Real-time biomimetic Central Pattern Generators in an FPGA for hybrid experiments

This investigation of the leech heartbeat neural network system led to the development of a low resources, real-time, biomimetic digital hardware for use in hybrid experiments. The leech heartbeat neural network is one of the simplest central pattern generators (CPG). In biology, CPG provide the rhythmic bursts of spikes that form the basis for all muscle contraction orders (heartbeat) and locomotion (walking, running, etc.). The leech neural network system was previously investigated and this CPG formalized in the Hodgkin–Huxley neural model (HH), the most complex devised to date. However, the resources required for a neural model are proportional to its complexity. In response to this issue, this article describes a biomimetic implementation of a network of 240 CPGs in an FPGA (Field Programmable Gate Array), using a simple model (Izhikevich) and proposes a new synapse model: activity-dependent depression synapse. The network implementation architecture operates on a single computation core. This digital system works in real-time, requires few resources, and has the same bursting activity behavior as the complex model. The implementation of this CPG was initially validated by comparing it with a simulation of the complex model. Its activity was then matched with pharmacological data from the rat spinal cord activity. This digital system opens the way for future hybrid experiments and represents an important step toward hybridization of biological tissue and artificial neural networks. This CPG network is also likely to be useful for mimicking the locomotion activity of various animals and developing hybrid experiments for neuroprosthesis development

A Mechanism of Co-Existence of Bursting and Silent Regimes of Activities of a Neuron

The co-existence of bursting activity and silence is a common property of various neuronal models. We describe a novel mechanism explaining the co-existence of and the transition between these two regimes. It is based on the specific homoclinic and Andronov-Hopf bifurcations of the hyper- and depolarized steady states that determine the co-existence domain in the parameter space of the leech heart interneuron models: canonical and simplified. We found that a sub-critical Andronov-Hopf bifurcation of the hyperpolarized steady state gives rise to small amplitude sub-threshold oscillations terminating through the secondary homoclinic bifurcation. Near the corresponding boundary the system can exhibit long transition from bursting oscillations into silence, as well as the bi-stability where the observed regime is determined by the initial state of the neuron. The mechanism found is shown to be generic for the simplified 4D and the original 14D leech heart interneuron models

Oscillatory behaviors in pharmacologically isolated heart interneurons from the medicinal leech

Abstract The central motor pattern for heartbeat in the medicinal leech is based upon the alternating bursting activity of mutually inhibitory pairs of heart interneurons (HNs). When pharmacologically isolated, these neurons spike tonically. Using a canonical model of an HN cell (Nadim et al., J. Comput. Neurosci. 2 (1995) 215}235) as a starting point, we generated three models, possessing di!erent subsets of the currents exhibited by HN cells, that are capable of autonomous bursting behavior. These three models represent three di!erent experimentally testable mechanisms that make HN cells potentially capable of bursting or generating slow oscillations under di!erent ionic and pharmacological conditions. The three di!erent mechanisms for producing bursting involve the interplay of: (1) fast Na> current, leakage current and outward currents, (2) rapidly inactivating low-threshold Ca> current, leakage current and outward currents, and (3) slowly inactivating low-threshold Ca> current, leakage current and outward currents

The Role of Plasma Membrane ATPase Pumps in the Regulation of Rhythmic Activity in Electrically Excitable Cells

Membrane bound ion pumps have long been studied in a housekeeping role, and it is well known that they play a major part in creating the ionic gradients which determine the electrical excitability in a cell. Recent work has begun to highlight other, more direct roles for ion pumps in rhythm generation and information processing. As many pumps obtain energy for active ion transport from adenosine triphosphate (ATP) hydrolysis, they can exchange ions in an electrically asymmetric manner, generating an outward current, which along with ion channel currents, drives the membrane potential of the cell. Membrane potential is a major determining characteristic for how information is transferred between neurons, and so in persistently active excitable cells, pumps can provide a considerable contribution to neuron dynamics. Specialized networks of neurons and non-neural cells which drive rhythmic behaviors such as breathing and locomotion, must robustly produce useful patterns for the animal under dynamic behavioral goals in a highly variable environment. Here we will focus on two well-studied classes of ATPase pumps (the plasma membrane calcium ATPase pump (PMCA) and the sodium-potassium ATPase pump (Na+/K+ pump)) and investigate the role of these pumps in two rhythm generating biological subsystems with a combination of modeling and experimental approaches. In a model of a leech heartbeat central pattern generator, we demonstrate how the neuromodulator myomodulin can regulate the temporal properties of rhythm generation through effects on the hyperpolarization-activated current and the Na+/K+ pump current, and discuss the benefits of modulators which target multiple currents. With this model, we also show how synaptic inhibition can support a functional pattern when pump current is downregulated. Then, in a model of interstitial cells of Cajal (ICC) in the muscular syncytium of the intestinal walls, we demonstrate that due to the importance of complex intracellular calcium oscillations in the generation of ICC rhythms, the PMCA pump can play a major role in regulating the temporal properties of rhythm generation. We discuss rhythm generation mechanisms in both systems and predict parameter domains of multistability which correspond to both functional and pathological states of rhythm generation

Mechanisms of the Coregulation of Multiple Ionic Currents for the Control of Neuronal Activity

An open question in contemporary neuroscience is how neuromodulators coregulate multiple conductances to maintain functional neuronal activity. Neuromodulators enact changes to properties of biophysical characteristics, such as the maximal conductance or voltage of half-activation of an ionic current, which determine the type and properties of neuronal activity. We apply dynamical systems theory to study the changes to neuronal activity that arise from neuromodulation. Neuromulators can act on multiple targets within a cell. The coregulation of mulitple ionic currents extends the scope of dynamic control on neuronal activity. Different aspects of neuronal activity can be independently controlled by different currents. The coregulation of multiple ionic currents provides precise control over the temporal characteristics of neuronal activity. Compensatory changes in multiple ionic currents could be used to avoid dangerous dynamics or maintain some aspect of neuronal activity. The coregulation of multiple ionic currents can be used as bifurcation control to ensure robust dynamics or expand the range of coexisting regimes. Multiple ionic currents could be involved in increasing the range of dynamic control over neuronal activity. The coregulation of multiple ionic currents in neuromodulation expands the range over which biophysical parameters support functional activity

The effects of varying the timing of inputs on a neural oscillator

The gastric mill network of the stomatogastric ganglion of the crab Cancer borealis is comprised of a set of neurons that require modulatory input from outside the stomatogastric ganglion and input from the pyloric network of the animal in order to oscillate. Here we study how the frequency of the gastric mill network is determined when it receives rhythmic input from two different sources but where the timing of these inputs may differ. We find that over a certain range of the time difference one of the two rhythmic inputs plays no role what so ever in determining the network frequency, while in another range, both inputs work together to determine the frequency. The existence and stability of periodic solutions to model sets of equations are obtained analytically using geometric singular perturbation theory. The results are validated through numerical simulations. Comparisons to experiments are also presented

A unified approach to linking experimental, statistical and computational analysis of spike train data

A fundamental issue in neuroscience is how to identify the multiple biophysical mechanisms through which neurons generate observed patterns of spiking activity. In previous work, we proposed a method for linking observed patterns of spiking activity to specific biophysical mechanisms based on a state space modeling framework and a sequential Monte Carlo, or particle filter, estimation algorithm. We have shown, in simulation, that this approach is able to identify a space of simple biophysical models that were consistent with observed spiking data (and included the model that generated the data), but have yet to demonstrate the application of the method to identify realistic currents from real spike train data. Here, we apply the particle filter to spiking data recorded from rat layer V cortical neurons, and correctly identify the dynamics of an slow, intrinsic current. The underlying intrinsic current is successfully identified in four distinct neurons, even though the cells exhibit two distinct classes of spiking activity: regular spiking and bursting. This approach – linking statistical, computational, and experimental neuroscience – provides an effective technique to constrain detailed biophysical models to specific mechanisms consistent with observed spike train data.Published versio

Modeling the Intersegmental Coordination of Heart Motor Neurons in the Medicinal Leech

We constructed a model of the coordination of segmental heart motor neurons driving blood circulation in leeches. The heart motor neuron models were conductance-based; conductances of voltage-gated and synaptic currents were adjusted to match the firing pattern of heart motor neurons from the living system. Each motor neuron receives a specific pattern of inhibitory input from rhythmic premotor heart interneurons and translates this spatiotemporal pattern into the fictive heartbeat motor pattern. The temporal pattern of synaptic input to the model was derived from extracellularly recorded spikes of the premotor heart interneurons. We focused on determining the components necessary to produce side-to-side asymmetry in the motor pattern: motor neurons on one side fire nearly in synchrony (synchronous coordination), while on the other they fire in a rear-to-front progression (peristaltic coordination). The model reproduces the general trends in phasing and was used to investigate the effective contribution of several synaptic and cellular properties of the motor neurons. The spatial and temporal pattern of premotor synaptic input, the electrical coupling between the segmental motor neurons, intra-burst, short-term synaptic plasticity of the synaptic inputs, and the axonal conduction delays all were integrated with the intrinsic membrane properties to influence intersegmental phasing.Ph.D.Committee Chair: Robert J. Butera, PhD; Committee Member: Lena Ting, PhD; Committee Member: Nael McCarty, PhD; Committee Member: Raymond Dingledine, PhD; Committee Member: Robert H. Lee, PhD; Committee Member: Ronald L. Calabrese, Ph

The control of frequency of a conditional oscillator simultaneously subjected to multiple oscillatory inputs

A conditional oscillator is one that requires input to oscillate. An example of such is the gastric mill network of the stomatogastric ganglion of the crab Cancer borealis which requires modulatory input from outside the stomatogastric ganglion and fast input from the pyloric network of the animal in order to become active. This dissertation studies how the frequency of the gastric mill network is determined when it is simultaneously subjected to two different rhythmic inputs whose timing may be mismatched. We derive a mathematical model of the gastric mill network and deduce that the difference in timing between the pyloric and modulatory inputs is crucial in determining what effect it will have on the frequency of the gastric mill network. Over a certain range of the time mismatch, the pyloric input plays no role in determining the network frequency, while in another range of the time mismatch, both inputs work together to determine the frequency. The existence and stability of periodic solutions to the modeling set of equations are obtained analytically using geometric singular perturbation theory and an analytic approximation of the frequency is obtained. The results are validated through numerical simulations of the model and are shown to extend to a detailed Hodgkin-Huxley type compartmental model of the gastric mill network. Comparisons to experiments are also presented

Nonlinear synchrony dynamics of neuronal bursters

We study the appearance of a novel phenomenon for coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage through a Bautin (codimension two degenerate Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf bifurcation at the onset of repetitive spiking while the end of burst occurs via a fold limit cycle bifurcation. We study synchronization behavior of two Bautin-type elliptic bursters for a linear direct coupling scheme as well as demonstrating its presence in an approximation of gap-junction and synaptic coupling. We also find similar behaviour in system consisted of three and four Bautin-type elliptic bursters. We note that higher order terms in the normal form that do not affect the behavior of a single burster can be responsible for changes in synchrony pattern; more precisely, we find within-burst synchrony changes associated with a turning point in the spontaneous spiking frequency (frequency transition). We also find multiple synchrony changes in similar system by incorporating multiple frequency transitions. To explain the phenomenon we considered a burst-synchronized constrained model and a bifurcation analysis of the this reduced model shows the existence of the observed within-burst synchrony states. Within-burst synchrony change is also found in the system of mutually delaycoupled two Bautin-type elliptic bursters with a constant delay. The similar phenomenon is shown to exist in the mutually-coupled conductance-based Morris-Lecar neuronal system with an additional slow variable generating elliptic bursting. We also find within-burst synchrony change in linearly coupled FitzHugh-Rinzel 2 3 elliptic bursting system where the synchrony change occurs via a period doubling bifurcation. A bifurcation analysis of a burst-synchronized constrained system identifies the periodic doubling bifurcation in this case. We show emergence of spontaneous burst synchrony cluster in the system of three Hindmarsh-Rose square-wave bursters with nonlinear coupling. The system is found to change between the available cluster states depending on the stimulus. Lyapunov exponents of the burst synchrony states are computed from the corresponding variational system to probe the stability of the states. Numerical simulation also shows existence of burst synchrony cluster in the larger network of such system.Exeter Research Scholarship