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

A phosphorylation cycle shapes gradients of the DYRK family kinase Pom1 at the plasma membrane.

Concentration gradients regulate many cell biological and developmental processes. In rod-shaped fission yeast cells, polar cortical gradients of the DYRK family kinase Pom1 couple cell length with mitotic commitment by inhibiting a mitotic inducer positioned at midcell. However, how Pom1 gradients are established is unknown. Here, we show that Tea4, which is normally deposited at cell tips by microtubules, is both necessary and, upon ectopic cortical localization, sufficient to recruit Pom1 to the cell cortex. Pom1 then moves laterally at the plasma membrane, which it binds through a basic region exhibiting direct lipid interaction. Pom1 autophosphorylates in this region to lower lipid affinity and promote membrane release. Tea4 triggers Pom1 plasma membrane association by promoting its dephosphorylation through the protein phosphatase 1 Dis2. We propose that local dephosphorylation induces Pom1 membrane association and nucleates a gradient shaped by the opposing actions of lateral diffusion and autophosphorylation-dependent membrane detachment.

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

Inhibition of protein kinase B activity induces cell cycle arrest and apoptosis during early G₁ phase in CHO cells.

Inhibition of PKB (protein kinase B) activity using a highly selective PKB inhibitor resulted in inhibition of cell cycle progression only if cells were in early G1 phase at the time of addition of the inhibitor, as demonstrated by time-lapse cinematography. Addition of the inhibitor during mitosis up to 2 h after mitosis resulted in arrest of the cells in early G1 phase, as deduced from the expression of cyclins D and A and incorporation of thymidine. After 24 h of cell cycle arrest, cells expressed the cleaved caspase-3, a central mediator of apoptosis. These results demonstrate that PKB activity in early G1 phase is required to prevent the induction of apoptosis. Using antibodies, it was demonstrated that active PKB translocates to the nucleus during early G1 phase, while an even distribution of PKB was observed through cytoplasm and nucleus during the end of G1 phase.

Robust synchronization of coupled circadian and cell cycle oscillators in single mammalian cells.

Circadian cycles and cell cycles are two fundamental periodic processes with a period in the range of 1 day. Consequently, coupling between such cycles can lead to synchronization. Here, we estimated the mutual interactions between the two oscillators by time-lapse imaging of single mammalian NIH3T3 fibroblasts during several days. The analysis of thousands of circadian cycles in dividing cells clearly indicated that both oscillators tick in a 1:1 mode-locked state, with cell divisions occurring tightly 5 h before the peak in circadian Rev-Erbα-YFP reporter expression. In principle, such synchrony may be caused by either unidirectional or bidirectional coupling. While gating of cell division by the circadian cycle has been most studied, our data combined with stochastic modeling unambiguously show that the reverse coupling is predominant in NIH3T3 cells. Moreover, temperature, genetic, and pharmacological perturbations showed that the two interacting cellular oscillators adopt a synchronized state that is highly robust over a wide range of parameters. These findings have implications for circadian function in proliferative tissues, including epidermis, immune cells, and cancer.

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

An exquisite cross-control mechanism among endothelial cell fate regulators directs the plasticity and heterogeneity of lymphatic endothelial cells.

Arteriovenous-lymphatic endothelial cell fates are specified by the master regulators, namely, Notch, COUP-TFII, and Prox1. Whereas Notch is expressed in the arteries and COUP-TFII in the veins, the lymphatics express all 3 cell fate regulators. Previous studies show that lymphatic endothelial cell (LEC) fate is highly plastic and reversible, raising a new concept that all 3 endothelial cell fates may co-reside in LECs and a subtle alteration can result in a reprogramming of LEC fate. We provide a molecular basis verifying this concept by identifying a cross-control mechanism among these cell fate regulators. We found that Notch signal down-regulates Prox1 and COUP-TFII through Hey1 and Hey2 and that activated Notch receptor suppresses the lymphatic phenotypes and induces the arterial cell fate. On the contrary, Prox1 and COUP-TFII attenuate vascular endothelial growth factor signaling, known to induce Notch, by repressing vascular endothelial growth factor receptor-2 and neuropilin-1. We show that previously reported podoplanin-based LEC heterogeneity is associated with differential expression of Notch1 in human cutaneous lymphatics. We propose that the expression of the 3 cell fate regulators is controlled by an exquisite feedback mechanism working in LECs and that LEC fate is a consequence of the Prox1-directed lymphatic equilibrium among the cell fate regulators.

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