This guest post is by Radu Zabet on his preprint (with Armin Schoech) Facilitated diffusion buffers noise in gene expression, arXived here.

How does the binding dynamics of transcription factors affect the noise in gene expression?

Transcription factors (TFs) are proteins that bind to DNA and control gene activity. Gene regulation can be modelled as a chemical reaction, which is fundamentally a stochastic process. Given the importance of an accurate control of the gene regulatory program in the cell, significant efforts have been made in understanding the noise properties of gene expression.

Why can noise in gene expression be modelled assuming an ON/OFF gene model?

With few exceptions, previous studies investigated the noise in gene expression assuming that the regulatory process is a two-state Markov model (genes switch stochastically between ON and OFF states). However, it is known that, mechanistically, transcription factors find their genomic target sites through facilitated diffusion, a combination of 3D diffusion in the cytoplasm/nucleoplasm and 1D random walk along the DNA, and this is likely to influence the noise properties of the gene regulation process. Previous experimental studies (e.g. see http://www.nature.com/ng/journal/v43/n6/full/ng.821.html) successfully modelled the noise measured experimentally by assuming an ON/OFF gene model (two-state Markov model) in bacterial and animal cells. In this manuscript, we built a three-state Markov model that accurately models the facilitated diffusion and we showed that for biologically relevant parameters, at least in bacteria (we assumed lac repressor system http://www.sciencemag.org/content/336/6088/1595), noise in gene expression can be modelled assuming the ON/OFF gene model, but only if the binding/unbinding rates are adjusted accordingly. This explains why in many cases the experimental noise in gene regulation can be modelled assuming an ON/OFF gene model. Note that there are several exceptions where the noise in gene expression does not seem to be accounted by the ON/OFF gene model (e.g. http://genome.cshlp.org/content/early/2014/07/16/gr.168773.113 or http://www.pnas.org/content/111/29/10598).

What is the effect of facilitated diffusion on the noise in gene expression?

Next, assuming the ON/OFF gene model we investigated the evolutionary advantage that a TF, which performs facilitated diffusion, has on noise in gene expression compared to an equivalent TF that only performs the 3D diffusion (and does not perform 1D random walk on the DNA). Our results show that the noise in gene expression can be reduced significantly when the TF performs facilitated diffusion compared to its equivalent TF that only performs 3D diffusion in the cell. This is important, because while the majority of the studies identify the speedup in the binding site search process as the main evolutionary advantage of why facilitated diffusion exists, we show that, in addition to this speedup in binding kinetics, facilitated diffusion also reduces the noise in gene expression. Interestingly, it seems that the noise level in gene expression is reduced close to the noise level of an unregulated gene (the lowest noise level in gene expression that could be achieved), while the noise of an equivalent TF that performs only 3D diffusion is significantly higher.

Finally, to test our model, we parameterise it with values measured experimentally in the case of lac repressor in E. coli and we estimated the mean mRNA level to be 0.16 and the Fano factor (variance divided by mean) to be 1.3 (as opposed to 2.0 in the case of TF performing only 3D diffusion). These values are similar to the values measured experimentally in the low inducer case of Plac by http://www.nature.com/ng/journal/v43/n6/full/ng.821.html (mean mRNA level of 0.15 and Fano factor of 1.25) and shows that facilitated diffusion is essential in explaining the experimentally measured noise in mRNA.