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The plasma membrane electrical activities of neurons that secrete gonadotropin releasing hormone (GnRH), referred to as GnRH neurons hereafter, have been studied extensively. A couple of mathematical models have been developed previously to explain different aspects of these activities including spontaneous spiking and responses to stimuli such as current injections, GnRH, thapsigargin (Tg) and apamin. The goal of this paper is to develop one single, minimal model that accounts for the experimental results reproduced by previously existing models and results that were not accounted for by these models. The latter includes two types of membrane potential bursting mechanisms and the associated calcium oscillations in the cytosol. One of them has not been reported in experimental literatures on GnRH neurons and is thus regarded as a model prediction. Other improvements achieved in this model include the incorporation of a more detailed description of calcium dynamics in a three dimensional cell body with the ion channels evenly distributed on the cell surface. Although the model is mainly based on data collected in cultured GnRH cell lines, we show that it is capable of explaining some properties of GnRH neurons observed in several of other preparations including mature GnRH neurons in hypothalamic slices. One potential explanation is suggested. A phenomenological reduction of this model into a simplified form is presented. The simplified model will facilitate the study of the roles of plasma membrane electrical activities on the pulsatile release of GnRH by these neurons when it is coupled with a model of pulsatile GnRH release based on the autoregulation mechanism.

The plasma membrane electrical activities of neurons that secrete gonadotropin releasing hormone (GnRH), referred to as GnRH neurons hereafter, have been studied extensively. A couple of mathematical models have been developed previously to explain different aspects of these activities including spontaneous spiking and responses to stimuli such as current injections, GnRH, thapsigargin (Tg) and apamin. The goal of this paper is to develop one single, minimal model that accounts for the experimental results reproduced by previously existing models and results that were not accounted for by these models. The latter includes two types of membrane potential bursting mechanisms and the associated calcium oscillations in the cytosol. One of them has not been reported in experimental literatures on GnRH neurons and is thus regarded as a model prediction. Other improvements achieved in this model include the incorporation of a more detailed description of calcium dynamics in a three dimensional cell body with the ion channels evenly distributed on the cell surface. Although the model is mainly based on data collected in cultured GnRH cell lines, we show that it is capable of explaining some properties of GnRH neurons observed in several of other preparations including mature GnRH neurons in hypothalamic slices. One potential explanation is suggested. A phenomenological reduction of this model into a simplified form is presented. The simplified model will facilitate the study of the roles of plasma membrane electrical activities on the pulsatile release of GnRH by these neurons when it is coupled with a model of pulsatile GnRH release based on the autoregulation mechanism. / Science, Faculty of / Mathematics, Department of / Graduate

Axons are injured after stroke, spinal cord injury, or neurodegenerative disease such as ALS. Most axons do not regenerate. A recent report suggests that not all neurons are poor regenerators, but rather a small subset can regenerate robustly. What intrinsic property of these regenerating neurons allows them to regenerate, but not their neighbors, remains a mystery. This subtype-specific regeneration has also been observed in Drosophila larvae sensory neurons. We exploited this powerful genetic system to unravel the intrinsic mechanism of subtype-specific neuron regeneration. We found that neuron bursting activity after axotomy correlates with regeneration ability. Furthermore, neuron bursting activity is necessary for regeneration of a regenerative neuron subtype, and sufficient for regeneration of a non-regenerative neuron subtype. This optogenetically-induced regeneration is dependent on a bursting pattern, not simply overall activity increase. We conclude that neuron bursting activity is an intrinsic mechanism of subtype-specific regeneration. We then discovered through a reverse genetic screen that an L-type voltage gated calcium channel (VGCC) promotes neuron bursting and subsequent regeneration. This VGCC has high expression in the regenerative neuron and weak expression in the non-regenerative neuron. This suggests that VGCC expression level is the molecular mechanism of subtype-specific neuron regeneration. Together, our findings identify a cellular and molecular intrinsic mechanism of subtype-specific regeneration, which is why some neurons are able to regenerate while the majority of neurons do not. Perhaps VGCC activation or neuron activity pattern modulation could be used therapeutically for patients with nerve injury.

In 2007, Modolo and colleagues derived a population density equation for a population of Izhekevich neurons. This population density equation can describe oscillations in the brain that occur in Parkinson’s disease. Numerical simulations of the population density equation showed bursting behaviour even though the individual neurons had parameters that put them in the tonic firing regime. The bursting comes from neuron interactions but the mechanism producing this behaviour was not clear. In this thesis we study numerical behaviour of the population density equation and then use a combination of analysis and numerical simulation to analyze the basic qualitative behaviour of the population model by means of a simplifying assumption: that the initial density is a Dirac function and all neurons are identical, including the number of inputs they receive, so they remain as a point mass over time. This leads to a new ODE model for the population. For the new ODE system, we define a Poincaré map and then to describe and analyze it under conditions on model parameters that are met by the typical values adopted by Modolo and colleagues. We show that there is a unique fixed point for this map and that under changes in a bifurcation parameter, the system transitions from fast tonic firing, through an interval where bursting occurs, the number of spikes decreasing as the bifurcation parameter increases, and finally to slow tonic firing. / Graduate

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yes / River morphological dynamics are complex phenomena in natural and environmental flows. In particular, the sediment transport around braid mid-channel bars has not gained enough understanding from previous research. The effect of submergence ratio on the turbulence behavior in the proximity of the bar has been investigated in this study. The spatial distribution of turbulent flow in the proximity of bar has been studied by plotting the depth-averaged two-dimensional contours of turbulent kinetic energy. The high value of TKE has been observed in regions just downstream from the bar. It is due to the vortex shedding occurring in that region. The interaction of sweep and ejection events have been analyzed using the parameter Dominance Function obtained from the ratio of occurrence probability of ejection events to the occurrence probability of sweep events. This outcome indicates that the depth averaged parameter Dominance Function has successfully predicted the high scouring region which makes it an ideal parameter for analyzing the scour phenomena in real-world water management projects. The high scouring zone lies in the close proximity of the bar. This shows that the scouring effect from the bar is limited to its close region. The magnitude of scouring occurring at the upstream region of the bar also increases with the increment of submergence ratio. The relationship of quadrant event inclination angles with the sediment transport occurring in the proximity of bar has been also studied, where an Angle Ratio parameter has been utilized for linking the bed elevation change with the inclination angle. The results indicate that the AR parameter has been successfully tested in this study to show its competence to represent the turbulent burst-induced bed sedimentation and scouring. / The author has confirmed that no changes were made to the content of this proof on publication, although the paper is watermarked uncorrected proof.

Yes / This paper reviews existing studies relating to the assessment of sediment concentration profiles within various flow conditions due to their importance in representing pollutant propagation. The effects of sediment particle size, flow depth, and velocity were considered, as well as the eddy viscosity and Rouse number influence on the drag of the particle. It is also widely considered that there is a minimum threshold velocity required to increase sediment concentration within a flow above the washload. The bursting effect has also been investigated within this review, in which it presents the mechanism for sediment to be entrained within the flow at low average velocities. A review of the existing state-of-the-art literature has shown there are many variables to consider, i.e., particle density, flow velocity, and turbulence, when assessing the suspended sediment characteristics within flow; this outcome further evidences the complexity of suspended sediment transport modelling.

Stochasticity is a ubiquitous feature of cellular processes such as gene expression that can give rise to phenotypic differences for genetically identical cells. Understanding how the underlying biochemical reactions give rise to variations in mRNA/protein levels is thus of fundamental importance to diverse cellular processes. Recent technological developments have enabled single-cell measurements of cellular macromolecules which can shed new light on processes underlying gene expression. Correspondingly, there is a need for the development of theoretical tools to quantitatively model stochastic gene expression and its consequences for cellular processes. In this dissertation, we address this need by developing general stochastic models of gene expression. By mapping the system to models analyzed in queueing theory, we derive analytical expressions for the noise in steady-state protein distributions. Furthermore, given that the underlying processes are intrinsically stochastic, cellular regulation must be designed to control the`noise' in order to adapt and respond to changing environments. Another focus of this dissertation is to develop and analyze stochastic models of post-transcription regulation. The analytical solutions of the models proposed provide insight into the effects of different mechanisms of regulation and the role of small RNAs in fine-tunning the noise in gene expression. The results derived can serve as building blocks for future studies focusing on regulation of stochastic gene expression. / Ph. D.