200 research outputs found
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 (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
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