Juliane Zimmermann

Actin Filament Elasticity and Retrograde Flow Shape the Force-Velocity Relation of Motile Cells

Cells migrate through a crowded environment during processes such as metastasis or wound healing, and must generate and withstand substantial forces. The cellular motility responses to environmental forces are represented by their force-velocity relation, which has been measured for fish keratocytes but remains unexplained. Even pN opposing forces slow down lamellipodium motion by three orders of magnitude. At larger opposing forces, the retrograde flow of the actin network accelerates until it compensates for polymerization, and cell motion stalls. Subsequently, the lamellipodium adapts to the stalled state. We present a mechanism quantitatively explaining the cells force-velocity relation and its changes upon application of drugs that hinder actin polymerization or actomyosin-based contractility. Elastic properties of filaments, close to the lamellipodium leading edge, and retrograde flow shape the force-velocity relation. To our knowledge, our results shed new light on how these migratory responses are regulated, and on the mechanics and structure of the lamellipodium.

Contact inhibition of locomotion determines cell–cell and cell–substrate forces in tissues

Significance Many cell types organize into tissues (e.g., in the skin). In most adult tissues, cells are tightly anchored and attached to each other through intercellular adhesions. However, during embryonic development and wound repair, cells reorganize and migrate to (re)establish the desired tissue shape. This reorganization involves a complex interplay of cell motility, cell contractility, and cell–cell adhesion. Here, we use a computational model to study the forces generated by cells in tissues and the resultant cell motion. A basic hypothesis, namely that cell–cell contacts repolarize moving cells and suppress their ability to exert forces on the environment, allows us to explain heretofore surprising findings showing that tissues are under tension and that this tension increases with cell density. Cells organized in tissues exert forces on their neighbors and their environment. Those cellular forces determine tissue homeostasis as well as reorganization during embryonic development and wound healing. To understand how cellular forces are generated and how they can influence the tissue state, we develop a particle-based simulation model for adhesive cell clusters and monolayers. Cells are contractile, exert forces on their substrate and on each other, and interact through contact inhibition of locomotion (CIL), meaning that cell–cell contacts suppress force transduction to the substrate and propulsion forces align away from neighbors. Our model captures the traction force patterns of small clusters of nonmotile cells and larger sheets of motile Madin–Darby canine kidney (MDCK) cells. In agreement with observations in a spreading MDCK colony, the cell density in the center increases as cells divide and the tissue grows. A feedback between cell density, CIL, and cell–cell adhesion gives rise to a linear relationship between cell density and intercellular tensile stress and forces the tissue into a nonmotile state characterized by a broad distribution of traction forces. Our model also captures the experimentally observed tissue flow around circular obstacles, and CIL accounts for traction forces at the edge.

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation, Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of “collective guidance” computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster’s size—clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.

Intercellular Stress Reconstitution from Traction Force Data

Cells migrate collectively during development, wound healing, and cancer metastasis. Recently, a method has been developed to recover intercellular stress in monolayers from measured traction forces upon the substrate. To calculate stress maps in two dimensions, the cell sheet was assumed to behave like an elastic material, and it remains unclear to what extent this assumption is valid. In this study, we simulate our recently developed model for collective cell migration, and compute intercellular stress maps using the method employed in the experiments. We also compute these maps using a method that does not depend on the traction forces or material properties. The two independently obtained stress patterns agree well for the parameters we have probed and provide a verification of the validity of the experimental method.

Formation of Transient Lamellipodia

Cell motility driven by actin polymerization is pivotal to the development and survival of organisms and individual cells. Motile cells plated on flat substrates form membrane protrusions called lamellipodia. The protrusions repeatedly appear and retract in all directions. If a lamellipodium is stabilized and lasts for some time, it can take over the lead and determine the direction of cell motion. Protrusions traveling along the cell perimeter have also been observed. Their initiation is in some situations the effect of the dynamics of the pathway linking plasma membrane receptors to actin filament nucleation, e.g. in chemotaxis. However, lamellipodia are also formed in many cells incessantly during motion with a constant state of the signaling pathways upstream from nucleation promoting factors (NPFs), or spontaneously in resting cells. These observations strongly suggest protrusion formation can also be a consequence of the dynamics downstream from NPFs, with signaling setting the dynamic regime but not initiating the formation of individual protrusions. A quantitative mechanism for this kind of lamellipodium dynamics has not been suggested yet. Here, we present a model exhibiting excitable actin network dynamics. Individual lamellipodia form due to random supercritical filament nucleation events amplified by autocatalytic branching. They last for about 30 seconds to many minutes and are terminated by filament bundling, severing and capping. We show the relevance of the model mechanism for experimentally observed protrusion dynamics by reproducing in very good approximation the repetitive protrusion formation measured by Burnette et al. with respect to the velocities of leading edge protrusion and retrograde flow, oscillation amplitudes, periods and shape, as well as the phase relation between protrusion and retrograde flow. Our modeling results agree with the mechanism of actin bundle formation during lamellipodium retraction suggested by Burnette et al. and Koestler et al.

On the existence and strength of stable membrane protrusions

We present a mathematical model for the protrusion of lamellipodia in motile cells. The model lamellipodium consists of a viscoelastic actin gel in the bulk and a dynamic boundary layer of newly polymerized filaments at the leading edge called the semiflexible region (SR). The density of filaments in the SR can increase due to nucleation of new filaments and decrease due to capping and severing of existing filaments. Following on from previous publications, we present important approximations that make the model feasible and accessible to fast computational analysis. It reveals that there are three qualitatively different parameter regimes: a stable, stationarily protruding lamellipodium; a stable lamellipodium showing oscillatory motion of the leading edge; and zero filament density and no stable lamellipodium. Hence, the model defines criteria for the existence of lamellipodia and the ability of cells to move effectively, and we discuss which parameter changes can induce transitions between the different states. Furthermore, stable lamellipodia have to be able to exert and withstand substantial forces. We can fit the experimentally measured dynamic force–velocity relation that describes how cells can adapt to increasing external forces when encountering an obstacle in their environment during motion. Moreover, we predict a different stationary force–velocity relation that should apply if cells experience a constant force, e.g. exerted by the surrounding tissue.

Calculating Intercellular Stress in a Model of Collectively Moving Cells

Cells move together in groups during development, wound healing, and cancer metastasis. It remains unclear how collectively moving cells coordinate their motion. In addition to external chemoattractants and exchanging signaling molecules, cells may also respond to mechanical cues. We developed a model of collective cell migration under the assumption that cells align their motility force with the direction of their velocity. This simple mechanism leads to large scale velocity correlations, swirling motion in the bulk of monolayers, and finger-like protrusions at the edge [1]. In experimental studies, the inter- and intracellular stress in the monolayer has been calculated from measured traction forces between the cells and the substrate. Stress builds up successively towards the center of the tissue as the majority of the cells pull outwards [2]. While one dimensional stress profiles are based on a simple force balance, two dimensional stress maps require the additional assumption of an elastic tissue [3], and the validity of this assumption remains disputable. In our model simulations, both the forces on the substrate and the intercellular forces are accessible. We can therefore apply a second method to calculate the stress based on forces between cells. Stress patterns calculated with both methods agree, showing that recovery of the intercellular stress is indeed mostly independent of specific material properties.1. Basan, M., J. Elgeti, E. Hannezo, W.-J. Rappel and H. Levine. PNAS. 2013.2. Trepat, X., M. R. Wasserman, T. E. Angelini, E. Millet, D. A. Weitz, J. P. Butler and J. J. Fredberg. Nat. Phys. 2009.3. Tambe, D. T., C. Corey Hardin, T. E. Angelini, K. Rajendran, C. Y. Park, X. Serra-Picamal, E. H. Zhou, M. H. Zaman, J. P. Butler, D. A. Weitz, J. J. Fredberg and X. Trepat. Nat. Mater. 2011.