Atypical collective oscillatory activity in cardiac tissue uncovered by optogenetics
Abstract
Many biological processes emerge as frequency-dependent responses to trains of external stimuli. Heart rhythm disturbances, that is cardiac arrhythmias, are important examples as they are often triggered by specific patterns of preceding stimuli. In this study, we investigated how ectopic arrhythmias can be induced by external stimuli in cardiac tissue containing a localised area of depolarisation. Using optogenetic in vitro experiments and in silico modelling, we systematically explored the dynamics of these arrhythmias, which are characterised by local oscillatory activity, by gradually altering the degree of depolarisation in a predefined region. Our findings reveal a bi-stable system, in which transitions between oscillatory ectopic activity and a quiescent state can be precisely controlled, that is by adjusting the number and frequency of propagating waves through the depolarised area oscillations could be turned on or off. These frequency-dependent responses arise from collective mechanisms involving stable, non-self-oscillatory cells, contrasting with the typical role of self-oscillations in individual units within biophysical systems. To further generalise these findings, we demonstrated similar frequency selectivity and bi-stability in a simplified reaction–diffusion model. This suggests that complex ionic cell dynamics are not required to reproduce these effects; rather, simpler non-linear systems can replicate similar behaviour, potentially extending beyond the cardiac context.
Introduction
Biological systems like the heart typically display complex dynamical behaviour through interactions among components such as genes, proteins, or cells (Dana et al., 2008). These systems exhibit non-linear dynamics, feedback loops, and adaptability, reflecting phenomena like homeostasis, evolution, and rhythm stability (Xiong and Garfinkel, 2023). Central to the framework of dynamical systems is the concept of the phase space, a multidimensional representation in which each point corresponds to a unique state of the system. In geography, when a small ball rolls on a raised-relief map, a state would include the planar position, elevation, speed, and acceleration of the ball.
Within the phase space, the long-term behaviour of a system can often be described in terms of attractors, which are subsets of the phase space that trajectories tend towards over time. Attractors can take various forms, including fixed points, periodic orbits, and chaotic sets, reflecting the rich diversity of behaviours possible in dynamical systems. By replacing the ball with local rain in the raised-relief map, rivers, lakes, and other bodies of water are attractors where that rain is collected. A watershed, also known as a drainage basin, is an area of land where any rain that falls will drain into the same river, lake, or body of water. Therefore, they are 00000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001101
