Colloquium
3:00 p.m., Wednesday (Jan. 15th)
Math Annex 1100
Peter J. Thomas
Computational Neurobiology Laboratory, The Salk Institute
Applications of Turing Pattern Formation,
from Geometric Visual Hallucinations to Eukaryotic Chemotaxis
In 1952 Alan Turing proposed a mechanism for the development
of spatial patterns, such as animal coat patterns, from
spatially homogeneous initial conditions, such as a putative
uniform embryo. Many systems have invited analogous analyses,
from segmentation of the Drosophila embryo to Meinhardt's model
for establishing direction in eukaryotic chemotaxis. The two
essential elements underlying the Turing mechanism, a shortrange
activator and a longrange inhibitor, have not always been easily
identified as the biology underlying pattern formation becomes
better understood. In this talk I will explore two systems in
which the biological details gave new insights into the
possibilities of pattern formation. In the cerebral cortex, the
local connectivity of nervous tissue gives an effective longrange
inhibitory and shortrange excitatory interaction that can lead
to the creation of spontaneous patterned activity in the cortical
sheet. In the visual cortex this spontaneous activity gives rise
to a distinct set of geometric visual hallucinations. Careful
analysis of the geometry of cortical connectivity allows
classification of the observed patterns in terms of a particular
class of subgroups of the Euclidean motions of the plane. As a
second example, I will return to the problem of eukaryotic
chemotaxis first addressed (incorrectly, from a biological
perspective) by Meinhardt. The problem is for an unbiased cell
to respond to a weak chemical gradient signal in the surrounding
medium, identifying the direction of the gradient and rearranging
its internal chemistry to prepare to crawl up the gradient
(chemotaxis). Using data from mutant screens of cells with
anomalous chemotaxis, we have identified a rapidly diffusing
intracellular inhibitory molecule that facilitates sharpening
of the directional response. In addition to amplifying the
weak spatial gradient signal, this variant of the Turing mechanism
also exploits timing characteristics of the extracellular signal.
(The Mathematical Biology Seminar on Thursday 1/16 will discuss
biochemical networks in more detail.)
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
