The Journal of Neuroscience, April 15, 2003, 23(8):3457
Coordination of Cellular Pattern-Generating Circuits that Control
Limb Movements: The Sources of Stable Differences in Intersegmental
Phases
Stephanie R.
Jones1,
Brian
Mulloney2,
Tasso J.
Kaper1, and
Nancy
Kopell1
1 Department of Mathematics and Center for BioDynamics,
Boston University, Boston, Massachusetts 02215, and
2 Section of Neurobiology, Physiology, and Behavior,
University of California, Davis, California 95616-8519
Neuronal mechanisms in nervous systems that keep
intersegmental phase lags the same at different frequencies are not
well understood. We investigated biophysical mechanisms that permit local pattern-generating circuits in neighboring segments to maintain stable phase differences. We use a modified version of an existing model of the crayfish swimmeret system that is based on three known
coordinating neurons and hypothesized intersegmental synaptic connections. Weakly coupled oscillator theory was used to derive coupling functions that predict phase differences between neurons in
neighboring segments. We show how features controlling the size of the
lag under simplified network configurations combine to create realistic
lags in the full network. Using insights from the coupled oscillator
theory analysis, we identify an alternative intersegmental connection
pattern producing realistic stable phase differences. We show that the
persistence of a stable phase lag to changes in frequency can arise
from complementary effects on the network with ascending-only or
descending-only intersegmental connections.
To corroborate the numerical results, we experimentally constructed
phase-response curves (PRCs) for two different coordinating interneurons in the swimmeret system by perturbing the firing of
individual interneurons at different points in the cycle of swimmeret
movement. These curves provide information about the contribution of
individual intersegmental connections to the stable phase lag. We also
numerically constructed PRCs for individual connections in the model.
Similarities between the experimental and numerical PRCs confirm the
plausibility of the network configuration that has been proposed and
suggest that the same stabilizing balance present in the model
underlies the normal phase-constant behavior of the swimmeret system.
Key words:
central pattern generators; crayfish swimmeret; coupled oscillator theory; phase lags; frequency regulation; phase-response curves
Copyright © 2003 Society for Neuroscience 0270-6474/03/2383457-12$05.00/0
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