Computational models for large-scale simulations of facilitated diffusion

Abstract

The binding of site-specific transcription factors to their genomic target sites is a key step in gene regulation. While the genome is huge, transcription factors belong to the least abundant protein classes in the cell. It is therefore fascinating how short the time frame is that they require to home in on their target sites. The underlying search mechanism is called facilitated diffusion and assumes a combination of three-dimensional diffusion in the space around the DNA combined with one-dimensional random walk on it. In this review, we present the current understanding of the facilitated diffusion mechanism and identify questions that lack a clear or detailed answer. One way to investigate these questions is through stochastic simulation and, in this manuscript, we support the idea that such simulations are able to address them. Finally, we review which biological parameters need to be included in such computational models in order to obtain a detailed representation of the actual process.

Fig. 1. TF one-dimensional random walk on the DNA

A TF molecule (green circle) can move on the DNA (black line) by either: (i) sliding (moving to a nearby position without losing contact with the DNA), (ii) hopping (disassociations and fast reassociations in close proximity from the unbinding position) and (iii) jumping (disassociation, release in the bulk and reassociation anywhere on the DNA).

Fig. 2. Experimental strategies aimed to prove the existence of hopping

(a) The addition of non-specific DNA co-linear with an enzyme restriction site leads to similar cleavage rate as in the case when the non-specific DNA is added by catenation. In the second scenario the restriction site is reachable from the catenane only if hopping exists. (b) The experimental setup assumes two DNAs each with two restriction sites, but while in the first DNA, the sites are repeated (and no reorientation of the enzyme is required), in the second DNA, the sites are inverted (and the enzyme needs to invert its orientation which is possible only through hopping). Ensuring that only one enzyme is bound to the DNA, Gowers et al. observed that for distances longer than 50 bp the two strands display similar cleavage rates at both sites. The processivity of the two sites is measured as P = ([A] + [C] − [BC] − [AC])/([A] + [C] + [BC] + [AC]). (c) This is a similar strategy as in (b), but the experiments assumes only one DNA with two damaged uracil sites where the hUNG enzyme can excise the DNA. The protein is released from a P site and if the protein leaves the DNA for long excursions then it gets inactivated by a trap molecule and, thus, only a pure sliding mechanism will ensure a similar excision rate as in the case of a system without the trap molecule.