Dynamical behavior of a neural network model of locomotor control in the
lamprey.
Jung, Ranu Tim Kiemel, and Avis H. Cohen.
Department of Zoology, University of Maryland, College Park, MD 20742.
APStracts 2:0301N, 1995.
SUMMARY AND CONCLUSIONS
1. Experimental studies have shown that a central pattern generator in the
spinal cord of the lamprey can produce the basic rhythm for locomotion. This
pattern generator interacts with the reticular neurons forming a spino-
reticulo-spinal loop. To better understand and investigate the mechanisms for
locomotor pattern generation in the lamprey we examine the dynamical behavior
of a simplified neural network model representing a unit spinal pattern
generator (uPG) and its interaction with the reticular system. We use the
techniques of bifurcation analysis and specifically examine the effects on the
dynamic behavior of the system of: (a) changing tonic drives to the different
neurons of the uPG; (b) altering inhibitory and excitatory interconnection
strengths amongst the uPG neurons; and (c) feedforward-feedback interactions
between the uPG and the reticular neurons. 2. The model analyzed is a
qualitative left-right symmetric network based on proposed functional
architecture with one class of phasic reticular neurons (R) and three classes
of uPG neurons: excitatory (E), lateral (L), and crossed (C) interneurons. In
the model each class is represented by one left and one right neuron. Each
neuron has basic passive properties akin to biophysical neurons and receives
tonic synaptic drive and weighted synaptic input from other connecting
neurons. The neuron's output as a function of voltage is given by a non-linear
function with a strict threshold and saturation. 3. With an appropriate set of
parameter values, the voltage of each neuron can oscillate periodically with
phase relationships amongst the different neurons that are qualitatively
similar to those observed experimentally. The uPG alone can also oscillate as
observed experimentally in isolated lamprey spinal cords. Varying the
parameters can, however, profoundly change the state of the system via
different kinds of bifurcations. Change in a single parameter can move the
system from nonoscillatory to oscillatory states via different kinds of
bifurcations. For some parameter values the system can also exhibit
multistable behavior (e.g. an oscillatory state and a nonoscillatory state).
The analysis also shows us how the amplitudes of the oscillations vary and the
periods of limit cycles change as different bifurcation points are approached.
4. Altering tonic drive to just one class of uPG neurons (without altering the
interconnections) can change the state of the system by altering the stability
of fixed points, converting fixed points to oscillations, single oscillations
to two stable oscillations, etc. Two-parameter bifurcation diagrams show the
critical regions in which a balance between the tonic drives is necessary to
maintain stable oscillations. A minimum tonic drive is necessary to obtain
stable oscillatory output. With appropriate changes in the tonic drives to the
L and C neurons stable oscillatory output can be obtained even after
eliminating the E neurons. Indeed, the presence of active Es in the biological
system does not prove they play a functional role in the system, since tonic
drive from other sources can substitute for them. On the other hand, very high
excitation of any one class of neurons can terminate oscillations. Appropriate
balance of tonic drives to different neuron classes can help sustain stable
oscillations for larger tonic drives. Published experimental results
concerning changes in amplitude and swimming frequency with increased tonic
drives are mimicked by the model's responses to increased tonic drive. 5.
Interconnectivity amongst the neurons plays a crucial role. The analysis
indicates that the C and L class of neurons are essential components of the
model network. Sufficient inhibition from the L to C neurons as well as mutual
inhibition between the left and right halves is necessary to obtain stable
oscillatory output. When the E neurons are present in the model network, they
must receive appropriate tonic drive and provide appropriate excitation to the
L and C neurons. 6. The feedback-feedforward interactions between the
reticular neurons and the spinal network influences the behavior of the
system. Increased excitatory feedforward input from the reticular to the uPG
neurons can terminate stable oscillations. However, in the presence of
appropriate feedback, greater feedforward input is needed to disrupt the
oscillatory output. Inhibitory, and not the excitatory component of the
feedback, has this beneficial effect. The frequency of oscillation changes as
the feedforward input is increased, with the direction of change dependent on
the level of feedback. This observation provides a probable explanation of
previously published curious experimental results. 7. Our results demonstrate
the richness and complexity that even a simple neural network can exhibit when
its parameters are varied critically. We show that the value of the connection
strength or tonic drive, to even a single neuron class, and the balance
between feedback and feedforward connection strengths between the reticular
neurons and the spinal neurons can all crucially influence the behavior of a
simple neural network model for the locomotor central pattern generator.
Received 20 June 1995; accepted in final form 5 October 1995.
APS Manuscript Number J396-5.
Article publication pending J. Neurophysiol.
ISSN 1080-4757 Copyright 1995 The American Physiological Society.
Published in APStracts on 6 November 95