The hippocampus is one of the most intensely studied brain structures and the oscillatory activity of the hippocampal neurons is believed to be involved in learning and memory consolidation. Therefore, studying rhythm generation and modulation in this structure is an important step in understanding its function. In this thesis, these phenomena are studied via mathematical models of networks of hippocampal interneurons. The two types of neural networks considered here are homogenous and heterogenous networks. In homogenous networks, the input current to each neuron is equal, while in heterogenous networks, this assumption is relaxed and there is a specified degree of heterogeneity in the input stimuli. A phase reduction technique is applied to the neural network model of the hippocampal interneurons and attempts are made to understand the implications of heterogeneity to the existence and stability of the synchronized oscillations. The Existence of a critical level of heterogeneity above which the synchronized rhythms are not stable is established, and linear analysis is applied to derive expressions for estimating the perturbations in the network frequency and timing of the neural spikes. The mathematical techniques developed in this thesis are general enough to be applied to models describing other types of neurons not considered here. Possible biological implications include the application of high frequency local stimulation to alleviate the synchronous neural oscillations in pathological conditions such as epilepsy and Parkinson's disease and the possible role of heterogeneity in controlling the rhythm frequency and switching between various cognitive states.

Reproduction de : Thèse de doctorat : Acoustique : Le Mans : 2006. / Titre provenant de l'écran-titre. Bibliogr. p. 93-103.

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published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

Iron (Fe) exerts strong control over environmental biogeochemistry. As the fourth most abundant element, Fe is present in nearly all earth environments, where it plays important roles in governing the transformation and movement of organic and inorganic constituents, and in microbial respiration. Consequently, the body of work on Fe biogeochemistry is vast. This study is specifically concerned with the dynamic changes in the oxidation state of Fe (i.e., redox cycling) and their impact on the inorganic, organic and microbial components in soil. I constructed a special apparatus to fluctuate redox potential on soil slurries while concurrently sampling a wide range of biogeochemical variables (pH, redox potential, major and trace elements, CO2 release, DNA community composition charges, etc.). Previous research has documented redox fluctuations along a climate gradient in Hawaii and a primary goal of this dissertation was to reconstruct these redox fluctuations, subjected to experimental constraints afforded by a laboratory setting, with minimal disruption to the biogeochemical processes controlling Fe redox cycling. By recasting the spatial and temporal characteristics of in situ Fe redox cycling in the laboratory, I was able to form testable hypotheses regarding the importance of Fe redox oscillations to soil mineral transformations, colloid composition/dynamics and microbial community structure. A second goal of this dissertation was to explore the utility of Fe isotopic composition for providing information on soil weathering processes along age and climate gradients at the field scale in Hawaii. This portion of the study tested emerging theories of Fe isotope fractionation during mineral dissolution using well-characterized sequences in soil weathering intensity.The principal findings of the laboratory redox fluctuation experiments are that Fe redox oscillations: (1) trigger an increase in the crystallinity of Fe-oxides; (2) mobilize colloids containing refractory elements (e.g., Zr, Nb, U, etc.); (3) reveal redox sensitive rare earth element (REE) anomalies in the aqueous phase; and (4) induce changes in the microbial community favoring microbes capable of growth under both oxic and anoxic conditions. The principal finding of the Fe isotope measurements is that isotopic composition is directly related to weathering intensity in the field, consistent with theoretical predictions.

Parkinson’s disease (PD) is a movement disorder that is of basal ganglia origin. It is characterized by a severe loss of dopaminergic input to the striatum and symptoms such as bradykinesia, rigidity and tremor. There is growing evidence that PD is associated with pathological synchronous oscillatory activity in the basal ganglia, which primarily occurs in the 11-30 Hz range, the so-called beta band. The aim of this project was to better understand the oscillatory activity recorded from the basal ganglia of PD patients and to elucidate the significance of this activity in PD. To do this, neuronal firing and local field potentials (LFPs) were recorded from the subthalamic nucleus (STN) and globus pallidus internus (GPi) of PD patients undergoing stereotactic neurosurgery for implantation of therapeutic deep brain stimulation electrodes. Beta oscillatory LFP activity in the STN and GPi was found to be coherent with, and reflect to a certain degree, rhythmic activity in a population of local neurons. I have demonstrated for the first time that the degree of beta oscillatory firing in the STN, which is maximal in the motor portion, correlates with the patients’ benefit from dopaminergic medications, but not with baseline motor deficits. My study has also established that beta oscillatory firing in the STN does not positively correlate with the patients’ tremor scores and that during periods of tremor patients tend to have less beta oscillatory firing and increased neuronal oscillatory firing at the tremor frequency. Temporal examination of the LFPs recorded during periods of intermittent resting tremor revealed that stronger tremor is associated with increased LFP power in the low gamma range (35-55 Hz) and there is a decrease in the ratio of beta to gamma coherence. Similarly, a change in balance between oscillatory activities was observed during levodopa-induced dyskinesias. Finally, when the oscillatory activity in the GPi of PD patients was compared to that in dystonia I found that in dystonia, oscillatory LFP activity is less likely to reflect the neuronal firing. These findings indicate that beta oscillatory activity in the basal ganglia might reflect the degree of dopamine deficiency in the striatum and that the relative strength of oscillatory rhythms may play an important role in mediating the pathological features in PD.

Stimulation of urine production by the Malpighian (renal) tubules in Rhodnius prolixus is regulated by at least two diuretic hormones, CRF-related peptide and serotonin, that have traditionally been believed to function through the activation of cAMP-mediated intracellular second messenger pathways. In this study I demonstrate that serotonin stimulation triggered, in addition to cAMP, intracellular Ca2+ waves in the Malpighian tubule cells of R. prolixus. Treatment with the intracellular Ca2+ chelator BAPTA-AM blocked the intracellular Ca2+ waves and reduced serotonin-stimulated fluid secretion by 75%. This suggests a role for intracellular Ca2+ signaling in the excretory system of R. prolixus. Serotonin stimulated Malpighian tubules (MTs) exposed to Ca2+-free saline plus BAPTA-AM secreted an abnormal fluid, showing: increased K+ concentration, reduced Na+ concentration and lower pH. These results along with measurement of transepithelial potential (TEP) suggest that the basolateral Na+:K+:2Cl- cotransporter (NKCC) activity is reduced in tubule cells treated with BAPTA-AM, suggesting that Ca2+ is required to modulate the activity of the basolateral NKCC. Treatment with the non-hydrolysable cell-permeable cAMP analog, 8Br-cAMP, produced fluid with the same K+ and Na+ concentration and at the same secretion rate as serotonin-stimulated tubules. In addition, 8Br-cAMP triggered intracellular Ca2+ oscillations similar to those obtained with serotonin. 8Br-cAMP-stimulated tubules treated with BAPTA-AM decreased their fluid secretion by about 40% and increased Na+ concentration, similar to the effect observed on serotonin-stimulated tubules. Therefore, I conclude that the intracellular Ca2+ waves triggered by serotonin are mediated by cAMP. The role of inositol-3-phospate (InsP3) in Ca2+ release was tested by treating the tubules with the InsP3 receptor blocker xestospongin. The treatment decreased fluid secretion rate as well as the amplitude of Ca2+ waves in serotonin-stimulated tubules. These results suggest that serotonin activates the production of InsP3 and, most likely, diacylglycerol (DAG). Thus, I decided to test whether the protein kinase C (PKC) may be involved in serotonin-stimulated secretion. The PKC inhibitors chelerythrine and bisindolylmaleimide (BIM) decreased secretion fluid rate in serotonin-stimulated tubules by 50% and 70%, respectively. Fluid secreted by tubules treated with BIM showed no differences in K+ and Na+ concentrations compared to controls, however both ion fluxes decreased. The evidence suggests that PKC is involved in serotonin stimulated secretion; the mechanism is still not understood. Taken together, the results suggest that cAMP, Ca2+ and PLC-PKC pathway are involved in serotonin stimulated secretion. However cAMP stimulation is enough for maximal secretion rate. Therefore PLC-PKC must act downstream of cAMP. Based on those results we hypothesize that serotonin binds a GPCR, increasing cAMP by activation of an adenylate cyclase (AC). Subsequently, cAMP is somehow able to activate PLC, which finally produces Ca2+ release, PKC activation and NKCC upregulation.

Parkinson’s disease (PD) is a movement disorder that is of basal ganglia origin. It is characterized by a severe loss of dopaminergic input to the striatum and symptoms such as bradykinesia, rigidity and tremor. There is growing evidence that PD is associated with pathological synchronous oscillatory activity in the basal ganglia, which primarily occurs in the 11-30 Hz range, the so-called beta band. The aim of this project was to better understand the oscillatory activity recorded from the basal ganglia of PD patients and to elucidate the significance of this activity in PD. To do this, neuronal firing and local field potentials (LFPs) were recorded from the subthalamic nucleus (STN) and globus pallidus internus (GPi) of PD patients undergoing stereotactic neurosurgery for implantation of therapeutic deep brain stimulation electrodes. Beta oscillatory LFP activity in the STN and GPi was found to be coherent with, and reflect to a certain degree, rhythmic activity in a population of local neurons. I have demonstrated for the first time that the degree of beta oscillatory firing in the STN, which is maximal in the motor portion, correlates with the patients’ benefit from dopaminergic medications, but not with baseline motor deficits. My study has also established that beta oscillatory firing in the STN does not positively correlate with the patients’ tremor scores and that during periods of tremor patients tend to have less beta oscillatory firing and increased neuronal oscillatory firing at the tremor frequency. Temporal examination of the LFPs recorded during periods of intermittent resting tremor revealed that stronger tremor is associated with increased LFP power in the low gamma range (35-55 Hz) and there is a decrease in the ratio of beta to gamma coherence. Similarly, a change in balance between oscillatory activities was observed during levodopa-induced dyskinesias. Finally, when the oscillatory activity in the GPi of PD patients was compared to that in dystonia I found that in dystonia, oscillatory LFP activity is less likely to reflect the neuronal firing. These findings indicate that beta oscillatory activity in the basal ganglia might reflect the degree of dopamine deficiency in the striatum and that the relative strength of oscillatory rhythms may play an important role in mediating the pathological features in PD.

A survey of the theory of neutrino oscillations in dense matter and neutrino backgrounds is presented. We discuss collective neutrino systems using the gyroscopic pendulum analogy and describe the motion that results from self-induced parametric resonances. The effects of dense matter on the flavour oscillations of neutrinos are also detailed. This theory is applied to the case of continuous supernova neutrino spectra and explanations of the spectral swapping behaviour seen in numerical studies are summarized. The results of numerical simulations of supernova oscillations in turbulent supernova backgrounds are presented and discussed. We study the motion of two example supernova neutrino spectra and examine the differences in the dynamics and flavour evolution that results from adding turbulent fluctuations to the supernova matter background. We also investigate the effect that fluctuations in the neutrino density can have on the oscillation behaviour. We find that in general the final neutrino spectra emerging from the inner supernova regions are quite robust to fluctuations in the backgrounds in our model, while the intermediate dynamics can be very strongly altered. Some significant changes in the final spectra are also found to occur when the neutrino background density fluctuations are large. We give a detailed review of the resonant matter effects that determine the survival probabilities of atmospheric muon neutrinos. The differences between various Earth density models are described, and these models are then used to predict the flux of muon-type neutrino events in the Deep Core extension to the IceCube detector. We use recent results from the detector collaboration and build on previous work which considered the sensitivity of the detector to the mass hierarchy, and show that uncertainties in the Earth's density can have a significant influence on the event rates.

The kidneys are amazingly versatile organs that perform a wide range of vital bodily functions. This thesis provides an analysis into a range of mathematical models of the tubuloglomerular feedback (TGF) mechanism. The TGF mechanism is an autoregulatory mechanism unique to the kidney that maintains approximately constant blood flow to the organ despite wide fluctuations in pressure. Oscillations in pressure, flow, and sodium chloride concentration have been attributed to the action of the TGF mechanism through a number of experimental studies. These oscillations appear spontaneously or in response to a natural or artificial pressure step or microperfusion. The reason for sustained oscillatory behaviour in nephrons is not immediately clear. Significant research has gone into experimentally determining the signal to the TGF mechanism, but the physiological significance is not mentioned in the literature. Considerable modelling of the oscillations attributed to the TGF mechanism has also been undertaken. However, this modelling uses models that are inherently oscillatory, such as a second-order differential equation or delay differential equations. While these models can be fitted to closely approximate the experimental results they do not address the physiological factors that contribute to sustained oscillations. This thesis aims to determine the contributing factors to the sustained oscillations. By understanding these factors a better hypothesis of the physiological role of the oscillations should be possible. Chapter 3 presents a mathematical model by Holstein-Rathlou and Marsh [28] that uses a partial differential equation (PDE) model for the tubule and a second-order differential equation for the TGF feedback. The remainder of this chapter shows that oscillations occur without an inherently oscillatory second-order differential equation due to the delays in the system. Tubular compliance was also shown to be necessary for sustained oscillations. Sustained oscillations were not exhibited in the TGF model with a noncompliant tubule. Although damped oscillations were exhibited for a wide range of parameter space. Adding compliance to the tubule increased the delay around the loop of Henle. This additional delay elicited sustained oscillations. The computationally expensive PDE model of 3 was simplified to an ordinary differential equation (ODE) model in Chapter 4 by assuming a spatial profile. This model exhibits much of the same qualitative behaviour as the PDE model including sustained oscillations for similar ranges of parameter space. Compliance was also found to be important in the generation of sustained oscillations in agreement with the PDE tubule model. This model is less computationally expensive than the PDE model and allows analysis that was unfeasible with the PDE model. Significant natural and artificial blood pressure fluctuation occur in experimental rat models. Chapter 5 examines the effect of inlet pressure forcing on a nonoscillatory and an oscillatory model. The inherently nonoscillatory noncompliant model becomes oscillatory with a physiologically realistic pressure forcing. The oscillatory compliant model remains oscillatory with the addition of a inlet pressure forcing. Pressure fluctuations were hypothesised to contribute to sustained oscillations and could be validated experimentally. Two extensions to the single nephron TGF models are presented in Chapter 6. A realistic juxtaglomerular delay is added to the single nephron models with both the ODE and PDE tubular models. Physiologically realistic juxtaglomerular delays induce sustained oscillations in the otherwise nonoscillatory noncompliant models. The remainder of this chapter presents a different model for a variable interstitial sodium chloride concentration profile. This model demonstrates experimentally observed function of the countercurrent mechanism by which a concentration gradient is set up and maintained in the interstitium. Two single nephron models with ODE tubular models are coupled in Chapter 7. The coupling is modelled through the effect on the resistance of their neighbouring nephron's afferent arteriole resistance. The coupled nephron model exhibits entrainment as observed experimentally. Inhibiting the oscillation in one nephron reduces the amplitude of the oscillation in its neighbour. This result compares well with experiments where the TGF mechanism in one nephron is blocked by the administration of furosemide.