A short course on theoretical problems in biophysics
(lectures at the University of Rome, Spring 2008)
Thursday 13 March, 17:00-19:00. Edifico “E Fermi” di Fisica, Aula 4
Thursday 20 March, 15:00-17:00. Edifico “G. Marconi” di Fisica, Aula Touschek
Thursday 27 March, 15:00-17:00. Edifico “G. Marconi” di Fisica, Aula Touschek
Here are brief abstracts of the lectures. Follow the links for references, notes, etc..
Lecture 1: Physics problems in early embryonic development (notes updated 17 March 2008)
One of the most beautiful phenomena in nature is the emergence of a fully formed, highly structured organism from a single, undifferentiated cell, the fertilized egg. Over the past decades, biologists have shown that in many cases the "blueprint" for the body is laid out with surprising speed and is readable as variations in the concentration of particular molecules (the expression levels of particular genes). In the fruit fly, we know the identity of essentially all the relevant molecules. In this lecture I'll give a brief review of this biological background, and then show how, as we try to make quantitative sense out of this qualitative picture, we encounter a number of interesting physics problems: How can spatial patterns in the concentration of these molecules scale with the size of the egg, so that organisms of different sizes have similar proportions? What insures that the spatial patterns are reproducible from one embryo to the next? Since the concentrations of all the relevant molecules are small, does the random behavior of individual molecules set a limit to the precision with which patterns can be constructed? I will try to give not just a formulation of these problems, but also report on recent progress toward solutions, which has involved considerable exchange between theory and experiment.
While I am very excited about the particular things my colleagues and I are doing on this set of problems, I also hope that this lecture will give us a chance to talk about the more general question of how one builds bridges between general theoretical principles and the details of specific biological systems. This theme will continue throughout the course.
Lecture 2: Optimization principles for information flow (notes updated 27 March 2008; still incomplete)
Much of biological function is about the transmission and processing of information. In our sensory systems, information about the outside world is encoded into sequences of discrete, identical electrical pulses called action potentials or spikes. In bacteria, information about the availability of different nutrients is translated into the activity of particular proteins (transcription factors) which regulate the expression of specific genes required to exploit these different nutrients. In the developing embryo, cells acquire information about their position, and hence their fate in the adult organism, by responding to spatial variations in the concentration of specific "morphogen" molecules; in many cases these morphogens are again transcription factors. Given the importance of these different signaling systems in the life of the organism, it is tempting to suggest that Nature may have selected mechanisms which maximize the information which can be transmitted given the physical constraints. For the case of the neural code, this is an old idea, with some important successes (and failures). For the regulation of gene expression by transcription factors, we have just begun to explore the problem, but already there are some exciting results. I'll outline how maximizing information transmission provides a theory (rather than a highly parameterized model) for small networks of gene regulation, such as those relevant in embryonic development, in which most of the behavior of the network should be predictable once we know how many molecules of each kind the cell is willing to "spend," since the counting of these molecules sets the overall scale for information transmission. Even simple versions of this problem make successful experimental predictions.
Once again, a central issue in this lecture is how we build bridges from general principles (optimizing information transmission) to the details of particular systems (e.g., the expression of specific genes in the fruit fly embryo). But I hope to show explicitly how the same general principles are being used to think about very different biological systems, from bacteria to brains, making concrete our physicists' hope that there are concepts which can unify our thinking about these complex systems.
Lecture 3: Maximum entropy models for biological networks (notes updated 27 March; still incomplete)
Most of the interesting things that happen in living organisms result from networks of interactions, whether among neurons in the brain, genes in a single cell, or amino acids in single protein molecule. Especially in the context of neural networks, there is a long tradition of using ideas from statistical physics to think about the emergence of collective behavior from the microscopic interactions, with the hope that this functional collective behavior will be robust (universal?) to our ignorance of many details in these systems. In the past decade or so, new experimental techniques have made it possible to monitor the activity of many biological networks much more completely, and the availability of these data has made the problems of analysis much more urgent: given what the new techniques can measure, can we extract a global picture of the network dynamics? In this lecture I'll show how an old idea, the maximum entropy construction, can be used to attack this problem. What is most exciting is that this construction provides a path directly from real data to the classical models of statistical mechanics. I'll describe in detail how this works for a network of neurons in the retina as it responds to complex, naturalistic inputs, where the relevant model is exactly the Ising model with pairwise, frustrated interactions. Remarkably, the data suggest that the system is poised very close to a critical point. I'll try to highlight some open theoretical questions in this field, as well as making connections to other systems. Again, I hope we'll see the outlines of how common theoretical ideas can unify our understanding of diverse systems.