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

Abstract

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.

Conformational dynamics and distribution of nitroxide spin labels

“…In early work on spin-labeled proteins it was assumed that this applies even for small proteins at X-band frequencies in highly viscous solutions prepared by adding 30% sucrose to water, which results in rotational diffusion rates of about 6·10 6 s -1 for a protein of the size of T4 lysozyme (18.7 kDa). Based on later theoretical work it was suggested that such rotational diffusion rates, corresponding to r = 28 ns, are not sufficiently slow for applications of the MOMD model at X-band frequencies [63]. Note however that for residue 131 in T4 lysozyme at a largely unrestricted -helical surface site, CW EPR spectra obtained in 30% sucrose solution and in a suspension of microcrystals are virtually identical [59],…”

“…This was approximately corrected for in some simulations by scaling the MD time step by a factor of 2.5 [63]. Note that such correction does not fully recover the true molecular relaxation times, since not all dynamic processes are slowed down in proportion to the viscosity of water.…”

“…Initially a 6 ns MD trajectory was considered sufficient and a potential in terms computations by a Brownian dynamics approach [81]. An efficient numerical integrator for such Brownian dynamics, which also allows for simulating anisotropic Brownian diffusion in an external potential, has been developed [63].…”

Cu(ii)–porphyrin molecular dynamics as seen in a novel EPR/Stochastic Liouville equation study

“…Due to numerical stability issues and memory requirements associated with the solution of high dimensional SLE in the frequency domain 24,25 a time domain trajectory based method is preferable. 11,[26][27][28][29][30][31] In this work we show for the first time a multi spin system solved under slow-motion conditions (||DH(O t )||t c Z 1) applied in a line shape study of EPR experiments. The key is the robust implicit numerical scheme developed for solving the SLEL, that conserves the norm of the density matrix and has a known error expansion for combined SLEL and molecular degrees of freedom.…”

Markov State and Diffusive Stochastic Models in Electron Spin Resonance

“…Such an approach is, after all, routinely used to analyze and interpret results from nuclear magnetic resonance (NMR) [34]. However, a straightforward all-atom MD strategy for calculating ESR spectra remains challenging, even with current computational resources [47,48]. The reason for this is both simple and complex.…”