  Molecular dynamics (MD) simulations can model the interactions between
macromolecules with high spatiotemporal resolution but at a high computational
cost. By combining high-throughput MD with Markov state models (MSMs), it is
now possible to obtain long-timescale behavior of small to intermediate
biomolecules and complexes. To model the interactions of many molecules at
large lengthscales, particle-based reaction-diffusion (RD) simulations are more
suitable but lack molecular detail. Thus, coupling MSMs and RD simulations
(MSM/RD) would be highly desirable, as they could efficiently produce
simulations at large time- and lengthscales, while still conserving the
characteristic features of the interactions observed at atomic detail. While
such a coupling seems straightforward, fundamental questions are still open:
Which definition of MSM states is suitable? Which protocol to merge and split
RD particles in an association/dissociation reaction will conserve the correct
bimolecular kinetics and thermodynamics? In this paper, we make the first step
towards MSM/RD by laying out a general theory of coupling and proposing a first
implementation for association/dissociation of a protein with a small ligand (A
+ B <--> C). Applications on a toy model and CO diffusion into the heme cavity
of myoglobin are reported.
