Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen–Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen–Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.     

Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays

This paper deals with the problem of function projective synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based Cohen–Grossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.     

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays

In this paper, we study the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.     

The role of transmitter diffusion and flow versus extracellular vesicles in volume transmission in the brain neural–glial networks

Two major types of intercellular communication are found in the central nervous system (CNS), namely wiring transmission (point-to-point communication, the prototype being synaptic transmission with axons and terminals) and volume transmission (VT; communication in the extracellular fluid and in the cerebrospinal fluid (CSF)) involving large numbers of cells in the CNS. Volume and synaptic transmission become integrated inter alia through the ability of their chemical signals to activate different types of receptor protomers in heteroreceptor complexes located synaptically or extrasynaptically in the plasma membrane. The demonstration of extracellular dopamine (DA) and serotonin (5-HT) fluorescence around the DA and 5-HT nerve cell bodies with the Falck–Hillarp formaldehyde fluorescence method after treatment with amphetamine and chlorimipramine, respectively, gave the first indications of the existence of VT in the brain, at least at the soma level. There exist different forms of VT. Early studies on VT only involved spread including diffusion and flow of soluble biological signals, especially transmitters and modulators, a communication called extrasynaptic (short distance) and long distance (paraaxonal and paravascular and CSF pathways) VT. Also, the extracellular vesicle type of VT was demonstrated. The exosomes (endosome-derived vesicles) appear to be the major vesicular carriers for VT but the larger microvesicles also participate. Both mainly originate at the soma–dendritic level. They can transfer lipids and proteins, including receptors, Rab GTPases, tetraspanins, cholesterol, sphingolipids and ceramide. Within them there are also subsets of mRNAs and non-coding regulatory microRNAs. At the soma–dendritic membrane, sets of dynamic postsynaptic heteroreceptor complexes (built up of different types of physically interacting receptors and proteins) involving inter alia G protein-coupled receptors including autoreceptors, ion channel receptors and receptor tyrosine kinases are hypothesized to be the molecular basis for learning and memory. At nerve terminals, the presynaptic heteroreceptor complexes are postulated to undergo plastic changes to maintain the pattern of multiple transmitter release reflecting the firing pattern to be learned by the heteroreceptor complexes in the postsynaptic membrane.     

FERN – a Java framework for stochastic simulation and evaluation of reaction networks

Background  

Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary.     

Seidel–Herzel model of human baroreflex in cardiorespiratory system with stochastic delays

The stochastic versus deterministic solution of the Seidel–Herzel model describing the baroreceptor control loop (which regulates the short-time heart rate) are compared with the aim of exploring the heart rate variability. The deterministic model solutions are known to bifurcate from the stable to sustained oscillatory solutions if time delays in transfer of signals by sympathetic nervous system to the heart and vasculature are changed. Oscillations in the heart rate and blood pressure are physiologically crucial since they are recognized as Mayer waves. We test the role of delays of the sympathetic stimulation in reconstruction of the known features of the heart rate. It appears that realistic histograms and return plots are attainable if sympathetic time delays are stochastically perturbed, namely, we consider a perturbation by a white noise. Moreover, in the case of stochastic model the bifurcation points vanish and Mayer oscillations in heart period and blood pressure are observed for whole considered space of sympathetic time delays.      

Robust stabilization and H(∞) controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties

This paper deals with the problem of stabilization design and H(∞) control for a class of genetic regulatory networks (GRNs) with both intrinsic perturbation and extrinsic perturbation. Some delay-dependent mean-square stabilization criteria are put forward for nominal systems and uncertain systems by using an improved free-weighting matrix approach. As a result, the corresponding stabilization controllers and H(∞) controllers of GRNs are constructed with time delays compensated and suboptimal solutions are obtained via exploiting an iterative procedure together with the linear matrix inequality (LMI) method and the cone complementarity liberalization (CCL) algorithm. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.     

Persistence and extinction of population in reaction–diffusion–advection model with strong Allee effect growth

Journal of Mathematical Biology - A reaction–diffusion–advection equation with strong Allee effect growth rate is proposed to model a single species stream population in a...     

Wavespeed in reaction–diffusion systems, with applications to chemotaxis and population pressure

We present a method based on the Melnikov function used in dynamical systems theory to determine the wavespeed of travelling waves in perturbed reaction–diffusion systems. We study reaction–diffusion systems which are subject to weak nontrivial perturbations in the reaction kinetics, in the diffusion coefficient, or with weak active advection. We find explicit formulæ for the wavespeed and illustrate our theory with two examples; one in which chemotaxis gives rise to nonlinear advection and a second example in which a positive population pressure results in both a density-dependent diffusion coefficient and a nonlinear advection. Based on our theoretical results we suggest an experiment to distinguish between chemotactic and population pressure in bacterial colonies.     

Mathematical analysis of a delayed stage-structured predator–prey model with impulsive diffusion between two predators territories

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete, but in reality, many species diffuse only during a single period, and diffusion often occurs in regular pulses. Further, in forest habitats, the highest-level predator species are restricted to a specific territory, but prey can impulsively move between territories. Therefore, in this paper, we consider a delayed stage-structured predator–prey model with impulsively diffusive prey between two patches; in the model, patches represent the territories of two different predator populations. Here, we analytically obtain the global attractivity condition of predator-extinction periodic solutions for the system by using the concepts of Hui and Chen (2005); a numerical simulation is also included to illustrate this result. Further, we establish permanence conditions for the coexistence of the species using the theory of impulsive delayed differential equations. Finally, we explore the possibilities of the permanence of the system by using the growth rates of immature predators and the impulse period as critical parameters, and we also obtain the parameters’ threshold limits using numerical experimentation.     

Existence and global asymptotic stability of positive periodic solutions of n-species delay impulsive Lotka–Volterra type systems

In this paper, the existence and global asymptotic stability of positive periodic solutions of periodic n-species Lotka–Volterra impulsive systems with several deviating arguments are studied. By using the continuation theorem of coincidence degree theory and Lyapunov–Razumikhin method, sufficient conditions are obtained. Some known results are improved and generalized.     

A reaction–diffusion mechanism influences cell lineage progression as a basis for formation, regeneration, and stability of intestinal crypts

Background

Translation efficiency of certain mRNAs can be regulated through a cytoplasmic polyadenylation process at the pre-initiation phase. A translational regulator controls the polyadenylation process and this regulation depends on its posttranslational modifications e.g., phosphorylation. The cytoplasmic polyadenylation binding protein (CPEB1) is one such translational regulator, which regulates the translation of some mRNAs by binding to the cytoplasmic polyadenylation element (CPE). The cytoplasmic polyadenylation process can be turned on or off by the phosphorylation or dephosphorylation state of CPEB1. A specific example could be the regulation of Calcium/Calmodulin-dependent protein kinase II (??CaMKII) translation through the phosphorylation/dephosphorylation cycle of CPEB1.

Result

Here, we show that CPEB1 mediated polyadenylation of ??CaMKII mRNA can result in a bistable switching mechanism. The switch for regulating the polyadenylation is based on a two state model of ??CaMKII and its interaction with CPEB1. Based on elementary biochemical kinetics a high dimensional system of non-linear ordinary differential equations can describe the dynamic characteristics of the polyadenylation loop. Here, we simplified this high-dimensional system into approximate lower dimension system that can provide the understanding of dynamics and fixed points of original system. These simplified equations can be used to develop analytical bifurcation diagrams without the use of complex numerical tracking algorithm, and can further give us intuition about the parameter dependence of bistability in this system.

Conclusion

This study provides a systematic method to simplify, approximate and analyze a translation/activation based positive feedback loop. This work shows how to extract low dimensional systems that can be used to obtain analytical solutions for the fixed points of the system and to describe the dynamics of the system. The methods used here have general applicability to the formulation and analysis of many molecular networks.     

The rate of the deoxygenation reaction limits myoglobin- and hemoglobin-facilitated O₂ diffusion in cells

A mathematical model describing facilitation of O(2) diffusion by the diffusion of myoglobin and hemoglobin is presented. The equations are solved numerically by a finite-difference method for the conditions as they prevail in cardiac and skeletal muscle and in red cells without major simplifications. It is demonstrated that, in the range of intracellular diffusion distances, the degree of facilitation is limited by the rate of the chemical reaction between myglobin or hemoglobin and O(2). The results are presented in the form of relationships between the degree of facilitation and the length of the diffusion path on the basis of the known kinetics of the oxygenation-deoxygenation reactions. It is concluded that the limitation by reaction kinetics reduces the maximally possible facilitated oxygen diffusion in cardiomyoctes by ～50% and in skeletal muscle fibers by ～ 20%. For human red blood cells, a reduction of facilitated O(2) diffusion by 36% is obtained in agreement with previous reports. This indicates that, especially in cardiomyocytes and red cells, chemical equilibrium between myoglobin or hemoglobin and O(2) is far from being established, an assumption that previously has often been made. Although the "O(2) transport function" of myoglobin in cardiac muscle cells thus is severely limited by the chemical reaction kinetics, and to a lesser extent also in skeletal muscle, it is noteworthy that the speed of release of O(2) from MbO(2), the "storage function," is not limited by the reaction kinetics under physiological conditions.     

A computational reaction–diffusion model for biosynthesis and linking of cartilage extracellular matrix in cell-seeded scaffolds with varying porosity

Biomechanics and Modeling in Mechanobiology - Cartilage tissue engineering is commonly initiated by seeding cells in porous materials such as hydrogels or scaffolds. Under optimal conditions, the...     

The kinetics of interconversion of intermediates of the reaction of pig muscle lactate dehydrogenase with oxidized nicotinamide–adenine dinucleotide and lactate

Oxamate competes with pyruvate for the substrate binding site on the E(NADH) complex of pig skeletal muscle lactate dehydrogenase. When this enzyme was mixed with saturating concentrations of NAD(+) and lactate in a stopped-flow rapid-reaction spectrophotometer there was no transient accumulation of enzyme complexes with the reduced nucleotide. The steady-state rate of formation of free NADH was reached within the dead-time of the instrument (3ms). When oxamate was added to inhibit the steady state and to uncouple the equilibration: [Formula: see text] through the rapid formation of E(NADH) (Oxamate), the rate of formation of E(NADH) could be measured by observation of the first turnover. This pH-dependent transient is controlled by the rate of dissociation of pyruvate and the fraction of the enzyme in the form E(NADH) (Pyruvate).     

The influence of space dimension on the large-time behavior in a reaction–diffusion system modeling diallelic selection

We study a mathematical model from population genetics, describing a single-locus diallelic (A/a) selection–migration process. The model consists of a coupled system of three reaction–diffusion equations, one for the density of each genotype, posed in the whole space \mathbb Rⁿ{\mathbb R^n}. The genotype AA is advantageous, due to a smaller death rate, and we consider the fully recessive case where the other two genotypes aa and Aa have the same (higher) death rate. In the nondiffusive (spatially homogeneous) case, the disadvantageous gene a is always eliminated in the large time limit. In the presence of diffusion, when the birth rate exceeds a certain threshold value, we prove that this conclusion is still true for dimensions n ≤ 2, whereas for n ≥ 3 there exist initial distributions for which the advantageous gene A ultimately disappears. This is the first rigorous result of this type for the full system, and it solves a problem which seems to have been open since the celebrated work of Aronson and Weinberger (Lecture notes in mathematics, vol 446, Springer, New York, pp 5–49, 1975; Adv Math 30, 33–76, 1977), where similar results had been obtained for a simplified scalar model, that they derived as an approximation of the full system. Interestingly, we moreover show that, at the threshold value of the birth rate, the cut-off dimension shifts from n = 2 to n = 6.