The energetics and ion coupling of cholesterol transport through Patched1

Patched1 (PTCH1) is a tumor suppressor protein of the mammalian Hedgehog (HH) signaling pathway, implicated in embryogenesis and tissue homeostasis. PTCH1 inhibits the G protein–coupled receptor Smoothened (SMO) via a debated mechanism involving modulating ciliary cholesterol accessibility. Using extensive molecular dynamics simulations and free energy calculations to evaluate cholesterol transport through PTCH1, we find an energetic barrier of ~15 to 20 kilojoule per mole for cholesterol export. In silico data are coupled to in vivo biochemical assays of PTCH1 mutants to probe coupling between cation binding sites, transmembrane motions, and PTCH1 activity. Using complementary simulations of Dispatched1, 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 one to three Na+ or two to three K+ couple to cholesterol export, and provide the first molecular description of transitions between distinct transport states.

builder 85,86 and solvated using TIP4P water 87 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/nm, 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 88 .
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 81 . 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') 46 . Detergent ligands were removed, and the missing loop modelled using Modeller9.20 81 . 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 70,84 . 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) 46 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 89 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
MDAnalysis 90 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 80 .
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.  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 89 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 100 ns 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 S7: Convergence of FEP calculations.
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).

A B C D E F
Na + to K + K + to Na + Convergence Na + to K + (solvent) Convergence Na + to K + (Site 1) Convergence K + to Na + (solvent)  Integrator Na + to K + (Site 1) Integrator Na + to K + (solvent) Integrator K + to Na + (Site 1) Integrator K + to Na + (solvent)