Microscopic simulations of macroscopic dielectric constants of solvated proteins

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Abstract
Microscopic simulation of solvated proteins are used to evaluate the relationship between the macroscopic field and macroscopic polarization, thus providing the corresponding dielectric constant, ε̄. This parameter is evaluated by two different methods which are first examined and calibrated by calculating the dielectric constant of bulk water. These calculations indicate that the reaction field, which represents the effect of the missing solvent around the given explicit region, must be included in the simulations in order to obtain a reasonable value for ε̄. The corresponding effect is not related to the reduction of the effective interactions between charges in the reference region but to the intrinsic value of ε̄ in that region. This means that vacuum calculations of ε̄ in proteins might underestimate its actual value. Or in other words, calculations of ε̄ in proteins must include the effect of the reaction field or a sufficiently large number of surrounding solvent molecules. Having included the surrounding solvent in simulations of trypsin, we find that ε̄ depends on the actual protein site. In particular, we find that ε̄ can be as large as 10 in sites of catalytic importance. It is pointed out that the dielectric constant that should be used in calculations of proteinproperties depends on the part of the system which is not treated explicitly and is not necessarily the macroscopic ε̄. For example, using ε̄ in electrostatic calculations that consider the protein polar groups explicitly accounts t w i c e for some aspects of the protein polarity. Finally, possible ways to use microscopically determined dielectric constants for electrostatic calculations in protein are considered.

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