The Energetics and Ion Coupling of Cholesterol Transport Through Patched1

Patched1 (PTCH1) is the principal tumour suppressor protein of the mammalian Hedgehog (HH) signalling pathway, implicated in embryogenesis and tissue homeostasis. PTCH1 inhibits the Class F G protein-coupled receptor Smoothened (SMO) via a debated mechanism involving modulating accessible cholesterol levels within ciliary membranes. Using extensive molecular dynamics (MD) simulations and free energy calculations to evaluate cholesterol transport through PTCH1, we find an energetic barrier of ~15–20 kJ mol−1 for cholesterol export. In simulations we identify cation binding sites within the PTCH1 transmembrane domain (TMD) which may provide the energetic impetus for cholesterol transport. In silico data are coupled to in vivo biochemical assays of PTCH1 mutants to probe coupling between transmembrane motions and PTCH1 activity. Using complementary simulations of Dispatched1 (DISP1) we find that transition between ‘inward-open’ and solvent ‘occluded’ states is accompanied by Na+ induced pinching of intracellular helical segments. Thus, our findings illuminate the energetics and ion-coupling stoichiometries of PTCH1 transport mechanisms, whereby 1–3 Na+ or 2–3 K+ couple to cholesterol export, and provide the first molecular description of transitions between distinct transport states.


PMF-1: between the SSD and SBD and PMF-2: between the SSD and bulk membrane
The SSD of PTCH1-molA and PTCH1-molB (PDB: 6RVD 7 ) were aligned to the x axis to assist generation of the reaction coordinate and the surrounding membrane and solvent expanded to a box size of 20 x 20 x 19 nm 3 using gmx genconf and VMD 8 . Two round of steepest decent energy minimisation were performed to relax the equilibrated bilayer around PTCH1. For PMF-1a the 'SHH-cholesterol' or 'free cholesterol' molecules were positioned in PTCH1-molA and PTCH1-molB ECDs respectively according to the cryo-EM densities 7 . PMF-1b was initiated with cholesterol bound at the base of the ECD, continuing from the final window in PMF-1a from PTCH1-molB. Since the 'free cholesterol' bound within PTCH1-molB was positioned with the ROH bead orientated towards the bilayer, a bash script was used to invert the cholesterol orientation in frames generated from the steered MD simulations to generate the PTCH1 'SHH-cholesterol' conformations. This was due to difficulties obtaining a reasonable steered MD simulation initiated from the final window of PMF-1a from PTCH1-molA and to standardise the reaction coordinate. For PMF-2 cholesterol was not present in the PTCH1 ECD. Instead, snapshots were selected with cholesterol bound to the SSD with either the ROH bead (equivalent to the β3-OH group) pointing towards the extracellular leaflet headgroups ('OH-up') or towards the bilayer midplane ('OH-down').

S2
A 10 x 10 x 18 nm 3 POPC:CHOL (3:1) bilayer patch without protein was built using insane.py 4,9 . The bilayer was solvated using MARTINI water 1 and 0.15 M NaCl before two round of steepest decent energy minimisation. A cholesterol molecule at the centre of the bilayer was selected for use in PMF calculations.

PMF-4: between the SBD and solvent
The ECD of PTCH1-molA and PTCH1-molB (residues A119-D436 and R772-G1023) from the PTCH1-SHH (2:1) structure (PDB: 6RVD 7 ) was extracted and coarsegrained 1 . The 'SHH-cholesterol' and 'free cholesterol' molecules were positioned in the SBD of PTCH1-molA and PTCH1-molB respectively accordioning to their positions in the cryo-EM density 7 (and identically to in PMF-1a). The PTCH1 ECDs were positioned at one end of a 9 x 9 x 18 nm 3 box with the SBD aligned to the z axis. The system was solvated with MARTINI water 1 and approximately 0.15 M NaCl followed by two rounds of steepest decent energy minimisation.
Execution and analysis of coarse-grained potential of mean force calculations Steered MD simulations were used to generate 1D reaction coordinates for each path of the PTCH1-molA and PTCH1-molB free energy cycles. The 1D reaction coordinate was generated by application of a distance dependant pulling force along specified axes between the COM of the cholesterol and the following selections: PMF-1a (I1092 BB bead), PMF-1b (F800 BB bead), PMF-2 (P504 BB bead), PMF-3 (COM bilayer) and PMF-4 (S331 BB bead). The umbrella pulling force was 1000 kJ mol -1 nm -2 and pulling rates of 0.1 nm ns -1 (PMF-1a, 2, 3, 4) or 10 nm ns -1 (PMF-1b) were used. Position restraints of 1000 kJ mol -1 nm -2 were applied to the following backbone beads to prevent protein rotation: PMF-1a/b, (A1088, A1157), PMF-2 (A1088, A1157) and PMF-4 (A182, A239). Frames were taken with spacing 0.05 nm along the reaction coordinate and subjected to 1-3 μs of simulation. For each window an umbrella pulling force of 1000 kJ mol -1 nm -2 was used to confine the cholesterol position along the reaction coordinate. Further details of the number of windows, simulations times and PMF convergence are given in Supplementary Table 1 and Supplementary Fig. 2. PMF profile analysis was assisted using the pmf.py tool 10 and the weighted-histogram analysis method 11 implemented in GROMACS (bootstrapped 2000 times).

Setup for atomistic simulations of PTCH1
A PTCH1 structure with ion-like density within the TMD (PDB: 6DMY) 12 was used in atomistic simulations. SHH, ligands and metal ions were removed. A short linker was modelled between TM6 and TM7 using Modeller 9.20 13 to give an overall sequence of (TM6)DRR-LDIFCC//TKWTLSSFAE-KHY(TM7), in accordance with the linker used in CG simulations of PTCH1 (PDB: 6RVD 7 ). A Na + ion was positioned according to the density in the centre of the TMD 12 . The H++ server and propKa 14,15 were used to predict the pKa of titratable groups (Supplementary Table 4), revealing at least two residues of the anionic triad to be protonated at pH 7 in the absence of bound Na + , decreasing to one protonated residue when Na + was present. The central residue, E1095, was therefore protonated using the CHARMM-GUI PDB generator which was also used to rename atoms to be compatible with the CHARMM-36 forcefield and model disulphide bonds between C203-C226, C234-C327, and C296-C304 16,17 . PTCH1 was embedded in a symmetric POPC:CHOL (3:1) membrane generated using S3 the CHARMM-GUI bilayer builder 18,19 and solvated using TIP4P water 20 and approximately 0.15 M NaCl. PTCH1 was subsequently energy minimised and equilibrated in 2 x 5 ns NVT and NPT steps with restraints applied to the PTCH1 backbone.

Application of a membrane potential
Atomistic simulations of the above setup were also run in the presence of a -100 mV or -200 mV membrane voltage (ΔV=E.Lz, E=-7.1429 or -14.286 mV, Lz=14 nm) for 3 x 100 ns each. Voltage is reported as inside relative to outside and was achieved using the constant electric field method 21 .
In silico mutation screen Modeller 9.20 was used to induce single amino acid substitutions at a specified location and induce disulphide bond formation in the cross-linked mutants 13 . The following mutations were performed: V510G, V510A, V510T, V510F, I1092A, L517C-P1125C, H1099C-S547C. Atomistic simulations of WT PTCH1 and each PTCH1 mutant were performed as described above with the exception that Na + was not initially bound in the TMD and each system was simulated for 3 x 50 ns.

Setup for atomistic simulations of DISP1
The DISP1 structure with three Na + ions bound was used in simulations (PDB: 7RPH, 'R conformation') 22 . Detergent ligands were removed, and the missing loop modelled using Modeller9.20 13 . CHARMM-GUI was used to generate DISP1 parameters (separated into two chains to account for the Furin cleavage site) and the anionic triad residue D1049 was protonated for consistency with the PTCH1 simulations 16,17 . DISP1 was simulated in the '3x Na + ' bound and apo states for 3 x 100 ns each. The '2x Na + ' state was generated from the end snapshots of the '3x Na + ' state by removing the ion missing in an alternative 'T conformation' of DISP1 (PDB: 7RPI) 22 bound to two Na + ions. The '1x Na + ' and '0x Na + ' states were generated by an identical process of sequential ion removal from the end snapshots of previous simulations. The ion retained in the '1x Na + ' state was chosen based on the apo state simulations whereby an ion spontaneously bound to D572 in all replicates. Each subsequent ion state was also simulated for 3 x 100 ns.

Protein-lipid interactions
The PyLipID analysis toolkit 23 was used to identify residues in the PTCH1 ECD which interacted with ECD bound cholesterol (https://github.com/wlsong/PyLipID). All windows in the PMF-1a profile or windows surrounding energetic bottlenecks in the PMF-1a profile were analysed collectively using PyLipID with a single 0.6 nm interaction cut-off. The top four residues with the highest occupancy i.e. those residues within 0.6 nm of cholesterol for the largest fraction of the window simulation times were reported for each bottleneck.

Water within PTCH1 and DISP1
S4 MDAnalysis 24 was used to analyse water within PTCH1 TMD. For each timepoint in the trajectory the O atom of water within a cylinder (radius 1.3 nm in xy) centred around the Cα atoms of residues V510 and I1092 was considered to localise within the TMD. For analysis of water z coordinates with time the length of the cylinder was 4 nm in z whereas for average water densities in the mutant screen a 3 nm cylinder was used to reduce contributions from bulk water molecules. Water within the extracellular and intracellular halves of the TMD was defined as having z coordinate of the O atom localised within the cylinder and either above or below the z coordinate of the midpoint between the Cα atoms V510 and I1092. Only the final 10 ns of each 50 ns simulation of PTCH1 were used in comparison of TMD water density to allow water to equilibrate in the TMD. PyMol and VMD were used to visualise trajectories 8 .
Analysis of water within the intracellular TMD half of DISP1 was performed identically to described above with the cylinder midpoint defined using the Cα atoms of I568 and L1046.

Supplementary Tables
Supplementary Table 1: Summary of the number of windows, simulations time per window and free energy value obtained from PTCH1 CG PMF calculations. The number of windows correspond to those included in the gmx wham step.     Free energy perturbation of A) Na + to K + or B) K + to Na + when bound to PTCH1 Site 1 or in solvent. The forward and reverse perturbations are in agreement. C-F) Convergence of FEP calculations as a fraction of λ window length for C) Na + to K + in solvent, D) Na + to K + at PTCH1 Site 1 E) K + to Na + in solvent and F) K + to Na + at PTCH1 Site 1. Error bars indicate the minimum/maximum values (A/B) or standard deviation between 5 FEP replicates (C-F). Na + to K + (solvent)

Supplementary
Integrator K + to Na + (Site 1)   Supplementary Figure 7: Energetic restrictions within PTCH1 sterol transport tunnels. A) Conserved energetic peaks within the ECD (numbered 1-3 in Fig. 2D) of PTCH1-molA (yellow) and PTCH1-molB (light blue). The four residues with highest cholesterol interaction occupancy at each peak were identified from umbrella sampling windows using PyLipID 70 and a 0.6 nm cut-off. Residues are shown as spheres coloured by localisation within the upper (red) or lower (blue) restrictions in the PTCH1 ECD, surrounding putative ECD sterol transport tunnels (grey mesh). Residues corresponding to a particular peak are opaque and labelled, overlaid with those residues which comprise the remaining two peaks (transparent). B) Cholesterol interaction occupancy of equivalent residues in PTCH1-molA and PTCH1-molB across PMF-1a windows, indicating the same high occupancy residues contribute to formation of the upper (red) and lower (blue) restrictions between PTCH1 conformations. Cholesterol contacts were defined using a 0.6 nm cut-off. A) The z coordinates of water oxygen atoms (light blue), Na + (blue), K + (yellow) and Cl -(salmon) ions localized within the PTCH1 TMD. A cylinder (length 4 nm, radius 1.3 nm) centred on the midpoint of V520 and I1092 Cα atoms was to identify water and ions within the PTCH1 TMD for WT and labelled PTCH1 mutants (V510G, V510A, V5105, V510F, I1092A, L517C/P1125C, S547C/H1099C). Simulations were initiated without Na + /K + bound within the TMD and simulated for 3 x 50 ns or 3 x 100ns replicates. B) Water and ions within the WT PTCH1 TMD (defined as in A) accounting in the presence of a -100 mV or -200 mV membrane potential (see methods). C) As in A-B for WT PTCH1 simulations initiated with 3 x Na + or 3 x K + ions bound at equivalent positions to three Na + ions observed within a structure of DISP1 (PDB: 7RPH). Figure 10: DISP1 extracellular TMD distances and PTCH1 TMD conformational changes. A) Minimum distances between the extracellular portions of transmembrane helices across 3 x 100 ns simulations of DISP1 in distinct ion coupled states. Distances were defined between the Cα atoms of A561-T1039 (TM4-TM10), V623-A985 (TM5-TM8) and Y542-V1022 (TM3-TM9). B) Time averaged water density (blue isosurface) across 100 ns simulations of PTCH1 (PDB: 6DMY) initiated with either 3 x Na + or 3 x K + ions bound within the TMD. Anionic triad residues are shown as spheres. C) Comparison of the intracellular PTCH1 TMD helices at the end of 100 ns atomistic simulations initiated in either an apo conformation or with 3x Na + ions bound within the TMD.