Determination of cellular tractions on elastic substrate based on an integral Boussinesq solution

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.

Revelation of adhesive proteins affecting cellular contractility through reference-free traction force microscopy

Over the past few decades, the critical role played by cellular contractility associated mechanotransduction in the regulation of cell functions has been revealed. In this case, numerous biomaterials have been chemically or structurally designed to manipulate cell behaviors through the regulation of cellular contractility. In particular, adhesive proteins including fibronectin, poly-L-lysine and collagen type I have been widely applied in various biomaterials to improve cell adhesion. Therefore, clarifying the effects of adhesive proteins on cellular contractility has been valuable for the development of biomaterial design. In this study, reference-free traction force microscopy with a well-organized microdot array was designed and prepared to investigate the relationship between adhesive proteins, cellular contractility, and mechanotransduction. The results showed that fibronectin and collagen type I were able to promote the assembly of focal adhesions and further enhance cellular contraction and YAP activity. In contrast, although poly-L-lysine supported cell spreading and elongation, it was inefficient at inducing cell contractility and activating YAP. Additionally, compared with cellular morphogenesis, cellular contraction was essential for YAP activation.

Imaging dynamic three-dimensional traction stresses

Traction stress between contact objects is ubiquitous and crucial for various physical, biological, and engineering processes such as momentum transfer, tactile perception, and mechanical reliability. Newly developed techniques including electronic skin or traction force microscopy enable traction stress measurement. However, measuring the three-dimensional distribution during a dynamic process remains challenging. Here, we demonstrated a method based on stereo vision to measure three-dimensional traction stress with high spatial and temporal resolution. It showed the ability to image the two-stage adhesion failure of bionic microarrays and display the contribution of elastic resistance and adhesive traction to rolling friction at different contact regions. It also revealed the distributed sucking and sealing effect of the concavity pedal waves that propelled a snail crawling in the horizontal, vertical, and upside-down directions. We expected that the method would advance the understanding of various interfacial phenomena and greatly benefit related applications across physics, biology, and robotics.

B cell mechanosensing: A mechanistic overview

B cells are essential to the adaptive immune system for providing the humoral immunity against cohorts of pathogens. The presentation of antigen to the B cell receptor (BCR) leads to the initiation of B cell activation, which is a process sensitive to the stiffness features of the substrates presenting the antigens. Mechanosensing of the B cells, potentiated through BCR signaling and the adhesion molecules, efficiently regulates B cell activation, proliferation and subsequent antibody responses. Defects in sensing of the antigen-presenting substrates can lead to the activation of autoreactive B cells in autoimmune diseases. The use of high-resolution, high-speed live-cell imaging along with the sophisticated biophysical materials, has uncovered the mechanisms underlying the initiation of B cell activation within seconds of its engagement with the antigen presenting substrates. In this chapter, we reviewed studies that have contributed to uncover the molecular mechanisms of B cell mechanosensing during the initiation of B cell activation.

Inferring intra-cellular mechanics using geometric metamorphosis: A preliminary study

Mechanotransduction plays an important role in sub-cellular processes and is an active area of research. Determining the forces/strains that the intra-cellular structures experience is vital for developing quantitative models of cellular behavior. Established techniques such as traction force microscopy, digital image correlation etc. track surface forces and kinematics of intra-cellular structures. However, difficulties arise when cells cannot be seeded on micro-patterned substrates or the intra-cellular structures vary (unstable landmarks). Here, we applied geometric metamorphosis, a global image registration method, to determine the kinematic profile of a cell during cell division. The method does not require stable landmarks, the registration is non-local in nature and constraints such as volume conservation can be enforced. The cell wall was tracked over time and a sequence of transformations relating the cell wall at the start of cytokinesis to the configuration prior to the daughters completely separate was determined. These transformations are associated with a scalar metric and a statistical atlas describing the wall kinematics from multiple tracking's of the wall shape is constructed. Using these transformations, the cellular kinematics can be described using a Lagrangian frame of reference and the evolution of a material point property can be easily modeled. To demonstrate this, we use the kinematic data derived from the atlas along with a model of stress-fiber (de)formation dynamics to simulate the stress-fiber configuration as the cell domain deforms.

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.

Endothelial Cell Senescence Increases Traction Forces due to Age-Associated Changes in the Glycocalyx and SIRT1

Endothelial cell (EC) aging and senescence are key events in atherogenesis and cardiovascular disease development. Age-associated changes in the local mechanical environment of blood vessels have also been linked to atherosclerosis. However, the extent to which cell senescence affects mechanical forces generated by the cell is unclear. In this study, we sought to determine whether EC senescence increases traction forces through age-associated changes in the glycocalyx and antioxidant regulator deacetylase Sirtuin1 (SIRT1), which is downregulated during aging. Traction forces were higher in cells that had undergone more population doublings and changes in traction force were associated with altered actin localization. Older cells also had increased actin filament thickness. Depletion of heparan sulfate in young ECs elevated traction forces and actin filament thickness, while addition of heparan sulfate to the surface of aged ECs by treatment with angiopoietin-1 had the opposite effect. While inhibition of SIRT1 had no significant effect on traction forces or actin organization for young cells, activation of SIRT1 did reduce traction forces and increase peripheral actin in aged ECs. These results show that EC senescence increases traction forces and alters actin localization through changes to SIRT1 and the glycocalyx.

A novel cell traction force microscopy to study multi-cellular system

Traction forces exerted by adherent cells on their microenvironment can mediate many critical cellular functions. Accurate quantification of these forces is essential for mechanistic understanding of mechanotransduction. However, most existing methods of quantifying cellular forces are limited to single cells in isolation, whereas most physiological processes are inherently multi-cellular in nature where cell-cell and cell-microenvironment interactions determine the emergent properties of cell clusters. In the present study, a robust finite-element-method-based cell traction force microscopy technique is developed to estimate the traction forces produced by multiple isolated cells as well as cell clusters on soft substrates. The method accounts for the finite thickness of the substrate. Hence, cell cluster size can be larger than substrate thickness. The method allows computing the traction field from the substrate displacements within the cells' and clusters' boundaries. The displacement data outside these boundaries are not necessary. The utility of the method is demonstrated by computing the traction generated by multiple monkey kidney fibroblasts (MKF) and human colon cancerous (HCT-8) cells in close proximity, as well as by large clusters. It is found that cells act as individual contractile groups within clusters for generating traction. There may be multiple of such groups in the cluster, or the entire cluster may behave a single group. Individual cells do not form dipoles, but serve as a conduit of force (transmission lines) over long distances in the cluster. The cell-cell force can be either tensile or compressive depending on the cell-microenvironment interactions.

Validation tool for traction force microscopy

Traction force microscopy (TFM) is commonly used to estimate cells' traction forces from the deformation that they cause on their substrate. The accuracy of TFM highly depends on the computational methods used to measure the deformation of the substrate and estimate the forces, and also on the specifics of the experimental set-up. Computer simulations can be used to evaluate the effect of both the computational methods and the experimental set-up without the need to perform numerous experiments. Here, we present one such TFM simulator that addresses several limitations of the existing ones. As a proof of principle, we recreate a TFM experimental set-up, and apply a classic 2D TFM algorithm to recover the forces. In summary, our simulator provides a valuable tool to study the performance, refine experimentally, and guide the extraction of biological conclusions from TFM experiments.

Improved-throughput traction microscopy based on fluorescence micropattern for manual microscopy

Traction force microscopy (TFM) is a quantitative technique for measuring cellular traction force, which is important in understanding cellular mechanotransduction processes. Traditional TFM has a significant limitation in that it has a low measurement throughput, commonly one per TFM dish, due to a lack of cell position information. To obtain enough cellular traction force data, an onerous workload is required including numerous TFM dish preparations and heavy cell-seeding activities, creating further difficulty in achieving identical experimental conditions among batches. In this paper, we present an improved-throughput TFM method using the well-developed microcontact printing technique and chemical modifications of linking microbeads to the gel surface to address these limitations. Chemically linking the microbeads to the gel surface has no significant influence on cell proliferation, morphology, cytoskeleton, and adhesion. Multiple pairs of force loaded and null force fluorescence images can be easily acquired by means of manual microscope with the aid of a fluorescence micropattern made by microcontact printing. Furthermore, keeping the micropattern separate from cells by using gels effectively eliminates the potential negative effect of the micropattern on the cells. This novel design greatly improves the analysis throughput of traditional TFM from one to at least twenty cells per petri dish without losing unique advantages, including a high spatial resolution of traction measurements. This newly developed method will boost the investigation of cell-matrix mechanical interactions.

Regulation of trabecular meshwork cell contraction and intraocular pressure by miR-200c

Lowering intraocular pressure (IOP) delays or prevents the loss of vision in primary open-angle glaucoma (POAG) patients with high IOP and in those with normal tension glaucoma showing progression. Abundant evidence demonstrates that inhibition of contractile machinery of the trabecular meshwork cells is an effective method to lower IOP. However, the mechanisms involved in the regulation of trabecular contraction are not well understood. Although microRNAs have been shown to play important roles in the regulation of multiple cellular functions, little is known about their potential involvement in the regulation of IOP. Here, we showed that miR-200c is a direct postranscriptional inhibitor of genes relevant to the physiologic regulation of TM cell contraction including the validated targets Zinc finger E-box binding homeobox 1 and 2 (ZEB1 and ZEB2), and formin homology 2 domain containing 1 (FHOD1), as well as three novel targets: lysophosphatidic acid receptor 1 (LPAR1/EDG2), endothelin A receptor (ETAR), and RhoA kinase (RHOA). Consistently, transfection of TM cells with miR-200c resulted in strong inhibition of contraction in collagen populated gels as well as decreased cell traction forces exerted by individual TM cells. Finally, delivery of miR-200c to the anterior chamber of living rat eyes resulted in a significant decrease in IOP, while inhibition of miR-200c using an adenoviral vector expressing a molecular sponge led to a significant increase in IOP. These results demonstrate for the first time the ability of a miRNA to regulate trabecular contraction and modulate IOP in vivo, making miR-200c a worthy candidate for exploring ways to alter trabecular contractility with therapeutic purposes in glaucoma.

Influence of substrate rigidity on primary nucleation of cell adhesion: a thermal fluctuation model

Experimental investigations have demonstrated that cells can actively sense and respond to physical aspects of their environments, such as substrate stiffness of biomaterials, via integrin receptors with the help of stochastic thermal undulations of cell membranes. This paper develops a physical model for the mechanism of integrin-dependent cell-substrate adhesion nucleation in order to investigate the influence of substrate stiffness on primary adhesion formation. In this model, a series of so-called energy potential wells are established to quantitatively describe force-driven conformational changes of integrins on elastic substrates with different rigidities. A concept of nucleation domain is proposed to characterize the necessary condition of integrin-mediated cell-substrate primary adhesion formation. In the framework of classical statistical mechanics, the competitive relationship is investigated between the local thermal undulations of plasma membranes and the conformational conversions of substrate-binding integrins. The quantitative dependence of integrin-mediated adhesion nucleation on substrate rigidities is systematically explored, which shows a reasonable agreement with existing experimental results.

Micromechanical regulation in cardiac myocytes and fibroblasts: implications for tissue remodeling

Cells of the myocardium are at home in one of the most mechanically dynamic environments in the body. At the cellular level, pulsatile stimuli of chamber filling and emptying are experienced as cyclic strains (relative deformation) and stresses (force per unit area). The intrinsic characteristics of tension-generating myocytes and fibroblasts thus have a continuous mechanical interplay with their extrinsic surroundings. This review explores the ways that the micromechanics at the scale of single cardiac myocytes and fibroblasts have been measured, modeled, and recapitulated in vitro in the context of adaptation. Both types of cardiac cells respond to externally applied strain, and many of the intracellular mechanosensing pathways have been identified with the careful manipulation of experimental variables. In addition to strain, the extent of loading in myocytes and fibroblasts is also regulated by cues from the microenvironment such as substrate surface chemistry, stiffness, and topography. Combinations of these structural cues in three dimensions are needed to mimic the micromechanical complexity derived from the extracellular matrix of the developing, healthy, or pathophysiologic heart. An understanding of cardiac cell micromechanics can therefore inform the design and composition of tissue engineering scaffolds or stem cell niches for future applications in regenerative medicine.

Influence of substrate stiffness on cell-substrate interfacial adhesion and spreading: a mechano-chemical coupling model

Cell interactions with extracellular matrix, such as cell adhesion and spreading, are crucial for many biological functions and processes. Recent experimental progresses have demonstrated that substrate rigidities exert a remarkable influence on cell-substrate interfacial adhesion and spreading behaviors. The underlying biophysical mechanism, however, remains elusive. Based on the classical Bell-Dembo's theory, this paper develops a mechano-chemical coupling model to physically describe cell adhesion and spreading mediated by substrate stiffness. By investigating the competitive nature between cell-substrate specific attraction and non-specific repulsion, the kinetic relation of receptor-ligand interplay is established, in which the influences of receptor-ligand separation, substrate elasticity and non-specific repulsion on cell adhesions are especially addressed. According to mechanical equilibrium conditions between cell membranes and underlying elastic substrates, an analytical expression is then deduced to relate the cell-substrate interfacial adhesion strength to the substrate rigidity. Moreover, by means of the conventional wetting theory, the dependence of steady-state cell spreading on substrate stiffness is also quantitatively studied. Comparisons with the existing experimental data show that the proposed model can be used to explore cell-substrate interactions regulated by substrate rigidities.

Cellular traction force recovery: An optimal filtering approach in two-dimensional Fourier space

Quantitative estimation of cellular traction has significant physiological and clinical implications. As an inverse problem, traction force recovery is essentially susceptible to noise in the measured displacement data. For traditional procedure of Fourier transform traction cytometry (FTTC), noise amplification is accompanied in the force reconstruction and small tractions cannot be recovered from the displacement field with low signal-noise ratio (SNR). To improve the FTTC process, we develop an optimal filtering scheme to suppress the noise in the force reconstruction procedure. In the framework of the Wiener filtering theory, four filtering parameters are introduced in two-dimensional Fourier space and their analytical expressions are derived in terms of the minimum-mean-squared-error (MMSE) optimization criterion. The optimal filtering approach is validated with simulations and experimental data associated with the adhesion of single cardiac myocyte to elastic substrate. The results indicate that the proposed method can highly enhance SNR of the recovered forces to reveal tiny tractions in cell-substrate interaction.