Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows

Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach.     

Coupling traction force patterns and actomyosin wave dynamics reveals mechanics of cell motion

Motile cells can use and switch between different modes of migration. Here, we use traction force microscopy and fluorescent labeling of actin and myosin to quantify and correlate traction force patterns and cytoskeletal distributions in Dictyostelium discoideum cells that move and switch between keratocyte‐like fan‐shaped, oscillatory, and amoeboid modes. We find that the wave dynamics of the cytoskeletal components critically determine the traction force pattern, cell morphology, and migration mode. Furthermore, we find that fan‐shaped cells can exhibit two different propulsion mechanisms, each with a distinct traction force pattern. Finally, the traction force patterns can be recapitulated using a computational model, which uses the experimentally determined spatiotemporal distributions of actin and myosin forces and a viscous cytoskeletal network. Our results suggest that cell motion can be generated by friction between the flow of this network and the substrate.     

The SCAR/WAVE complex is necessary for proper regulation of traction stresses during amoeboid motility

Cell migration requires a tightly regulated, spatiotemporal coordination of underlying biochemical pathways. Crucial to cell migration is SCAR/WAVE-mediated dendritic F-actin polymerization at the cell's leading edge. Our goal is to understand the role the SCAR/WAVE complex plays in the mechanics of amoeboid migration. To this aim, we measured and compared the traction stresses exerted by Dictyostelium cells lacking the SCAR/WAVE complex proteins PIR121 (pirA(-)) and SCAR (scrA(-)) with those of wild-type cells while they were migrating on flat, elastic substrates. We found that, compared to wild type, both mutant strains exert traction stresses of different strengths that correlate with their F-actin levels. In agreement with previous studies, we found that wild-type cells migrate by repeating a motility cycle in which the cell length and strain energy exerted by the cells on their substrate vary periodically. Our analysis also revealed that scrA(-) cells display an altered motility cycle with a longer period and a lower migration velocity, whereas pirA(-) cells migrate in a random manner without implementing a periodic cycle. We present detailed characterization of the traction-stress phenotypes of the various cell lines, providing new insights into the role of F-actin polymerization in regulating cell-substratum interactions and stresses required for motility.     

Friction-controlled traction force in cell adhesion

The force balance between the extracellular microenvironment and the intracellular cytoskeleton controls the cell fate. We report a new (to our knowledge) mechanism of receptor force control in cell adhesion originating from friction between cell adhesion ligands and the supporting substrate. Adherent human endothelial cells have been studied experimentally on polymer substrates noncovalently coated with fluorescent-labeled fibronectin (FN). The cellular traction force correlated with the mobility of FN during cell-driven FN fibrillogenesis. The experimental findings have been explained within a mechanistic two-dimensional model of the load transfer at focal adhesion sites. Myosin motor activity in conjunction with sliding of FN ligands noncovalently coupled to the surface of the polymer substrates is shown to result in a controlled traction force of adherent cells. We conclude that the friction of adhesion ligands on the supporting substrate is important for mechanotransduction and cell development of adherent cells in vitro and in vivo.     

Automated characterization of cell shape changes during amoeboid motility by skeletonization

Background  

The ability of a cell to change shape is crucial for the proper function of many cellular processes, including cell migration. One type of cell migration, referred to as amoeboid motility, involves alternating cycles of morphological expansion and retraction. Traditionally, this process has been characterized by a number of parameters providing global information about shape changes, which are insufficient to distinguish phenotypes based on local pseudopodial activities that typify amoeboid motility.     

Cell influx and contractile actomyosin force drive mammary bud growth and invagination

The mammary gland develops from the surface ectoderm during embryogenesis and proceeds through morphological phases defined as placode, hillock, bud, and bulb stages followed by branching morphogenesis. During this early morphogenesis, the mammary bud undergoes an invagination process where the thickened bud initially protrudes above the surface epithelium and then transforms to a bulb and sinks into the underlying mesenchyme. The signaling pathways regulating the early morphogenetic steps have been identified to some extent, but the underlying cellular mechanisms remain ill defined. Here, we use 3D and 4D confocal microscopy to show that the early growth of the mammary rudiment is accomplished by migration-driven cell influx, with minor contributions of cell hypertrophy and proliferation. We delineate a hitherto undescribed invagination mechanism driven by thin, elongated keratinocytes—ring cells—that form a contractile rim around the mammary bud and likely exert force via the actomyosin network. Furthermore, we show that conditional deletion of nonmuscle myosin IIA (NMIIA) impairs invagination, resulting in abnormal mammary bud shape.     

Alpha-smooth muscle actin expression enhances cell traction force

Using an established corneal stromal cell differentiation model, we manipulated alpha-smooth muscle actin (alpha-SMA) protein expression levels in fibroblasts by treating them with TGF-beta1, bFGF, TGF-beta type I receptor inhibitor (SB-431542), and siRNA against alpha-SMA. The corresponding cell traction forces (CTFs) were determined by cell traction force microscopy. With all these treatments, we found that alpha-SMA is not required for CTF induction, but its expression upregulates CTF. This upregulation involves the modification of stress fibers but does not appear to relate to non-muscle myosin II expression or beta-actin expression. Moreover, there exists a linear relationship between alpha-SMA protein expression level and CTF magnitude. Finally, CTFs were found to vary among a population of myofibroblasts, suggesting that alpha-SMA protein expression levels of individual cells also vary.     

Actin dynamics and turnover in cell motility

Cell migration is a highly coordinated process involving a multitude of separable but intertwined phenomena traditionally studied in multiple cell types, tissues and model systems. In spite of the multitude of mechanisms and modes of motility described in all these different systems, the ability to dynamically reorganize the actin cytoskeleton is common to all of them. However, defining the key molecular players in motility and their precise molecular functions continues to be challenging, last not least owing to robustness and flexibility common to complex biological phenomena. Here we will draft the future steps essential for achieving true progress towards the goal to increase our understanding of actin cytoskeleton dynamics driving cell migration.     

Reconstitution of amoeboid motility in vitro identifies a motor-independent mechanism for cell body retraction

Crawling movement in eukaryotic cells requires coordination of leading-edge protrusion with cell body retraction [1-3]. Protrusion is driven by actin polymerization along the leading edge [4]. The mechanism of retraction is less clear; myosin contractility may be involved in some cells [5] but is not essential in others [6-9]. In Ascaris sperm, protrusion and retraction are powered by the major sperm protein (MSP) motility system instead of the conventional actin apparatus [10, 11]. These cells lack motor proteins [12] and so are well suited to explore motor-independent mechanisms of retraction. We reconstituted protrusion and retraction simultaneously in MSP filament meshworks, called fibers, that assemble behind plasma membrane-derived vesicles. Retraction is triggered by depolymerization of complete filaments in the rear of the fiber [13]. The surviving filaments reorganize to maintain their packing density. By packing fewer filaments into a smaller volume, the depolymerizing network shrinks and thereby generates sufficient force to move an attached load. Our work provides direct evidence for motor-independent retraction in the reconstituted MSP motility system of nematode sperm. This mechanism could also apply to actin-based cells and may explain reports of cells that crawl even when their myosin activity is compromised.     

Simulation of cell-substrate traction force dynamics in response to soluble factors

Finite element (FE) simulations of contractile responses of vascular muscular thin films (vMTFs) and endothelial cells resting on an array of microposts under stimulation of soluble factors were conducted in comparison with experimental measurements reported in the literature. Two types of constitutive models were employed in the simulations, i.e. smooth muscle cell type and non-smooth muscle cell type. The time histories of the effects of soluble factors were obtained via calibration against experimental measurements of contractile responses of tissues or cells. The numerical results for vMTFs with micropatterned tissues suggest that the radius of curvature of vMTFs under stimulation of soluble factors is sensitive to width of the micropatterned tissue, i.e. the radius of curvature increases as the tissue width decreases. However, as the tissue response is essentially isometric, the time history of the maximum principal stress of the micropatterned tissues is not sensitive to tissue width. Good agreement has been achieved for predictions of the vasoconstrictor endothelin-1-induced contraction stress between the FE numerical simulation and the experiment-based approach of Alford (Integr Biol 3:1063–1070, 2011) for the vMTFs with 40, 60, 80 and 100 \(\upmu \hbox {m}\) width patterns. This may suggest the contraction stress is weakly sensitive to the tissue width for these patterns. However, for 20 \(\upmu \hbox {m}\) width tissue patterning, the numerical simulation result for contraction stress is less than the average value of experimental measurements, which may suggest the thinner and more elongated spindle-like cells within the 20 \(\upmu \hbox {m}\) width tissue patterning have higher contractile output. The constitutive model for non-smooth muscle cells was used to simulate the contractile response of the endothelial cells. The substrate was treated as an effective continuum. For agonists such as lysophosphatidic acid and vascular endothelial growth factor, the deformation of the cell diminishes from edge to centre and the central part of the cell is essentially under isometric state. Numerical studies demonstrated the scenarios that cell polarity can be triggered via manipulation of the effective stiffness and Possion’s ratio of the substrate.     

Tissue engineering science: Consequences of cell traction force

Blood and tissue cells mechanically interact with soft tissues and tissue-equivalent reconstituted collagen gels in a variety of situations relevant to biomedicine and biotechnology. A key phenomenon in these interactions is the exertion of traction force by cells on local collagen fibers which typically constitute the solid network of these tissues and gels and impart gross mechanical integrity. Two important consequences of cells exerting traction on such collagen networks are first, when the cells co-ordinate their traction, resulting in cell migration, and second, when their traction is sufficient to deform the network. Such cell-collagen network interactions are coupled in a number of ways. Network deformation, for example, can result in net alignment of collagen fibers, eliciting contact guidance, wherein cells move with bidirectional bias along an axis of fiber alignment, potentially leading to a nonuniform cell distribution. This may govern cell accumulation in wounds and be exploited to control cell infiltration of bioartificial tissues and organs. Another consequence of cell traction is the resultant stress and strain in the network which modulate cell protein and DNA synthesis and differentiation. We summarize, here, relevant mathematical theories which we have used to describe the inherent coupling of cell dynamics and tissue mechanics in cell-populated collagen gels via traction. The development of appropriate models based on these theories, in an effort to understand how events in wound healing govern the rate and extent of wound contraction, and to measure cell traction forces in vitro, are described. Relevant observations and speculation from cell biology and medicine that motivate or serve to critique the assumptions made in the theories and models are also summarized.Abbreviations ECM Extracellular Matrix - FPCL Fibroblast-Populated Collagen Lattice - FPCM Fibroblast-Populated Collagen Microsphere     

Rho mediates the shear-enhancement of endothelial cell migration and traction force generation

The migration of vascular endothelial cells in vivo occurs in a fluid dynamic environment due to blood flow, but the role of hemodynamic forces in cell migration is not yet completely understood. Here we investigated the effect of shear stress, the frictional drag of blood flowing over the cell surface, on the migration speed of individual endothelial cells on fibronectin-coated surfaces, as well as the biochemical and biophysical bases underlying this shear effect. Under static conditions, cell migration speed had a bell-shaped relationship with fibronectin concentration. Shear stress significantly increased the migration speed at all fibronectin concentrations tested and shifted the bell-shaped curve upwards. Shear stress also induced the activation of Rho GTPase and increased the traction force exerted by endothelial cells on the underlying substrate, both at the leading edge and the rear, suggesting that shear stress enhances both the frontal forward-pulling force and tail retraction. The inhibition of a Rho-associated kinase, p160ROCK, decreased the traction force and migration speed under both static and shear conditions and eliminated the shear-enhancement of migration speed. Our results indicate that shear stress enhances the migration speed of endothelial cells by modulating the biophysical force of tractions through the biochemical pathway of Rho-p160ROCK.     

Regulation of substrate adhesion dynamics during cell motility

The movement of a metazoan cell entails the regulated creation and turnover of adhesions with the surface on which it moves. Adhesion sites form as a result of signaling between the extracellular matrix on the outside and the actin cytoskeleton on the inside, and they are associated with specific assembles of actin filaments. Two broad categories of adhesion sites can be distinguished: (1) "focal complexes" associated with lamellipodia and filopodia that support protrusion and traction at the cell front; and (2) "focal adhesions" at the termini of stress fibre bundles that serve in longer term anchorage. Focal complexes are signaled via Rac1 or Cdc42 and can either turnover on a minute scale or differentiate, via intervention of the RhoA pathway, into longer-lived focal adhesions. All classes of adhesion sites depend on the stress in the actin cytoskeleton for their formation and maintenance. Different cell types use different adhesion strategies to move, in terms of the relative engagement of filopodia and lamellipodia in focal complex formation and protrusion and the extent of focal adhesion formation. These differences can be attributed to variations in the relative activities of Rho family members. However, the Rho GTPases alone are unable to signal asymmetry in the actin cytoskeleton, necessary for polarisation and movement. Polarisation requires the collaboration of the microtubule cytoskeleton. Changes in the polymerisation state of microtubules influences the activities of both Rac1 and RhoA and microtubules interact directly with adhesion foci and promote their turnover. Possible mechanisms of cross-talk between the microtubule and actin cytoskeletons in determining polarity are discussed.     

Cell traction force and measurement methods

Cell traction forces (CTFs) are crucial to many biological processes such as inflammation, wound healing, angiogenesis, and metastasis. CTFs are generated by actomyosin interactions and actin polymerization and regulated by intracellular proteins such as alpha-smooth muscle actin (α-SMA) and soluble factors such as transforming growth factor-β (TGF-β). Once transmitted to the extracellular matrix (ECM) through stress fibers via focal adhesions, which are assemblies of ECM proteins, transmembrane receptors, and cytoplasmic structural and signaling proteins (e.g., integrins), CTFs direct many cellular functions, including cell migration, ECM organization, and mechanical signal generation. Various methods have been developed over the years to measure CTFs of both populations of cells and of single cells. At present, cell traction force microscopy (CTFM) is among the most efficient and reliable method for determining CTF field of an entire cell spreading on a two-dimensional (2D) substrate surface. There are currently three CTFM methods, each of which is unique in both how displacement field is extracted from images and how CTFs are subsequently estimated. A detailed review and comparison of these methods are presented. Future research should improve CTFM methods such that they can automatically track dynamic CTFs, thereby providing new insights into cell motility in response to altered biological conditions. In addition, research effort should be devoted to developing novel experimental and theoretical methods for determining CTFs in three-dimensional (3D) matrix, which better reflects physiological conditions than 2D substrate used in current CTFM methods.     

A novel cell force sensor for quantification of traction during cell spreading and contact guidance

In this work, we present a ridged, microfabricated, force sensor that can be used to investigate mechanical interactions between cells exhibiting contact guidance and the underlying cell culture substrate, and a proof-of-function evaluation of the force sensor performance. The substrates contain arrays of vertical pillars between solid ridges that were microfabricated in silicon wafers using photolithography and deep reactive ion etching. The spring constant of the pillars was measured by atomic force microscopy. For time-lapse experiments, cells were seeded on the pillared substrates and cultured in an on-stage incubator on a microscope equipped with reflected differential interference contrast optics. Endothelial cells (ECs) and fibroblasts were observed during attachment, spreading, and migration. Custom image analysis software was developed to resolve cell borders, cell alignment to the pillars and migration, displacements of individual pillars, and to quantify cell traction forces. Contact guidance classification was based on cell alignment and movement angles with respect to microfabricated ridges, as well as cell elongation. In initial investigations made with the ridged cell force sensor, we have observed contact guidance in ECs but not in fibroblast cells. A difference in maximal amplitude of mechanical forces was observed between a contact-guided and non-contact-guided, but mobile, EC. However, further experiments are required to determine the statistical significance of this observation. By chance, we observed another feature of cell behavior, namely a reversion of cell force direction. The direction of forces measured under rounded fibroblast cells changed from outwards during early cell attachment to inwards during further observation of the spreading phase. The range of forces measured under fibroblasts (up to 138 nN) was greater than that measured in EC (up to 57 nN), showing that the rigid silicon sensor is capable of resolving a large range of forces, and hence detection of differences in traction forces between cell types. These observations indicate proof-of-function of the ridged cell force sensor to induce contact guidance, and that the pillared cell force sensor constructed in rigid silicon has the necessary sensitivity to detect differences in traction force vectors between different cell phenotypes and morphologies.     

Arrestins regulate cell spreading and motility via focal adhesion dynamics

Focal adhesions (FAs) play a key role in cell attachment, and their timely disassembly is required for cell motility. Both microtubule-dependent targeting and recruitment of clathrin are critical for FA disassembly. Here we identify nonvisual arrestins as molecular links between microtubules and clathrin. Cells lacking both nonvisual arrestins showed excessive spreading on fibronectin and poly-d-lysine, increased adhesion, and reduced motility. The absence of arrestins greatly increases the size and lifespan of FAs, indicating that arrestins are necessary for rapid FA turnover. In nocodazole washout assays, FAs in arrestin-deficient cells were unresponsive to disassociation or regrowth of microtubules, suggesting that arrestins are necessary for microtubule targeting–dependent FA disassembly. Clathrin exhibited decreased dynamics near FA in arrestin-deficient cells. In contrast to wild-type arrestins, mutants deficient in clathrin binding did not rescue the phenotype. Collectively the data indicate that arrestins are key regulators of FA disassembly linking microtubules and clathrin.