Markov State and Diffusive Stochastic Models in Electron Spin Resonance

Abstract

Electron spin resonance (ESR) spectra of biological macromolecules reflect a wide range of dynamical molecular motions. However, because an electron spin is strongly coupled to its environment, the quantal degrees of freedom must be propagated for hundreds of nanoseconds to calculate spectra with a reasonable resolution of detail. Furthermore, a large number of independent “samples” are necessary for a reliable estimate of the ESR spectrum. For this reason, a direct calculation from molecular dynamics (MD) simulations is inefficient and wasteful route. As a practical alternative, we present a methodology in which stochastic are first constructed from MD simulations and then used to calculate ESR spectra. Discrete Markov state models (MSMs) offer a natural representation of the jump-like isomerization dynamics of a spin label attached to a protein through a flexible linker. A pedagogical introduction to the second half of the formalism—accounting for the coupling between the molecular and the spin dynamics—is also provided. The chapter concludes with a successful application of the methodology to multi-frequency ESR spectroscopy of spin-labeled T4 Lysozyme.