Abstract
We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we do this without specifying the function performed by the network. Specifically, we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations. We perform this analysis for all biochemical circuits, including various feedback loops, that can be built out of 3 chemical species, each under the control of one regulator. We find that a generic network, constrained to low molecule numbers and reasonable response times, can transduce more information than a simple binary switch and, in fact, manages to achieve close to the optimal information transmission fidelity. These high-information solutions are robust to tenfold changes in most of the networks' biochemical parameters; moreover they are easier to achieve in networks containing cycles with an odd number of negative regulators (overall negative feedback) due to their decreased molecular noise (a result which we derive analytically). Finally, we demonstrate that a single circuit can support multiple high-information solutions. These findings suggest a potential resolution of the “cross-talk” phenomenon as well as the previously unexplained observation that transcription factors that undergo proteolysis are more likely to be auto-repressive.
Highlights
Genetic regulatory networks act as biochemical computing machines in cells, measuring, processing, and integrating inputs from the cellular and extracellular environment and producing appropriate outputs in the form of gene expression
The behavior of these networks is not deterministic; many of the molecules involved in genetic regulation (e.g., DNA, mRNA, transcription factors) are found in low copy numbers, and are subject to severe copy number fluctuations
Strong is the perception that the noise dominates the dynamics of regulatory networks, that the standard model of gene regulation has been that of Boolean logic [14,15,16,17,18], effectively implying that, at best, only two distinct states can be resolved in the noisy genetic output
Summary
Genetic regulatory networks act as biochemical computing machines in cells, measuring, processing, and integrating inputs from the cellular and extracellular environment and producing appropriate outputs in the form of gene expression. The behavior of these networks is not deterministic; many of the molecules involved in genetic regulation (e.g., DNA, mRNA, transcription factors) are found in low copy numbers, and are subject to severe copy number fluctuations. Strong is the perception that the noise dominates the dynamics of regulatory networks, that the standard model of gene regulation has been that of Boolean logic [14,15,16,17,18], effectively implying that, at best, only two distinct states (on or off) can be resolved in the noisy genetic output. One can build stable binary biochemical switches with just tens of copies of a transcription factor molecule [19], which begs the question: Can we do even better with slightly more molecules? That is, is the genetic regulation, binary?
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