A Neural Model of Demyelination of the Mouse Spinal Cord

This paper presents a neural network model of demyelination of the mouse motor pathways, coupled to a central pattern generation (CPG) model for quadruped walking. Demyelination is the degradation of the myelin layer covering the axons which can be caused by several neurodegenerative autoimmune diseases such as multiple sclerosis. We use this model - to our knowledge first of its kind - to investigate the locomotion deficits that appear following demyelination of axons in the spinal cord. Our model meets several physiological and behavioral results and predicts that whereas locomotion can still occur at high percentages of demyelination damage, the distribution and location of the lesion are the most critical factors for the locomotor performance

Coordinated motor activity in simulated spinal networks emerges from simple biologically plausible rules of connectivity

The spinal motor circuits of the Xenopus embryo have been simulated in a 400- neuron network. To explore the consequences of differing patterns of synaptic connectivity within the network for the generation of the motor rhythm, a system of biologically plausible rules was devised to control synapse formation by three parameters. Each neuron had an intrinsic probability of synapse formation ( P-soma, specified by a space constant.) that was a monotonically decreasing function of its soma location in the rostro- caudal axis of the simulated network. The neurons had rostral and caudal going axons of specified length ( L-axon) associated with a probability of synapse formation ( P-axon). The final probability of synapse formation was the product of P-soma and P-axon. Realistic coordinated activity only occurred when L-axon and the probabilities of interconnection were sufficiently high. Increasing the values of the three network parameters reduced the burst duration, cycle period, and rostro- caudal delay and increased the reliability with which the network functioned as measured by the coefficient of variance of these parameters. Whereas both L-axon and P-axon had powerful and consistent effects on network output, the effects of lambda on burst duration and rostro- caudal delay were more variable and depended on the values of the other two parameters. This network model can reproduce the rostro- caudal coordination of swimming without using coupled oscillator theory. The changes in network connectivity and resulting changes in activity explored by the model mimic the development of the motor pattern for swimming in the real embryo

Longitudinal neuronal organization and coordination in a simple vertebrate: a continuous, semi-quantitative computer model of the central pattern generator for swimming in young frog tadpoles

When frog tadpoles hatch their swimming requires co-ordinated contractions of trunk muscles, driven by motoneurons and controlled by a Central Pattern Generator (CPG). To study this co-ordination we used a 3.5 mm long population model of the young tadpole CPG with continuous distributions of neurons and axon lengths as estimated anatomically. We found that: (1) alternating swimming-type activity fails to self-sustain unless some excitatory interneurons have ascending axons, (2) a rostro-caudal (R-C) gradient in the distribution of excitatory premotor interneurons with short axons is required to obtain the R-C gradient in excitation and resulting progression of motoneuron firing necessary for forward swimming, (3) R-C delays in motoneuron firing decrease if excitatory motoneuron to premotor interneuron synapses are present, (4) these feedback connections and the electrical synapses between motoneurons synchronise motoneuron discharges locally, (5) the above findings are independent of the detailed membrane properties of neurons

Dynamical systems and their applications in neuroscience

This thesis deals with dynamical systems, numerical software for the continuation study of dynamical systems, and some important neurobiological applications. First there are two introductory chapters, in which a background is given in dynamical systems and neuroscience. We elucidate what the problems are with some existing classifications of neural models, and suggest an improved version. We introduce the Phase Response Curve (PRC), which is a curve that describes the effect of an input on a periodic orbit. We derive an efficient method to compute this PRC. The extended functionalities of MatCont, a software package for the study of dynamical systems and their bifurcations, are explained: the user can compute the PRC of a limit cycle and its derivative, he can detect and continue homoclinic bifurcations, initiate these curves from different bifurcations and detect many codim 2 bifurcations on these curves. The speed of the software was improved by introducing C-code among the matlab-routines. We have for the first time made a complete bifurcation diagram of the Morris-Lecar neural model. We show that PRCs can be used to determine the synchronizing and/or phase-locking abilities of neural networks, and how the connection delay plays a role in this, and demonstrate some phenomena to do with PRCs and bifurcations. In collaboration with biologists at the University of Bristol, we have built detailed models of the neurons in the spinal cord of the hatchling Xenopus laevis. The biological background and the equations and parameters for the models of individual neurons and synapses are listed elaborately. These models are used to construct biologically realistic networks of neurons. The first network was used to simulate the swimming behaviour of the tadpole and to show that to disregard some important differences in the models for different neurons, will result in breakdown of the good network output. Then we have used the individual models to study a hypothesis regarding synaptogenesis, which states that the specificity in connection between neurons could be purely based on the anatomical organization of the neurons, instead of the ability of growing synapses to make a distinction between the different neurons

Locomotor patterns and persistent activity in self-organizing neural models

The thesis investigates principles of self-organization that may account for the observed structure and behaviour of neural networks that generate locomotor behaviour and complex spatiotemporal patterns such as spiral waves, metastable states and persistent activity. This relates to the general neuroscience problem of finding the correspondence between the structure of neural networks and their function. This question is both extremely important and difficult to answer because the structure of a neural network defines a specific type of neural dynamics which underpins some function of the neural system and also influences the structure and parameters of the network including connection strengths. This loop of influences results in a stable and reliable neural dynamics that realises a neural function. In order to study the relationship between neural network structure and spatiotemporal dynamics, several computational models of plastic neural networks with different architectures are developed. Plasticity includes both modification of synaptic connection strengths and adaptation of neuronal thresholds. This approach is based on a consideration of general modelling concepts and focuses on a relatively simple neural network which is still complex enough to generate a broad spectrum of spatio-temporal patterns of neural activity such as spiral waves, persistent activity, metastability and phase transitions. Having considered the dynamics of networks with fixed architectures, we go on to consider the question of how a neural circuit which realizes some particular function establishes its architecture of connections. The approach adopted here is to model the developmental process which results in a particular neural network structure which is relevant to some particular functionality; specifically we develop a biologically realistic model of the tadpole spinal cord. This model describes the self-organized process through which the anatomical structure of the full spinal cord of the tadpole develops. Electrophysiological modelling shows that this architecture can generate electrical activity corresponding to the experimentally observed swimming behaviour