MC 6460

## Candidate

Leon Avery , Applied Mathematics, University of Waterloo

## Title

Models
of
social
behavior
in
*
C.
elegans*
larvae

## Abstract

Newly
hatched
larvae
(L1s)
of
the
nematode
*
Caenorhabditis
elegans*
can
survive
for
more
than
two
weeks
without
food.
Alex
Artyukhin
has
shown
that
when
placed
on
a
petri
plate
after
two
days
of
starvation,
these
L1s
spontaneously
come
together
into
roughly
circular
aggregates.
We
neither
know
how
they
aggregate,
nor
why.
Artyukhin
proposes
that
the
worms
release
a
diffusible,
unstable
attractant
into
solution.
This
attractant
diffuses
away
from
the
source
and
decomposes,
forming
a
gradient.
The
worms
are
then
proposed
to
move
up
the
gradient
--
this
leads
to
the
formation
of
aggregates.

This "Active Walker" model is described mathematically by a reaction-diffusion partial differential equation (PDE) governing the diffusion and decomposition of the attractant, and a series of stochastic different equations, one for each worm. Since the number of worms is large (typically a million in a single experiment), the worms may be approximated by a continuous density function, whose behavior is governed by an advection-diffusion PDE. Together the attractant PDE and density PDE form a nonlinear coupled system. Keller and Segel (1970) showed that this coupled PDE system becomes unstable above a threshold density, leading to spontaneous aggregation. Numerical solution of the PDEs will produce results that can be compared to experiments in animals, testing and refining the model.

An equally interesting question, but a more difficult one, is why the worms aggregate? That is, what purpose (if any) does aggregation serve, or why would such a behavior have evolved? We speculate that it improves the ability of the worms to survive starvation, perhaps by allowing them to pool information about the environment. This speculation is supported by the observation that the survival of C elegans L1 larvae is indeed improved when they aggregate. Furthermore, of four Caenorhabditis species tested, two show both density-dependent survival and L1 aggregation, and two show neither behavior. We hope to test the feasibility of these explanations in future modeling work.