A “parallel plate” electrostatic model for bimolecular rate constants applied to electron transfer proteins

Abstract

A "parallel plate" model describing the electrostatic potential energy of protein-protein interactions is presented that provides an analytical representation of the effect of ionic strength on a bimolecular rate constant. The model takes into account the asymmetric distribution of charge on the surface of the protein and localized charges at the site of electron transfer that are modeled as elements of a parallel plate condenser. Both monopolar and dipolar interactions are included. Examples of simple (monophasic) and complex (biphasic) ionic strength dependencies obtained from experiments with several electron transfer protein systems are presented, all of which can be accommodated by the model. The simple cases do not require the use of both monopolar and dipolar terms (i.e., they can be fit well by either alone). The biphasic dependencies can be fit only by using dipolar and monopolar terms of opposite sign, which is physically unreasonable for the molecules considered. Alternatively, the high ionic strength portion of the complex dependencies can be fit using either the monopolar term alone or the complete equation; this assumes a model in which such behavior is a consequence of electron transfer mechanisms involving changes in orientation or site of reaction as the ionic strength is varied. Based on these analyses, we conclude that the principal applications of the model presented here are to provide information about the structural properties of intermediate electron transfer complexes and to quantify comparisons between related proteins or site-specific mutants. We also conclude that the relative contributions of monopolar and dipolar effects to protein electron transfer kinetics cannot be evaluated from experimental data by present approximations.

Kinetics of photo-induced electron transfer from high-potential iron-sulfur protein to the photosynthetic reaction center of the purple phototroph Rhodoferax fermentans.

“…The effect is quantitatively similar to that obtained with cytochrome c2 in either Rb. sphaeroides (47) protein-protein interactions (48), can be applied. A fit of the experimental data to the following equation (48) e-Kp lnk = lnk,.-Viil + Kp, [2] in which K …”

Electrostatic effects in electron transfer reactions of [2Fe‐2S] ferredoxins with inorganic reagents

“…To clarify the role of electrostatics in the reactions with the tripositive cobalt reagents, the rates of electron transfer between 7: vaginalis and Anabaena ferredoxins with Co(NH-Jb3+ under varying ionic strength conditions were determined. The values of the apparent second-order rate constants were then analyzed in terms of a "parallel plate" model for the electrostatic potential energy (Tollin et al, 1984;Watkins et al, 1994). This model emphasizes local electrostatic interactions between the charged moieties, and gives a more realistic description of the reaction than does an earlier model of Wherland and Gray (1976), which considers the entire charge of the protein.…”

“…Values for the parameters were obtained by nonlinear least-squares fits of the data to the theoretical model, while fixing the values for r I 2 to 3.5 A, and Z, to +3 (Table 4). Uncertainties in the values for p are less than 1 A, and less than 10% for the other parameters, according to the originators of the analytical solution to the model (Watkins et al, 1994).…”

“…The ionic strength effects were used to probe the electrostatic features of the reactive site on the proteins' surfaces. The dependences of the apparent second-order rate constants k (= Kk,,) for reoxidation of the two [2Fe-2S] ferredoxins with Co(NH3),,+ on ionic strength were analyzed in terms of a "parallel plate" electrostatic model (Watkins et al, 1994) (Table 4).…”

“…The theoretical model of the dependence of the rate constants for oxidation of reduced Z vaginalis and Anabaenn ferredoxins with the tripositively charged cobalt complex CO(NH,),~+ on ionic strength was based on a "parallel plate" electrostatic model developed by Tollin and coworkers (Watkins et al, 1994). Values for parameters were obtained by nonlinear least-squares fits of the data to the theoretical model, while fixing the values for r , , to 3.5 A, and Z, to +3.…”