To advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) simulations and Markov state models (MSMs) has enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increases exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called independent Markov decomposition (IMD) that leverages weak coupling between subsystems to compute a global kinetic model without requiring the sampling of all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD models can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.

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 time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, 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 length scales, 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 toward 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.

Abstract. There is growing concern that blast-exposed individuals are at risk of developing neurological disorders later in life. Therefore, it is important to understand the dynamic properties of blast forces on brain cells, including the endothelial cells that maintain the blood-brain barrier (BBB), which regulates the passage of nutrients into the brain and protects it from toxins in the blood. To better understand the effect of shock waves on the BBB we have investigated an in vitro model in which BBB endothelial cells are grown in transwell vessels and exposed in a shock tube, confirming that BBB integrity is directly related to shock wave intensity. It is difficult to directly measure the forces acting on these cells in the transwell container during the experiments, and so a computational tool has been developed and presented in this paper.Two-dimensional axisymmetric Euler equations with the Tammann equation of state were used to model the transwell materials, and a high-resolution finite volume method based on Riemann solvers and the Clawpack software was used to solve these equations in a mixed Eulerian/Lagrangian frame. Results indicated that the geometry of the transwell plays a significant role in the observed pressure time series in these experiments. We also found that pressures can fall below vapor pressure due to the interaction of reflecting and diffracting shock waves, suggesting that cavitation bubbles could be a damage mechanism. Computations that include a simulated hydrophone inserted in the transwell suggest that the instrument itself could significantly alter blast wave properties. These findings illustrate the need for further computational modeling studies aimed at understanding possible blastinduced BBB damage.

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