We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial coupling, the system exhibits birhythmicity with two oscillation modes at largely different frequencies. Stability of uniform oscillations in the birhythmic region is analyzed by means of the phase dynamics approximation. Numerical simulations show that, depending on its parameters, the system has irregular intermittent regimes with local bursts of synchronization or desynchronization.

Spatiotemporal pattern formation in a product-activated enzymic reaction at high enzyme concentrations is investigated. Stochastic simulations show that catalytic turnover cycles of individual enzymes can become coherent and that complex wave patterns of molecular synchronization can develop. The analysis based on the mean-field approximation indicates that the observed patterns result from the presence of Hopf and wave bifurcations in the considered system.

Enzymatic reactions often involve slow conformational changes, with reaction cycles that sometimes require milliseconds or seconds to complete. The dynamics are strongly affected by fluctuations at the nanoscale. However, such enzymes often occur in small numbers in a cell; hence, the fluctuations caused by finite numbers of molecules should also be substantial. Because of these factors, the behavior of the system is likely to deviate from that of classical reaction-diffusion equations, in which immediate reaction events are assumed to occur without memory and between a huge number of molecules. In this work, we model each enzyme as a unit represented by a phase variable to investigate the effects of fluctuations in arrays of enzymes. Using an analysis based on partial differential equations and stochastic simulations, we show that fluctuations arising from internal states of enzymes (intramolecular fluctuations) and those arising from the stochastic nature of interactions between molecules (intermolecular fluctuations) have distinctive effects on spatiotemporal patterns; the former generally disturb synchronization at high frequencies, whereas the latter can enhance synchronization. The balance of the two types of fluctuations may determine the spatiotemporal behavior of biochemical processes.

The phenomenon of cardiac memory refers to the property of cardiac tissue whereby the effect of an external electrical activation outlasts the duration of presentation of stimulus by significant margin. Several molecular mechanisms have been proposed in literature to explain the possible basis of this memory. Electrophysiological models of cardiac cells coupled by GJ conductances are studied. Simulations include cell pair models and grid models. Memory effect is shown in cell pair as a lasting change in phase difference between the oscillations of two autorhythmic type of cardiac cells. Memory effect is demonstrated in grid models also where an external current input presented for prolonged duration induces long term changes in activation pattern of the grid. These lasting changes are also reflected in computed Electrocardiogram. Physiological validity of the proposed mechanism of adaptation of GJs is also addressed. The proposed mechanism is inspired by results from learning and memory literature in neuroscience and comparing the same with the cardiac case. Just as neuronal signaling is mediated by synapses, cardiac cells electrically interact with each other via GJs. Activity-dependent adaptation of synaptic ''strength'' is generally considered an important biological substrate of learning and memory in the brain. Similarly, according to the proposed mechanism of GJ adaptation, the GJ conductance varies as a function of membrane voltages of the cells coupled by the GJ. But from biophysical literature, GJs are known to depend on junctional voltage between a pair of coupled cells. The link between biophysics of GJs and the proposed mechanism is explored. It is demonstrated with the help of a theoretical model of voltage-sensitive dynamics of GJ channel, followed up by simulation studies, that the proposed dynamics of GJs is compatible with biophysics of GJs.

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