Parametric modeling of protein–DNA binding kinetics: A discrete event based simulation approach

To understand the stochastic behavior of biological systems, we adopt an “in silico” stochastic event based simulation methodology that can determine the temporal dynamics of different molecules. The main requirement for this technique is the event execution time models for the different biological functions of the system. This paper presents a parametric model to determine the execution time of one such biological function: protein–DNA binding. This biological function is modeled as a combination of microlevel biological events using a coarse-grained probability measure to estimate the stochastic parameters of the function. Our model considers the actual binding mechanism along with some approximated protein and DNA structural information. We use a collision theory based approach to transform the thermal and concentration gradients of this biological function into their corresponding probability measure. This information theoretic approach significantly removes the complexity of the classical protein sliding along the DNA model, improves the speed of computation and can bypass the speed-stability paradox. This model can produce acceptable estimates of DNA–protein binding time necessary for our event based stochastic system simulator where the higher order (more than second order statistics) uncertainties can be ignored. The results show good correspondence with available experimental estimates. The model depends very little on experimentally generated rate constants and brings the important biological parameters and functions into consideration. We also present some “in silico” results showing the effects of protein–DNA binding on gene expression in prokaryotic cells.