From molecular force generation to large scale cellular movements

[eng] The propulsion mechanisms that drive the movements of living cells constitute perhaps the most impressive engineering works of nature. Still, it is simply the interaction between molecules which is responsible for these complex and robust motility mechanisms. A question that arises naturally is thus how the underlying molecules self-organize to perform such highly coordinated tasks. Although a global understanding of cell behavior is still out of reach, the study of particular aspects of biological systems may help building up a more clear picture. Biologists have made lots of efforts to characterize the proteins involved in cellular movements, to identify their interactions and to understand their regulation. This information is very important and has explained several aspects of the motility of living cells. The discovery of proteins able to generate forces at molecular scales, known as motor proteins, provided essential information to understand the observed cellular movements. However, the force developed at the molecular level by a single protein is too weak to drive cellular movement on its own. Probably the clearest example is the functioning of muscles. The forces developed are about 12 orders of magnitude larger than the forces generated at molecular scales. This is possible because the contraction of muscles involves the collective action of many motor proteins (Alberts et al., 2004; Bray, 1992). Although each one of these proteins generates a small force (in the picoNewton range), the sum of their individual contributions leads to large forces. At the cellular scales something similar occurs. The necessary forces for the motion of a cell and even for intracellular movements, are larger than molecular forces. The collective action of molecular force generators is thus essential to understand most cellular movements. Here we study theoretically some examples of cellular movements and compare quantitatively, when possible, our results to the experimental observations. The work is divided in three parts: we first study the motion of oil drops propelled by an actin comet tail, which closely mimics the motility mechanism of several bacterial pathogens, as the bacteria Listeria. The second part is devoted to particular aspects of intracellular transport. We study the physical mechanism of membrane tube extraction by motor proteins, the traffic of motor proteins at large scales and the collective force generation of molecular motors pulling on fluid membranes. In the last part we address both the motion of chromosomes in eukaryotic cell division and the stability of spindle-like structures, as the mitotic spindle. Our aim is to understand how these movements arise from the cooperative action of molecular force generators. The forces developed by ensembles of force generators are not static, but depend on the dynamic state of the system. This is so because the kinetics of the individual force generators is strongly affected by the forces created by themselves. As we discuss below, this force-dependent kinetics imposes a highly non-linear dynamics for the system and, as a consequence, several dynamic instabilities occur. Our work shows that the collective behavior of molecular force generators is essential to understand some features of cellular movements.[cat] Els mecanismes de propulsió responsables dels moviments cel·lulars són potser les obres d’enginyeria més impressionants de la natura. Tot i així, són simplement interaccions entre molècules les responsables d’aquests moviments tan complexes. La pregunta és doncs com s’autoorganitzen les molècules per dur a terme aquestes tasques que requereixen un alt grau de coordinació. Malgrat que la comprensió global del comportament cel·lular està encara lluny del nostre abast, l’estudi d’aspectes particulars dels sistemes biològics pot contribuir a la seva comprensió. Els biòlegs han fet molt esforços per caracteritzar les proteïnes involucrades en els moviments cel·lulars, per identificar les seves interaccions i per entendre la seva regulació. Aquesta informació és molt important i ha permès explicar diversos aspectes del moviment cel·lular. El descobriment de proteïnes capaces de generar forces a escales moleculars, anomenades proteïnes motores, va aportar una informació essencial per a la comprensió dels moviments cel·lulars. La força creada a nivell molecular per una proteïna és massa petita per tal d’induir el moviment cel·lular per sí sola. Probablement l’exemple més clar és el funcionament dels músculs. Les forces que nosaltres som capaços de crear són aproximadament 12 ordres de magnitud més grans que les forces generades a l’escala molecular. Això és possible perquè les forces necessàries per a la contracció muscular estan generades col·lectivament per grans grups de proteïnes motores. Malgrat que cada una d’aquestes proteïnes desenvolupa una força petita (de l’ordre d’alguns pico Newtons), la suma de totes les contribucions individuals pot generar forces molt més grans. A nivell de la cèl·lula té lloc un fenomen similar. Les forces necessàries per induir el moviment de la cèl·lula i/o els moviments intracel·lulars són majors que les originades a nivell molecular. Per aquesta raó, l’acció col·lectiva de generadors de força moleculars és essencial per comprendre els moviments cel·lulars. En aquest treball estudiem a nivell teòric diversos casos de moviments cel·lulars i comparem quantitativament, quan això és possible, els nostres resultats a les observacions experimentals. El treball està dividit en tres parts: primer estudiem el moviments de gotes d’oli propulsades per un cometa d’actina, les quals mimetitzen el mecanisme de propulsió de bacteris com ara Listeria. La segona part està dedicada a diversos aspectes del transport intracel·lular. Estudiem el mecanisme físic pel qual proteïnes motores estiren nanotubs de membrana, el tràfic a gran escala de proteïnes motores i també la generació col·lectiva de força de motors moleculars que estiren membranes fluïdes. En la última part, estudiem el moviment de cromosomes i l’estabilitat del fus mitòtic en la divisió cel·lular eucariota. El nostre objectiu és entendre com l’acció col·lectiva de generadors de força moleculars dona lloc a aquests moviments cel·lulars. Com demostrem en el nostre estudi, la combinació de la dinàmica col·lectiva i la cinètica del generadors de força elementals, la qual depèn fortament de la força que ells mateixos generen, dona lloc a inestabilitats dinàmiques. Així doncs, la dinàmica col·lectiva dels generadors elementals de força és essencial per entendre diversos aspectes dels moviments cel·lulars

Chromosome Oscillations in Mitosis

Successful cell division requires a tight regulation of chromosome motion via the activity of molecular motors. Many of the key players at the origin of the forces generating the movement have been identified, but their spatial and temporal organization remains elusive. The protein complex Kinetochore on the chromosome associates with microtubules emanating from one of the spindle poles and drives the chromosome toward the pole. Chromokinesin motors on the chromosome arms also interact with microtubules, ejecting the chromosome away from the pole. In animal cells, a monooriented chromosome (associated to a single pole) periodically switches between phases of poleward and away from the pole movement[, a behavior tentatively explained so far by the existence of a complex switching mechanism within the kinetochore itself. Here we show that the interplay between the morphology of the mitotic spindle and the collective kinetics of chromokinesins can account for the highly non-linear periodic chromosome motion. Our analysis provides a natural explanation for the origin of chromosome directional instability and for the mechanism by which chromosomes feel their position in space.Comment: http://hogarth.pct.espci.fr/~pierre

Coordination of Kinesin Motors Pulling on Fluid Membranes

AbstractIntracellular transport relies on the action of motor proteins, which work collectively to either carry small vesicles or pull membranes tubes along cytoskeletal filaments. Although the individual properties of kinesin-1 motors have been extensively studied, little is known on how several motors coordinate their action and spatially organize on the microtubule when pulling on fluid membranes. Here we address these questions by studying, both experimentally and numerically, the growth of membrane tubes pulled by molecular motors. Our in vitro setup allows us to simultaneously control the parameters monitoring tube growth and measure its characteristics. We perform numerical simulations of membrane tube growth, using the experimentally measured values of all parameters, and analyze the growth properties of the tube considering various motor cooperation schemes. The comparison of the numerical results and the experimental data shows that motors use simultaneously several protofilaments of a microtubule to pull a single tube, as motors moving along a single protofilament cannot generate the forces required for tube extraction. In our experimental conditions, we estimate the average number of motors pulling the tube to be approximately nine, distributed over three contiguous protofilaments. Our results also indicate that the motors pulling the tube do not step synchronously

Fluid front morphologies in gap-modulated Hele-Shaw cells

We consider the displacement of an inviscid fluid (air) by a viscous fluid (oil) in a narrow channel with gap-thickness modulations. The interfacial dynamics of this problem is strongly nonlocal and exhibits competing effects from capillarity and permeability. We derive analytical predictions of steady-state front morphologies, which are exact at linear level in the case of a persistent modulation in the direction of front advancement. The theoretical predictions are in good agreement with experimental measurements of steady-state front morphologies obtained in a Hele-Shaw cell with modulations of the channel depth, consisting on three parallel tracks of reduced depth, for small gap modulations. The relative average distance between theoretical and experimental fronts in the region around the central track is smaller than about 4%, provided that the height of the tracks is less than 13% of the total channel depth and the local distortion of the front height h is small enough (|∇h|<0.8) for the linear approximation to hold

Dynamic regulation of tissue fluidity controls skin repair during wound healing

During wound healing, different pools of stem cells (SCs) contribute to skin repair. However, how SCs become activated and drive the tissue remodeling essential for skin repair is still poorly understood. Here, by developing a mouse model allowing lineage tracing and basal cell lineage ablation, we monitor SC fate and tissue dynamics during regeneration using confocal and intravital imaging. Analysis of basal cell rearrangements shows dynamic transitions from a solid-like homeostatic state to a fluid-like state allowing tissue remodeling during repair, as predicted by a minimal mathematical modeling of the spatiotemporal dynamics and fate behavior of basal cells. The basal cell layer progressively returns to a solid-like state with re-epithelialization. Bulk, single-cell RNA, and epigenetic profiling of SCs, together with functional experiments, uncover a common regenerative state regulated by the EGFR/AP1 axis activated during tissue fluidization that is essential for skin SC activation and tissue repair

Physical constraints on early blastomere packings.

At very early embryonic stages, when embryos are composed of just a few cells, establishing the correct packing arrangements (contacts) between cells is essential for the proper development of the organism. As early as the 4-cell stage, the observed cellular packings in different species are distinct and, in many cases, differ from the equilibrium packings expected for simple adherent and deformable particles. It is unclear what are the specific roles that different physical parameters, such as the forces between blastomeres, their division times, orientation of cell division and embryonic confinement, play in the control of these packing configurations. Here we simulate the non-equilibrium dynamics of cells in early embryos and systematically study how these different parameters affect embryonic packings at the 4-cell stage. In the absence of embryo confinement, we find that cellular packings are not robust, with multiple packing configurations simultaneously possible and very sensitive to parameter changes. Our results indicate that the geometry of the embryo confinement determines the packing configurations at the 4-cell stage, removing degeneracy in the possible packing configurations and overriding division rules in most cases. Overall, these results indicate that physical confinement of the embryo is essential to robustly specify proper cellular arrangements at very early developmental stages

Shape and Dynamics of Tip-Growing Cells Report

Walled cells have the ability to remodel their shape while sustaining an internal turgor pressure that can reach values up to 10 atmospheres [1–7]. Although it is undisputed that this requires a tight and simultaneous regulation of cell wall assembly and mechanics, previous theoretical studies on tip growth focused either on the mechanical behavior of the cell wall or on its assembly [8–14]. To study the interplay between growth and mechanics in shaping a walled cell, we examine the particularly simple geometry of tip-growing cells [1, 3, 15, 16], which elongate via the assembly and expansion of cell wall in the apical region of the cell. We describe the observed irreversible expansion of the cell wall during growth as the extension of an inhomogeneous viscous fluid shell under the action of turgor pressure, fed by a material source in the neighborhood of the growin

Connecting individual to collective cell migration

Abstract Collective cell migration plays a pivotal role in the formation of organs, tissue regeneration, wound healing and many disease processes, including cancer. Despite the considerable existing knowledge on the molecular control of cell movements, it is unclear how the different observed modes of collective migration, especially for small groups of cells, emerge from the known behaviors of individual cells. Here we derive a physical description of collective cellular movements from first principles, while accounting for known phenomenological cell behaviors, such as contact inhibition of locomotion and force-induced cell repolarization. We show that this theoretical description successfully describes the motion of groups of cells of arbitrary numbers, connecting single cell behaviors and parameters (e.g., adhesion and traction forces) to the collective migration of small groups of cells and the expansion of large cell colonies. Specifically, using a common framework, we explain how cells characterized by contact inhibition of locomotion can display coherent collective behavior when in groups, even in the absence of biochemical signaling. We find an optimal group size leading to maximal group persistence and show that cell proliferation prevents the buildup of intercellular forces within cell colonies, enabling their expansion

Coordinating cell polarization and morphogenesis through mechanical feedback.

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis