Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Expression and function of the neurotrophic factors GDF5 and GDNF in the nigrostriatal system during development and in rat models of Parkinson's disease

Growth/differentiation factor 5 (GDF5) and glial cell line-derived neurotrophic factor (GDNF) are neurotrophic factors that promote the survival of midbrain dopaminergic neurons in vitro and in vivo. Both factors have potent neurotrophic and neuroprotective effects in rat models of Parkinson's disease (PD), and may represent promising new therapies for PD. The aim of the present study was to investigate the endogenous expression and function of GDF5 and GDNF in the nigrostriatal dopaminergic system during development and in rat models of PD. Examination of the temporal expression patterns of endogenous GDF5, GDNF, and their respective receptors, in the developing and adult nigrostriatal dopaminergic system suggest that these factors play important roles in promoting the survival and maturation of midbrain dopaminergic neurons during the period of postnatal programmed cell death. The relative levels of GDF5 and GDNF mRNAs in the midbrain and striatum, and their individual temporal expression patterns during development, suggest that their modes of actions are quite distinct in vivo. Furthermore, the sustained expression of GDF5, GDNF, and their receptors into adulthood suggest roles for these factors in the continued support and maintenance of mature nigrostriatal dopaminergic neurons. The present study found that endogenous GDF5, GDNF, and their receptors are differentially expressed in two 6-hydroxydopamine-induced lesion adult rat models of PD. In both terminal and axonal lesion models of PD, GDF5 mRNA levels in the striatum increased at 10 days post-lesion, while GDNF mRNA levels in the nigrostriatal system decreased at 10 and 28 days post-lesion. Thus, despite the fact that exogenous GDF5 and GDNF have similar effects on midbrain dopaminergic neurons in vitro and in vivo, their endogenous responses to a neurotoxic injury are quite distinct. These results highlight the importance of studying the temporal dynamic changes in neurotrophic factor expression during development and in animal models of PD.

Investigations into the cellular and molecular changes in the amygdala in models of temporal lobe epilepsy and maternal immune activation

The amygdala is a limbic structure that is involved in many of our emotions and processing of these emotions such as fear, anger and pleasure. Conditions such as anxiety, autism, and also epilepsy, have been linked to abnormal functioning of the amygdala, owing to improper neurodevelopment or damage. This thesis investigated the cellular and molecular changes in the amygdala in models of temporal lobe epilepsy (TLE) and maternal immune activation (MIA). The kainic acid (KA) model of temporal lobe epilepsy (TLE) was used to induce Ammon’s-horn sclerosis (AHS) and to investigate behavioural and cytoarchitectural changes that occur in the amygdala related to Neuropeptide Y1 receptor expression. Results showed that KA-injected animals showed increased anxiety-like behaviours and displayed histopathological hallmarks of AHS including CA1 ablation, granule cell dispersion, volume reduction and astrogliosis. Amygdalar volume and neuronal loss was observed in the ipsilateral nuclei which was accompanied by astrogliosis. In addition, a decrease in Y1 receptor expressing cells in the ipsilateral CA1 and CA3 sectors of the hippocampus, ipsi- and contralateral granule cell layer of the dentate gyrus and ipsilateral central nucleus of the amygdala was found, consistent with a reduction in Y1 receptor protein levels. The results suggest that plastic changes in hippocampal and/or amygdalar Y1 receptor expression may negatively impact anxiety levels. Gamma-aminobutyric acid (GABA) is the main inhibitory neurotransmitter in the brain and tight regulation and appropriate control of GABA is vital for neurochemical homeostasis. GABA transporter-1 (GAT-1) is abundantly expressed by neurones and astrocytes and plays a key role in GABA reuptake and regulation. Imbalance in GABA homeostasis has been implicated in epilepsy with GAT-1 being an attractive pharmacological target. Electron microscopy was used to examine the distribution, expression and morphology of GAT-1 expressing structures in the amygdala of the TLE model. Results suggest that GAT-1 was preferentially expressed on putative axon terminals over astrocytic processes in this TLE model. Myelin integrity was examined and results suggested that in the TLE model myelinated fibres were damaged in comparison to controls. Synaptic morphology was studied and results suggested that asymmetric (excitatory) synapses occurred more frequently than symmetric (inhibitory) synapses in the TLE model in comparison to controls. This study illustrated that the amygdala undergoes ultrastructural alterations in this TLE model. Maternal immune activation (MIA) is a risk factor for neurodevelopmental disorders such as autism, schizophrenia and also epilepsy. MIA was induced at a critical window of amygdalar development at E12 using bacterial mimetic lipopolysaccharide (LPS). Results showed that MIA activates cytokine, toll-like receptor and chemokine expression in the fetal brain that is prolonged in the postnatal amygdala. Inflammation elicited by MIA may prime the fetal brain for alterations seen in the glial environment and this in turn have deleterious effects on neuronal populations as seen in the amygdala at P14. These findings may suggest that MIA induced during amygdalar development may predispose offspring to amygdalar related disorders such as heightened anxiety, fear impairment and also neurodevelopmental disorders.