[Show abstract][Hide abstract] ABSTRACT: During migration, amoeboid cells perform a cycle of quasi-periodic repetitive
events (motility cycle). the cell length and the strain energy exchanged with
the substrate oscillate in time with an average frequency, f, on top of which
are imposed smaller random fluctuations. the fact that a considerable portion
of the changes in cell shape are due to periodic repetitive events enables the
use of conditional statistics methods to analyze the network of biochemical
processes involved in cell motility. taking advan- tage of this cyclic nature,
we apply Principal Component analysis (PCa) and phase- average statistics to
analyze the dominant modes of shape change and their association to the
activity and localization of molecular motors. We analyze time-lapse measure-
ments of cell shape, traction forces and fluorescence from green fluorescent
protein (GfP) reporters for f-actin in Dictyostelium cells undergoing guided
chemotactic migration. using wild-type cells (wt) as reference, we investigated
the contractile and actin crosslinking functions of myosin II by studying
myosin II heavy chain null mutant cells (mhcA-) and myosin II essential light
chain null cells (mlcE-).
[Show abstract][Hide abstract] ABSTRACT: We introduce a novel three-dimensional (3D) traction force microscopy (TFM) method motivated by the recent discovery that cells adhering on plane surfaces exert both in-plane and out-of-plane traction stresses. We measure the 3D deformation of the substratum on a thin layer near its surface, and input this information into an exact analytical solution of the elastic equilibrium equation. These operations are performed in the Fourier domain with high computational efficiency, allowing to obtain the 3D traction stresses from raw microscopy images virtually in real time. We also characterize the error of previous two-dimensional (2D) TFM methods that neglect the out-of-plane component of the traction stresses. This analysis reveals that, under certain combinations of experimental parameters (cell size, substratums' thickness and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by neglecting the out-of-plane component of the traction stresses. Finally, we consider the cell's mechanosensing of substratum thickness by 3D traction stresses, finding that, when cells adhere on thin substrata, their out-of-plane traction stresses can reach four times deeper into the substratum than their in-plane traction stresses. It is also found that the substratum stiffness sensed by applying out-of-plane traction stresses may be up to 10 times larger than the stiffness sensed by applying in-plane traction stresses.
[Show abstract][Hide abstract] ABSTRACT: Mesenchymal stem cells (MSCs) respond to niche elasticity, which varies between and within tissues. Stiffness gradients result from pathological conditions but also occur through normal variation, e.g. muscle. MSCs undergo directed migration even in response to shallow stiffness gradients before differentiating. More refined gradients of both stiffness range and strength are needed to better understand mechanical regulation of migration in normal and disease pathologies. We describe polyacrylamide stiffness gradient fabrication using three distinct systems that generate stiffness gradients of physiological (1 Pa/μm), pathological (10 Pa/μm), and step (≥ 100 Pa/μm) strength spanning physiologically relevant stiffness for most soft tissue, i.e. 1-12 kPa. MSCs migrated to the stiffest region for each gradient. Time-lapse microscopy revealed that migration velocity scaled directly with gradient strength. Directed migration was reduced in the presence of the contractile agonist lysophosphatidic acid (LPA) and cytoskeletal-perturbing drugs nocodazole and cytochalasin; LPA- and nocodazole-treated cells remained spread and protrusive, while cytochalasin-treated cells did not. Untreated and nocodazole-treated cells spread in a similar manner, but nocodazole-treated cells had greatly diminished traction forces. These data suggest that actin is required for migration whereas microtubules are required for directed migration. The data also imply that in vivo, MSCs may have a more significant contribution to repairs in stiffer regions where they may preferentially accumulate.
[Show abstract][Hide abstract] ABSTRACT: We use a novel 3D inter-/intracellular force microscopy technique based on 3D traction force microscopy to measure the cell-cell junctional and intracellular tensions in subconfluent and confluent vascular endothelial cell (EC) monolayers under static and shear flow conditions. We found that z-direction cell-cell junctional tensions are higher in confluent EC monolayers than those in subconfluent ECs, which cannot be revealed in the previous 2D methods. Under static conditions, subconfluent cells are under spatially non-uniform tensions, whereas cells in confluent monolayers are under uniform tensions. The shear modulations of EC cytoskeletal remodeling, extracellular matrix (ECM) adhesions, and cell-cell junctions lead to significant changes in intracellular tensions. When a confluent monolayer is subjected to flow shear stresses with a high forward component comparable to that seen in the straight part of the arterial system, the intracellular and junction tensions preferentially increase along the flow direction over time, which may be related to the relocation of adherens junction proteins. The increases in intracellular tensions are shown to be a result of chemo-mechanical responses of the ECs under flow shear rather than a direct result of mechanical loading. In contrast, the intracellular tensions do not show a preferential orientation under oscillatory flow with a very low mean shear. These differences in the directionality and magnitude of intracellular tensions may modulate translation and transcription of ECs under different flow patterns, thus affecting their susceptibility for atherogenesis.
Full-text · Article · Jun 2012 · Proceedings of the National Academy of Sciences
[Show abstract][Hide abstract] ABSTRACT: We used principal component analysis to dissect the mechanics of chemotaxis of amoeboid cells into a reduced set of dominant components of cellular traction forces and shape changes. The dominant traction force component in wild-type cells accounted for ~40% of the mechanical work performed by these cells, and consisted of the cell attaching at front and back contracting the substrate towards its centroid (pole-force). The time evolution of this pole-force component was responsible for the periodic variations of cell length and strain energy that the cells underwent during migration. We identified four additional canonical components, reproducible from cell to cell, overall accounting for an additional ~20% of mechanical work, and associated with events such as lateral protrusion of pseudopodia. We analyzed mutant strains with contractility defects to quantify the role that non-muscle Myosin II (MyoII) plays in amoeboid motility. In MyoII essential light chain null cells the polar-force component remained dominant. On the other hand, MyoII heavy chain null cells exhibited a different dominant traction force component, with a marked increase in lateral contractile forces, suggesting that cortical contractility and/or enhanced lateral adhesions are important for motility in this cell line. By compressing the mechanics of chemotaxing cells into a reduced set of temporally-resolved degrees of freedom, the present study may contribute to refined models of cell migration that incorporate cell-substrate interactions.
Electronic supplementary material
The online version of this article (doi:10.1007/s12195-011-0184-9) contains supplementary material, which is available to authorized users.
Full-text · Article · Dec 2011 · Cellular and Molecular Bioengineering
[Show abstract][Hide abstract] ABSTRACT: 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.
Full-text · Article · Sep 2011 · Molecular biology of the cell
[Show abstract][Hide abstract] ABSTRACT: We have studied the 3D traction forces exerted by migrating Dictyostelium cells moving over flat elastic substrates. For that purpose, we have developed a method to calculate both vertical and tangential cell traction forces from measurements of 3D substrate deformation, based on the solution of the elastostatic equation for a linearly elastic medium. 3D substrate deformation is measured by applying correlation techniques to a volume of substrate containing fluorescent markers. We have performed experiments for wild-type (WT) and mutant cell lines with crosslinking defects to study how cytoskeletal organization affects the overall distribution of traction forces. We find that cells push the substrate downwards near their center and pull upwards at their periphery with forces of comparable magnitude. Our initial findings show that the effect of the crosslinking mutations on the tangential forces do not necessarily predict the effect on the vertical forces. For instance, myosin II-null cells show a significant reduction of the front-back organization of the tangential traction forces, while the distribution of vertical forces basically remains unaffected.
No preview · Article · Feb 2011 · Biophysical Journal
[Show abstract][Hide abstract] ABSTRACT: Amoeboid motility requires spatiotemporal coordination of biochemical pathways regulating force generation and consists of the quasi-periodic repetition of a motility cycle driven by actin polymerization and actomyosin contraction. Using new analytical tools and statistical methods, we provide, for the first time, a statistically significant quantification of the spatial distribution of the traction forces generated at each phase of the cycle (protrusion, contraction, retraction, and relaxation). We show that cells are constantly under tensional stress and that wild-type cells develop two opposing "pole" forces pulling the front and back toward the center whose strength is modulated up and down periodically in each cycle. We demonstrate that nonmuscular myosin II complex (MyoII) cross-linking and motor functions have different roles in controlling the spatiotemporal distribution of traction forces, the changes in cell shape, and the duration of all the phases. We show that the time required to complete each phase is dramatically increased in cells with altered MyoII motor function, demonstrating that it is required not only for contraction but also for protrusion. Concomitant loss of MyoII actin cross-linking leads to a force redistribution throughout the cell perimeter pulling inward toward the center. However, it does not reduce significantly the magnitude of the traction forces, uncovering a non-MyoII-mediated mechanism for the contractility of the cell.
Full-text · Article · Dec 2009 · Molecular biology of the cell
[Show abstract][Hide abstract] ABSTRACT: Amoeboid motility results from the cyclic repetition of shape changes leading to periodic oscillations of the cell length (motility cycle). We analyze the dominant modes of shape change and their association to the traction forces exerted on the substrate using Principal Component Analysis (PCA) of time-lapse measurements of cell shape and traction forces in migrating Dictyostelium cells. Using wild-type cells (wt) as reference, we investigated myosin II activity by studying myosin II heavy chain null cells (mhcA-) and myosin II essential light chain null cells (mlcE-). We found that wt, mlcE-and mhcA- cells utilize similar modes of shape changes during their motility cycle, although these shape changes are implemented at a slower pace in myosin II null mutants. The number of dominant modes of shape changes is surprisingly few with only four modes accounting for 75% of the variance in all cases. The three principal shape modes are dilation/elongation, bending, and bulging of the front/back. The second mode, resulting from sideways protrusion/retraction, is associated to lateral asymmetries in the cell traction forces, and is significantly less important in mhcA-cells. These results indicate that the mechanical cycle of traction stresses and cell shape changes remains remarkably similar for all cell lines but is slowed down when myosin function is lost, probably due to a reduced control on the spatial organization of the traction stresses.
[Show abstract][Hide abstract] ABSTRACT: Amoeboid motility results from the repetition of a repertoire of shape changes (motility cycle). We studied the dominant changes and their relation to the activity and localization of cytoskeletal proteins by applying Principal Component Analysis (PCA) to measurements of cell shape, traction forces and F-actin concentration in migrating Dictyostelium cells. Using wild-type cells (wt) as reference, we investigated myosin II activity by studying myosin II-null (mhc-) and essential light chain-null cells (mlc-). Only three PCA modes are enough to represent 67% of the variance of cell area: dilation/elongation, a half-moon shape and a bulging of the front/back. These modes are similar for wt, mlc- and mhc- but they are implemented more slowly in mhc-. The second mode, which represents sideways protrusion/retraction and is associated to lateral asymmetry in the traction forces, is significantly less important in mhc-. These results suggest that migration speed decreases in the absence of myosin II due to a reduced control on the spatial organization of the cell stresses.
Full-text · Article · Feb 2009 · Biophysical Journal
[Show abstract][Hide abstract] ABSTRACT: Amoeboid motility results from the repetition of stereotypic steps that produce quasi-periodic oscillations of cell length and speed. We characterize the steps of the motility cycle of Dictyostelium cells crawling on elastic substrates by analyzing their traction forces. Using a high-resolution force cytometry method for wild type cells and mutants with contractility and adhesion defects, we find that the time evolution of the traction forces is quasi-periodic, with a period (T) that correlates strongly with the cell speed (V) according to a simple law VT=L. The constant L is the distance traveled per cycle. The cellular traction forces are much larger than needed to overcome the viscous drag from the lubrication layer between the cells and the substrate, but they do not correlate with V. These results suggest that the speed of amoeboid migration is determined by the ability of the cell to repeat the steps of the motility cycle in a coordinated way. The phase average allowed us to combine time sequences of force maps derived from different cells to obtain a spatio-temporal representation of a canonical motility cycle divided into four steps: protrusion, contraction, retraction and relaxation. We find that myosin II-dependent contraction is present in all the steps of the wild-type motility cycle, including protrusion. JCA supported by MEC/Fulbright (Spain).
[Show abstract][Hide abstract] ABSTRACT: Cell motility plays an essential role in many biological systems, but precise quantitative knowledge of the biophysical processes involved in cell migration is limited. Better measurements are needed to ultimately build models with predictive capabilities. We present an improved force cytometry method and apply it to the analysis of the dynamics of the chemotactic migration of the amoeboid form of Dictyostelium discoideum. Our explicit calculation of the force field takes into account the finite thickness of the elastic substrate and improves the accuracy and resolution compared with previous methods. This approach enables us to quantitatively study the differences in the mechanics of the migration of wild-type (WT) and mutant cell lines. The time evolution of the strain energy exerted by the migrating cells on their substrate is quasi-periodic and can be used as a simple indicator of the stages of the cell motility cycle. We have found that the mean velocity of migration v and the period of the strain energy T cycle are related through a hyperbolic law v = L/T, where L is a constant step length that remains unchanged in mutants with adhesion or contraction defects. Furthermore, when cells adhere to the substrate, they exert opposing pole forces that are orders of magnitude higher than required to overcome the resistance from their environment.
Full-text · Article · Sep 2007 · Proceedings of the National Academy of Sciences
[Show abstract][Hide abstract] ABSTRACT: The motion of Dictyostelium discoideum cells moving on a elastic substrate has been studied. Joint analysis of time-lapse DIC movies of the cells and UV fluorescence from the beads embedded in the substrate, allows for identification of characteristic time scales of the motion and the quantitative description of the crawling cycle. From the measured displacements of the beads, forces can be computed by analytically solving the elasto-static equation in a finite thickness slab. We found that the finite thickness of the substrate and the distance of the beads to its surface have a substantial effect and that the previous traction cytometry techniques based on the Boussinesq solution effectively low-pass-filtered the force field, reducing the spatial resolution and damping the range of the measured forces by as much as 50%. The improved spatial resolution of this method enables us to determine the spatial extent of the regions where the cells apply force on the substrate and, consequently, the magnitude of the elastic energy spent in its deformation. The measured forces, as well as the elastic energy communicated by the cell to the substrate, will be correlated to the different stages of the crawling cycle for various cell strains.
[Show abstract][Hide abstract] ABSTRACT: We present some recent observations of the motion of cells of the amoeba Dictyostelium Dicoideum under the effects of a well-controlled linear distribution of chemo-attractant concentration (chemotaxis). The kinematics and dynamics of chemotaxis have been analyzed from microscopy images using a combination of image processing and feature tracking techniques. The trajectory of the cell's center of mass, as well as cell polarization along gradient lines, have been found to follow a quasi-periodic evolution. The frequency of this motion can be related to biochemical processes that are known to be responsible for the internal remodeling of the structure of the cell cytoskeleton and cell motion. The traction force that the cell exerts, through adhesion points, on the substrate has been estimated from the contribution of cell inertia, lubrication layer between the cell and the substrate, and hydrodynamic drag of the flow around the cell.
[Show abstract][Hide abstract] ABSTRACT: We measure the forces exerted by Dictyostelium discoideum cells crawling over a deformable substrate from the displacements of fluorescent beads embedded in it. A particle tracking technique similar to PIV is used to obtain the displacements. From them, forces are computed by solving the elasto-static equation in a finite thickness slab. We will show that the finite thickness of the substrate and the distance of the beads to its surface affect substantially the results, although previous traction cytometry techniques neglected them. The measured forces are correlated to the different stages of the crawling cycle for various cell strains. It has been observed that a large fraction of the forces measured on the substrate are originated by the cell's internal tension through all the stages of motion, including the protrusion of pseudopods. This result suggests that the viscous drag exerted by the fluid in which the cells are immersed is very small compared to the forces applied by the cytoskeleton on the substrate.