A predictive model of cell traction forces based on cell geometry

Recent work has indicated that the shape and size of a cell can influence how a cell spreads, develops focal adhesions, and exerts forces on the substrate. However, it is unclear how cell shape regulates these events. Here we present a computational model that uses cell shape to predict the magnitude and direction of forces generated by cells. The predicted results are compared to experimentally measured traction forces, and show that the model can predict traction force direction, relative magnitude, and force distribution within the cell using only cell shape as an input. Analysis of the model shows that the magnitude and direction of the traction force at a given point is proportional to the first moment of area about that point in the cell, suggesting that contractile forces within the cell act on the entire cytoskeletal network as a single cohesive unit. Through this model, we demonstrate that intrinsic properties of cell shape can facilitate changes in traction force patterns, independently of heterogeneous mechanical properties or signaling events within the cell.     

Spatial and temporal coordination of traction forces in one-dimensional cell migration

ABSTRACT

Migration of a fibroblast along a collagen fiber can be regarded as cell locomotion in one-dimension (1D). In this process, a cell protrudes forward, forms a new adhesion, produces traction forces, and releases its rear adhesion in order to advance itself along a path. However, how a cell coordinates its adhesion formation, traction forces, and rear release in 1D migration is unclear. Here, we studied fibroblasts migrating along a line of microposts. We found that when the front of a cell protruded onto a new micropost, the traction force produced at its front increased steadily, but did so without a temporal correlation in the force at its rear. Instead, the force at the front coordinated with a decrease in force at the micropost behind the front. A similar correlation in traction forces also occurred at the rear of a cell, where a decrease in force due to adhesion detachment corresponded to an increase in force at the micropost ahead of the rear. Analysis with a bio-chemo-mechanical model for traction forces and adhesion dynamics indicated that the observed relationship between traction forces at the front and back of a cell is possible only when cellular elasticity is lower than the elasticity of the cellular environment.     

Hypergravity affects cell cycle progression and caveolin-1 expression of in vitro cultured human primary endothelial cells

In hypogravity conditions unloading of skeletal muscle fibres causes alterations in skeletal muscle structure and functions including growth, gene expression, cell differentiation, cytoskeletal organization, contractility and plasticity. Recent studies have identified sphingosine I -phosphate (SPP) as a lipid mediator capable of eliciting intracellular Ca2+ transients, cell proliferation, differentiation, suppression of apoptosis, as well as cell injury repair. The aim of this research is to evaluate a possible involvement of SPP in skeletal muscle cells differentiation and repair from space-flight damage. Particularly, we investigated the Ca2+ sources and the changes on the cytoskeletal rearrangement induced by SPP in a mouse skeletal (C2C12) myoblastic cell line. Confocal fluorescence imaging revealed that SPP elicited Ca2+ transients which propagated throughout the cytosol and nucleus. This response required extracellular and intracellular Ca2+ mobilization. SPP also induced cell contraction through a Ca2(+)- independent/Rho-dependent pathway. The nuclear Ca2+ transients are suggestive for an action of SPP in the differentiation program and damage repair.     

Keratocytes generate traction forces in two phases

Forces generated by goldfish keratocytes and Swiss 3T3 fibroblasts have been measured with nanonewton precision and submicrometer spatial resolution. Differential interference contrast microscopy was used to visualize deformations produced by traction forces in elastic substrata, and interference reflection microscopy revealed sites of cell-substratum adhesions. Force ranged from a few nanonewtons at submicrometer spots under the lamellipodium to several hundred nanonewtons under the cell body. As cells moved forward, centripetal forces were applied by lamellipodia at sites that remained stationary on the substratum. Force increased and abruptly became lateral at the boundary of the lamellipodium and the cell body. When the cell retracted at its posterior margin, cell-substratum contact area decreased more rapidly than force, so that stress (force divided by area) increased as the cell pulled away. An increase in lateral force was associated with widening of the cell body. These mechanical data suggest an integrated, two-phase mechanism of cell motility: (1) low forces in the lamellipodium are applied in the direction of cortical flow and cause the cell body to be pulled forward; and (2) a component of force at the flanks pulls the rear margins forward toward the advancing cell body, whereas a large lateral component contributes to detachment of adhesions without greatly perturbing forward movement.     

Hypergravity exposure affects ventral root activity in tadpoles (Xenopus laevis)

In tadpoles, it is possible to observe the rhythmical, burstlike activity of spinal motoneurons by extracellular recordings from the ventral roots. We examined the effects of hypergravity on tadpole locomotion by using a model of fictive swimming in paralysed larvae of Xenopus laevis. Hypergravity (3g) treatment lasted 10 or 11 days. After the 3g-exposure, the mean burst duration of the 3g-animals was significantly (p < or = 0.01) increased compared to the 1g-controls. Readaptation was observed for 8 days after the end of the 3g-period. Burst duration also increases with the age of the tadpoles. Therefore, we postulate that hypergravity has a reversible effect on motor development, probably caused by a neurotrophic effect of a tonic base activity of the vestibular nuclei.     

Development of micropost force sensor array with culture experiments for determination of cell traction forces

Cell traction forces (CTFs) are critical for cell motility and cell shape maintenance. As such, they play a fundamental role in many biological processes such as angiogenesis, embryogenesis, inflammation, and wound healing. To determine CTFs at the sub-cellular level with high sensitivity, we have developed high density micropost force sensor array (MFSA), which consists of an array of vertically standing poly(dimethylsiloxane) (PDMS) microposts, 2 microm in diameter and 6 microm in height, with a center-to-center distance of 4 microm. In combination with new image analysis algorithms, the MFSA can achieve a spatial resolution of 40 nm and a force sensitivity of 0.5 nN. Culture experiments with various types of cells showed that this MFSA technology can effectively determine CTFs of cells with different sizes and traction force magnitudes.     

Flow mechanotransduction regulates traction forces, intercellular forces, and adherens junctions

Endothelial cells respond to fluid shear stress through mechanotransduction responses that affect their cytoskeleton and cell-cell contacts. Here, endothelial cells were grown as monolayers on arrays of microposts and exposed to laminar or disturbed flow to examine the relationship among traction forces, intercellular forces, and cell-cell junctions. Cells under laminar flow had traction forces that were higher than those under static conditions, whereas cells under disturbed flow had lower traction forces. The response in adhesion junction assembly matched closely with changes in traction forces since adherens junctions were larger in size for laminar flow and smaller for disturbed flow. Treating the cells with calyculin-A to increase myosin phosphorylation and traction forces caused an increase in adherens junction size, whereas Y-27362 cause a decrease in their size. Since tugging forces across cell-cell junctions can promote junctional assembly, we developed a novel approach to measure intercellular forces and found that these forces were higher for laminar flow than for static or disturbed flow. The size of adherens junctions and tight junctions matched closely with intercellular forces for these flow conditions. These results indicate that laminar flow can increase cytoskeletal tension while disturbed flow decreases cytoskeletal tension. Consequently, we found that changes in cytoskeletal tension in response to shear flow conditions can affect intercellular tension, which in turn regulates the assembly of cell-cell junctions.     

A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes

The phenomenological model for cell shape deformation and cell migration Chen (BMM 17:1429–1450, 2018), Vermolen and Gefen (BMM 12:301–323, 2012), is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et al. (LC 13:340–348, 2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.

     

Flexible substrata for the detection of cellular traction forces

By modulating adhesion signaling and cytoskeletal organization, mechanical forces play an important role in various cellular functions, from propelling cell migration to mediating communication between cells. Recent developments have resulted in several new approaches for the detection, analysis and visualization of mechanical forces generated by cultured cells. Combining these methods with other approaches, such as green-fluorescent protein (GFP) imaging and gene manipulation, proves to be particularly powerful for analyzing the interplay between extracellular physical forces and intracellular chemical events.     

Interaction of serum and cell spreading affects the growth of neoplastic and non-neoplastic fibroblasts

Both growth factor availability and cell-to-cell contact have been mechanisms used to explain cell growth regulation at high cell density. Recently Folkman and colleagues have shown that changes in cell shape, rather than cell-to-cell contact, can regulate the growth of fibroblasts. However, in those studies the relation between serum and shape regulation of growth was not studied, nor were neoplastic and non-neoplastic cells compared. In this report we have studied these aspects by varying cell spreading and serum concentration independently for 2 non-neoplastic and 3 neoplastic cell lines. Cell spreading (projected cell area) was controlled by decreasing the adhesiveness of tissue culture plastic plates with poly (hydroxyethyl methacrylate) [poly (HEMA)]. Cell growth was measured as the increase in cell number/day. We have found that more spreading increased net growth of both neoplastic and non-neoplastic cells, while less spreading (toward rounded configuration) depressed growth. There were also quantitative differences between neoplastic and non-neoplastic cells. Neoplastic cells continued to grow under conditions of cell rounding, which completely prevented the growth of their non-neoplastic counterparts. Some neoplastic cells also tended to show little or no increase in net cell number for serum concentrations above 10% as cells became more spread; in contrast, all non-neoplastic cells grew more with increasing concentrations of serum as they became well spread. Thus, in normal cells, it appears that the sensitivity of cells to humoral factors is governed by cell spreading. This interaction between serum and cell shape is less prominent in some neoplastic cells.     

Regulation of SMC traction forces in human aortic thoracic aneurysms

Smooth muscle cells (SMCs) usually express a contractile phenotype in the healthy aorta. However, aortic SMCs have the ability to undergo profound changes in phenotype in response to changes in their extracellular environment, as occurs in ascending thoracic aortic aneurysms (ATAA). Accordingly, there is a pressing need to quantify the mechanobiological effects of these changes at single cell level. To address this need, we applied Traction Force Microscopy (TFM) on 759 cells coming from three primary healthy (AoPrim) human SMC lineages and three primary aneurysmal (AnevPrim) human SMC lineages, from age and gender matched donors. We measured the basal traction forces applied by each of these cells onto compliant hydrogels of different stiffness (4, 8, 12, 25 kPa). Although the range of force generation by SMCs suggested some heterogeneity, we observed that: 1. the traction forces were significantly larger on substrates of larger stiffness; 2. traction forces in AnevPrim were significantly higher than in AoPrim cells. We modelled computationally the dynamic force generation process in SMCs using the motor-clutch model and found that it accounts well for the stiffness-dependent traction forces. The existence of larger traction forces in the AnevPrim SMCs were related to the larger size of cells in these lineages. We conclude that phenotype changes occurring in ATAA, which were previously known to reduce the expression of elongated and contractile SMCs (rendering SMCs less responsive to vasoactive agents), tend also to induce stronger SMCs. Future work aims at understanding the causes of this alteration process in aortic aneurysms.

     

Measuring traction forces of motile dendritic cells on micropost arrays

Dendritic cells (DCs) migrate from sites of inflammation to secondary lymphoid organs where they initiate the adaptive immune response. Although motility is essential to DC function, the mechanisms by which they migrate are not fully understood. We incorporated micropost array detectors into a microfluidic gradient generator to develop what we consider to be a novel method for probing low magnitude traction forces during directional migration. We found migration of primary murine DCs is driven by short-lived traction stresses at the leading edge or filopodia. The traction forces generated by DCs are smaller in magnitude than found in neutrophils, and of similar magnitude during chemotaxis and chemokinesis, at 18 ± 1.4 and 16 ± 1.3 nN/cell, respectively. The characteristic duration of local DC traction forces was 3 min. The maximum principal stress in the cell occurred in the plane perpendicular to the axis of motion, forward of the centroid. We illustrate that the spatiotemporal pattern of traction stresses can be used to predict the direction of future DC motion. Overall, DCs show a mode of migration distinct from both mesenchymal cells and neutrophils, characterized by rapid turnover of traction forces in leading filopodia.     

Nystatin affects zinc uptake in human fibroblasts

The mechanism(s) by which zinc is transported into cells has not been identified. Since zinc uptake is inhibited by reducing the temperature, zinc uptake may depend on the movement of plasma membrane micoenvironments, such as endocytosis or potocytosis. We investigated the potential role of potocytosis in cellular zinc uptake by incubating normal and acrodermatitis enteropathica fibroblasts with nystatin, a sterol-binding drug previously shown to inhibit potocytosis. Zinc uptake was determined during initial rates of uptake (10 min) following incubation of the fibroblasts in 50 μg nystatin/mL or 0.1% dimethyl-sulfoxide for 10 min at 37°C. The cells were then incubated with 1 to 30 μM ⁶⁵zinc. Michaelis-Menten kinetics were observed for zinc uptake. Nystatin inhibited zinc uptake in both the normal and AE fibroblasts. Reduced cellular uptake of zinc was associated with its internalization, not its external binding. In normal fibroblasts, nystatin significantly reduced theK _m 56% and theV _max 69%. In the AE fibroblasts, nystatin treatment significantly reduced theV _max 59%, but did not significantly affect theK _m. The AE mutation alone affected theV _max for cellular zinc uptake. The control AE fibroblasts exhibited a 40% reduction inV _max compared to control normal fibroblasts. We conclude that nystatin exerts its effect on zinc uptake by reducing the velocity at which zinc traverses the cell membrane, possibly through potocytosis. Furthermore, the AE mutation also effects zinc transport by reducing zinc transport.     

Direct physical formation of anatomical structures by cell traction forces. An interview with Albert Harris by Lev Beloussov

Albert Harris was educated at The Norfolk Academy, Norfolk, Virginia, USA (1961). He then earned a Batchelor of Arts Degree in Biology from Swarthmore College, in Pennsylvania, USA (1965), followed by a Ph.D. in Biology (1971) from Yale University, where his Dissertation Advisor was the great John Phillip Trinkaus. He held a Damon-Runyon Postdoctoral Fellowship in Cancer Research in 1970-72, under Michael Abercrombie, FRS, at the Strangeways Research Laboratory of Cambridge University, England. Then he accepted a position as Assistant Professor in the Zoology Department of the University of North Carolina at Chapel Hill, N.C. USA. In 1977, he was promoted to Associate Professor of Zoology, and in 1983 was promoted to Full Professor of Biology. In Oct.-Nov. 1991 he was honored to be Distinguished Visiting Professor of Zoology at the University of California at Davis.     

Cell spread area and traction forces determine myosin-II-based cortex thickness regulation

Actomyosin network under the plasma membrane of cells forms a cortical layer that regulates cellular deformations during different processes. What regulates the cortex? Characterized by its thickness, it is believed to be regulated by actin dynamics, filament-length regulators and myosin motor proteins. However, its regulation by cellular morphology (e.g. cell spread area) or mechanical microenvironment (e.g. substrate stiffness) has remained largely unexplored. In this study, super- and high-resolution imaging of actin in CHO cells demonstrates that at high spread areas (>450 μm²), the cortex is thinner, better separated as layers, and sensitive to deactivation of myosin II motors or reduction of substrate stiffness (and traction forces). In less spread cells (<400 μm²) such perturbations do not elicit a response. Myosin IIA's mechanosensing is limited here due to its lowered actin-bound fraction and higher turnover rate. Cofilin, in line with its competitive inhibitory role, is found to be overexpressed in these cells. To establish the causal relation, we initiate a spread area drop by de-adhesion and find enhanced actin dynamics and fragmentation along with oscillations and increase in thickness. This is more correlated to the reduction of traction forces than the endocytosis-based reduction in cell volume. Cortex thickness control by spread area is also found be true during differentiation of THP-1 monocytes to macrophages. Thus, we propose that spread area regulates cortex and its thickness by traction-based mechanosensing of myosin II.     

Quantitative analysis of collagen gel contractile forces generated by dermal fibroblasts and the relationship to cell morphology

The force generated in granulation tissue during wound contraction is thought to be cell mediated; however, it is unclear whether contractile forces are generated by fibroblast locomotion or contraction of myofibroblasts. To help clarify this question the force of this contraction can now be determined accurately in a human dermal fibroblast collagen lattice system using a novel instrument known as a Culture Force Monitor. Three distinct phases of contraction of such collagen gels could be identified over the first 24 hours. Most of the force generated by human dermal fibroblasts was produced during the first stage in parallel with cell attachment and associated changes in cell shape, and the appearance of cell processes. During this initial 24 hours no evidence could be found for the presence of myofibroblasts, but stereoscopic and electron microscopic analysis at a range of time points indicated that migratory fibroblasts were present in the system. Comparison of the contraction profiles of cells extracted from other tissues (tendon and articular cartilage), and extracted by different means from the same tissue specimen, indicated that different populations of fibroblasts can be distinguished on the basis of their pattern of contractions. It would seem that most of the force generated in this model is a result of fibroblast attachment and movement within the collagen lattice. Furthermore, different groups of fibroblasts, even within the same tissue, may vary in their contraction (hence locomotory) activity. © 1996 Wiley-Liss, Inc.     

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.