Residue–Residue Mutual Work Analysis of Retinal–Opsin Interaction in Rhodopsin: Implications for Protein–Ligand Binding

Abstract

crystal structure of Batho (chain A of PDB ID 2G87). 1 ASP83 and GLU122 were considered to be neutral 2 while all other charged amino acids were set to default protonation states. The spatial positions of Batho with respect to the lipid bilayer were taken from the Orientations of Proteins in Membranes (OPM) database. 3 All histidines were protonated either in the N position (HIS65, HIS152, HIS195, and HIS278) or in the N δ position (HIS100 and HIS211) 4 . The Schiff base linkage between the retinal and LYS296 was positively charged. The retinal and all crystallographic water molecules were preserved, other heteroatoms were removed.The CHARMM-GUI web-server 5 was used to embed the Batho system in an explicit membrane bilayer, and then immerse the resulted protein-lipid system in a box of explicit waters and ions at physiological concentration. Two palmitoyl chains bound to CYS322 and CYS323 were added to Batho before it was inserted in the membrane, which consisted of 128 palmitoyl-oleoyl-phosphatidyl choline (POPC) lipids. The final system was neutral and the size of the periodic box was approximately 71×71×92Å 3 with 8589 water molecules, 20 sodium ions, and 18 chloride ions (see Fig. S6).Simulation Details All simulations were performed with the software suite GROMACS-5.1.1. 6The c36 CHARMM force field 7 was used for protein and lipids. The force field parameters of retinal were adapted from recent literatures. 8,9 The TIP3P water model was used. The energy of the system was first minimized with very strong position restraints to heavy atoms of the protein (including retinal and two palmitoyl chains bound to rhodopsin). The position of the phosphorus atom and two dihedrals of lipids were also restrained strongly. Then, the system was under a series of equilibration with position and dihedral restraints were gradually released. The early stage of equilibration was performed in the NVE ensemble, then all the subsequent simulations were switched to the NPT ensemble. The system was coupled to a Berendsen thermostat with τ t =1.0 ps to keep the temperature constant at 303.15 K, and a semiisotropic Berendsen barostat with τ p =5.0 ps to keep the pressure constant at 1 bar. 10 An integration time step of 2 fs was used with constraints to bonds involving hydrogen atoms using the LINCS algorithm. 11 Lennard-Jones interactions were calculated using S2

Potential Energy Weighted Reactive Flux and Total Rate of Change of Potential Energy: Theory and Illustrative Applications

“…Usually, a proper subsystem is selected to reduce the dimension and the noisiness due to the large fluctuations in the environment or bath modes. For example, it is shown to be feasible and useful when only the residues close to the retinal were included in the analysis of residue–residue mutual works in rhodopsin . Let us define that the subsystem is described by y , and the rest of the system is described by y ′ (i.e., { y , y ′} is another complete and independent set of configurational coordinates).…”

Energy Decomposition along Reaction Coordinate and Energy Weighted Reactive Flux: 1. Theory

“…( 29), we thus seek for an energy function ȂU V (y) of y (thus a multidimensional free energy analogue in the subspace of CVs) such that J U V (y) = ȂU V (y)J U (y). One immediately finds that ȂU V (y) = J U V (y) • J U (y) J U (y) • J U (y) (34) and that in the one-dimensional case ȂU V (ξ ′ ) = V (x) F lux ξ(x)=ξ ′ ,U . In analogue to Eq.…”

“…For example, it is shown to be feasible and useful when only the residues close to the retinal were included in the analysis of residue-residue mutual works in rhodopsin. 34 Let us define that the subsystem is described by y, and the rest of the system is described by y ′ (i.e., {y, y ′ } is another complete and independent set of configurational coordinates). In terms of {y, y ′ }, the potential energy V (y, y ′ ) = V y (y)+V y ′ (y ′ )+V coupl (y, y ′ ).…”

“…Following this thinking path, the potential energy was then decomposed along the committor at the singlecoordinate level in the TPE. This so-called emergent potential energy approach was extended by Li into a residue-residue mutual work analysis approach, 34 in which the energy contribution is quantified by a so-called ensemble averaged work (EAW) and the EWA on a residue is simply the summation of the per-coordinate EAW over all the coordinates of the residue. Importantly, the EWA on a residue due to its interaction with another residue is provided by decomposing the atomic force on an atom into pairwise forces (the force on one atom from its interaction with another atom).…”

“…We would like to emphasize that the MM-GBSA method assumes the residue-residue mutual works from each other are the same and the interaction energy between two residues are evenly divided in the per-residue decomposition. In the residue-residue mutual work approach, 34 the energy contribution of a residue can be further decomposed into contributions due to translational, rotational, and internal motions of the residue.…”