A Computationally Fast and Parametric Model to Estimate Protein-Ligand Docking Time for Stochastic Event Based Simulation

This paper presents a computationally fast analytical model to estimate the time taken for protein-ligand docking in biological pathways. The environment inside the cell has been reported to be unstable with a considerable degree of randomness creating a stochastic resonance. To facilitate the understanding of the dynamic behavior of biological systems, we propose an “in silico” stochastic event based simulation. The implementation of this simulation requires the computation of the execution times of different biological events such as the protein-ligand docking process (time required for ligand-protein binding) as a random variable. The next event time of the system is computed by adding the event execution time to the clock value of the event start time. Our mathematical model takes special consideration of the actual biological process of ligand-protein docking with emphasis on the structural configurations of the ligands, proteins and the binding mechanism that enable us to control the model parameters considerably. We use a modification of the collision theory based approach to capture the randomness of this problem in discrete time and estimate the first two moments of this process. The numerical results for the first moment show promising correspondence with experimental results and demonstrate the efficacy of our model.