Trend to Equilibrium for a Reaction–Diffusion System Modelling Reversible Enzyme Reaction

A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four-component reaction–diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour of the system is studied by means of entropy methods.     

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.     

Study and Simulation of Reaction–Diffusion Systems Affected by Interacting Signaling Pathways

Possible effects of interaction (cross-talk) between signaling pathways is studied in a system of Reaction-Diffusion (RD) equations. Furthermore, the relevance of spontaneous neurite symmetry breaking and Turing instability has been examined through numerical simulations. The interaction between Retinoic Acid (RA) and Notch signaling pathways is considered as a perturbation to RD system of axon-forming potential for N2a neuroblastoma cells. The present work suggests that large increases to the level of RA-Notch interaction can possibly have substantial impacts on neurite outgrowth and on the process of axon formation. This can be observed by the numerical study of the homogeneous system showing that in the absence of RA-Notch interaction the unperturbed homogeneous system may exhibit different saddle-node bifurcations that are robust under small perturbations by low levels of RA-Notch interactions, while large increases in the level of RA-Notch interaction result in a number of transitions of saddle-node bifurcations into Hopf bifurcations. It is speculated that near a Hopf bifurcation, the regulations between the positive and negative feedbacks change in such a way that spontaneous symmetry breaking takes place only when transport of activated Notch protein takes place at a faster rate.     

Modelling a Wolbachia Invasion Using a Slow–Fast Dispersal Reaction–Diffusion Approach

This paper uses a reaction–diffusion approach to examine the dynamics in the spread of a Wolbachia infection within a population of mosquitoes in a homogeneous environment. The formulated model builds upon an earlier model by Skalski and Gilliam (Am. Nat. 161(3):441–458, 2003), which incorporates a slow and fast dispersal mode. This generates a faster wavespeed than previous reaction–diffusion approaches, which have been found to produce wavespeeds that are unrealistically slow when compared with direct observations. In addition, the model incorporates cytoplasmic incompatibility between male and female mosquitoes, which creates a strong Allee effect in the dynamics. In previous studies, linearised wavespeeds have been found to be inaccurate when a strong Allee effect is underpinning the dynamics. We provide a means to approximate the wavespeed generated by the model and show that it is in close agreement with numerical simulations. Wavespeeds are approximated for both Aedes aegypti and Drosophila simulans mosquitoes at different temperatures. These wavespeeds indicate that as the temperature decreases within the optimal temperature range for mosquito survival, the speed of a Wolbachia invasion increases for Aedes aegypti populations and decreases for Drosophila simulans populations.     

An Efficient Wavelet Based Approximation Method to Steady State Reaction–Diffusion Model Arising in Mathematical Chemistry

The mathematical model of Rahamathunissa and Rajendran (J Math Chem 44:849–861, 2008) in an amperometric biosensor response is discussed. In this paper, we have applied the shifted second kind Chebyshev wavelets (CW) to obtain the numerical solutions of reaction–diffusion equations containing a nonlinear term related to Michaelis–Menton kinetics of the enzymatic reaction. The application of the shifted second kind CW operational matrices for solving initial and boundary value problems is presented. The obtained numerical results demonstrate efficient and applicability of the proposed method. The power of the manageable method is confirmed. Moreover the use of shifted second kind CW method is found to be simple, efficient, accurate, small computation cost, and computationally attractive.     

Evolutionarily Stable and Convergent Stable Strategies in Reaction–Diffusion Models for Conditional Dispersal

We consider a mathematical model of two competing species for the evolution of conditional dispersal in a spatially varying, but temporally constant environment. Two species are different only in their dispersal strategies, which are a combination of random dispersal and biased movement upward along the resource gradient. In the absence of biased movement or advection, Hastings showed that the mutant can invade when rare if and only if it has smaller random dispersal rate than the resident. When there is a small amount of biased movement or advection, we show that there is a positive random dispersal rate that is both locally evolutionarily stable and convergent stable. Our analysis of the model suggests that a balanced combination of random and biased movement might be a better habitat selection strategy for populations.     

Optimal Culling and Biocontrol in a Predator–Prey Model

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward–backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.     

Chaos and Peak-to-Peak Dynamics in a Plankton–Fish Model

A plankton–fish model, comprising phosphorus, algae, zooplankton, and young fish, with light intensity and water temperature varying periodically with the seasons, is analyzed in this paper. For realistic values of the parameters the model behaves chaotically, but its dynamics within the strange attractor can be described by a few one-dimensional maps that allow one to forecast the next yearly peak of plankton or fish from the last peaks. This property is an unambiguous mark of a special form of chaos. Unfortunately, the estimate of such peak-to-peak maps from field data is possible only if plankton or young fish biomass has been sampled accurately and frequently for a paramount number of years. In conclusion, the analysis shows that it might be that plankton dynamics are characterized by an interesting and peculiar form of chaos, but that inferences from recorded data on the existence of these forms of chaos are premature.     

The Inhibitory Action of Several Bioantioxidants and Their Mixtures in a Model Hemoglobin–Hydrogen Peroxide–Luminol Chemiluminescent System

Determination of the antioxidant activities of various biological objects, for example, food, medicinal preparations, beverages, blood plasma, and other human biological fluids, is an important task for biomedical research. Chemiluminescent methods are widely used for this purpose. These methods are sensitive and rapid and make it possible to directly control the kinetics of inhibition of oxidation by an antioxidant. In the present work, a chemiluminescent model was used of free-radical oxidation of luminol, as initiated by a mixture of hemoglobin–hydrogen peroxide in an aqueous medium. The kinetics of the inhibitory effect of eight water-soluble bioantioxidants with different molecular structures and their binary mixtures was studied; the inhibition parameters of luminol oxidation by these antioxidants and their stoichiometric coefficients were determined. Features of the inhibition kinetics for glutathione are revealed. The synergistic and antagonistic effects of antioxidants in the mixtures were evaluated. The independence of chemiluminescence quenching by individual antioxidants was noted for the majority of the studied binary antioxidant mixtures, with more “active” antioxidants inhibiting oxidation earlier than less “active” ones. Mixtures of some antioxidants that strengthened or weakened each other upon interacting, thus exhibiting synergism or antagonism, were an exception.     

Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia

Two multiscale (hybrid) stochastic reaction–diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction–diffusion models. The first hybrid model is based on the models previously developed in the literature. The second hybrid model is based on the application of a recently developed two-regime method (TRM) to a fully molecular-based model, which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model.     

Differences in the Mode of Growth Inhibition of Baker’s Yeast Brought about by Arsenate and Methanearsonate

The bite force of three surimi gels with molars was measured in the mouth using a multiple-point sheet sensor. A peak force appeared at the breaking point of each sample, and then the force increased again, accompanied by a decrease in the opening between the upeer and lower teeth. Low values in the peak force, pressure, and time at the first peak, the time at which the maximum contact area was engaged, impulse, and slope of bite curve were observed in samples with low breaking force and low breaking deformation found by the mechanical measurement of gel strength, and with less toughness in the sensory assessment. The duration of the bite force, the second peak time, and active bite pressure at the second peak did not change with a change in the surimi texture. The active pressure at the breaking point of each gel was affected by gel strength, while that at the second peak was independent of the gel strength.     

Dynamical Transitions in a Pollination–Herbivory Interaction: A Conflict between Mutualism and Antagonism

Plant-pollinator associations are often seen as purely mutualistic, while in reality they can be more complex. Indeed they may also display a diverse array of antagonistic interactions, such as competition and victim–exploiter interactions. In some cases mutualistic and antagonistic interactions are carried-out by the same species but at different life-stages. As a consequence, population structure affects the balance of inter-specific associations, a topic that is receiving increased attention. In this paper, we developed a model that captures the basic features of the interaction between a flowering plant and an insect with a larval stage that feeds on the plant’s vegetative tissues (e.g. leaves) and an adult pollinator stage. Our model is able to display a rich set of dynamics, the most remarkable of which involves victim–exploiter oscillations that allow plants to attain abundances above their carrying capacities and the periodic alternation between states dominated by mutualism or antagonism. Our study indicates that changes in the insect’s life cycle can modify the balance between mutualism and antagonism, causing important qualitative changes in the interaction dynamics. These changes in the life cycle could be caused by a variety of external drivers, such as temperature, plant nutrients, pesticides and changes in the diet of adult pollinators.     

Type 2 Ryanodine Receptor Domain A Contains a Unique and Dynamic α-Helix That Transitions to a β-Strand in a Mutant Linked with a Heritable Cardiomyopathy

Ryanodine receptors (RyRs) are large tetrameric calcium (Ca^2 +) release channels found on the sarcoplasmic reticulum that respond to dihydropyridine receptor activity through a direct conformational interaction and/or indirect Ca^2 + sensitivity, propagating sarcoplasmic reticulum luminal Ca^2 + release in the process of excitation–contraction coupling. There are three human RyR subtypes, and several debilitating diseases are linked to heritable mutations in RyR1 and RyR2 including malignant hypothermia, central core disease, catecholaminergic polymorphic ventricular tachycardia (CPVT) and arrhythmogenic right ventricular dysplasia type 2 (ARVD2). Despite the recent appreciation that many disease-associated mutations within the N-terminal RyRABC domains (i.e., residues 1–559) are located in the putative interfaces mediating tetrameric channel assembly, the precise structural and dynamical consequences of the mutations are not well understood. We used solution nuclear magnetic resonance (NMR) spectroscopy and X-ray crystallography to examine the effect of ARVD2-associated (i.e., R176Q) and CPVT-associated [i.e., P164S, R169Q and delta exon 3 (Δ3)] mutations on the structure and dynamics of RyR2A. Our solution NMR data exposed a mobile α-helix, unique to type 2; further, this α2 helix rescues the β-strand lost in RyR2A Δ3 but remains dynamic in the hot-spot loop (HS-loop) P164S, R169Q and R176Q mutant proteins. Docking of our X-ray crystal/NMR hybrid structure into the RyR1 cryo-electron microscopy map revealed that this RyR2A α2 helix is in close proximity to dense “columns” projecting toward the channel pore. This is in contrast to the HS-loop mutations that cause structural changes largely localized to the intersubunit interface between adjacent ABC domains. Taken together, our data suggest that ARVD2 and CPVT mutations have at least two distinct structural consequences linked to channel dysfunction: perturbation of the HS-loop (i.e., domain A):domain B intersubunit interface and disruption of the communication between the N-terminal region and the channel domain.     

Regulation of plankton by omnivore cyprinids in a shallow lake in the Kis–Balaton Reservoir System

Hydrobiologia - A long-term food web manipulation experiment was started in 1999 with monitoring in the eutrophic shallow Major Lake (area 11 ha, mean depth 1.1 m). In 2000, studies were continued...     

The response of shrubland patterns' properties to rainfall changes and to the catastrophic removal of plants in semi-arid regions predicted by Reaction–Diffusion simulations

Extended areas of the Mediterranean and semi-arid ecosystems are predicted to face decreased water availability, alongside increased human disturbances owing to an increase in population during this century. The use of geosimulations is instrumental for studying the expected ecosystem's response to predicted changes in habitat conditions due to the lack of field data at appropriate spatial and temporal resolutions over wide regional extents throughout sufficient time spans. Computational simulations, based on reaction‐diffusion equations (RDE), were performed in order to quantitatively assess the form of shrubland pattern changes in response to decreasing and increasing rainfall regimes and during recovery following catastrophic removal of plants, which would result from fires or droughts. Patch pattern properties were analyzed using the Shannon–Wiener fragmentation (SW) metric (= Ʃ Si Ln Si, where Si is the area fraction of patch i of n patches) and the edge ratio (ER) metric (= sum of edge area/sum of patches' area). The SW fragmentation change during pattern formation is characterized by 3 phases, where in the first phase there is decreased fragmentation, and the third phase represents the evolution of equilibrium. The second phase is the most interesting one, where we have observed pattern regularization obtained by rearranging the shrubs' patches while increasing the fragmentation of the shrub patches. Such regularization phases seem to be a primary characteristic of self-organized behavior in these ecosystems. The general form of pattern properties change with decreasing or increasing rainfall according to SW fragmentation levels reached at equilibrium, which revealed a non-linear configuration with three divergence points. At these divergence points, the pattern evolution trajectories diverge according to the rainfall change rates. The most important divergence point occurs when rainfall drops below the critical desertification level. Whereas a slow reduction in rainfall would allow the shrub patches to be maintained below this critical rainfall level, rapid changes would cause immediate desertification. Edge ratios are closely linked to rainfall levels, and thus, they may provide early warnings and allow changes in the habitat conditions to be monitored due to climate changes.     

Parametric Analysis of a Predator–prey System Stabilized by a Top Predator

We present a complete parametric analysis of a predator–prey system influenced by a top predator. We study ecosystems with abundant nutrient supply for the prey where the prey multiplication can be considered as proportional to its density. The main questions we examine are the following: (1) Can the top predator stabilize such a system at low densities of prey? (2) What possible dynamic behaviors can occur? (3) Under which conditions can the top predation result in the system stabilization? We use a system of two nonlinear ordinary differential equations with the density of the top predator as a parameter. The model is investigated with methods of qualitative theory of ODEs and the theory of bifurcations. The existence of 12 qualitatively different types of dynamics and complex structure of the parametric space are demonstrated. Our studies of phase portraits and parametric diagrams show that a top predator can be an important factor leading to stabilization of the predator-prey system with abundant nutrient supply. Although the model here is applied to the plankton communities with fish (or carnivorous zooplankton) as the top trophic level, the general form of the equations allows applications of our results to other ecological systems.     

Antitumor Effect of AZD4547 in a Fibroblast Growth Factor Receptor 2–Amplified Gastric Cancer Patient–Derived Cell Model

BACKGROUND: FGFR2 amplification is associated with aggressive gastric cancer (GC), and targeted drugs have been developed for treatment of GC. We evaluated the antitumor activity of an FGFR inhibitor in FGFR2-amplified GC patients with peritoneal carcinomatosis. METHODS: Two GC patients with FGFR2 amplification confirmed by fluorescence in situ hybridization showed peritoneal seeding and malignant ascites. We used the patient-derived xenograft model; patient-derived cells (PDCs) from malignant ascites were used to assess FGFR2 expression and its downstream pathway using immunofluorescence analysis and immunoblot assay in vitro. Apoptosis and cell cycle arrest after treatment of FGFR inhibitor were analyzed by Annexin V-FITC assay and cell cycle analysis. RESULTS: FGFR2 amplification was verified in both PDC lines. AZD4547 as an FGFR inhibitor decreased proliferation of PDCs, and the IC₅₀ value was estimated to be 250 nM in PDC#1 and 210 nM in PDC#2. FGFR inhibitor also significantly decreased levels of phosphorylated FGFR2 and downstream signaling molecules in FGFR2-amplified PDC lines. In cell cycle analysis, apoptosis was significantly increased in AZD4547-treated cells compared with nontreated cells. The proportion of cells in the sub-G1 stage was significantly higher in AZD4547-treated PDCs than in control cells. CONCLUSION: Our findings suggest that FGFR2 amplification is a relevant therapeutic target in GC with peritoneal carcinomatosis.     

Characterization and Modulation of Glucose Uptake in a Human Blood–Brain Barrier Model

The blood–brain barrier (BBB) plays a key role in limiting and regulating glucose access to glial and neuronal cells. In this work glucose uptake on a human BBB cell model (the hCMEC/D3 cell line) was characterized. The influence of some hormones and diet components on glucose uptake was also studied. ³H-2-deoxy-d-glucose ([³H]-DG) uptake for hCMEC/D3 cells was evaluated in the presence or absence of tested compounds. [³H]-DG uptake was sodium- and energy-independent. [³H]-DG uptake was regulated by Ca²⁺ and calmodulin but not by MAPK kinase pathways. PKC, PKA and protein tyrosine kinase also seem to be involved in glucose uptake modulation. Progesterone and estrone were found to decrease ³H-DG uptake. Catechin and epicatechin did not have any effect, but their methylated metabolites increased [³H]-DG uptake. Quercetin and myricetin decreased [³H]-DG uptake, and glucuronic acid-conjugated quercetin did not have any effect. These cells expressed GLUT1, GLUT3 and SGLT1 mRNA.