Design and applications of reduced point charge models of proteins

From the formalism given in references [1,2], the smoothed analytical charge density (CD) distribution function of an atom ρa,s(r) can be expressed as:

where s is the smoothing factor and qa is, e.g., the Amber99 [3] atomic charge.
A topological analysis procedure is applied to locate extrema in smoothed CD distribution functions. The approach is applied to the design of amino acid (AA) reduced point charge (RPC) templates (Figure 1).
Figure 1. RPC model of Tyrosin as obtained from a smoothed Amber99-based CD distribution function.
To generate charge values, various fitting conditions are selected, i.e., from either electrostatic Coulomb potential or forces, considering reference grid points located within various distances from the protein atoms, with or without separate treatment of main and side chain charges.
Full protein RPC descriptions are generated through a superposition algorithm of the AA templates onto the protein structure. The program GROMACS [4,5] is used to generate molecular dynamics (MD) trajectories of the solvated proteins modelled using the various RPC models. Point charges that are not located on atoms are considered as virtual sites with a null mass and radius.
Applications are carried out on Ubiquitin systems to assess the RPC models [6-8]. All models involve a partial loss in the protein secondary and lead to a less structured solute solvation shell. Various stable conformations of a protein can be generated more rapidly than with the all-atom point charge representation. The model built by fitting charges on Coulomb forces calculated at grid points ranging between 1.4 and 2.0 times the van der Waals radius of the atoms, with a separate treatment of main chain and side chain charges, appears to best approximate all-atom MD trajectories due to a better approximation of the Coulomb-14 interactions and short-range forces.

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