Heart Motorneuron Dynamics of Leeches (original) (raw)
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A mathematical model of motorneuron dynamics in the heartbeat of the leech
Physica D: Nonlinear Phenomena, 2004
The heartbeat of the medicinal leech is driven by direct contact between two arrays of motorneurons and two lateral blood vessels. At any given time, motorneurons exhibit one of two alternating states so that, on one side of the animal, the heart beats in a rear-to-front fashion (peristaltic), while on the other side the heart beats synchronously. Every 20 heartbeats, approximately, the two sides switch modes. It is known that the heartbeat rhythm is generated through burst of oscillatory activity produced by a central pattern generator (CPG) network of neurons. However, to the best of our knowledge, how the CPG activity is translated into peristaltic and synchronous rhythms in the motorneurons is yet unknown. In this work, we use symmetric systems of differential equations, accompanied with computational simulations, to investigate possible mechanisms for generating the motorneuron activity that characterizes the heartbeat of leeches and in particular the switching scenario.
Temporal structure in the bursting activity of the leech heartbeat CPG neurons
Neurocomputing, 2007
Neural signatures are cell-specific interspike interval distributions found in bursting neurons. These intraburst signatures have been first described for the neurons of the pyloric CPG of crustacean. Their functional role is still unknown and their presence in other CPG systems has not been shown yet. Modeling has shown that neural signatures can be part of a multicoding strategy in spiking-bursting neurons. In this paper, we analyze the interspike interval distribution of bursting motoneurons of the leech heartbeat CPG. We describe the cell-specific characteristics of the neural signatures found in this circuit and we discuss plausible functional roles. r
J Comp Physiol A Neuroethol Sens Neural Behav Physiol, 2012
The central pattern generator for heartbeat in the medicinal leech, Hirudo generates rhythmic activity conveyed by heart excitor motor neurons in segments 3-18 to coordinate the bilateral tubular hearts and side vessels. We focus on behavior and on the influence of previously undescribed peripheral nerve circuitry. Extracellular recordings from the valve junction where afferent vessels join the heart tube were combined with optical recording of contractions. Action potential bursts at valve junctions occurred in advance of heart tube and afferent vessel contractions. Transections of nerves were performed to reduce the output of the central pattern generator reaching the heart tube. Muscle contractions persisted but with a less regular rhythm despite normal central pattern generator rhythmicity. With no connections between the central pattern generator and heart tube a much slower rhythm became manifest. Heart excitor neuron recordings showed that peripheral activity might contribute to the disruption of centrally entrained contractions. In the model presented, peripheral activity would normally modify the activity actually reaching the muscle. We also propose that the fundamental efferent unit is not a single heart excitor neuron, but rather is a functionally defined unit of about 3 adjacent motor neurons and the peripheral assembly of coupled peripheral oscillators.
Journal of Neurophysiology, 2013
The cardiac ganglion (CG) of Homarus americanus is a central pattern generator that consists of two oscillatory groups of neurons: "small cells" (SCs) and "large cells" (LCs). We have shown that SCs and LCs begin their bursts nearly simultaneously but end their bursts at variable phases. This variability contrasts with many other central pattern generator systems in which phase is well maintained. To determine both the consequences of this variability and how CG phasing is controlled, we modeled the CG as a pair of Morris-Lecar oscillators coupled by electrical and excitatory synapses and constructed a database of 15,000 simulated networks using random parameter sets. These simulations, like our experimental results, displayed variable phase relationships, with the bursts beginning together but ending at variable phases. The model suggests that the variable phasing of the pattern has important implications for the functional role of the excitatory synapses. In networks in which the two oscillators had similar duty cycles, the excitatory coupling functioned to increase cycle frequency. In networks with disparate duty cycles, it functioned to decrease network frequency. Overall, we suggest that the phasing of the CG may vary without compromising appropriate motor output and that this variability may critically determine how the network behaves in response to manipulations. neuronal oscillators; central pattern generator; morris-lecar model; phase relationships THE TIMING OF NEURON FIRING in central pattern generators (CPGs) is often described in terms of phase, the latency from the start of a periodic cycle normalized to cycle period. For example, the pyloric CPG of the stomatogastric ganglion (STG) produces a stereotyped triphasic motor pattern, in which the phase relationships are highly conserved between individuals despite significant variability in the cycle frequency of the motor pattern, as well as in the maximal conductances of intrinsic currents (
From cellular automata model of vagal control of the human right atrium to heart beats patterns
Physica D: Nonlinear Phenomena, 2021
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Three oscillator model of the heartbeat generator
Communications in Nonlinear Science and Numerical Simulation, 2009
The sinoatrial (SA) node is a group of self-oscillatory cells in the heart which beat rhythmically and initiate electric potentials, producing a wave of contraction that travels through the heart resulting in the circulation of blood. The SA node is an inhomogeneous collection of cells which have varying intrinsic frequencies. Experimental measurements of these frequencies have shown that the peripheral cells of the SA node have a higher natural frequency than do the interior cells. This is surprising to us since in 1:1 phase-locked motion of two oscillators of different frequency, the oscillator with the higher frequency leads the other oscillator by a phase angle. If the wave originates in the center of the SA node as one expects, then the interior cells would be leading in a 1:1 phase-locked motion and should therefore have a higher frequency than the peripheral cells. Our objective in this work is to explain this discrepancy between intuition and the measured results, and to determine possible advantages of having cells of lower frequency in the interior. Using a model of the SA node consisting of three coupled phase-only oscillators, we show that increased robustness of synchronized behavior (represented by a larger region of parameter space) comes as a result of the experimentally observed distribution of frequencies in the SA node. Associated with the loss of synchronized behavior is a complicated series of bifurcations called the ''devil's staircase". We use our system to derive a 1D discontinuous map which exhibits the devil's staircase, and we analyze its dynamics.
IEEE Transactions on Biomedical Engineering, 2005
Low-dimensional oscillators are a valuable model for the neuronal activity of isolated neurons. When coupled, the self-sustained oscillations of individual free oscillators are replaced by a collective network dynamics. Here, dynamical features of such a network, consisting of three electronic implementations of the Hindmarsh-Rose mathematical model of bursting neurons, are compared to those of a biological neural motor system, specifically the pyloric CPG of the crustacean stomatogastric nervous system. We demonstrate that the network of electronic neurons exhibits realistic synchronized bursting behavior comparable to the biological system. Dynamical properties were analyzed by injecting sinusoidal currents into one of the oscillators. The temporal bursting structure of the electronic neurons in response to periodic stimulation is shown to bear a remarkable resemblance to that observed in the corresponding biological network. These findings provide strong evidence that coupled nonlinear oscillators realistically reproduce the network dynamics experimentally observed in assemblies of several neurons.
Coexistence of Tonic Spiking Oscillations in a Leech Neuron Model
Journal of Computational Neuroscience, 2005
The leech neuron model studied here has a remarkable dynamical plasticity. It exhibits a wide range of activities including various types of tonic spiking and bursting. In this study we apply methods of the qualitative theory of dynamical systems and the bifurcation theory to analyze the dynamics of the leech neuron model with emphasis on tonic spiking regimes. We show that the model can demonstrate bi-stability, such that two modes of tonic spiking coexist. Under a certain parameter regime, both tonic spiking modes are represented by the periodic attractors. As a bifurcation parameter is varied, one of the attractors becomes chaotic through a cascade of period-doubling bifurcations, while the other remains periodic. Thus, the system can demonstrate co-existence of a periodic tonic spiking with either periodic or chaotic tonic spiking. Pontryagin’s averaging technique is used to locate the periodic orbits in the phase space.