MAXIMUM-ENTROPY ANALYSIS OF KINETIC PROCESSES INVOLVING CHEMICAL AND FOLDING-UNFOLDING CHANGES IN PROTEINS

We show that numerical inversion of the Laplace transform by using the maximum entropy method can be successfully applied to the analysis of complex kinetic processes involving chemical and folding-unfolding ch anges in proteins. First, we present analyses of simulated data which support that: (i) the maximum entropy calculation of rate distribution s, combined with Monte Carlo analyses of the associated uncertainties, yields results consistent with the information actually supplied by t he data, thus preventing their overinterpretation; (ii) maximum entrop y analysis may be used to extract discrete rates (corresponding to ind ividual exponential contributions), as well as broad rate distribution s (provided, of course, that the adequate information is supplied by t he data). We further illustrate the applicability of the maximum entro py analysis with experimental data corresponding to two nontrivial mod el processes: (a) the kinetics of chemical modification of sulfhydryl groups in glycogen synthase by reaction with Ellman's reagent; (b) the kinetics of folding of ribonuclease a under strongly folding conditio ns, as monitored by fluorescence and optical absorption. Finally, we d iscuss that the maximum entropy approach should be particularly useful in studies on protein folding kinetics, which generally involve the c omparison between several complex kinetic profiles obtained by using d ifferent physical probes. Thus, protein folding kinetics is usually in terpreted in terms of kinetic mechanisms involving a comparatively sma ll number of kinetic steps between well-defined protein states. Accord ing to this picture, rate distributions derived from experimental kine tic profiles by maximum entropy analysis are expected to show a small number of comparatively narrow peaks, from which we can determine, wit hout a priori assumptions, the number of exponential contributions req uired to describe each experimental kinetic profile (the number of pea ks), together with their amplitudes (from the peak areas), time consta nt values (from the peak positions), and associated Monte Carlo uncert ainties. On the other hand, recent theoretical studies describe protei n folding kinetics in terms of the protein energy landscape (the multi dimensional surface of energy versus conformational degrees of freedom ), emphasize the difficulty in defining a single reaction coordinate f or folding, and point out that individual chains may fold by multiple pathways. This indicates that, in some cases at least, folding kinetic s might have to be described in terms of broad rate distributions (rat her than in terms of a small number of discrete exponential contributi ons related to kinetic steps between well-defined protein states). We suggest that the maximum entropy procedures described in this work may provide a method to detect this situation and to derive such broad ra te distributions from experimental data. (C) 1997 Academic Press