Solvent Role in Ligand-Binding Reactions

The binding of ligands by transport and storage proteins and the binding of substrates and cofactors by enzymes play an essential role in their function. A 

The simplest treatment of diffusive encounters considers two noninteracting hard spheres that have radii r, and r2, diffusion constants D and Di, and isotropic reactivities such that any collision (i.e., when the distance between the two spheres is equal to the sum of their radii) leads to the reaction. This model requires solution of the Smoluchowski equation215 with a perfectly absorbing condition at R = r, + r2. The resulting rate constant k(R) has the simple form 

To treat more realistic models for the kinetics of biomolecular encounters, a simulation approach has been developed and applied to proteins.370,371,3718 This approach merges stochastic dynamics methodology (Chapt. IV.D) with the analytic result for the Debye rate constant for a pair of particles, moving diffusively through solvent with a centrosymmetric interaction potential.365 The analytical expression for the Debye rate constant, ko(,R), to first achieve a separation, R, is given by 

Reduced Rates and Electrostatic Models for SOD O2- Encounter Kinetics 

A Single point charge of —4 at center of 28.5-A spherical enzyme 0.056 0.004 

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