Signalling centre vortices coordinate collective behaviour in social amoebae

Self-sustaining signalling waves provide a source of information in living systems. A classic example is the rotating spiral waves of cAMP (chemoattractant) release that encode Dictyostelium morphogenesis. These patterns remain poorly characterised due to limitations in tracking the signalling behaviour of individual cells in the context of the whole collective. Here, we have imaged Dictyostelium populations over millimetre length scales and track the emergence, structure, progression and biological effects of cAMP waves by monitoring the signalling states and motion of individual cells. Collective migration coincides with a decrease in the period and speed of waves that stem from an increase in the rotational speed and curvature of spiral waves. The dynamics and structure of spiral waves are generated by the vortex motion of the spiral tip. Spiral tip circulation spatially organises a small group of cells into a ring pattern, which also constrains spiral tip motion. Both the cellular ring and tip path gradually contract over time, resulting in the acceleration of spiral rotation and change in global wave dynamics. Aided by mathematical modelling, we show that this contraction is due to an instability driven by a deflection in cell chemotaxis around the spiral tip cAMP field, resulting in a deformation of the cellular ring pattern towards its centre. That is, vortex contraction modulates the source of information which, upon dissemination (excitable signal relay) and decoding (chemotaxis), triggers morphogenesis. By characterising rotating spiral waves at this level of detail, our results describe a mechanism by which information generated by a self-sustaining signal, and disseminated across the population, is modulated at the organisational source.

Spiral waves within a bistability parameter region of an excitable medium

Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

Dynamics of spiral waves and bubble formation in a closed chemical system of thin photosensitive excitable media

Spiral waves have been observed in a thin layer of excitable media. Especially, electrical spiral waves in cardiac tissues connect to cardiac tachycardia and life-threatening fibrillations. The Belousov-Zhabotinsky (BZ) reaction is the most widely used system to study the dynamics of spiral waves in experiments. When the light sensitive Ru(bpy)3 2+ is used as the catalyst, the BZ reaction becomes photosensitive and the excitability of the reaction can be controlled by varying the illumination intensity. However, the typical photosensitive BZ reaction produces many CO2 bubbles so the spiral waves are always studied in thin layer media with opened top surfaces to release the bubbles. In this work, we develop new chemical recipes of the photosensitive BZ reaction which produces less bubbles. To observe the production of bubbles, we investigate the dynamics of spiral waves in a closed thin layer system. The results show that both the speed of spiral waves and the number of bubbles increase with the concentration of sulfuric acid (H2SO4) and sodium bromate (NaBrO3). For high initial concentrations of both reactants, the size of bubbles increases with time until the wave structures are destroyed. We expect that the chemical recipes reported here can be used to study complicated dynamics of three-dimensional spiral waves in thick BZ media where the bubbles cannot escape.

Realization of fully biological restoration of cardiac rhythm: a computational translational exploration

Background Recently it was demonstrated how the heart itself could be enabled to quickly restore its rhythm by realizing a biologically-integrated cardiac defibrillator (BioICD) through modification and subsequent expression of ion channels in cardiomyocytes [1]. By incorporating these frequency-dependent depolarizing ion channels, abnormal cardiac rhythm could be rapidly detected and terminated to restore sinus rhythm in a fully biological and shock-free manner. However, from a translational point of view, it remains unclear how such rhythm restoration can be realized via ion channel gene therapy. Purpose To explore and understand the importance of the distribution and number of BioICD-expressing cardiomyocytes in realizing fully biological restoration of cardiac rhythm. Methods To this purpose, two different realistic gene therapy configurations, i.e. those corresponding to systemic and local transgene delivery, were tested in human ventricular virtual cardiac monolayers. For the systemic delivery group, BioICD-expressing cells were homogeneously distributed (10 random variations) over the tissue with fixed total expression percentage (14 percentages). For the local delivery group, circular areas (7 radii) were given BioICD-expressing cells randomly patterned (10 variations) in a Gaussian distribution with 3 fixed total expression percentages. For both groups, spiral waves were initiated (9 locations) and studied for the following 10 seconds for each test condition, thereby equaling 1260 and 1890 conditions, respectively. Results For systemic delivery, normal rhythm was restored in all cases for >50% BioICD expressing cells, with time till termination being inversely related to the percentage, resulting in only 4.3s and 2.5s for 50% and 100%, respectively. Regarding termination, it was observed that conduction blocks appeared throughout the tissue and subsequently connected to force arrhythmic waves to terminate, while this process remained incomplete in the <50% groups. Local delivery, on the other hand, resulted in islands of ionic heterogeneity, causing attraction and anchoring of the spiral waves in a size and distance-dependent manner. Hence, BioICD-based self-termination was not observed in any of the investigated conditions, leaving spiral waves to persist. Conclusion This study reveals that wide-spread distribution of BioICD-expressing cardiomyocytes is required for the realization of fully biological self-restoration of cardiac rhythm, of which the efficiency is dosage-dependent. Local expression, however, results in stabilization of spiral wave activity. Further exploration of this emerging concept of biological cardioversion may not only expand our understanding of cardiac arrhythmias, but also pave the way to breakthrough advances in arrhythmia management. FUNDunding Acknowledgement Type of funding sources: Public grant(s) – EU funding. Main funding source(s): European Research Council (Starting grant 716509) to D.A. Pijnappels.

Formation of spiral waves in cylindrical containers under orbital excitation

The lowest swirling wave mode arising in upright circular cylinders as a response to circular orbital excitation has been widely studied in the last decade, largely due to its high practical relevance for orbitally shaken bioreactors. Our recent theoretical study (Horstmann et al., J. Fluid Mech., vol. 891, 2020, A22) revealed a damping-induced symmetry breaking mechanism that can cause spiral wave structures manifested in the so far widely disregarded higher rotating wave modes. Building on this work, we develop a linear criterion describing the degree of spiralisation and classify different spiral regimes as a function of the most relevant dimensionless groups. The analysis suggests that high Bond numbers and shallow liquid layers favour the formation of coherent spiral waves. This result paved the way to find the predicted wave structures in our interfacial sloshing experiment. We present two sets of experiments, with different characteristic damping rates, verifying the formation of both coherent and overdamped spiral waves in conformity with the theoretical predictions.

Numerical continuation of spiral waves in heteroclinic networks of cyclic dominance

Heteroclinic-induced spiral waves may arise in systems of partial differential equations that exhibit robust heteroclinic cycles between spatially uniform equilibria. Robust heteroclinic cycles arise naturally in systems with invariant subspaces, and their robustness is considered with respect to perturbations that preserve these invariances. We make use of particular symmetries in the system to formulate a relatively low-dimensional spatial two-point boundary-value problem in Fourier space that can be solved efficiently in conjunction with numerical continuation. The standard numerical set-up is formulated on an annulus with small inner radius, and Neumann boundary conditions are used on both inner and outer radial boundaries. We derive and implement alternative boundary conditions that allow for continuing the inner radius to zero and so compute spiral waves on a full disk. As our primary example, we investigate the formation of heteroclinic-induced spiral waves in a reaction–diffusion model that describes the spatiotemporal evolution of three competing populations in a 2D spatial domain—much like the Rock–Paper–Scissors game. We further illustrate the efficiency of our method with the computation of spiral waves in a larger network of cyclic dominance between five competing species, which describes the so-called Rock–Paper–Scissors–Lizard–Spock game.