Noise-induced escape in an excitable system

We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation

IMMUNOSUPPRESSIVE EFFECTS OF ARGININE DEIMINASE FROM STREPTOCOCCUS PYOGENES

Many pathogens use metabolic pathway of arginine for successful dissemination. Bacterial arginine deiminase hydrolyzes arginine to form one molecule of ammonia and two molecules of ATP. The activity of the enzyme contributes to the improvement of survival of pathogenic bacteria in conditions of low pH at the site of infection or in phagolysosome, as well as in anaerobic conditions, and also leads to deficiency of arginine. Metabolism of arginine plays an important role in regulating the functions of immune system cells in mammals. Arginine is a substrate of enzymes NOS and arginase. Arginine depletion, potentially contributs to immunosuppression. The review analyzed the literature data on the effect of streptococcal arginine deiminase on the metabolism of arginine eukaryotic cells, and discusses immunosuppressive action of the enzyme

Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter

The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any integral representation. For completeness, we also briefly describe the well-known scheme developed by V.P.Maslov for constructing global-in-time solutions.Comment: 27 page

Influence of streptococcal arginine deiminase on the leukocyte infiltration in murine air pouch model

Numerous pathogens express arginine deiminase, an enzyme that catalyzes the hydrolysis of L-arginine in a chain of biochemical reactions aimed at the synthesis of ATP in bacterial cells. L-arginine is a semi-essential, proteinogenic amino acid that plays an important role in regulating the functions of the immune system cells in mammals. Depletion of L-arginine may cause a weakening of the immune reaction. In order to improve the conditions of dissemination, many pathogens use a strategy of L-arginine depletion in the microenvironment of host cells. Bacterial arginine deiminase can be a pathogenicity factor aimed for dysregulating the processes of inflammation and immune response. In general, the effect of arginine deiminase on immune cells may result into disturbed production of regulatory proinflammatory molecules, such as NO, and related substances, inhibition of activation, migration and differentiation of individual leukocyte subsets. The aim of this study was to investigate the effect of arginine deiminase on the formation of inflammatory infiltrate in murine air pouch model of streptococcal infection. Materials and methods: The study was performed using S. pyogenes M49-16 expressing arginine deiminase and its isogenic mutant S. pyogenes M49-16delArcA with inactivated arginine deiminase gene. The flow cytometry analysis of the inflammatory infiltrate leukocytes subpopulation in mice infected with the original strain of S. pyogenes M49-16 and its isogenic mutant S. pyogenes M49-16delArcA at different periods of infection was performed. It was shown that the inflammation reached its peak 6 hours after streptococcal inoculation, being more pronounced in mice infected with the mutant strain. Тhis finding was affirmed by a simultaneous and more pronounced increase in the absolute numbers of all leukocyte subsets in the focus of inflammation in this group of mice when compared to mice infected with original bacterial strain. Despite the decrease in the absolute number of all leukocyte types in the inflammatory infiltrate in both groups of mice for 24 hours, this trend was more pronounced in the group of mice infected with mutant microbial strain. Comparison of the inflammatory infiltrates developing in mice infected with original versus mutant strains showed that arginine deiminase may be a pathogenicity factor leading to dysregulation of protective immune response, due to impaired migration of white blood cells to the site of infection

The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension

We extend the previously developed weak noise scheme, applied to the noisy Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing interface in arbitrary dimensions. By means of the Cole-Hopf transformation we show that the growth morphology can be interpreted in terms of dynamically evolving textures of localized growth modes with superimposed diffusive modes. In the Cole-Hopf representation the growth modes are static solutions to the diffusion equation and the nonlinear Schroedinger equation, subsequently boosted to finite velocity by a Galilei transformation. We discuss the dynamics of the pattern formation and, briefly, the superimposed linear modes. Implementing the stochastic interpretation we discuss kinetic transitions and in particular the properties in the pair mode or dipole sector. We find the Hurst exponent H=(3-d)/(4-d) for the random walk of growth modes in the dipole sector. Finally, applying Derrick's theorem based on constrained minimization we show that the upper critical dimension is d=4 in the sense that growth modes cease to exist above this dimension.Comment: 27 pages, 19 eps figs, revte

The geometry of spontaneous spiking in neuronal networks

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a certain continuous function on the surface of the unit n-cube encodes the most likely activity patterns generated by the network. By studying how the minima of this function evolve under the variation of the coupling strength, we describe the principal transformations in the network dynamics. The minimization problem is also used for the quantitative description of the main dynamical regimes and transitions between them. In particular, for the weak and strong coupling regimes, we present asymptotic formulas for the network activity rate as a function of the coupling strength and the degree of the network. The variational analysis is complemented by the stability analysis of the synchronous state in the strong coupling regime. The stability estimates reveal the contribution of the network connectivity and the properties of the cycle subspace associated with the graph of the network to its synchronization properties. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior

Nuclear transcription factor kB (NF-kB) activity in lymphocyte populations in children with Wilson-Konovalov disease

Wilson's disease (WD) is a rare hereditary disease caused by a deficiency of the ATF7B transporter. The accumulation of copper can cause damage to organs and cells, mainly the liver. Copper exposure can modulate cytokine synthesis through molecular and cellular signaling pathways, including the nuclear transcription factor NF-kB pathway. NF-kB is the main regulator of inflammation and cell death, acts as a central link between liver damage, fibrosis and hepatocellular carcinoma. An excess of NF-kB-dependent cytokine response stimulates inflammatory reactions, but excessive inhibition of NF-kB can negatively affect the viability of hepatocytes. Method of flow cytometry with visualization — Amnis ImageStreamX allows to evaluate the activity of NF-kB (% of activated cells in cell populations). The aim: to evaluate the activity of NF-kB in lymphocyte populations in children with WD disease. Immunophenotyping of lymphocytes and assessment of the level of translocation of NF-kB were performed in 52 children with WD and in 25 children of comparison group. The mass concentration of copper in daily urine was determined by atomic absorption method using the AAnalyst 800 spectrometer. In children with WD, the content of cells with NF-kB translocation varied from 5 to 90% depending on the lymphocyte population; the highest level was detected in B cells — 57.5 (37-68) %. A significant difference in distributions of the number of cells with NF-kB translocation between WD and healthy children was shown (F-criterion, p < 0.01). In most cases, children with WD are characterized by a decrease in the activity of NF-kB in populations of B cells (in 43% of cases), T helper cells (48%), T cytotoxic (44%) and Th17 lymphocytes (41%). In children with WD, the concentration of copper varied from 9.7 to 2582 mcg/day, Me = 616 (210-1173). A direct relationship was obtained between the copper content in urine and the level of translocation of NF-kB in B lymphocytes, r = 0.34, p = 0.016. The activity of the NF-kB correlates with biochemical markers of the severity of liver damage (ALT, AST, GGT) and with copper content in urine. The study of the NF-kB signaling pathway seems promising for a better understanding of the pathogenetic mechanisms of the formation of inflammation and liver fibrosis in children with WD

Population extinction in a time-modulated environment

The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent branching rate. The population extinction is treated in eikonal approximation, where it is described as an instanton trajectory of a proper reaction Hamiltonian. The modulation of the environment perturbs this trajectory and synchronizes it with the modulation phase. We calculate the corresponding change in the action along the instanton using perturbation techniques supported by numerical calculations. The techniques include a first-order theory with respect to the modulation amplitude, a second-order theory in the spirit of the Kapitsa pendulum effect, and adiabatic theory valid for low modulation frequencies.Comment: 13 pages, 10 figure

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio