laboratoire de physique statistique
laboratoire de physique statistique


Modeling the Kinetics of Open Self-Assembly - Verdier, Timothee and Foret, Lionel and Castelnovo, Martin

Abstract : In this work, we explore theoretically the kinetics of molecular self-assembly in the presence of constant monomer flux as an input, and a maximal size. The proposed model is supposed to reproduce the dynamics of viral self-assembly for enveloped virus. It turns out that the kinetics of open self-assembly is rather quantitatively different from the kinetics of similar closed assembly. In particular, our results show that the convergence toward the stationary state is reached through assembly waves. Interestingly, we show that the production of complete clusters is much more efficient in the presence of a constant input flux, rather than providing all monomers at the beginning of the self-assembly.
The physics of lipid droplet nucleation, growth and budding - Thiam, Abdou Rachid and Foret, Lionel

Abstract : Lipid droplets (Ws) are intracellular oil-in-water emulsion droplets, covered by a phospholipid monolayer and mainly present in the cytosol. Despite their important role in cellular metabolism and growing number of newly identified functions, LD formation mechanism from the endoplasmic reticulum remains poorly understood. To form a LD, the oil molecules synthesized in the ER accumulate between the monolayer leaflets and induce deformation of the membrane. This formation process works through three steps: nucleation, growth and budding, exactly as in phase separation and dewetting phenomena. These steps involve sequential biophysical membrane remodeling mechanisms for which we present basic tools of statistical physics, membrane biophysics, and soft matter science underlying them. We aim to highlight relevant factors that could control LD formation size, site and number through this physics description. An emphasis will be given to a currently underestimated contribution of the molecular interactions between lipids to favor an energetically costless mechanism of LD formation. (C) 2016 Elsevier B.V. All rights reserved.
Comparing open and closed molecular self-assembly - Castelnovo, M. and Verdier, T. and Foret, L.
EPL 105 (2014) 

Abstract : We study theoretically in the present work the self-assembly of molecules in an open system, which is fed by monomers and depleted in partial or complete clusters. Such a scenario is likely to occur for example in the context of viral self-assembly. We provide a general formula for the mean-field size distribution which is valid both at equilibrium in a closed system, and in the stationary state in an open system. This allows us to explore in a simple way out-of-equilibrium features for self-assembly and compare them to equilibrium properties. In particular, we identify a region of parameter space for which the out-of-equilibrium size distribution in the presence of external fluxes is equal to the equilibrium size distribution in the absence of external fluxes, up to a constant renormalization factor. The range of validity of this result and its consequences are discussed. Copyright (c) EPLA, 2014
Shape and energy of a membrane bud induced by protein coats or viral protein assembly - Foret, Lionel

Abstract : Intracellular transport vesicles and enveloped virus production is mediated by the polymerization of proteins that form bi-dimensional curved and rigid structures, or ``coats'', on a membrane. Using the classical framework of fluid membrane elasticity, we compute numerically the shape and the mechanical energy of the membrane deformation induced by a coat at different stage of growth. We furthermore derive analytical approximate expressions for the membrane shape and energy. They are found to be very accurate when compared to numerical calculations. These analytical expressions should be useful when building a relevant model of coat polymerization kinetics. We also discuss some consequences of the membrane energy features on the coat assembly process, showing that at high tension a kinetically arrested state of incomplete assembly could exist.
Aggregation on a membrane of particles undergoing active exchange with a reservoir - Foret, L.

Abstract : We investigate the dynamics of clusters made of aggregating particles on a membrane which exchanges particles with a reservoir. Exchanges are driven by chemical reactions which supply energy to the system, leading to the establishment of a non-equilibrium steady state. We predict the distribution of cluster size at steady state. We show in particular that in a regime, that cannot exist at equilibrium, the distribution is bimodal: the membrane is mainly populated of single particles and finite-size clusters. This work is motivated by the observations that have revealed the existence of submicrometric clusters of proteins in biological membranes.
A General Theoretical Framework to Infer Endosomal Network Dynamics from Quantitative Image Analysis - Foret, Lionel and Dawson, Jonathan E. and Villasenor, Roberto and Collinet, Claudio and Deutsch, Andreas and Brusch, Lutz and Zerial, Marino and Kalaidzidis, Yannis and Juelicher, Frank
CURRENT BIOLOGY 221381-1390 (2012) 

Abstract : Background: Endocytosis allows the import and distribution of cargo into a series of endosomes with distinct morphological and biochemical characteristics. Our current understanding of endocytic cargo trafficking is based on the kinetics of net cargo transport between endosomal compartments without considering individual endosomes. However, endosomes form a dynamic network of membranes undergoing fusion and fission, thereby continuously exchanging and redistributing cargo. The macroscopic kinetic properties, i.e., the properties of the endosomal network as a whole, result from the collective behaviors of many individual endosomes, a problem so far largely unaddressed. Results: Here, we developed a general theoretical framework to describe the dynamics of cargo distributions in the endosomal network. We combined the theory with quantitative experiments to study how the macroscopic kinetic properties of the endosomal network emerge from microscopic processes at the level of individual endosomes. We compared our theory predictions to experimental data in which dynamic distributions of endocytosed low-density lipoprotein (LDL) were quantified. Conclusions: Our theory can quantitatively describe the observed cargo distributions as a function of time. Remarkably, the theory allows determining microscopic kinetic parameters such as the fusion rate between endosomes from still images of cargo distributions at different times of internalization. We show that this method is robust and sensitive because cargo distributions result from an average over many stochastic events in many cells. Our results provide theoretical and experimental support to the ``funnel model'' of endosome progression and suggest that the conversion of early to late endosomes is the major mode of LDL trafficking.
The radial growth phase of malignant melanoma: multi-phase modelling, numerical simulations and linear stability analysis - Ciarletta, P. and Foret, L. and Ben Amar, M.

Abstract : Cutaneous melanoma is disproportionately lethal despite its relatively low incidence and its potential for cure in the early stages. The aim of this study is to foster understanding of the role of microstructure on the occurrence of morphological changes in diseased skin during melanoma evolution. The authors propose a biomechanical analysis of its radial growth phase, investigating the role of intercellular/stromal connections on the initial stages of epidermis invasion. The radial growth phase of a primary melanoma is modelled within the multi-phase theory of mixtures, reproducing the mechanical behaviour of the skin layers and of the epidermal-dermal junction. The theoretical analysis takes into account those cellular processes that have been experimentally observed to disrupt homeostasis in normal epidermis. Numerical simulations demonstrate that the loss of adhesiveness of the melanoma cells both to the basal laminae, caused by deregulation mechanisms of adherent junctions, and to adjacent keratynocytes, consequent to a downregulation of E-cadherin, are the fundamental biomechanical features for promoting tumour initiation. Finally, the authors provide the mathematical proof of a long wavelength instability of the tumour front during the early stages of melanoma invasion. These results open the perspective to correlate the early morphology of a growing melanoma with the biomechanical characteristics of its micro-environment.
Thermodynamics of nanocluster phases: A unifying theory - Destainville, N. and Foret, L.

Abstract : We propose a unifying, analytical theory accounting for the self-organization of colloidal systems in nanocluster or microcluster phases. We predict the distribution of cluster sizes with respect to interaction parameters and colloid concentration. In particular, we anticipate a proportionality regime where the mean cluster size grows proportionally to the concentration, as observed in several experiments. We emphasize the interest in a predictive theory in soft matter, nanotechnologies, and biophysics.