Colloquium on December 19th, 2005

William Bialek
Joseph Henry Laboratories of Physics, and
Lewis-Sigler Institute for Integrative Genomics
Princeton University

Maximum entropy models for biological networks

Most of what we know about biological systems comes from studying one element at a time, yet we also know that most important functions emerge from interactions among many elements. Although much excitement has been generated by new experimental techniques that provide a more global view (recording the activity of many individual neurons, the expression levels of many genes, ... ), no realistic experiments will allow an exhaustive exploration of even modest sized networks: progress depends on simplifying hypotheses. This talk will describe our recent efforts to construct maximum entropy models of biological networks that are consistent with the easily measured correlations among pairs of elements. I'll start with the network of neurons in the vertebrate retina, which present some striking puzzles. These puzzles in the data are resolved with remarkable accuracy using the maximum entropy construction. Because neural responses are composed of discrete action potentials, it turns out that the relevant maximum entropy models actually are Ising models, and this leads to wonderful connections with statistical mechanics and with now classic theories of neural networks. As a second example I'll look at the MAP kinase network in cells of the immune system, and once again we'll see that the maximum entropy models based on pairwise correlations are strikingly successful. Small deviations from these models point to particular elements in the network that have genuinely combinatorial interactions. Finally, just for fun, we'll look at how these ideas apply to the correlations between symbols in written English. I hope to convince you that the venerable physical idea of maximum entropy provides a powerful tool for currently emerging quantitative experiments on biological systems, perhaps giving us a clear enough view of the network structure that we can move beyond data analysis to some deeper theoretical questions.

This is joint work with E Schneidman, GJ Stephens and G Tkacik, motivated by experiments from MJ Berry II and R Segev.