Critical properties of phase transitions in lattices of coupled logistic maps

We numerically demonstrate that collective bifurcations in two-dimensional lattices of locally coupled logistic maps share most of the defining features of equilibrium second-order phase transitions. Our simulations suggest that these transitions between distinct collective dynamical regimes belong to the universality class of Miller and Huse model with synchronous update

Robustness of force and stress inference in an epithelial tissue

During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to analyze the mechanisms controlling tissue morphogenesis. Recently, a mechanical measurement method based on force inference from cell shapes and connectivity has been developed. It is non-invasive, and can provide space-time maps of force and stress within an epithelial tissue, up to prefactors. We previously performed a comparative study of three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces. In the present study, to further validate and compare the three force inference methods, we tested their robustness by measuring temporal fluctuation of estimated forces. Quantitative data of cell-level dynamics in a developing tissue suggests that variation of forces and stress will remain small within a short period of time ($\sim$minutes). Here, we showed that cell-junction tensions and global stress inferred by the Bayesian force inference method varied less with time than those inferred by the method that estimates only tension. In contrast, the amplitude of temporal fluctuations of estimated cell pressures differs less between different methods. Altogether, the present study strengthens the validity and robustness of the Bayesian force-inference method.Comment: 4 pages, 4 figure

Tissue fusion over non-adhering surfaces

Tissue fusion eliminates physical voids in a tissue to form a continuous structure and is central to many processes in development and repair. Fusion events in vivo, particularly in embryonic development, often involve the purse-string contraction of a pluricellular actomyosin cable at the free edge. However in vitro, adhesion of the cells to their substrate favors a closure mechanism mediated by lamellipodial protrusions, which has prevented a systematic study of the purse-string mechanism. Here, we show that monolayers can cover well-controlled mesoscopic non-adherent areas much larger than a cell size by purse-string closure and that active epithelial fluctuations are required for this process. We have formulated a simple stochastic model that includes purse-string contractility, tissue fluctuations and effective friction to qualitatively and quantitatively account for the dynamics of closure. Our data suggest that, in vivo, tissue fusion adapts to the local environment by coordinating lamellipodial protrusions and purse-string contractions

Co-transport-induced instability of membrane voltage in tip-growing cells

A salient feature of stationary patterns in tip-growing cells is the key role played by the symports and antiports, membrane proteins that translocate two ionic species at the same time. It is shown that these co-transporters destabilize generically the membrane voltage if the two translocated ions diffuse differently and carry a charge of opposite (same) sign for symports (antiports). Orders of magnitude obtained for the time and lengthscale are in agreement with experiments. A weakly nonlinear analysis characterizes the bifurcation

Polarity patterns of stress fibers

Stress fibers are contractile actomyosin bundles commonly observed in the cytoskeleton of metazoan cells. The spatial profile of the polarity of actin filaments inside contractile actomyosin bundles is either monotonic (graded) or periodic (alternating). In the framework of linear irreversible thermodynamics, we write the constitutive equations for a polar, active, elastic one-dimensional medium. An analysis of the resulting equations for the dynamics of polarity shows that the transition from graded to alternating polarity patterns is a nonequilibrium Lifshitz point. Active contractility is a necessary condition for the emergence of sarcomeric, alternating polarity patterns.Comment: 5 pages, 3 figure

Magnetic order in the Ising model with parallel dynamics

It is discussed how the equilibrium properties of the Ising model are described by an Hamiltonian with an antiferromagnetic low temperature behavior if only an heat bath dynamics, with the characteristics of a Probabilistic Cellular Automaton, is assumed to determine the temporal evolution of the system.Comment: 9 pages, 3 figure

Relation between coupled map lattices and kinetic Ising models

A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity to a symmetry breaking bifurcation point. In parameter space four phases with different ergodic behaviour are observed. Although the coupling in the map lattice is diffusive, antiferromagnetic ordering is predominant. Via coarse graining the deterministic model is mapped to a master equation which establishes an equivalence between our system and a kinetic Ising model. Such an approach sheds some light on the dependence of the transient behaviour on the system size and the nature of the phase transitions.Comment: 15 pages, figures included, Phys. Rev. E in pres

Escape of the martian protoatmosphere and initial water inventory

Latest research in planet formation indicate that Mars formed within a few million years (Myr) and remained a planetary embryo that never grew to a more massive planet. It can also be expected from dynamical models, that most of Mars' building blocks consisted of material that formed in orbital locations just beyond the ice line which could have contained ~0.1-0.2 wt. % of H2O. By using these constraints, we estimate the nebula-captured and catastrophically outgassed volatile contents during the solidification of Mars' magma ocean and apply a hydrodynamic upper atmosphere model for the study of the soft X-ray and extreme ultraviolet (XUV) driven thermal escape of the martian protoatmosphere during the early active epoch of the young Sun. The amount of gas that has been captured from the protoplanetary disk into the planetary atmosphere is calculated by solving the hydrostatic structure equations in the protoplanetary nebula. Depending on nebular properties such as the dust grain depletion factor, planetesimal accretion rates and luminosities, hydrogen envelopes with masses >=3x10^{19} g to <=6.5x10^{22} g could have been captured from the nebula around early Mars. Depending of the before mentioned parameters, due to the planets low gravity and a solar XUV flux that was ~100 times stronger compared to the present value, our results indicate that early Mars would have lost its nebular captured hydrogen envelope after the nebula gas evaporated, during a fast period of ~0.1-7.5 Myr. After the solidification of early Mars' magma ocean, catastrophically outgassed volatiles with the amount of ~50-250 bar H2O and ~10-55 bar CO2 could have been lost during ~0.4-12 Myr, if the impact related energy flux of large planetesimals and small embryos to the planet's surface lasted long enough, that the steam atmosphere could have been prevented from condensing. If this was not the case... (continued)Comment: 47 pages, 10 figures, 3 tables, submitted to PS