Information flow and optimization in transcriptional regulation

Abstract

In the simplest view of transcriptional regulation, the expression of a gene is turned on or off by changes in the concentration of a transcription factor (TF). We use recent data on noise levels in gene expression to show that it should be possible to transmit much more than just one regulatory bit. Realizing this optimal information capacity would require that the dynamic range of TF concentrations used by the cell, the input/output relation of the regulatory module, and the noise in gene expression satisfy certain matching relations, which we derive. These results provide parameter-free, quantitative predictions connecting independently measurable quantities. Although we have considered only the simplified problem of a single gene responding to a single TF, we find that these predictions are in surprisingly good agreement with recent experiments on the Bicoid/Hunchback system in the early Drosophila embryo and that this system achieves ϳ90% of its theoretical maximum information transmission.gene regulatory networks ͉ information theory C ells control the expression of genes in part through transcription factors (TFs), proteins which bind to particular sites along the genome and thereby enhance or inhibit the transcription of nearby genes. We can think of this control process as an input/output device in which the input is the concentration of TF and the output is the concentration of the gene product. Although this qualitative picture has been with us for ϳ40 years (1), only recently have there been quantitative measurements of in vivo input/output relations and of the noise in output level when the input is fixed (2-11). Because these input/output relations have a limited dynamic range, noise limits the ''power'' of the cell to control gene expression levels. In this article, we quantify these limits and derive the strategies that cells could use to take maximum advantage of the available regulatory power.To make precise our intuition about regulatory power, we need to quantify the number of reliably distinguishable regulatory settings of the transcription apparatus, a task to which Shannon's mutual information (12, 13) is ideally suited. Although there are many ways to associate a scalar measure of correlation or control with a joint distribution of input and output signals, Shannon proved that mutual information is the only such quantity that satisfies certain plausible general requirements, independent of the details of the underlying distributions. We can then show that maximizing the mutual information between the input and output of a regulatory element-in effect, maximizing the control that the cell can exert over the expression level of a gene-requires a quantitative matching among the input/output relation, the noise level, and the distribution of TF concentrations used during the life of the cell. If the regulation of gene expression has been optimized, these matching conditions provide parameter-free predictions that connect several independently measurable quantities.The general problem of optim...

Extending the dynamic range of transcription factor action by translational regulation

“…Introducing, consistently with our previous work, a dimensionless concentration unit c 0 = N max /D c c τ , and measuring expression levels g in units of maximal induction N max = rτ, we observe that the mean expression is simply ḡ = f (c), and the noise can be written as (8) If the input concentration c has a limited dynamic range, i.e., c ∈ [0,C], where C = c max /c 0 is the maximal allowed concentration of the input in units of c 0 , the relative importance of the two noise terms is set by C. For C ≫ 1, it is possible to regulate the gene such that the input noise contribution [second term of Eq. (8)] is negligible compared to the output noise [first term of Eq.…”

“…As described more fully in Refs. [8,[15][16][17][18][19], we can think of the regulatory mechanism as propagating information from c to g, and this information transmission is a measure of the control power achieved by the system.…”

The dynamics of genetic control in the cell: the good and bad of being late

“…Moreover, rate equations neglect the physical fact that all the processes involved in genetic control are affected by noise. As shown by Bialek and co-workers [25], a noisy system displaying sigmoidal response and controlled by realistic parameters can give only a two-state response. In terms of Shannon's information entropy, its capacity is I = 1 bit.…”

The effect of reactions on the formation and readout of the gradient of Bicoid

“…As we have already mentioned, Bcd acts as a transcription factor for the expression of hb. This process has been studied in detail both experimentally and theoretically [Gregor et al, 2007b, Tkaik et al, 2008, Dubuis et al, 2013. In particular, the observed (fluorescence) distributions coming from Bcd and Hb in fixed embryos have been used to develop the theory.…”