Free energy profiles: Coarse-grained (CG) potential of mean force (PMF) free energy and histogram outputs, obtained via the gromacs weighted-histogram analysis method (WHAM). PMF profile numbers match those described in the accompanying manuscript for cholesterol movement between the: - PTCH1-molA ECD base and the sterol binding domain (SBD) (PMF_1a_PTCH1_molA-SHH_cholesterol) - PTCH1-molB ECD base and the SBD (PMF_1a_PTCH1_molB-free_cholesterol) - PTCH1-molA ECD base and the sterol sensing domain (SSD) (PMF_1b_PTCH1_molA-SHH_cholesterol) - PTCH1-molA SSD and the membrane (PMF_2_PTCH1_molA-SSD_cholesterol_OHup) - PTCH1-molB SSD and the membrane (PMF_2_PTCH1_molB-SSD_cholesterol_OHup) - PTCH1-molB SSD and the membrane in a flipped conformation (PMF_2_PTCH1_molB-SSD_cholesterol_OHdown) - Membrane and solvent (PMF_3_Membrane_cholesterol) - PTCH1-molA SBD and the solvent (PMF_4_PTCH1_molA-SSH_cholesterol) - PTCH1-molB SBD and the solvent (PMF_4_PTCH1_molB-free_cholesterol) 2000 rounds of Bayesian Bootstrapping were performed. File description for each system: - histo.xvg: umbrella window histograms - bsres.xvg: Average free energy profile and computed bootstrapping error. Atomistic simulations: Subset of atomistic molecular dynamics simulations of wild-type (WT) Patched1 (PTCH1) and Dispatched1 (DISP1) in distinct ion-bound states: - PTCH1 with Na+ bound at Site 1 initially (PTCH1_WT_Na_Site1) - PTCH1 apo in 0.15 M NaCl (PTCH1_WT_apo_inNaCl) - PTCH1 apo in 0.15 M KCl (PTCH1_WT_apo_inKCl) - PTCH1 with 3 x Na+ ions bound to anionic triad residues (PTCH1_WT_3xNa) - PTCH1 with 3 x K+ ions bound to anionic triad residues (PTCH1_WT_3xK) - DISP1 apo in 0.15 M NaCl (DISP1_WT_apo) - DISP1 with 3 x Na+ ions bound to anionic triad residues (DISP1_WT_3xNa) - DISP1 with 2 x Na+ ions bound, generated by sequential ion removal from the end of DISP1_WT_3xNa simulations (DISP1_WT_2xNa) - DISP1 with 1 x Na+ ion bound, generated by sequential ion removal from the end of DISP1_WT_2xNa simulations (DISP1_WT_1xNa) - DISP1 without Na+ bound, generated by sequential ion removal from the end of DISP1_WT_1xNa simulations (DISP1_WT_0xNa) All simulations were run for 3 x 100 ns except for PTCH1_WT_apo_inNaCl which was run for 3 x 50 ns. The PTCH1 and DISP1 conformations were obtained from the Protein Data Bank (PDB IDs: 6DMY, 7RPH). File description for each system: - md_fit_firstframe.pdb : Initial frame used for atomistic simulations (replicate 1, each replicate equilibrated independently). - md_fit_X.xtc : Gromacs trajectory file for each replicate (X=replicate number).