"Cross-graining": efficient multi-scale simulation via Markov state models

Accurate and efficient methods to simulate biomolecular systems at multiple levels of detail simultaneously are an ongoing challenge for the simulation community. Here we present a new method for multi-scale simulation where a complex system can be partitioned into two loosely-coupled sub-systems, one coarse-grained and one atomistic. If the coupling between the coarse-grained and atomistic systems can be encoded into discrete states that interconvert slowly, we can construct a Markov state model where we approximate any given transition P[(s(i),t(j))->(s(k),t(1))] in the joint space of the coarse-grained and atomistic systems as the product of two orthogonal transitions P(s(i)->s(k) mid R: t(j)) and P(t(j)->t(1) mid R: s(j)). We provide a formalism for constructing such models and describe how they may be applied to multi-scale simulation of membrane proteins. This "cross-graining" methodology may provide a general means to efficiently simulate mixed-scale systems.