Dielectric relaxation in proteins: Microscopic and macroscopic models

Dielectric relaxation in response to charge separation or transfer is a crucial component of protein electrostatics. Theoretical studies can give valuable insights; for example, they allow a separate analysis of protein and solvent relaxation. We review recent theoretical studies performed with macroscopic and microscopic models. Macroscopic continuum models provide a simple framework in which to interpret the results of detailed molecular dynamics simulations of dielectric relaxation. They are also widely used in protein modeling. Molecular dynamics simulations allow the Fröhlich-Kirkwood dielectric constant of a protein to be calculated. This dielectric constant is a linear response coefficient, which is appropriate in principle to describe protein relaxation in response to perturbing fields and charges. The internal dielectric constant of several proteins was found to be small (2-3), while the overall dielectric constant is large (15-25) due to motions of charged side chains at the protein surface. Poisson calculations using the low internal dielectric constant of cytochrome c reproduced approximately molecular dynamics relaxation free energies for charge insertion at multiple sites within this protein. In the protein aspartyl-tRNA synthetase, the relaxation and nonrelaxation ("static") components of the free energy were calculated for charge insertion in the active site. The assumption of linear response leads to a linear relation between the static and relaxation free energies. This relation was verified by continuum calculations if and only if different protein dielectric constants were used for the static and relaxation components of the free energy; namely one for the static free energy and 4-8 for the relaxation free energy. These were also the only values that gave at least fair agreement with molecular dynamics estimates of the free energy for this process. Applications of continuum models to other systems and more complex processes, such as ligand binding or calculation of titration curves, are discussed briefly.