Three-dimensional Traction Force Microscopy Research Articles

Advanced in silico validation framework for three-dimensional traction force microscopy and application to an in vitro model of sprouting angiogenesis

In the last decade, cellular forces in three-dimensional hydrogels that mimic the extracellular matrix have been calculated by means of Traction Force Microscopy (TFM). However, characterizing the accuracy limits of a traction recovery method is critical to avoid obscuring physiological information due to traction recovery errors. So far, 3D TFM algorithms have only been validated using simplified cell geometries, bypassing image processing steps or arbitrarily simulating focal adhesions. Moreover, it is still uncertain which of the two common traction recovery methods, i.e., forward and inverse, is more robust against the inherent challenges of 3D TFM. In this work, we established an advanced in silico validation framework that is applicable to any 3D TFM experimental setup and that can be used to correctly couple the experimental and computational aspects of 3D TFM. Advancements relate to the simultaneous incorporation of complex cell geometries, simulation of microscopy images of varying bead densities and different focal adhesion sizes and distributions. By measuring the traction recovery error with respect to ground truth solutions, we found that while highest traction recovery errors occur for cases with sparse and small focal adhesions, our implementation of the inverse method improves two-fold the accuracy with respect to the forward method (average error of 23% vs. 50%). This advantage was further supported by recovering cellular tractions around angiogenic sprouts in an in vitro model of angiogenesis. The inverse method recovered higher traction peaks and a clearer pulling pattern at the sprout protrusion tips than the forward method. Statement of significanceBiomaterial performance is often studied by quantifying cell-matrix mechanical interactions by means of Traction Force Microscopy (TFM). However, 3D TFM algorithms are often validated in simplified scenarios, which do not allow to fully assess errors that could obscure physiological information. Here, we established an advanced in silico validation framework that mimics real TFM experimental conditions and that characterizes the expected errors of a 3D TFM workflow. We apply this framework to demonstrate the enhanced accuracy of a novel inverse traction recovery method that is illustrated in the context of an in vitro model of sprouting angiogenesis. Together, our study shows the importance of a proper traction recovery method to minimise errors and the need for an advanced framework to assess those errors.

Epifluorescence-based three-dimensional traction force microscopy

We introduce a novel method to compute three-dimensional (3D) displacements and both in-plane and out-of-plane tractions on nominally planar transparent materials using standard epifluorescence microscopy. Despite the importance of out-of-plane components to fully understanding cell behavior, epifluorescence images are generally not used for 3D traction force microscopy (TFM) experiments due to limitations in spatial resolution and measuring out-of-plane motion. To extend an epifluorescence-based technique to 3D, we employ a topology-based single particle tracking algorithm to reconstruct high spatial-frequency 3D motion fields from densely seeded single-particle layer images. Using an open-source finite element (FE) based solver, we then compute the 3D full-field stress and strain and surface traction fields. We demonstrate this technique by measuring tractions generated by both single human neutrophils and multicellular monolayers of Madin–Darby canine kidney cells, highlighting its acuity in reconstructing both individual and collective cellular tractions. In summary, this represents a new, easily accessible method for calculating fully three-dimensional displacement and 3D surface tractions at high spatial frequency from epifluorescence images. We released and support the complete technique as a free and open-source code package.

Collective forces of tumor spheroids in three-dimensional biopolymer networks.

We describe a method for quantifying the contractile forces that tumor spheroids collectively exert on highly nonlinear three-dimensional collagen networks. While three-dimensional traction force microscopy for single cells in a nonlinear matrix is computationally complex due to the variable cell shape, here we exploit the spherical symmetry of tumor spheroids to derive a scale-invariant relationship between spheroid contractility and the surrounding matrix deformations. This relationship allows us to directly translate the magnitude of matrix deformations to the total contractility of arbitrarily sized spheroids. We show that our method is accurate up to strains of 50% and remains valid even for irregularly shaped tissue samples when considering only the deformations in the far field. Finally, we demonstrate that collective forces of tumor spheroids reflect the contractility of individual cells for up to 1 hr after seeding, while collective forces on longer timescales are guided by mechanical feedback from the extracellular matrix.

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.

Roles of Cell‐Cell Junction and Substrate Stiffness in Determining 3D Forces of Endothelial Cells

Mechanical forces play an important role in regulating structure and functions of cells, including motility, proliferation, and survival. The integrity of cell‐cell junction is crucial in the physiological behavior of endothelial cells. Thus, it is essential to understand the modulation of endothelial cells by their micro‐environment such as substrate stiffness, confluency, and cell‐cell junction.We have developed three‐dimensional traction force microscopy (3D‐TFM) and intracellular force microscopy (3D‐IFM) to measure cell‐ECM, cell‐cell, and intracellular stresses of live cells in three dimensions at the subcellular level. These novel methods have been applied in order to investigate the mechanical responses of endothelial cells to changes in substrate stiffness, cell confluency, and cell‐cell junction. The results indicate that endothelial cells exhibit differences in the magnitude and spatial distribution of mechanical behaviors (traction and intracellular stress) and morphological features (area and aspect ratio) in response to substrate stiffness (1.5 kPa and 10b kPa hydrogel), cell confluency (existence of cell‐cell junction), and junction‐affecting drugs (thrombin and angiopoietin).We have shown that biophysical and biochemical environments are important in the control of endothelial cell structure and function. Studying how the forces are regulated spatially and temporally at the subcellular level in response to changes of cellular microenvironment can lead to further understanding of the physiology of endothelial cells and pathogenesis of vascular diseases.This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Determination of Green's function for three-dimensional traction force reconstruction based on geometry and boundary conditions of cell culture matrices.

This study focused on the fundamental issue regarding extension of linear elasticity-based TFM to deal with physically realistic matrices (where cells are encapsulated), which concerns determination of the Green's function matching their geometry and boundary conditions. To increase fidelity in the estimate of traction forces for extreme conditions such as a sparse sampling of deformation field or targeting small focal adhesions, we numerically solved the singularity problem of the Green's function to avoid exclusion of singular point regions that could contain representative deformation indicators for such extreme conditions. The proposed approach to adapting the Green's function for the specific 3D cell culture situation was examined in a single case experimental study of endothelial cells in sprouting angiogenesis.

Collective migration in tissues.

The Minisymposium on “Cell Migration in Tissues” focused on analysis of dynamic collective cell migration in several model systems and was cochaired by Alissa M. Weaver (Vanderbilt University Medical Center) and Celeste M. Nelson (Princeton University). The program highlighted both the physical forces exerted during migration and the signaling pathways involved in the process. Celeste Nelson (Princeton University) presented results suggesting that cells migrate collectively through fibrous extracellular matrix (ECM) by exerting tensile forces at the leading edge of the cohort. Three-dimensional traction force microscopy was used to quantify the physical forces exerted by normal and malignant mammary epithelial cells undergoing collective migration through collagen gels (Gjorevski et al., 2015 ). The forces and displacements were surprisingly dynamic, with the cohort periodically relaxing as it migrated forward. Jessica Konen (Marcus laboratory, Emory University) described a new technique called spatiotemporal genomic analysis, which was used to select rare populations of leader cells from three-dimensional (3D) lung cancer spheroids and compare their gene expression patterns to that of follower cells. Leader cells were found to express higher levels of genes related to cell adhesion and vascular sprouting. These gene expression changes persisted in purified cultures. Eliah Shamir (Ewald laboratory, Johns Hopkins University) showed that in 3D culture of mammary epithelial organoids, the myoepithelial layer was required to prevent invasion and dissemination of Twist1-expressing luminal epithelial cells. Surprisingly, Twist1-induced invasion required the expression of E-cadherin, and knocking down expression of this cell–cell adhesion protein prevented dissemination downstream of Twist1 (Shamir et al., 2014 ). Joshua Bloomekatz (Yelon laboratory, University of California, San Diego) showed a critical role for platelet-derived growth factor (PDGF) in the movement of cardiomyocytes during cardiac fusion. A forward genetic screen was used to identify a mutation called refuse-to-fuse, which causes inhibition of cardiac fusion and the subsequent formation of a bifurcated ventricle. This mutation was found to disrupt splicing of pdgfra, leading to expression of a truncated form of the PDGF receptor. Expression of PDGF ligands in relatively medial locations suggested a model in which PDGF signaling coordinates the movement of cardiomyocytes toward the midline during cardiac fusion. Bong Hwan Sung (Weaver laboratory, Vanderbilt University) showed that directionally persistent migration of cancer cells is promoted by autocrine secretion of exosomes, late endosome–derived extracellular vesicles (Sung et al., 2015 ). Exosomes were shown to contain ECM proteins as cargo and to be secreted at sites of nascent adhesions. Accordingly, exosome secretion promoted adhesion assembly, migrational polarity, and the stability of lamellipodia. David Matus (Stony Brook University) used an RNA interference screen to identify a transcriptional program that maintains invasive anchor cells in a cell cycle–arrested state during uterine-vulval attachment in Caenorhabditis elegans. Nuclear hormone receptor nhr-67 (TLX) expression leads to up-regulation of cyclin-dependent kinase inhibitor cki-1, causing cell cycle arrest in G1 (Matus et al., 2015 ). Cells that lack nhr-67 are proliferative and noninvasive, failing to express matrix or form invadopodia. The Minisymposium concluded with three lightning talks. Micah Webster (Fan laboratory, Carnegie Institution for Science) showed a role for “ghost fibers,” ECM remnants of damaged muscle fibers, in organizing skeletal muscle progenitor migration, division, and fusion during regeneration in mice (Webster et al., 2016 ). Rebecca Green (Oegema laboratory, University of California, San Diego) developed a four-dimensional high-content imaging approach to screen for developmentally important genes within C. elegans embryos. Yutaka Matsubayashi (Stramer laboratory, King’s College London) showed that formation of the basement membrane in the Drosophila embryo requires rapid anterior–posterior dispersal of macrophages (hemocytes), which first appear in the head of the embryo.

Matrix Confinement Plays a Pivotal Role in Regulating Neutrophil-generated Tractions, Speed, and Integrin Utilization

Neutrophils are capable of switching from integrin-dependent motility on two-dimensional substrata to integrin-independent motion following entry into the confined three-dimensional matrix of an afflicted tissue. However, whether integrins still maintain a regulatory role for cell traction generation and cell locomotion under the physical confinement of the three-dimensional matrix is unknown, and this is challenging to deduce from motility studies alone. Using three-dimensional traction force microscopy and a double hydrogel sandwich system, we determined the three-dimensional spatiotemporal traction forces of motile neutrophils at unprecedented resolution and show, for the first time, that entry into a highly confined space (2.5D) is a sufficient trigger to convert to integrin-independent migration. We find that integrins exert a significant regulatory role in determining the magnitude and spatial distribution of tractions and cell speed on confined cells. We also find that 90% of neutrophil tractions are in the out-of-plane axis, and this may be a fundamental element of neutrophil traction force generation.

Three-Dimensional Analysis of the Effect of Epidermal Growth Factor on Cell-Cell Adhesion in Epithelial Cell Clusters

The effect that growth factors such as epidermal growth factor (EGF) have on cell-cell adhesion is of interest in the study of cellular processes such as epithelial-mesenchymal transition. Because cell-cell adhesions cannot be measured directly, we use three-dimensional traction force microscopy to measure the tractions applied by clusters of MCF-10A cells to a compliant substrate beneath them before and after stimulating the cells with EGF. To better interpret the results, a finite element model, which simulates a cluster of individual cells adhered to one another and to the substrate with linear springs, is developed to better understand the mechanical interaction between the cells in the experiments. The experiments and simulations show that the cluster of cells acts collectively as a single unit, indicating that cell-cell adhesion remains strong before and after stimulation with EGF. In addition, the experiments and model emphasize the importance of three-dimensional measurements and analysis in these experiments.

Three-dimensional Traction Force Microscopy for Studying Cellular Interactions with Biomaterials

The interactions between biochemical and mechanical signals during cell adhesion, migration, spreading and other processes influence cellular behavior. Three-dimensional measurement techniques are needed to investigate the effect of mechanical properties of the substrate on cellular behavior. This paper discusses a three-dimensional full-field measurement technique that has been developed for measuring large deformations in soft materials. The technique utilizes a digital volume correlation (DVC) algorithm to track motions of sub-volumes within 3-D images obtained using laser scanning confocal microscopy. The technique is well-suited for investigating 3-D mechanical interactions between cells and the extracellular matrix and for obtaining local constitutive properties of soft biomaterials. Results from the migration of single fibroblast cells on polyacrylamide gels and their implications for cell motility models are discussed. The implications that the traction distributions of epithelial cell clusters have on the inhibition of proliferation due to cell contact and scattering of cells in a cluster are discussed. These results provide insights on force fields generated by cells and the role of the mechanical properties of the substrate on cellular interactions and mechanotransduction. Analytical solutions and finite element simulations are used to elucidate the mechanics of cellular forces exerted on the extracellular matrix.

Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions.

The interactions between biochemical processes and mechanical signaling play important roles during various cellular processes such as wound healing, embryogenesis, metastasis, and cell migration. While traditional traction force measurements have provided quantitative information about cell matrix interactions in two dimensions, recent studies have shown significant differences in the behavior and morphology of cells when placed in three-dimensional environments. Hence new quantitative experimental techniques are needed to accurately determine cell traction forces in three dimensions. Recently, two approaches both based on laser scanning confocal microscopy have emerged to address this need. This study highlights the details, implementation and advantages of such a three-dimensional imaging methodology with the capability to compute cellular traction forces dynamically during cell migration and locomotion. An application of this newly developed three-dimensional traction force microscopy (3D TFM) technique to single cell migration studies of 3T3 fibroblasts is presented to show that this methodology offers a new quantitative vantage point to investigate the three-dimensional nature of cell-ECM interactions.