Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

Redox dysregulation and oxidative stress in schizophrenia: genetic and functional anomalies of glutathione synthesis in patients and experimental models involving GABA interneurons and NMDA receptors

Objective: Converging evidence speak in favor of an abnormal susceptibility to oxidative stress in schizophrenia. A decreased level of glutathione (GSH), the principal non-protein antioxidant and redox regulator, was observed both in cerebrospinal-fluid and prefrontal cortex of schizophrenia patients (Do et al., 2000). Results: Schizophrenia patients have an abnormal GSH synthesis most likely of genetic origin: Two independent case-control studies showed a significant association between schizophrenia and a GAG trinucleotide repeat (TNR) polymorphism in the GSH key synthesizing enzyme glutamate-cysteine-ligase (GCL) catalytic subunit (GCLC) gene. The most common TNR genotype 7/7 was more frequent in controls, whereas the rarest TNR genotype 8/8 was three times more frequent in patients. The disease-associated genotypes correlated with a decrease in GCLC protein expression, GCL activity and GSH content. Such a redox dysregulation during development could underlie the structural and functional anomalies in connectivity: In experimental models, GSH deficit induced anomalies similar to those observed in patients. (a) morphology: In animal models with GSH deficit during the development we observed in prefrontal cortex a decreased dendritic spines density in pyramidal cells and an abnormal development of parvalbumine (but not of calretinine) immunoreactive GABA interneurones in anterior cingulate cortex. (b) physiology: GSH depletion in hippocampal slices induces NMDA receptors hypofunction and an impairment of long term potentiation. In addition, GSH deficit affected the modulation of dopamine on NMDA-induced Ca 2+ response in cultured cortical neurons. While dopamine enhanced NMDA responses in control neurons, it depressed NMDA responses in GSH-depleted neurons. Antagonist of D2-, but not D1-receptors, prevented this depression, a mechanism contributing to the efficacy of antipsychotics. The redox sensitive ryanodine receptors and L-type calcium channels underlie these observations. (c) cognition: Developing rats with low [GSH] and high dopamine lead deficit in olfactory integration and in object recognition which appears earlier in males that females, in analogy to the delay of the psychosis onset between man and woman. Conclusion: These clinical and experimental evidence, combined with the favorable outcome of a clinical trial with N-Acetyl Cysteine, a GSH precursor, on both the negative symptoms (Berk et al., submitted) and the mismatch negativity in an auditory oddball paradigm supported the proposal that a GSH synthesis impairment of genetic origin represent, among other factors, one major risk factor in schizophrenia.

Dynamical features of reaction-diffusion fronts in fractals

The speed of front propagation in fractals is studied by using (i) the reduction of the reaction-transport equation into a Hamilton-Jacobi equation and (ii) the local-equilibrium approach. Different equations proposed for describing transport in fractal media, together with logistic reaction kinetics, are considered. Finally, we analyze the main features of wave fronts resulting from this dynamic process, i.e., why they are accelerated and what is the exact form of this acceleration

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

Study of chemical modification of alkaline lignin by the glyoxalation reaction

In this study, glyoxalated alkaline lignins with a non-volatile and non-toxic aldehyde, which can be obtained from several natural resources, namely glyoxal, were prepared and characterized for its use in wood adhesives. The preparation method consisted of the reaction of lignin with glyoxal under an alkaline medium. The influence of reaction conditions such as the molar ratio of sodium hydroxide-to-lignin and reaction time were studied relative to the properties of the prepared adducts. The analytical techniques used were FTIR and 1H-NMR spectroscopies, gel permeation chromatography (GPC), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). Results from both the FTIR and 1H-NMR spectroscopies showed that the amount of introduced aliphatic hydroxyl groups onto the lignin molecule increased with increasing reaction time and reached a maximum value at 10 h, and after they began to decrease. The molecular weights remained unchanged until 10 h of reaction time, and then started to increase, possibly due to the repolymerization reactions. DSC analysis showed that the glass transition temperature (Tg) decreased with the introduction of glyoxal onto the lignin molecule due to the increase in free volume of the lignin molecules. TGA analysis showed that the thermal stability of glyoxalated lignin is not influenced and remained suitable for wood adhesives. Compared to the original lignin, the improved lignin is reactive and a suitable raw material for adhesive formula

Altered Local Beta and Gamma Synchronization in Prefrontal Cortex of Mice with Redox Dysregulation or Maternal Immune Activation

Background: A developmental dysregulation of glutathione (GSH) synthesis leading to oxidative stress, when combined with environmental risk factors (viral infections) generating reactive oxygen species, can play a critical role in inducing schizophrenia phenotypes. GSH deficit induces morphological, physiological and behavioral anomalies analogous to those reported in schizophrenic patients, including disrupted parvalbumine (PV) inhibitory interneuron's integrity and neuronal synchrony (β/γ-oscillations). Methods: We assessed PV immunoreactivity (PV-IR) and local synchronization in prefrontal cortex of two mouse models: (1) mice with a genetic deficit in GSH (GCLM-/-) and (2) mice with prenatal immune activation at embryonic day17 (PolyI:C). Results: Adults from both mice models display reduced PV-IR in prefrontal cortex. In anterior cingulate (ACC) of GCLM-/-, appearance and maturation of PVI are delayed and worsened with peribubertal stress but not in adult one. This effect is reversed by treatment with the GSH precursor N-acetyl-cysteine. The power of beta and gamma oscillations are decreased in ACC of GCLM-/- while they increased in prelimbic cortex of PolyI:C mice. Conclusions: Despite reduced PV-IR in both models, alteration of the synchronization was different, indicating that the structural/functional disruption of the cortical circuitry was partly different in both models. Novel therapeutic strategies are proposed, based on interference with oxidative stress and inflammatory processes.

Hyperbolic reaction-diffusion equations for a forest fire model

Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail

Irreversible thermodynamics of Poisson processes with reaction

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics

Reaction-diffusion wave fronts: Multigeneration biological species under climate change

A generalization of reaction-diffusion models to multigeneration biological species is presented. It is based on more complex random walks than those in previous approaches. The new model is developed analytically up to infinite order. Our predictions for the speed agree to experimental data for several butterfly species better than existing models. The predicted dependence for the speed on the number of generations per year allows us to explain the change in speed observed for a specific invasion

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

Speed of reaction-transport processes

We present an approach to determining the speed of wave-front solutions to reaction-transport processes. This method is more accurate than previous ones. This is explicitly shown for several cases of practical interest: (i) the anomalous diffusion reaction, (ii) reaction diffusion in an advective field, and (iii) time-delayed reaction diffusion. There is good agreement with the results of numerical simulations

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Time-delayed reaction-diffusion fronts

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J.Fort and V.Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

Acute inflammatory reaction associated with endoluminal bypass grafts.

PURPOSE: Nonspecific inflammatory reactions characterized by local tenderness, fever, and flu-like discomfort have been seen in patients undergoing endoluminal graft placement in the abdominal aorta or the femoral arteries. We undertook a study to assess the clinical and laboratory parameters of this inflammation. METHODS: Ten patients with femoropopliteal artery (n = 9) or aortic (n = 1) lesions were treated with EndoPro System 1 stent-grafts made of nitinol alloy and covered with a polyester (Dacron) fabric. Eleven patients implanted with a bare nitinol stent served as the control group. RESULTS: In the stent-graft group, four patients showed clinical signs of acute inflammation manifested by fever and local tenderness. Three of these patients suffered thrombosis of the stent-grafts during the first month of follow-up. Plasma levels of interleukin-1 beta and interleukin-6 in all stent-graft patients were markedly increased 1 day after intervention (7.3 +/- 2.8 versus 90.2 +/- 34.1 pg/mL and 15.6 +/- 5.8 versus 175.5 +/- 66.3 pg/mL, respectively; p < 0.01). This was followed by an increase in fibrinogen (3.0 +/- 0.2 versus 5.0 +/- 0.2 g/L; p < 0.05) and C-reactive protein (14.6 +/- 3.3 versus 77.5 +/- 15.0 mg/L; p < 0.01) at 1 week. No direct correlation between the inflammatory markers and symptoms could be found. In vitro analysis showed that individual components of the stent-graft did not activate human neutrophils, whereas the intact stent-graft itself induced a marked neutrophil activation. CONCLUSIONS: The component of the self-expanding stent-graft responsible for the nonspecific inflammatory reaction was not identified in this study. It is likely that the stent-graft itself or some as yet unrecognized element of the device other than the Dacron fabric or metal alloy may be a potent in vivo inducer of cytokine reaction by neutrophils.