A Quantitative Model for cAMP Binding to the Binding Domain of MloK1

Ligand-protein binding processes are essential in biological systems. A well-studied system is the binding of cyclic adenosine monophosphate to the cyclic nucleotide binding domain of the bacterial potassium channel MloK1. Strikingly, the measured on-rate for cyclic adenosine monophosphate binding is two orders of magnitude slower than a simple Smoluchowski diffusion model would suggest. To resolve this discrepancy and to characterize the ligand-binding path in structural and energetic terms, we calculated 1100 ligand-binding molecular dynamics trajectories and tested two scenarios: In the first scenario, the ligand transiently binds to the protein surface and then diffuses along the surface into the binding site. In the second scenario, only ligands that reach the protein surface in the vicinity of the binding site proceed into the binding site. Here, a binding funnel, which increasingly confines the translational as well as the rotational degrees of freedom, determines the binding pathways and limits the on-rate. From the simulations, we identified five surface binding states and calculated the rates between these surface binding states, the binding site, and the bulk. We find that the transient binding of the ligands to the surface binding states does not affect the on-rate, such that this effect alone cannot explain the observed low on-rate. Rather, by quantifying the translational and rotational degrees of freedom and by calculating the binding committor, our simulations confirmed the existence of a binding funnel as the main bottleneck. Direct binding via the binding funnel dominates the binding kinetics, and only ∼10% of all ligands proceed via the surface into the binding site. The simulations further predict an on-rate between 15 and 40μs^-1(mol/l)^-1, which agrees with the measured on-rate.