Polar fluctuations in proteins: molecular-dynamic studies of cytochrome c in aqueous solution

The equilibrium fluctuations (the polar fluctuations), of yeast cytochrome c are studied using nanosecond molecular-dynamic simulations in a spherical droplet of water, with a particular emphasis on the fluctuations of the total dipole moment, which determine the average relative permittivity. These fluctuations follow a simple probability distribution, predicted by continuum electrostatics, and already observed in simulations of several polar liquids. An important component consists of diffusive, mutually independent, motions of the charged side chains at the protein surface. A quasiharmonic normal mode analysis of the trajectory shows that while motions covering a large range of frequencies contribute to the polar fluctuations, the four lowest frequency modes account for 50% of the overall static relative permittivity of ca. 25. The fluctuations of the protein bulk, i.e. parts other than the charged side chains, are distributed over a larger number of modes. Modes up to at least 60 cm-1 contribute to the average relative permittivity of the protein interior of ca. 4. The water surrounding the protein, despite the structural perturbation represented by the protein, has fluctuations similar to pure water, consistent with the idea of a linear solvent response to the protein charges. The relationship between the microscopic fluctuations seen in the simulations and simple continuum models is discussed.