Analysis and modelling of the PY complex in the pyloric circuit of the crab stomatogastric ganglion

PhD ThesisCentral pattern generators (CPGs) are neural circuits that control rhythmic motor patterns such as walking running and swallowing. Injuries can sever the spinal cord or conditions such as Huntington's disease and Parkinson's disease can damage nerves from the brain that control CPGs. Understanding the connectivity of neural circuits has proved insu cient to understand the dynamics of such circuits. Neuromodulators and neurohormones can di erentially a ect every connection in neural circuits and di erent circuits are a ected in very di erent ways. The resulting complexity of such systems make them very di cult to study but research is greatly facilitated by the use of model organisms and computational models. The crustacean stomatogastric ganglion (STG) has been used as a model system for many years. Its relative simplicity and accessibility to neurons makes it an ideal system for the study of neural interaction, CPGs and the e ect of neuromodulators on neural systems. The e ect of dopamine on the pyloric CPG of the crab STG was recorded using voltage sensitive dye imaging and electrophysiological techniques. To analyse voltage sensitive dye (VSD) imaging data a heuristic method was devised that uses the timing of the activity plateaus of neurons for the estimation of the dynamics of the temporal relationship of the neurons' activities. MATLABR was used to create a Hodgkin-Huxley based model of the pyloric constrictor pyloric dilator neurons (PDs) with parameters that could capture the dynamics of neuromodulation. The MATLABR model includes two compartments, the soma and the axon, for the anterior burster neuron, the lateral pyloric neurons (LPs), two PDs and ve individual pyloric constrictor neurons (PYs). By di erentially changing the values of the model synapses, the model is able to reproduce the de-synchronisation of the pyloric constrictor neurons as was observed experimentally i on the dea erented stomatogastric nervous system. Existing models model PYs and PDs as single neurons. These models are unable to show the desynchronising e ect of dopamine on multiple neurons of the same type. The model created for this research is able to re ect the e ect of neuromodulation on the complete circuit by allowing parameters of synapses between neurons of the same type to be adjusted di erentially, re ecting the biological system more accurately

Intermediate Stable Phase Locked States In Oscillator Networks

The study of nonlinear oscillations is important in a variety of physical and biological contexts (especially in neuroscience). Synchronization of oscillators has been a problem of interest in recent years. In networks of nearest neighbor coupled oscillators it is possible to obtain synchrony between oscillators, but also a variety of constant phase shifts between 0 and pi. We coin these phase shifts intermediate stable phase-locked states. In neuroscience, both individual neurons and populations of neurons can behave as complex nonlinear oscillators. Intermediate stable phase-locked states are shown to be obtainable between individual oscillators and populations of identical oscillators.These intermediate stable phase-locked states may be useful in the construction of central pattern generators: autonomous neural cicuits responsible for motor behavior. In large chains and two-dimenional arrays of oscillators, intermediate stable phase-locked states provide a mechanism to produce waves and patterns that cannot be obtained in traditional network models. A particular pattern of interest is known as an anti-wave. This pattern corresponds to the collision of two waves from opposite ends of an oscillator chain. This wave may be relevant in the spinal central pattern generators of various fish. Anti-wave solutions in both conductance based neuron models and phase oscillator models are analyzed. It is shown that such solutions arise in phase oscillator models in which the nonlinearity (interaction function) contains both higher order odd and even Fourier modes. These modes are prominent in pairs of synchronous oscillators which lose stability in a supercritical pitchfork bifurcation

Efficient Numerical Population Density Techniques with an Application in Spinal Cord Modelling

MIIND is a neural simulator which uses an innovative numerical population density technique to simulate the behaviour of multiple interacting populations of neurons under the influence of noise. Recent efforts have produced similar techniques but they are often limited to a single neuron model or type of behaviour. Extensions to these require a great deal of further work and specialist knowledge. The technique used in MIIND overcomes this limitation by being agnostic to the underlying neuron model of each population. However, earlier versions of MIIND still required a high level of technical knowledge to set up the software and involved an often time-consuming manual pre-simulation process. It was also limited to only two-dimensional neuron models. This thesis presents the development of an alternative population density technique, based on that already in MIIND, which reduces the pre-simulation step to an automated process. The new technique is much more flexible and has no limit on the number of time-dependent variables in the underlying neuron model. For the first time, the population density over the state space of the Hodgkin-Huxley neuron model can be observed in an efficient manner on a single PC. The technique allows simulation time to be significantly reduced by gracefully degrading the accuracy without losing important behavioural features. The MIIND software itself has also been simplified, reducing technical barriers to entry, so that it can now be run from a Python script and installed as a Python module. With the improved usability, a model of neural populations in the spinal cord was simulated in MIIND. It showed how afferent signals can be integrated into common reflex circuits to produce observed patterns of muscle activation during an isometric knee extension task. The influence of proprioception in motor control is not fully understood as it can be both task and subject-specific. The results of this study show that afferent signals have a significant effect on sub-maximal muscle contractions even when the limb remains static. Such signals should be considered when developing methods to improve motor control in activities of daily living via therapeutic or mechanical means

Bifurcation Analysis of Large Networks of Neurons

The human brain contains on the order of a hundred billion neurons, each with several thousand synaptic connections. Computational neuroscience has successfully modeled both the individual neurons as various types of oscillators, in addition to the synaptic coupling between the neurons. However, employing the individual neuronal models as a large coupled network on the scale of the human brain would require massive computational and financial resources, and yet is the current undertaking of several research groups. Even if one were to successfully model such a complicated system of coupled differential equations, aside from brute force numerical simulations, little insight may be gained into how the human brain solves problems or performs tasks. Here, we introduce a tool that reduces large networks of coupled neurons to a much smaller set of differential equations that governs key statistics for the network as a whole, as opposed to tracking the individual dynamics of neurons and their connections. This approach is typically referred to as a mean-field system. As the mean-field system is derived from the original network of neurons, it is predictive for the behavior of the network as a whole and the parameters or distributions of parameters that appear in the mean-field system are identical to those of the original network. As such, bifurcation analysis is predictive for the behavior of the original network and predicts where in the parameter space the network transitions from one behavior to another. Additionally, here we show how networks of neurons can be constructed with a mean-field or macroscopic behavior that is prescribed. This occurs through an analytic extension of the Neural Engineering Framework (NEF). This can be thought of as an inverse mean-field approach, where the networks are constructed to obey prescribed dynamics as opposed to deriving the macroscopic dynamics from an underlying network. Thus, the work done here analyzes neuronal networks through both top-down and bottom-up approaches

Rhythmic Oscillations of Excitatory Bursting Hodkin-Huxley Neuronal Network with Synaptic Learning

Rhythmic oscillations of neuronal network are actually kind of synchronous behaviors, which play an important role in neural systems. In this paper, the properties of excitement degree and oscillation frequency of excitatory bursting Hodkin-Huxley neuronal network which incorporates a synaptic learning rule are studied. The effects of coupling strength, synaptic learning rate, and other parameters of chemical synapses, such as synaptic delay and decay time constant, are explored, respectively. It is found that the increase of the coupling strength can weaken the extent of excitement, whereas increasing the synaptic learning rate makes the network more excited in a certain range; along with the increasing of the delay time and the decay time constant, the excitement degree increases at the beginning, then decreases, and keeps stable. It is also found that, along with the increase of the synaptic learning rate, the coupling strength, the delay time, and the decay time constant, the oscillation frequency of the network decreases monotonically