Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions

TL;DR

This paper introduces membership functions as macrostates in Markov processes, deriving equations for their dynamics, and applies the ISOKANN method to analyze molecular simulations, providing new insights into macroscopic behavior.

Contribution

It proposes a novel framework using membership functions for macrostates, deriving their properties, and applying ISOKANN to extract transition paths from molecular dynamics data.

Findings

Derived equations for macrostate holding times

Demonstrated consistency with classical definitions

Successfully extracted transition paths in opioid receptor simulations

Abstract

Markov processes serve as foundational models in many scientific disciplines, such as molecular dynamics, and their simulation forms a common basis for analysis. While simulations produce useful trajectories, obtaining macroscopic information directly from microstate data presents significant challenges. This paper addresses this gap by introducing the concept of membership functions being the macrostates themselves. We derive equations for the holding times of these macrostates and demonstrate their consistency with the classical definition. Furthermore, we discuss the application of the ISOKANN method for learning these quantities from simulation data. In addition, we present a novel method for extracting transition paths from simulations based on the ISOKANN results and demonstrate its efficacy by applying it to simulations of the {\mu}-opioid receptor. With this approach we provide a new perspective on the analysis of macroscopic behaviour of Markov systems.