Emergent patterns of activity in disordered biological systems: Role of heterogeneities in organizing the collective dynamics of excitable cell-assemblies and tissues[HBNI Th215]

Abstract

Many important physiological functions in living organisms are mediated by cells and tissue that are electrically excitable, such as neurons in the brain, cardiac myocytes, and uterine muscle cells. Excitable systems remain in a steady state in the absence of external perturbations. However, a supra-threshold stimulus results in the initiation of an excitation wave propagating through the medium. This allows a rich variety of collective dynamical patterns to be observed in such systems, including planar waves, spiral waves, spatio-temporal chaos and chimera states to name a few. Some of the observed dynamical regimes are especially important from the perspective of physiology for their functional implications. For example, spiral waves that can appear in cardiac tissue have been associated with potentially fatal arrhythmic phenomena such as tachycardia and fibrillation. In the gravid uterus, just prior to parturition, a transition to a coherent regime is observed where all cells exhibit phase synchrony. Thus, understanding the mechanisms underlying the emergence of these collective dynamical patterns observed in excitable media can have important benefits in terms of devising ecient therapies. While previous work has largely focused on homogeneous excitable media, biological systems are often quite heterogeneous. Biological tissue not only comprise di↵erent types of cells, but cellular processes can also have inherent randomness associated with them. The resulting disordered systems can yield collective phenomena unlike those observed in homogeneous systems and have possible relevance in understanding physiological anomalies. Heterogeneities can manifest themselves in a system in a number of ways. For instance, the medium can exhibit variable excitability. This can either be for structural reasons,such as the occurrence of cells with di↵erent properties, or because of transient changes in the medium arising from the non-linear nature of the wave propagation dynamics. It is observed that in organs and tissues, electrically passive cells are found alongside excitable cells, giving rise to structural heterogeneities in the medium. Unlike excitable cells, passive cells cannot generate action potentials. Such cells interact with neighboring excitable cells via di↵usion-like local transport processes mediated by gap-junctions. A spatially extended system of coupled excitable and passive cells can show periodic activity and display a wide variety of complex spatio-temporal patterns. Thus, in recent years, there has been considerable e↵ort in trying to understand the e↵ect that passive cells have on the dynamics of excitable systems. In this thesis, we have investigated a spectrum of emergent complex patterns that can arise in cell-assemblies and tissues comprising excitable, oscillatory or passive cells. Heterogeneity can be organized spatially, whereby the relative density of passive cells can vary in di↵erent regions of an organ. This can lead to a gradient in the frequency of periodic activity propagating through the medium that helps sustain directed waves of excitation in the tissue. We find that a suciently steep frequency gradient will result in the creation of one or few organizing centers in the domain that can drive system-wide activity. A possible consequence would be the appearance of coordinated unidirectional activation waves even in the absence of pacemaker cells, e.g., as seen in the gravid uterus. In this thesis we have also provided a generalisation of the mechanism of auto-rhythmicity in coupled heterogeneous quiescent units. Additionally, we have observed a reduction in the complexity of the collective dynamics - an emergent simplicity - when going from smaller units to a large, spatially extended system. Further, we have considered heterogeneous coupled biological oscillators, whose period varies depending on the cellular micro-environment, and have studied the topological transition to vortex unbinding in these systems - specifically to understand the creation and destruction of self-sustaining rotating waves and their potential role in generating Braxton-Hicks contraction of the uterus.