Genetic regulatory networks enable cells to respond to changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits has deepened our understanding of what kinds of computations genetic regulatory networks can perform, and with what reliability. These advances have motivated researchers to look for connections between the architecture and function of genetic regulatory networks. Transmitting information between a network's inputs and outputs has been proposed as one such possible measure of function, relevant in certain biological contexts. Here we summarize recent developments in the application of information theory to gene regulatory networks. We first review basic concepts in information theory necessary for understanding recent work. We then discuss the functional complexity of gene regulation, which arises from the molecular nature of the regulatory interactions. We end by reviewing some experiments that support the view that genetic networks responsible for early development of multicellular organisms might be maximizing transmitted 'positional information'.
Optimization theory has been used to analyze evolutionary adaptation. This theory has explained many features of biological systems, from the genetic code to animal behavior. However, these systems show important deviations from optimality. Typically, these deviations are large in some particular components of the system, whereas others seem to be almost optimal. Deviations from optimality may be due to many factors in evolution, including stochastic effects and finite time, that may not allow the system to reach the ideal optimum. However, we still expect the system to have a higher probability of reaching a state with a higher value of the proposed indirect measure of fitness. In systems of many components, this implies that the largest deviations are expected in those components with less impact on the indirect measure of fitness. Here, we show that this simple probabilistic rule explains deviations from optimality in two very different biological systems. In Caenorhabditis elegans, this rule successfully explains the experimental deviations of the position of neurons from the configuration of minimal wiring cost. In Escherichia coli, the probabilistic rule correctly obtains the structure of the experimental deviations of metabolic fluxes from the configuration that maximizes biomass production. This approach is proposed to explain or predict more data than optimization theory while using no extra parameters. Thus, it can also be used to find and refine hypotheses about which constraints have shaped biological structures in evolution.