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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 Ž . Automatic Map Refinement Procedure AMRP and two-dimensional Weighted Ž . 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 C135C14 and C155N16 bonds in the retinal of bacteriorhodopsin is described. In dark-adapted Ž . bacteriorhodopsin bR , the retinal moiety exists in two conformers, all-trans and Correspondence to: S. Crouzy; e-mail: scrouzy@cea.fr * Present address: Beckman Institute, 405 N. Matthews, Urbana, Illinois 61801 ( ) Journal of Computational Chemistry, Vol. 20, No. 15, 1644]1658 1999 Q 1999 John Wiley & Sons, Inc. CCC 0192-8651 / 99 / 151644-15 CALCULATION OF 2D ADIABATIC AND FREE ENERGY MAPS ( ) 13,15 cis, with the latter making , 67% of the population. This experimental free energy difference is reproduced here to within k T. Q 1999 John Wiley & B Sons, Inc. J Comput Chem 20: 1644]1658, 1999

j. comput. chem.

Efficient calculation of two-dimensional adiabatic and free energy maps: Application to the isomerization of the C13C14 and C15N16 bonds in the retinal of bacteriorhodopsin