Spatial Fluctuations at Vertices of Epithelial Layers: Quantification of Regulation by Rho Pathway.

In living matter, shape fluctuations induced by acto-myosin are usually studied in vitro via reconstituted gels, whose properties are controlled by changing the concentrations of actin, myosin, and cross-linkers. Such an approach deliberately avoids consideration of the complexity of biochemical signaling inherent to living systems. Acto-myosin activity inside living cells is mainly regulated by the Rho signaling pathway, which is composed of multiple layers of coupled activators and inhibitors. Here, we investigate how such a pathway controls the dynamics of confluent epithelial tissues by tracking the displacements of the junction points between cells. Using a phenomenological model to analyze the vertex fluctuations, we rationalize the effects of different Rho signaling targets on the emergent tissue activity by quantifying the effective diffusion coefficient, and the persistence time and length of the fluctuations. Our results reveal an unanticipated correlation between layers of activation/inhibition and spatial fluctuations within tissues. Overall, this work connects regulation via biochemical signaling with mesoscopic spatial fluctuations, with potential application to the study of structural rearrangements in epithelial tissues.

Active Mechanics Reveal Molecular-Scale Force Kinetics in Living Oocytes.

Active diffusion of intracellular components is emerging as an important process in cell biology. This process is mediated by complex assemblies of molecular motors and cytoskeletal filaments that drive force generation in the cytoplasm and facilitate enhanced motion. The kinetics of molecular motors have been precisely characterized in vitro by single molecule approaches, but their in vivo behavior remains elusive. Here, we study the active diffusion of vesicles in mouse oocytes, where this process plays a key role in nuclear positioning during development, and combine an experimental and theoretical framework to extract molecular-scale force kinetics (force, power stroke, and velocity) of the in vivo active process. Assuming a single dominant process, we find that the nonequilibrium activity induces rapid kicks of duration τ ∼ 300 µs resulting in an average force of F ∼ 0.4 pN on vesicles in in vivo oocytes, remarkably similar to the kinetics of in vitro myosin-V. Our results reveal that measuring in vivo active fluctuations allows extraction of the molecular-scale activity in agreement with single-molecule studies and demonstrates a mesoscopic framework to access force kinetics.

How Far from Equilibrium Is Active Matter?

Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturbatively their steady-state measure and show that, for short persistent times, the entropy production rate vanishes. This endows such systems with an effective fluctuation-dissipation theorem akin to that of thermal equilibrium systems. Last, we show how interacting particle systems with viscous drags and correlated noises can be seen as in equilibrium with a viscoelastic bath but driven out of equilibrium by nonconservative forces, hence providing energetic insight into the departure of active systems from equilibrium.

Switching and growth for microbial populations in catastrophic responsive environments.

Phase variation, or stochastic switching between alternative states of gene expression, is common among microbes, and may be important in coping with changing environments. We use a theoretical model to assess whether such switching is a good strategy for growth in environments with occasional catastrophic events. We find that switching can be advantageous, but only when the environment is responsive to the microbial population. In our model, microbes switch randomly between two phenotypic states, with different growth rates. The environment undergoes sudden catastrophes, the probability of which depends on the composition of the population. We derive a simple analytical result for the population growth rate. For a responsive environment, two alternative strategies emerge. In the no-switching strategy, the population maximizes its instantaneous growth rate, regardless of catastrophes. In the switching strategy, the microbial switching rate is tuned to minimize the environmental response. Which of these strategies is most favorable depends on the parameters of the model. Previous studies have shown that microbial switching can be favorable when the environment changes in an unresponsive fashion between several states. Here, we demonstrate an alternative role for phase variation in allowing microbes to maximize their growth in catastrophic responsive environments.

Statistical physics of a model binary genetic switch with linear feedback.

We study the statistical properties of a simple genetic regulatory network that provides heterogeneity within a population of cells. This network consists of a binary genetic switch in which stochastic flipping between the two switch states is mediated by a "flipping" enzyme. Feedback between the switch state and the flipping rate is provided by a linear feedback mechanism: the flipping enzyme is only produced in the on switch state and the switching rate depends linearly on the copy number of the enzyme. This work generalizes the model of Visco [Phys. Rev. Lett. 101, 118104 (2008)] to a broader class of linear feedback systems. We present a complete analytical solution for the steady-state statistics of the number of enzyme molecules in the on and off states, for the general case where the enzyme can mediate flipping in either direction. For this general case we also solve for the flip time distribution, making a connection to first passage and persistence problems in statistical physics. We show that the statistics are non-Poissonian, leading to a peak in the flip time distribution. The occurrence of such a peak is analyzed as a function of the parameter space. We present a relation between the flip time distributions measured for two relevant choices of initial condition. We also introduce a correlation measure and use this to show that this model can exhibit long-lived temporal correlations, thus providing a primitive form of cellular memory. Motivated by DNA replication as well as by evolutionary mechanisms involving gene duplication, we study the case of two switches in the same cell. This results in correlations between the two switches; these can be either positive or negative depending on the parameter regime.

Non-poissonian statistics in a low-density fluid.

Our interest lies in the collisional statistics in an arbitrary interacting fluid. We show that even in the low-density limit and contrary to naive expectation, the number of collisions experienced by a tagged particle in a given time does not obey Poisson law, and that, conversely, the free flight time distribution is not a simple exponential. As an illustration, the hard sphere fluid case is worked out in detail. For this model, we analytically quantify those deviations and successfully compare our predictions against molecular dynamics simulations.

Collisional statistics of the hard-sphere gas.

We investigate the probability distribution functions of the free flight time and of the number of collisions in a hard-sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit, which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writing an equation for the generating function of the cumulants of the number of collisions, we came across a perfect mapping between our problem and a previously introduced model: the probabilistic ballistic annihilation process [Coppex, Phys. Rev. E 69, 11303 (2004)]. We exploit this analogy to construct a Monte Carlo-like algorithm able to investigate the asymptotically large time behavior of the collisional statistics within a reasonable computational time. In addition, our predictions are compared with the results of molecular dynamics simulations and the direct simulation Monte Carlo technique. An excellent agreement is reported.

Dynamics of a tracer granular particle as a nonequilibrium Markov process.

The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation, describing the dynamics of the tracer into a master equation for a continuous Markov process. The transition rates depend on the stationary velocity distribution of the gas. When the gas has a Gaussian velocity probability distribution function (PDF), the stationary velocity PDF of the tracer is Gaussian with a lower temperature and satisfies detailed balance for any value of the restitution coefficient alpha. As soon as the velocity PDF of the gas departs from the Gaussian form, detailed balance is violated. This nonequilibrium state can be characterized in terms of a Lebowitz-Spohn action functional W(tau) defined over trajectories of time duration tau. We discuss the properties of this functional and of a similar functional W(tau), which differs from the first for a term that is nonextensive in time. On the one hand, we show that in numerical experiments (i.e., at finite times tau), the two functionals have different fluctuations and W always satisfies an Evans-Searles-like symmetry. On the other hand, we cannot observe the verification of the Lebowitz-Spohn-Gallavotti-Cohen (LS-GC) relation, which is expected for W(tau) at very large times tau. We give an argument for the possible failure of the LS-GC relation in this situation. We also suggest practical recipes for measuring W(tau) and W(tau) in experiments.

Active cage model of glassy dynamics.

We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture some characteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a crossover between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage and the ratio of the hopping length to the cage size.

Exact solution of a model DNA-inversion genetic switch with orientational control.

DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA-inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in E. coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behavior: the distribution of times in the on state shows a peak and successive flip times are correlated.

Fluctuations of internal energy flow in a vibrated granular gas.

The nonequilibrium fluctuations of power flux in a fluidized granular media have been recently measured in an experiment [Phys. Rev. Lett. 92, 164301 (2004)], which was announced to be a verification of the fluctuation relation (FR) by Gallavotti and Cohen. An effective temperature was also identified and proposed to be a useful probe for such nonequilibrium systems. We explain these results in terms of a two-temperature Poisson process. Within this model, supported by independent molecular dynamics simulations, power flux fluctuations do not satisfy the FR and the nature of the effective temperature is clarified. In the pursuit of a hypothetical global quantity fulfilling the FR, this points to the need of considering candidates other than the power flux.