Non-Gaussian Statistics and Nanosecond Dynamics of Electrostatic Fluctuations Affecting Optical Transitions in Proteins

Abstract

We show that electrostatic fluctuations of the protein-water interface are globally non-Gaussian. The electrostatic component of the optical transition energy (energy gap) in a hydrated green fluorescent protein is studied here by classical molecular dynamics simulations. The distribution of the energy gap displays a high excess in the breadth of electrostatic fluctuations over the prediction of the Gaussian statistics. The energy gap dynamics include a nanosecond component. When simulations are repeated with frozen protein motions, the statistics shifts to the expectations of linear response and the slow dynamics disappear. We therefore suggest that both the non-Gaussian statistics and the nanosecond dynamics originate largely from global, low-frequency motions of the protein coupled to the interfacial water. The non-Gaussian statistics can be experimentally verified from the temperature dependence of the first two spectral moments measured at constant-volume conditions. Simulations at different temperatures are consistent with other indicators of the non-Gaussian statistics. In particular, the high-temperature part of the energy gap variance (second spectral moment) scales linearly with temperature and extrapolates to zero at a temperature characteristic of the protein glass transition. This result, violating the classical limit of the fluctuation-dissipation theorem, leads to a non-Boltzmann statistics of the energy gap and corresponding non-Arrhenius kinetics of radiationless electronic transitions, empirically described by the Vogel-Fulcher-Tammann law.

Protein electron transfer: Dynamics and statistics

“…Simulations of hydrated proteins consistently report sub-nanosecond to nanosecond relaxation times associated with these modes. 30,44,45 These time-scales have also been reported experimentally by measurements of the Stokes-shift dynamics. 40,[46][47][48][49][50] These, and possibly even longer, 28 electrostatic relaxation times create the possibility for breaking the ergodicity of the system and making some parts of the proteinwater phase space inaccessible on the time-scale of the reaction or on the time-scale of electron residence on a cofactor in a redox chain.…”

“…The slower component in χ (ω) arises from the coupled elastic motions of the protein and its hydration shells. This attribution is clearly demonstrated by the disappearance of the slow peak when the protein is frozen, 45,81 as is shown by the dotted line in Fig. 3.…”

“…The characteristic feature of several such functions reported so far 30,45,79 is the existence of two peaks, with a possibility that even slower relaxation times are still not resolved on the length of the simulation trajectory. 30 and green fluorescent proteins (GFP) 45 obtained from MD simulations. The dotted line indicates simulations in which the motions of both the protein and the GFP chromophore were frozen during the simulation run.…”

“…3 shows the typical Stokes-shift loss function calculated from atomistic simulations (∼100-150 ns Molecular Dynamics (MD) trajectories) of two hydrated proteins, cytochrome c (cytC), 30 and green fluorescent protein (GFP). 45 In the former case, the energy gap coordinate corresponds to changing the oxidation state of the iron of the heme, in the latter case the energy gap is between the ground and excited singlets of GFP's chromophore. The characteristic feature of several such functions reported so far 30,45,79 is the existence of two peaks, with a possibility that even slower relaxation times are still not resolved on the length of the simulation trajectory.…”

“…45 In the former case, the energy gap coordinate corresponds to changing the oxidation state of the iron of the heme, in the latter case the energy gap is between the ground and excited singlets of GFP's chromophore. The characteristic feature of several such functions reported so far 30,45,79 is the existence of two peaks, with a possibility that even slower relaxation times are still not resolved on the length of the simulation trajectory. 30 and green fluorescent proteins (GFP) 45 obtained from MD simulations.…”