Design of reduced point charge models for proteins

Reduced point charge (RPC) descriptions of proteins are designed from local extrema in charge density (CD) distributions ρs obtained from the Poisson equation applied to smoothed molecular electrostatic potentials. From the formalism given in references [1,2], the smoothed analytical 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.
To follow the pattern of local maxima and minima in a CD field, as a function of the degree of smoothing, the following strategy is adopted. 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 CD gradient value vanishes. Convergence of trajectories leads to a reduction of the number of points.
The approach is applied to the design of amino acid (AA) RPC templates (Figure 1-left). A variant distribution is built by locating point charges on atoms (Figure 1-right).



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 so obtained. Point charges that are not located on atoms are considered as virtual sites with a nul mass and radius.
Applications are carried out on a variety of protein 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. However, the model built by fitting charges on Coulomb forces calculated at grid points ranging between 1.2 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. In other models, the backbone dynamics is increased versus the all-atom simulations and results obtained at various temperatures suggest that the use of RPC models allows to probe local potential hyper-surface minima that are similar to the all-atom ones, but are characterized by lower energy barriers. Various conformations of a protein can thus be generated more rapidly than with the all-atom point charge representation.

References:
[1] L. Leherte et al., J. Chem. Theory Comput. 5, 3279 (2009).
[2] L. Leherte et al., J. Comput.-Aided Mol. Des. 25, 913 (2011).
[3] J. Wang et al., J. Comput. Chem. 21, 1999 (2000).
[4] B. Hess et al., J. Chem. Theory Comput. 4, 435 (2008).
[5] S. Pronk et al., Bioinformatics 29, 845 (2013).
[6] L. Leherte et al., J. Phys. Chem. A 115, 12531 (2011).
[7] L. Leherte et al., J. Molec. Graphics Model. 47, 44 (2014).
[8] L. Leherte et al., Sci. China Chem. 57, 1340 (2014).