Birds, brains, and B-cells: Statistical mechanics for real biological networks

William Bialek (September 21, 2012)

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Abstract

Most of the phenomena of life that attract our attention result from interactions among many components in a network. Examples include the interactions among neurons in the brain, among birds in a flock or fish in a school, and even the interactions among amino acids in a single protein. In all these cases there are "emergent" or collective behaviors that are properties of the network but not the individual components. In the physics of systems at thermal equilibrium, we have many examples of such emergent phenomena (some mundane, like the rigidity of solids, others more spectacular, such as superconductivity), and we have a language for describing such phenomena, statistical mechanics. There is a long standing intuition that this same language should be useful in thinking about collective phenomena in biological systems, an idea which is best developed in the context of neural networks, but one has to admit that much of what is done theoretically is not terribly well connected to experiment. I will review the argument that the maximum entropy construction gives us a way of going directly from real data to the more abstract statistical mechanics models, emphasizing the opportunities created by new, larger scale experiments. I'll start with flocks of birds, where the simplest version of these ideas seems remarkably successful. I'll then say a few words about proteins, using recent data on complete antibody repertoires in zebrafish as motivation. Finally, I'll discuss neurons, focusing on the response of the vertebrate retina to natural movies. Along the way I hope to make clear the connections between things that seem natural and interesting in the statistical mechanics context and things that seem relevant for the organism. Most startlingly, in all of these systems we find that the particular models which describe the real systems sit close to critical surfaces in the space of all possible models. I'll explain several different ways of seeing that this is true, why it is surprising, and speculate on why it is important. It certainly suggests that there is something deeper going on here, which we don't yet understand.