Experimental and numerical determination of cellular traction force on polymeric hydrogels

Particle retracking algorithm capable of quantifying large, local matrix deformation for traction force microscopy

Deformation measurement is a key process in traction force microscopy (TFM). Conventionally, particle image velocimetry (PIV) or correlation-based particle tracking velocimetry (cPTV) have been used for such a purpose. Using simulated bead images, we show that those methods fail to capture large displacement vectors and that it is due to a poor cross-correlation. Here, to redeem the potential large vectors, we propose a two-step deformation tracking algorithm that combines cPTV, which performs better for small displacements than PIV methods, and newly-designed retracking algorithm that exploits statistically confident vectors from the initial cPTV to guide the selection of correlation peak which are not necessarily the global maximum. As a result, the new method, named 'cPTV-Retracking', or cPTVR, was able to track more than 92% of large vectors whereas conventional methods could track 43-77% of those. Correspondingly, traction force reconstructed from cPTVR showed better recovery of large traction than the old methods. cPTVR applied on the experimental bead images has shown a better resolving power of the traction with different-sized cell-matrix adhesions than conventional methods. Altogether, cPTVR method enhances the accuracy of TFM in the case of large deformations present in soft substrates. We share this advance via our TFMPackage software.

Soft Polymer-Based Technique for Cellular Force Sensing

Soft polymers have emerged as a vital type of material adopted in biomedical engineering to perform various biomechanical characterisations such as sensing cellular forces. Distinct advantages of these materials used in cellular force sensing include maintaining normal functions of cells, resembling in vivo mechanical characteristics, and adapting to the customised functionality demanded in individual applications. A wide range of techniques has been developed with various designs and fabrication processes for the desired soft polymeric structures, as well as measurement methodologies in sensing cellular forces. This review highlights the merits and demerits of these soft polymer-based techniques for measuring cellular contraction force with emphasis on their quantitativeness and cell-friendliness. Moreover, how the viscoelastic properties of soft polymers influence the force measurement is addressed. More importantly, the future trends and advancements of soft polymer-based techniques, such as new designs and fabrication processes for cellular force sensing, are also addressed in this review.

Long-range mechanical signaling in biological systems

Cells can respond to signals generated by other cells that are remarkably far away. Studies from at least the 1920's showed that cells move toward each other when the distance between them is on the order of a millimeter, which is many times the cell diameter. Chemical signals generated by molecules diffusing from the cell surface would move too slowly and dissipate too fast to account for these effects, suggesting that they might be physical rather than biochemical. The non-linear elastic responses of sparsely connected networks of stiff or semiflexible filament such as those that form the extracellular matrix (ECM) and the cytoskeleton have unusual properties that suggest multiple mechanisms for long-range signaling in biological tissues. These include not only direct force transmission, but also highly non-uniform local deformations, and force-generated changes in fiber alignment and density. Defining how fibrous networks respond to cell-generated forces can help design new methods to characterize abnormal tissues and can guide development of improved biomimetic materials.

The role of bifurcation angles on collective smooth muscle cell biomechanics and the implication in atherosclerosis development

A vascular bifurcation angle affects mechanotransduction of a smooth muscle cell sheet and reveals geometrical cues related to early localization of atherosclerosis.

Contractile dynamics change before morphological cues during fluorescence [corrected] illumination

Illumination can have adverse effects on live cells. However, many experiments, e.g. traction force microscopy, rely on fluorescence microscopy. Current methods to assess undesired photo-induced cell changes rely on qualitative observation of changes in cell morphology. Here we utilize a quantitative technique to identify the effect of light on cell contractility prior to morphological changes. Fibroblasts were cultured on soft elastic hydrogels embedded with fluorescent beads. The adherent cells generated contractile forces that deform the substrate. Beads were used as fiducial markers to quantify the substrate deformation over time, which serves as a measure of cell force dynamics. We find that cells exposed to moderate fluorescence illumination (λ = 540–585 nm, I = 12.5 W/m², duration = 60 s) exhibit rapid force relaxation. Strikingly, cells exhibit force relaxation after only 2 s of exposure, suggesting that photo-induced relaxation occurs nearly immediately. Evidence of photo-induced morphological changes were not observed for 15–30 min after illumination. Force relaxation and morphological changes were found to depend on wavelength and intensity of excitation light. This study demonstrates that changes in cell contractility reveal evidence of a photo-induced cell response long before any morphological cues.

Hybrid amphiphilic bimodal hydrogels having mechanical and biological recognition characteristics for cardiac tissue engineering

Tissue engineering strategies rely on the favourable microniche scaffolds for 3D cell growth.

Colored polydimethylsiloxane micropillar arrays for high throughput measurements of forces applied by genetic model organisms

Measuring forces applied by multi-cellular organisms is valuable in investigating biomechanics of their locomotion. Several technologies have been developed to measure such forces, for example, strain gauges, micro-machined sensors, and calibrated cantilevers. We introduce an innovative combination of techniques as a high throughput screening tool to assess forces applied by multiple genetic model organisms. First, we fabricated colored Polydimethylsiloxane (PDMS) micropillars where the color enhances contrast making it easier to detect and track pillar displacement driven by the organism. Second, we developed a semi-automated graphical user interface to analyze the images for pillar displacement, thus reducing the analysis time for each animal to minutes. The addition of color reduced the Young's modulus of PDMS. Therefore, the dye-PDMS composite was characterized using Yeoh's hyperelastic model and the pillars were calibrated using a silicon based force sensor. We used our device to measure forces exerted by wild type and mutant Caenorhabditis elegans moving on an agarose surface. Wild type C. elegans exert an average force of ∼1 μN on an individual pillar and a total average force of ∼7.68 μN. We show that the middle of C. elegans exerts more force than its extremities. We find that C. elegans mutants with defective body wall muscles apply significantly lower force on individual pillars, while mutants defective in sensing externally applied mechanical forces still apply the same average force per pillar compared to wild type animals. Average forces applied per pillar are independent of the length, diameter, or cuticle stiffness of the animal. We also used the device to measure, for the first time, forces applied by Drosophila melanogaster larvae. Peristaltic waves occurred at 0.4 Hz applying an average force of ∼1.58 μN on a single pillar. Our colored microfluidic device along with its displacement tracking software allows us to measure forces applied by multiple model organisms that crawl or slither to travel through their environment.

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.

Collective cell traction force analysis on aligned smooth muscle cell sheet between three-dimensional microwalls

During the past two decades, novel biomaterial scaffold for cell attachment and culture has been developed for applications in tissue engineering, biosensing and regeneration medicine. Tissue engineering of blood vessels remains a challenge owing to the complex three-layer histology involved. In order to engineer functional blood vessels, it is essential to recapitulate the characteristics of vascular smooth muscle cells (SMCs) inside the tunica media, which is known to be critical for vasoconstriction and vasodilation of the circulatory system. Until now, there has been a lack of understanding on the mechanotransduction of the SMC layer during the transformation from viable synthetic to quiescent contractile phenotypes. In this study, microfabricated arrays of discontinuous microwalls coated with fluorescence microbeads were developed to probe the mechanotransduction of the SMC layer. First, the system was exploited for stimulating the formation of a highly aligned orientation of SMCs in native tunica medium. Second, atomic force microscopy in combination with regression analysis was applied to measure the elastic modulus of a polyacrylamide gel layer coated on the discontinuous microwall arrays. Third, the conventional traction force assay for single cell measurement was extended for applications in three-dimensional cell aggregates. Then, the biophysical effects of discontinuous microwalls on the mechanotransduction of the SMC layer undergoing cell alignment were probed. Generally, the cooperative multiple cell-cell and cell-microwall interactions were accessed quantitatively by the newly developed assay with the aid of finite-element modelling. The results show that the traction forces of highly aligned cells lying in the middle region between two opposing microwalls were significantly lower than those lying adjacent to the microwalls. Moreover, the spatial distributions of Von Mises stress during the cell alignment process were dependent on the collective cell layer orientation. Immunostaining of the SMC sheet further demonstrated that the collective mechanotransduction induced by three-dimensional topographic cues was correlated with the reduction of actin and vinculin expression. In addition, the online two-dimensional LC-MS/MS analysis verified the modulation of focal adhesion formation under the influence of microwalls through the regulation in the expression of three key cytoskeletal proteins.

Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials

The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.