From discrete to continuum models of three-dimensional deformations in epithelial sheets

International audienceEpithelial tissue, in which cells adhere tightly to each other and to theunderlying substrate, is one of the four major tissue types in adultorganisms. In embryos, epithelial sheets serve as versatile substratesduring the formation of developing organs. Some aspects of epithelialmorphogenesis can be adequately described using vertex models, in which thetwo-dimensional arrangement of epithelial cells is approximated by apolygonal lattice with an energy that has contributions reflecting theproperties of individual cells and their interactions. Previous studieswith such models have largely focused on dynamics confined to two spatialdimensions and analyzed them numerically. We show how these models can beextended to account for three-dimensional deformations and studiedanalytically. Starting from the extended model, we derive a continuumplate description of cell sheets, in which the effective tissue properties,such as bending rigidity, are related explicitly to the parameters of thevertex model. To derive the continuum plate model, we duly take intoaccount a microscopic shift between the two sublattices of the hexagonalnetwork, which has been ignored in previous work. As an application of thecontinuum model, we analyze tissue buckling by a line tension applied alonga circular contour, a simplified set-up relevant to several situations inthe developmental context. The buckling thresholds predicted by thecontinuum description are in good agreement with the results of directstability calculations based on the vertex model. Our results establish adirect connection between discrete and continuum descriptions of cellsheets and can be used to probe a wide range of morphogenetic processes inepithelial tissues

Radiative acceleration and transient, radiation-induced electric fields

The radiative acceleration of particles and the electrostatic potential fields that arise in low density plasmas hit by radiation produced by a transient, compact source are investigated. We calculate the dynamical evolution and asymptotic energy of the charged particles accelerated by the photons and the radiation-induced electric double layer in the full relativistic, Klein-Nishina regime. For fluxes in excess of $10^{27}$ ${\rm erg} {\rm cm}^{-2} {\rm s}^{-1}$, the radiative force on a diluted plasma (n\la 10^{11} cm$^{-3}$) is so strong that electrons are accelerated rapidly to relativistic speeds while ions lag behind owing to their larger inertia. The ions are later effectively accelerated by the strong radiation-induced double layer electric field up to Lorentz factors $\approx 100$, attainable in the case of negligible Compton drag. The asymptotic energies achieved by both ions and electrons are larger by a factor 2--4 with respect to what one could naively expect assuming that the electron-ion assembly is a rigidly coupled system. The regime we investigate may be relevant within the framework of giant flares from soft gamma-repeaters.Comment: 14 pages, 7 figures, ApJ, in press (tentatively scheduled for the v. 592, 2003 issue

Where Are All The Fallback Disks? Constraints on Propeller Systems

Fallback disks are expected to form around new-born neutron stars following a supernova explosion. In almost all cases, the disk will pass through a propeller stage. If the neutron star is spinning rapidly (initial period $\sim 10$ ms) and has an ordinary magnetic moment ($\sim 10^{30}$ G cm$^3$), the rotational power transferred to the disk by the magnetic field of the neutron star will exceed the Eddington limit by many orders of magnitude, and the disk will be rapidly disrupted. Fallback disks can thus survive only around slow-born neutron stars and around black holes, assuming the latter do not torque their surrounding disks as strongly as do neutron stars. This might explain the apparent rarity of fallback disks around young compact objects.Comment: Submitted to Astrophysical Journal Letter

A variational approach to the stochastic aspects of cellular signal transduction

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making more transparent the physical significance of the variational method. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure

Relativistic Structure, Stability and Gravitational Collapse of Charged Neutron Stars

Charged stars have the potential of becoming charged black holes or even naked singularities. It is presented a set of numerical solutions of the Tolman-Oppenheimer-Volkov equations that represents spherical charged compact stars in hydrostatic equilibrium. The stellar models obtained are evolved forward in time integrating the Einstein-Maxwell field equations. It is assumed an equation of state of a neutron gas at zero temperature. The charge distribution is taken as been proportional to the rest mass density distribution. The set of solutions present an unstable branch, even with charge to mass ratios arbitrarily close to the extremum case. It is performed a direct check of the stability of the solutions under strong perturbations, and for different values of the charge to mass ratio. The stars that are in the stable branch oscillates and do not collapse, while models in the unstable branch collapse directly to form black holes. Stars with a charge greater or equal than the extreme value explode. When a charged star is suddenly discharged, it don't necessarily collapse to form a black hole. A non-linear effect that gives rise to the formation of an external shell of matter (see Ghezzi and Letelier 2005), is negligible in the present simulations. The results are in agreement with the third law of black hole thermodynamics and with the cosmic censorship conjecture.Comment: 27 pages, 14 figures, 4 tables, paper accepte

Simultaneous direct measurement of the electrocaloric and dielectric dynamics of ferroelectrics with microsecond temporal resolution

A contactless technique for direct time-resolved measurements of the full dynamics of the adiabatic temperature change in electrocaloric materials is introduced. The infrared radiation emitted by the electrocaloric sample is sensitively detected with $\mu$s time resolution and mK temperature resolution. We present time-resolved measurements of the electrocaloric effect up to kHz frequencies of the driving electric field and down to small field strengths. The simultaneous recording of transients for applied electric field and induced polarization gives a comprehensive view on the correlation of electrocaloric and ferroelectric properties. The technique can further be applied to the continuous measurement of fatigue for $> 10^6$ electric field cycles.Comment: 12 pages, 11 figure

Pattern formation by a moving morphogen source

Abstract During Drosophila melanogaster oogenesis, the follicular epithelium that envelops the germline cyst gives rise to an elaborate eggshell, which houses the future embryo and mediates its interaction with the environment. A prominent feature of the eggshell is a pair of dorsal appendages, which are needed for embryo respiration. Morphogenesis of this structure depends on broad, a zinc-finger transcription factor, regulated by the EGFR pathway. While much has been learned about the mechanisms of broad regulation by EGFR, current understanding of processes that shape the spatial pattern of broad expression is incomplete. We propose that this pattern is defined by two different phases of EGFR activation: an early, posterior-to-anterior gradient of EGFR signaling sets the posterior boundary of broad expression, while the anterior boundary is set by a later phase of EGFR signaling, distributed in a dorsoventral gradient. This model can explain the wild-type pattern of broad in D. melanogaster, predicts how this pattern responds to genetic perturbations, and provides insight into the mechanisms driving diversification of eggshell patterning. The proposed model of the broad expression pattern can be used as a starting point for the quantitative analysis of a large number of gene expression patterns in Drosophila oogenesis

Nonadiabatic charged spherical gravitational collapse

We present a complete set of the equations and matching conditions required for the description of physically meaningful charged, dissipative, spherically symmetric gravitational collapse with shear. Dissipation is described with both free-streaming and diffusion approximations. The effects of viscosity are also taken into account. The roles of different terms in the dynamical equation are analyzed in detail. The dynamical equation is coupled to a causal transport equation in the context of Israel-Stewart theory. The decrease of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamic state, is reobtained, with the viscosity terms included. In accordance with the equivalence principle, the same decrease factor is obtained for the gravitational force term. The effect of the electric charge on the relation between the Weyl tensor and the inhomogeneity of energy density is discussed.Comment: 23 pages, Latex. To appear in Phys. Rev. D. Some references correcte

Gravitational clustering of relic neutrinos and implications for their detection

We study the gravitational clustering of big bang relic neutrinos onto existing cold dark matter (CDM) and baryonic structures within the flat $\Lambda$CDM model, using both numerical simulations and a semi-analytical linear technique, with the aim of understanding the neutrinos' clustering properties for direct detection purposes. In a comparative analysis, we find that the linear technique systematically underestimates the amount of clustering for a wide range of CDM halo and neutrino masses. This invalidates earlier claims of the technique's applicability. We then compute the exact phase space distribution of relic neutrinos in our neighbourhood at Earth, and estimate the large scale neutrino density contrasts within the local Greisen--Zatsepin--Kuzmin zone. With these findings, we discuss the implications of gravitational neutrino clustering for scattering-based detection methods, ranging from flux detection via Cavendish-type torsion balances, to target detection using accelerator beams and cosmic rays. For emission spectroscopy via resonant annihilation of extremely energetic cosmic neutrinos on the relic neutrino background, we give new estimates for the expected enhancement in the event rates in the direction of the Virgo cluster.Comment: 38 pages, 8 embedded figures, iopart.cls; v2: references added, minor changes in text, to appear in JCA