Determination of protein reduced electrostatic models from smoothed molecular electrostatic potentials

The design of protein coarse-grain (CG) models and their corresponding interaction potentials is an active field of research, especially for solving problems such as protein folding, docking, … Among the essential parameters involved in CG potentials, electrostatic interactions are of crucial importance since they govern local and global properties, e.g., their stability, their flexibility, … Following our development of an original approach to hierarchically decompose a protein structure into fragments from its electron density distribution1,2, the method is here applied to molecular electrostatic potentials (MEP), calculated from point charges as implemented in well-known force fields. To follow the pattern of local maxima and minima in a MEP, as a function of the degree of smoothing, we adopted the following strategy. First, each atom of a molecule is considered as a starting point. As the smoothing degree increases, each point moves along a path to reach a location where the MEP gradient value vanishes. Convergence of trajectories leads to a reduction of the number of points. Practically, to determine the protein backbone representations, we analyzed CG models obtained for a β-strand of 15 glycine residues. A fitting algorithm was used to assign charges to the obtained local maxima and minima vs. the unsmoothed MEP, as a function of t. The best fit obtained allowed to determine the degree of smoothing to be considered. Then, the influence of the different amino acid (AA) side chains was studied at the selected value of t for different rotamers by substituting the central glycine residue. The particular example of Asn is illustrated in Figure 1. Figure 1: CG point description of amino acid Asn obtained from the Amber MEP function3 smoothed at t = 1.35 bohr2. Charges were obtained using a fitting algorithm vs. the unsmoothed MEP function. One observes two opposite charges located on the backbone, -0.200 and +0.261 e-), and three additional charges on the side chain, close to the O and H atoms. Applications to the potassium ion channel KcsA (PDB access code 1BL8) are also presented. The protein CG description is generated through a superposition algorithm of the AA templates (as shown in Figure 1) onto the protein structure. It is observed that MEP-based descriptions lead to CG motifs that are different from those based on AA centers-of-mass, and better fit the original MEP functions. 1. L. Leherte, Acta Cryst. D 2004, 60, 1254 2. L. Leherte et al., in The Quantum Theory of Atoms in Molecules - From Solid State to DNA and Drug Design; Eds. Matta & Boyd, Wiley-VCH, 2007, 285 3. Y. Duan et al., Comput. Chem. 2003, 24, 1999