A Novel Method for Force-Field Calibration Based on Maximum-Likelihood Approach and Thermal Unfolding Data

Abstract

Calibration is the final and critical stage of the design of the force fields for proteins and other biological macromolecules. For proteins, the usual goal of this procedure is to optimize the force-field parameters to reproduce the native structures of selected training proteins. However, the resulting force fields are usually not sufficiently predictive, because only the structures of folded proteins are used. Thus, a force field is not sufficiently trained to distinguish folded structures from misfolded ones. In this work, we propose a novel approach, in which a force field is calibrated with the ensembles of structures determined by NMR at various temperatures that encompass the region of thermal unfolding. The method is based on applying the maximum-likelihood principle. Each conformation of the NMR-determined ensemble at a given temperature is an experimental point and the theoretical probability-density function is represented by a sum of Gaussians centred at the decoys from the corresponding ensembles generated by simulations; in this work the replica exchange molecular dynamics procedure was used. The maximum-likelihood function (-logL) is minimized using the current decoy set, then new decoys are generated with the optimized force-field parameters. The procedure is iterated until convergence. The method was applied to the physics-based coarse-grained UNRES force field developed in our laboratory. On the first attempt, NMR structures of a small alpha-helical protein, the tryptophan cage, were used. The resulting force field predicted correctly the structures of 13 out of 14 alpha-helical proteins with different helix-packing topology and size from 36 to 104 amino-acid residues. Results of the calibration of the UNRES force field with more proteins, including villin headpiece (alpha), the C-terminal fragment of the IGG protein (beta), and full-sequence design 1 (alpha+beta), will be presented.