Extension of the Force Matching Method to Anisotropic Coarse-Grained Transferable Force Fields: Application to the Unres Model of Proteins

Coarse-grained models of biological macromolecules are nowadays extensively used in simulations because of tremendous extension of the time- and size-scale that they offer. To provide the link between coarse-grained and all-atom dynamics, the Force Matching (FM) [1] and, further, the Multi-Scale Coarse-Graining (MSCG) approaches to biomolecular systems have been developed by the Voth group [2], in which the forces computed at the all-atom level are averaged over the degrees of freedom omitted from a coarse-grained representation. However, because isotropic site-site interactions have been assumed, aggressive coarse graining is not possible and the resulting force fields are not transferable. We propose a new approach to FM, which overcomes both problems. Anisotropic forces have been introduced by least-squares fitting the forces computed over the entire coarse-grained sites to the all-atom forces. To achieve transferability, the factor-expansion approach developed in our earlier work [3] has been implemented, in which the PMF of a system is expanded into Kubo cluster-cumulant functions [4], termed factors, that can be identified with the respective energy terms; the mean forces are partitioned likewise. The new FM variant has been applied to our highly reduced physics-based UNRES model of polypeptide chains [5], in which only united peptide groups and united side chains are the interaction sites. Comparison of the all-atom dynamics and coarse-grained dynamics will be presented