Pattern formation at cellular membranes by phosphorylation and dephosphorylation of proteins

We consider a classical model on activation of proteins, based in two reciprocal enzymatic biochemical reactions. The combination of phosphorylation and dephosphorylation reactions of proteins is a well established mechanism for protein activation in cell signalling. We introduce different affinity of the two versions of the proteins to the membrane and to the cytoplasm. The difference in the diffusion coefficient at the membrane and in the cytoplasm together with the high density of proteins at the membrane which reduces the accessible area produces domain formation of protein concentration at the membrane. We differentiate two mechanisms responsible for the pattern formation inside of living cells and discuss the consequences of these models for cell biology.Peer ReviewedPreprin

Reentry produced by small-scale heterogeneities in a discrete model of cardiac tissue

Reentries are reexcitations of cardiac tissue after the passing of an excitation wave which can cause dangerous arrhythmias like tachycardia or life-threatening heart failures like fibrillation. The heart is formed by a network of cells connected by gap junctions. Under ischemic conditions some of the cells lose their connections, because gap junctions are blocked and the excitability is decreased. We model a circular region of the tissue where a fraction of connections among individual cells are removed and substituted by non-conducting material in a twodimensional (2D) discrete model of a heterogeneous excitable medium with local kinetics based on electrophysiology. Thus, two neighbouring cells are connected (disconnected) with a probability f (1 - f). Such a region is assumed to be surrounded by homogeneous tissue. The circular heterogeneous area is shown to act as a source of new waves which reenter into the tissue and reexcitate the whole domain. We employ the Fenton-Karma equations to model the action potential for the local kinetics of the discrete nodes to study the statistics of the reentries in two dimensional networks with different topologies. We conclude that the probability of reentry is determined by the proximity of the fraction of disrupted connections between neighboring nodes (Peer ReviewedPostprint (published version

Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue

Arrhythmias in cardiac tissue are related to irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. A localized region with a fraction of nonconducting links surrounded by homogeneous conducting tissue can become a source of reentry and ectopic beats. Extensive simulations in a discrete model of cardiac tissue show that a wave crossing a heterogeneous region of cardiac tissue can disintegrate into irregular patterns, provided the fraction of nonconducting links is close to the percolation threshold of the cell network. The dependence of the reentry probability on this fraction, the system size, and the degree of excitability can be inferred from the size distribution of nonconducting clusters near the percolation threshold.Peer ReviewedPostprint (published version

Effective medium approach for heterogeneous reaction-diffusion media

An effective medium theory that can be used to calculate effective diffusion and reaction rate coefficients in random heterogeneous reaction-diffusion systems is described. The predictions of the theory are compared with simulations of spatially distributed media with different types of heterogeneity. The magnitude of the front velocity in bistable media is used to gauge the accuracy of the theoretical predictions. Quantitative agreement is found if the diffusion length in the heterogeneities is large compared to the characteristic width of the front. However, for small diffusion lengths the agreement depends on the type of heterogeneity. The effective medium predictions are also compared with simulations on systems with regular or temporal disorder.Peer ReviewedPostprint (published version

Complex excitable media: activators design, while inhibitors embellish

A system composed by coupled reaction–diffusion equations is one of the most classical scenarios of pattern formation. There are also other mechanisms of pattern formation, however, all have in common the interplay between a mechanism of transport and the nonlinearities of the system. Probably, the simplest example of pattern formation involving reaction–diffusion equations is a bistable front moving with constant velocity. A certain concentration U experiences an autocatalytic nonlinear growth and the corresponding increase of U travels along the media by diffusion. Such a process is simply modeled by a single reaction–diffusion equation. where F(U ) is a nonlinear function, typically a cubic function on U, giving rise to two stable solutions, i.e., bistable system. Under an adequate initial condition a front changes the stability from the metastable to the more stable solution. In such a case, the concentration U activates his own production and can be noted as activator. Such activation propagates by diffusion through the medium forming a traveling front with a fixed velocity which depends on the parameters on Eq. (1). The resulting fronts are robust and very stable waves which propagate through the system…Postprint (author's final draft

Optimization of extraction of bioactives from sea buckthorn (Hippophae rhamnoides L.) woody waste

The main objective of the research is studying the antioxidant activity of the extracts of stem and branches of sea buckthorn, using different extraction methods such as stirred tank extraction and Soxhlet extraction in laboratory scales with different solvents such as pure ethanol, water, ethanol-water solutions and n-pentane. The optimization of extraction conditions, such as water content in the ethanol-water solutions, the extraction temperature is the main focus of this work for producing an extract which has strong antioxidant activity.Budapest University of Technology and Economics. Faculty of Chemical Technology and BiotechnologyGrado en Ingeniería Químic

Complex wave patterns in an effective reaction–diffusion model for chemical reactions in microemulsions

An effective medium theory is employed to derive a simple qualitative model of a pattern forming chemical reaction in a microemulsion. This spatially heterogeneous system is composed of water nanodroplets randomly distributed in oil. While some steps of the reaction are performed only inside the droplets, the transport through the extended medium occurs by diffusion of intermediate chemical reactants as well as by collisions of the droplets. We start to model the system with heterogeneous reaction–diffusion equations and then derive an equivalent effective spatially homogeneous reaction–diffusion model by using earlier results on homogenization in heterogeneous reaction–diffusion systems [ S. Alonso, M. Bär, and R. Kapral, J. Chem. Phys. 134, 214102 (2009)]. We study the linear stability of the spatially homogeneous state in the resulting effective model and obtain a phase diagram of pattern formation, that is qualitatively similar to earlier experimental results for the Belousov–Zhabotinsky reaction in an aerosol OT (AOT)-water-in-oil microemulsion [ V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. 87, 228301 (2001)]. Moreover, we reproduce many patterns that have been observed in experiments with the Belousov–Zhabotinsky reaction in an AOT oil-in-water microemulsion by direct numerical simulations.Peer ReviewedPostprint (published version

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Surfactant-induced gradients in the three-dimensional Belousov-Zhabotinsky reaction

Scroll waves are prominent patterns formed in three-dimensional excitable media, and they are frequently considered highly relevant for some types of cardiac arrhythmias. Experimentally, scroll wave dynamics is often studied by optical tomography in the Belousov-Zhabotinsky reaction, which produces CO2 as an undesired product. Addition of small concentrations of a surfactant to the reaction medium is a popular method to suppress or retard CO2 bubble formation. We show that in closed reactors even these low concentrations of surfactants are sufficient to generate vertical gradients of excitability which are due to gradients in CO2 concentration. In reactors open to the atmosphere such gradients can be avoided. The gradients induce a twist on vertically oriented scroll waves, while a twist is absent in scroll waves in a gradient-free medium. The effects of the CO2 gradients are reproduced by a numerical study, where we extend the Oregonator model to account for the production of CO2 and for its advection against the direction of gravity. The numerical simulations confirm the role of solubilized CO2 as the source of the vertical gradient of excitability in reactors closed to the atmosphere.Peer ReviewedPostprint (published version