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Description du livre

Paolo Maiuri, Jean-Francois Rupprecht, Stefan Wieser, Verena Ruprecht, Olivier Benichou, Nicolas Carpi, Mathieu Coppey, Simon De Beco, Nir Gov, Carl-Philipp Heisenberg, Carolina Lage Crespo, Franziska Lautenschlaeger, Mael Le Berre, Ana-Maria Lennon-Dumenil, Matthew Raab, Hawa-Racine Thiam, Matthieu Piel, Michael Sixt and Raphael Voituriez.  Cell(2015), in press. Available online at:

Eukaryotic cell migration is essential for a large set of biological processes, from development to immunity or  cancer. Assessing quantitatively the exploratory efficiency of cell trajectories is therefore crucial. In the absence of external guidance, cell movement can be described as a random motion, and proposed models have ranged from simple Brownian motion to persistent random walks, Levy walks, or composite processes such as intermittent random walks. Such models differ in the cell persistence, which quantifies the ability of a cell to maintain its direction of motion. The variety of behaviors, observed even along a single cell trajectory, stems from the fact that, as opposed to a passive tracer in a medium at thermal equilibrium, which performs a classical Brownian motion, a cell is self-propelled, and as such, belongs to the class of active Brownian particles. This class of processes is extremely vast and needs to be restricted to have some predicting power.

 In this work, we show on the basis of experimental data in vitro and in vivo that cell persistence is robustly coupled to cell migration speed. We suggest that this universal coupling constitutes a generic law of cell migration, which originates in the advection of polarity cues by an actin cytoskeleton undergoing flows at the cellular scale. Our analysis relies on a theoretical model that we validate by measuring the persistence of cells upon modulation of actin flow speeds. Beyond the quantitative prediction of the coupling, the model yields a generic phase diagram of cellular trajectories, which recapitulates the full range of observed migration patterns.


Evaluation of departure from equilibrium at cellular scale
Carlo Bianca and Annie Lemarchand
J. Chem. Phys. 141, 144102 (2014)

The complex spatiotemporal structures that appear in biological systems require farfrom equilibrium conditions which lead to the circulation of reaction fluxes. Recent developments in nonequilibrium statistical physics propose a theoretical framework for estimating these reaction fluxes. In particular, the time asymmetry of fluctuations could be a priori exploited. Fluorescence imaging gives directly access to the observation of the dynamics of cellular events. The temporal ordering of three proteins in the endocytic pathway has been extracted and reaction flux has been estimated for an assumed mechanism with linear dynamics [D. R. Sisan, D. Yarar, C. M. Waterman, and J. S. Urbach, Biophys. J. 98, 2432 (2010)]. However, endocytosis is known to involve complex regulation mechanisms and our aim is to warn against the blind use of the simple relation between reaction flux and crosscorrelation function of concentration fluctuations found for linear deterministic dynamics [W. J. Heuett and H. Qian, J. Chem. Phys. 124, 044110 (2006)].

In the biologically relevant case of a reactive system which may admit periodic oscillations, our results show that the amplitude of the crosscorrelation functions is not only proportional to the reaction flux but also to a specific parameterdependent function which diverges as the Hopf bifurcation approaches. In order to harvest the determination of correlation functions for reaction flux estimation in a given chemical system, it is therefore essential first to identify the reactionmechanism and secondly to evaluate the associated rate constants. If these demanding requirements may be fulfilled, the stochastic differential equations of Langevin type governing the fluctuating
dynamics of concentrations provides a reliable, analytical formula relating the reaction flux and the correlations of fluctuations. From the theoretical viewpoint, the interplay between fluctuations and nonlinearities of deterministic dynamics is subtle and leads to specific formulas for the time crosscorrelations
of concentration fluctuations, that depend on the details of dynamics.



Difference of time cross-correlation functions of concentration fluctuations, I(t)=<(X(0)-XS)(Y(t)-YS)>-<(X(t)-XS)(Y(0)-YS)>,

in the case of the Brusselator model, known to possess a stationary state (XS,YS) and a Hopf bifurcation. The concentrations of species A, B, and C are fixed and the concentrations X(t) and Y(t) of species X and Y are variable. The results of the numerical solution of the master equation (blue dashed line) confirm the analytical approach by Langevin equations (red dashed line) and invalidate the result obtained when assuming that dynamics is linear (black dotted line).



F. Léonard and B. Delamotte
Phys. Rev. Lett. 115, 200601 – Published 10 November 2015


We present models where γ+ and γ−, the exponents of the susceptibility in the high- and low-temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete anisotropies that are irrelevant in the renormalization-group sense. The Zq-invariant models are the simplest examples for two-component order parameters (N=2) and the model with icosahedral symmetry for N=3. We accurately compute γ+−γ− as well as the ratio ν/ν′ of the exponents of the two correlation lengths present for T<Tc.