Universal statistical fluctuations in thermodynamics and kinetics of single molecular recognition

We investigated the main universal statistical distributions of single molecular recognition. The distributions of the single molecule binding free energy spectrum or density of states were characterized in the ligand-receptor binding energy landscape. The analytical results are consistent with the microscopic molecular simulations. The free energy distribution of different binding modes or states for a single molecule ligand receptor pair is approximately Gaussian near the mean and exponential at the tail. The equilibrium constant of single molecule binding is log-normal distributed near the mean and power law distributed near the tail. Additionally, we found that the kinetics distribution of single molecule ligand binding can be characterized by log-normal around the mean and power law distribution near the tail. This distribution is caused by exploration of the underlying inhomogeneous free energy landscape. Different ligand-receptor binding complexes have the same universal form of distribution but differ in parameters.