Simulating electron spin resonance spectra of nitroxide spin labels from molecular dynamics and stochastic trajectories

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics.