# Computing Long Timescale Biomolecular Dynamics using Quasi-Stationary Distribution Kinetic Monte Carlo (QSD-KMC)

## TL;DR

The paper introduces QSD-KMC, a novel kinetic Monte Carlo method that accurately models long timescale biomolecular dynamics by addressing non-Markovian effects, outperforming traditional Markov State Models.

## Contribution

It presents a new QSD-KMC approach that captures non-Markovian dynamics and allows for optimized state boundaries, improving long-term biomolecular simulations.

## Key findings

- QSD-KMC produces trajectories statistically indistinguishable from MD.
- The method effectively models non-Markovian dynamics in biomolecular systems.
- It enables optimization of state boundaries independently of initial choices.

## Abstract

It is a challenge to obtain an accurate model of the state-to-state dynamics of a complex biological system from molecular dynamics (MD) simulations. In recent years, Markov State Models have gained immense popularity for computing state-to-state dynamics from a pool of short MD simulations. However, the assumption that the underlying dynamics on the reduced space is Markovian induces a systematic bias in the model, especially in biomolecular systems with complicated energy landscapes. To address this problem, we have devised a new approach we call quasi-stationary distribution kinetic Monte Carlo (QSD-KMC) that gives accurate long time state-to-state evolution while retaining the entire time resolution even when the dynamics is highly non-Markovian. The proposed method is a kinetic Monte Carlo approach that takes advantage of two concepts: (i) the quasi-stationary distribution and (ii) dynamical corrections theory. Implementation of QSD-KMC imposes stricter requirements on the lengths of the trajectories than in a Markov State Model approach, as the trajectories must be long enough to dephase. However, the QSD-KMC model produces state-to-state trajectories that are statistically indistinguishable from an MD trajectory mapped onto the discrete set of states, for an arbitrary choice of state decomposition. Furthermore, the aforementioned concepts can be used to construct a Monte Carlo approach to optimize the state boundaries regardless of the initial choice of states. We demonstrate the QSD-KMC method on two one-dimensional model systems, one of which is a driven nonequilibrium system, and on two well-characterized biomolecular systems.