Anmar Khadra

Application of impulsive synchronization to communication security

In this paper, criteria on uniform equi-boundedness and equi-Lagrange stability for impulsive systems are derived. These criteria are used to synchronize two nonidentical chaotic systems by impulsively controlling a nonautonomous second order system, which leads to the development of an induced-message scheme for communication system security. With the scheme, message signals are not transmitted across public channels, but induced at the receiver end. The scheme overcomes the transmission time-frame congestion in impulsive cryptosystems discussed in the literature and improves system security. Simulation results are given to demonstrate the performance of the proposed scheme.

Experimental Characterization and Mathematical Modeling of P2X7 Receptor Channel Gating

The P2X7 receptor is a trimeric channel with three binding sites for ATP, but how the occupancy of these sites affects gating is still not understood. Here we show that naive receptors activated and deactivated monophasically at low and biphasically at higher agonist concentrations. Both phases of response were abolished by application of Az10606120, a P2X7R-specific antagonist. The slow secondary growth of current in the biphasic response coincided temporally with pore dilation. Repetitive stimulation with the same agonist concentration caused sensitization of receptors, which manifested as a progressive increase in the current amplitude, accompanied by a slower deactivation rate. Once a steady level of the secondary current was reached, responses at high agonist concentrations were no longer biphasic but monophasic. Sensitization of receptors was independent of Na+ and Ca2+ influx and ∼30 min washout was needed to reestablish the initial gating properties. T15E- and T15K-P2X7 mutants showed increased sensitivity for agonists, responded with monophasic currents at all agonist concentrations, activated immediately with dilated pores, and deactivated slowly. The complex pattern of gating exhibited by wild-type channels can be accounted for by a Markov state model that includes negative cooperativity of agonist binding to unsensitized receptors caused by the occupancy of one or two binding sites, opening of the channel pore to a low conductance state when two sites are bound, and sensitization with pore dilation to a high conductance state when three sites are occupied.

Analyzing the Robustness of Impulsive Synchronization Coupled by Linear Delayed Impulses

In this technical note, a class of autonomous impulsive differential systems with linear delayed impulses is considered. Sufficient conditions required for this particular class of systems with varying and constant impulse durations to be equi-attractive in the large are obtained. These conditions are then applied to impulsively synchronize two coupled chaotic systems by using delayed impulses and a robustness analysis of the model is also provided. Simulation results are given to demonstrate the analytical results.

Impulsively synchronizing chaotic systems with delay and applications to secure communication

In this paper, the presence of transmission delay and sampling delay in chaos-based secure communication systems by employing impulsive synchronization is studied. A time delayed impulsive differential system with delayed impulses, modeling the synchronization error between the driving and response schemes employed in such communication systems, is presented. The equi-attractivity property of the error dynamics is investigated and the sufficient conditions leading to this property are obtained. A set of upper bounds on the delay terms involved in the system are also obtained, and a numerical example is given. A communication security scheme employing hyperchaotic systems possessing continuous driving, impulsive driving and delay is proposed and simulation results are given to demonstrate the performance of the scheme.

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.

Immunogenetics of type 1 diabetes mellitus

Type 1 diabetes mellitus (T1DM) is an autoimmune disease arising through a complex interaction of both genetic and immunologic factors. Similar to the majority of autoimmune diseases, T1DM usually has a relapsing remitting disease course with autoantibody and T cellular responses to islet autoantigens, which precede the clinical onset of the disease process. The immunological diagnosis of autoimmune diseases relies primarily on the detection of autoantibodies in the serum of T1DM patients. Although their pathogenic significance remains uncertain, they have the practical advantage of serving as surrogate biomarkers for predicting the clinical onset of T1DM. Type 1 diabetes is a polygenic disease with a small number of genes having large effects (i.e. HLA), and a large number of genes having small effects. Risk of T1DM progression is conferred by specific HLA DR/DQ alleles [e.g., DRB1*03-DQB1*0201 (DR3) or DRB1*04-DQB1*0302 (DR4)]. In addition, HLA alleles such as DQB1*0602 are associated with dominant protection from T1DM in multiple populations. A discordance rate of greater than 50% between monozygotic twins indicates a potential involvement of environmental factors on disease development. Viral infections may play a role in the chain of events leading to disease, albeit conclusive evidence linking infections with T1DM remains to be firmly established. Two syndromes have been described in which an immune-mediated form of diabetes occurs as the result of a single gene defect. These syndromes are termed autoimmune polyglandular syndrome type I (APS-I) or autoimmune polyendocrinopathy-candidiasis-ectodermal dystrophy (APECED), and X-linked poyendocrinopathy, immune dysfunction and diarrhea (XPID). These two syndromes are unique models to understand the mechanisms involved in the loss of tolerance to self-antigens in autoimmune diabetes and its associated organ-specific autoimmune disorders. A growing number of animal models of these diseases have greatly helped elucidate the immunologic mechanisms leading to autoimmune diabetes.

Dual Gating Mechanism and Function of P2X7 Receptor Channels

The ATP-gated P2X7 receptor channel (P2X7R) operates as a cytolytic and apoptotic receptor but also controls sustained cellular responses, including cell growth and proliferation. However, it has not been clarified how the same receptor mediates such opposing effects. To address this question, we have combined electrophysiological, imaging, and mathematical studies using wild-type and mutant rat P2X7Rs. Activation of naïve (not previously stimulated) receptors by low agonist concentrations caused monophasic slow desensitizing currents and internalization of receptors without other changes in the cellular morphology, much like other P2XRs. In contrast, saturating agonist concentrations induced high-amplitude biphasic currents, reflecting pore dilation and causing rapid cell swelling and lysis. The existence of these two signaling patterns was accounted for using a revised Markov-state model that included, in addition to naïve and sensitized states, desensitized states. Occupancy of one or two ATP-binding sites of naïve receptors favored a slow transition to desensitized states, whereas occupancy of the third binding site favored a transition to sensitized/dilated states. Consistent with model predictions, nondilating P2X7R mutants always generated desensitizing currents. These results suggest that the level of saturation of the ligand binding sites determines the nature of the P2X7R gating and cellular actions.

Gating properties of the P2X2a and P2X2b receptor channels: Experiments and mathematical modeling

Adenosine triphosphate (ATP)-gated P2X2 receptors exhibit two opposite activation-dependent changes, pore dilation and pore closing (desensitization), through a process that is incompletely understood. To address this issue and to clarify the roles of calcium and the C-terminal domain in gating, we combined biophysical and mathematical approaches using two splice forms of receptors: the full-size form (P2X2aR) and the shorter form missing 69 residues in the C-terminal domain (P2X2bR). Both receptors developed conductivity for N-methyl-d-glucamine within 2–6 s of ATP application. However, pore dilation was accompanied with a decrease rather than an increase in the total conductance, which temporally coincided with rapid and partial desensitization. During sustained agonist application, receptors continued to desensitize in calcium-independent and calcium-dependent modes. Calcium-independent desensitization was more pronounced in P2X2bR, and calcium-dependent desensitization was more pronounced in P2X2aR. In whole cell recording, we also observed use-dependent facilitation of desensitization of both receptors. Such behavior was accounted for by a 16-state Markov kinetic model describing ATP binding/unbinding and activation/desensitization. The model assumes that naive receptors open when two to three ATP molecules bind and undergo calcium-independent desensitization, causing a decrease in the total conductance, or pore dilation, causing a shift in the reversal potential. In calcium-containing media, receptor desensitization is facilitated and the use-dependent desensitization can be modeled by a calcium-dependent toggle switch. The experiments and the model together provide a rationale for the lack of sustained current growth in dilating P2X2Rs and show that receptors in the dilated state can also desensitize in the presence of calcium.

The role of low avidity T cells in the protection against type 1 diabetes: A modeling investigation

Cytotoxic T lymphocytes (CTLs) play a dominant role in the pathogenesis of autoimmune diabetes, commonly denoted Type 1 Diabetes (T1D). These CTLs (notably CD8(+) T cells) recognize and kill insulin-secreting pancreatic beta cells, reducing their number by approximately 90%. The resulting reduction of insulin secretion causes the defective regulation of glucose metabolism, leading to the characteristic symptoms of diabetes. Recognition of beta cells as targets by CTLs depends on the interactions between MHC-peptide complexes on the surface of beta cells and receptors (TCRs) on T cells. Those CTLs with high affinity TCRs (also called high avidity T cells) cause most of the harm, while those with low affinity TCRs (also called low avidity T cells) play a more mysterious role. Recent experimental evidence suggests that low avidity T cells accumulate as memory T cells during the disease and may be protective in NOD mice (a strain prone to developing T1D), delaying disease progression. It has been hypothesized that such low avidity T cells afford disease protection either by crowding the islets of Langerhans, where beta cells reside, or by killing antigen presenting cells (APCs). In this paper, we explore the hypothesized mechanisms for this protective effect in the context of a series of models for (1) the interactions of low and high avidity T cells, (2) the effect of APCs and (3) the feedback from beta cell killing to autoantigen-induced T cell proliferation. We analyze properties of these models, noting consistency of predictions with observed behaviour. We then use the models to examine the influence of various treatment strategies on the progression of the disease. The model reveals that progressive accumulation of memory low avidity autoreactive T cells during disease progression makes treatments aimed at expanding these protective T cell types more effective close to, or at the onset of clinical disease. It also provides evidence for the hypothesis that low avidity T cells kill APCs (rather than the alternate hypothesis that they crowd the islets).

Prediction and prevention of type 1 diabetes: update on success of prediction and struggles at prevention.

Type 1 diabetes mellitus (T1DM) is the archetypal example of a T cell‐mediated autoimmune disease characterized by selective destruction of pancreatic β cells. The pathogenic equation for T1DM presents a complex interrelation of genetic and environmental factors, most of which have yet to be identified. On the basis of observed familial aggregation of T1DM, it is certain that there is a decided heritable genetic susceptibility for developing T1DM. The well‐known association of T1DM with certain human histocompatibility leukocyte antigen (HLA) alleles of the major histocompatibility complex (MHC) was a major step toward understanding the role of inheritance in T1DM. Type 1 diabetes is a polygenic disease with a small number of genes having large effects (e.g., HLA) and a large number of genes having small effects. Risk of T1DM progression is conferred by specific HLA DR/DQ alleles [e.g., DRB1*03‐DQB1*0201 (DR3/DQ2) or DRB1*04‐DQB1*0302 (DR4/DQ8)]. In addition, the HLA allele DQB1*0602 is associated with dominant protection from T1DM in multiple populations. A concordance rate lower than 100% between monozygotic twins indicates a potential involvement of environmental factors on disease development. The detection of at least two islet autoantibodies in the blood is virtually pre‐diagnostic for T1DM. The majority of children who carry these biomarkers, regardless of whether they have an a priori family history of the disease, will develop insulin‐requiring diabetes. Facilitating pre‐diagnosis is the timing of seroconversion which is most pronounced in the first 2 yr of life. Unfortunately the significant progress in improving prediction of T1DM has not yet been paralleled by safe and efficacious intervention strategies aimed at preventing the disease. Herein we summarize the chequered history of prediction and prevention of T1DM, describing successes and failures alike, and thereafter examine future trends in the exciting, partially explored field of T1DM prevention.