Resetting wave forms in dictyostelium territories

Dynamic surface patterns on cells

Dynamic pattern formations are commonly observed in multicellular systems, such as cardiac tissue and slime molds, and modeled using reaction–diffusion systems. Recent experiments have revealed dynamic patterns in the concentration profile of various cortical proteins at a much smaller scale, namely, embryos at their single-cell stage. Spiral waves of Rho and F-actin proteins have been reported in Xenopus frog and starfish oocytes [Bement et al., Nat. Cell Biol. 17, 1471 (2015)], while a pulsatile pattern of Rho and myosin proteins has been found in C. elegans embryo [Nishikawa et al., eLife 6, e30537 (2017)]. Here, we propose that these two seemingly distinct dynamic patterns are signatures of a single reaction–diffusion network involving active-Rho, inactive-Rho, actin, and myosin. We show that a small variation in the concentration of other ancillary proteins can give rise to different dynamical states from the same chemical network.

Predicting the distribution of spiral waves from cell properties in a developmental-path model of Dictyostelium pattern formation

The slime mold Dictyostelium discoideum is one of the model systems of biological pattern formation. One of the most successful answers to the challenge of establishing a spiral wave pattern in a colony of homogeneously distributed D. discoideum cells has been the suggestion of a developmental path the cells follow (Lauzeral and coworkers). This is a well-defined change in properties each cell undergoes on a longer time scale than the typical dynamics of the cell. Here we show that this concept leads to an inhomogeneous and systematic spatial distribution of spiral waves, which can be predicted from the distribution of cells on the developmental path. We propose specific experiments for checking whether such systematics are also found in data and thus, indirectly, provide evidence of a developmental path.

Self-organized pacemakers and bistability of pulses in an excitable medium

Pattern formation in an excitable medium described by a three-component reaction-diffusion system is investigated. Our focus is on stable self-organized pacemakers which give rise to spatially extended target patterns. Bistability of pulse solutions in the excitable regime is also reported, and interactions of the different pulses with each other and the pacemaker are studied. Self-organized pacemakers are created by a suitable perturbation from the steady state or through interaction of pulses. Bound states of one-dimensional pacemakers and phase flips are also observed.

Biology by numbers: mathematical modelling in developmental biology

In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.

Temperature Changes Visualization during Chemical Wave Propagation

Magnetic resonance imaging was used for two-dimensional temperature visualization of chemical waves propagation in the autocatalytic exothermal reaction of thiosulfate oxidation by chlorite. The technique presented is based on the temperature dependence of the water chemical shift. Temperature maps were acquired by employing the TurboFLASH imaging method. The results obtained allow one to judge about directions of buoyancy flows. Two types of convection critical modes in a vertical tube during the wave propagation were detected.

Noise can play an organizing role for the recurrent dynamics in excitable media

We analyze patterns of recurrent activity in a prototypical model of an excitable medium in the presence of noise. Without noise, this model robustly predicts the existence of spiral waves as the only recurrent patterns in two dimensions. With small noise, however, we found that this model is also capable of generating coherent target patterns, another type of recurrent activity that is widely observed experimentally. These patterns remain essentially deterministic despite the presence of the noise, yet their existence is impossible without it. Their degree of coherence can also be made arbitrarily high for wide ranges of the parameters, which does not require fine-tuning. Our findings demonstrate the need to reexamine current modeling approaches to active biological media.

Complex-periodic spiral waves in confluent cardiac cell cultures induced by localized inhomogeneities

Spatiotemporal wave activities in excitable heart tissues have long been the subject of numerous studies because they underlie different forms of cardiac arrhythmias. In particular, understanding the dynamics and the instabilities of spiral waves have become very important because they can cause reentrant tachycardia and their subsequent transitions to fibrillation. Although many aspects of cardiac spiral waves have been investigated through experiments and model simulations, their complex properties are far from well understood. Here, we show that intriguing complex-periodic (such as period-2, period-3, period-4, or aperiodic) spiral wave states can arise in monolayer tissues of cardiac cell culture in vitro, and demonstrate that these different dynamic states can coexist with abrupt and spontaneous transitions among them without any change in system parameters; in other words, the medium supports multistability. Based on extensive image data analysis, we have confirmed that these spiral waves are driven by their tips tracing complex orbits whose unusual, meandering shapes are formed by delicate interplay between localized conduction blocks and nonlinear properties of the culture medium.

Transverse instability of line defects of period-2 spiral waves

Spiral waves that arise in period-2 oscillatory media extended in space generically bear "line defects" along which the local kinetics exhibits a period-1 oscillation. Locally, these defect structures can be viewed as a front separating two period-2 oscillatory domains oscillating 2pi out of phase. Here we show that their shape can become sinusoidal with a transverse instability as in bistable fronts. This instability eventually leads to a line-defect filled spatiotemporal chaotic state having erratic proliferations, annihilations, and regenerations of line defects. The same sequence of phenomena is observed in a model reaction-diffusion system as well as in an experimental system.

Regular and alternant spiral waves of contractile motion on rat ventricle cell cultures

We demonstrate that meandering as well as regular spiral waves can form in a well-controlled culture layer of rat ventricle cells and that the meandering spiral wave, in particular, can generate an alternant rhythm. These observations are made possible by a newly developed, noninvasive phase contrast macro-optics that is simple but highly effective in visualizing the contractile motion of the populations of cardiac cells.

Spiking patterns emerging from wave instabilities in a one-dimensional neural lattice

The dynamics of a one-dimensional lattice (chain) of electrically coupled neurons modeled by the FitzHugh-Nagumo excitable system with modified nonlinearity is investigated. We have found that for certain conditions the lattice exhibits a countable set of pulselike wave solutions. The analysis of homoclinic and heteroclinic bifurcations is given. Corresponding bifurcation sets have the shapes of spirals twisting to the same center. The appearance of chaotic spiking patterns emerging from wave instabilities is discussed.

Shock structures and bunching fronts in excitable reaction-diffusion systems

We report experimental results on the dynamics of excitation waves in a modified Belousov-Zhabotinsky reaction. The waves in this system obey nonmonotonic dispersion relations. This anomaly induces the stacking of excitation fronts into patterns with stable interpulse distances. The stacking process creates either a traveling shock structure or a cascade of bunching events in which metastable wave packets are formed. The direction and the speed of the shock are explained in terms of a simple geometrical analysis. We also present experimental evidence for the corresponding instabilities in two-dimensional systems. Here, wave stacking generates atypical structures in the collision of target patterns and wave bunching is accompanied by complex front deformations.