Abstract
The development of models of macromolecular electrostatics capable of delivering improved fidelity to quantum mechanical calculations is an active field of research in computational chemistry. Most molecular force field development takes place in the context of models with full Cartesian coordinate degrees of freedom. Nevertheless, a number of macromolecular modeling programs use a reduced set of conformational variables limited to rotatable bonds. Efficient algorithms for minimizing the energies of macromolecular systems with torsional degrees of freedom have been developed with the assumption that all atom-atom interaction potentials are isotropic. We describe novel modifications to address the anisotropy of higher order multipole terms while retaining the efficiency of these approaches. In addition, we present a treatment for obtaining derivatives of atom-centered tensors with respect to torsional degrees of freedom. We apply these results to enable minimization of the Amoeba multipole electrostatics potential in a system with torsional degrees of freedom, and validate the correctness of the gradients by comparison to finite difference approximations. In the interest of enabling a complete model of electrostatics with implicit treatment of solvent-mediated effects, we also derive expressions for the derivative of solvent accessible surface area with respect to torsional degrees of freedom.
Highlights
Two aspects of molecular modeling under continual improvement are the accurate scoring and sampling of molecular conformations
Multipole descriptions of electrostatics can provide representations of charge distributions that are orders of magnitude more faithful to distributions obtained from quantum mechanical calculations that those provided by atomcentered partial charges alone [1], introducing off-atom partial charges provides improvements in this respect [2,3]
Dipole moments provide an attractive mechanism for introducing polarization of charge, which allows for a contextual dependence of electrostatics that is not possible when fixed partial charges are assigned to atoms irrespective of their exposure to polar solvents or their burial in hydrophobic environments
Summary
Two aspects of molecular modeling under continual improvement are the accurate scoring and sampling of molecular conformations. Multipole descriptions of electrostatics can provide representations of charge distributions that are orders of magnitude more faithful to distributions obtained from quantum mechanical calculations that those provided by atomcentered partial charges alone [1], introducing off-atom partial charges provides improvements in this respect [2,3]. Dipole moments provide an attractive mechanism for introducing polarization of charge, which allows for a contextual dependence of electrostatics that is not possible when fixed partial charges are assigned to atoms irrespective of their exposure to polar solvents or their burial in hydrophobic environments.
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