Improved Whitten-Rabinovitch approximation for the Rice-Ramsperger-Kassel-Marcus calculation of unimolecular reaction rate constants for proteins

The Whitten-Rabinovitch (WR) approximation used in the semi-classical calculation of the Rice-Ramsperger-Kassel-Marcus (RRKM) unimolecular reaction rate constant was improved for reliable application to protein reactions. The state sum data for the 10-mer of each amino acid calculated by the accurate Beyer-Swinehart (BS) algorithm were used to obtain the residue-specific correction functions (w). The correction functions were obtained down to a much lower internal energy range than reported in the original work, and the cubic, rather than quadratic, polynomial was used for data fitting. For a specified sequence of amino acid residues in a protein, an average was made over these functions to obtain the sequence-specific correction function to be used in the rate constant calculation. Reliability of the improved method was tested for dissociation of various peptides and proteins. Even at low internal energies corresponding to the RRKM rate constant as small as 0.1 s(-1), the rate constant calculated by the present method differed from the accurate BS result by 60% only. In contrast, the result from the original WR calculation differed from the accurate result by a factor of 3000. Compared to the BS method, which is difficult to use for proteins, the main advantage of the present method is that the RRKM rate constant can be calculated instantly regardless of the protein mass.