| Understanding protein flexibility is of key importance in order to understand protein function. Any computational modeling of protein flexibility requires an appropriate energy function, which can either rely on first principles (physics based) or on statistics of known protein structures (knowledge-based). The first group generally uses Classical Mechanics force fields with parameters derived from theoretical computations to optimally reproduce the physicochemical properties of small molecules. Despite of their high computational cost, they are yet not completely accurate. Knowledge-based potentials (KBP) are nevertheless, simpler, easier to computer, but still useful to describe protein folded states. There are two main ways of obtaining KBPs: 1) Optimizing the likelihood of the protein native structure vs. the artificially generated decoys [1]; 2) Deriving Boltzmann-like statistics as Potential of the Mean Force (PMF) [2]. The former strategy can be limited because of the high dimensionality of the parameter space and/or the coarse-grained energy model adopted to cope with this problem. In the case of the PMF, the observed atomic contact frequencies must be normalized versus a reference state, defined as the one with no interactions between any two atoms. But this state is never achieved in protein structures. Here we present the DICAM (Direct Interactions in Crowded Anisotropic Media) force field, a novel PMF that is totally independent of any reference state. Considering only directly interacting atom pairs (such as that there are no intermediate atom), it computes the interaction energy between atoms of type a and b, as the minus log of the probability density function to find a pair of atoms of type a, b in direct contact plus a normalization constant that is determined by equaling the average interaction energy to the propensity of atoms of type a, b to establish direct contacts. In order to obtain an analytical function, a least squares non-linear fit of the computed values is performed to a quadruple exponential function (Morse-like). Finally we will ensure that native protein structures are in the actual energy minimum of the DICAM force field by optimizing the parameters over a set of well determined protein structures, so that torsional fluctuations due to DICAM are minimized. 1. Bastolla, U., M. Vendruscolo, and E.W. Knapp, A statistical mechanical method to optimize energy functions for protein folding. Proc Natl Acad Sci U S A, 2000. 97(8): p. 3977-81. 2. Tanaka, S. and H.A. Scheraga, Medium- and long-range interaction parameters between amino acids for predicting three-dimensional structures of proteins. Macromolecules, 1976. 9(6): p. 945-50. 3. Mendez, R. and U. Bastolla, Torsional network model: normal modes in torsion angle space better correlate with conformation changes in proteins. Phys Rev Lett, 2010. 104(22): p. 228103. |
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