Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces

Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of multiscale models.

Automated summary

Systematic bottom-up coarse-graining is a useful approach for exploring different length and time scales in molecular systems. However, the configuration dependence of coarse-grained interactions limits their applicability. In this study, a statistical mechanical theory is proposed to design coarse-grained interactions across different configurations and conditions. By identifying classical coarse-grained free energy surfaces for characteristic configurations and quantifying the coupling interaction between them, the theory accurately captures the underlying potential of mean force in coarse-grained variables and offers a new protocol for multiscale model design.