Searching for principles

William Bialek (Princeton University)

Abstract

This is a lecture for after dinner, so I'll start with some philosophical remarks about the difference between models (which have lots of parameters) and theories (which don't). Assuming that I survive any resulting protests from the audience, I'll go on to talk about two concrete, if modest, attempts at theory in the context of signaling and information flow in biological systems.

1. Is it possible that biological signaling systems are optimized to provide maximum information transmission? This idea has its origins in work on neural coding, where it has had important successes in predicting that the input/output relations of neurons will be matched to the statistical structure of sensory inputs. More recently we have tried to use the same idea to think about transcriptional regulation, making (we think) surprisingly successful connections to recent experiments on the first steps in the cascade of events leading to pattern formation in the fruit fly embryo; this work also gives a new perspective on the classical idea of "positional information" in developmental biology. Maximizing information transmission also involves minimizing the effects of noise, and I'll give a brief review of the evidence that many different biological systems have managed to reduce noise levels down to some fundamental physical limits. Finally, we are trying to understand more generally the connection between seemingly abstract information theoretic quantities and the things that organisms really care about, such as their evolutionary fitness.

2. Do large biological networks have interesting collective states? New experimental techniques have focused attention on the construction of more complete, global models for networks of genes, metabolites, neurons, ... . Long before these experiments were possible, theorists conjectured that, for neural networks in particular, interactions among many elements could lead to collective behaviors, as in statistical mechanics, which really are qualitatively different from things that one can understand by tracing "pathways" from one element to the next. I'll describe how we have been using maximum entropy methods to build bridges between theory and experiment. In particular, we'll see that the network of retinal neurons which provides us with information about the visual world exhibits surprisingly strong collective or correlated behavior. More precisely, the correlations are so strong that the network is poised near the analog of a phase transition, a result which (if confirmed) would have interesting implications for how we think about the brain more generally. This analysis of the retinal network also contains some cautionary tales for the analysis of genetic and biochemical networks, which I'll outline. Finally, I'll suggest that there may be connections between what we are finding in this "bottom up" analysis of a network and the "top down" ideas about optimization in item (1) above.

While I hope that some of our theories turn out to be correct (!), I also want to make clear that searching for more general theoretical principles is productive because it leads to new ideas for experiments, often with startling conclusions.

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