Synchronization in autonomous mercury beating heart systems

The ability of the mercury beating heart (MBH) system to exhibit sustained mechanical and electrochemical activities simultaneously without any external agent (fluctuating or constant), has attracted researchers for decades. The interplay of these activities could mimic the biological phenomena such as a pulsating heart that occurs due to the coupled tissues exhibiting mechanical as well as electrical dynamics. In the present work, we have studied experimentally the dynamics of electrically coupled two and three autonomous MBH systems. A dynamical triangular (heart) shape, in the traditional watch glass geometry, has been chosen for the experiments. It is found that the redox potentials (electrical behavior) of the quasi-identical (due to the inherent heterogeneities in the setup) MBH systems get synchronized at the intermediate coupling strengths whereas coherence in their mechanical activities occur only at large coupling strengths. To the best of our knowledge, this synchronization phenomenon involving two distinct activities (electrical and mechanical) and different coupling thresholds has not been reported, so far. The coherent mechanical activities means the simultaneous occurrence of compressions and expansions in the coupled Hg drops, which are shown using snapshots. In addition to this, the redox time series have also been provided to demonstrate the synchronization in the electrical behavior of MBH systems. Moreover, a mathematical framework considering only electrical and mechanical components of the MBH systems is presented to validate the experimental findings that the strong synchrony in the redox potentials of the MBH systems is a prerequisite for the synchrony in their mechanical activities.