Density wave propagation of a wave train in a closed excitable medium

Instability of the Homogeneous Distribution of Chemical Waves in the Belousov-Zhabotinsky Reaction

Chemical traveling waves play an important role in biological functions, such as the propagation of action potential and signal transduction in the nervous system. Such chemical waves are also observed in inanimate systems and are used to clarify their fundamental properties. In this study, chemical waves were generated with equivalent spacing on an excitable medium of the Belousov–Zhabotinsky reaction. The homogeneous distribution of the waves was unstable and low- and high-density regions were observed. In order to understand the fundamental mechanism of the observations, numerical calculations were performed using a mathematical model, the modified Oregonator model, including photosensitive terms. However, the homogeneous distribution of the traveling waves was stable over time in the numerical results. These results indicate that further modification of the model is required to reproduce our experimental observations and to discover the fundamental mechanism for the destabilization of the homogeneous-distributed chemical traveling waves.

Local Membrane Curvature Pins and Guides Excitable Membrane Waves in Chemotactic and Macropinocytic Cells - Biomedical Insights From an Innovative Simple Model

PIP3 dynamics observed in membranes are responsible for the protruding edge formation in cancer and amoeboid cells. The mechanisms that maintain those PIP3 domains in three-dimensional space remain elusive, due to limitations in observation and analysis techniques. Recently, a strong relation between the cell geometry, the spatial confinement of the membrane, and the excitable signal transduction system has been revealed by Hörning and Shibata (2019) using a novel 3D spatiotemporal analysis methodology that enables the study of membrane signaling on the entire membrane (Hörning and Shibata, 2019). Here, using 3D spatial fluctuation and phase map analysis on actin polymerization inhibited Dictyostelium cells, we reveal a spatial asymmetry of PIP3 signaling on the membrane that is mediated by the contact perimeter of the plasma membrane — the spatial boundary around the cell-substrate adhered area on the plasma membrane. We show that the contact perimeter guides PIP3 waves and acts as a pinning site of PIP3 phase singularities, that is, the center point of spiral waves. The contact perimeter serves as a diffusion influencing boundary that is regulated by a cell size- and shape-dependent curvature. Our findings suggest an underlying mechanism that explains how local curvature can favor actin polymerization when PIP3 domains get pinned at the curved protrusive membrane edges in amoeboid cells.

Self-organization of multiarmed spiral waves in excitable media

We present an investigation of self-organized multiarmed spiral waves pinned to unexcitable circular obstacles in a thin layer of the excitable Belousov-Zhabotinsky reaction and in simulations using the Oregonator model. The multiarmed waves are initiated by a series of wave stimuli. In the proximity of the obstacle boundary, the wave rotation around the obstacle causes damped oscillations of the wave periods of all spiral arms. The dynamics of wave periods cause the wave velocities as well as the angular displacements between the adjacent arms to oscillate with decaying amplitudes. Eventually, all displacements approach approximately the same stable value so that all arms are distributed evenly around the obstacle. A further theoretical analysis reveals that the temporal dynamics of the angular displacements can be interpreted as underdamped harmonic oscillations. Far from the obstacles, the wave dynamics are less pronounced. The wave period becomes stable very soon after the initiation. When the number of spiral arms increases, the rotation of individual arms slows down but the wave period of the multiarmed spiral waves decreases. Due to their short period, multiarmed spiral waves emerging in the heart potentially result in severe pathological conditions.

Three-Dimensional Cell Geometry Controls Excitable Membrane Signaling in Dictyostelium Cells

Phosphatidylinositol (3-5)-trisphosphate (PtdInsP3) is known to propagate as waves on the plasma membrane and is related to the membrane-protrusive activities in Dictyostelium and mammalian cells. Although there have been a few attempts to study the three-dimensional (3D) dynamics of these processes, most studies have focused on the dynamics extracted from single focal planes. However, the relation between the dynamics and 3D cell shape remains elusive because of the lack of signaling information about the unobserved part of the membrane. Here, we show that PtdInsP3 wave dynamics are directly regulated by the 3D geometry (i.e., size and shape) of the plasma membrane. By introducing an analysis method that extracts the 3D spatiotemporal activities on the entire cell membrane, we show that PtdInsP3 waves self-regulate their dynamics within the confined membrane area. This leads to changes in speed, orientation, and pattern evolution, following the underlying excitability of the signal transduction system. Our findings emphasize the role of the plasma membrane topology in reaction-diffusion-driven biological systems and indicate its importance in other mammalian systems.

Geometry of Wave Propagation on Active Deformable Surfaces

Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between surface geometry and contraction wave dynamics remains poorly understood, but it will be essential for the future design of chemically driven soft robots and active materials. Here, we couple prototypical chemical wave and reaction-diffusion models to non-Euclidean shell mechanics to identify and characterize generic features of chemomechanical wave propagation on active deformable surfaces. Our theoretical framework is validated against recent data from contractile wave measurements on ascidian and starfish oocytes, producing good quantitative agreement in both cases. The theory is then applied to illustrate how geometry and preexisting discrete symmetries can be utilized to focus active elastic surface waves. We highlight the practical potential of chemomechanical coupling by demonstrating spontaneous wave-induced locomotion of elastic shells of various geometries. Altogether, our results show how geometry, elasticity, and chemical signaling can be harnessed to construct dynamically adaptable, autonomously moving mechanical surface waveguides.

Mechanism of spiral formation in heterogeneous discretized excitable media

Spiral waves on excitable media strongly influence the functions of living systems in both a positive and negative way. The spiral formation mechanism has thus been one of the major themes in the field of reaction-diffusion systems. Although the widely believed origin of spiral waves is the interaction of traveling waves, the heterogeneity of an excitable medium has recently been suggested as a probable cause. We suggest one possible origin of spiral waves using a Belousov-Zhabotinsky reaction and a discretized FitzHugh-Nagumo model. The heterogeneity of the reaction field is shown to stochastically generate unidirectional sites, which can induce spiral waves. Furthermore, we found that the spiral wave vanished with only a small reduction in the excitability of the reaction field. These results reveal a gentle approach for controlling the appearance of a spiral wave on an excitable medium.