title: Trajectory-Based Simulation of EPR Spectra: Models of Rotational Motion for Spin Labels on Proteins
author: Peter D. Martin
description: Direct time-domain simulation of continuous-wave (CW) electron paramagnetic resonance (EPR) spectra from molecular dynamics (MD) trajectories has become increasingly popular, especially for proteins labeled with nitroxide spin labels. Due to the time-consuming nature of simulating adequately long MD trajectories, two approximate methods have been developed to reduce the MD-trajectory length required for modeling EPR spectra: hindered Brownian diffusion (HBD) and hidden Markov models (HMMs). Here, we assess the accuracy of these two approximate methods relative to direct simulations from MD trajectories for three spin-labeled protein systems (a simple helical peptide, a soluble protein, and a membrane protein) and two nitroxide spin labels with differing mobilities (R1 and 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (TOAC)). We find that the HMMs generally outperform HBD. Although R1 dynamics partially resembles hindered Brownian diffusion, HMMs accommodate the multiple dynamic time scales for the transitions between rotameric states of R1 that cannot be captured accurately by a HBD model. The MD trajectories of the TOAC-labeled proteins show that its dynamics closely resembles slow multisite exchange between twist-boat and chair ring puckering states. This motion is modeled well by HMM but not by HBD. All MD-trajectory data processing, stochastic trajectory simulations, and CW EPR spectral simulations are implemented in EasySpin, a free software package for MATLAB.