University of Toronto
			 Special Colloquium
                    Friday 2 February, 12:10-1:00pm
                          6183 Bahen Center      



SPEAKER:  Doron Levy

TITLE:    Group Dynamics of Phototaxis: Interacting Stochastic 
	  Many-Particle Systems and their Continuum Limit

ABSTRACT: Microbes live in fluctuating environments that are often limiting 
	  for growth. They have evolved several sophisticated mechanisms to 
	  sense changes in important environmental parameters such as light 
	  and nutrients.Most bacteria also have complex appendages that allow 
	  them to move,so they can swim or crawl into optimal conditions. 
	  This combination of sensing changes in the immediate environment 
	  and transducing these changes to the motion organisms, allows for 
	  movement ina particular direction: a phenomenon known as 
	  ''chemotaxis'' or ''phototaxis''.

	  Using time-lapse video microscopy we have monitored the movement of 
	  Cyanobacteria (which are phototaxis, i.e., bacteria that move 
	  towards light). These movies suggest that single cells are able to 
	  move directionally but atthe same time, the group dynamics is 
	  equally important. The various patterns ofmovement that we observe 
	  appear to be a complex function of cell density, surfaceproperties 
	  and genotype. Very little is known about the interactions between 
	  these parameters.  

	  In this talk, we will present a hierarchy of new models for 
	  describing the motion of phototaxis, that were constructed based 
	  on the experimental observations.  The first model is a stochastic 
	  model that describes the locations of bacteria, the group dynamics, 
	  and the interaction between the bacteria and the medium in which it 
	  resides.  The second model is a new multi-particle system that is 
	  obtained from a discretization of the first model.  Our third 
	  model is obtained as the continuum limit of the second model, and 
	  as such it is a system of nonlinear PDEs.  Our main theorems 
	  clarify the sense in which the system of PDEs can be considered as 
	  the limit dynamics of the multi-particle system.  We conclude with 
	  several numerical simulations that demonstrate the properties of 
	  our models.  Thisis a joint work with Devaki Bhaya (Department of 
	  Plant Biology, Carnegie Institute) and Tiago Requeijo (Math, 
	  Stanford).




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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2006-2007 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
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