Efficient calculation of two-dimensional adiabatic and free energy maps: Application to the isomerization of the C13?C14 and C15?N16 bonds in the retinal of bacteriorhodopsin

Accurate calculation of potential energy and free-energy profiles along reaction coordinates of biological processes such as enzymatic reactions or conformational changes is fundamental to the obtention of theoretical insight into protein function. We describe here the practical implementation of the Automatic Map Refinement Procedure (AMRP) and two-dimensional Weighted Histogram Analysis Method (WHAM) for efficient computation of adiabatic potential energy and free-energy maps, respectively. Methods for efficiently sampling configuration space with high-energy barriers and for removing hysteresis in the case of periodic reaction coordinates are presented. The application of these techniques to the isomerization of the C13C14 and C15N16 bonds in the retinal of bacteriorhodopsin is described. In dark-adapted bacteriorhodopsin (bR), the retinal moiety exists in two conformers, all-trans and (13,15)cis, with the latter making ≃67% of the population. This experimental free energy difference is reproduced here to within kBT.