Spontaneous suppression of spiral turbulence based on feedback strategy

Optogenetics enables real-time spatiotemporal control over spiral wave dynamics in an excitable cardiac system

Propagation of non-linear waves is key to the functioning of diverse biological systems. Such waves can organize into spirals, rotating around a core, whose properties determine the overall wave dynamics. Theoretically, manipulation of a spiral wave core should lead to full spatiotemporal control over its dynamics. However, this theory lacks supportive evidence (even at a conceptual level), making it thus a long-standing hypothesis. Here, we propose a new phenomenological concept that involves artificially dragging spiral waves by their cores, to prove the aforementioned hypothesis in silico, with subsequent in vitro validation in optogenetically modified monolayers of rat atrial cardiomyocytes. We thereby connect previously established, but unrelated concepts of spiral wave attraction, anchoring and unpinning to demonstrate that core manipulation, through controlled displacement of heterogeneities in excitable media, allows forced movement of spiral waves along pre-defined trajectories. Consequently, we impose real-time spatiotemporal control over spiral wave dynamics in a biological system.

From a spinning galaxy to a swarm of honeybees, rotating spirals are widespread in nature. Even within the muscles of the heart, waves of electrical activity sometimes rotate spirally, leading to irregular heart rhythms or arrhythmia – a condition that can be fatal.

Irrespective of where they occur, spiral waves organize around a center or core with different biophysical properties compared to the rest of the medium. The properties of the core determine the overall dynamics of the spiral. This means that, theoretically, it should be possibly to completely control a spiral wave just by manipulating its core.

Now, Majumder, Feola et al. have tested this long-standing hypothesis using a combination of computer modeling and experiments with single layers of rat heart cells grown in a laboratory. First, the heart cells were genetically modified so that their electrical properties could be altered with light; in other words, the cells were put under optical control. Next, by using of a narrow beam of light, Majumder, Feola et al. precisely controlled the electrical properties of a small number of cells, which then attracted and supported a rotating spiral wave by acting as its new core. Moving the light beam allowed the core of the spiral wave to be shifted too, meaning the spiral wave could now be steered along any desired path in the cell layer.

Majumder, Feola et al. hope that these underlying principles may one day provide the basis of new treatments for irregular heartbeats that are more effective and less damaging to the heart than existing options. Yet first, more work is needed to translate these findings from single layers of cells to actual hearts.

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.

Proportional-integral control of propagating wave segments in excitable media

Numerical simulations are performed to demonstrate that proportional-integral control, one of the most commonly used feedback schemes in control engineering, can stabilize propagating wave segments in excitable media to a desired size. The proportional-integral controller measures the size of a wave segment and applies a spatially uniform signal to the medium. This controller has the following features: difficult trial-and-error adjustment is not necessary, wave segments can be stabilized to different sizes without readjusting the controller, and the wave segment size can be maintained even in media having position-dependent parameters.

A comparative study of nonequilibrium dynamics in complex and real Ginzburg-Landau equations

Complex and real Ginzburg-Landau equations have been numerically studied by implementing Euler discretization technique. In addition to characterizing the differences and similarities of patterns involving these two continuum dynamical equations, in a wide range of appropriate parameter space, we have also made quantitative comparisons of growth dynamics in the two cases. In most part of the above-mentioned parameter space the complex Ginzburg-Landau equation exhibits frozen spiral dynamics. Results on the unlocking of this freezing are also presented.

Unlocking of frozen dynamics in the complex Ginzburg-Landau equation

We present results for pattern formation and related dynamics in the two-dimensional complex Ginzburg-Landau equation. Both single and multispiral morphologies have been considered. For the former, Hagan's solution has been tested. In case of the multispiral morphology, at a late time, depending upon certain parameter values, the dynamics is found to be frozen. However, upon introduction of disorder in these parameters the frozen dynamics is observed to be unlocked. This latter result is counterintuitive considering our current knowledge of dynamics in disorder systems. We also present results for the role of shocks (the regions where Hagan's solution is violated) in the multispiral dynamics. It is observed that the suppression of the order-parameter amplitude, in this region, to the value allowed by Hagan's single-spiral solution, also unlocks the dynamical freezing. In this case, both the pattern and dynamics are observed to be very similar to the the dynamical XY model.

Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh-Nagumo model

Elimination and control of nonlinear phenomena in excitable media are important for academic interests and practical applications. This paper provides a systematic procedure to design external forces for eliminating a traveling wave in a one-dimensional piecewise linear FitzHugh-Nagumo model. This procedure allows us to design nonfeedback and feedback control systems. The feedback control systems are designed using classical control theory. Furthermore, this procedure is extended to a two-dimensional model and verified using numerical simulation.

Pattern formation controlled by time-delayed feedback in bistable media

Effects of time-delayed feedback on pattern formation are studied both numerically and theoretically in a bistable reaction-diffusion model. The time-delayed feedback applied to the activator and/or the inhibitor alters the behavior of the nonequilibrium Ising-Bloch (NIB) bifurcation. If the intensities of the feedbacks applied to the two species are identical, only the velocities of Bloch fronts are changed. If the intensities are different, both the critical point of the NIB bifurcation and the threshold of stability of front to transverse perturbations are changed. The effect of time-delayed feedback on the activator opposes the effect of time-delayed feedback on the inhibitor. When the time-delayed feedback is applied individually to one of the species, positive and negative feedbacks make the bifurcation point shift to different directions. The time-delayed feedback provides a flexible way to control the NIB bifurcation and the pattern formation.