Cytoskeleton and Cell Motility

The present article is an invited contribution to the Encyclopedia of Complexity and System Science, Robert A. Meyers Ed., Springer New York (2009). It is a review of the biophysical mechanisms that underly cell motility. It mainly focuses on the eukaryotic cytoskeleton and cell-motility mechanisms. Bacterial motility as well as the composition of the prokaryotic cytoskeleton is only briefly mentioned. The article is organized as follows. In Section III, I first present an overview of the diversity of cellular motility mechanisms, which might at first glance be categorized into two different types of behaviors, namely "swimming" and "crawling". Intracellular transport, mitosis - or cell division - as well as other extensions of cell motility that rely on the same essential machinery are briefly sketched. In Section IV, I introduce the molecular machinery that underlies cell motility - the cytoskeleton - as well as its interactions with the external environment of the cell and its main regulatory pathways. Sections IV D to IV F are more detailed in their biochemical presentations; readers primarily interested in the theoretical modeling of cell motility might want to skip these sections in a first reading. I then describe the motility mechanisms that rely essentially on polymerization-depolymerization dynamics of cytoskeleton filaments in Section V, and the ones that rely essentially on the activity of motor proteins in Section VI. Finally, Section VII is devoted to the description of the integrated approaches that have been developed recently to try to understand the cooperative phenomena that underly self-organization of the cell cytoskeleton as a whole.Comment: 31 pages, 16 figures, 295 reference

Differential Models, Numerical Simulations and Applications

This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems

Cell migration in complex environments: chemotaxis and topographical obstacles

Cell migration is a complex phenomenon that plays an important role in many biological processes. Our aim here is to build and study models of reduced complexity to describe some aspects of cell motility in tissues. Precisely, we study the impact of some biochemical and mechanical cues on the cell dynamics in a 2D framework. For that purpose, we model the cell as an active particle with a velocity solution to a particular Stochastic Differential Equation that describes the intracellular dynamics as well as the presence of some biochemical cues. In the 1D case, an asymptotic analysis puts to light a transition between migration dominated by the cell’s internal activity and migration dominated by an external signal. In a second step, we use the contact algorithm introduced in [15,18] to describe the cell dynamics in an environment with obstacles. In the 2D case, we study how a cell submitted to a constant directional force that mimics the action of chemoattractant, behaves in the presence of obstacles. We numerically observe the existence of a velocity value that the cell can not exceed even if the directional force intensity increases. We find that this threshold value depends on the number of obstacles. Our result confirms a result that was already observed in a discrete framework in [3,4]

Large-scale dynamics of self-propelled particles moving through obstacles: model derivation and pattern formation

We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations model for the interactions between the self-propelled particles and the obstacles, for which we assume large tether stiffness. The result is a coupled system of non linear, non-local partial differential equations. Linear stability analysis shows that patterning is expected if the interactions are strong enough and allows for the predictions of pattern size from model parameters. The macroscopic equations reveal that the obstacle interactions induce short-ranged SPP aggregation, irrespective of whether obstacles and SPPs are attractive or repulsive

Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation

We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations model for the interactions between the self-propelled particles and the obstacles, for which we assume large tether stiffness. The result is a coupled system of nonlinear, non-local partial differential equations. Linear stability analysis shows that patterning is expected if the interactions are strong enough and allows for the predictions of pattern size from model parameters. The macroscopic equations reveal that the obstacle interactions induce short-ranged SPP aggregation, irrespective of whether obstacles and SPPs are attractive or repulsive

Mathematical models for chemotaxis and their applications in self-organisation phenomena

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and mathematicians into biology. The Patlak-Keller-Segel (PKS) system forms part of the bedrock of mathematical biology, a go-to-choice for modellers and analysts alike. For the former it is simple yet recapitulates numerous phenomena; the latter are attracted to these rich dynamics. Here I review the adoption of PKS systems when explaining self-organisation processes. I consider their foundation, returning to the initial efforts of Patlak and Keller and Segel, and briefly describe their patterning properties. Applications of PKS systems are considered in their diverse areas, including microbiology, development, immunology, cancer, ecology and crime. In each case a historical perspective is provided on the evidence for chemotactic behaviour, followed by a review of modelling efforts; a compendium of the models is included as an Appendix. Finally, a half-serious/half-tongue-in-cheek model is developed to explain how cliques form in academia. Assumptions in which scholars alter their research line according to available problems leads to clustering of academics and the formation of "hot" research topics.Comment: 35 pages, 8 figures, Submitted to Journal of Theoretical Biolog

Physique statistique de la matière active

Active systems, composed of particles capable of using the energy stored in theirmedium to self-propel, are ubiquitous in nature. They are found at all scales :from molecular motors to cellular tissues, bacterial colonies and animal groups.These out-of-equilibrium systems have attracted a lot of attention from the physicscommunity because they show a richer phenomenology than passive systems thatwe can still understand using simple models.In this thesis, we study analytically and numerically minimal models of activeparticles. They allow us to understand different phenomena that are characteristicof active matter and to study the large-scale behavior of several classes of systems.The thermodynamics of active systems is fundamentally different from thatof equilibrium systems. In particular, we show that the mechanical pressure ofan active particle fluid is not given by an equation of state. The pressure isnot a property of the fluid and depends on the details of the interaction with thecontaining vessel.We also study two phase transitions that specific to active matter : The motility-induced phase separation and the transition to collective motion. In both cases, weobserve a phase separation between a liquid and a gas and study their coexistence.For the transition to collective motion, we exhibit two universality classes, basedon the particles’ symmetry, which have different types of coexistence phases.Les systèmes actifs, composés de particules capables de transformer l’énergiestockée dans leur environnement pour s’autopropulser, sont omniprésents dans lanature. On les trouve à toutes les échelles : des moteurs moléculaires aux groupesd’animaux, en passant par les tissus cellulaires et les colonies de bactéries. Cessystèmes hors d’équilibre ont attiré l’attention des physiciens car ils présententune phénoménologie plus riche que les systèmes passifs, que l’on peut cependantcomprendre à partir de modèles simples.Dans cette thèse, nous avons étudié analytiquement et numériquement desmodèles minimaux de particules actives. Ceux-ci nous ont permis de comprendredifférents phénomènes spécifiques à la matière active et d’étudier le comportementà grand échelle de plusieurs classes de systèmes.La thermodynamique des systèmes actifs est fondamentalement différente decelle des systèmes d’équilibre. Nous montrons en particulier que la pression méca-nique d’un fluide de particules actives n’est pas donnée par une équation d’état.La pression n’est donc pas seulement une propriété du fluide et dépend du détaildes interactions avec les parois du récipient dans lequel il est confiné.Nous étudions également deux transitions de phase propres à la matière active :la séparation de phase induite par la motilité et la transition vers le mouvementcollectif. Dans les deux cas, on observe une séparation de phase entre un liquideet un gaz dont nous étudions la coexistence. Pour la transition vers le mouvementcollectif on distingue deux classes d’universalité, en fonction de la symétrie desparticules, qui ont des coexistences de phase différentes