></mml:msubsup><mml:mo>≡</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>V</mml:mi></mml:mrow></mml:msub></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mi>v</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula></p><p>if <inline-formula><mml:math id="inf27"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mtext>”</mml:mtext></mml:mrow></mml:msubsup></mml:mrow></mml:mstyle></mml:math></inline-formula> is calculated between 0 and 1. Otherwise, <inline-formula><mml:math id="inf28"><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is calculated using <xref ref-type="disp-formula" rid="equ4">Equation (4)</xref>.</p></sec><sec id="s4-2-2"><title>Peptide Gaussian accelerated molecular dynamics (Pep-GaMD)</title><p>Peptides often undergo large conformational changes during binding to target proteins, being distinct from small-molecule ligand binding or protein-protein interactions (PPIs). In this regard, Peptide GaMD or ‘Pep-GaMD’ has been developed to enhance the sampling of peptide binding (<xref ref-type="bibr" rid="bib64">Wang and Miao, 2020</xref>). In Pep-GaMD, we consider a system of peptide <italic>L</italic> binding to a protein <italic>P</italic> in a biological environment <italic>E</italic>. Presumably, peptide binding mainly involves in both the bonded and non-bonded interaction energies of the peptide since peptides often undergo large conformational changes during binding to the target proteins. Thus, the essential peptide potential energy is <inline-formula><mml:math id="inf29"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi>L</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi>L</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>L</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>. In Pep-GaMD, we add boost potential selectively to the essential peptide potential energy according to the GaMD algorithm:<disp-formula id="equ6"><label>(6)</label><mml:math id="m6"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext></mml:mtd><mml:mtd><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext></mml:mtd><mml:mtd><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>≥</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"/></mml:mrow></mml:mrow></mml:math></disp-formula></p><p>where <italic>E<sub>L</sub></italic> is the threshold energy for applying boost potential and <italic>k<sub>L</sub></italic> is the harmonic constant. In addition to selectively boosting the peptide, another boost potential is applied to the protein and solvent to enhance conformational sampling of the protein and facilitate peptide rebinding. This boost represents the total system potential energy without the essential peptide potential energy included:<disp-formula id="equ7"><label>(7)</label><mml:math id="m7"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext></mml:mtd><mml:mtd><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="1em"/><mml:mspace width="2em"/><mml:mspace width="2em"/><mml:mspace width="2em"/><mml:mspace width="1em"/><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext></mml:mtd><mml:mtd><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>≥</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"/></mml:mrow></mml:mrow></mml:math></disp-formula></p><p>Where <italic>V<sub>D</sub></italic> represents the total system potential energy without the essential peptide potential energy included, <italic>E<sub>D</sub></italic> represents the second boost potential threshold energy and <italic>k<sub>D</sub></italic> represents the harmonic constant. Hence, this contributes to the dual-boost Pep-GaMD as the total boost potential <inline-formula><mml:math id="inf30"><mml:mo>∆</mml:mo><mml:mi>V</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mo>∆</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mfenced separators="|"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mo>∆</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:msub><mml:mfenced separators="|"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:mfenced></mml:math></inline-formula>.</p></sec><sec id="s4-2-3"><title>Energetic reweighting of Pep-GaMD simulations</title><p>For energetic reweighting of Pep-GaMD simulations to calculate potential mean force (PMF), the probability distribution along a reaction coordinate is written as <inline-formula><mml:math id="inf31"><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:math></inline-formula>. Given the boost potential <inline-formula><mml:math id="inf32"><mml:mo>∆</mml:mo><mml:mi>V</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:math></inline-formula> of each frame, <inline-formula><mml:math id="inf33"><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:math></inline-formula> can be reweighted to recover the canonical ensemble distribution <inline-formula><mml:math id="inf34"><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:math></inline-formula>, as:<disp-formula id="equ8"><label>(8)</label><mml:math id="m8"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>p</mml:mi><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mfrac><mml:msub><mml:mrow><mml:mo>⟨</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>⟩</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mo>⟨</mml:mo><mml:mrow><mml:msup><mml:mi>p</mml:mi><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow><mml:mo>⟩</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>M</mml:mi></mml:mstyle></mml:mrow></mml:math></disp-formula></p><p>where <italic>M</italic> is the number of bins, <inline-formula><mml:math id="inf35"><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mi>T</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="inf36"><mml:msub><mml:mrow><mml:mfenced open="〈" close="〉" separators="|"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>β</mml:mi><mml:mo>∆</mml:mo><mml:mi>V</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is the ensemble-averaged Boltzmann factor of <inline-formula><mml:math id="inf37"><mml:mo>∆</mml:mo><mml:mi>V</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:math></inline-formula> for simulation frames found in the <italic>j</italic><sup>th</sup> bin. The ensemble-averaged reweighting factor can be approximated using cumulant expansion:<disp-formula id="equ9"><label>(9)</label><mml:math id="m9"><mml:msub><mml:mrow><mml:mfenced open="〈" close="〉" separators="|"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>β</mml:mi><mml:mo>∆</mml:mo><mml:mi>V</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">x</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mfenced open="{" close="}" separators="|"><mml:mrow><mml:mrow><mml:munderover><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:munderover><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>!</mml:mo></mml:mrow></mml:mfrac><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mrow></mml:mfenced></mml:math></disp-formula></p><p>where the first two cumulants are given by<disp-formula id="equ10"><mml:math id="m10"><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="〈" close="〉" separators="|"><mml:mrow><mml:mo>∆</mml:mo><mml:mi>V</mml:mi></mml:mrow></mml:mfenced></mml:math></disp-formula><disp-formula id="equ11"><label>(10)</label><mml:math id="m11"><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="〈" close="〉" separators="|"><mml:mrow><mml:msup><mml:mrow><mml:mo>∆</mml:mo><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mfenced open="〈" close="〉" separators="|"><mml:mrow><mml:mo>∆</mml:mo><mml:mi>V</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math></disp-formula></p><p>The boost potential obtained from Pep-GaMD simulations usually follows near-Gaussian distribution. Cumulant expansion to the second order thus provides a good approximation for computing the reweighting factor. The reweighted free energy <inline-formula><mml:math id="inf38"><mml:mi>F</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:math></inline-formula> is calculated as<disp-formula id="equ12"><label>(11)</label><mml:math id="m12"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>F</mml:mi><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:munderover><mml:mfrac><mml:msup><mml:mi>β</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mi>k</mml:mi><mml:mo>!</mml:mo></mml:mrow></mml:mfrac><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:math></disp-formula></p><p>where <inline-formula><mml:math id="inf39"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:msup><mml:mi>p</mml:mi><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula> is the modified free energy obtained from GaMD simulation and <inline-formula><mml:math id="inf40"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is a constant.</p></sec><sec id="s4-2-4"><title>Computational model of peptide agonist-bound ΔStalk PC1 CTF and HPEPDOCK docking</title><p>With GaMD simulations of the WT PC1 CTF obtained from the previous study that revealed an active TA/stalk-mediated allosteric signaling (<xref ref-type="bibr" rid="bib44">Pawnikar et al., 2022</xref>), structural clustering of the extracellular regions of PC1 CTF, including the Stalk, TM2-TM3, and TM4-TM5 loops, TOP domain, S3-S4 loop and pore loop, was performed using the hierarchical agglomerative algorithm in CPPTRAJ (<xref ref-type="bibr" rid="bib49">Roe and Cheatham, 2013</xref>). The top-ranked representative conformation of PC1 CTF was used for peptide docking after removal of the TA/stalk (ΔStalk). Then the HPEPDOCK (<xref ref-type="bibr" rid="bib69">Zhou et al., 2018</xref>) webserver was applied to dock the p9, p17, and p21 stalk-derived peptides to ΔStalk CTF.</p></sec><sec id="s4-2-5"><title>Simulation system setup</title><p>We embedded ΔStalk CTF in a palmitoyl-oleoyl-phosphatidyl-choline (POPC) bilayer and solvated the system in 0.15 M NaCl explicit solvent using CHARMM-GUI (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1C</xref>). Neutral patches (acetyl and methylamide) were added to the protein termini residues. The peptide termini were kept as charged (NH3 + and COO-). The CHARMM36m (<xref ref-type="bibr" rid="bib60">Vanommeslaeghe and MacKerell, 2015</xref>) force field parameters were used for the protein, peptides, and lipids. CHARMM-GUI output files and scripts were used with default parameters to prepare the systems for Pep-GaMD simulations. Energy minimization was performed for 5000 steps using a constant number, volume, and temperature (NVT) ensemble at 310 K. Further equilibration was done for 375 ps at 310 K using an NPT ensemble. Conventional MD (cMD) simulations was performed on the systems for 10 ns at 1 atm pressure and 310 K temperature. All-atom Pep-GaMD simulations were performed with a short cMD for 10 ns, Pep-GaMD equilibration for 55 ns followed by three independent Pep-GaMD production runs for 500 ns for each system with randomized initial atomic velocities. A cutoff distance of 9 Å was used for the van der Waals and short-range electrostatic interactions, and long-range electrostatic interactions were computed with the particle-mesh Ewald summation method (<xref ref-type="bibr" rid="bib7">Darden et al., 1993</xref>). The simulation systems were ~90×136×117 Å<sup>3</sup> in dimension, containing a total of ~100 K atoms with explicit solvent and lipid molecules.</p></sec><sec id="s4-2-6"><title>Simulation analysis</title><p>Pep-GaMD simulation trajectories were analyzed using CPPTRAJ (<xref ref-type="bibr" rid="bib49">Roe and Cheatham, 2013</xref>) and VMD (<xref ref-type="bibr" rid="bib17">Humphrey et al., 1996</xref>) tools. Trajectory analysis showed peptides binding to the TOP domain of PC1 CTF. A previously identified salt bridge formed between the TOP domain R3848 and the pore loop E4078 of the PC1 protein is an important interaction during PC1 signal activation. The number of contacts formed between peptides p9, p17 and p21, respectively, and the R3848-E4078 salt bridge distance were used as reaction coordinates to calculate 2D free energy profiles using the <italic>PyReweighting</italic> toolkit (<xref ref-type="bibr" rid="bib32">Miao et al., 2014</xref>). A bin size of 2 Å was used for distances and 10 for the number of contacts. Three independent Pep-GaMD simulations were combined to perform structural clustering using the hierarchical agglomerative clustering algorithm in CPPTRAJ (<xref ref-type="bibr" rid="bib49">Roe and Cheatham, 2013</xref>). A 3 Å RMSD cutoff was used for each peptide system. PyReweighting (<xref ref-type="bibr" rid="bib32">Miao et al., 2014</xref>) was then applied to calculate the original free energy values of each peptide structural cluster with a cutoff of 500 frames. The structural clusters were finally ranked according to the reweighted free energy values.</p></sec><sec id="s4-2-7"><title>Potts sequence covariation model</title><p>Using a seed alignment of 189 orthologs of human <italic>PKD1</italic> obtained from the Ensemble database (<xref ref-type="bibr" rid="bib1">Aoto et al., 2016</xref>), we used iterative searching of the UniProt Database using HHblits (<xref ref-type="bibr" rid="bib16">Howe et al., 2021</xref>) to obtain a multiple-sequence alignment of 4384 homologs, and after filtering using standard methods with an 80% identity threshold (<xref ref-type="bibr" rid="bib11">Haldane and Levy, 2021</xref>), we obtained 1022 effective sequences of length 853. These sequences had an average of 23% sequence identity reflecting extensive diversity across Eukaryotes. As this number of sequences and sequence length could lead to an overfit model (<xref ref-type="bibr" rid="bib10">Haldane and Levy, 2019</xref>), we used a subset the MSA to limit to 394 positions on the extracellular side of <italic>PKD1</italic> including the GAIN domain, stalk, the TOP domain, and ends of the transmembrane helices. We inferred a Potts model from this reduced MSA using the Mi3-GPU software (<xref ref-type="bibr" rid="bib11">Haldane and Levy, 2021</xref>). We evaluated the position-pair statistical interactions using the ‘weighted Frobenius norm’ interaction score (<xref ref-type="bibr" rid="bib11">Haldane and Levy, 2021</xref>), and computed the residue-residue covariation values <inline-formula><mml:math id="inf41"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msubsup><mml:mi>C</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msubsup><mml:mo>−</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mstyle></mml:math></inline-formula> as the difference between the pair-residue frequency <inline-formula><mml:math id="inf42"><mml:msubsup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> of letters a and b at positions i,j and the null expectation under the assumption of site-independence by multiplying the two single-site frequencies, <inline-formula><mml:math id="inf43"><mml:msubsup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> and <inline-formula><mml:math id="inf44"><mml:msubsup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>. The maximum possible covariance is 25%. Statistically significant covariations scores will be greater than the expected binomial sampling error given our dataset size of N~1022,, and for bivariate count <inline-formula><mml:math id="inf45"><mml:msubsup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> the binomial-sampling standard deviation is <inline-formula><mml:math id="inf46"><mml:msqrt><mml:msubsup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msubsup><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msubsup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:msqrt></mml:math></inline-formula> which for the typical bivariate frequency of ~10% corresponds to a ~1% error. To choose a cutoff in Frobenius Norm to distinguish likely contacts from noise, we compared the Potts interactions scores to the contacts predicted using the Alphafold (<xref ref-type="bibr" rid="bib20">Jumper et al., 2021</xref>) structure, choosing the plotting cutoff at a false-positive rate of 50% relative to the contacts predicted using the Alphafold structure using a 8 Å nearest heavy atom side chain distance.</p></sec><sec id="s4-2-8"><title>Peptide binding free energy calculations</title><p>Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) analysis was performed to calculate the binding free energies of peptides p9, p17, and p21 to PC1 CTF. The analysis was performed using the trajectory in which the peptide was bound to the receptor. In MM/PBSA (<xref ref-type="bibr" rid="bib63">Wang et al., 2019</xref>), the binding free energy of the ligand (L) to the receptor (R) to form the complex (RL) is calculated as:<disp-formula id="equ13"><label>(12)</label><mml:math id="m13"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula></p><p>where G<sub>RL</sub> is the Gibbs free energy of the complex RL, G<sub>R</sub> is the Gibbs free energy of the molecule R in its unbound state and G<sub>L</sub> is the Gibbs free energy of the molecule L in its unbound state, respectively.</p><p><inline-formula><mml:math id="inf47"><mml:msub><mml:mrow><mml:mi>Δ</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> can be divided into contributions of diﬀerent interactions as (<xref ref-type="bibr" rid="bib54">Srinivasan et al., 1998</xref>):<disp-formula id="equ14"><label>(13)</label><mml:math id="m14"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>H</mml:mi><mml:mo>−</mml:mo><mml:mi>T</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>T</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:math></disp-formula></p><p>in which<disp-formula id="equ15"><label>(14)</label><mml:math id="m15"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>d</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula><disp-formula id="equ16"><label>(15)</label><mml:math id="m16"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>B</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>G</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula><disp-formula id="equ17"><label>(16)</label><mml:math id="m17"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>γ</mml:mi><mml:mo>.</mml:mo><mml:mi>S</mml:mi><mml:mi>A</mml:mi><mml:mi>S</mml:mi><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:math></disp-formula></p><p>where ΔE<sub>MM</sub>, ΔG<sub>sol</sub>, <bold>Δ</bold>H, and −TΔS are the changes in the gas-phase molecular mechanics (MM) energy, solvation-free energy, enthalpy, and conformational entropy upon ligand binding, respectively. ΔE<sub>MM</sub> includes the changes in the internal energies ΔE<sub>int</sub> (bond, angle, and dihedral energies), electrostatic energies ΔE<sub>elec</sub>, and the van der Waals energies ΔE<sub>vdW</sub>. ΔG<sub>sol</sub> is the sum of the electrostatic solvation energy ΔG<sub>PB/GB</sub> (polar contribution) and the nonpolar contribution ΔG<sub>SA</sub> between the solute and the continuum solvent. The polar contribution is calculated using either the Poisson Boltzmann (PB) or Generalized Born (GB) model, while the nonpolar energy is usually estimated using the solvent-accessible surface area (SASA) (<xref ref-type="bibr" rid="bib9">Gilson and Honig, 1988</xref>; <xref ref-type="bibr" rid="bib61">Wang et al., 2006</xref>) where <bold>γ</bold> is surface tension coefficient and b is the constant offset. The change in conformational entropy −TΔS is usually calculated by normal-mode analysis (<xref ref-type="bibr" rid="bib54">Srinivasan et al., 1998</xref>) on a set of conformational snapshots taken from MD simulations. However, due to the large computational cost, changes in the conformational entropy are usually neglected as we were concerned more on relative binding free energies of the similar peptide ligands.</p><p>MM/PBSA analysis was performed using the gmx_MMPBSA (<xref ref-type="bibr" rid="bib59">Valdés-Tresanco et al., 2021</xref>) software with the following command line:</p><p><monospace>gmx_MMPBSA -O -i mmpbsa.in -cs com.tpr -ci index.ndx -cg 1 13 -ct com_traj.xtc -cp topol.top -o FINAL_RESULTS_MMPBSA.dat -eo FINAL_RESULTS_MMPBSA.csv</monospace></p><p>Input file for running MM/PBSA analysis:</p><p><code xml:space="preserve">&amp;general
sys_name=&quot;Prot-Pep-CHARMM&quot;,
startframe=1,
endframe=200,
# In gmx_MMPBSA v1.5.0 we have added a new PB radii set named charmm_radii
# This radii set should be used only with systems prepared with CHARMM force fields.
# Uncomment the line below to use charmm_radii set
#PBRadii=7,
/
&amp;pb
# radiopt=0 is recommended which means using radii from the prmtop file for both the PB calculation and for the NP
# calculation
istrng=0.15, fillratio=4.0, radiopt=0</code></p><p>Residue-wise interaction energy analysis was performed on peptides p9, p17, and p21 using the trajectory in which the peptide was bound to the PC1 CTF using the gmx_MMPBSA (<xref ref-type="bibr" rid="bib59">Valdés-Tresanco et al., 2021</xref>) software with the following command line:</p><p><code xml:space="preserve">gmx_MMPBSA -O -i mmpbsa.in -cs com.tpr -ct com_traj.xtc -ci index.ndx -cg 3 4 -cp topol.top -o FINAL_RESULTS_MMPBSA.dat -eo FINAL_RESULTS_MMPBSA.csv -do FINAL_DECOMP_MMPBSA.dat -deo FINAL_DECOMP_MMPBSA.csv</code></p><p>Input file for running residue-wise energy decomposition analysis:</p><p><code xml:space="preserve">&amp;general
sys_name=&quot;Decomposition&quot;,
startframe=1,
endframe=200,
#forcefields=&quot;leaprc.protein.ff14SB&quot;
/
&amp;gb
igb=5, saltcon=0.150,
/
#make sure to include at least one residue from both the receptor
#and peptide in the print_res mask of the &amp;decomp section.
#this requirement is automatically fulfilled when using the within keyword.
#http://archive.ambermd.org/201308/0075.html
&amp;decomp
idecomp=2, dec_verbose=3,
print_res=&quot;A/854-862 A/1-853”,
/
</code></p></sec></sec></sec></body><back><sec sec-type="additional-information" id="s5"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="COI-statement" id="conf1"><p>No competing interests declared</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>Data curation, Formal analysis, Investigation, Visualization, Methodology, Writing – original draft</p></fn><fn fn-type="con" id="con2"><p>Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology</p></fn><fn fn-type="con" id="con3"><p>Data curation, Formal analysis, Investigation, Visualization, Writing – review and editing</p></fn><fn fn-type="con" id="con4"><p>Formal analysis, Validation, Investigation, Visualization</p></fn><fn fn-type="con" id="con5"><p>Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing</p></fn><fn fn-type="con" id="con6"><p>Conceptualization, Formal analysis, Writing – original draft, Writing – review and editing</p></fn><fn fn-type="con" id="con7"><p>Conceptualization, Formal analysis, Supervision, Validation, Investigation, Writing – original draft, Writing – review and editing</p></fn></fn-group></sec><sec sec-type="supplementary-material" id="s6"><title>Additional files</title><supplementary-material id="mdar"><label>MDAR checklist</label><media xlink:href="elife-95992-mdarchecklist1-v1.pdf" mimetype="application" mime-subtype="pdf"/></supplementary-material></sec><sec sec-type="data-availability" id="s7"><title>Data availability</title><p>The authors declare that the data supporting the findings of this study are available within the paper files have been uploaded in Figshare database with DOIs <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.6084/m9.figshare.26793067.v1">https://doi.org/10.6084/m9.figshare.26793067.v1</ext-link>; <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.6084/m9.figshare.26792983.v1">https://doi.org/10.6084/m9.figshare.26792983.v1</ext-link>; <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.6084/m9.figshare.26793088.v1">https://doi.org/10.6084/m9.figshare.26793088.v1</ext-link>.</p><p>The following datasets were generated:</p><p><element-citation publication-type="data" specific-use="isSupplementedBy" id="dataset1"><person-group person-group-type="author"><name><surname>Pawnikar</surname><given-names>S</given-names></name><name><surname>Magenheimer</surname><given-names>BS</given-names></name><name><surname>Joshi</surname><given-names>K</given-names></name><name><surname>Munoz</surname><given-names>EN</given-names></name><name><surname>Haldane</surname><given-names>A</given-names></name><name><surname>Maser</surname><given-names>RL</given-names></name><name><surname>Miao</surname><given-names>Y</given-names></name></person-group><year iso-8601-date="2024">2024</year><data-title>p9 peptide simulation data. Dataset includes imaged trajectory files for the five Pep-GaMD simulations runs. We have also provided the topology and the pdb file</data-title><source>figshare</source><pub-id pub-id-type="doi">10.6084/m9.figshare.26793067.v1</pub-id></element-citation></p><p><element-citation publication-type="data" specific-use="isSupplementedBy" id="dataset2"><person-group person-group-type="author"><name><surname>Pawnikar</surname><given-names>S</given-names></name><name><surname>Magenheimer</surname><given-names>BS</given-names></name><name><surname>Joshi</surname><given-names>K</given-names></name><name><surname>Munoz</surname><given-names>EN</given-names></name><name><surname>Haldane</surname><given-names>A</given-names></name><name><surname>Maser</surname><given-names>RL</given-names></name><name><surname>Miao</surname><given-names>Y</given-names></name></person-group><year iso-8601-date="2024">2024</year><data-title>p17 peptide simulation data. Dataset includes imaged trajectory files for the five Pep-GaMD simulations runs. We have also provided the topology and the pdb file</data-title><source>figshare</source><pub-id pub-id-type="doi">10.6084/m9.figshare.26792983.v1</pub-id></element-citation></p><p><element-citation publication-type="data" specific-use="isSupplementedBy" id="dataset3"><person-group person-group-type="author"><name><surname>Pawnikar</surname><given-names>S</given-names></name><name><surname>Magenheimer</surname><given-names>BS</given-names></name><name><surname>Joshi</surname><given-names>K</given-names></name><name><surname>Munoz</surname><given-names>EN</given-names></name><name><surname>Haldane</surname><given-names>A</given-names></name><name><surname>Maser</surname><given-names>RL</given-names></name><name><surname>Miao</surname><given-names>Y</given-names></name></person-group><year iso-8601-date="2024">2024</year><data-title>p21 peptide simulation data. Dataset includes imaged trajectory files for the five Pep-GaMD simulations runs. We have also provided the topology and the pdb file</data-title><source>figshare</source><pub-id pub-id-type="doi">10.6084/m9.figshare.26793088.v1</pub-id></element-citation></p></sec><ack id="ack"><title>Acknowledgements</title><p>We thank Dr. Yan Zhang for valuable discussions. This work used supercomputing resources with allocation award TG-MCB180049 through the Advanced Cyberinfrastructure Coordination Ecosystem: Services &amp; Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296, and project M2874 through the National Energy Research Scientific Computing Center (NERSC), which is a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231, and the Research Computing Cluster at the University of Kansas. This work was supported in part by National Institutes of Health (R01DK123590 and R56DK135824), Department of Defense CDMRP PRMRP Discovery Award (PR160710/W81XWH-17-1-0301), and Pilot Grant funding from the School of Health Professions at KU Medical Center (to RLM), Pilot award 1004015 from Jared Grantham Kidney Institute at KU Medical Center (to YM and RLM), the National Institutes of Health (R56DK135824) and startup project 27110 at University of North Carolina - Chapel Hill (to YM), and the National Institutes of Health (R35-GM132090 and OD020095) (to AH). 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id="sa0"><front-stub><article-id pub-id-type="doi">10.7554/eLife.95992.3.sa0</article-id><title-group><article-title>eLife assessment</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Cui</surname><given-names>Qiang</given-names></name><role specific-use="editor">Reviewing Editor</role><aff><institution>Boston University</institution><country>United States</country></aff></contrib></contrib-group><kwd-group kwd-group-type="evidence-strength"><kwd>Convincing</kwd></kwd-group><kwd-group kwd-group-type="claim-importance"><kwd>Valuable</kwd></kwd-group></front-stub><body><p>This joint computational/experimental study demonstrates the ability of synthetic peptides derived from the stalk tethered agonist in polycystin-1 (PC1) to re-activate signaling by a stalkless C-terminal fragment of PC1. The study is <bold>valuable</bold> as it discovered peptide agonists for PC1 and the integrated <italic>in vitro</italic> and <italic>in silico</italic> approach is potentially applicable to the analysis of related systems. Following the revision, the line of evidence presented in the current manuscript is considered <bold>convincing</bold>.</p></body></sub-article><sub-article article-type="referee-report" id="sa1"><front-stub><article-id pub-id-type="doi">10.7554/eLife.95992.3.sa1</article-id><title-group><article-title>Reviewer #1 (Public Review):</article-title></title-group><contrib-group><contrib contrib-type="author"><anonymous/><role specific-use="referee">Reviewer</role></contrib></contrib-group></front-stub><body><p>Summary:</p><p>This research used cell-based signaling assay and Gaussian-accelerated molecular dynamics (GaMD) to study peptide-mediated signaling activation of polycystin-1 (PC1), which is responsible for the majority of autosomal dominant Polycystic Kidney Disease (ADPKD) cases. Synthetic peptides of various lengths derived from the N-terminal portion of the PC1 C-terminal fragment (CTF) were applied to HEK293T cells transfected with stalkless mouse CTF expression construct. It was shown that peptides including the first 7, 9, and 17 residues of the N-terminal portion could activate signaling to the NFAT reporter. To further understand the underlying mechanism, docking and peptide-GaMD simulations of peptides composed of the first 9, 17, and 21 residues from the N-terminal portion of the human PC1 CTF were performed. These simulations revealed the correlation between peptide-CTF binding and PC1 CTF activation characterized by the close contact (salt bridge interaction) between residues R3848 and E4078. Finally, a Potts statistical model was inferred from diverged PC1 homologs to identify strong/conserved interacting pairs within PC1 CTF, some of which are highly relevant to the findings from the peptide GaMD simulations. The peptide binding pockets identified in the GaMD simulations may serve as novel targets for design of therapeutic approaches for treating ADPKD.</p><p>Strengths:</p><p>(1) The experimental and computational parts of this study complement and mostly support each other, thus increasing the overall confidence in the claims made by the authors.</p><p>(2) The use of exogenous peptides and a stalkless CTF in the GaMD is a step forward compared to earlier simulations using the full CTF, CTF mutants, or the stalkless CTF alone. And it led to findings of novel binding pockets.</p><p>(3) Since the PC1 shares characteristics with the Adhesion class of GPCRs, the approaches used in this work may be extended to other similar systems.</p><p>Weaknesses:</p><p>(1) Only results for selective peptides (p9, p17 p21) binding with the protein were shown. It would be interesting to see the interaction between some (if not all) of the other peptides with the protein.</p><p>(2) The convergence of the simulations is not very good. The results should be interpreted more qualitatively rather than quantitively because large variations in the free energy profile were seen between different replicates. Although these simulations might have identified representative low-energy binding conformations of the peptides, whether they have explored all possible conformations is still a question.</p></body></sub-article><sub-article article-type="referee-report" id="sa2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.95992.3.sa2</article-id><title-group><article-title>Reviewer #2 (Public Review):</article-title></title-group><contrib-group><contrib contrib-type="author"><anonymous/><role specific-use="referee">Reviewer</role></contrib></contrib-group></front-stub><body><p>Summary:</p><p>This manuscript, &quot;Activation of polycystin-1 Signaling by Binding of Stalk-derived Peptide Agonists&quot;, by Miao and coworkers. The autosomal dominant Polycystic Kidney Disease (ADPKD) is a major form of Polycystic Kidney Disease (PKD). To provide better treatment and avoid side effects associated with currently available options, the authors investigated an interesting GPCR, polycystin-1 (PC1), as a potential therapeutic target. <italic>In vitro</italic> and <italic>in silico</italic> studies were combined to identify peptide agonists for PC1 and to elucidate their roles in PC1 signaling. Overall, regarding the significance of the findings, this work described valuable peptide agonists for PC1 and the combined <italic>in vitro</italic> and <italic>in silico</italic> approach can be useful to study a complex system like PC1. However, the strength of the evidence is incomplete, as more experiments are needed as controls to validate the computational observations. The work appears premature.</p><p>Strengths:</p><p>(1) This work first described the experimental discovery of short peptides designed to mimic the stalk region of PC1, followed by computational investigation using docking and MD simulations. PC1 is a complex membrane protein and an emerging target for ADPKD, but it can be challenging to study. The knowledge and the peptide discovery can be valuable and useful to understand the mechanism and potential modulation of PC1.</p><p>(2) The authors published the mechanistic study of PC1 and identified key interacting residues such as N3074-S3585 and R3848-E4078, using very similar techniques (PNAS 2022, 119(19), e2113786119). This work furthers this research by identifying peptides that are stalk mimics for PC1 activation.</p><p>(3) Eight peptides were designed and tested experimentally first; three were computationally studied with docking and GaMD simulations to understand their mechanism (s).</p><p>Weaknesses:</p><p>(1) The selectivity of the peptides between PC1 and PC2 remains unknown in this revision.</p><p>Overall, my comments were mostly addressed properly.</p></body></sub-article><sub-article article-type="referee-report" id="sa3"><front-stub><article-id pub-id-type="doi">10.7554/eLife.95992.3.sa3</article-id><title-group><article-title>Reviewer #3 (Public Review):</article-title></title-group><contrib-group><contrib contrib-type="author"><anonymous/><role specific-use="referee">Reviewer</role></contrib></contrib-group></front-stub><body><p>Summary:</p><p>The authors demonstrate the activation of polycystin-1 (PC1), a G-protein coupled receptor, using small peptides derived from its original agonist, the stalk TA protein. In the experimental part of the study, the authors performed cellular assays to check the peptide-induced reactivation of a mutant form of PC1 which does not contain the stalk agonist. The experimental data is supported by computational studies using state-of-the-art Gaussian accelerated Molecular Dynamics (GaMD) and bioinformatics analysis based on sequence covariance. The computer simulations revealed the mechanistic details of the binding of the said peptides with the mutant PC1 protein and discovered different bound, unbound, and intermediate conformations depending on the peptide size and sequence. Due to the use of reliable and well-established molecular simulation algorithms and the physiological relevance of this protein autosomal dominant Polycystic Kidney Disease (ADPKD) make this work particularly valuable.</p><p>Strengths:</p><p>This work is exploratory and its goal is to establish that small peptides can be used to probe the PC1 signaling process. The authors have provided sufficient evidence to justify this claim. Their GaMD simulations have produced free-energy landscapes that differentiate the interaction of PC1 with three different synthetic peptides and demonstrate the associated conformational dynamics of the receptor protein. Their trajectory analysis and sequence covariance analysis could identify residue-specific interactions that facilitate this process. The authors also performed residue-wise and total interaction energy calculations to substantiate their findings.</p><p>Weaknesses:</p><p>The reported free energy landscapes are not fully converged. But they are still sufficient to gain biological insight.</p></body></sub-article><sub-article article-type="author-comment" id="sa4"><front-stub><article-id pub-id-type="doi">10.7554/eLife.95992.3.sa4</article-id><title-group><article-title>Author response</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Pawnikar</surname><given-names>Shristi</given-names></name><role specific-use="author">Author</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/001tmjg57</institution-id><institution>University of Kansas</institution></institution-wrap><addr-line><named-content content-type="city">Lawrence</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Magenheimer</surname><given-names>Brenda</given-names></name><role specific-use="author">Author</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/036c9yv20</institution-id><institution>University of Kansas Medical Center</institution></institution-wrap><addr-line><named-content content-type="city">Kansas City</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Joshi</surname><given-names>Keya</given-names></name><role specific-use="author">Author</role><aff><institution>University of North Carolina at Chapel Hill</institution><addr-line><named-content content-type="city">Chapel Hill</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Nevarez-Munoz</surname><given-names>Ericka</given-names></name><role specific-use="author">Author</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/036c9yv20</institution-id><institution>University of Kansas Medical Center</institution></institution-wrap><addr-line><named-content content-type="city">Kansas City</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Haldane</surname><given-names>Allan</given-names></name><role specific-use="author">Author</role><aff><institution>Temple University</institution><addr-line><named-content content-type="city">Philadelphia</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Maser</surname><given-names>Robin</given-names></name><role specific-use="author">Author</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/036c9yv20</institution-id><institution>University of Kansas Medical Center</institution></institution-wrap><addr-line><named-content content-type="city">Kansas City</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Miao</surname><given-names>Yinglong</given-names></name><role specific-use="author">Author</role><aff><institution>University of North Carolina at Chapel Hill</institution><addr-line><named-content content-type="city">Chapel Hill</named-content></addr-line><country>United States</country></aff></contrib></contrib-group></front-stub><body><p>The following is the authors’ response to the original reviews.</p><disp-quote content-type="editor-comment"><p><bold>Reviewer 1:</bold></p><p>This research used cell-based signaling assay and Gaussian-accelerated molecular dynamics (GaMD) to study peptide-mediated signaling activation of polycystin-1 (PC1), which is responsible for the majority of autosomal dominant Polycystic Kidney Disease (ADPKD) cases. Synthetic peptides of various lengths derived from the N-terminal portion of the PC1 C-terminal fragment (CTF) were applied to HEK293T cells transfected with stalkless mouse CTF expression construct. It was shown that peptides including the first 7, 9, and 17 residues of the N-terminal portion could activate signaling to the NFAT reporter. To further understand the underlying mechanism, docking and peptide-GaMD simulations of peptides composed of the first 9, 17, and 21 residues from the N-terminal portion of the human PC1 CTF were performed. These simulations revealed the correlation between peptide-CTF binding and PC1 CTF activation characterized by the close contact (salt bridge interaction) between residues R3848 and E4078. Finally, a Potts statistical model was inferred from diverged PC1 homologs to identify strong/conserved interacting pairs within PC1 CTF, some of which are highly relevant to the findings from the peptide GaMD simulations. The peptide binding pockets identified in the GaMD simulations may serve as novel targets for the design of therapeutic approaches for treating ADPKD.</p></disp-quote><p>We greatly appreciate the reviewer’s encouraging and positive comments. The reviewer’ specific comments are addressed pointwise below and changes to the text will be highlighted in yellow in the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(1) The GaMD simulations all include exogenous peptides, thus lacking a control where no such peptide is present (and only stalkless CTF). An earlier study (PNAS 2022 Vol. 119 No. 19 e2113786119) covered this already, but it should be mentioned here that there was no observation of close/activation for the stalkless CTF.</p></disp-quote><p>We appreciate the reviewer’s concern about the lack of a control where no exogenous peptide is present. As suggested by the reviewer, we are adding more details about the study on the stalkless CTF as a control in the Introduction of the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(2) Although 5 independent trajectories were generated for each peptide, the authors did not provide sufficient details regarding the convergence of the simulation. This leaves some uncertainties in their results. Given that the binding poses changed relative to the starting docked poses for all three peptides, it is possible that some other binding pockets and/or poses were not explored.</p></disp-quote><p>We appreciate the reviewer’s comment regarding the convergence of the simulation results. This is clarified in the revised manuscript as:</p><p>“We have calculated free energy profiles of individual simulations for each system, including the p9, p17, and p21, as shown below (Figs. S5, S6 and S8). For the p9 peptide, the “Bound” lowenergy state was consistently identified in the 2D free energy profile of each individual simulation (Fig. S5). For the p17 peptide, Pep-GaMD simulations were able to refine the peptide conformation from the &quot;Unbound” to the &quot;Intermediate” and “Bound” states in Sim1 and Sim5, while the peptide reached only the &quot;Intermediate” state in the other three simulations (Fig. S6). For the p21 peptide, Pep-GaMD was able to refine the peptide docking conformation to the</p><p>&quot;Bound” state in all the five individual simulations (Fig. S8).”</p><p>“It is important to note that the free energy profiles calculated from GaMD simulations of PC1 CTF were not fully converged since certain variations were observed among the individual simulations. Nevertheless, these calculations allowed us to identify representative low-energy binding conformations of the peptides.”</p><disp-quote content-type="editor-comment"><p>(3) The free energy profiles (Figures 2 to 4) based on the selected coordinates provide important information regarding binding and CTF conformational change. However, it is a coarsegrained representation and complementary analysis such as RDFs, and/or contact maps between the peptide and CTF residues might be helpful to understand the details of their interactions. These details are currently only available in the text.</p></disp-quote><p>Following the reviewer's suggestion, we have now included a set of protein contact maps showing contacts between the peptides and the TOP domain for each peptide in the representative &quot;Bound” state in revised Supplementary Information (Fig. S4). The contact maps serve to visualize the list of contacts mentioned in the main text. This will be clarified in the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(4) The use of a stalkless CTF is necessary for studying the functions of the exogenous peptides. However, the biological relevance of the stalkless CTF to ADPKD was not clearly explained, if any.</p></disp-quote><p>We appreciate the reviewer’s comment. As correctly assessed by the reviewer, the stalkless CTF is not a biological form of PC1 observed in ADPKD, but rather was used as the simplest or least complex system in which the activities and binding of exogenous peptides could be studied. However, in ADPKD, there are numerous missense mutations reported within the GPCR autoproteolysis-inducing (GAIN) domain that have been shown to prevent or inhibit cleavage at the GPCR-coupled proteolysis site (GPS). Loss of PC1 GPS cleavage, which is known to cause ADPKD, would retain or sequester the stalk tethered agonist within the interior of the GAIN domain, which would presumably interfere with interactions between stalk tethered agonist residues and the remainder of the CTF. Furthermore, there are 10 single nucleotide polymorphisms reported within the stalk sequence (ADPKD Variant Database; <ext-link ext-link-type="uri" xlink:href="https://pkdb.mayo.edu/welcome">https://pkdb.mayo.edu/welcome</ext-link>), most of which we have found to significantly reduce CTF-mediated activation of the NFAT reporter (Magenheimer BS, et al., <ext-link ext-link-type="uri" xlink:href="https://www.biorxiv.org/content/10.1101/2021.08.20.457171v1">Constitutive signaling by the C-terminal fragment of polycystin1 is mediated by a tethered peptide agonist;</ext-link> bioRxiv 2021.08.05.455255). In particular, the ADPKD-associated G3052R stalk mutation that was analyzed along with the stalkless CTF by GaMD simulations (Pawnikar et al, PNAS, 2022) has the same reduction in activity as the stalkless CTF in the cellular signaling reporter assays and the same loss of closed conformation interactions in GaMD analyses. As such, we believe the stalkless CTF has biological relevance from the aspect that it mimics the deficiency in signaling activation observed for PC1 CTF stalk mutants. This is clarified in the revised manuscript in the Introduction, page 5, “constructs encoding a stalkless PC1 CTF (a nonbiological mutant of PC1 with deletion of the first 21 N-terminal residues of CTF and three ADPKD-associated…”) and near the beginning of the Discussion, page 16, where the biological relevance of studying the stalkless CTF is explained</p><disp-quote content-type="editor-comment"><p>(5) The authors might want to clarify if a stalkless CTF is commonly seen in ADPKD, or if it is just a construct used for this study.</p></disp-quote><p>The stalkless CTF is not a biological form of PC1, but rather a construct used for this study. This was clarified in the revised manuscript (see response above).</p><disp-quote content-type="editor-comment"><p>(6) (Pages 7-8) &quot;...we generated expression constructs of mouse (m) PC1 consisting of the CD5 signal peptide sequence fused in frame with the stalk sequence of mCTF ...&quot;. What is the CD5 signal peptide sequence here? What is its use?</p></disp-quote><p>The CD5 signal peptide sequence is “MPMGSLQPLATLYLLGMLVASVLG” from the T cell surface glycoprotein, CD5. Since the N-terminus of PC1 CTF is derived from a posttranslational, autocatalytic, endoproteolytic cleavage event, this isoform is already membraneembedded and therefore lacks its endogenous signal peptide. The CD5 signal peptide coding sequence is added to the PC1 CTF expression constructs in order to ensure translation and insertion of the encoded protein at the endoplasmic reticulum. Additional details were added to the Experimental Procedures, page 2 of Supporting Information.</p><disp-quote content-type="editor-comment"><p>(7) (Page 8) &quot;All peptides were appended with a C-terminal, 7-residue hydrophilic sequence (GGKKKKK) to increase solubility&quot;. How did the authors make sure that this sequence has no influence on the signaling?</p></disp-quote><p>To determine the possible effect of the hydrophilic GGKKKKK sequence on signaling, we had a ‘solubility tag’ peptide (LGGKKKKK) synthesized and purified by GenScript. It was necessary to add an N-terminal Leu residue to the 7-residue hydrophilic tag sequence in order for the highly hydrophilic peptide to be recovered. Effect of treatment with the solubility tag peptide on activation of the NFAT reporter was assessed for both empty vector- and ∆stalkCTF-transfected cells in 3 separate signaling experiments (see figure below). Each experiment also included a negative control treatment (no peptide/culture medium only addition) and a positive control treatment (stalk peptide p17). The p17 peptide we had available was derived from the stalk sequence of human PC1 that differs from the mouse PC1 sequence at residues 15 and 17, which are two poorly conserved positions within the stalk sequence (see Reviewer 2, Response 3). In the first experiment with the solubility tag and human p17 peptides (B in figure below), we inadvertently used the empty expression vector and ∆stalkCTF expression construct from mouse PC1. After realizing our error, we then performed 2 additional signaling experiments (C and D in figure below) with the ‘correct’ human ∆stalkCTF expression construct and empty vector. In the revised manuscript, we have provided the results from each of the 3 experiments as Fig. S2 (below).</p><disp-quote content-type="editor-comment"><p>(8) (Page 9) &quot;Using a computational model of the ΔStalk PC1 CTF developed previously&quot;. The authors might want to expand here a little to give a short review about the structure preparation.</p></disp-quote><p>We appreciate the reviewer’s suggestion regarding the addition of details for structure preparation for Stalkless CTF. We have added these details in section “Docking and Pep-GaMD simulations of peptide agonist binding to stalkless PC1 CTF” on Page 10 in the revised manuscript: “The cryo-EM structure of human PC1-PC2 complex (PDB: 6A70) was used to build the computational model for WT PC1 CTF. As the protein had several missing regions including the Stalk and several loops, homology modeling of the missing regions was done using I-TASSER web server. Using the WT PC1 CTF model, computational model for ΔStalk was generated by deleting the first 21 residues (3049-3069) of the WT PC1 and using the structure for stalkless CTF, we successfully docked the p9, p17 and p21 stalk peptides with HPEPDOCK. The peptides all bound to the TOP domain and the interface between the TOP domain and extracellular loop 1 (ECL1) of CTF.”</p><disp-quote content-type="editor-comment"><p>(9) How was &quot;contact&quot; defined when counting the number of contacts used in the 2D PMFs (Figures 2-4). Response: We appreciate the reviewer’s comment regarding the definition of the number of contacts used in the 2D PMFs. This has been clarified in the revised manuscript as: “The number of contacts is calculated between any atom pairs within 4 Å distance of the peptide and extracellular domains of PC1 protein.”</p><p>(10) How was the ranking of GaMD clusters done? It looks from Figure 3A that the &quot;intermediate&quot; state is more favorable compared to the &quot;bound&quot; state, but it was claimed in the text the &quot;bound&quot; state was ranked 1st.</p></disp-quote><p>Thanks to the reviewer for this comment. It has been clarified in the revised</p><p>Supplementary Information: “Three independent Pep-GaMD simulations were combined to perform structural clustering using the hierarchical agglomerative clustering algorithm in CPPTRAJ. A 3 Å RMSD cutoff was used for each peptide system. PyReweighting was then applied to calculate the original free energy values of each peptide structural cluster with a cutoff of 500 frames. The structural clusters were finally ranked according to the reweighted free energy values.” And in the revised main text: “It is important to note that the free energy profiles calculated from GaMD simulations of PC1 CTF were not fully converged since certain variations were observed among the individual simulations. The free energy values of 2D PMF minima shown in Figure 3A could differ from those in the 1D PMF minima of peptide structural clusters, especially with the usage of distinct reaction coordinates. Nevertheless, these calculations allowed us to identify representative low-energy binding conformations of the peptides.”</p><disp-quote content-type="editor-comment"><p>(11) When mentioning residue pair distances, such as in the sentence &quot;The distance between the TOP domain residue R3848 and PL residue E4078 was 3.8 Å (Fig. 4D)&quot; on page 12, it should be clarified if these distances are average distance, or a statistical error can be given.</p></disp-quote><p>We appreciate the reviewer’s comment regarding the TOP Domain and PL distance between residues R3848-E4078. This has been clarified on page 14 in the revised manuscript as:</p><p>“The distance between the TOP domain residue R3848 and PL residue E4078 was 3.8 Å. The distance was extracted from the top-ranked structural cluster of the p21 bound to the ΔStalk CTF, corresponding to the “Closed/Active” low-energy conformational state. (Fig. 4E)”.</p><disp-quote content-type="editor-comment"><p>(12) More analysis of the GaMD can be performed. For example, the authors observed a single &quot;bound&quot; state for p21, but there must be some flexibility in the peptide and the protein itself. The authors might want to consider adding some plots illustrating the flexibility of the peptide residues (for example, a RMSD plot). Contact maps can also be added to visualize the results currently discussed in the text.</p></disp-quote><p>We thank the reviewer for their constructive suggestions. To characterize flexibility of the peptide and protein in the revised manuscript, we have added plots of the TOP-PL interaction distance between residues R3848-E4078 in PC1, the radius of gyration (Rg) of p21 and root-mean square deviation (RMSD) of p21 relative to the starting HPEPDOCK conformation of the peptide in the new Fig. S7. The peptide-protein contact map has also been added in the new Fig. S4.</p><disp-quote content-type="editor-comment"><p>(13) (Page 7) In the sentence `...sampled the &quot;Closed/Active&quot; low-energy state relative to the large number of Stalk-TOP contacts`, I suggest using &quot;related to&quot; instead of &quot;relative to&quot;</p></disp-quote><p>We thank the reviewer for the comment, and we have replaced &quot;relative to&quot; to “related to” in the following sentence `...sampled the &quot;Closed/Active&quot; low-energy state relative to the large number of Stalk-TOP contacts`</p><disp-quote content-type="editor-comment"><p>(14) (Page 7) In the sentence `Our previous study utilized expression constructs of human PC1 CTF, however, in order to prepare for ...`, &quot;PC1 CTF, however,&quot; -&gt; &quot;PC1 CTF. However,&quot;</p></disp-quote><p>We thank the reviewer for the comment, and we have replaced &quot;PC1 CTF, however,&quot; to &quot;PC1 CTF. However,&quot; in the following sentence `Our previous study utilized expression constructs of human PC1 CTF, however, in order to prepare for ...`.</p><disp-quote content-type="editor-comment"><p><bold>Reviewer 2:</bold></p><p>The autosomal dominant Polycystic Kidney Disease (ADPKD) is a major form of Polycystic Kidney Disease (PKD). To provide better treatment and avoid side effects associated with currently available options, the authors investigated an interesting GPCR, polycystin-1 (PC1), as a potential therapeutic target. <italic>In vitro</italic> and <italic>in silico</italic> studies were combined to identify peptide agonists for PC1 and to elucidate their roles in PC1 signaling. Overall, regarding the significance of the findings, this work described valuable peptide agonists for PC1 and the combined <italic>in vitro</italic> and <italic>in silico</italic> approach can be useful to study a complex system like PC1. However, the strength of the evidence is incomplete, as more experiments are needed as controls to validate the computational observations. The work appears premature.</p></disp-quote><p>We greatly appreciate the reviewer’s encouraging and positive comments. The reviewer’ specific comments are addressed pointwise below and changes to the text will be highlighted in yellow in the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(1) The therapeutic potential of PC1 peptide agonists is unclear in the introduction. For example, while the FDA-approved drug Jynarque was mentioned, the text was misleading as it sounded like Jynarque targeted PC1. In fact, it targets another GPCR, the vasopressin receptor 2 (V2). A clear comparison of targeting PC1 over V2 pathways and their therapeutic relevance can help the readers better understand the importance of this work. Importantly, a clear background on the relationship between PC1 agonism and treatments for ADPKD is necessary.</p></disp-quote><p>We understand the confusion that was caused by the brevity of our introductory paragraph and will clarify the differences in therapeutic targeting between Jynarque and our PC1 stalk-derived peptides in the revised manuscript. We will also expound on the rationale for targeting PC1 agonism as a therapeutic approach for ADPKD versus Jynarque. For example: It is known that ADPKD disease severity is dependent on the functional levels of PC1. Jynarque is a small molecule antagonist of the arginine vasopressin receptor 2, V2R, whose signaling, and production of cAMP has been shown to be increased in ADPKD. As this drug targets one of the downstream aberrant pathways, it is only capable of slowing disease progression and has numerous undesirable side effects. We reasoned that a therapeutic agent capable of stimulating and thus augmenting PC1 signaling function would be a safer, cyst initiation-proximal treatment capable of preventing cyst formation with few side effects.</p><disp-quote content-type="editor-comment"><p>(2) PC1 is a complex membrane protein, and most figures focus on the peptide-binding site. For general readers (or readers that did not read the previous PNAS publication), it is hard to imagine the overall structure and understand where the key interactions (e.g., R3848-E4078) are in the protein and how peptide binding affects locally and globally. I suggest enhancing the illustrations.</p></disp-quote><p>We thank the reviewer for the constructive comment on adding more illustrations for the PC1 protein to understand the overall structure and the location of the key interaction R3848E4078. We have included these suggestions and modified the main figures in the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(3) The authors used the mouse construct for the cellular assays and the peptide designs in preparation for future in vivo assays. This is helpful in understanding biology, but the relevance of drug discovery is weakened. Related to Point 1, the therapeutic potential of PC1 peptide agonist is largely missing.</p></disp-quote><p>The therapeutic potential of a PC1 peptide agonist is addressed in response #1 above. As mentioned in the manuscript and recognized by the reviewer, the cellular signaling assays were performed with the mouse PC1 CTF expression construct and with peptides based on the mouse PC1 stalk sequence for future, pre-clinical studies, while the peptide binding studies were performed with the human PC1 stalk sequence. We feel the relevance for drug discovery is not significantly weakened for a number of reasons: (1) as shown in Fig. 1A, the stalk sequence is highly conserved between mouse and human PC1, specifically there are only 2 residue differences present within peptides p17 and p21. One of the differences is a ‘semi-conservative’ Gln-Arg substitution at peptide residue 15, while the second difference is a conservative Ile-Val substitution at peptide residue 17; (2) we have found that an Arg to Cys mutation within the mouse PC1 CTF stalk has the same effect on signaling as the corresponding human Gln to Cys ADPKD-associated mutation which was analyzed in (Pawnikar et al., 2022); and (3) both peptide residues 15 and 17 represent highly variable positions within the PC1 stalk as shown in the sequence logo (below) of the stalk sequence from 16 vertebrate species; and (4) while addressing the potential effect of the hydrophilic solubility tag on stalk peptide-mediated rescue of CTF∆stalk signaling (see Reviewer 1 comments, point #7), we utilized the ‘human’ version of p17 as a positive control and tested its activation with both mouse and human CTF∆stalk expression constructs and found that human p17 peptide was also capable of stimulating the mouse CTF∆stalk protein (Fig. S2).</p><fig id="sa4fig1" position="float"><label>Author response image 1.</label><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-95992-sa4-fig1-v1.tif"/></fig><disp-quote content-type="editor-comment"><p>(4) More control experiments are needed. For example, a 7-residue hydrophilic sequence (GGKKKKK) is attached to the peptide design to increase solubility. This 7-residue peptide should be tested for PC1 activation as a control. Second, there is no justification for why the peptide design must begin with residue T3041. Can other segments of the stalk also be agonists?</p></disp-quote><p>As mentioned above for Reviewer 1, the hydrophilic peptide has been synthesized and tested for activation of signaling by the stalkless CTF in the revised manuscript as Fig. S2. The design of peptides that begin with residue T3041 of mouse PC1 CTF is modeled on numerous similar studies for the family of adhesion GPCRs. Optimization of the binding and activity of the PC1 peptide agonist will be investigated in future studies and could include such parameters as whether the peptide must include the first residue and whether subsegments of the stalk are also agonists, however, we feel these questions are beyond the scope of this initial report.</p><disp-quote content-type="editor-comment"><p>(5) There are some major concerns about the simulations: The GaMD simulations showed different binding sites of p-21, p-17, and p-9, and the results report the simulated conformations as &quot;active conformational states&quot;. However, these are only computational findings without structural biology or mutagenesis data to validate. Further, neither docking nor the simulation data can explain the peptide SAR. Finally, it will be interesting if the authors can use docking or GaMD and explain why some peptide designs (like P11-P15) are less active (as control simulations).</p></disp-quote><p>The reviewer brings up an important observation regarding differences in binding sites between peptides p9, p17 and p21. We will include discussion of this observation and our interpretations to the revised manuscript. While the present study is focused on identification of initial peptides that are able to activate the PC1 CTF, we shall include further mutation experiments and simulations, peptide SAR and optimization of the lead peptides in future studies. This has been clarified in the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(6) Additional experiments for the controls and for validating the simulations. Additional simulations to explain the SAR.</p></disp-quote><p>We appreciate the reviewer’s comment for additional experiments for the controls and additional simulations to explain the SAR. For future studies, we shall include further mutation experiments and simulations, peptide SAR and optimization of the lead peptides.</p><disp-quote content-type="editor-comment"><p>(7) What is the selectivity of the peptides between PC1 and PC2?</p></disp-quote><p>We have not tested the selectivity of the peptides for PC1 versus PC2 primarily because transfection of PC2 does not activate the NFAT reporter. However, it is possible that co-transfection of PC2 with the PC1 CTF could alter stalk peptide binding. This will be important to consider in future studies.</p><disp-quote content-type="editor-comment"><p><bold>Reviewer 3:</bold></p><p>The authors demonstrate the activation of polycystin-1 (PC1), a G-protein coupled receptor, using small peptides derived from its original agonist, the stalk TA protein. In the experimental part of the study, the authors performed cellular assays to check the peptide-induced reactivation of a mutant form of PC1 which does not contain the stalk agonist. The experimental data is supported by computational studies using state-of-the-art Gaussian accelerated Molecular Dynamics (GaMD) and bioinformatics analysis based on sequence covariance. The computer simulations revealed the mechanistic details of the binding of the said peptides with the mutant PC1 protein and discovered different bound, unbound, and intermediate conformations depending on the peptide size and sequence. The use of reliable and well-established molecular simulation algorithms and the physiological relevance of this protein autosomal dominant Polycystic Kidney Disease (ADPKD) make this work particularly valuable.</p></disp-quote><p>We greatly appreciate the reviewer’s encouraging and positive comments. The reviewer’ specific comments are addressed pointwise below and changes to the text will be highlighted in yellow in the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(1) No control has been used for the computational (GaMD) study as the authors only report the free energy surface for 3 highly agonistic peptides but for none of the other peptides that did not induce an agonistic effect. Therefore, in the current version, the reliability of the computational results is not foolproof.</p></disp-quote><p>We appreciate the reviewer’s concern about the lack of control with the other peptides that did not induce an agonistic effect. To address the reviewer’s concern, we have included more details on the study of the stalkless CTF and the solubility tag peptide (Fig. S2) as controls in the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(2) All discussions about the residue level interactions focused only on geometric aspects (distance, angle, etc) but not the thermodynamic aspect (e.g. residue-wise interaction energy). Considering they perform a biased simulation; the lack of interaction energy analysis only provides a qualitative picture of the mechanism.</p></disp-quote><p>As mentioned by the reviewer, we have added MM/PBSA analysis results in the revised manuscript and SI.</p><p>Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) analysis was performed to calculate the binding free energies of peptides p9, p17 and p21 to PC1 CTF. The analysis was performed using the trajectory in which the peptide was bound to the receptor. In MM/PBSA, the binding free energy of the ligand (L) to the receptor (R) to form the complex (RL) is calculated as:</p><p><inline-formula><mml:math id="sa4m1"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula></p><p>where GRL is the Gibbs free energy of the complex RL, GR is the Gibbs free energy of the molecule R in its unbound state and GL is the Gibbs free energy of the molecule L in its unbound state, respectively.</p><p>𝛥𝐺𝑏𝑖𝑛𝑑 can be divided into contributions of different interactions as:</p><p><inline-formula><mml:math id="sa4m2"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>H</mml:mi><mml:mo>−</mml:mo><mml:mi>T</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mtext>sol </mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>T</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula></p><p>in which</p><p><inline-formula><mml:math id="sa4m3"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mtext>sol </mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>B</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>G</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math></inline-formula></p><p><inline-formula><mml:math id="sa4m4"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>γ</mml:mi><mml:mo>⋅</mml:mo><mml:mi>S</mml:mi><mml:mi>A</mml:mi><mml:mi>S</mml:mi><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:mstyle></mml:math></inline-formula></p><p>where ΔEMM , ΔGsol , 𝞓H and −TΔS are the changes in the gas-phase molecular mechanics (MM) energy, solvation free energy, enthalpy and conformational entropy upon ligand binding, respectively. ΔEMM includes the changes in the internal energies ΔEint (bond, angle and dihedral energies), electrostatic energies ΔEelec , and the van der Waals energies ΔEvdW. ΔGsol is the sum of the electrostatic solvation energy ΔGPB/GB (polar contribution) and the nonpolar contribution ΔGSA between the solute and the continuum solvent. The polar contribution is calculated using either the Poisson Boltzmann (PB) or Generalized Born (GB) model, while the nonpolar energy is usually estimated using the solvent-accessible surface area (SASA) where 𝞬 is surface tension coefficient and b is the constant offset. The change in conformational entropy −TΔS is usually calculated by normal-mode analysis on a set of conformational snapshots taken from MD simulations. However, due to the large computational cost, changes in the conformational entropy are usually neglected as we were concerned more on relative binding free energies of the similar peptide ligands.</p><p>MM/PBSA analysis was performed using the gmx_MMPBSA software with the following command line:</p><p>gmx_MMPBSA -O -i mmpbsa.in -cs com.tpr -ci index.ndx -cg 1 13 -ct com_traj.xtc -cp topol.top -o FINAL_RESULTS_MMPBSA.dat -eo FINAL_RESULTS_MMPBSA.csv Input file for running MM/PBSA analysis:</p><p>&amp;generalsys_name=&quot;Prot-Pep-CHARMM&quot;,startframe=1, endframe=200, # In gmx_MMPBSA v1.5.0 we have added a new PB radii set named charmm_radii.# This radii set should be used only with systems prepared with CHARMM force fields.# Uncomment the line below to use charmm_radii set# PBRadii=7,</p><p>/</p><p>&amp;pb</p><p># radiopt=0 is recommended which means using radii from the prmtop file for both the PB calculation and for the NP</p><p># calculation</p><p>istrng=0.15, fillratio=4.0, radiopt=0</p><p>The relative rank of the overall peptide binding free energies (Table S1) was consistent with the experimental signaling data, i.e., p21&gt;p9&gt;p17, for which p21 showed the largest binding free energy value of binding (-40.29±6.94 kcal/mol).</p><disp-quote content-type="editor-comment"><p>(3) It is not mentioned clearly whether the reader should interpret the free energy landscapes quantitatively or qualitatively. Considering no error analysis or convergence plots are reported for the GaMD free energy surfaces, it may be assumed the results are qualitative. The readers should consider this caveat and not try to quantitatively reproduce these free energy landscapes with other comparable techniques.</p></disp-quote><p>We appreciate the reviewer’s comment whether the free energy landscapes should be interpreted quantitatively or qualitatively. The presented free energy landscapes could be considered semi-quantitative since the simulations are not fully converged. This will be clarified in the revised manuscript as: “It is important to note that the free energy profiles calculated from GaMD simulations of PC1 CTF were not fully converged since certain variations were observed among the individual simulations. Nevertheless, these calculations allowed us to identify representative low-energy binding conformations of the peptides.”</p><disp-quote content-type="editor-comment"><p>(4) Energy decomposition analysis similar to the following paper (https://pubs.acs.org/doi/10.1021/bi201856m) should be provided to understand the residue level enthalpic contribution in the peptide-protein interaction.</p></disp-quote><p>As mentioned by the reviewer, we have performed residue-wise interaction energy analysis and included the analysis results in the revised manuscript and SI.</p><p>Residue-wise interaction energy analysis was performed on peptides p9, p17 and p21 using the trajectory in which the peptide was bound to the PC1 CTF using the gmx_MMPBSA software with the following command line:</p><p>gmx_MMPBSA -O -i mmpbsa.in -cs com.tpr -ct com_traj.xtc -ci index.ndx -cg 3 4 -cp topol.top -o FINAL_RESULTS_MMPBSA.dat -eo FINAL_RESULTS_MMPBSA.csv -do FINAL_DECOMP_MMPBSA.dat -deo FINAL_DECOMP_MMPBSA.csv</p><p>Input file for running residue-wise energy decomposition analysis:</p><p>&amp;generalsys_name=&quot;Decomposition&quot;, startframe=1, endframe=200,# forcefields=&quot;leaprc.protein.ff14SB&quot;</p><p>/</p><p>&amp;gb</p><p>igb=5, saltcon=0.150,</p><p>/</p><p># make sure to include at least one residue from both the receptor #and peptide in the print_res mask of the &amp;decomp section.</p><p># this requirement is automatically fulfilled when using the within keyword.</p><p># <ext-link ext-link-type="uri" xlink:href="http://archive.ambermd.org/201308/0075.html">http://archive.ambermd.org/201308/0075.html</ext-link></p><p>&amp;decomp</p><p>idecomp=2, dec_verbose=3, print_res=&quot;A/854-862 A/1-853”,</p><p>/</p><p>Residue-wise energy decomposition analysis allowed us to identify key residues that contributed the most to the peptide binding energies. These included residues T1 and V9 in p9 (Table S2), residues T1, R15 and V17 in p17 (Table S3), and residues P10, P11, P19 and P21 in p21 and residue W3726 in the PC1 CTF (Table S4). The energetic contributions of these residues apparently correlated to the sequence coevolution predicted from the Potts model.</p><disp-quote content-type="editor-comment"><p>(5) To showcase the reliability of the computational approach, the authors should perform the MD simulation studies with one peptide that did not show any significant agonistic effect in the experiment. This will work as a control for the computational protocol and will demonstrate the utility of the pep-GaMD simulation in this work.</p></disp-quote><p>We appreciate the reviewer’s concern about the lack of control with the other peptides that did not induce an agonistic effect. It is difficult for us to add more MD simulations on the other peptides, due to student leave after PhD graduation. But to address the reviewer’s concern, we have included more details on the study of the stalkless CTF as a control in the revised manuscript.</p><disp-quote content-type="editor-comment"><p>(6) To assess the accuracy of the computational results the authors should mention (either in the main text or SI) whether the reported free energy surfaces were the average of the five simulations or computed from one simulation. In the latter case, free energy surfaces computed from the other four simulations should be provided in the SI. In addition, how many binding unbinding events have been observed in each simulation should be mentioned.</p></disp-quote><p>We appreciate the reviewer’s comment regarding convergence of the simulation free energy surfaces. In response to Reviewer 1, we have calculated free energy profiles of individual simulations for each system, including the p9, p17, and p21 (Figs. S5, S6 and S8).</p><p>“We have calculated free energy profiles of individual simulations for each system, including the p9, p17, and p21 (Figs. S5, S6 and S8). For the p9 peptide, the “Bound” low-energy state was consistently identified in the 2D free energy profile of each individual simulation (Fig. S5). For the p17 peptide, Pep-GaMD simulations were able to refine the peptide conformation from the &quot;Unbound” to the &quot;Intermediate” and “Bound” states in Sim1 and Sim5, while the peptide reached only the &quot;Intermediate” state in the other three simulations (Fig. S6). For the p21 peptide, PepGaMD was able to refine the peptide docking conformation to the &quot;Bound” state in all the five individual simulations (Fig. S8).”</p><p>“It is important to note that the free energy profiles calculated from GaMD simulations of PC1 CTF were not fully converged since certain variations were observed among the individual simulations. Nevertheless, these calculations allowed us to identify representative low-energy binding conformations of the peptides.”</p></body></sub-article></article>