Active bundles of polar and bipolar filaments.

Bundles of actin filaments and molecular motors of the myosin family are a common subcellular organizational motif. Typically, such bundles are under contractile stress resulting from interactions between the filaments and the motors. This holds in particular for contractile rings that appear in the late stages of cell division in animal cells and that cleave the mother into two daughter cells. It was recently shown that myosin organizes into regularly spaced clusters along rings in mammalian cells, whereas myosin clusters in fission yeast travel along the perimeter of actomyosin rings [Wollrab et al., Nat. Commun. 7, 11860 (2016)2041-172310.1038/ncomms11860]. A mechanism based on the association of the structurally polar actin filaments into bipolar structures was shown to provide a common explanation for both observations. Here, we analyze the dynamics of this mechanism in detail. We find a rich phase diagram depending on the actomyosin interaction strength and the stability of the bipolar structures. The system can notably organize into traveling waves. Furthermore, we identify the nature of the bifurcations connecting the various patterns as parameters are changed. Finally, we report experimental patterns observed in cytokinetic rings in fission yeast and link them to solutions of our dynamic equations. Our analysis highlights the possible role played by local polarity sorting of actin filaments for the dynamics and functionality of actomyosin networks.

Methods for rectifying cell motions in vitro: breaking symmetry using microfabrication and microfluidics.

Cell motility is an important phenomenon in cell biology, developmental biology, and cancer. Here we report methods that we designed to identify and characterize external factors which direct cell motions by breaking locally the symmetry. We used microfabrication and microfluidics techniques to impose and combine mechanical and chemical cues to moving fibroblasts. Gradients can thereby be engineered at the cellular scale and this approach has allowed to disentangle roles of the nucleus and protrusion activity in setting cell directions.

Periodic adhesive fingers between contacting cells.

We study in detail the properties of fingers, a particular type of cell-cell adhesive structures appearing in adherens junctions. These periodic patterns break the symmetry of cell-cell contacts. We show that finger formation is driven by cadherin interactions and actin growth. A theoretical model is introduced in which the growth of fingers is limited by membrane tension. The steady shape and formation kinetics of fingers are experimentally measured and compared with the theoretical predictions.

Membrane and acto-myosin tension promote clustering of adhesion proteins.

Physicists have studied the aggregation of adhesive proteins, giving a central role to the elastic properties of membranes, whereas cell biologists have put the emphasis on the cytoskeleton. However, there is a dramatic lack of experimental studies probing both contributions on cellular systems. Here, we tested both mechanisms on living cells. We compared, for the same cell line, the growth of cadherin-GFP patterns on recombinant cadherin-coated surfaces, with the growth of vinculin-GFP patterns on extracellular matrix protein-coated surfaces by using evanescent wave microscopy. In our setup, cadherins are not linked to actin, whereas vinculins are. This property allows us to compare formation of clusters with proteins linked or not to the cytoskeleton and thus study the role of membrane versus cytoskeleton in protein aggregation. Strikingly, the motifs we obtained on both surfaces share common features: they are both elongated and located at the cell edges. We showed that a local force application can impose this symmetry breaking in both cases. However, the origin of the force is different as demonstrated by drug treatment (butanedione monoxime) and hypotonic swelling. Cadherins aggregate when membrane tension is increased, whereas vinculins (cytoplasmic proteins of focal contacts) aggregate when acto-myosin stress fibers are pulling. We propose a mechanism by which membrane tension is localized at cell edges, imposing flattening of membrane and enabling aggregation of cadherins by diffusion. In contrast, cytoplasmic proteins of focal contacts aggregate by opening cryptic sites in focal contacts under acto-myosin contractility.

Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization.

Forces exerted by stationary cells have been investigated on the level of single focal adhesions by combining elastic substrates, fluorescence labeling of focal adhesions, and the assumption of localized force when solving the inverse problem of linear elasticity theory. Data simulation confirms that the inverse problem is ill-posed in the presence of noise and shows that in general a regularization scheme is needed to arrive at a reliable force estimate. Spatial and force resolution are restricted by the smoothing action of the elastic kernel, depend on the details of the force and displacement patterns, and are estimated by data simulation. Corrections arising from the spatial distribution of force and from finite substrate size are treated in the framework of a force multipolar expansion. Our method is computationally cheap and could be used to study mechanical activity of cells in real time.

Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism.

The transition of cell-matrix adhesions from the initial punctate focal complexes into the mature elongated form, known as focal contacts, requires GTPase Rho activity. In particular, activation of myosin II-driven contractility by a Rho target known as Rho-associated kinase (ROCK) was shown to be essential for focal contact formation. To dissect the mechanism of Rho-dependent induction of focal contacts and to elucidate the role of cell contractility, we applied mechanical force to vinculin-containing dot-like adhesions at the cell edge using a micropipette. Local centripetal pulling led to local assembly and elongation of these structures and to their development into streak-like focal contacts, as revealed by the dynamics of green fluorescent protein-tagged vinculin or paxillin and interference reflection microscopy. Inhibition of Rho activity by C3 transferase suppressed this force-induced focal contact formation. However, constitutively active mutants of another Rho target, the formin homology protein mDia1 (Watanabe, N., T. Kato, A. Fujita, T. Ishizaki, and S. Narumiya. 1999. Nat. Cell Biol. 1:136-143), were sufficient to restore force-induced focal contact formation in C3 transferase-treated cells. Force-induced formation of the focal contacts still occurred in cells subjected to myosin II and ROCK inhibition. Thus, as long as mDia1 is active, external tension force bypasses the requirement for ROCK-mediated myosin II contractility in the induction of focal contacts. Our experiments show that integrin-containing focal complexes behave as individual mechanosensors exhibiting directional assembly in response to local force.

Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates.

Mechanical forces play a major role in the regulation of cell adhesion and cytoskeletal organization. In order to explore the molecular mechanism underlying this regulation, we have investigated the relationship between local force applied by the cell to the substrate and the assembly of focal adhesions. A novel approach was developed for real-time, high-resolution measurements of forces applied by cells at single adhesion sites. This method combines micropatterning of elastomer substrates and fluorescence imaging of focal adhesions in live cells expressing GFP-tagged vinculin. Local forces are correlated with the orientation, total fluorescence intensity and area of the focal adhesions, indicating a constant stress of 5.5 +/- 2 nNmicrom(-2). The dynamics of the force-dependent modulation of focal adhesions were characterized by blocking actomyosin contractility and were found to be on a time scale of seconds. The results put clear constraints on the possible molecular mechanisms for the mechanosensory response of focal adhesions to applied force.

Caldesmon inhibits nonmuscle cell contractility and interferes with the formation of focal adhesions.

Caldesmon is known to inhibit the ATPase activity of actomyosin in a Ca(2+)-calmodulin-regulated manner. Although a nonmuscle isoform of caldesmon is widely expressed, its functional role has not yet been elucidated. We studied the effects of nonmuscle caldesmon on cellular contractility, actin cytoskeletal organization, and the formation of focal adhesions in fibroblasts. Transient transfection of nonmuscle caldesmon prevents myosin II-dependent cell contractility and induces a decrease in the number and size of tyrosine-phosphorylated focal adhesions. Expression of caldesmon interferes with Rho A-V14-mediated formation of focal adhesions and stress fibers as well as with formation of focal adhesions induced by microtubule disruption. This inhibitory effect depends on the actin- and myosin-binding regions of caldesmon, because a truncated variant lacking both of these regions is inactive. The effects of caldesmon are blocked by the ionophore A23187, thapsigargin, and membrane depolarization, presumably because of the ability of Ca(2+)-calmodulin or Ca(2+)-S100 proteins to antagonize the inhibitory function of caldesmon on actomyosin contraction. These results indicate a role for nonmuscle caldesmon in the physiological regulation of actomyosin contractility and adhesion-dependent signaling and further demonstrate the involvement of contractility in focal adhesion formation.

Acting on actin: the electric motility assay.

We have developed a novel technique which allows one to direct the two dimensional motion of actin filaments on a myosin coated sheet using a weak electric field parallel to the plane of motion. The filament velocity can be increased or decreased, and even reversed, as a function of orientation and strength of the field. PMMA (poly(methylmethacrylate)) gratings, which act as rails for actin, allow one for the first time to explore three quadrants of the force velocity diagram. We discuss effective friction, duty ratio and stall force at different myosin densities. A discontinuity in the velocity force relationship suggests the existence of dynamical phase transition.

Trapping and wiggling: elastohydrodynamics of driven microfilaments.

We present an analysis of the planar motion of single semiflexible filaments subject to viscous drag or point forcing. These are the relevant forces in dynamic experiments designed to measure biopolymer bending moduli. By analogy with the "Stokes problems" in hydrodynamics (motion of a viscous fluid induced by that of a wall bounding the fluid), we consider the motion of a polymer, one end of which is moved in an impulsive or oscillatory way. Analytical solutions for the time-dependent shapes of such moving polymers are obtained within an analysis applicable to small-amplitude deformations. In the case of oscillatory driving, particular attention is paid to a characteristic length determined by the frequency of oscillation, the polymer persistence length, and the viscous drag coefficient. Experiments on actin filaments manipulated with optical traps confirm the scaling law predicted by the analysis and provide a new technique for measuring the elastic bending modulus. Exploiting this model, we also present a reanalysis of several published experiments on microtubules.