Pulsed low-energy stimulation initiates electric turbulence in cardiac tissue.

Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks. In particular, two very important questions are: 1) What determines the potential of a wave break to initiate re-entry? and 2) How do these breaks evolve such that the system is able to maintain spatiotemporally chaotic electrical activity? Here we approach these questions numerically using optogenetics in an in silico model of human atrial tissue that has undergone chronic atrial fibrillation (cAF) remodelling. In the lesser studied sub-threshold illumination régime, we discover a new mechanism of wave break initiation in cardiac tissue that occurs for gentle slopes of the restitution characteristics. This mechanism involves the creation of conduction blocks through a combination of wavefront-waveback interaction, reshaping of the wave profile and heterogeneous recovery from the excitation of the spatially extended medium, leading to the creation of re-excitable windows for sustained re-entry. This finding is an important contribution to cardiac arrhythmia research as it identifies scenarios in which low-energy perturbations to cardiac rhythm can be potentially life-threatening.

Spatiotemporal Changes in the Bacterial Community of the Meromictic Lake Uchum, Siberia.

Lake Uchum is a newly defined meromictic lake in Siberia with clear seasonal changes in its mixolimnion. This study characterized the temporal dynamics and vertical profile of bacterial communities in oxic and anoxic zones of the lake across all four seasons: October (autumn), March (winter), May (spring), and August (summer). Bacterial richness and diversity in the anoxic zone varied widely between time points. Proteobacteria was the dominant bacterial phylum throughout the oxic and anoxic zones across all four seasons. Alphaproteobacteria (Loktanella) and Gammaproteobacteria (Aliidiomarina) exhibited the highest abundance in the oxic and anoxic zone, respectively. Furthermore, there was a successional shift in sulfate-reducing bacteria (SRB) and sulfur-oxidizing bacteria in the anoxic zone across the seasons. The most dominant SRB, Desulfonatronovibrio sp., is likely one of the main producers of hydrogen sulfide (H2S) and typically accumulates the most H2S in winter. The representative anoxygenic phototrophic bacterial group in Lake Uchum was purple sulfur bacteria (PSB). PSB were dominant (60.76%) in summer, but only had 0.2-1.5% relative abundance from autumn to spring. Multivariate analysis revealed that the abundance of these SRB and PSB correlated to the concentration of H2S in Lake Uchum. Taken together, this study provides insights into the relationships between changes in bacterial community and environmental features in Lake Uchum.

Fast propagation regions cause self-sustained reentry in excitable media.

Self-sustained waves of electrophysiological activity can cause arrhythmia in the heart. These reentrant excitations have been associated with spiral waves circulating around either an anatomically defined weakly conducting region or a functionally determined core. Recently, an ablation procedure has been clinically introduced that stops atrial fibrillation of the heart by destroying the electrical activity at the spiral core. This is puzzling because the tissue at the anatomically defined spiral core would already be weakly conducting, and a further decrease should not improve the situation. In the case of a functionally determined core, an ablation procedure should even further stabilize the rotating wave. The efficacy of the procedure thus needs explanation. Here, we show theoretically that fundamentally in any excitable medium a region with a propagation velocity faster than its surrounding can act as a nucleation center for reentry and can anchor an induced spiral wave. Our findings demonstrate a mechanistic underpinning for the recently developed ablation procedure. Our theoretical results are based on a very general and widely used two-component model of an excitable medium. Moreover, the important control parameters used to realize conditions for the discovered phenomena are applicable to quite different multicomponent models.

Geometrical factors in propagation block and spiral wave initiation.

Many theoretical and experimental studies indicate that a propagation block represents an important factor in spiral wave initiation in excitable media. The analytical and numerical results we obtained for a generic two-component reaction-diffusion system demonstrate quantitative conditions for the propagation block in a one-dimensional and a two-dimensional medium due to a sharp spatial increase of the medium's excitability or the coupling strength above a certain critical value. Here, we prove that this critical value strongly depends on the medium parameters and the geometry of the inhomogeneity. For an exemplary two-dimensional medium, we show how the propagation block can be used to initiate spiral waves by a specific choice of the size and shape of the medium's inhomogeneity.

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model.

In a reaction-diffusion-advection system, with a convectively unstable regime, a perturbation creates a wave train that is advected downstream and eventually leaves the system. We show that the convective instability coexists with a local absolute instability when a fixed boundary condition upstream is imposed. This boundary induced instability acts as a continuous wave source, creating a local periodic excitation near the boundary, which initiates waves travelling both up and downstream. To confirm this, we performed analytical analysis and numerical simulations of a modified Martiel-Goldbeter reaction-diffusion model with the addition of an advection term. We provide a quantitative description of the wave packet appearing in the convectively unstable regime, which we found to be in excellent agreement with the numerical simulations. We characterize this new instability and show that in the limit of high advection speed, it is suppressed. This type of instability can be expected for reaction-diffusion systems that present both a convective instability and an excitable regime. In particular, it can be relevant to understand the signaling mechanism of the social amoeba Dictyostelium discoideum that may experience fluid flows in its natural habitat.

Influence of fast advective flows on pattern formation of Dictyostelium discoideum.

We report experimental and numerical results on pattern formation of self-organizing Dictyostelium discoideum cells in a microfluidic setup under a constant buffer flow. The external flow advects the signaling molecule cyclic adenosine monophosphate (cAMP) downstream, while the chemotactic cells attached to the solid substrate are not transported with the flow. At high flow velocities, elongated cAMP waves are formed that cover the whole length of the channel and propagate both parallel and perpendicular to the flow direction. While the wave period and transverse propagation velocity are constant, parallel wave velocity and the wave width increase linearly with the imposed flow. We also observe that the acquired wave shape is highly dependent on the wave generation site and the strength of the imposed flow. We compared the wave shape and velocity with numerical simulations performed using a reaction-diffusion model and found excellent agreement. These results are expected to play an important role in understanding the process of pattern formation and aggregation of D. discoideum that may experience fluid flows in its natural habitat.

Selection mechanism for rotating patterns in weakly excitable media.

Two types of patterns rigidly rotating within a disk of a weakly excitable medium are studied using the free-boundary approach. The patterns are spots moving along the boundary of the disk and spiral waves rotating around the disk center. The study reveals a selection mechanism that uniquely determines the shape and the angular velocity of these patterns as a function of the medium excitability and the disk radius. These two types of patterns coexist below some critical parameter value, coincide at a bifurcation point, and do not exist above it. The same selection mechanism is applied to describe a limiting case of a spiral wave rotating in an unbounded medium.

External forcing and feedback control of nonlinear dissipative waves.

The dynamics of traveling waves in a nonlinear dissipative system are studied analytically and numerically. Spatiotemporal forcing and feedback forcing are applied to the traveling waves in a phase-separated system undergoing chemical reactions. The stability of the traveling waves and interesting, unexpected behavior, including the reversal of the propagation direction are analyzed in one dimension. The phase dynamical approach is applied to gain a theoretical understanding of the dynamics.

Dynamics of spiral waves under global feedback in excitable domains of different shapes.

It is found that the dynamics of spiral waves subjected to global feedback is extremely sensitive to the domain shape. Bifurcations in the velocity field which specifies the resonant drift of the spiral wave core induced by global feedback are analyzed. It is shown, for example, that smooth variation of the eccentricity of an elliptical domain induces a cascade of bifurcations that can dramatically change the spiral wave evolution. In a square domain a set of point attractors appears instead of the circular resonance attractor typical of a circular domain. These predictions are in good quantitative agreement with numerical integrations of an excitable reaction-diffusion system performed under global feedback.

Resonance attractors of spiral waves in excitable media under global feedback.

The dynamics of spiral waves on a circular domain is studied by numerical integration of an excitable reaction-diffusion system with a global feedback. A theory based on the Fourier expansion of the feedback signal is developed to explain the existence and the stability of resonance attractors of spiral waves on domains of different sizes. The theoretical analysis predicts the existence of a discrete set of stable attractors with radii depending on the time delay in the feedback loop. These predictions are in good quantitative agreement with performed numerical simulations.

Instabilities of the resonance attractor for spiral waves in an excitable medium.

During an experimental study of the resonance attractor for spiral waves in the light-sensitive Belousov-Zhabotinsky reaction, strong deviations of the attractor trajectories from circular orbits are observed if the time delay in the feedback loop becomes relatively long. A theory is developed that reduces the spiral wave dynamics under a long-delayed control to a higher order iterative map. Then the observed deviations are explained to be a result of instabilities appearing due to the Neimark bifurcation of the map. The theoretical predictions are in good agreement with the experimental data.

External forcing of spiral waves.

The effect of an external rhythm on rotating spiral waves in excitable media is investigated. Parameters of the unperturbed medium were chosen, such that the organizing spiral tip describes meandering (hypocyclic) trajectories, which are the most general shape for the experimentally observed systems. Periodical modulation of excitability in a model of the Belousov-Zhabotinsky (BZ) reaction forces meandering spiral tips to describe trajectories that are not found at corresponding stationary conditions. For different modulation periods, two types of resonance drift, phase-locked tip motion, a spectrum of hypocyclic trajectories, and complex multifrequency patterns were computed. The computational results are complemented by experimental data obtained for periodically changing illumination of the photosensitive BZ reaction. The observed drastic deformation of the tip trajectory is considered as an efficient means to study and to control wave processes in excitable media.

Wave front interaction model of stabilized propagating wave segments.

A wave front interaction model is developed to describe the relationship between excitability and the size and shape of stabilized wave segments in a broad class of weakly excitable media. These wave segments of finite size are unstable but can be stabilized by feedback to the medium excitability; they define a separatrix between spiral wave behavior and contracting wave segments. Unbounded wave segments (critical fingers) lie on the asymptote of this separatrix, defining the boundary between excitable and subexcitable media. The model predictions are compared with results from numerical simulations.