where A...B denotes the nonspecific encounter pairs, A-B denotes the precursor state(s) leading to the docked conformation AB [20]. If long-range interactions can be neglected, the first reaction step is the random collision of the protein and ligand (A and B), resulting in a nonspecific encounter complex A...B within the desolvation layer. To a good approximation, the limiting rate k+ of this first regime is given by the Smoluchowski limit [21], kcou. Indeed, the overall repulsion of the force fields has little effect on k+. The authors in [19] report that the typical lifetime of a nonspecific encounter complex A... B diffusing within the desolvation layer is about 4 ± 1 ns. This value is consistent with the nonspecific affinity between proteins that is estimated to be 102M-1 or less [22].

The third reaction step in Eq. 5 i.e., the late transition between the favorable intermediate(s) A — B and the bound state AB, substantially differs from the first two steps. The onset of the late transition coincides with the need to remove steric clashes and charge overlaps in the binding mechanism. Although the first two steps are governed by diffusion, the third is a process of induced fit that requires structural rearrangements involving mostly side chains. [19] reports that this late transition is not diffusive. For ligands that bind in a diffusion-controlled (or diffusion limited) reaction, the rate-limiting step must be the diffusive search for the partially desolvated intermediate(s) or precursor state(s) rather than the third step, and thus k+B ^ k-.

In this paper, we focus on the kinetics of the total binding process. In particular, the collision theory model incorporates the first two steps together, whereas the Ligand axis rotation model estimates the third step.

2.1 Rotation of the Ligand Axis with Respect to Protein A

Fig 3 shows the rotation of the ligand axis to bring about the final docking configuration. The final orientation can be reached by the rotation of the ligand

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