4D traction force microscopy reveals asymmetric cortical forces in migrating Dictyostelium cells

Ultimately Adaptive Fluid Interfacial Phospholipid Membranes Unveiled Unanticipated High Cellular Mechanical Work

Living cells actively interact biochemically and mechanically with the surrounding extracellular matrices (ECMs) and undergo dramatic morphological and dimensional transitions, concomitantly remodeling ECMs. However, there is no suitable method to quantitatively discuss the contribution of mechanical interactions in such mutually adaptive processes. Herein, a highly deformable "living" cellular scaffold is developed to evaluate overall mechanical energy transfer between cell and ECMs. It is based on the water-perfluorocarbon interface decorated with phospholipids bearing a cell-adhesive ligand and fluorescent tag. The bioinert nature of the phospholipid membranes prevents the formation of solid-like protein nanofilms at the fluid interface, enabling to visualize and quantify cellular mechanical work against the ultimately adaptive model ECM. A new cellular wetting regime is identified, wherein interface deformation proceeds to cell flattening, followed by its eventual restoration. The cellular mechanical work during this adaptive wetting process is one order of magnitude higher than those reported with conventional elastic platforms. The behavior of viscous liquid drops at the air-water interface can simulate cellular adaptive wetting, suggesting that overall viscoelasticity of the cell body predominates the emergent wetting regime and regulates mechanical output. Cellular-force-driven high-energy states on the adaptive platform can be useful for cell fate manipulation.

Elastocapillary effects determine early matrix deformation by glioblastoma cell spheroids

During cancer pathogenesis, cell-generated mechanical stresses lead to dramatic alterations in the mechanical and organizational properties of the extracellular matrix (ECM). To date, contraction of the ECM is largely attributed to local mechanical stresses generated during cell invasion, but the impact of "elastocapillary" effects from surface tension on the tumor periphery has not been examined. Here, we embed glioblastoma cell spheroids within collagen gels, as a model of tumors within the ECM. We then modulate the surface tension of the spheroids, such that the spheroid contracts or expands. Surprisingly, in both cases, at the far-field, the ECM is contracted toward the spheroids prior to cellular migration from the spheroid into the ECM. Through computational simulation, we demonstrate that contraction of the ECM arises from a balance of spheroid surface tension, cell-ECM interactions, and time-dependent, poroelastic effects of the gel. This leads to the accumulation of ECM near the periphery of the spheroid and the contraction of the ECM without regard to the expansion or contraction of the spheroid. These results highlight the role of tissue-level surface stresses and fluid flow within the ECM in the regulation of cell-ECM interactions.

Dynamics of centipede locomotion revealed by large-scale traction force microscopy

We present a novel approach to traction force microscopy (TFM) for studying the locomotion of 10 cm long walking centipedes on soft substrates. Leveraging the remarkable elasticity and ductility of kudzu starch gels, we use them as a deformable gel substrate, providing resilience against the centipedes' sharp leg tips. By optimizing fiducial marker size and density and fine-tuning imaging conditions, we enhance measurement accuracy. Our TFM investigation reveals traction forces along the centipede's longitudinal axis that effectively counterbalance inertial forces within the 0-10 mN range, providing the first report of non-vanishing inertia forces in TFM studies. Interestingly, we observe waves of forces propagating from the head to the tail of the centipede, corresponding to its locomotion speed. Furthermore, we discover a characteristic cycle of leg clusters engaging with the substrate: forward force (friction) upon leg tip contact, backward force (traction) as the leg pulls the substrate while stationary, and subsequent forward force as the leg tip detaches to reposition itself in the anterior direction. This work opens perspectives for TFM applications in ethology, tribology and robotics.

Field Guide to Traction Force Microscopy

Introduction

Traction force microscopy (TFM) is a widely used technique to measure cell contractility on compliant substrates that mimic the stiffness of human tissues. For every step in a TFM workflow, users make choices which impact the quantitative results, yet many times the rationales and consequences for making these decisions are unclear. We have found few papers which show the complete experimental and mathematical steps of TFM, thus obfuscating the full effects of these decisions on the final output.

Methods

Therefore, we present this "Field Guide" with the goal to explain the mathematical basis of common TFM methods to practitioners in an accessible way. We specifically focus on how errors propagate in TFM workflows given specific experimental design and analytical choices.

Results

We cover important assumptions and considerations in TFM substrate manufacturing, substrate mechanical properties, imaging techniques, image processing methods, approaches and parameters used in calculating traction stress, and data-reporting strategies.

Conclusions

By presenting a conceptual review and analysis of TFM-focused research articles published over the last two decades, we provide researchers in the field with a better understanding of their options to make more informed choices when creating TFM workflows depending on the type of cell being studied. With this review, we aim to empower experimentalists to quantify cell contractility with confidence.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00801-6.

Cargo Size Limits and Forces of Cell-Driven Microtransport

The integration of motile cells into biohybrid microrobots offers unique properties such as sensitive responses to external stimuli, resilience, and intrinsic energy supply. Here, biohybrid cell-cargo systems that are driven by amoeboid Dictyostelium discoideum cells are studied and how the cargo speed and the resulting viscous drag force scales with increasing radius of the spherical cargo particle are explored. Using a simplified geometrical model of the cell-cargo interaction, the findings toward larger cargo sizes, which are not accessible with the experimental setup, are extrapolated and a maximal cargo size is predicted beyond which active cell-driven movements will stall. The active forces exerted by the cells to move a cargo show mechanoresponsive adaptation and increase dramatically when challenged by an external pulling force, a mechanism that may become relevant when navigating cargo through complex heterogeneous environments.

High-resolution assessment of multidimensional cellular mechanics using label-free refractive-index traction force microscopy

A critical requirement for studying cell mechanics is three-dimensional assessment of cellular shapes and forces with high spatiotemporal resolution. Traction force microscopy with fluorescence imaging enables the measurement of cellular forces, but it is limited by photobleaching and a slow acquisition speed. Here, we present refractive-index traction force microscopy (RI-TFM), which simultaneously quantifies the volumetric morphology and traction force of cells using a high-speed illumination scheme with 0.5-Hz temporal resolution. Without labelling, our method enables quantitative analyses of dry-mass distributions and shear (in-plane) and normal (out-of-plane) tractions of single cells on the extracellular matrix. When combined with a constrained total variation-based deconvolution algorithm, it provides 0.55-Pa shear and 1.59-Pa normal traction sensitivity for a 1-kPa hydrogel substrate. We demonstrate its utility by assessing the effects of compromised intracellular stress and capturing the rapid dynamics of cellular junction formation in the spatiotemporal changes in non-planar traction components.

Mechanobiological cell adaptations to changing microenvironments determine cancer invasiveness: Experimentally validated finite element modeling

Metastases are the leading cause of cancer-associated deaths. A key process in metastasis is cell invasiveness, which is driven and controlled by cancer cell interactions with their microenvironment. We have previously shown that invasive cancer cells forcefully push into and indent physiological stiffness gels to cell-scale depths, where the percentage of indenting cells and their attained depths provide clinically relevant predictions of tumor invasiveness and the potential metastatic risk. The cell-attained, invasive indentation depths are directly affected by gel-microenvironment mechanics, which can concurrently modulate the cells' mechanics and force application capacity, in a complex, coordinated mechanobiological response. As it is impossible to experimentally isolate the different contributions of cell and gel mechanics to cancer cell invasiveness, we perform finite element modeling with literature-based parameters. Under average-scale, cell cytoplasm and nucleus mechanics and cell-applied force levels, increasing gel stiffness 1-50 kPa significantly reduced the attained indentation depth by >200%, while the gel's Poisson ratio reduced depths only by up to 20% and only when the ratio was >0.4; this reveals microenvironment mechanics that can promote invasiveness. Experiments with varying-invasiveness cancer cells exhibited qualitative variations in their responses to gel stiffness increase, for example large/small reduction in indentation depth or increase and then reduction. We quantitatively and qualitatively reproduced the different experimental responses via coordinated changes in cell mechanics and applied force levels. Thus, the different cancer cell capacities to adapt their mechanobiology in response to mechanically changing microenvironments likely determine the varying cancer invasiveness and metastatic risk levels in patients.

2.5D Traction Force Microscopy: Imaging three-dimensional cell forces at interfaces and biological applications

The forces that cells, tissues, and organisms exert on the surface of a soft substrate can be measured using Traction Force Microscopy (TFM), an important and well-established technique in Mechanobiology. The usual TFM technique (two-dimensional, 2D TFM) treats only the in-plane component of the traction forces and omits the out-of-plane forces at the substrate interfaces (2.5D) that turn out to be important in many biological processes such as tissue migration and tumour invasion. Here, we review the imaging, material, and analytical tools to perform "2.5D TFM" and explain how they are different from 2D TFM. Challenges in 2.5D TFM arise primarily from the need to work with a lower imaging resolution in the z-direction, track fiducial markers in three-dimensions, and reliably and efficiently reconstruct mechanical stress from substrate deformation fields. We also discuss how 2.5D TFM can be used to image, map, and understand the complete force vectors in various important biological events of various length-scales happening at two-dimensional interfaces, including focal adhesions forces, cell diapedesis across tissue monolayers, the formation of three-dimensional tissue structures, and the locomotion of large multicellular organisms. We close with future perspectives including the use of new materials, imaging and machine learning techniques to continuously improve the 2.5D TFM in terms of imaging resolution, speed, and faithfulness of the force reconstruction procedure.

All-Optical Modulation of Single Defects in Nanodiamonds: Revealing Rotational and Translational Motions in Cell Traction Force Fields

Measuring the mechanical interplay between cells and their surrounding microenvironment is vital in cell biology and disease diagnosis. Most current methods can only capture the translational motion of fiduciary markers in the deformed matrix, but their rotational motions are normally ignored. Here, by utilizing single nitrogen-vacancy (NV) centers in nanodiamonds (NDs) as fluorescent markers, we propose a linear polarization modulation (LPM) method to monitor in-plane rotational and translational motions of the substrate caused by cell traction forces. Specifically, precise orientation measurement and localization with background suppression were achieved via optical polarization selective excitation of single NV centers with precisions of ∼0.5°/7.5 s and 2 nm/min, respectively. Additionally, we successfully applied this method to monitor the multidimensional movements of NDs attached to the vicinity of cell focal adhesions. The experimental results agreed well with our theoretical calculations, demonstrating the practicability of the NV-based LPM method in studying mechanobiology and cell-material interactions.

May the force be with your (immune) cells: an introduction to traction force microscopy in Immunology

For more than a couple of decades now, "force" has been recognized as an important physical parameter that cells employ to adapt to their microenvironment. Whether it is externally applied, or internally generated, cells use force to modulate their various actions, from adhesion and migration to differentiation and immune function. T lymphocytes use such mechano-sensitivity to decipher signals when recognizing cognate antigens presented on the surface of antigen presenting cells (APCs), a critical process in the adaptive immune response. As such, many techniques have been developed and used to measure the forces felt/exerted by these small, solitary and extremely reactive cells to decipher their influence on diverse T cell functions, primarily activation. Here, we focus on traction force microscopy (TFM), in which a deformable substrate, coated with the appropriate molecules, acts as a force sensor on the cellular scale. This technique has recently become a center of interest for many groups in the "ImmunoBiophysics" community and, as a consequence, has been subjected to refinements for its application to immune cells. Here, we present an overview of TFM, the precautions and pitfalls, and the most recent developments in the context of T cell immunology.

Cell-Matrix Elastocapillary Interactions Drive Pressure-based Wetting of Cell Aggregates

Cell-matrix interfacial energies and the energies of matrix deformations may be comparable on cellular length-scales, yet how capillary effects influence tis sue shape and motion are unknown. In this work, we induce wetting (spreading and migration) of cell aggregates, as models of active droplets onto adhesive substrates of varying elasticity and correlate the dynamics of wetting to the balance of interfacial tensions. Upon wetting rigid substrates, cell-substrate tension drives outward expansion of the monolayer. By contrast, upon wetting compliant substrates, cell substrate tension is attenuated and aggregate capillary forces contribute to internal pressures that drive expansion. Thus, we show by experiments, data-driven modeling and computational simulations that myosin-driven 'active elasto-capillary' effects enable adaptation of wetting mechanisms to substrate rigidity and introduce a novel, pressure-based mechanism for guiding collective cell motion.

A primer to traction force microscopy

Traction force microscopy (TFM) has emerged as a versatile technique for the measurement of single-cell-generated forces. TFM has gained wide use among mechanobiology laboratories, and several variants of the original methodology have been proposed. However, issues related to the experimental setup and, most importantly, data analysis of cell traction datasets may restrain the adoption of TFM by a wider community. In this review, we summarize the state of the art in TFM-related research, with a focus on the analytical methods underlying data analysis. We aim to provide the reader with a friendly compendium underlying the potential of TFM and emphasizing the methodological framework required for a thorough understanding of experimental data. We also compile a list of data analytics tools freely available to the scientific community for the furtherance of knowledge on this powerful technique.

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.

Quantifying force transmission through fibroblasts: changes of traction forces under external shearing

Mammalian cells have evolved complex mechanical connections to their microenvironment, including focal adhesion clusters that physically connect the cytoskeleton and the extracellular matrix. This mechanical link is also part of the cellular machinery to transduce, sense and respond to external forces. Although methods to measure cell attachment and cellular traction forces are well established, these are not capable of quantifying force transmission through the cell body to adhesion sites. We here present a novel approach to quantify intracellular force transmission by combining microneedle shearing at the apical cell surface with traction force microscopy at the basal cell surface. The change of traction forces exerted by fibroblasts to underlying polyacrylamide substrates as a response to a known shear force exerted with a calibrated microneedle reveals that cells redistribute forces dynamically under external shearing and during sequential rupture of their adhesion sites. Our quantitative results demonstrate a transition from dipolar to monopolar traction patterns, an inhomogeneous distribution of the external shear force to the adhesion sites as well as dynamical changes in force loading prior to and after the rupture of single adhesion sites. Our strategy of combining traction force microscopy with external force application opens new perspectives for future studies of force transmission and mechanotransduction in cells.

Modeling force application configurations and morphologies required for cancer cell invasion

We show that cell-applied, normal mechanical stresses are required for cells to penetrate into soft substrates, matching experimental observations in invasive cancer cells, while in-plane traction forces alone reproduce observations in non-cancer/noninvasive cells. Mechanobiological interactions of cells with their microenvironment drive migration and cancer invasion. We have previously shown that invasive cancer cells forcefully and rapidly push into impenetrable, physiological stiffness gels and indent them to cell-scale depths (up to 10 μm); normal, noninvasive cells indent at most to 0.7 μm. Significantly indenting cells signpost increased cancer invasiveness and higher metastatic risk in vitro and in vivo, as verified experimentally in different cancer types, yet the underlying cell-applied, force magnitudes and configurations required to produce the cell-scale gel indentations have yet to be evaluated. Hence, we have developed finite element models of forces applied onto soft, impenetrable gels using experimental cell/gel morphologies, gel mechanics, and force magnitudes. We show that in-plane traction forces can only induce small-scale indentations in soft gels (< 0.7 μm), matching experiments with various single, normal cells. Addition of a normal force (on the scale of experimental traction forces) produced cell-scale indentations that matched observations in invasive cancer cells. We note that normal stresses (force and area) determine the indentation depth, while contact area size and morphology have a minor effect, explaining the origin of experimentally observed cell morphologies. We have thus revealed controlling features facilitating invasive indentations by single cancer cells, which will allow application of our model to complex problems, such as multicellular systems.

A Review of Single-Cell Adhesion Force Kinetics and Applications

Cells exert, sense, and respond to the different physical forces through diverse mechanisms and translating them into biochemical signals. The adhesion of cells is crucial in various developmental functions, such as to maintain tissue morphogenesis and homeostasis and activate critical signaling pathways regulating survival, migration, gene expression, and differentiation. More importantly, any mutations of adhesion receptors can lead to developmental disorders and diseases. Thus, it is essential to understand the regulation of cell adhesion during development and its contribution to various conditions with the help of quantitative methods. The techniques involved in offering different functionalities such as surface imaging to detect forces present at the cell-matrix and deliver quantitative parameters will help characterize the changes for various diseases. Here, we have briefly reviewed single-cell mechanical properties for mechanotransduction studies using standard and recently developed techniques. This is used to functionalize from the measurement of cellular deformability to the quantification of the interaction forces generated by a cell and exerted on its surroundings at single-cell with attachment and detachment events. The adhesive force measurement for single-cell microorganisms and single-molecules is emphasized as well. This focused review should be useful in laying out experiments which would bring the method to a broader range of research in the future.

A new agarose-based microsystem to investigate cell response to prolonged confinement

Emerging evidence suggests the importance of mechanical stimuli in normal and pathological situations for the control of many critical cellular functions. While the effect of matrix stiffness has been and is still extensively studied, few studies have focused on the role of mechanical stresses. The main limitation of such analyses is the lack of standard in vitro assays enabling extended mechanical stimulation compatible with dynamic biological and biophysical cell characterization. We have developed an agarose-based microsystem, the soft cell confiner, which enables the precise control of confinement for single or mixed cell populations. The rigidity of the confiner matches physiological conditions and its porosity enables passive medium renewal. It is compatible with time-lapse microscopy, in situ immunostaining, and standard molecular analyses, and can be used with both adherent and non-adherent cell lines. Cell proliferation of various cell lines (hematopoietic cells, MCF10A epithelial breast cells and HS27A stromal cells) was followed for several days up to confluence using video-microscopy and further documented by Western blot and immunostaining. Interestingly, even though the nuclear projected area was much larger upon confinement, with many highly deformed nuclei (non-circular shape), cell viability, assessed by live and dead cell staining, was unaffected for up to 8 days in the confiner. However, there was a decrease in cell proliferation upon confinement for all cell lines tested. The soft cell confiner is thus a valuable tool to decipher the effects of long-term confinement and deformation on the biology of cell populations. This tool will be instrumental in deciphering the impact of nuclear and cytoskeletal mechanosensitivity in normal and pathological conditions involving highly confined situations, such as those reported upon aging with fibrosis or during cancer.

Inferring domain of interactions among particles from ensemble of trajectories

An information-theoretic scheme is proposed to estimate the underlying domain of interactions and the timescale of the interactions for many-particle systems. The crux is the application of transfer entropy which measures the amount of information transferred from one variable to another, and the introduction of a "cutoff distance variable" which specifies the distance within which pairs of particles are taken into account in the estimation of transfer entropy. The Vicsek model often studied as a metaphor of collectively moving animals is employed with introducing asymmetric interactions and an interaction timescale. Based on ensemble data of trajectories of the model system, it is shown that using the interaction domain significantly improves the performance of classification of leaders and followers compared to the approach without utilizing knowledge of the domain. Given an interaction timescale estimated from an ensemble of trajectories, the first derivative of transfer entropy averaged over the ensemble with respect to the cutoff distance is presented to serve as an indicator to infer the interaction domain. It is shown that transfer entropy is superior for inferring the interaction radius compared to cross correlation, hence resulting in a higher performance for inferring the leader-follower relationship. The effects of noise size exerted from environment and the ratio of the numbers of leader and follower on the classification performance are also discussed.

Three-Dimensional Traction Microscopy with a Fiber-Based Constitutive Model

Tractions exerted by cells on their surroundings play an important role in many biological processes including stem cell differentiation, tumorigenesis, cell migration, cancer metastasis, and angiogenesis. The ability to quantify these tractions is important in understanding and manipulating these processes. Three-dimensional traction force microscopy (3DTFM) provides reliable means of evaluating cellular tractions by first measuring the displacement of fluorescent beads in response to these tractions in the surrounding matrix, and then using this measurement to compute the tractions. However, most applications of 3DTFM assume that the surrounding extra-cellular matrix (ECM) is non-fibrous, despite the fact that in many natural and synthetic environments the ECM contains a significant proportion of fibrous components. Motivated by this, we develop a computational approach for determining tractions, while accounting for the fibrous nature of the ECM. In particular, we make use of a fiber-based constitutive model in which the stress contains contributions from a distribution of nonlinear elastic fibers and a hyperelastic matrix. We solve an inverse problem with the nodal values of the traction vector as unknowns, and minimize the difference between a predicted displacement field, obtained by solving the equations of equilibrium in conjunction with the fiber-based constitutive model, and the measured displacement field at the bead locations. We employ a gradient-based minimization method to solve this problem and determine the gradient efficiently by solving for the appropriate adjoint field. We apply this algorithm to problems with experimentally observed cell geometries and synthetic, albeit realistic, traction fields to gauge its sensitivity to noise, and quantify the impact of using an incorrect constitutive model: the so-called model error. We conclude that the approach is robust to noise, yielding about 10% error in tractions for 5% displacement noise. We also conclude that the impact of model error is significant, where using a nonlinear exponential hyperelastic model instead of the fiber-based model, can lead to more than 100% error in the traction field. These results underline the importance of using appropriate constitutive models in 3DTFM, especially in fibrous ECM constructs.

Impact of PDMS surface treatment in cell-mechanics applications

As a widely used elastomer in cell mechanics studies, PDMS is exposed to a variety of surface treatments during cell culture preparation. Considering its viscoelastic nature in particular, effects of the aforementioned treatments on PDMS mechanical behaviour, especially at the relevant length scale of 100 μm, received limited attention. This is despite the fact that significant errors were reported in the quantification of cellular traction forces as a result of minute changes in PDMS mechanical properties. Hence, the effects of plasma oxidation, sterilization and incubation on PDMS modulus of elasticity, relaxation modulus and Poisson's ratio are studied here through tension and stress relaxation tests, with the results of the latter interpreted via the linear viscoelastic formulation. It is observed that although significant deviations from the properties of untreated PDMS are measured through this cycle of surface treatment, properties of untreated PDMS are almost recovered following incubation in cell medium. For example, the modulus of elasticity of treated PDMS was found to be 6% smaller than that of the untreated PDMS. The corresponding deviation was <3% and <1% for the relaxation modulus and time-averaged Poisson's ratio, respectively. The rate of change of the Poisson's ratio with time was also found to be reduced at the end of incubation process in cell medium. As a result, viscoelastic properties of untreated PDMS can safely be used within the error margins provided by this work.

Differential Homeostasis of Sessile and Pendant Epithelium Reconstituted in a 3D-Printed "GeminiChip"

Local mechanical cues can affect crucial fate decisions of living cells. Transepithelial stress has been discussed in the context of epithelial monolayers, but the lack of appropriate experimental systems leads current studies to approximate it simply as an in-plane stress. To evaluate possible contribution of force vectors acting in other directions, double epithelium in a 3D-printed "GeminiChip" containing a sessile and a pendant channel is reconstituted. Intriguingly, the sessile epithelia is prone to apoptotic cell extrusion upon crowding, whereas the pendant counterpart favors live cell delamination. Transcriptome analyses show upregulation of RhoA, BMP2, and hypoxia-signaling genes in the pendant epithelium, consistent with the onset of an epithelial-mesenchymal transition program. HepG2 microtumor spheroids also display differential spreading patterns in the sessile and pendant configuration. Using this multilayered GeminiChip, these results uncover a progressive yet critical role of perpendicular force vectors in collective cell behaviors and point at fundamental importance of these forces in the biology of cancer.

Elastic interactions between anisotropically contracting circular cells

We study interactions between biological cells that apply anisotropic active mechanical forces on an elastic substrate. We model the cells as thin disks that along their perimeters apply radial, but angle-dependent forces on the substrate. We obtain analytical expressions for the elastic energy stored in the substrate as a function of the distance between the cells, the Fourier modes of applied forces, and their phase angles. We show how the relative phases of the forces applied by the cells can switch the interaction between attractive and repulsive, and relate our results to those for linear force dipoles. For long enough distances, the interaction energy decays in magnitude as a power law of the cell-cell distance with an integer exponent that generally increases with the Fourier modes of the applied forces.

Adhesion Strength and Rolling Properties of Descemet Membrane Endothelial Keratoplasty Grafts in a Rabbit Eye Model

Purpose: To investigate the optimal time for Descemet membrane endothelial keratoplasty (DMEK) graft peeling, and to analyze the rolling properties of endothelial denuded grafts in a rabbit eye model. Materials and Methods: The vertical peeling force required to peel 1 mm wide Descemet membrane (DM) strips, was measured as the change in weight of the system during force application in a rabbit model. Twenty-one rabbit corneoscleral rims were stored in phosphate-buffered saline (PBS) at 4°C, and force analysis was performed at days 1, 5, or 21 after harvesting. After half of the strips of day 5 corneas were peeled and analyzed, the rims were moved to Optisol GS at 4°C, and the remaining strips were peeled off for force analysis at day 10. Separate DM grafts (n = 7) were analyzed by intraoperative optical coherence tomography (OCT) to determine the tissue rolling diameter before and after removal of endothelial cells by a swab. Unpaired t-test was used for statistical analysis. Results: There was a decrease in DM peeling force (p = .008) between days 1 and 5 (556.04 ± 111.76 and 324.30 ± 96.4 mg, respectively), and no difference between days 5 and 21 (p = .53). Peeling force for day 5 corneas placed in Optisol was higher at day 10 (324.30 ± 96.4 to 669.92 ± 166.24 mg, p = .005). The average rolling diameter of DM grafts was similar before and after the removal of endothelial cells (257.9 ± 131.1 and 249.8 ± 126.6 μm, respectively). Conclusions: DMEK Graft procurement could be potentially facilitated by lower DM-stromal adhesion strength at day five after obtaining corneoscleral rims, in a rabbit eye model. Time in the storage medium may influence adhesion strength. Endothelial cells do not appear to play a significant role in the rolling diameter of DM grafts.

Ultraflexible Nanowire Array for Label- and Distortion-Free Cellular Force Tracking

Living cells interact with their immediate environment by exerting mechanical forces, which regulate important cell functions. Elucidation of such force patterns yields deep insights into the physics of life. Here we present a top-down nanostructured, ultraflexible nanowire array biosensor capable of probing cell-induced forces. Its universal building block, an inverted conical semiconductor nanowire, greatly enhances both the functionality and the sensitivity of the device. In contrast to existing cellular force sensing architectures, microscopy is performed on the nanowire heads while cells deflecting the nanowires are confined within the array. This separation between the optical path and the cells under investigation excludes optical distortions caused by cell-induced refraction, which can give rise to feigned displacements on the 100 nm scale. The undistorted nanowire displacements are converted into cellular forces via the nanowire spring constant. The resulting distortion-free cellular force transducer realizes a high-resolution and label-free biosenor based on optical microscopy. Its performance is demonstrated in a proof-of-principle experiment with living Dictyostelium discoideum cells migrating through the nanowire array. Cell-induced forces are probed with a resolution of 50 piconewton, while the most flexible nanowires promise to enter the 100 femtonewton realm.

Continuum Models of Collective Cell Migration

Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key biological question is how cells integrate molecular activities for force generation on multicellular scales. In this review we discuss recent advances in modeling collective cell migration using quantitative tools and approaches rooted in soft matter physics. We focus on theoretical models of cell aggregates as continuous active media, where the feedback between mechanical forces and regulatory biochemistry gives rise to rich collective dynamical behavior. This class of models provides a powerful predictive framework for the physiological dynamics that underlies many developmental processes, where cells need to collectively migrate like a viscous fluid to reach a target region, and then stiffen to support mechanical stresses and maintain tissue cohesion.

Dynamics of force generation by spreading platelets

In order to gain more insight into the role of human platelets for blood clot formation, here we investigate the dynamics of force generation by platelet spreading onto elastic substrates of variable stiffness. Despite their small size, platelets generate high and rapidly varying traction forces on their extracellular environment, which we reconstruct with adapted implementations of Fourier transform traction cytometry. We find that while the final spread area is reached within a few minutes, the build-up of forces typically takes 10-30 minutes. In addition, we identify two distinct behaviors of individual cells, namely oscillating and non-oscillating platelets. An eigenvalue analysis of the platelet dipole tensor reveals a small anisotropy of the exerted force, which is compatible with a random distribution of a few force transmitting centers, in agreement with the observed shapes and traction patterns. We find a correlation between the maximum force level a platelet reaches and its spread area, which we explain by a thin film model for the actively contracting cell. The model reveals a large internal stress of hundreds of kPa. Experimentally we do not find any statistically relevant relation between the force level reached and the substrate stiffness within the stiffness range from 19 to 83 kPa, which might be related to the high platelet activation level used in our study. In addition, our model suggests that due to the uniquely small thickness of platelets, their mechanosensitivity might be limited to a lower stiffness range.

Eukaryotic Cell Dynamics from Crawlers to Swimmers

Movement requires force transmission to the environment, and motile cells are robustly, though not elegantly, designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission used. As with humans, the available modes range from momentary attachment to a substrate when crawling, to shape deformations when swimming, and at the cellular level this involves sensing the mechanical properties of the environment and altering the mode appropriately. While many types of cells can adapt their mode of movement to their microenvironment (ME), our understanding of how they detect, transduce and process information from the ME to determine the optimal mode is still rudimentary. The shape and integrity of a cell is determined by its cytoskeleton (CSK), and thus the shape changes that may be required to move involve controlled remodeling of the CSK. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of motility in even simple cells such as bacteria is not at hand. In this review we discuss recent advances in our understanding of cell motility and some of the problems remaining to be solved.

Mechanisms and impact of altered tumour mechanics

The physical characteristics of tumours are intricately linked to the tumour phenotype and difficulties during treatment. Many factors contribute to the increased stiffness of tumours; from increased matrix deposition, matrix remodelling by forces from cancer cells and stromal fibroblasts, matrix crosslinking, increased cellularity, and the build-up of both solid and interstitial pressure. Increased stiffness then feeds back to increase tumour invasiveness and reduce therapy efficacy. Increased understanding of this interplay is offering new therapeutic avenues.

Nanoparticle-Cell Interaction: A Cell Mechanics Perspective

Progress in the field of nanoparticles has enabled the rapid development of multiple products and technologies; however, some nanoparticles can pose both a threat to the environment and human health. To enable their safe implementation, a comprehensive knowledge of nanoparticles and their biological interactions is needed. In vitro and in vivo toxicity tests have been considered the gold standard to evaluate nanoparticle safety, but it is becoming necessary to understand the impact of nanosystems on cell mechanics. Here, the interaction between particles and cells, from the point of view of cell mechanics (i.e., bionanomechanics), is highlighted and put in perspective. Specifically, the ability of intracellular and extracellular nanoparticles to impair cell adhesion, cytoskeletal organization, stiffness, and migration are discussed. Furthermore, the development of cutting-edge, nanotechnology-driven tools based on the use of particles allowing the determination of cell mechanics is emphasized. These include traction force microscopy, colloidal probe atomic force microscopy, optical tweezers, magnetic manipulation, and particle tracking microrheology.

Holographic Traction Force Microscopy

Traction Force Microscopy (TFM) computes the forces exerted at the surface of an elastic material by measuring induced deformations in volume. It is used to determine the pattern of the adhesion forces exerted by cells or by cellular assemblies grown onto a soft deformable substrate. Typically, colloidal particles are dispersed in the substrate and their displacement is monitored by fluorescent microscopy. As with any other fluorescent techniques, the accuracy in measuring a particule's position is ultimately limited by the number of evaluated fluorescent photons. Here, we present a TFM technique based on the detection of probe particle displacements by holographic tracking microscopy. We show that nanometer scale resolutions of the particle displacements can be obtained and determine the maximum volume fraction of markers in the substrate. We demonstrate the feasibility of the technique experimentally and measure the three-dimensional force fields exerted by colorectal cancer cells cultivated onto a polyacrylamide gel substrate.

Mechanical Forces in Cutaneous Wound Healing: Emerging Therapies to Minimize Scar Formation

Significance: Excessive scarring is major clinical and financial burden in the United States. Improved therapies are necessary to reduce scarring, especially in patients affected by hypertrophic and keloid scars. Recent Advances: Advances in our understanding of mechanical forces in the wound environment enable us to target mechanical forces to minimize scar formation. Fetal wounds experience much lower resting stress when compared with adult wounds, and they heal without scars. Therapies that modulate mechanical forces in the wound environment are able to reduce scar size. Critical Issues: Increased mechanical stresses in the wound environment induce hypertrophic scarring via activation of mechanotransduction pathways. Mechanical stimulation modulates integrin, Wingless-type, protein kinase B, and focal adhesion kinase, resulting in cell proliferation and, ultimately, fibrosis. Therefore, the development of therapies that reduce mechanical forces in the wound environment would decrease the risk of developing excessive scars. Future Directions: The development of novel mechanotherapies is necessary to minimize scar formation and advance adult wound healing toward the scarless ideal. Mechanotransduction pathways are potential targets to reduce excessive scar formation, and thus, continued studies on therapies that utilize mechanical offloading and mechanomodulation are needed.

Opto-acoustic microscopy reveals adhesion mechanics of single cells

Laser-generated GHz-ultrasonic-based technologies have shown the ability to image single cell adhesion and stiffness simultaneously. Using this new modality, we here demonstrate quantitative indicators to investigate contact mechanics and adhesion processes of the cell. We cultured human cells on a rigid substrate, and we used an inverted pulsed opto-acoustic microscope to generate acoustic pulses containing frequencies up to 100 GHz in the substrate. We map the reflection of the acoustic pulses at the cell-substrate interface to obtain images of the acoustic impedance of the cell, Z_c, as well as of the stiffness of the interface, K, with 1 μm lateral resolution. Our results show that the standard deviation ΔZ_c reveals differences between different cell types arising from the multiplicity of local conformations within the nucleus. From the distribution of K-values within the nuclear region, we extract a mean interfacial stiffness, K_m, that quantifies the average contact force in areas of the cell displaying weak bonding. By analogy with classical contact mechanics, we also define the ratio of the real to nominal contact areas, S_r/S_t. We show that K_m can be interpreted as a quantitative indicator of passive contact at metal-cell interfaces, while S_r/S_t is sensitive to active adhesive processes in the nuclear region. The ability to separate the contributions of passive and active adhesion processes should allow gaining insight into cell-substrate interactions, with important applications in tissue engineering.

Progress in Integrative Biomaterial Systems to Approach Three-Dimensional Cell Mechanotransduction

Mechanotransduction between cells and the extracellular matrix regulates major cellular functions in physiological and pathological situations. The effect of mechanical cues on biochemical signaling triggered by cell-matrix and cell-cell interactions on model biomimetic surfaces has been extensively investigated by a combination of fabrication, biophysical, and biological methods. To simulate the in vivo physiological microenvironment in vitro, three dimensional (3D) microstructures with tailored bio-functionality have been fabricated on substrates of various materials. However, less attention has been paid to the design of 3D biomaterial systems with geometric variances, such as the possession of precise micro-features and/or bio-sensing elements for probing the mechanical responses of cells to the external microenvironment. Such precisely engineered 3D model experimental platforms pave the way for studying the mechanotransduction of multicellular aggregates under controlled geometric and mechanical parameters. Concurrently with the progress in 3D biomaterial fabrication, cell traction force microscopy (CTFM) developed in the field of cell biophysics has emerged as a highly sensitive technique for probing the mechanical stresses exerted by cells onto the opposing deformable surface. In the current work, we first review the recent advances in the fabrication of 3D micropatterned biomaterials which enable the seamless integration with experimental cell mechanics in a controlled 3D microenvironment. Then, we discuss the role of collective cell-cell interactions in the mechanotransduction of engineered tissue equivalents determined by such integrative biomaterial systems under simulated physiological conditions.

BioFlow: a non-invasive, image-based method to measure speed, pressure and forces inside living cells

Cell motility is governed by a complex molecular machinery that converts physico-chemical cues into whole-cell movement. Understanding the underlying biophysical mechanisms requires the ability to measure physical quantities inside the cell in a simple, reproducible and preferably non-invasive manner. To this end, we developed BioFlow, a computational mechano-imaging method and associated software able to extract intracellular measurements including pressure, forces and velocity everywhere inside freely moving cells in two and three dimensions with high spatial resolution in a non-invasive manner. This is achieved by extracting the motion of intracellular material observed using fluorescence microscopy, while simultaneously inferring the parameters of a given theoretical model of the cell interior. We illustrate the power of BioFlow in the context of amoeboid cell migration, by modelling the intracellular actin bulk flow of the parasite Entamoeba histolytica using fluid dynamics, and report unique experimental measures that complement and extend both theoretical estimations and invasive experimental measures. Thanks to its flexibility, BioFlow is easily adaptable to other theoretical models of the cell, and alleviates the need for complex or invasive experimental conditions, thus constituting a powerful tool-kit for mechano-biology studies. BioFlow is open-source and freely available via the Icy software.

Full L1-regularized Traction Force Microscopy over whole cells

Background

Traction Force Microscopy (TFM) is a widespread technique to estimate the tractions that cells exert on the surrounding substrate. To recover the tractions, it is necessary to solve an inverse problem, which is ill-posed and needs regularization to make the solution stable. The typical regularization scheme is given by the minimization of a cost functional, which is divided in two terms: the error present in the data or data fidelity term; and the regularization or penalty term. The classical approach is to use zero-order Tikhonov or L₂-regularization, which uses the L₂-norm for both terms in the cost function. Recently, some studies have demonstrated an improved performance using L₁-regularization (L₁-norm in the penalty term) related to an increase in the spatial resolution and sensitivity of the recovered traction field. In this manuscript, we present a comparison between the previous two regularization schemes (relying in the L₂-norm for the data fidelity term) and the full L₁-regularization (using the L₁-norm for both terms in the cost function) for synthetic and real data.

Results

Our results reveal that L₁-regularizations give an improved spatial resolution (more important for full L₁-regularization) and a reduction in the background noise with respect to the classical zero-order Tikhonov regularization. In addition, we present an approximation, which makes feasible the recovery of cellular tractions over whole cells on typical full-size microscope images when working in the spatial domain.

Conclusions

The proposed full L₁-regularization improves the sensitivity to recover small stress footprints. Moreover, the proposed method has been validated to work on full-field microscopy images of real cells, what certainly demonstrates it is a promising tool for biological applications.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1771-0) contains supplementary material, which is available to authorized users.

Long-term imaging of cellular forces with high precision by elastic resonator interference stress microscopy

Cellular forces are crucial for many biological processes but current methods to image them have limitations with respect to data analysis, resolution and throughput. Here, we present a robust approach to measure mechanical cell-substrate interactions in diverse biological systems by interferometrically detecting deformations of an elastic micro-cavity. Elastic resonator interference stress microscopy (ERISM) yields stress maps with exceptional precision and large dynamic range (2 nm displacement resolution over a >1 μm range, translating into 1 pN force sensitivity). This enables investigation of minute vertical stresses (<1 Pa) involved in podosome protrusion, protein-specific cell-substrate interaction and amoeboid migration through spatial confinement in real time. ERISM requires no zero-force reference and avoids phototoxic effects, which facilitates force monitoring over multiple days and at high frame rates and eliminates the need to detach cells after measurements. This allows observation of slow processes such as differentiation and further investigation of cells, for example, by immunostaining.

Self-organized mechano-chemical dynamics in amoeboid locomotion of Physarum fragments

The aim of this work is to quantify the spatio-temporal dynamics of flow-driven amoeboid locomotion in small (~100 µm) fragments of the true slime mold Physarum polycephalum. In this model organism, cellular contraction drives intracellular flows, and these flows transport the chemical signals that regulate contraction in the first place. As a consequence of these non-linear interactions, a diversity of migratory behaviors can be observed in migrating Physarum fragments. To study these dynamics, we measure the spatio-temporal distributions of the velocities of the endoplasm and ectoplasm of each migrating fragment, the traction stresses it generates on the substratum, and the concentration of free intracellular calcium. Using these unprecedented experimental data, we classify migrating Physarum fragments according to their dynamics, finding that they often exhibit spontaneously coordinated waves of flow, contractility and chemical signaling. We show that Physarum fragments exhibiting symmetric spatio-temporal patterns of endoplasmic flow migrate significantly slower than fragments with asymmetric patterns. In addition, our joint measurements of ectoplasm velocity and traction stress at the substratum suggest that forward motion of the ectoplasm is enabled by a succession of stick-slip transitions, which we conjecture are also organized in the form of waves. Combining our experiments with a simplified convection-diffusion model, we show that the convective transport of calcium ions may be key for establishing and maintaining the spatiotemporal patterns of calcium concentration that regulate the generation of contractile forces.

Microfabricated tissues for investigating traction forces involved in cell migration and tissue morphogenesis

Cell-generated forces drive an array of biological processes ranging from wound healing to tumor metastasis. Whereas experimental techniques such as traction force microscopy are capable of quantifying traction forces in multidimensional systems, the physical mechanisms by which these forces induce changes in tissue form remain to be elucidated. Understanding these mechanisms will ultimately require techniques that are capable of quantifying traction forces with high precision and accuracy in vivo or in systems that recapitulate in vivo conditions, such as microfabricated tissues and engineered substrata. To that end, here we review the fundamentals of traction forces, their quantification, and the use of microfabricated tissues designed to study these forces during cell migration and tissue morphogenesis. We emphasize the differences between traction forces in two- and three-dimensional systems, and highlight recently developed techniques for quantifying traction forces.

High-resolution traction force microscopy on small focal adhesions - improved accuracy through optimal marker distribution and optical flow tracking

The accurate determination of cellular forces using Traction Force Microscopy at increasingly small focal attachments to the extracellular environment presents an important yet substantial technical challenge. In these measurements, uncertainty regarding accuracy is prominent since experimental calibration frameworks at this size scale are fraught with errors – denying a gold standard against which accuracy of TFM methods can be judged. Therefore, we have developed a simulation platform for generating synthetic traction images that can be used as a benchmark to quantify the influence of critical experimental parameters and the associated errors. Using this approach, we show that TFM accuracy can be improved >35% compared to the standard approach by placing fluorescent beads as densely and closely as possible to the site of applied traction. Moreover, we use the platform to test tracking algorithms based on optical flow that measure deformation directly at the beads and show that these can dramatically outperform classical particle image velocimetry algorithms in terms of noise sensitivity and error. We then report how optimized experimental and numerical strategy can improve traction map accuracy, and further provide the best available benchmark to date for defining practical limits to TFM accuracy as a function of focal adhesion size.

Surface Curvature Differentially Regulates Stem Cell Migration and Differentiation via Altered Attachment Morphology and Nuclear Deformation

Signals from the microenvironment around a cell are known to influence cell behavior. Material properties, such as biochemical composition and substrate stiffness, are today accepted as significant regulators of stem cell fate. The knowledge of how cell behavior is influenced by 3D geometric cues is, however, strongly limited despite its potential relevance for the understanding of tissue regenerative processes and the design of biomaterials. Here, the role of surface curvature on the migratory and differentiation behavior of human mesenchymal stem cells (hMSCs) has been investigated on 3D surfaces with well-defined geometric features produced by stereolithography. Time lapse microscopy reveals a significant increase of cell migration speed on concave spherical compared to convex spherical structures and flat surfaces resulting from an upward-lift of the cell body due to cytoskeletal forces. On convex surfaces, cytoskeletal forces lead to substantial nuclear deformation, increase lamin-A levels and promote osteogenic differentiation. The findings of this study demonstrate a so far missing link between 3D surface curvature and hMSC behavior. This will not only help to better understand the role of extracellular matrix architecture in health and disease but also give new insights in how 3D geometries can be used as a cell-instructive material parameter in the field of biomaterial-guided tissue regeneration.

Two-Layer Elastographic 3-D Traction Force Microscopy

Cellular traction force microscopy (TFM) requires knowledge of the mechanical properties of the substratum where the cells adhere to calculate cell-generated forces from measurements of substratum deformation. Polymer-based hydrogels are broadly used for TFM due to their linearly elastic behavior in the range of measured deformations. However, the calculated stresses, particularly their spatial patterns, can be highly sensitive to the substratum's Poisson's ratio. We present two-layer elastographic TFM (2LETFM), a method that allows for simultaneously measuring the Poisson's ratio of the substratum while also determining the cell-generated forces. The new method exploits the analytical solution of the elastostatic equation and deformation measurements from two layers of the substratum. We perform an in silico analysis of 2LETFM concluding that this technique is robust with respect to TFM experimental parameters, and remains accurate even for noisy measurement data. We also provide experimental proof of principle of 2LETFM by simultaneously measuring the stresses exerted by migrating Physarum amoeboae on the surface of polyacrylamide substrata, and the Poisson's ratio of the substrata. The 2LETFM method could be generalized to concurrently determine the mechanical properties and cell-generated forces in more physiologically relevant extracellular environments, opening new possibilities to study cell-matrix interactions.

Measuring cellular traction forces on non-planar substrates

Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory. Such procedures have already been established mainly for planar substrates, in which case one can use the Green's function formalism. Here we introduce a workflow to measure traction forces of cardiac myofibroblasts on non-planar elastic substrates. Soft elastic substrates with a wave-like topology were micromoulded from polydimethylsiloxane and fluorescent marker beads were distributed homogeneously in the substrate. Using feature vector-based tracking of these marker beads, we first constructed a hexahedral mesh for the substrate. We then solved the direct elastic boundary volume problem on this mesh using the finite-element method. Using data simulations, we show that the traction forces can be reconstructed from the substrate deformations by solving the corresponding inverse problem with an L1-norm for the residue and an L2-norm for a zeroth-order Tikhonov regularization. Applying this procedure to the experimental data, we find that cardiac myofibroblast cells tend to align both their shapes and their forces with the long axis of the deformable wavy substrate.

Three-Dimensional Reflectance Traction Microscopy

Cells in three-dimensional (3D) environments exhibit very different biochemical and biophysical phenotypes compared to the behavior of cells in two-dimensional (2D) environments. As an important biomechanical measurement, 2D traction force microscopy can not be directly extended into 3D cases. In order to quantitatively characterize the contraction field, we have developed 3D reflectance traction microscopy which combines confocal reflection imaging and partial volume correlation postprocessing. We have measured the deformation field of collagen gel under controlled mechanical stress. We have also characterized the deformation field generated by invasive breast cancer cells of different morphologies in 3D collagen matrix. In contrast to employ dispersed tracing particles or fluorescently-tagged matrix proteins, our methods provide a label-free, computationally effective strategy to study the cell mechanics in native 3D extracellular matrix.

Single cell rigidity sensing: A complex relationship between focal adhesion dynamics and large-scale actin cytoskeleton remodeling

Many physiological and pathological processes involve tissue cells sensing the rigidity of their environment. In general, tissue cells have been shown to react to the stiffness of their environment by regulating their level of contractility, and in turn applying traction forces on their environment to probe it. This mechanosensitive process can direct early cell adhesion, cell migration and even cell differentiation. These processes require the integration of signals over time and multiple length scales. Multiple strategies have been developed to understand force- and rigidity-sensing mechanisms and much effort has been concentrated on the study of cell adhesion complexes, such as focal adhesions, and cell cytoskeletons. Here, we review the major biophysical methods used for measuring cell-traction forces as well as the mechanosensitive processes that drive cellular responses to matrix rigidity on 2-dimensional substrates.

Mechanics regulates ATP-stimulated collective calcium response in fibroblast cells

Cells constantly sense their chemical and mechanical environments. We study the effect of mechanics on the ATP-induced collective calcium response of fibroblast cells in experiments that mimic various tissue environments. We find that closely packed two-dimensional cell cultures on a soft polyacrylamide gel (Young's modulus E = 690 Pa) contain more cells exhibiting calcium oscillations than cultures on a rigid substrate (E = 36 000 Pa). Calcium responses of cells on soft substrates show a slower decay of calcium level relative to those on rigid substrates. Actin enhancement and disruption experiments for the cell cultures allow us to conclude that actin filaments determine the collective Ca(2+) oscillatory behaviour in the culture. Inhibition of gap junctions results in a decrease of the oscillation period and reduced correlation of calcium responses, which suggests additional complexity of signalling upon cell-cell contact. Moreover, the frequency of calcium oscillations is independent of the rigidity of the substrate but depends on ATP concentration. We compare our results with those from similar experiments on individual cells. Overall, our observations show that collective chemical signalling in cell cultures via calcium depends critically on the mechanical environment.

For whom the cells pull: Hydrogel and micropost devices for measuring traction forces

While performing several functions, adherent cells deform their surrounding substrate via stable adhesions that connect the intracellular cytoskeleton to the extracellular matrix. The traction forces that deform the substrate are studied in mechanotrasduction because they are affected by the mechanics of the extracellular milieu. We review the development and application of two methods widely used to measure traction forces generated by cells on 2D substrates: (i) traction force microscopy with polyacrylamide hydrogels and (ii) calculation of traction forces with arrays of deformable microposts. Measuring forces with these methods relies on measuring substrate displacements and converting them into forces. We describe approaches to determine force from displacements and elaborate on the necessary experimental conditions for this type of analysis. We emphasize device fabrication, mechanical calibration of substrates and covalent attachment of extracellular matrix proteins to substrates as key features in the design of experiments to measure cell traction forces with polyacrylamide hydrogels or microposts. We also report the challenges and achievements in integrating these methods with platforms for the mechanical stimulation of adherent cells. The approaches described here will enable new studies to understand cell mechanical outputs as a function of mechanical inputs and advance the understanding of mechanotransduction mechanisms.

Free Form Deformation-Based Image Registration Improves Accuracy of Traction Force Microscopy

Traction Force Microscopy (TFM) is a widespread method used to recover cellular tractions from the deformation that they cause in their surrounding substrate. Particle Image Velocimetry (PIV) is commonly used to quantify the substrate’s deformations, due to its simplicity and efficiency. However, PIV relies on a block-matching scheme that easily underestimates the deformations. This is especially relevant in the case of large, locally non-uniform deformations as those usually found in the vicinity of a cell’s adhesions to the substrate. To overcome these limitations, we formulate the calculation of the deformation of the substrate in TFM as a non-rigid image registration process that warps the image of the unstressed material to match the image of the stressed one. In particular, we propose to use a B-spline -based Free Form Deformation (FFD) algorithm that uses a connected deformable mesh to model a wide range of flexible deformations caused by cellular tractions. Our FFD approach is validated in 3D fields using synthetic (simulated) data as well as with experimental data obtained using isolated endothelial cells lying on a deformable, polyacrylamide substrate. Our results show that FFD outperforms PIV providing a deformation field that allows a better recovery of the magnitude and orientation of tractions. Together, these results demonstrate the added value of the FFD algorithm for improving the accuracy of traction recovery.