In vivo facilitated diffusion model

TL;DR

This paper develops a semi-analytical model to evaluate the efficiency of facilitated diffusion for transcription factor target search in living bacterial cells, showing it aligns well with experimental data and operates near optimal conditions.

Contribution

It introduces a simple, semi-analytical in vivo model for facilitated diffusion, bridging the gap between in vitro mechanisms and cellular conditions, and quantifies search times in bacteria.

Findings

Facilitated diffusion effectively explains in vivo target search times.

Search time is robust against DNA configuration variations.

Cells operate near optimal conditions for target localization.

Abstract

Under dilute in vitro conditions transcription factors rapidly locate their target sequence on DNA by using the facilitated diffusion mechanism. However, whether this strategy of alternating between three-dimensional bulk diffusion and one-dimensional sliding along the DNA contour is still beneficial in the crowded interior of cells is highly disputed. Here we use a simple model for the bacterial genome inside the cell and present a semi-analytical model for the in vivo target search of transcription factors within the facilitated diffusion framework. Without having to resort to extensive simulations we determine the mean search time of a lac repressor in a living E. coli cell by including parameters deduced from experimental measurements. The results agree very well with experimental findings, and thus the facilitated diffusion picture emerges as a quantitative approach to gene regulation in living bacteria cells. Furthermore we see that the search time is not very sensitive to the parameters characterizing the DNA configuration and that the cell seems to operate very close to optimal conditions for target localization. Local searches as implied by the colocalization mechanism are only found to mildly accelerate the mean search time within our model.