2005 72nd Annual Meeting of the Southeastern Section of the APS
Thursday–Saturday, November 10–12, 2005;
Gainesville, FL
Session MA: Biophysics Invited Session
8:30 AM–10:18 AM,
Saturday, November 12, 2005
Hilton
Room: Century A
Chair: Stephen Hagen, University of Florida
Abstract ID: BAPS.2005.SES.MA.3
Abstract: MA.00003 : Genesis and Control of bursting activity in a neuronal model
9:42 AM–10:18 AM
Preview Abstract
Abstract
Author:
Gennady Cymbalyuk
(Dept Physics \& Astronomy, GSU)
Neurons are observed in one of four fundamental activity modes:
silence,
sub-threshold oscillations, tonic spiking, and bursting. Neurons
exhibit
various activity regimes and regime transitions that reflect their
complement of ionic channels and modulatory state. The leech
presents unique
opportunities for experimental and theoretical studies on the
dynamics of
neuronal activity. The central pattern generator controlling the
leech's
heartbeat contains identified pairs of mutually inhibitory neurons.
Bursting activity of neurons is an oscillatory activity
consisting of
intervals of repetitive spiking separated by intervals of
quiescence. It has
been observed in neurons under normal and pathological
conditions. Neurons
which are capable of generating bursting activity endogenously
play an
important role in motor control and other brain functions. Burst
duration,
interburst interval and spike frequency are crucial temporal
characteristics
of bursting activity and thus have to be regulated. Application
of the
bifurcation theory of dynamical systems suggests new mechanism of
how
bursting activity can be generated by neurons and how burst
duration can be
regulated.
Here we describe two mechanisms for the transition between tonic
spiking and
bursting. First mechanism describes a smooth, continuous and
reversible
transition from tonic spiking into bursting in a model neuron. The
burst duration increases with no bound as
1/(\textbf{\textit{a-a}}$_{0})^{1/2}$, where
\textbf{\textit{a}}$_{0}$ is
a parameter determining the transition. The characteristic
features of this
mechanism are that (a) the burst duration can be made arbitrarily
long while
(b) inter-burst interval does not depend on the parameter. The
second
mechanism is concerned with bi-stability where simultaneous tonic
spiking
and bursting activities co-exist in a neuron. The mechanism is
based on a saddle-node periodic orbit bifurcation with non-central
homoclinic orbits. This bifurcation describes a transition
between three
qualitatively different types of dynamics of a neuron. If one
varies the
control parameter \textbf{\textit{a}} towards the critical value
\textbf{\textit{a}}$_{0}$ at which the transition from the
bistability
region to the region where only tonic spiking is observed, the burst
duration of the bursting activity becomes proportional to
\textit{ln}(\textbf{\textit{a-a}}$_{0})$. The interburst interval
does not correlate
with the burst duration.
In terms of neuron's activity these two mechanisms describe a
biophysically
plausible means for regulation of burst duration. We show how this
bifurcation can be found in a Hodgkin-Huxley type model of a
neuron and how
to identify control parameters determining properties of bursting
activity.
The work is supported by NIH NS 43098.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2005.SES.MA.3