A Stochastic model to estimate the time taken for Protein-Ligand Docking

Quantum mechanics and molecular dynamic simulation provide important insights into structural configurations and molecular interaction data today. To extend this atomic/molecular level capability to system level understanding, we propose an "in silico" stochastic event based simulation technique. This simulation characterizes the time domain events as random variables represented by probabilities. This random variable is called the execution time and is different for different biological functions (e.g. the protein-ligand docking time). The simulation model requires fast computational speed and we need a simple transformation of the energy plane dynamics of the molecular behavior to the information plane. We use a variation of the collision theory model to get this transformation. The velocity distribution and energy threshold are the two parameters that capture the effects of the energy dynamics within the cell in our model. We use this technique to approximately determine the time required for the ligand-protein docking event. The model is parametric and uses the structural configurations of the ligands, proteins and the binding mechanism. The numerical results for the first moment show good correspondence with experimental results and demonstrate the efficacy of our model. The model is fast in computing and is less dependent on experimental data like rate constants