Trajectory-Based Simulation of EPR Spectra: Models of Rotational Motion for Spin Labels on Proteins

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.