Impulsive Control and Synchronization of Chaos-Generating-Systems with Applications to Secure Communication

When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area

Calcium-dependent block of P2X7 receptor channel function is allosteric

Among purinergic P2X receptor (P2XR) channels, the P2X7R exhibits the most complex gating kinetics; the binding of orthosteric agonists at the ectodomain induces a conformational change in the receptor complex that favors a gating transition from closed to open and dilated states. Bath Ca2+ affects P2X7R gating through a still uncharacterized mechanism: it could act by reducing the adenosine triphosphate4− (ATP4−) concentration (a form proposed to be the P2X7R orthosteric agonist), as an allosteric modulator, and/or by directly altering the selectivity of pore to cations. In this study, we combined biophysical and mathematical approaches to clarify the role of calcium in P2X7R gating. In naive receptors, bath calcium affected the activation permeability dynamics indirectly by decreasing the potency of orthosteric agonists in a concentration-dependent manner and independently of the concentrations of the free acid form of agonists and status of pannexin-1 (Panx1) channels. Bath calcium also facilitated the rates of receptor deactivation in a concentration-dependent manner but did not affect a progressive delay in receptor deactivation caused by repetitive agonist application. The effects of calcium on the kinetics of receptor deactivation were rapid and reversible. A438079, a potent orthosteric competitive antagonist, protected the rebinding effect of 2’(3′)-O-4-benzoylbenzoyl)ATP on the kinetics of current decay during the washout period, but in the presence of A438079, calcium also increased the rate of receptor deactivation. The corresponding kinetic (Markov state) model indicated that the decrease in binding affinity leads to a decrease in current amplitudes and facilitation of receptor deactivation, both in an extracellular calcium concentration–dependent manner expressed as a Hill function. The results indicate that calcium in physiological concentrations acts as a negative allosteric modulator of P2X7R by decreasing the affinity of receptors for orthosteric ligand agonists, but not antagonists, and not by affecting the permeability dynamics directly or indirectly through Panx1 channels. We expect these results to generalize to other P2XRs

Investigating the Role of T-Cell Avidity and Killing Efficacy in Relation to Type 1 Diabetes Prediction

During the progression of the clinical onset of Type 1 Diabetes (T1D), high-risk individuals exhibit multiple islet autoantibodies and high-avidity T cells which progressively destroy beta cells causing overt T1D. In particular, novel autoantibodies, such as those against IA-2 epitopes (aa1-577), had a predictive rate of 100% in a 10-year follow up (rapid progressors), unlike conventional autoantibodies that required 15 years of follow up for a 74% predictive rate (slow progressors). The discrepancy between these two groups is thought to be associated with T-cell avidity, including CD8 and/or CD4 T cells. For this purpose, we build a series of mathematical models incorporating first one clone then multiple clones of islet-specific and pathogenic CD8 and/or CD4 T cells, together with B lymphocytes, to investigate the interaction of T-cell avidity with autoantibodies in predicting disease onset. These models are instrumental in examining several experimental observations associated with T-cell avidity, including the phenomenon of avidity maturation (increased average T-cell avidity over time), based on intra- and cross-clonal competition between T cells in high-risk human subjects. The model shows that the level and persistence of autoantibodies depends not only on the avidity of T cells, but also on the killing efficacy of these cells. Quantification and modeling of autoreactive T-cell avidities can thus determine the level of risk associated with each type of autoantibodies and the timing of T1D disease onset in individuals that have been tested positive for these autoantibodies. Such studies may lead to early diagnosis of the disease in high-risk individuals and thus potentially serve as a means of staging patients for clinical trials of preventive or interventional therapies far before disease onset

Dynamic and mechanosensitive properties of nascent adhesions

Cellular migration is a tightly regulated process that involves actin cytoskeleton, adaptor proteins, and integrin receptors. Forces are transmitted extracellularly through complexes of these molecules called adhesions. We recently developed a biophysical model of nascent adhesions (NA), as co-localized clusters of integrins and adaptor proteins, to understand their dynamics and mechanosensitive properties. The model was then analyzed to characterize the dependence of NA area on biophysical parameters that regulate the number of integrins and adaptor proteins within NA through a mechanosensitive co-aggregation mechanism. Our results revealed that NA formation is triggered beyond a threshold of adaptor protein, integrin, or extracellular ligand densities (listed in a decreasing order of relative influence), that an increase in co-aggregation or reductions in integrin mobility inside NA potentiate their formation, and that stress (rather than adhesion load) is the permissive mechanical parameter which allows for NA-assembly/disassembly via a bistable-switch possessing a hysteresis. These results were then confirmed by performing stochastic simulations of the model. In this talk, I will give an overview of the model and the predictions made in connection with experimental findings.Non UBCUnreviewedAuthor affiliation: McGill UniversityResearche

Impulsive Control and Synchronization of Chaos-GeneratingSystems with Aplications to Secure Communication

any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public

Analyzing protein-protein interactions governing focal adhesion dynamics and stability

Non UBCUnreviewedAuthor affiliation: McGill UniversityResearche

A Model for the Pulsatile Secretion of Gonadotropin-Releasing Hormone from Synchronized Hypothalamic Neurons

Cultured gonadotropin-releasing hormone (GnRH) neurons have been shown to express GnRH receptors. GnRH binding to its receptors activates three types of G-proteins at increasing doses. These G-proteins selectively activate or inhibit GnRH secretion by regulating the intracellular levels of Ca(2+) and cAMP. Based on these recent observations, we build a model in which GnRH plays the roles of a feedback regulator and a diffusible synchronizing agent. We show that this GnRH-regulated GnRH-release mechanism is sufficient for generating pulsatile GnRH release. The model reproduces the observed effects of some key drugs that disturb the GnRH pulse generator in specific ways. Simulations of 100 heterogeneous neurons revealed that the synchronization mediated by a common pool of diffusible GnRH is robust. The population can generate synchronized pulsatile signals even when all the individual GnRH neurons oscillate at different amplitudes and peak at different times. These results suggest that the positive and negative effects of the autocrine regulation by GnRH on GnRH neurons are sufficient and robust in generating GnRH pulses