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

Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh-Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue

Effects of reduced discrete coupling on filament tension in excitable media

Wave propagation in the heart has a discrete nature, because it is mediated by discrete intercellular connections via gap junctions. Although effects of discreteness on wave propagation have been studied for planar traveling waves and vortexes (spiral waves) in two dimensions, its possible effects on vortexes (scroll waves) in three dimensions are not yet explored. In this article, we study the effect of discrete cell coupling on the filament dynamics in a generic model of an excitable medium. We find that reduced cell coupling decreases the line tension of scroll wave filaments and may induce negative filament tension instability in three-dimensional excitable lattices.Peer Reviewe

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 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

Towards active microfluidics: Interface turbulence in thin liquid films with floating molecular machines

Thin liquid films with floating active protein machines are considered. Cyclic mechanical motions within the machines, representing microscopic swimmers, lead to molecular propulsion forces applied to the air-liquid interface. We show that, when the rate of energy supply to the machines exceeds a threshold, the flat interface becomes linearly unstable. As the result of this instability, the regime of interface turbulence, characterized by irregular traveling waves and propagating machine clusters, is established. Numerical investigations of this nonlinear regime are performed. Conditions for the experimental observation of the instability are discussed.Comment: 9 pages, 8 figures, RevTeX, submitted to Physical Review

The antecedents and consequences of customer loyalty: The roles of customer satisfaction and consumer trust -commitment

The objective of this dissertation is to develop and test a model of customer loyalty. This model can help explain the process that a customer follows to pledge loyalty, sometimes even subconsciously, to a product or service provider. From the provider\u27s perspective, this process enables a firm to have a superior marketing performance based on the consideration that a loyal customer always is going to repurchase from the same provider. The whole model is composed of two sides: the firm and the consumer side. The firm is the entity that starts the process with the production of a consumer value package that includes a product or service and a strategy to deliver it into the consumer\u27s hands. On the consumer side, the customer may or may not be satisfied with his or her first consumption experience. Only when the consumer is satisfied can it be said that the process for him or her to become loyal starts. Finally, again on the firm side, the consequence of customer loyalty is a firm\u27s superior marketing performance. This superior marketing performance includes higher market share, profitability, and competitive advantage (Moon and Kang 1999). This dissertation focuses on the process that occurs on the consumer side. It is specifically proposed that after a first satisfying experience, a customer requires some kind of reinforcement to become loyal. Such reinforcement would come either by a cognitive process (familiarity and perceived risk) or by an affective process (shared values and norms and opportunistic behavior). The result of those processes is the formation of consumer trust and commitment, which in turn, lead to customer loyalty. This dissertation suggests that consumer trust and commitment have a key-mediating role in the process of building loyalty. Consumer trust and commitment have been regarded previously as important conditions necessary to increase cooperation and loyalty among partners (Morgan and Hunt 1994, Moorman, Deshpande, and Zaltman 1993). The contention of this dissertation is that a buying process with trust and commitment will be able to generate customer loyalty involving repeated purchases in a long-term relationship between a firm and its customers. Guided by a modeled set of relationships, some hypotheses were tested using survey data in the long-distance phone industry. After a rigorous sample data collection and several statistical analyses (factor analysis, correlation analysis, regression analysis, and structural equation modeling) it is concluded that the existence of trust and commitment as mediating variables is important to increase the explanation of customer loyalty. Because not all the initially suggested variables were found significant, a post-hoc model is developed including only the significant variables (see figure 7). This tested model explains about 40% of the variance of the dependent variable customer loyalty and has goodness of fit indexes that are adequate