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This paper revisits Markov state models (MSMs) by introducing a dual transition matrix approach to estimate unbiased observables from molecular dynamics simulations, addressing the biases inherent in traditional single-matrix frameworks. By allowing for the estimation of observables at any fixed lag time, the method overcomes the limitations of long lag times that obscure short-timescale dynamics. The key result demonstrates that with infinite, properly weighted data, this new approach yields accurate coarse-grained observables without the biases that typically arise in MSM analyses.
Unbiased observables can be estimated at any lag time using a dual transition matrix approach, revolutionizing how we analyze molecular dynamics data.
Markov state models (MSMs) have become ubiquitous tools for analyzing molecular dynamics (MD) simulations because of their simple, powerful premise: although complete MD sampling may be impossible, the MSM can"stitch together"transition probabilities derived from local sampling to provide a global picture of kinetics and mechanisms. In the standard MSM framework, the available MD data is organized into a single transition matrix, which is then used to estimate all observables at a lag time chosen so the coarse-grained dynamics are approximately Markovian. This approach leads to avoidable model bias and motivates long lag times that obscure short-timescale processes of interest. In contrast, this paper shows how to obtain unbiased coarse-grained observables at any fixed lag time and for any fixed coarse-graining in the limit of infinite, properly weighted data. The central idea is to replace the single-matrix framework with two transition matrices -- one representing equilibrium dynamics and another representing source-sink recycling dynamics -- and use the correct matrix or matrices to estimate the matched dynamical observables.