Universal calcium fluctuations inHydramorphogenesis.

Understanding the collective physical processes that drive robust morphological transitions in animal development necessitates the characterization of the relevant fields involved in morphogenesis. Calcium (Ca2+) is recognized as one such field. In this study, we demonstrate that the spatial fluctuations of Ca2+duringHydraregeneration exhibit universal characteristics. To investigate this phenomenon, we employ two distinct controls, an external electric field andheptanol, a gap junction-blocking drug. Both lead to the modulation of the Ca2+activity and a reversible halting of the regeneration process. The application of an electric field enhances Ca2+activity in theHydra's tissue and increases its spatial correlations, while the administration ofheptanolinhibits its activity and diminishes the spatial correlations. Remarkably, the statistical characteristics of Ca2+spatial fluctuations, including the coefficient of variation and skewness, manifest universal shape distributions across tissue samples and conditions. We introduce a field-theoretic model, describing fluctuations in a tilted double-well potential, which successfully captures these universal properties. Moreover, our analysis reveals that the Ca2+activity is spatially localized, and theHydra's tissue operates near the onset of bistability, where the local Ca2+activity fluctuates between low and high excited states in distinct regions. These findings highlight the prominent role of the Ca2+field inHydramorphogenesis and provide insights into the underlying mechanisms governing robust morphological transitions.

Laplacian growth with an isolated bubble near a tip.

We construct exact solutions for the Saffman-Taylor problem in a planar Hele-Shaw cell for the case of an isolated bubble near the tip of an expanding bubble in the limit of zero surface tension. This construction utilizes the integrability of the problem in the limit of vanishing surface tension. It exploits the connection, brought by the Schwarz function, between the constants of motion and the shape of the bubbles. The results of this paper provide a step toward the theoretical understanding of the dynamics of Saffman-Taylor problem in a Hele-Shaw cell with randomly distributed tiny bubbles.

Observation of universal ageing dynamics in antibiotic persistence.

Stress responses allow cells to adapt to changes in external conditions by activating specific pathways1. Here we investigate the dynamics of single cells that were subjected to acute stress that is too strong for a regulated response but not lethal. We show that when the growth of bacteria is arrested by acute transient exposure to strong inhibitors, the statistics of their regrowth dynamics can be predicted by a model for the cellular network that ignores most of the details of the underlying molecular interactions. We observed that the same stress, applied either abruptly or gradually, can lead to totally different recovery dynamics. By measuring the regrowth dynamics after stress exposure on thousands of cells, we show that the model can predict the outcome of antibiotic persistence measurements. Our results may account for the ubiquitous antibiotic persistence phenotype2, as well as for the difficulty in attempts to link it to specific genes3. More generally, our approach suggests that two different cellular states can be observed under stress: a regulated state, which prepares cells for fast recovery, and a disrupted cellular state due to acute stress, with slow and heterogeneous recovery dynamics. The disrupted state may be described by general properties of large random networks rather than by specific pathway activation. Better understanding of the disrupted state could shed new light on the survival and evolution of cells under stress.

Instability of the Abrikosov Lattice due to Nonanalytic Core Reconstruction of Vortices in Bosonic Superfluids.

We study the impact of the nonanalytic reconstruction of vortex cores on static vortex structures in weakly coupled superfluids. We show that, in rotating two-dimensional systems, the Abrikosov vortex lattice is unstable to vortex core deformation: Each zero of the wave function becomes a cut of finite length. The directors characterizing the orientations of the cuts are themselves ordered in superstructures due either to surface effects or to interaction with shear deformations of the lattice (spiral structure). Similar instability may also be observable in clean superconducting films.

Lineage correlations of single cell division time as a probe of cell-cycle dynamics.

Stochastic processes in cells are associated with fluctuations in mRNA, protein production and degradation, noisy partition of cellular components at division, and other cell processes. Variability within a clonal population of cells originates from such stochastic processes, which may be amplified or reduced by deterministic factors. Cell-to-cell variability, such as that seen in the heterogeneous response of bacteria to antibiotics, or of cancer cells to treatment, is understood as the inevitable consequence of stochasticity. Variability in cell-cycle duration was observed long ago; however, its sources are still unknown. A central question is whether the variance of the observed distribution originates from stochastic processes, or whether it arises mostly from a deterministic process that only appears to be random. A surprising feature of cell-cycle-duration inheritance is that it seems to be lost within one generation but to be still present in the next generation, generating poor correlation between mother and daughter cells but high correlation between cousin cells. This observation suggests the existence of underlying deterministic factors that determine the main part of cell-to-cell variability. We developed an experimental system that precisely measures the cell-cycle duration of thousands of mammalian cells along several generations and a mathematical framework that allows discrimination between stochastic and deterministic processes in lineages of cells. We show that the inter- and intra-generation correlations reveal complex inheritance of the cell-cycle duration. Finally, we build a deterministic nonlinear toy model for cell-cycle inheritance that reproduces the main features of our data. Our approach constitutes a general method to identify deterministic variability in lineages of cells or organisms, which may help to predict and, eventually, reduce cell-to-cell heterogeneity in various systems, such as cancer cells under treatment.

Fluctuations in the relaxation dynamics of mixed chaotic systems.

The relaxation dynamics in mixed chaotic systems are believed to decay algebraically with a universal decay exponent that emerges from the hierarchical structure of the phase space. Numerical studies, however, yield a variety of values for this exponent. In order to reconcile these results, we consider an ensemble of mixed chaotic systems approximated by rate equations and analyze the fluctuations in the distribution of Poincaré recurrence times. Our analysis shows that the behavior of these fluctuations, as a function of time, implies a very slow convergence of the decay exponent of the relaxation.

Localized rayleigh instability in evaporation fronts.

A qualitatively different manifestation of the Rayleigh instability is demonstrated, where, instead of the usual extended undulations and breakup of the liquid into many droplets, the instability is localized, leading to an isolated narrowing of the liquid filament. The localized instability, caused by a nonuniform curvature of the liquid domain, plays a key role in the evaporation of thin liquid films off solid surfaces.

Viscous fingering in volatile thin films.

A thin water film on a cleaved mica substrate undergoes a first-order phase transition between two values of film thickness. By inducing a finite evaporation rate of the water, the interface between the two phases develops a fingering instability similar to that observed in the Saffman-Taylor problem. We draw the connection between the two problems, and construct solutions describing the dynamics of evaporation in this system.

Correlated tunneling and the instability of the fractional quantum Hall edge.

We consider a class of interaction terms that describes correlated tunneling of composite fermions between effective Landau levels. Despite being generic and of similar strength to that of the usual density-density couplings, these terms are not included in the accepted theory of the edges of fractional quantum Hall systems. Here we show that they may lead to an instability of the edge towards a new reconstructed state with additional channels, and thereby demonstrate the incompleteness of the traditional edge theory.

Long-range correlations in the speckle patterns of directed waves.

We develop a general method for calculating statistical properties of the speckle pattern of coherent waves propagating in disordered media. In some aspects this method is similar to the Boltzmann-Langevin approach for the calculation of classical fluctuations. We apply the method to the case where the incident wave experiences many small angle scattering events during propagation, but the total angle change remains small. In many aspects our results for this case are different from results previously known in the literature. The correlation function of the wave intensity at two points separated by a distance r, has a long-range character. It decays as a power of r and changes sign. We also consider sensitivities of the speckles to changes of external parameters, such as the wave frequency and the incidence angle.

Singularities of the Hele-Shaw flow and shock waves in dispersive media.

We show that singularities developed in the Hele-Shaw problem have a structure identical to shock waves in dissipativeless dispersive media. We propose an experimental setup where the cell is permeable to a nonviscous fluid and study continuation of the flow through singularities. We show that a singular flow in this nontraditional cell is described by the Whitham equations identical to Gurevich-Pitaevski solution for a regularization of shock waves in Korteveg-de Vriez equation. This solution describes regularization of singularities through creation of disconnected bubbles.

Statistical properties of spike trains: universal and stimulus-dependent aspects.

Statistical properties of spike trains measured from a sensory neuron in vivo are studied experimentally and theoretically. Experiments are performed on an identified neuron in the visual system of the blowfly. It is shown that the spike trains exhibit universal behavior over a short time, modulated by a stimulus-dependent envelope over a long time. A model of the neuron as a nonlinear oscillator driven by noise and by an external stimulus is suggested to account for these results. In the short-time universal regime, the main biophysical effect is refractoriness, which can be described as a repulsive ( 1/x) interaction law among spikes. A universal distribution function for intervals is found, defining a point process with special symmetry properties. The long-time modulations in the spike train are related in a simple way to the properties of the input stimulus as seen through the neuronal nonlinearity. Thus our model enables a separation of the effects of internal neuronal properties from the effect of external stimulus properties. Explicit formulas are derived for different statistical properties, which are in very good agreement with the data in both the universal and the stimulus-dependent regimes.

Viscous fingering and the shape of an electronic droplet in the quantum Hall regime.

We show that the semiclassical dynamics of an electronic droplet, confined in a plane in a quantizing inhomogeneous magnetic field in the regime where the electrostatic interaction is negligible, is similar to viscous (Saffman-Taylor) fingering on the interface between two fluids with different viscosities confined in a Hele-Shaw cell. Both phenomena are described by the same equations with scales differing by a factor of up to 10(-9). We also report the quasiclassical wave function of the droplet in an inhomogeneous magnetic field.