Abstract:

Biology presents us with several interesting kinds of networks that transmit and process information. Neurons communicate by exchanging action potentials; proteins in a signaling pathway detect chemicals at the cell surface and conduct the information to the nucleus in a cascade of chemical reactions; and in gene regulation, transcription factors are responsible for integrating environmental signals and appropriately regulating their target genes.

Understanding the collective behavior of biological networks is not easy. These systems are inherently noisy and thus require a model of the mean dynamics as well as that of the noise; in addition, if we view the regulatory networks as information transmission devices, implemented by the "hardware" of chemical reactions, we need to describe them in a probabilistic, not deterministic (or noiseless), language. Unfortunately, connecting theory with experiment then becomes exponentially hard due to sampling problems as the number of interacting elements grows, and progress depends on finding some simplifying principle.

In this work two such principles are presented. In the first half I discuss a bottom-up approach and analyze the responses of a set of retinal ganglion cells to a naturalistic movie clip, and the activation states of proteins in a signaling cascade of immune system cells. The simplifying principle here is the idea that the distribution of activities over elements of the network is maximum entropy (or most random), but still consistent with some experimentally measured moments (specifically, pairwise correlations). The analogies between maximum entropy and Ising models are illustrated and connected to the previously existing theoretical work on spin-glass properties of neural networks.

In the second part a top-down approach is presented: viewing genetic regulatory networks as being driven to maximize the reliability of the information transmission between their inputs and outputs, I first examine the best performance of genetic regulatory elements achievable given experimentally motivated models of noise in gene regulation; and second, make the hypothesis that, in some systems at least, such optimization is beneficial for the organism and that its predictions are verifiable. Data from early morphogenesis in the fruit fly, Drosophila melanogaster , are used to illustrate these claims.