1. shraiman
  2. Research

Research

Research Interests:

  1. Population Genetics and Evolution

  2. Morphogenesis and Quantitative System Biology.

  3. Search Behavior: Exploration, Exploitation and Information.

  4. Statistical Mechanics of Non-Equilibrium Systems.   

Current and Recent Research:

I. Dynamics of Natural Selection: developing the Statistical Genetics Theory

Evolution works through natural selection that acts on genetic variation. A mounting body of evidence suggests that large populations harbor a great deal of such “selectable” variation. This implies that in order to understand how genetic variants (a.k.a. polymorphisms) spread through populations, theoretical models must account for interactions between polymorphisms at different genetic loci and in different individuals. The problem is further encumbered by the effect of sex and recombination that reshuffle polymorphisms between individual genomes. Yet, this “many-body problem” of evolutionary dynamics lends itself to a Statistical Genetics approach with many parallels to Statistical Physics: as is the case with Thermodynamics, a complex system with very many interacting degrees of freedom recovers certain simplicity in its macroscopic or statistical behavior. Thus as we proceed with the development of Statistical Genetics (i.e. of a quantitative  description for the structure of genetic diversity and the rate of adaptation in populations whose evolutionary dynamics is dominated by numerious, deleterious and beneficial, mutations each having a small effect) we hope to uncover the EMERGENT SIMPLICITY of  evolutionary dynamics.

A representative sample of our recent work on this subject:

II. Patterning and growth in development: "Growth and Form" revisited.

Understanding how a multicellular organism developes is one of the fundamental problems in science. Despite widely held belief that "theory" has no place in biology, this field is clearly in need of new ideas and concepts which can be generated  by oldfashioned process of developing models which explain observations and make falsifiable predictions. In fact, "theories" such as Turing's and Wolpert's idea of morphogen gradients have had a massive impact in the development field. Our current work is focused on the problem of coordination of patterning and growth in the process of organogenesis in Drosophila.  For example, in the wing imaginal disc patterning induced by morphogen gradient is concurrent with cell growth and proliferation (the number of cells increases by a factor of > 1000). How is this patterning coordinated with growth? How is the growth controlled? How does the developing limb know when to stop growing?

A representative sample of our recent work on subject:

III. Search behavior: Exploration, Exploitation and Information.

Olfactory source location at high Reynolds number and Infotaxis

Olfactory search involves "climbing" the concentration gradient of the odorant. At least naively. At least at low Reynolds number, e.g. the conditions appropriate to bacterial chemotaxis. At high Reynold number, local gradient of concentration is far too intermittent to point in the right direction. What is then an optimal, or at least reasonable search strategy? A paper with Eugene Balkovsky, "Olfactory search at high Reynolds number", PNAS (2002), provided a simple strategy for olfactory search in the presence of a steady (mean) wind velocity. Subsequent work in collaboration with Massimo Vergassola (Inst Pasteur, Paris) went beyond a heuristic algorithm to provide a unified description of search strategies. Specifically, thinking about the olfactory search problem has lead us to a rather general search strategy which is based on maximizing the rate of information gain which we called "Infotaxis" described in "Infotaxis: a strategy for searching without gradients", Nature (2007), by M. Vergassola, E. Villermaux and BIS. Remarkably this approach appears to be a particular limiting case of dealing with the well known "exploration and exploitation" problem of reinforcement learning and infotaxis strategy is various modified forms is applicable in a broad range of applications.

IV. Statistical Hydrodynamics.

Statistical Geometry of Turbulence

This effort (currently in the background) centers on the construction of a phenomenological model describing the dynamics of large fluctuations in the inertial scaling range of a fully turbulent flow. The goal is to understand the statistics of large fluctuations on small scales (which does not follow Kolmogorov's 1941 scaling theory) and to understand how it depends on the strain and vorticity structure of the larger scales. A paper with Alain Pumir and Misha Chertkov, "Lagrangian Tetrad Dynamics..." argued that the simplest non-trivial model must follow (for a short time only) the evolution of not one or two but at least 4 Lagrangian points - enough to define a "shape" tensor which integrates over the history of the strain along the trajectory. Energy transfer was found to be associated with formation of "pancakes" or "ribbons"  by strain configurartions with two stretching and one compressing eigenvalues (tr s^3 ) <0 product.

Many other geometrical aspects can be addressed (see a talk at http://online.itp.ucsb.edu/online/hydrot_c00/shraiman/). The kinematics of Lagrangian shapes was examined in another paper with Pumir and Chertkov: "Geometry of Lagrangian Dispersion..."  The emphasis on the Lagrangian dynamics and multipoint correlators derives from my earlier work with Eric Siggia on the Passive Scalar Problem (for review see "Scalar Turbulence", for technical details see "Anomalous Scaling fo a Passive Scalar near Batchelor Limit" and "Lagrangian Path Integrals ..."