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  • 1
    Publication Date: 2023-11-03
    Description: Markov state models (MSMs) have received an unabated increase in popularity in recent years, as they are very well suited for the identification and analysis of metastable states and related kinetics. However, the state-of-the-art Markov state modeling methods and tools enforce the fulfillment of a detailed balance condition, restricting their applicability to equilibrium MSMs. To date, they are unsuitable to deal with general dominant data structures including cyclic processes, which are essentially associated with nonequilibrium systems. To overcome this limitation, we developed a generalization of the common robust Perron Cluster Cluster Analysis (PCCA+) method, termed generalized PCCA (G-PCCA). This method handles equilibrium and nonequilibrium simulation data, utilizing Schur vectors instead of eigenvectors. G-PCCA is not limited to the detection of metastable states but enables the identification of dominant structures in a general sense, unraveling cyclic processes. This is exemplified by application of G-PCCA on nonequilibrium molecular dynamics data of the Amyloid β (1−40) peptide, periodically driven by an oscillating electric field.
    Language: English
    Type: article , doc-type:article
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  • 2
    Publication Date: 2024-03-26
    Description: Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.
    Language: English
    Type: article , doc-type:article
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