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

Involvement of the extracellular signal-regulated kinase cascade for cocaine-rewarding properties

A central feature of drugs of abuse is to induce gene expression in discrete brain structures that are critically involved in behavioral responses related to addictive processes. Although extracellular signal-regulated kinase (ERK) has been implicated in several neurobiological processes, including neuronal plasticity, its role in drug addiction remains poorly understood. This study was designed to analyze the activation of ERK by cocaine, its involvement in cocaine-induced early and long-term behavioral effects, as well as in gene expression. We show, by immunocytochemistry, that acute cocaine administration activates ERK throughout the striatum, rapidly but transiently. This activation was blocked when SCH 23390 [a specific dopamine (DA)-D1 antagonist] but not raclopride (a DA-D2 antagonist) was injected before cocaine. Glutamate receptors of NMDA subtypes also participated in ERK activation, as shown after injection of the NMDA receptor antagonist MK 801. The systemic injection of SL327, a selective inhibitor of the ERK kinase MEK, before cocaine, abolished the cocaine-induced ERK activation and decreased cocaine-induced hyperlocomotion, indicating a role of this pathway in events underlying early behavioral responses. Moreover, the rewarding effects of cocaine were abolished by SL327 in the place-conditioning paradigm. Because SL327 antagonized cocaine-induced c-fos expression and Elk-1 hyperphosphorylation, we suggest that the ERK intracellular signaling cascade is also involved in the prime burst of gene expression underlying long-term behavioral changes induced by cocaine. Altogether, these results reveal a new mechanism to explain behavioral responses of cocaine related to its addictive properties.

Inhibition of Mitogen-Activated Protein Kinase Erk1/2 Promotes Protein Degradation of ATP Binding Cassette Transporters A1 and G1 in CHO and in HuH7 cells.

Signal transduction modulates expression and activity of cholesterol transporters. We recently demonstrated that the Ras/mitogen-activated protein kinase (MAPK) signaling cascade regulates protein stability of Scavenger Receptor BI (SR-BI) through Proliferator Activator Receptor (PPARα) -dependent degradation pathways. In addition, MAPK (Mek/Erk 1/2) inhibition has been shown to influence liver X receptor (LXR) -inducible ATP Binding Cassette (ABC) transporter ABCA1 expression in macrophages. Here we investigated if Ras/MAPK signaling could alter expression and activity of ABCA1 and ABCG1 in steroidogenic and hepatic cell lines. We demonstrate that in Chinese Hamster Ovary (CHO) cells and human hepatic HuH7 cells, extracellular signal-regulated kinase 1/2 (Erk1/2) inhibition reduces PPARα-inducible ABCA1 protein levels, while ectopic expression of constitutively active H-Ras, K-Ras and MAPK/Erk kinase 1 (Mek1) increases ABCA1 protein expression, respectively. Furthermore, Mek1/2 inhibitors reduce ABCG1 protein levels in ABCG1 overexpressing CHO cells (CHO-ABCG1) and human embryonic kidney 293 (HEK293) cells treated with LXR agonist. This correlates with Mek1/2 inhibition reducing ABCG1 cell surface expression and decreasing cholesterol efflux onto High Density Lipoproteins (HDL). Real Time reverse transcriptase polymerase chain reaction (RT-PCR) and protein turnover studies reveal that Mek1/2 inhibitors do not target transcriptional regulation of ABCA1 and ABCG1, but promote ABCA1 and ABCG1 protein degradation in HuH7 and CHO cells, respectively. In line with published data from mouse macrophages, blocking Mek1/2 activity upregulates ABCA1 and ABCG1 protein levels in human THP1 macrophages, indicating opposite roles for the Ras/MAPK pathway in the regulation of ABC transporter activity in macrophages compared to steroidogenic and hepatic cell types. In summary, this study suggests that Ras/MAPK signaling modulates PPARα- and LXR-dependent protein degradation pathways in a cell-specific manner to regulate the expression levels of ABCA1 and ABCG1 transporters.

Barrier for the reaction X20+ + X20+ -> X402+ in alkali-metal clusters related to electron density at the bond midpoint of the supermolecule (X20+)2

Using the extended Thomas-Fermi version of density-functional theory (DFT), calculations are presented for the barrier for the reaction Na20++Na20+¿Na402+. The deviation from the simple Coulomb barrier is shown to be proportional to the electron density at the bond midpoint of the supermolecule (Na20+)2. An extension of conventional quantum-chemical studies of homonuclear diatomic molecular ions is then effected to apply to the supermolecular ions of the alkali metals. This then allows the Na results to be utilized to make semiquantitative predictions of position and height of the maximum of the fusion barrier for other alkali clusters. These predictions are confirmed by means of similar DFT calculations for the K clusters.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Semiclassical back reaction in the formation of a straight cosmic string

We derive the back reaction on the gravitational field of a straight cosmic string during its formation due to the gravitational coupling of the string to quantum matter fields. A very simple model of string formation is considered. The gravitational field of the string is computed in the linear approximation. The vacuum expectation value of the stress tensor of a massless scalar quantum field coupled to the string gravitational field is computed to one loop order. Finally, the back-reaction effect is obtained by solving perturbatively the semiclassical Einsteins equations.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Front propagation in the A+B->2A reaction under subdiffusion

We consider an irreversible autocatalytic conversion reaction A+B->2A under subdiffusion described by continuous-time random walks. The reactants transformations take place independently of their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov equation leading to the existence of a nonzero minimal front propagation velocity, which is really attained by the front in its stable motion. We show that for subdiffusion, this minimal propagation velocity is zero, which suggests propagation failure.