The deletion cassette plasmid was constructed by amplifying pTEF::KAN^R from pUG6 (Euroscarf) and tTEF from pUG6, with an overlapping junction between KAN^R and tTEF containing two BbsI sites for golden-gate mediated barcode cloning. These pieces were assembled into pUC19 using gibson isothermal assembly to generate DGP304. This plasmid was then modified by linearizing with BamHI and XbaI, amplifying a bacterial GFP expression cassette from pWS158 (Addgene), and assembled using gibson isothermal assembly to generate DGP306.

Gene deletion barcodes were created by synthesizing an oligonucleotide containing flanking PCR handles (M13F and M13R), flanking BbsI sites for golden gate cloning, and the degenerate sequence caNNgNNgtNNgNNgtNNgNNgt. The mixture of oligonucleotides was double-stranded using E. coli DNA Polymerase I, Large (Klenow) fragment. Klenow buffer (1x NEB Buffer 2.1 [NEB #B7202S]) was mixed with 250 nM barcode oligonucleotide, 250 nM M13R primer, 200 nM/each dNTP [NEB #N0447S], incubated at 80°C and slowly cooled to room temperature. The DNA Polymerase I, Large (Klenow) Fragment (NEB #M0210S) was added to 0.1 U/µL and the reaction was incubated at 37°C for 30 min. The polymerase was heat-inactivated by placing the reaction at 75°C for 20 min. The resulting dsDNA cassette was used with no further cleanup.

The barcode was inserted into the 3’ untranslated region of the pTEF::KAN^R::tTEF yeast selection marker cassette in DGP306 by BbsI-mediated golden gate cloning. A golden gate reaction was prepared with 1x Thermo FastDigest Buffer [Thermo #ER1011], 1 mM ATP, 10 mM DTT, 2 U/µL T4 DNA Ligase [NEB #M0202S], 1 U/µL BpiI [Thermo #ER1011], 10 ng/µL DGP306, 25 nM barcode dsDNA, and incubated in a thermocycler using the following program: 37°C 20 min; 25x cycles of 37°C for 5 min and 16°C for 5 min; 37°C for 20 min; 80°C for 20 min. An additional 1 U/µL BpiI was then added to the reaction mix and incubated at 37°C for 30 min to linearize any remaining uncloned plasmid.

The golden gate cloning reaction was transformed into One Shot TOP10 E. coli (ThermoFisher #C404003). Cloning and transformation efficiency was estimated by plating 2% of the transformation onto LB + ampicillin plate and counting GFP⁺ and GFP^- colonies. The remainder of the reaction was inoculated into 200 mL molten LB + ampicillin + 0.6% (w/v) SeaPrep Agarose (Lonza 50302) media, thoroughly mixed, snap cooled in an ice bucket, and incubated overnight at 37°C. The soft agar culture was then collected by centrifugation, washed with PBS, and resuspended in 2 mL 50% glycerol. 100 µL of this mixture was used to inoculate a culture of 100 mL LB + ampicillin and the remainder stored at −80°C in aliquots. The 100 mL culture was grown for 8 hr at 37°C, harvested, washed with PBS, and stored at −20°C until midiprepped (Qiagen) according to the manufacturer’s protocol.

The degenerate barcoded plasmid was used as template for PCR using primers containing gene-specific targeting homology arms (1x NEB Q5 Master Mix #M0494S, 1 ng template plasmid, 250 nM/each oligo). The PCR amplicon was then transformed into FY4 and plated on YPD+G418 to select transformants. Transformants containing the gene deletion were confirmed using colony PCR and gene-specific primers and a KANR primer. PCR products of correct transformants were cleaned using silica spin columns (Qiagen) according to the manufacturer’s protocol and the barcode identified by Sanger sequencing. At least six uniquely barcoded strains (i.e. biological replicates) were generated for each genotype, with the criteria that each barcode had to differ by at least three bases, ensuring that the probability of barcode collisions is extremely low.

The plasmid DGP328 (pTEF::NATR::tTEF) was used as template for PCR using primers containing the same gene-specific targeting homology. The PCR amplicon was transformed into FY5 and plated on YPD+nourseothricin. Positive transformants were confirmed using colony PCR with gene-specific primers and a NATR primer.

FY4-derived MATa strains were arrayed in a 96-well plate (Corning 3788) and then pinned (V and P Scientific #VP407FP12) onto YPD in an OmniTray (Nunc 165218). FY5-derived MATɑ strains were arrayed in a 96-well plate so that the same gene was disrupted in matching wells of the MATa and MATɑ plates and then pinned onto YPD. These arrays are grown overnight at 30°C. The MATa array and MATɑ array were then pinned to the same YPD plate to create spots where MATa and MATɑ strains were overlaid. The plate layout was designed so that some locations had only MATa strains, only MATɑ strains, or no strains, to control for mating, contamination, and the efficacy of diploid selection. The mating array was grown overnight at 30°C to allow mating to occur and then pinned to a YPD+G418+nourseothricin plate to select for MATa/MATɑ diploids. This diploid selection plate was grown overnight and then pinned to a YPD+G418+nourseothricin plate for a second round of diploid selection. The second diploid selection plate was grown overnight at 30°C and then pinned to a YPD+G418+nourseothricin plate for a third round of diploid selection at 30°C. This plate was then pinned to several replicate 96 well round-bottom plates containing 200 µL YPD+G418+nourseothricin in each well. These plates were cultured with shaking overnight at 30°C, then centrifuged and the media aspirated. The cells were resuspended in 50% glycerol and the plates stored at −80°C.

The barcoded deletion array was pinned from a frozen stock plate at −80°C onto a YPD plate for recovery and grown overnight at 30°C. The first recovery plate was then pinned to a second recovery YPD plate and grown overnight at 30°C. The second recovery plate was pinned to a 96 well round-bottom plate containing 200 µL YPD in each well and grown overnight at 30°C. The cultures from this plate were pooled, washed 2x with 50 mL PBS, and then resuspended in 1 mL PBS. 250 µL of the washed cells were used to inoculate 50 mL of the relevant media for the specific experimental condition in a shake flask. These flasks were grown for 4 hr. The experiment grown to diauxic shift was grown for 10 hr. We confirmed that glucose in the media was exhausted between hour 9 and hour 10 using a hexokinase-based assay (R-Biopharm #10716251035). All other steps of harvesting cells were identical to the 4 hr experiments. The experiment treated with rapamycin was grown for 3 hr and 30 min in YPD, and then 10 µL of rapamycin stock (1 mg/mL Millipore #553210 in ethanol) was added to a final concentration of 200 ng/mL. Cells were then harvested at 4 hr (after 30 min in rapamycin).

Cell count per mL at harvest was determined using a Beckman Coulter Z2 Particle Counter #6605700. Cell density (cells/mL) for each condition at harvest was as follows: (YPD 1.4e7; RAPA 1.2e7; YPEtOH 1.0e7; NLIM-GLN 0.5e7; NLIM-NH4 0.8e7; NLIM-PRO 0.4e7; NLIM-UREA 0.5e7; MMD 1.1e7; MMEtOH 0.7e7; CSTARVE 0.1e7) A volume of culture containing ~10⁸ cells was collected and the cells pelleted by centrifugation. These cells were immediately resuspended in 1 mL RNALater (Qiagen #76104), washed 2x with 1 mL RNALater and resuspended in a final volume of 500 µL RNALater. This suspension was stored at −20°C for 12 to 72 hr.

Cells stored in RNALater were removed from −20°C and ~10⁷ cells were washed 2x with 1 mL spheroplasting buffer (50 mM Sodium Phosphate pH 7.5, 1M Sorbitol, 10 mM EDTA, 2 mM DTT, 100 µg/mL BSA). Cells from fermentative phase growth cultures were then resuspended in 100 µL spheroplasting buffer + 0.1 U Zymolyase 100T (Zymo Research #E1004). Cells from respiratory phase growth cultures or starvation cultures were resuspended in 100 µL spheroplasting buffer + 0.25U Zymolyase 100T. The spheroplasting reaction was incubated at 37°C for exactly 20 min, and then the spheroplasted cells were pelleted and resuspended in 500 µL RNALater for 5 min on ice. After this incubation the spheroplasted cells were pelleted and washed 3x with 1 mL wash buffer (10 mM TRIS pH 8, 1M Sorbitol, 100 µg/mL BSA) and resuspended in 1 mL wash buffer. The cells were visualized to confirm spheroplasting and counted using a hemocytometer. A dilution equal to ~5×10⁶ cells/mL in wash buffer was prepared and then immediately used for single cell isolation.

Single cell library preparation was done using the 10x Genomics Chromium 3’ v2 Single Cell Gene Expression Kit (10x Genomics #120237), following the kit protocol. 66.2 µL of single-cell master mix was prepared to which 27.7 µL H₂O was added. The microfluidic Chromium Single Cell A Chip (10x Genomics #120236) was then prepared for use. 6 µL of prepared spheroplast cell suspension was added to the single-cell master mix, and then immediately transferred to the microfluidics chip. Hydrogel beads and partitioning oil were added according to the manufacturer’s protocol, and the cells were encapsulated with hydrogel beads using the 10x Genomics Chromium Controller. Following emulsification, reverse transcription and cleanup was performed according to the manufacturer’s protocol. Whole transcriptome amplification was performed using a total of 10 cycles of PCR. Cleanup, fragmentation, adapter ligation, and indexing was performed according to the manufacturer’s protocol, using 8–10 cycles of PCR for the indexing reaction.

Transcribed barcodes were amplified from the whole transcriptome amplification prior to fragmentation. The KAN^R transcript containing the genotype barcode was amplified in a reaction(1x KAPA HiFi Hotstart Readymix [Kapa #KK2602], 200 nM/each primer, 1 µL 10x whole-transcriptome DNA), using 6 cycles of PCR (98°C for 3:00; 6 cycles of 98°C for 0:20, 63°C for 0:20, and 72°C for 0:20 min; 72°C for 1:00 min). The amplicon pool was then purified with 1x volume of SPRIselect beads (Beckman Coulter #B23317) and eluted into 24 µL H₂O. To this eluate, 25 µL of 2x KAPA HiFi Hotstart Readymix was added, as well as 200 nM/each indexing primers. The indexing reaction was cycled for 8–10 cycles of PCR, using the 10x Genomics indexing PCR reaction settings (98°C for 0:45; 8-10x cycles of 98°C for 0:20, 54°C for 0:30, and 72°C for 0:20; 72°C for 1:00).

Library fragment sizes were determined using a High Sensitivity D1000 Screentape (Agilent #5067–5584) and quantified with the KAPA illumina library quantification system (Roche #KK4953) on a Roche lightcycler 480. Libraries from each condition were pooled so that 99% of the pool consisted of the single-cell transcriptome library and 1% of the pool consisted of the genotype barcode amplicon. Samples were then pooled for multiplex sequencing on an Illumina NextSeq 500 with the NextSeq 500/550 v2.5 High Output 150 Cycle kit (Illumina #20024907), using the sequencing parameters recommended by 10x Genomics (Read 1: 26 bp, Read 2: 98 bp, Index 2: 8 bp) and standard illumina read and indexing primers.

Each of the six wild-type yeast strains (MAT a/ɑ Δho::KanMX/Δho::NatMX) were separately grown overnight in YPD at 30°C.~10⁸ cells (0.5 mL) of overnight culture was subcultured into separate 50 mL flasks of pre-warmed YPD and cultured with shaking for 4 hr at 30°C. At 4 hr, for each culture flask,~10⁸ cells were pelleted by centrifugation and immediately transferred to a microfuge tube, then snap-frozen in liquid nitrogen for storage at −80°C.

For each of six wild-type samples snap-frozen in liquid nitrogen and stored at −80°C, cell pellets were removed from −80°C storage and immediately resuspended in 1 mL TRIZOL (ThermoFisher #15596026), which is an organic extraction reagent with phenol and the chaotropic salt guanidinium thiocyanate (Chomczynski and Sacchi, 2006). After sitting at RT for 5 min, 200 µL chloroform was added and tubes were mixed by inversion. Organic and aqueous phases were separated by centrifugation at 4°C. The aqueous phase was re-extracted with 500 µL acid phenol:chloroform (ThermoFisher #AM9720), then the aqueous phase from that extraction was re-extracted with 500 µL chloroform. 1:10th volume 5M NH₄OAc (ThermoFisher #AM9070G) and 2.5x volumes of ice-cold absolute ethanol were added to the aqueous phase from the chloroform extraction, and RNA was precipitated overnight at −80°C. After precipitation, the RNA pellet was washed with ice-cold 70% ethanol and dissolved into 100 µL RNA elution buffer (10 mM TRIS pH8, 0.05% TWEEN-20). RNA was quantified by Qbit (ThermoFisher #Q10210) and a working stock of 5 ng/µL RNA was prepared for each sample.

15 µL of reverse transcription mix (5 µL 5x Maxima RT Buffer, 5 µL 20% (w/v) Ficoll PM-400 [GE Life Sciences #17030010], 2.5 µL 10 mM/each dNTP [New England Biolabs #N0447S], 0.5 µL Lucigen NxGen RNase Inhibitor [Lucigen #30281–1], 0.5 µL 50 µM Template Switch Oligo [IDT], 0.5 µL 50 µM Barcode/UMI/poly-dT Oligo [IDT], 0.5 µL Maxima H Minus Reverse Transcriptase [ThermoFisher #EP0752], 0.5 µL H₂O) was added to 50 ng (10 µL) of RNA. Each reaction contained a separate barcoded poly-dT oligo such that each of the six biological replicate samples contain a unique, identifiable barcode sequence. Reverse transcription was carried out at 53°C for 1 hr, followed by heat inactivation at 85°C for 5 min. 98 µL RLT Buffer [Qiagen] and 2 µL MyOne Silane beads [ThermoFisher #37002D] were added, mixed, and allowed to sit at RT for 10 min. cDNA was then isolated by magnetic separation of beads, followed by 2x washes with 200 µL 80% ethanol. Beads were pooled together and all cDNA was eluted into 40 µL of DNA elution buffer (10 mM TRIS pH8, 0.05% TWEEN-20, 1 mM DTT). 60 µL WTA master mix (50 µL 2x KAPA HiFi Hotstart Readymix, 1 µL 100 µM Forward Oligo, 1 µL 100 µM Reverse Oligo, 8 µL H₂O) was added and whole transcriptomes were amplified using 12 cycles of PCR (98°C for 3:00; 12 cycles of 98°C for 0:20, 55°C for 0:20, and 72°C for 1:15 min; 72°C for 3:00 min). The amplified pool was then purified with 0.6x volume of SPRIselect beads and eluted into 25 µL DNA elution buffer. Amplified DNA was quantified using a high sensitivity D5000 ScreenTape (Agilent #5067–5592).

Amplified whole-transcriptome DNA was tagmented with a nextera XT kit (Illumina #FC-131–1096) as follows. 3 ng of DNA was diluted to a total volume of 10 µL with DNA elution buffer. 20 µL TD buffer and 10 µL ATM was added and DNA was tagemented at 55C for 10 min. The reaction was halted with 10 µL NT buffer, and the fragment pool was indexed by adding 30 µL NPM buffer, 5 µL illumina index 2 (i7) adapter primer, 5 µL 5 µM DG1954 (no-index primer) and amplifying using 12 cycles of PCR (95°C for 0:30; 12 cycles of 95°C for 0:10, 55°C for 0:30, and 72°C for 0:30 min; 72°C for 5:00 min). Libraries were purified by double-sided SPRI selection. 55 µL SPRIselect beads (0.55x) were added to the nextera indexing reaction, and the unbound supernatant was transferred to a clean tube. 20 µL SPRIselect beads were added (0.75x total), and after binding and washing, DNA was eluted into 20 µL DNA elution buffer. Libraries were checked for size with a High Sensitivity D1000 Screentape, and quantified with the KAPA illumina library quantification system on a Roche lightcycler 480. Libraries were sequenced on an Illumina NextSeq 500 with the NextSeq 500/550 v2.5 High Output 150 Cycle kit, using the sequencing parameters recommended by 10x Genomics (Read 1: 26 bp, Read 2: 98 bp, Index 2: 8 bp) and standard illumina read and indexing primers.

Sequencing results were analyzed using the Cellranger pipeline (10x Genomics) v2.1.0 and custom python scripts written for this project, which are located in the fastqTomat0 GitHub repository (https://github.com/flatironinstitute/fastqToMat0). The reference genome was obtained from Ensembl (Version R64-1-1) as a FASTA file, and the reference annotations were obtained from Ensembl (Version R64-1-1.93) in GTF format. The reference transcript annotations were altered to incorporate 5’ and 3’ untranslated regions using data from generated using TIF-seq (Pelechano et al., 2013) and the gffAnnotate.py script from fastqTomat0. The antibiotic resistance marker cassettes was added to both the FASTA and GTF files using command line tools. A STAR reference genome was then created from the modified GTF and FASTA files using cellranger mkref.

Raw single-cell sequencing reads were converted into FASTQ files using cellranger mkfastq and a 10x Genomics Index CSV file. These FASTQ reads were then aligned to the reference genome and counted using cellranger count. The FASTQ files for indexes not corresponding to the 10x single-cell transcriptome library were processed with the fastqBCLinker.py script from fastqTomat0, which identifies the genotype for each single-cell read and creates a TSV file mapping cell barcodes to genotypes. The count data from cellranger count and the barcode data from fastqBCLinker.py was combined by the tenXtomatrix.py script from fastqTomat0. This processing step discards doublet single-cell reads, which are identified by removing ‘cells’ which map to more than one of the 72 genotype-specific barcodes. We expect that 1/72 of these doublets will have the same barcode, and so we expect that ~ 98.5% of doublets will be removed and ~1.5% will be retained. This script produces a dense TSV matrix of counts per gene per cell that can be imported with python’s pandas.read_table() or R’s read.table(). This matrix is provided as Source code 2. This final data matrix is assembled from 11 independent single-cell sequencing batches, each corresponding to a single shake flask with a different growth condition.

Raw bulk RNA sequencing reads were converted into FASTQ files using bcl2fastq. These FASTQ reads were then aligned to the reference genome and counted using cellranger count, after adding the appropriate custom chemistry configuration and barcode whitelist to cellranger. The count data from cellranger count was processed by the tenXtomatrix.py script from fastqTomat0 into a TSV matrix of counts per gene per sample, which is included in Source code 1.

Network inference with the Inferelator consists of three major steps; data preprocessing and filtering, estimation of transcription factor activities, and regularized regression. Cross-validation of network inference parameters was performed by randomly selecting half of the genes in the gold standard network and removing them. To prevent circularity, any genes that were used in the gold standard were removed from the prior data during cross-validation; for tests where the gold standard network was also used as a prior, this meant that half of the genes in the gold standard network were retained and defined as the gold standard, and half of the genes in the gold standard network were used as priors. A summary table of the cross-validation results is provided as Supplementary file 1-Supplemental Table 5.

The randomized negative control was performed by randomly reassigning gene names in the prior data. Transcription factor labels and expression values were otherwise unchanged. The simulated negative control was performed using simulated data by constructing a probability distribution for the yeast transcriptome from estimates of absolute mRNA abundances (Lahtvee et al., 2017) and randomly sampling this distribution using the synthesize_data.py script from the fastqToMat0 package. Metadata and total UMI count for each cell were retained in this negative control; only the individual gene counts were synthesized from the simulated control probability distribution.

See below for details on each step of the network inference procedure.

Single cell data was loaded as an integer UMI count matrix (Cells x Genes). Genes with a variance of 0 for all cells were removed. The count matrix was then transformed by log scaling using log₂(x+1). For data sets that had already undergone library normalization and transformation as a result of an imputation method, this transformation preprocessing step was skipped.

All imputation methods used the untransformed integer UMI count matrix (Cells x Genes) in which genes with a variance of 0 had been removed. For MAGIC, count data was library size normalized with the library.size.normalize() function from the Rmagic package, then transformed by square-root, and subjected to imputation with the magic() function from the Rmagic package. For VIPER, count data was subjected directly to the VIPER() function from the VIPER package, using the parameters recommended by the VIPER authors for 10x genomics UMI count data. For ScImpute, count data was normalized by the method included in the ScImpute package and then subjected to imputation with the imputation_wlabel_model8() function from the ScImpute package. The R script to perform these imputations is included with Source code 1.

Construction of the gold standard prior network has been previously described (Tchourine et al., 2018); this gold standard network consists of 1403 signed [−1, 0, 1] interactions, for which sign represents activation (+) or inhibition (-), in a 998 genes by 98 transcription factors regulatory matrix. YEASTRACT priors were retrieved from the YEASTRACT database (Teixeira et al., 2018) using the generate regulation matrix tool. Both activation and inhibition interactions were included, but only those that are supported by both DNA binding and expression evidence. The YEASTRACT prior network consists of 11486 unsigned [0, 1] interactions in a 3912 genes by 152 transcription factors regulatory matrix. Construction of the ATAC-motif priors has been previously described (Castro et al., 2019; Miraldi et al., 2019), and are built from chromatin accessibility data and known transcription factor binding motifs. The ATAC-motif prior network consists of 71,865 signed integer interactions with a range of [−11,. .., 26], for which sign represents activation (+) or inhibition (-) and absolute values represent the number of motif occurrences, in a 5551 genes by 138 transcription factors regulatory matrix. Bussemaker-priors were generated from modeling transcription factor affinities for regulatory DNA motifs (Ward and Bussemaker, 2008). The Bussemaker prior network consists of unsigned floating-point values [0, 20] that reflect estimated binding affinities in a dense 6516 genes by 123 transcription factors regulatory matrix.

Log-transformed single-cell data was transposed into matrix X, in which columns are individual cells and rows are genes. P is the connectivity matrix of known prior regulatory interactions between transcription factors (in columns) and genes (in rows). P_i,k is zero if there is no known regulatory interaction between transcription factor k and gene i. A is the activity matrix, where the columns are the individual cells as in X and rows are the transcription factors. We model the expression of gene i in individual cell j as a linear combination of the activities of the a priori known regulators of gene i in individual cell j (1). In practice, this means that we use the known targets of a transcription factor to derive its activity.(1)Xi,j=∑k∈TFsPi,kAk,j

In matrix form, Equation 1 can be written as X=PA. This is an overdetermined system, meaning that there are more equations than unknowns and therefore there is no solution if all equations are linearly independent. We approximate A by finding  that minimizes ‖PÂ-X‖22. If a transcription factor has no prior targets present in P, we use the expression of that transcription factor as a proxy for its activity.

We utilize a bayesian best-subset regression (BBSR) method, previously described (Greenfield et al., 2013), for single-task network inference. At steady state, we model the expression of a gene i in individual cell j as a linear combination of the activities of its regulators in individual cell j (2). For each gene i, we limit the number of potential regulators Ri to the ten with the highest context likelihood of relatedness, calculated from the mutual information between all regulators and the gene i (Madar et al., 2010), in addition to any a priori known regulator of gene i. Limiting the regulators is necessary before best subset regression, when we find the least squares solution to all possible combinations of predictors in set Ri. Because we expect a limited number of transcription factors to regulate a particular gene, our goal is to find a sparse solution for β, in which non-zero entries define both the strength and direction (activation or repression) of a regulatory relationship.(2)Xi,j=∑k∈Riβi,kAk,j

Prior knowledge can be incorporated using Zellner’s g-prior on the regression parameters β; in this work, we include prior interactions in the set of predictors to be modeled by best subset regression, but we do not further bias the predictors chosen with a g-prior on the regression parameters. We select the model with the lowest Bayesian Information Criterion, which adds a theoretically derived penalty term to the training error to account for model complexity and thereby reduce generalization error. After this step, the output is a matrix of inferred regression parameters β, where each entry corresponds to a regulatory relationship between transcription factor k and gene i.

The multitask approach used here entails a joint inference of regulatory networks across multiple expression datasets. In addition to the linear assumption, in which gene expression is a linear function of the activities of regulators, we also assume that much of the underlying regulatory network is shared among related datasets (conditions). Here, we extend a previous version of the Inferelator that implements Adaptive Multiple Sparse Regression (AMuSR), which is designed to leverage cross-dataset commonalities while preserving relevant differences (Castro et al., 2019).

There are multiple ways of dividing the existing yeast data into multiple network data subsets, which we refer to as tasks. Within our experimental design, cells are processed and sequenced as batches, which are taken from separate environmental growth conditions. Differences between these batches are a combination of technical and biological variation. The technical variation can come from batch effect due to stress and energy-source differences associated with differing growth conditions (for example via direct effects on cell wall and thus cell lysis/yield), as well as from differences in sample preparation and sequencing. Differences in growth condition also generate biologically significant variation in gene expression due to differences in regulatory program activation. Removing technical variation while retaining biological variation through batch normalization is not feasible, and therefore these individual sample batches from separate growth conditions are taken as individual tasks for the network inference. Thus, the index ‘d’, below, ranges from 1 to 11 and is an index over the separate datasets corresponding to growth conditions. This separation into tasks results in the joint learning of 11 networks (one for each growth condition), followed by combination into a single global network.

Briefly, the network model is represented as a matrix W for each target gene (where columns are individual single-cell batches d and rows are potential regulators k) with signed entries corresponding to strength and type of regulation. We then decompose the model coefficient matrix W into a dataset-specific component S and a conserved component B to enable us to penalize dataset-unique and conserved interactions separately for each target gene; this separation captures differences in regulatory networks across datasets. Specifically, we apply an l₁/l_∞ penalty to the B component to encourage similarity between network models, and an l₁/ l₁ penalty to the other to accommodate differences to S (Jalali et al., 2010). Regularization parameters ƛs and ƛb, representing the strength of each penalty, were chosen via Extended Bayesian Information Criterion (Chen and Chen, 2008). We set ƛb to cbd log pn, where d is the number of tasks, n is the mean number of samples per task, and p is the number of predictors. We then search for c_b in the log interval [0.1, 10.0] with 20 steps. We then set ƛs such that 1d<ƛsƛb<1, where d is the number of tasks and csƛs=ƛb. We search for c_s in the linear interval [1d+ 0.01, 0.99] with 10 steps.

We can incorporate prior knowledge by using adaptive weights (ɸƛs) when penalizing different coefficients in the l₁/ l₁ penalty (Zou, 2006). In this work, however, we chose not to bias predictors to the priors using adaptive weights, and set ɸ to 1. For each gene, we minimize the following function (Castro et al., 2019):(3)argminS, B=∑d|| Xi(d)−A^dT(S∗,d+B∗,d)||22+λs∑k,d|Φk,dSk,d|+λb||B||1,∞output: W=S + B

Interactions were ranked by both the overall performance of the model for each gene i and the proportion of variance explained by each β_i,k. The output of this procedure is a matrix S where S_i,k is the confidence score on the interaction between transcription factor k and gene i. In order to avoid overfitting and sampling biases, we repeat this procedure N times by resampling the input data matrix with replacement. Finally, we rank combine the confidence scores generated by running the above inference procedure on each of the N bootstrapped datasets and obtain a final matrix of combined confidence scores for the possible interactions between transcription factors (columns) and genes (rows).

Individual task networks were assembled into a global network by rank combining the confidence scores generated for each possible interaction between transcription factors and genes, obtaining a final matrix of combined confidence scores for the global network. Global interactions were ordered by combined confidence score, and the top interactions were kept to a threshold defined by precision = 0.5, as determined by recovery of the priors.

This normalized count matrix was reduced to 50 principal components by principal component analysis (PCA) with multiBatchPCA from the scater package in R. MultiBatchPCA is standard PCA with the modification that each environmental condition batch contributes equally to the covariance matrix, even when batches are imbalanced in cell count. These principal components were projected into two dimensional space by Uniform Manifold Approximation and Projection (UMAP) (McInnes et al., 2018) and plotted.

To analyze each growth condition separately, the cells corresponding to a growth condition were selected from the raw count matrix, library-size normalized and log₂(x+1) transformed, and reduced to 50 principal components with PCA. These principal components were projected into two dimensional space by UMAP for plotting, and also used to generate a shared nearest-neighbor (sNN) graph, which is used to cluster cells using the Louvain clustering method. Each growth condition was processed and plotted separately.

The raw, unmodified UMI counts of all cells from each biological replicate (with the same strain barcode) within a specific environmental growth condition were summed, resulting in 72 samples per condition (six biological replicates for each of the 12 transcription factor deletions). Summed pseudobulk expression data was then tested with DESeq2 (Love et al., 2014) for differential gene expression (testing against a null hypothesis of Fold Change < 1.5 and considering changes significant when p<0.05 at a false discovery rate of 0.1) with no additional processing or normalization.

Cell-cycle associated genes are categorized using the Spellman annotations (Spellman et al., 1998). Ribosomal genes, ribosomal biogenesis genes, and induced environmental stress response genes are categorized using the Gasch annotations (Gasch et al., 2017). Gene category annotations are included as Supplementary file 1-Supplemental Table 6.

The number of interactions was determined for each gene and each transcription factor. Interactions are considered Learned (new) if they are present in the learned network and not in the prior network; Learned (In Prior) if they are present in the learned network and not in the prior; and, Not Learned (In Prior) if they are present in the prior and not in the learned network. Each gene was mapped to Gene Ontology (GO) slim terms using the YeastGenome slim mapping (https://downloads.yeastgenome.org/curation/literature/go_slim_mapping.tab), which is a curated gene ontology mapping of high-level, broad GO terms. Interactions for all genes annotated with a GO term were summed. The generic terms ‘biological_process’, ‘not_yet_annotated’, and ‘other’ are removed from both target genes and regulatory transcription factors, and the common term ‘transcription from RNA polymerase II promoter’ was removed from regulatory transcription factors GO annotations. The 25 remaining terms with the highest number of learned (new) interactions were plotted separately for both the target genes and the regulatory transcription factors.

Gene expression data was derived experimentally in this work (FY4/FY5) or obtained from GEO. All samples are from early-log phase growth in YPD. Single-cell yeast data sets are from GSE122392 (BY4741) (Nadal-Ribelles et al., 2019) and GSE102475 (BY4741) (Gasch et al., 2017). A comparable bulk RNA control is from GSE135430 (BY4741) (Scholes and Lewis, 2019). Genes were ranked by expression in each cell or sample. All cells or samples from a specific experiment were rank-combined and ranks were pairwise plotted for each experiment with GGally in R.

Coefficient of variation (mean over standard deviation) is calculated for each gene in each growth condition. Pearson residuals (model residual over expected standard deviation) are calculated for each gene in each cell and then the mean of the pearson residuals is taken for each growth condition. This calculation is done with the vst function from the sctransform package in R (Hafemeister and Satija, 2019). In short, this builds for each gene a regularized negative binomial model, which is then used to calculate pearson residuals for each cell compared to the model. This is done separately for each growth condition.

Raw sequencing data, the output from the cellranger pipeline to count reads, and the output from the fastqToMat0 pipeline to extract and attach genotype metadata to the count matrix are available in NCBI GEO under the accession number GEO: GSE125162.

The cellranger pipeline is available from 10x Genomics under the MIT license (https://github.com/10XGenomics/cellranger). The fastqToMat0 pipeline is available from GitHub (https://github.com/flatironinstitute/fastqToMat0; Jackson, 2020; copy archived at https://github.com/elifesciences-publications/fastqToMat0) and is released under the MIT license. Genome sequence and annotations are included as Source code 4.

The Inferelator is implemented in Python, with dependencies on the widely-distributed scientific packages Numpy (van der Walt et al., 2011), Scipy (Virtanen et al., 2020), Pandas (McKinney, 2010), and Scikit-learn (Pedregosa et al., 2011). Scaling to a high-performance computing cluster is implemented with dask (Rocklin, 2015). All network inference in this work was performed with the inferelator v0.3.0, using Python v3.7.3, Numpy v1.16.2, Pandas v0.24.2, Scikit-learn v0.20.3, Scipy v1.2.1, and dask v1.1.4. The inferelator package is available under the Simplified BSD licence and can be installed from PyPI (https://pypi.org/project/inferelator/) or cloned from GitHub (https://github.com/flatironinstitute/inferelator; Jackson and Gibbs, 2020; copy archived at https://github.com/elifesciences-publications/inferelator).

Figure 1 and Figure 1—figure supplement 1 are constructed using Adobe Illustrator. Figures 2–7 and accompanying supplementary figures are constructed with R. The R (v3.5.1) (R Development Core Team, 2018) packages used are as follows: for plotting, ggplot2 (v3.1.0) (Wickham, 2016), cowplot (v0.9.4) (Wilke, 2019), ggridges (v0.5.1) (Wilke, 2018), ggrastr (v0.1.7) (Petukhov, 2019), GGally (v1.4.0) (Schloerke et al., 2018), viridis (v0.5.1) (Garnier, 2018), RColorBrewer (v1.1–2) (Neuwirth, 2014), and scales (v1.0.0) (Wickham, 2018a); for data manipulation, dplyr (v0.7.8) (Wickham et al., 2018), data.table (v1.12.0) (Dowle and Srinivasan, 2019), reshape2 (v1.4.3) (Wickham, 2007), and stringr (v1.3.1) (Wickham, 2018b); and for single-cell analysis, scater (v1.10.1) (McCarthy et al., 2017), scran (v1.10.2) (Lun et al., 2016), umap (R: v0.2.0.0, python: v0.3.6) (Konopka, 2018), igraph (v1.2.2) (Csardi and Nepusz, 2006), DESeq2 (1.22.2) (Love et al., 2014), corpcor (v1.6.9) (Schafer et al., 2017), and sctransform (v0.2.0) (Hafemeister and Satija, 2019). The R scripts to generate these figures and all required data are included with Source code 1. Network illustrations in Figures 6 and 7 were generated using Gephi 0.9.2 from the inferelator output network (gefx formatted); the layouts used are Force Atlas 2, Noverlap and Label Adjust. Figures were minimally modified from R outputs to enhance layout and aesthetics using Adobe Illustrator.

Interactive versions of several panels from Figures 1–4 are available as Shiny (Chang et al., 2018) apps online at http://shiny.bio.nyu.edu/YeastSingleCell2019/. Source code for the Shiny app is available upon request under the MIT license.