Dynamics in a Bistable-Element-Network with Delayed Coupling and Local Noise

The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a dichotomous model. We find that for a strong enough positive feedback the system undergoes a phase transition and adopts a non-zero stationary mean field. A variety of coexisting oscillatory mean field states are found for positive and negative couplings. The magnitude of the oscillatory states is maximal for a certain noise temperature, i.e., the system demonstrates the phenomenon of coherence resonance. While away form the transition points the system dynamics is well described by the Gaussian approximation, near the bifurcations it is more adequately described by the dichotomous model.Comment: 2 pages, 2 figures. To be published in the proceedings of "The 3rd International Symposium on Slow Dynamics in Complex Systems", eds. M. Tokuyama, I. Oppenheim, AIP Conf. serie

Statistical Theory of Asymmetric Damage Segregation in Clonal Cell Populations

Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the mother cell. Previous studies demonstrated that ADS provides a selective advantage over symmetrically dividing cells by rejuvenating and perpetuating the population as a whole. In this work we focus on the statistical properties of damage in individual lineages and the overall damage distributions in growing populations for a variety of ADS models with different rules governing damage accumulation, segregation, and the lifetime dependence on damage. We show that for a large class of deterministic ADS rules the trajectories of damage along the lineages are chaotic, and the distributions of damage in cells born at a given time asymptotically becomes fractal. By exploiting the analogy of linear ADS models with the Iterated Function Systems known in chaos theory, we derive the Frobenius-Perron equation for the stationary damage density distribution and analytically compute the damage distribution moments and fractal dimensions. We also investigate nonlinear and stochastic variants of ADS models and show the robustness of the salient features of the damage distributions.Comment: Mathematical Biosciences, 2023 (in press

Swarming and swirling in self-propelled polar granular rods

Using experiments with anisotropic vibrated rods and quasi-2D numerical simulations, we show that shape plays an important role in the collective dynamics of self-propelled (SP) particles. We demonstrate that SP rods exhibit local ordering, aggregation at the side walls, and clustering absent in round SP particles. Furthermore, we find that at sufficiently strong excitation SP rods engage in a persistent swirling motion in which the velocity is strongly correlated with particle orientation.Comment: 4 page

Discrete stochastic modeling of calcium channel dynamics

We propose a simple discrete stochastic model for calcium dynamics in living cells. Specifically, the calcium concentration distribution is assumed to give rise to a set of probabilities for the opening/closing of channels which release calcium thereby changing those probabilities. We study this model in one dimension, analytically in the mean-field limit of large number of channels per site N, and numerically for small N. As the number of channels per site is increased, the transition from a non-propagating region of activity to a propagating one changes in nature from one described by directed percolation to that of deterministic depinning in a spatially discrete system. Also, for a small number of channels a propagating calcium wave can leave behind a novel fluctuation-driven state, in a parameter range where the limiting deterministic model exhibits only single pulse propagation.Comment: 4 pages, 5 figures, submitted to PR