We first simulated the translocation mode in which cholesterol enters the TMD of SMO from the outer leaflet (Pathway 1). To model this process, cholesterol was placed outside of the TMD in the membrane outer leaflet, between the TM2-TM3 interface. The entry of cholesterol from the membrane into the protein was steered towards the TMD to sample the entry pathway. The frames generated were then used to seed unbiased simulations for adaptive sampling (see Methods section for details). This was done to estimate the energetic barriers involved in the cholesterol entry from the outer leaflet.

To enter the TMD from the membrane, cholesterol must overcome the entropic barrier of being restrained inside the protein. Additionally, cholesterol faces an enthalpic barrier caused by the change in environment which is mostly hydrophobic in the membrane and both hydrophobic and hydrophilic inside the protein. This can make the entry process energetically expensive. To identify the barrier associated with entry, we projected the entire dataset on different translocation related metrics and identifed the mechanism of cholesterol translocation. The z-coordinate of cholesterol’s center of mass (z-axis is perpendicular to the plane of the membrane) was used as a proxy for the progress of the overall translocation from the membrane to the CRD. The angle of cholesterol with the x-y plane (the plane of the membrane) was calculated to identify cholesterol pose. We observe that this angle (Fig. 2a and S2) shows multiple minima (α/β along the Pathway 1). This provides evidence for multiple stable poses along the pathway as observed in the multiple stable poses of cholesterol in Cryo-EM structures of SMO bound to sterols.^44–46 Overall, the highest barrier along Pathway 1 is ∼ 5.8 ± 0.7 kcal/mol and it is associated with the entry of cholesterol into the TMD (Fig S15). Several factors contribute to this high barrier; first, cholesterol needs to be at the correct position just outside the protein. In addition, cholesterol needs to be in the correct orientation-angled, with the isooctyl tail pointing towards the protein core. Additionally, the steric hinderances from the hydrophobic residues at the interface provide further obstacles for entry. Therefore, the TM2/3 residues at the entry point need to undergo conformational change to facilitate cholesterol entry – making it a rare event.

In the first stage of translocation, cholesterol is in the membrane (α, Fig. 2), just outside the TM2/3 helices of SMO as identified in literature.⁵¹ At this cholesterol recognition site, SMO primarily contains hydrophobic residues (Fig. 2 c-f), which preferentially interact with the hydrophobic isooctyl tail of cholesterol. Therefore, the cholesterol entry involves the insertion of the tail into the TMD first, which is then followed by the hydrophilic androsterolic moiety. For the sake of clarity, we divide this entry pocket at the TM2-TM3-membrane interface into two parts – ‘lower’ and ‘upper’ pocket. The ‘upper’ pocket corresponds to the residues that coordinate with the androsterolic moiety of cholesterol (Fig. 2c, d), and the ‘lower’ pocket corresponds to residues that lie closer to the isooctyl tail of cholesterol (Fig. 2e, f). The upper (M286^ECL1, A289^ECL1 and I^ECL2A^ECL2) and the lower (W281^2.58f, F391^ECL2 and M525^7.45f) pocket residues undergo conformational changes to open the space for the entry of cholesterol (Fig. 2c-f). Here, the superscript refers to the Wang numbering scheme.² This flexible motion is facilitated by G280^2.57f in the lower pocket and G288^ECL1 in the upper pocket. Upon the entry of the cholesterol tail, an intermediate state, β (Fig. 2d, f) is observed where cholesterol lies flat with respect to the membrane plane and forms extensive hydrophobic contacts with A283^2.60f, I317^3.28f, F318^3.29f and the disulfide bridge forming residues C314^3.25f – C390^ECL2.

To reach the TMD binding site, cholesterol must first “rock”back to its upright pose (α^∗) from its flat conformation in the state β. This rocking motion is facilitated by the polar interactions between S313^3.24f, Q284^2.63f and the alcoholic oxygen in cholesterol. The entry of cholesterol is thus captured by a α → β → α^∗ transition. To further elucidate the position of cholesterol as it enters the protein, we projected the x and y coordinates of cholesterol on a free energy landscape (Fig. 2b, Fig. 4b and Fig. S2b, d). In this figure, the state β clearly marks the transition state between cholesterol outside and inside the TMD. Overall, the angle between cholesterol and the x-y plane transitions from 90^◦ → 0^◦ → 90^◦ in order for cholesterol to enter the protein.

To further dive into the details of cholesterol translocation, we designed mutations along Pathway 1, and measured the change in activity with respect to Wild-Type (WT) mouse Smoothened mSMO. mSMO was chosen since there are no human SHH responsive cell lines that can be passaged, edited, or transduced with genes. In addition, mSMO shows 92.8% sequence identity and 94.6% sequence similarity with hSMO for full length sequences. Previous studies that have resolved hSMO structures have used mSMO for their structure guided mutagenesis studies to comment on SMO activity.¹⁸ Activity was measured using Gli1 mRNA fold change in the presence of SHH (Fig. 3a). To further validate the mutations, simulations were performed on hSMO to compute the Potential of Mean Force (PMF) of cholesterol entry^53,54 (additional details presented in Methods). Here, the PMF is able to characterize the barriers associated with the translocation of cholesterol, and a difference in the peak value of PMF is presented for each mutant (Fig. 3b). We mutated G280^2.57f to valine-G^2.57f V to test whether reducing the flexibility of TM2 prevents cholesterol entry into the TMD. Consequently, the activity of mSMO showed a decrease. We designed I^ECL2AA to check the importance of hydrophobic contacts during translocation along Pathway 1. However this mutant did not affect the activity nor the barrier for translocation significantly (Fig. 3b, S4). Finally, we mutated A283^2.60f to methionine – A^2.60f M to test whether the presence of a bulkier residue would block translocation. Surprisingly, the effect on activity was not significant. When we calculated the PMF for cholesterol entry, A^2.60f M mutant showed restricted tunnel but it did not fully block the tunnel. Therefore, the change in the PMF and experimentally measured activity were not significant (Fig. 3b, c, S4).

To quantitatively assess the validity of cholesterol translocation from the second mode, that is, starting from the inner leaflet, we performed adaptive sampling simulations to obtain the associated free energy barriers. For Pathway 2, cholesterol first binds at the interface between TM5 and TM6 in the inner leaflet.^45,50 However, cholesterol in the inner leaflet has a downward orientation, with the polar hydroxyl group pointing intracellularly (η, Fig. 4). Thus, if cholesterol has to translocate from the inner leaflet, it has to undergo “flipping”motion, as the resolved structure with the lowermost position of a sterol inside the tunnel⁴⁴ shows the alcoholic moiety pointing towards the CRD⁴⁵ (Fig. 1a). The energetic barrier associated with flipping the motion of cholesterol can be observed by estimating the angle cholesterol makes with the x-y plane and the barrier associated with translocation towards the TMD binding site can be estimated by projecting the data on the z-coordinate of cholesterol.

In Fig. 4a, multiple free energy minima are observed. The state η corresponds to cholesterol outside of the TMD and pointing downwards, forming a –90^◦ angle with the x-y plane. The state E corresponds to cholesterol at the membrane-TMD interface and forming a 45^◦ angle with the x-y plane. Finally, the state α^∗ corresponds to cholesterol inside the TMD and forming a +90^◦ angle with the x-y plane. The state α^∗ which represents the TMD binding site is the most stable pose of cholesterol inside SMO. According to the free-energy landscapes (Fig. 2a, Fig. 4a and 2c,d and Fig. 4c,d), the entry of cholesterol from the inner leaflet is associated with the highest barrier for the entire translocation process, ∼6.5 ± 0.8 kcal/mol and it corresponds to the transition between the states η and θ. These values are comparable to ATP-Binding Cassette (ABC) transporters of membrane lipids which use ATP hydrolysis (−7.54 ± 0.3 kcal/mol)⁵⁵ to drive lipid transport from the membrane to an extracellular acceptor. Some of these transporters share the same mechanism as SMO where the lipid from the inner leaflet is flipped and transported to the extracellular acceptor protein.⁵⁶

The computed values of free energy barriers are dependent on the projections of the data. Upon projecting the data using the z-coordinate of cholesterol versus the angle between the cholesterol and the x-y plane (Fig. 4a) and the y-coordinate of cholesterol versus the xcoordinate (Fig. 4b), the barrier between η and θ is different. A reliable estimate of the barriers in such a case comes from using the time-lagged Independent Components (tICs), which project the entire dataset along the slowest kinetic degrees of freedom. On plotting the first two components of tICs, (Fig. S15,c), we observe that energetic barrier between η and θ is ∼6.5 ± 0.8 kcal/mol. We further validate that the slowest degrees of freedom in the model correspond to the entry of cholesterol from the inner leaflet of the membrane into SMO TMD (Fig. S15,d).

Contrary to Pathway 1, the entry of cholesterol into the TMD happens via the alcoholic moiety first, which forms a hydrogen bond with the backbone oxygen of R421^5.64f (Fig. 4e). Furthermore, the TM5 loses some of its helicity, between residues R421^5.64f –M424^5.67f due to the flexibility provided by G422^5.65f, which is a part of the conserved WGM motif implicated in SMO activation.⁵² Here, we also designate the “upper”and “lower”pocket, which coordinate with the isooctyl and androsterolic moieties of cholesterol, respectively (Fig. 4c-f). In the upper pocket, the isooctyl tail entry is blocked by the strong hydrophobic patch formed by Y417^5.60f, L419^5.62f, I420^5.63f, F457^6.38f and F460^6.41f (Fig. 4c,e). Flexible residues such as glycine are also not present that would allow for the fluctuations leading to opening of the hydrophobic patch and enable entry of the cholesterol tail. Therefore, the androsterolic moiety of cholesterol enters first followed by the isooctyl tail of cholesterol to reach the state E. To stabilize and facilitate the androsterolic moiety’s entry, F460^6.41f and F455^6.36f form π − π contacts, and L419^5.62f, L452^6.33f form hydrophobic contacts (Fig. 4d,f) in state θ.

Once cholesterol has flipped in θ, it allows for further translocation towards the TMD binding site (α^∗) and finally arrival at the CRD site (ζ) with the hydroxyl group pointing extracellularly. The translocation of cholesterol from membrane to the CRD binding site via Pathway 2 is captured by a η → θ → α^∗ → ζ transition. Overall, the angle between cholesterol and the x-y plane involves an entire cycle of –90^◦→ 0^◦→ 90^◦ and cholesterol must flip, in order for cholesterol to enter the protein.

Interestingly, mutants along Pathway 2 showed a significant decrease in activity compared to Pathway 1 (Fig. 3a, 3d, S5), along with an increased thermodynamic barrier for translocation (Fig. 3d, S6). Mutating R421^5.64f to alanine or glutamine did not decrease SMO activity significantly (Fig. 3d), because the interaction with cholesterol is mediated by the protein backbone, and not the side-chain (Fig. 4e). However, mutations like F^6.36f I and L^5.62f A reduce SMO activity. Their expression levels of these mutants are comparable to the wild-type mSMO (Fig. S5). The mutants compared to WT SMO showed a significant increase in PMF, due to the lack of the hydrophobic π-stacking provided by F455^6.36f and hydrophobic contacts provided by L419^5.62f during cholesterol translocation. Overall, we report that the mutants for Pathway 2 show a decrease in the activity of SMO and show a strong correlation between the reduction in activity and the barrier for cholesterol translocation (Fig. 3b,d). These results validate the role of critical residues involved in cholesterol translocation from the inner leaflet as observed in the simulations.

On the basis of our experimental and computational data, we conclude that cholesterol translocation can happen via either pathway. This is supported on the basis of the following observations: mutations along pathway 2 affect SMO activity more significantly, and the presence of a direct conduit that connects the inner leaflet to the TMD binding site. However, we also observe that pathway 1 shows a lower thermodynamic barrier. Additionally, PTCH1 controls cholesterol accessibility in the outer leaflet,²⁵ and there is no experimental structure with cholesterol in the inner leaflet region of SMO TMD. This shows that there is a possibility for transport from both leaflets.

Once cholesterol has reached the TMD binding site (α^∗), it must translocate along the TMD-CRD interface to reach the orthosteric binding site in the CRD. This common pathway is shared by cholesterol molecules translocating from the inner and outer leaflets. The translocation of cholesterol from the TMD to the CRD binding site involves a linear movement of the androsterolic moeity through the extracellular end of the TMD, where cholesterol maintains a primarily upright position, with the polar androsterolic moeity pointing towards the CRD site. The energetic barrier associated with the transition (α^∗(TMD site) → ζ(CRD site)) can be visualized by plotting the z-coordinate of cholesterol versus the angle it forms with the x-y plane (Fig. 2a, 4a). We observe that the highest barrier along the common pathway is ∼4.1 ± 0.3 kcal/mol, which is lower than the highest energetic barrier for cholesterol entry from the inner and outer leaflet. Another interesting observation is that the stability of the cholesterol in the TMD binding site (α^∗) is higher than the CRD binding site (ζ). This is counter-intuitive, as the CRD binding site is considered the orthosteric binding site of SMO.³⁵ This observation can be explained on the basis of the thermodynamic driving forces in the two pockets. The TMD binding site is composed mainly of hydrophobic residues, which forms strong interactions with cholesterol (Fig. S7) in contrast to the CRD binding site, where the cholesterol is exposed to the solvent. The CRD binding site being exposed to the solvent increases the conformational entropy associated with the cholesterol compared to the restrained TMD binding site. In addition, the CRD binding site is more flexible than the TMD binding site in the absence of cholesterol as reported previously.³⁵ This increased flexibility of the CRD binding site further leads to formation of multiple conformational states between the CRD and cholesterol.

Once cholesterol reaches the TMD-CRD interface, it can adopt multiple poses before reaching the CRD binding site (Fig. 2a, 4a). Cholesterol at this position can be upright (δ, Fig. 2a, 4a), where it interacts with F484^6.65f, W480^6.61f, V488^6.69f and L221^LD, forming hydrophobic contacts (Fig. 5a). However, there exists a thermodynamic barrier to take a completely upright path to the CRD binding site (angle ∼+90^◦). This is due to the presence of the long beta sheet of the linker domain (residues L197^LD-I215^LD) of SMO at the TMD-CRD interface, blocking the direct upright translocation of cholesterol (Fig. S8). Hence, the major conformation of cholesterol at this position is slightly tilted, away from the plane of the membrane (γ, Fig. 2a, 4a). Additionally, in γ, Y207^LD creates a hydrophobic interaction with cholesterol, stabilizing the bent pose (Fig. 5b). γ has been identified as the binding site of the synthetic agonist SAG in SMO.⁴⁴ This provides further validation for γ being the major intermediate state in the common pathway.

Since the degrees of freedom accessible to cholesterol at this point in the pathway are higher than at the TMD, cholesterol can can undergo “overtilting” as it approaches the CRD (E, Fig. 5c). This state (E) attributes to an off-pathway intermediate state in the cholesterol translocation process, raising the timescales required for cholesterol to translocate to the CRD binding site. This overtilted pose is stabilized by hydrophobic interactions between the sterol and Y487^6.78f, L221^LD and I509^ECL3, and a hydrogen bond between the sidechain of N511^ECL3 and the alcoholic oxygen (Fig. 5c). Once the cholesterol has crossed the TMD-CRD interface, it can reach the orthosteric binding site (ζ, Fig. 5d) in the CRD. In summary, we identify numerous conformational states of cholesterol bound SMO which are distinct from the available structures of sterol bound SMO.

We performed experimental mutagenesis to validate the critical residues along this pathway, from the TMD to the CRD binding site. These mutants – Y^LDA, F^6.65f A and I^ECL3A, all showed a significant decrease in activity compared to WT SMO (Fig. 6a,b, S9). When compared to the difference in PMFs induced by the mutants, we observe that the mutants consistently show a higher peak PMF, suggesting that the force required to translocate cholesterol is higher than the wild-type residue in this position (Fig. 6b, S10). This further implies that the mutants reduce the activity of SMO by increasing the energetic barriers for cholesterol translocation. In particular, the effect is pronounced for Y^LDA, which forms hydrophobic contacts along the pathway (Fig. 6c). F^6.65f A showed a significant decrease in SMO activity, which can be attributed to reduction in hydrophobic stabilizing contacts that enable cholesterol’s entry to the CRD (Fig. 6d).

Overall, the entire cholesterol translocation process can be divided into two parts-entry from the membrane to the TMD binding site via Pathway 1 or 2, and translocation from the SMO TMD to CRD binding site via common pathway. The entire process is mapped out in Fig. S11 The experimental and computational analysis shows that both Pathway 1 and Pathway 2 are thermodynamically feasible pathways and exhibit similar energetic barriers for cholesterol to take from the membrane to the CRD binding site.

To further elucidate the structural changes that happen in SMO during cholesterol translocation, we sought to characterize the conformation of the hydrophobic tunnel inside SMO. We calculated the tunnel diameter along the channel as cholesterol traverses through the protein (Fig. 7 and Fig. S12). The tunnel calculations were done with cholesterol at different points along the pathway as indicated by the metastable states in the Markov state models-with cholesterol in the TMD binding site, cholesterol at the CRD-TMD interface, and cholesterol present at the binding site in the CRD. When we plot cholesterol’s position at different points along its transit through the TMD, we observed that the tunnel diameter varies along the z-coordinate as cholesterol moves through the channel. This corroborates that the tunnel radius is a function of the position of cholesterol in SMO. Furthermore, we observe that the tunnel radius shows a peak at z ∼ –7 when cholesterol is present in the core of the TMD (Fig. 7 a,b). In the rest of the tunnel, the average radius remains relatively small (Fig. S13). This peak in diameter is seen to move along with the cholesterol position (Fig. 7 c,d). This provides evidence that SMO uses a squeezing mechanism to translocate cholesterol. The term ‘squeezing’ here implies that the tunnel remains open only around cholesterol and it closes as cholesterol moves away from its current position in the tunnel. Once cholesterol has reached the binding site in the CRD, the tunnel in the TMD region is closed (Fig. 7 e,f, Fig. S13).

The cholesterol translocation mechanism of SMO shows similarities to the alternating access model proposed for substrate transport in membrane transporter proteins-where the transport tunnel closes behind the substrate to facilitate substrate transport across membrane. Membrane transporters including lipid transporters use either an ion-based gradient or ATP hydrolysis to facilitate the substrate transport. An ion binding site for SMO is currently unknown in contrast to Class A receptors, which have a sodium binding site.^57–59 There is no experimental evidence of ion-coupling with the cholesterol export via SMO. Therefore, we posit that cholesterol translocation through SMO involves passive or concentration-dependent diffusion driven by a shift in the pool of accessible cholesterol, which rises once PTCH1 is inhibited. Thus, we provide a mechanistic overview of the dynamics of the cavity during cholesterol translocation in SMO.

To give a perspective on the overall translocation process from a kinetic standpoint, we sought to calculate the timescales associated with the translocation of cholesterol from the membrane to the binding site in the CRD. Using a combination of Transition Path Theory and Markov state models, the reactive fluxes associated with each stage of the translocation cycle can be calculated. This enables us to calculate the mean first passage time (MFPT), which gives us an estimate of the timescales associated with the process (Fig. 8). The Pathway 1 was divided into two stages-the first being the translocation of cholesterol from the outer leaflet (Fig. 8d) to the TMD-yielding a mean first passage time of 700 ± 122 µs. Here, the cholesterol tail has entered in the TMD (Fig. 8a). This was followed by cholesterol reaching the TMD binding site, with a timescale of 205 ± 41 µs (Fig. 8b). For Pathway 2, cholesterol starts in the inner leaflet (Fig. 8f). In the first stage, cholesterol undergoes flipping which leads to a higher timescale than stage 1 of Pathway 1 – 823 ± 132 µs. This is followed by 122 ± 22 µs for cholesterol to reach the TMD binding site (Fig. 8b).

Once cholesterol has reached the TMD binding site, it is followed by translocation of cholesterol from the TMD to the CRD binding site with a timescale of 255 ± 36 µs. Over-all, the calculated timescales for cholesterol to reach the CRD site from the inner/outer leaflet of the membrane are 1023 ± 223 µs (Pathway 1) and 1134 ± 188 µs (Pathway 2).

These timescales are comparable to the substrate transport timescales of Major Facilitator Superfamily (MFS) transporters.⁶⁰ Interestingly, the timescales for the reverse process of translocating cholesterol from the CRD binding site to the membrane are higher for each step (Fig. 8) indicating that the reverse process has higher energetic barrier associated with it. This provides kinetic evidence for the overall translocation process from membrane to the CRD binding site is thermodynamically favorable. Thus, it can be concluded that SMO facilitates the translocation of cholesterol.

The cholesterol translocation process in SMO was simulated in a stage-wise process-with the four starting points having cholesterol present at different points along the translocation pathway (Fig. 1). To accelerate the sampling of the entire translocation process, simulations were performed using an approach that parallelizes the exploration of conformational space. Adaptive sampling^85–87 was utilized to achieve this acceleration-which uses an iterative sampling approach involving picking the next round of simulation starting points based on the current data. Several different types of machine learning and heuristic based adaptive sampling approaches have been proposed in the literature.^87–93 However, least count based sampling where the least visited states are chosen as the starting points for the next set of simulations has been shown to be among the best sampling strategies for exploration of the conformational free energy landscapes.^93,94 The following approach was used to collect the data:

Initially, sampling was started from the 4 starting points with cholesterol at different points along the tunnel (Fig. 1). Each starting point was simulated as a separate system.

The entire process of cholesterol translocation-from cholesterol present in the membrane to cholesterol bound to orthosteric binding site in the extracellular domain-was simulated. Total 2 milliseconds of unbiased simulation data was collected using this approach.

Dimensionality reduction was performed on the high-dimensional data set using Time-Lagged Independent Component Analysis (tICA).⁹⁶ tICA uses a linear transformation to project the input data into a lower-dimensional basis set, the components of which approximate the slowest processes observed in the simulations. In our case, the slowest process simulated was identified by tICA as the translocation of cholesterol (Fig. S15). The dataset was divided into 2 different groups-separately for Pathways 1 and 2. To further gain insights from the simulations, we constructed a Markov state model from the tICA-projected simulation data.

Markov State Model (MSM) is a kinetic modeling technique that uses short trajectory data that sample local transitions to provide a global estimate of the thermodynamics and kinetics of the physical process.^97–102 A MSM discretizes the dataset into kinetically distinct microstates, and calculates the rates of transitions among such microstates. This methodology has been used extensively to investigate the conformational dynamics of membrane proteins including G-protein coupled receptors.^{52,59–61,103–106} To construct the Markov state model, the data collected from simulations was first featurized (Table S4). Pathways 1 and 2 were treated independently of each other. Time-lagged independent component analysis (tICA) was performed on the data to reduce the dimensionality of the input data and identify the slowest processes observed in the simulations. A Markov state model was then constructed on the 42 and 28 components from the tIC space for Pathways 1 and 2 respectively. To construct the models for both the pathways, the following approach was used:

The data was clustered into different number of clusters, ranging from 100-1000 and the implied timescales were calculated as a function of the MSM lag time. The lag time after which the implied timescales converged (30ns) in both cases, was chosen as the MSM lag time (Fig. S16a, S17a).

This information can be used to calculate the probability of each state, which can be used to recover the thermodynamic and kinetic properties of the entire ensemble. One of the use cases of the probabilities is that they can be used to reweigh the projected free energy of each datapoint along a said reaction co-ordinate, which has been used in Fig. 2, 4, 5 and The errors in free energies were computed using the errors in the projected probabilities from the bootstrapped MSMs (Fig. S2nd S12.

Trajectories were stripped of waters and imaged before analysis to allow faster computation. cpptraj¹⁰⁸ was used for this purpose. For constructing the figures, VMD^83,84 and open-source PyMOL¹⁰⁹ (rendering) MDTraj¹¹⁰ (computing observables from trajectories), matplotlib¹¹¹ and seaborn¹¹² (Plot rendering), Numpy¹¹³ (numerical computations), HOLE¹¹⁴ (tunnel diameter calculations) were used.

Mouse embryonic fibroblasts (MEFs) lacking Smoothened (Smo^−/−) were tested to ensure lack of endogenous SMO protein using immunoblotting, as described previously.⁹ These Smo^−/− MEF cells were used to generate stable cell lines expressing SMO mutants, which were then authenticated by immunoblotting to ensure stable expression of the transgene.⁴⁰ Cell lines were confirmed to be negative for mycoplasma infection.

MEF cells were grown in high-glucose DMEM (Thermo Fisher Scientific, catalog no. SH30081FS) containing 10% FBS (Sigma-Aldrich, catalog no. S11150) and the following supplements: 1 mM sodium pyruvate (Gibco, catalog no. 11-360-070), 2 mM L-glutamine (GeminiBio, catalog no. 400106), 1× minimum essential medium NEAA solution (Gibco, catalog no. 11140076), penicillin (40 U/ml), and streptomycin (40 µg/ml) (GeminiBio, catalog no. 400109). This media, hereafter referred to as supplemented DMEM, was sterilized through a 0.2-µm filter and stored at 4^◦C.

To measure Hedgehog responsiveness by quantitative polymerase chain reaction (PCR) or Western blotting, cells were seeded in 10% FBS-supplemented DMEM and grown to confluence. To induce ciliation, a requirement for Hedgehog signaling, cells were serum-starved in 0.5% FBS supplemented DMEM and simultaneously treated with Sonic Hedgehog (SHH) for 24 hours before analysis.

Western blotting was carried out to assess SMO protein expression for all mutants. Briefly, whole-cell extracts were prepared in lysis buffer containing 150 mM NaCl, 50 mM Tris-HCl (pH 8), 1% NP-40, 1× protease inhibitor (SigmaFast Protease inhibitor cocktail, EDTA-free; Sigma-Aldrich, catalog no. S8830), 1 mM MgCl₂, and 10% glycerol. After lysate clarification by centrifugation at 20,000g, samples were resuspended in 50 mM tris(2-carboxyethyl) phosphine and 1× Laemmli buffer for 30 min at 37^◦C. Samples were then subjected to SDS-polyacrylamide gel electrophoresis, followed by immunoblotting with antibodies against GLI1 [anti-GLI1 mouse monoclonal (clone L42B10); Cell Signaling Technology, catalog no. 2643, RRID: AB 2294746], SMO (rabbit polyclonal),⁹ or GAPDH [anti-GAPDH mouse monoclonal (clone 1E6D9); Protein tech, catalog no. 60004-1-Ig, RRID: AB 2107436].

Gli1 mRNA transcript levels were measured using the Power SYBR Green Cells-to-CT kit (Thermo Fisher Scientific). Gli1 levels relative to Gapdh were calculated using the Delta-Ct method (CT(Gli1) – CT(Gapdh)). The RT-PCR was carried out using custom primers for Gli1 (forward primer: 5¹-ccaagccaactttatgtcaggg-3¹ and reverse primer: 5¹-agcccgcttctttgttaatttga-3¹), and Gapdh (forward primer: 5¹-agtggcaaagtggagatt-3¹ and re-verse primer: 5¹-gtggagtcatactggaaca-3¹).