Remarkable Insensitivity of Protein Diffusion to Protein Charge

Friction to translational diffusion of ionic particles in polar liquids should scale linearly with the squared ion charge, according to standard theories. Substantial slowing of translational diffusion is expected for proteins in water. In contrast, our simulations of charge mutants of green fluorescent proteins in water show remarkable insensitivity of the translational diffusion constant to protein's charge in the range of charges between -29 and +35. The friction coefficient is given as a product of the force variance and the memory function relaxation time. We find remarkably accurate equality between the variance of the electrostatic force and the negative cross-correlation of the electrostatic and van der Waals forces. The charge invariance of the diffusion constant is a combined effect of the force variance and relaxation time invariances with the protein charge. The temperature dependence of the protein diffusion constant is highly non-Arrhenius, with a fragile-to-strong crossover at the glass transition.