Simulating cw-ESR Spectrum Using Discrete Markov Model of Single Brownian Trajectory

TL;DR

This paper introduces a Markov State Model-based method to simulate cw-ESR spectra from single Brownian trajectories, offering a computationally efficient alternative to traditional averaging methods.

Contribution

The study demonstrates that a Markov model derived from a single Brownian trajectory can accurately reproduce ESR spectra, reducing computational effort and enabling direct spectrum calculation from MD data.

Findings

Good agreement between MSM-based spectra and averaged trajectories.

Method reduces computational effort in spectrum simulation.

Potential to analyze molecular motion and transitions more efficiently.

Abstract

Dynamic trajectories can be modeled with a Markov State Model (MSM). The reduction of continuous space coordinates to discretized coordinates can be done by statistical binning process. In addition to that, the transition probabilities can be determined by recording each event in the dynamic trajectory. This framework is put to a test by the electron spin resonance (ESR) spectroscopy of nitroxide spin label in X- and Q- bands. Calculated derivative spectra from MSM model with transition matrix obtained from a single Brownian trajectory by statistical binning process with the derivative spectra generated from the average of a large number of Brownian trajectories, are compared and yield a very good agreement. It is suggested that this method can be implemented to calculate absorption spectra from molecular dynamics (MD) simulation data. One of its advantages is that due to its reduction of computational effort, the parametrization process will be quicker. Secondly, the transition matrix defined in this manner, may indicate separable potential changes during the motion of the molecule and may have advantages when working with reducible set of coordinates. Thirdly, one can calculate the ESR spectra from a single MD trajectory directly without extending it artificially in the time axis. However, for short MD trajectories, the required statistical information can not be obtained depending on the timescale of transitions. Therefore, some statistical improvement will be needed in order to reach a better convergence.