System size reduction in stochastic simulations of the facilitated diffusion mechanism

Site-specific Transcription Factors (TFs) are proteins that bind to specific sites on the DNA and control the activity of a target gene by enhancing or decreasing the rate at which the gene is transcribed by RNA polymerase. The process by which TF molecules locate their target sites is a key component of transcriptional regulation. Therefore it is essential to gain insight into the mechanisms by which TFs search for the target sites.Research in this area uses experimental and analytical approaches, but also stochastic simulations of the search process. Previous work based on stochastic simulations focussed only on short sequences, primarily for reasons of technical feasibility. Many of these studies had to disregard possible biases introduced by reducing a genome-wide system to a smaller subsystem. In particular, we identified crucial parameters that require adjustment, which were not adequately changed in these previous studies.

We investigated several methods that adequately adapt the parameters of stochastic simulations of the facilitated diffusion, when the full sequence space is reduced to smaller regions of interest. We found two methods that scale the system accordingly: the copy number model and the association rate model. We systematically compared the results produced by simulations of the subsystem with respect to the original system. Our results confirmed that the copy number model is adequate only for high abundance TFs, while for low abundance TFs the association rate model is the only one that reproduces with high accuracy the results of the full system.

We propose a strategy to reduce the size of the system that adequately adapts important parameters to capture the behaviour of the full system. This enables correct simulations of a smaller sequence space (which can be as small as 100 Kbp) and, thus, provides independence from computationally intensive genome-wide simulations of the facilitated diffusion mechanism.