Live Cells Exert 3-Dimensional Traction Forces on Their Substrata

Compressive stresses in cancer: characterization and implications for tumour progression and treatment

Beyond their many well-established biological aberrations, solid tumours create an abnormal physical microenvironment that fuels cancer progression and confers treatment resistance. Mechanical forces impact tumours across a range of biological sizes and timescales, from rapid events at the molecular level involved in their sensing and transmission, to slower and larger-scale events, including clonal selection, epigenetic changes, cell invasion, metastasis and immune response. Owing to challenges with studying these dynamic stimuli in biological systems, the mechanistic understanding of the effects and pathways triggered by abnormally elevated mechanical forces remains elusive, despite clear correlations with cancer pathophysiology, aggressiveness and therapeutic resistance. In this Review, we examine the emerging and diverse roles of physical forces in solid tumours and provide a comprehensive framework for understanding solid stress mechanobiology. We first review the physiological importance of mechanical forces, especially compressive stresses, and discuss their defining characteristics, biological context and relative magnitudes. We then explain how abnormal compressive stresses emerge in tumours and describe the experimental challenges in investigating these mechanically induced processes. Finally, we discuss the clinical translation of mechanotherapeutics that alleviate solid stresses and their potential to synergize with chemotherapy, radiotherapy and immunotherapies.

Inferring cellular contractile forces and work using deep morphology traction microscopy

Traction-force microscopy (TFM) has emerged as a widely used standard methodology to measure cell-generated traction forces and determine their role in regulating cell behavior. While TFM platforms have enabled many discoveries, their implementation remains limited due to complex experimental procedures, specialized substrates, and the ill-posed inverse problem whereby low-magnitude high-frequency noise in the displacement field severely contaminates the resulting traction measurements. Here, we introduce deep morphology traction microscopy (DeepMorphoTM), a deep-learning alternative to conventional TFM approaches. DeepMorphoTM first infers cell-induced substrate displacement solely from a sequence of cell shapes and subsequently computes cellular traction forces, thus avoiding the requirement of a specialized fiduciarily marked deformable substrate or force-free reference image. Rather, this technique drastically simplifies the overall experimental methodology, imaging, and analysis needed to conduct cell-contractility measurements. We demonstrate that DeepMorphoTM quantitatively matches conventional TFM results while offering stability against the biological variability in cell contractility for a given cell shape. Without high-frequency noise in the inferred displacement, DeepMorphoTM also resolves the ill-posedness of traction computation, increasing the consistency and accuracy of traction analysis. We demonstrate the accurate extrapolation across several cell types and substrate materials, suggesting robustness of the methodology. Accordingly, we present DeepMorphoTM as a capable yet simpler alternative to conventional TFM for characterizing cellular contractility in two dimensions.

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.

Comparative analysis of traction forces in normal and glaucomatous trabecular meshwork cells within a 3D, active fluid-structure interaction culture environment

This study presents a 3D in vitro cell culture model, meticulously 3D printed to replicate the conventional aqueous outflow pathway anatomical structure, facilitating the study of trabecular meshwork (TM) cellular responses under glaucomatous conditions. Glaucoma affects TM cell functionality, leading to extracellular matrix (ECM) stiffening, enhanced cell-ECM adhesion, and obstructed aqueous humor outflow. Our model, reconstructed from polyacrylamide gel with elastic moduli of 1.5 and 21.7 kPa, is based on serial block-face scanning electron microscopy images of the outflow pathway. It allows for quantifying 3D, depth-dependent, dynamic traction forces exerted by both normal and glaucomatous TM cells within an active fluid-structure interaction (FSI) environment. In our experimental design, we designed two scenarios: a control group with TM cells observed over 20 hours without flow (static setting), focusing on intrinsic cellular contractile forces, and a second scenario incorporating active FSI to evaluate its impact on traction forces (dynamic setting). Our observations revealed that active FSI results in higher traction forces (normal: 1.83-fold and glaucoma: 2.24-fold) and shear strains (normal: 1.81-fold and glaucoma: 2.41-fold), with stiffer substrates amplifying this effect. Glaucomatous cells consistently exhibited larger forces than normal cells. Increasing gel stiffness led to enhanced stress fiber formation in TM cells, particularly in glaucomatous cells. Exposure to active FSI dramatically altered actin organization in both normal and glaucomatous TM cells, particularly affecting cortical actin stress fiber arrangement. This model while preliminary offers a new method in understanding TM cell biomechanics and ECM stiffening in glaucoma, highlighting the importance of FSI in these processes. STATEMENT OF SIGNIFICANCE: This pioneering project presents an advanced 3D in vitro model, meticulously replicating the human trabecular meshwork's anatomy for glaucoma research. It enables precise quantification of cellular forces in a dynamic fluid-structure interaction, a leap forward from existing 2D models. This advancement promises significant insights into trabecular meshwork cell biomechanics and the stiffening of the extracellular matrix in glaucoma, offering potential pathways for innovative treatments. This research is positioned at the forefront of ocular disease study, with implications that extend to broader biomedical applications.

Dynamic traction force in trabecular meshwork cells: A 2D culture model for normal and glaucomatous states

Glaucoma, which is associated with intraocular pressure (IOP) elevation, results in trabecular meshwork (TM) cellular dysfunction, leading to increased rigidity of the extracellular matrix (ECM), larger adhesion forces between the TM cells and ECM, and higher resistance to aqueous humor drainage. TM cells sense the mechanical forces due to IOP dynamic and apply multidimensional forces on the ECM. Recognizing the importance of cellular forces in modulating various cellular activities and development, this study is aimed to develop a 2D in vitro cell culture model to calculate the 3D, depth-dependent, dynamic traction forces, tensile/compressive/shear strain of the normal and glaucomatous human TM cells within a deformable polyacrylamide (PAM) gel substrate. Normal and glaucomatous human TM cells were isolated, cultured, and seeded on top of the PAM gel substrate with embedded FluoSpheres, spanning elastic moduli of 1.5 to 80 kPa. Sixteen-hour post-seeding live confocal microscopy in an incubator was conducted to Z-stack image the 3D displacement map of the FluoSpheres within the PAM gels. Combined with the known PAM gel stiffness, we ascertained the 3D traction forces in the gel. Our results revealed meaningfully larger traction forces in the glaucomatous TM cells compared to the normal TM cells, reaching depths greater than 10-µm in the PAM gel substrate. Stress fibers in TM cells increased with gel rigidity, but diminished when stiffness rose from 20 to 80 kPa. The developed 2D cell culture model aids in understanding how altered mechanical properties in glaucoma impact TM cell behavior and aqueous humor outflow resistance. STATEMENT OF SIGNIFICANCE: Glaucoma, a leading cause of irreversible blindness, is intricately linked to elevated intraocular pressures and their subsequent cellular effects. The trabecular meshwork plays a pivotal role in this mechanism, particularly its interaction with the extracellular matrix. This research unveils an advanced 2D in vitro cell culture model that intricately maps the complex 3D forces exerted by trabecular meshwork cells on the extracellular matrix, offering unparalleled insights into the cellular biomechanics at play in both healthy and glaucomatous eyes. By discerning the changes in these forces across varying substrate stiffness levels, we bridge the gap in understanding between cellular mechanobiology and the onset of glaucoma. The findings stand as a beacon for potential therapeutic avenues, emphasizing the gravity of cellular/extracellular matrix interactions in glaucoma's pathogenesis and setting the stage for targeted interventions in its early stages.

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.

Early committed polarization of intracellular tension in response to cell shape determines the osteogenic differentiation of mesenchymal stromal cells

Within the heterogeneous tissue architecture, a comprehensive understanding of how cell shapes regulate cytoskeletal mechanics by adjusting focal adhesions (FAs) signals to correlate with the lineage commitment of mesenchymal stromal cells (MSCs) remains obscure. Here, via engineered extracellular matrices, we observed that the development of mature FAs, coupled with a symmetrical pattern of radial fiber bundles, appeared at the right-angle vertices in cells with square shape. While circular cells aligned the transverse fibers parallel to the cell edge, and moved them centripetally in a counter-clockwise direction, symmetrical bundles of radial fibers at the vertices of square cells disrupted the counter-clockwise swirling and bridged the transverse fibers to move centripetally. In square cells, the contractile force, generated by the myosin IIA-enriched transverse fibers, were concentrated and transmitted outwards along the symmetrical bundles of radial fibers, to the extracellular matrix through FAs, and thereby driving FA organization and maturation. The symmetrical radial fiber bundles concentrated the transverse fibers contractility inward to the linkage between the actin cytoskeleton and the nuclear envelope. The tauter cytoskeletal network adjusted the nuclear-actomyosin force balance to cause nuclear deformability and to increase nuclear translocation of the transcription co-activator YAP, which in turn modulated the switch in MSC commitment. Thus, FAs dynamically respond to geometric cues and remodel actin cytoskeletal network to re-distribute intracelluar tension towards the cell nucleus, and thereby controlling YAP mechanotransduction signaling in regulating MSC fate decision. STATEMENT OF SIGNIFICANCE: We decipher how cellular mechanics is self-organized depending on extracellular geometric features to correlate with mesenchymal stromal cell lineage commitment. In response to geometry constrains on cell morphology, symmetrical radial fiber bundles are assembled and clustered depending on the maturation state of focal adhesions and bridge with the transverse fibers, and thereby establishing the dynamic cytoskeletal network. Contractile force, generated by the myosin-IIA-enriched transverse fibers, is transmitted and dynamically drives the retrograde movement of the actin cytoskeletal network, which appropriately adjusts the nuclear-actomyosin force balance and deforms the cell nucleus for YAP mechano-transduction signaling in regulating mesenchymal stromal cell fate decision.

Mimicking natural electrical environment with cellulose acetate scaffolds enhances collagen formation of osteoblasts

The medical field is continuously seeking new solutions and materials, where cellulose materials due to their high biocompatibility have great potential. Here we investigate the applicability of cellulose acetate (CA) electrospun fibers for bone tissue regeneration. For the first time we show the piezoelectric properties of electrospun CA fibers via high voltage switching spectroscopy piezoresponse force microscopy (HVSS-PFM) tests, which are followed by surface potential studies using Kelvin probe force microscopy (KPFM) and zeta potential measurements. Piezoelectric coefficient for CA fibers of 6.68 ± 1.70 pmV^-1 along with high surface (718 mV) and zeta (-12.2 mV) potentials allowed us to mimic natural electrical environment favoring bone cell attachment and growth. Importantly, the synergy between increased surface potential and highly developed structure of the fibrous scaffold led to the formation of a vast 3D network of collagen produced by osteoblasts only after 7 days of in vitro culture. We clearly show the advantages of CA scaffolds as a bone replacement material, when long-lasting structural support is needed.

Heparin-mimicking polymer-based hydrogel matrix regulates macrophage polarization by controlling cell adhesion

The physicochemical properties of biomaterials influence cell adhesion, shape, and polarization of macrophages. In this study, we aimed to evaluate the polarization of macrophages in terms of the regulation of cell adhesion and how synthetic mimics for heparin and poly(sodium-4-styrenesulfonate) can regulate macrophage polarization by modulating cell shape, focal adhesion, cell traction force, and intracellular tension. Our initial findings showed that macrophages cultured with heparin-mimicking polymer-based hydrogel matrix showed reduced expression of cell adhesion markers such as integrins, vinculin, RhoA, and ROCK1/2 and reduced cell shape, elongation, cell-matrix traction force, and intracellular tension. Furthermore, we observed a significant decrease in cell adhesion in cells cultured on the hydrogel, resulting in the promotion of M1 polarization. These findings offer insights into the important roles of cell-matrix interactions in macrophage polarization and offer a platform for heparin-mimicking polymer-based hydrogel matrices to induce M1 polarization by inducing cell adhesion without classical activators.

Toward Measuring the Mechanical Stresses Exerted by Branching Embryonic Airway Epithelial Explants in 3D Matrices of Matrigel

Numerous organs in the bodies of animals, including the lung, kidney, and mammary gland, contain ramified networks of epithelial tubes. These structures arise during development via a process known as branching morphogenesis. Previous studies have shown that mechanical forces directly impact this process, but the patterns of mechanical stress exerted by branching embryonic epithelia are not well understood. This is, in part, owing to a lack of experimental tools. Traditional traction force microscopy assays rely on the use of compliant hydrogels with well-defined mechanical properties. Isolated embryonic epithelial explants, however, have only been shown to branch in three-dimensional matrices of reconstituted basement membrane protein, or Matrigel, a biomaterial with poorly characterized mechanical behavior, especially in the regime of large deformations. Here, to compute the traction stresses generated by branching epithelial explants, we quantified the finite-deformation constitutive behavior of gels of reconstituted basement membrane protein subjected to multi-axial mechanical loads. We then modified the mesenchyme-free assay for the ex vivo culture of isolated embryonic airway epithelial explants by suspending fluorescent microspheres within the surrounding gel and tracking their motion during culture. Surprisingly, the tracked bead motion was non-zero in regions of the gel far away from the explants, suggestive of passive swelling deformations within the matrix. To compute accurate traction stresses, these swelling deformations must be decomposed from those generated by the branching explants. We thus tracked the motion of beads suspended within cell-free matrices and quantified spatiotemporal patterns of gel swelling. Taken together, these passive swelling data can be combined with the measured mechanical properties of the gel to compute the traction forces exerted by intact embryonic epithelial explants.

Anisotropy profoundly alters stress fields within contractile cells and cell aggregates

Many biological phenomena such as cell proliferation and death are correlated with stress fields within cells. Stress fields are quantified using computational methods which rely on fundamental assumptions about local mechanical properties. Most existing methods such as Monolayer Stress Microscopy assume isotropic properties, yet experimental observations strongly suggest anisotropy. We first model anisotropy in circular cells analytically using Eshelby's inclusion method. Our solution reveals that uniform anisotropy cannot exist in cells due to the occurrence of substantial stress concentration in the central region. A more realistic non-uniform anisotropy model is then introduced based on experimental observations and implemented numerically which interestingly clears out stress concentration. Stresses within the entire aggregate also drastically change compared to the isotropic case, resulting in better agreement with observed biomarkers. We provide a physics-based mechanism to explain the low alignment of stress fibers in the center of cells, which might explain certain biological phenomena e.g., existence of disrupted rounded cells, and higher apoptosis rate at the center of circular aggregates.

Local lateral contact governs shear traction of micropatterned surfaces on hydrogel substrates

Micropatterned surfaces exhibit enhanced shear traction on soft, aqueous tissue-like materials and, thus, have the potential to advance medical technology by improving the anchoring performance of medical devices on tissue. However, the fundamental mechanism underlying the enhanced shear traction is still elusive, as previous studies focused on interactions between micropatterned surfaces and rigid substrates rather than soft substrates. Here, we present a particle tracking method to experimentally measure microscale three-dimensional (3D) deformation of a soft hydrogel in normal and shear contact with arrays of microscale pillars. The measured 3D strain and stress fields reveal that the lateral contact between each individual pillar and the deformed hydrogel substrate governs the shear response. Moreover, by comparing pillars with different cross-sectional geometries, we observe experimental evidence that the shear traction of a pillar on the hydrogel substrate is sensitive to the convex features of its leading edge in the shear direction.

Computational modeling reveals a vital role for proximity-driven additive and synergistic cell-cell interactions in increasing cancer invasiveness

Solid-tumor cell invasion typically occurs by collective migration of attached cell-cohorts, yet we show here that indirect cell-interactions through the substrate can also drive invasiveness. We have previously shown that well-spaced, invasive cancer cells push-into and indent gels to depths of 10 µm, while closely adjacent, non-contacting cancer cells may reach up to 18 µm, potentially relying on cell-cell interactions through the gel-substrate. To test that, we developed finite element models of indenting cells, using experimental gel mechanics, cell mechanostructure, and force magnitudes. We show that under 50-350 nN of combined traction and normal forces, a stiff nucleus-region is essential in facilitating 5-10 µm single-cell indentations, while uniformly soft cells attain 1.6-fold smaller indentations. We observe that indentation depths of cells in close proximity (0.5-50 µm distance) increase relative to well-spaced cells, due to additive, continuum mechanics-driven contributions. Specifically, 2-3 cells applying 220 nN normal forces gained up to 3% in depth, which interestingly increased to 7.8% when two cells, 10 µm apart, applied unequal force-magnitudes (i.e., 220 and 350 nN). Such additive, energy-free contributions can reduce cell mechanical energy -output required for invasiveness, yet the experimentally observed 10-18 µm depths likely necessitate synergistic, mechanobiological changes, which may be mechanically triggered. We note that nucleus stiffening or cytoplasm softening by 25-50% increased indentation depths by only 1-7%, while depths increase nearly linearly with force-magnitude even to two-fold levels. Hence, cell-proximity triggered, synergistic and additive cell-interactions through the substrate can drive collective cancer-cell invasiveness, even without direct cell-cell interactions. STATEMENT OF SIGNIFICANCE: Metastatic cancer invasion typically occurs collectively in attached cell-cohorts. We have previously shown increased invasiveness in closely adjacent cancer cells that are able to push-into and indent soft-gels more deeply than single, well-spaced cells. Using finite element models, we reveal mechanisms of cell-proximity driven invasiveness, demonstrating an important role for the stiff nucleus. Cell-proximity can additively induce small increase in indentation depth via continuum mechanics contributions, especially when adjacent cells apply unequal forces, and without requiring increased cell-mechanical-energy-output. Concurrently, proximity-triggered synergistic interactions that produce changes in cell mechanics or capacity for increased force-levels can facilitate deep invasive-indentations. Thus, we reveal concurrent additive and synergistic mechanisms to drive collective cancer-cell invasiveness even without direct cell-cell interactions.

Microsphere sensors for characterizing stress fields within three-dimensional extracellular matrix

Stress in the three-dimensional extracellular matrix is one of the key cues in regulating multiscale biological processes. Thus far, noticeable progress in methods and techniques (e.g., micropipette aspiration, AFM, and molecule probes) has been made to quantify stress in cell microenvironment at different length scales. Among them, the microsphere sensor-based method (MSS-based method) has emerged as an advantageous approach over conventional techniques in quantifying stress in situ and in vivo at cellular and supra-cellular scales. This method is implemented by seven sequential steps, including fabrication, modification, characterization, cell adhesion, imaging, displacement field extraction and stress calculation. Precise control of each step and inter-tunning between steps can provide quantitative characterization of stress field. However, detailed procedural information associated with each step and process has been scattered. This review aims to provide a comprehensive overview of MSS-based method, systematically summarizing the principles and research progresses. Firstly, the basic principles are introduced, and the specific experiment and calculation processes of MSS-based method are presented in detail. Then, recent advances and applications of this method are summarized. Finally, perspectives of the limitations and development trends of MSS-based method are discussed. This specific and comprehensive review would provide a guideline for the widespread application of MSS-based method as an advantageous method for in situ and in vivo stress characterization at cellular and supra-cellular scale within three-dimensional extracellular matrix. STATEMENT OF SIGNIFICANCE: In this review, a method based on a microsphere sensor (MSS-based method) as an advantageous approach over conventional techniques in quantifying stress in situ and in vivo at cellular and supra-cellular scales is introduced and discussed. This technique is implemented by seven sequential steps, including fabrication, modification, characterization, cell junction, imaging, displacement field extraction, and stress calculation. Precise control of each step and inter-tunning between steps can provide quantitative stress field. However, detailed procedural information associated with each step has been scattered. Thus, a comprehensive review collating recent advances and perspective discussions is a necessity to introduce a better option for quantifying the stress field in biological processes at the cellular and supra-cellular scales.

Comparison of direct and inverse methods for 2.5D traction force microscopy

Essential cellular processes such as cell adhesion, migration and division strongly depend on mechanical forces. The standard method to measure cell forces is traction force microscopy (TFM) on soft elastic substrates with embedded marker beads. While in 2D TFM one only reconstructs tangential forces, in 2.5D TFM one also considers normal forces. Here we present a systematic comparison between two fundamentally different approaches to 2.5D TFM, which in particular require different methods to deal with noise in the displacement data. In the direct method, one calculates strain and stress tensors directly from the displacement data, which in principle requires a divergence correction. In the inverse method, one minimizes the difference between estimated and measured displacements, which requires some kind of regularization. By calculating the required Green's functions in Fourier space from Boussinesq-Cerruti potential functions, we first derive a new variant of 2.5D Fourier Transform Traction Cytometry (FTTC). To simulate realistic traction patterns, we make use of an analytical solution for Hertz-like adhesion patches. We find that FTTC works best if only tangential forces are reconstructed, that 2.5D FTTC is more precise for small noise, but that the performance of the direct method approaches the one of 2.5D FTTC for larger noise, before both fail for very large noise. Moreover we find that a divergence correction is not really needed for the direct method and that it profits more from increased resolution than the inverse method.

Inverse method based on 3D nonlinear physically constrained minimisation in the framework of traction force microscopy

Traction force microscopy is a methodology that enables to estimate cellular forces from the measurement of the displacement field of an extracellular matrix (ECM)-mimicking hydrogel that a cell is mechanically interacting with. In this paper, a new inverse and physically-consistent methodology is developed and implemented in the context of 3D nonlinear elasticity. The proposed method searches for a displacement field that approximates the measured one, through the imposition of fulfillment of equilibrium with real and known forces acting in the hydrogel. The overall mathematical formulation leads to a constrained optimisation problem that is treated through a Lagrange operator and that is solved numerically by means of a nonlinear finite element framework. In order to illustrate the potential and enhanced accuracy of the proposed inverse method, it is applied to a total of 5 different real cases of cells cultured in a 3D hydrogel that is considered to behave as a nonlinear elastic material. Different error indicators are defined in order to compare ground truth simulated displacements and tractions to the ones recovered by the new inverse as well as by the forward method. Results indicate that the evaluation of displacement gradients leads to errors, in terms of recovered tractions, that are more than three times lower (on average) for the inverse method compared to the forward method. They highlight the enhanced accuracy of the developed methodology and the importance of appropriate inverse methods that impose physical constraints to traction and stress recovery in the context of traction force microscopy.

Traction force microscopy - Measuring the forces exerted by cells

Cells generate mechanical forces (traction forces, TFs) while interacting with the extracellular matrix or neighbouring cells. Forces are generated by both cells and extracellular matrix (ECM) and transmitted within the cell-ECM or cell-cell contacts involving focal adhesions or adherens junctions. Within more than two decades, substantial progress has been achieved in techniques that measure TFs. One of the techniques is traction force microscopy (TFM). This review discusses the TFM and its advances in measuring TFs exerted by cells (single cells and multicellular systems) at cell-ECM and cell-cell junctional intracellular interfaces. The answers to how cells sense, adapt and respond to mechanical forces unravel their role in controlling and regulating cell behaviour in normal and pathological conditions.

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 SIGNIFICANCE: Biomaterial 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.

Elucidating the Biomechanics of Leukocyte Transendothelial Migration by Quantitative Imaging

Leukocyte transendothelial migration is crucial for innate immunity and inflammation. Upon tissue damage or infection, leukocytes exit blood vessels by adhering to and probing vascular endothelial cells (VECs), breaching endothelial cell-cell junctions, and transmigrating across the endothelium. Transendothelial migration is a critical rate-limiting step in this process. Thus, leukocytes must quickly identify the most efficient route through VEC monolayers to facilitate a prompt innate immune response. Biomechanics play a decisive role in transendothelial migration, which involves intimate physical contact and force transmission between the leukocytes and the VECs. While quantifying these forces is still challenging, recent advances in imaging, microfabrication, and computation now make it possible to study how cellular forces regulate VEC monolayer integrity, enable efficient pathfinding, and drive leukocyte transmigration. Here we review these recent advances, paying particular attention to leukocyte adhesion to the VEC monolayer, leukocyte probing of endothelial barrier gaps, and transmigration itself. To offer a practical perspective, we will discuss the current views on how biomechanics govern these processes and the force microscopy technologies that have enabled their quantitative analysis, thus contributing to an improved understanding of leukocyte migration in inflammatory diseases.

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.

Ameliorating Fibrotic Phenotypes of Keloid Dermal Fibroblasts through an Epidermal Growth Factor-Mediated Extracellular Matrix Remodeling

Keloid and hypertrophic scars are skin fibrosis-associated disorders that exhibit an uncontrollable proliferation of fibroblasts and their subsequent contribution to the excessive accumulation of extracellular matrix (ECM) in the dermis. In this study, to elucidate the underlying mechanisms, we investigated the pivotal roles of epidermal growth factor (EGF) in modulating fibrotic phenotypes of keloid and hypertrophic dermal fibroblasts. Our initial findings revealed the molecular signatures of keloid dermal fibroblasts and showed the highest degree of skin fibrosis markers, ECM remodeling, anabolic collagen-cross-linking enzymes, such as lysyl oxidase (LOX) and four LOX-like family enzymes, migration ability, and cell–matrix traction force, at cell–matrix interfaces. Furthermore, we observed significant EGF-mediated downregulation of anabolic collagen-cross-linking enzymes, resulting in amelioration of fibrotic phenotypes and a decrease in cell motility measured according to the cell–matrix traction force. These findings offer insight into the important roles of EGF-mediated cell–matrix interactions at the cell–matrix interface, as well as ECM remodeling. Furthermore, the results suggest their contribution to the reduction of fibrotic phenotypes in keloid dermal fibroblasts, which could lead to the development of therapeutic modalities to prevent or reduce scar tissue formation.

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.

Traction force microscopy for understanding cellular mechanotransduction

Under physiological and pathological conditions, mechanical forces generated from cells themselves or transmitted from extracellular matrix (ECM) through focal adhesions (FAs) and adherens junctions (AJs) are known to play a significant role in regulating various cell behaviors. Substantial progresses have been made in the field of mechanobiology towards novel methods to understand how cells are able to sense and adapt to these mechanical forces over the years. To address these issues, this review will discuss recent advancements of traction force microscopy (TFM), intracellular force microscopy (IFM), and monolayer stress microscopy (MSM) to measure multiple aspects of cellular forces exerted by cells at cell-ECM and cell-cell junctional intracellular interfaces. We will also highlight how these methods can elucidate the roles of mechanical forces at interfaces of cell-cell/cell-ECM in regulating various cellular functions. [BMB Reports 2020; 53(2): 74-81].

Development of a 3-D Physical Dynamics Monitoring System Using OCM with DVC for Quantification of Sprouting Endothelial Cells Interacting with a Collagen Matrix

The extracellular matrix (ECM) plays a key role during cell migration, proliferation, and differentiation by providing adhesion sites and serving as a physical scaffold. Elucidating the interaction between the cell and ECM can reveal the underlying mechanisms of cellular behavior that are currently unclear. Analysis of the deformation of the ECM due to cell-matrix interactions requires microscopic, three-dimensional (3-D) imaging methods, such as confocal microscopy and second-harmonic generation microscopy, which are currently limited by phototoxicity and bleaching as a result of the point-scanning approach. In this study, we suggest the use of optical coherence microscopy (OCM) as a live-cell, volumetric, fast imaging tool for analyzing the deformation of fibrous ECM. We optimized such OCM parameters as the sampling rate to obtain images of the best quality that meet the requirements for robust digital volume correlation (DVC) analysis. Visualization and analysis of the mechanical interaction between collagen ECM and human umbilical vein endothelial cells (HUVECs) show that cellular adhesion during protrusion can be analyzed and quantified. The advantages of OCM, such as fine isotropic spatial resolution, fast time resolution, and low phototoxicity, make it the ideal optic tool for 3-D traction force microscopy.

A Multiscale Model to Predict Neuronal Cell Deformation with Varying Extracellular Matrix Stiffness and Topography

INTRODUCTION

Neuronal cells are sensitive to mechanical properties of extracellular matrix (ECM) such as stiffness and topography. Cells contract and exert a force on ECM to detect the microenvironment, which activates the signaling pathway to influence the cell functions such as differentiation, migration, and proliferation. There are numerous transmembrane proteins that transmit signals; however, integrin and neural cellular adhesion molecules (NCAM) play an important role in sensing the ECM mechanical properties. Mechanotransduction of cell-ECM is the key to understand the influence of ECM stiffness and topography; therefore, in this study, we develop a multiscale computational model to investigate these properties.

METHODS

This model couples the molecular behavior of integrin and NCAM to microscale interactions of neuronal cell and the ECM. We analyze the atomistic/molecular behavior of integrin and NCAM due to mechanical stimuli using steered molecular dynamics. The microscale properties of the neuronal cell and the ECM are simulated using non-linear finite element analysis by applying cell contractility.

RESULTS

We predict that by increasing the ECM stiffness, a neuronal cell exerts greater stress on the ECM. However, this stress reaches a saturation value for a threshold stiffness of ECM, and the saturation value is affected by the ECM thickness, topography, and clustering of integrin and NCAMs. Further, the ECM topography leads to asymmetric stress and deformation in the neuronal cell. Predicted stress distribution in neuronal cell and ECM are consistent with experimental results from the literature.

CONCLUSION

The multiscale computational model will guide in selecting the optimal ECM stiffness and topography range for in vitro studies.

From force-responsive molecules to quantifying and mapping stresses in soft materials

Directly quantifying a spatially varying stress in soft materials is currently a great challenge. We propose a method to do that by detecting a change in visible light absorption. We incorporate a spiropyran (SP) force-activated mechanophore cross-linker in multiple-network elastomers. The random nature of the network structure of the polymer causes a progressive activation of the SP force probe with load, detectable by the change in color of the material. We first calibrate precisely the chromatic change in uniaxial tension. We then demonstrate that the nominal stress around a loaded crack can be detected for each pixel and that the measured values match quantitatively finite element simulations. This direct method to quantify stresses in soft materials with an internal force probe is an innovative tool that holds great potential to compare quantitatively stresses in different materials with simple optical observations.

Self-Organization of Fibroblast-Laden 3D Collagen Microstructures from Inkjet-Printed Cell Patterns

One of the major challenges encountered in engineering complex tissues in vitro is to increase levels of complexity at the micron scale in 3D structures. Here, a strategy to create self-organized 3D collagen microstructures by 2D micropatterning of fibroblasts is developed. Drop-on-demand inkjet printing is used to pattern fibroblast cells on a collagen substrate in pre-designed patterns and with controlled density. It is found that cell-to-ECM interaction promotes cellular self-organization of 3D microstructures on collagen hydrogel, whereas the formation of 3D microstructure is inhibited by disruption of actin polymerization. Using this phenomena, the controlled sizes and morphologies of the 3D collagen microstructures is demonstrated by manipulating the designs of cell patterns and the density of cells. Finally, this technique is applied to build a human skin model with papillary microstructures at the dermo-epidermal junction. This approach to create 3D cell-laden collagen microstructures by cell patterning provides a simple and powerful way to mimic the structures and functions of complex tissues and organs, and can make a contribution to reduce the gap between the human body and in vitro tissue models.

Fast quantitative time lapse displacement imaging of endothelial cell invasion

In order to unravel rapid mechano-chemical feedback mechanisms in sprouting angiogenesis, we combine selective plane illumination microscopy (SPIM) and tailored image registration algorithms - further referred to as SPIM-based displacement microscopy - with an in vitro model of angiogenesis. SPIM successfully tackles the problem of imaging large volumes while upholding the spatial resolution required for the analysis of matrix displacements at a subcellular level. Applied to in vitro angiogenic sprouts, this unique methodological combination relates subcellular activity - minute to second time scale growing and retracting of protrusions - of a multicellular systems to the surrounding matrix deformations with an exceptional temporal resolution of 1 minute for a stack with multiple sprouts simultaneously or every 4 seconds for a single sprout, which is 20 times faster than with a conventional confocal setup. Our study reveals collective but non-synchronised, non-continuous activity of adjacent sprouting cells along with correlations between matrix deformations and protrusion dynamics.

Force and Collective Epithelial Activities

Cells apply forces to their surroundings to perform basic biological activities, including division, adhesion, and migration. Similarly, cell populations in epithelial tissues coordinate forces in physiological processes of morphogenesis and repair. These activities are highly regulated to yield the correct development and function of the body. The modification of this order is at the onset of pathological events and malfunctions. Mechanical forces and their translation into biological signals are the focus of an emerging field of research, shaping as a central discipline in the study of life and gathering knowledge at the interface of engineering, physics, biology and medicine. Novel engineering methods are needed to complement the classic instruments developed by molecular biology, physics and medicine. These should enable the measurement of forces at the cellular and multicellular level, and at a temporal and spatial resolution which is fully compatible with the ranges experienced by cells in vivo.

Chemically Responsive Hydrogel Deformation Mechanics: A Review

A hydrogel is a polymeric three-dimensional network structure. The applications of this material type are diversified over a broad range of fields. Their soft nature and similarity to natural tissue allows for their use in tissue engineering, medical devices, agriculture, and industrial health products. However, as the demand for such materials increases, the need to understand the material mechanics is paramount across all fields. As a result, many attempts to numerically model the swelling and drying of chemically responsive hydrogels have been published. Material characterization of the mechanical properties of a gel bead under osmotic loading is difficult. As a result, much of the literature has implemented variants of swelling theories. Therefore, this article focuses on reviewing the current literature and outlining the numerical models of swelling hydrogels as a result of exposure to chemical stimuli. Furthermore, the experimental techniques attempting to quantify bulk gel mechanics are summarized. Finally, an overview on the mechanisms governing the formation of geometric surface instabilities during transient swelling of soft materials is provided.

A practical review on the measurement tools for cellular adhesion force

Cell-cell and cell-matrix adhesions are fundamental in all multicellular organisms. They play a key role in cellular growth, differentiation, pattern formation and migration. Cell-cell adhesion is substantial in the immune response, pathogen-host interactions, and tumor development. The success of tissue engineering and stem cell implantations strongly depends on the fine control of live cell adhesion on the surface of natural or biomimetic scaffolds. Therefore, the quantitative and precise measurement of the adhesion strength of living cells is critical, not only in basic research but in modern technologies, too. Several techniques have been developed or are under development to quantify cell adhesion. All of them have their pros and cons, which has to be carefully considered before the experiments and interpretation of the recorded data. Current review provides a guide to choose the appropriate technique to answer a specific biological question or to complete a biomedical test by measuring cell adhesion.

Analysis of the Precision, Robustness, and Speed of Elastic Resonator Interference Stress Microscopy

Localization-microscopy-based methods are widely used to map the forces that cells apply to their substrates and to study important questions of cellular biomechanics. By contrast, elastic resonator interference stress microscopy (ERISM) uses an interference-based approach, which requires low light intensity and facilitates imaging of cellular forces with extreme precision (down to pN forces) and robustness (e.g., for continuous force monitoring over weeks). Here, the measurement trade-offs and numerical considerations required to optimize the performance of ERISM are described. The crucial parts of the fitting algorithm and the computational tools used to evaluate the data are explained in detail, and the precision and accuracy achievable with ERISM are analyzed. Additional features that can improve the robustness of ERISM further are discussed. The implementation of the analysis algorithm is verified with simulated test data and with experimental data. In addition, an approach to increase the acquisition speed of ERISM by a factor of four compared to the original implementation is described. In combination, these strategies allow us to measure the forces generated by a neural growth cone with high temporal resolution and continuously over several hours.

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.

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.

Modeling cardiac complexity: Advancements in myocardial models and analytical techniques for physiological investigation and therapeutic development in vitro

Cardiomyopathies, heart failure, and arrhythmias or conduction blockages impact millions of patients worldwide and are associated with marked increases in sudden cardiac death, decline in the quality of life, and the induction of secondary pathologies. These pathologies stem from dysfunction in the contractile or conductive properties of the cardiomyocyte, which as a result is a focus of fundamental investigation, drug discovery and therapeutic development, and tissue engineering. All of these foci require in vitro myocardial models and experimental techniques to probe the physiological functions of the cardiomyocyte. In this review, we provide a detailed exploration of different cell models, disease modeling strategies, and tissue constructs used from basic to translational research. Furthermore, we highlight recent advancements in imaging, electrophysiology, metabolic measurements, and mechanical and contractile characterization modalities that are advancing our understanding of cardiomyocyte physiology. With this review, we aim to both provide a biological framework for engineers contributing to the field and demonstrate the technical basis and limitations underlying physiological measurement modalities for biologists attempting to take advantage of these state-of-the-art techniques.

Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells

Adherent cells exert traction forces on to their environment which allows them to migrate, to maintain tissue integrity, and to form complex multicellular structures during developmental morphogenesis. Traction force microscopy (TFM) enables the measurement of traction forces on an elastic substrate and thereby provides quantitative information on cellular mechanics in a perturbation-free fashion. In TFM, traction is usually calculated via the solution of a linear system, which is complicated by undersampled input data, acquisition noise, and large condition numbers for some methods. Therefore, standard TFM algorithms either employ data filtering or regularization. However, these approaches require a manual selection of filter- or regularization parameters and consequently exhibit a substantial degree of subjectiveness. This shortcoming is particularly serious when cells in different conditions are to be compared because optimal noise suppression needs to be adapted for every situation, which invariably results in systematic errors. Here, we systematically test the performance of new methods from computer vision and Bayesian inference for solving the inverse problem in TFM. We compare two classical schemes, L1- and L2-regularization, with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization. Using artificial data and experimental data, we show that these methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Thus, Bayesian methods can mitigate the considerable uncertainty inherent in comparing cellular tractions in different conditions.

Where No Hand Has Gone Before: Probing Mechanobiology at the Cellular Level

Physical forces and other mechanical stimuli are fundamental regulators of cell behavior and function. Cells are also biomechanically competent: they generate forces to migrate, contract, remodel, and sense their environment. As the knowledge of the mechanisms of mechanobiology increases, the need to resolve and probe increasingly small scales calls for novel technologies to mechanically manipulate cells, examine forces exerted by cells, and characterize cellular biomechanics. Here, we review novel methods to quantify cellular force generation, measure cell mechanical properties, and exert localized piconewton and nanonewton forces on cells, receptors, and proteins. The combination of these technologies will provide further insight on the effect of mechanical stimuli on cells and the mechanisms that convert these stimuli into biochemical and biomechanical activity.

Unloading of intercellular tension induces the directional translocation of PKCα

The migration of endothelial cells (ECs) is closely associated with a Ca²⁺ -dependent protein, protein kinase Cα (PKCα). The disruption of intercellular adhesion by single-cell wounding has been shown to induce the directional translocation of PKCα. We hypothesized that this translocation of PKCα is induced by mechanical stress, such as unloading of intercellular tension, or by intercellular communication, such as gap junction-mediated and paracrine signaling. In the current study, we found that the disruption of intercellular adhesion induced the directional translocation of PKCα even when gap junction-mediated and paracrine signaling were inhibited. Conversely, it did not occur when the mechanosensitive channel was inhibited. In addition, the strain field of substrate attributable to the disruption of intercellular adhesion tended to be larger at the areas corresponding with PKCα translocation. Recently, we found that a direct mechanical stimulus induced the accumulation of PKCα at the stimulus area, involving Ca ²⁺ influx from extracellular space. These results indicated that the unloading of intercellular tension induced directional translocation of PKCα, which required Ca ²⁺ influx from extracellular space. The results of this study indicate the involvement of PKCα in the Ca ²⁺ signaling pathway in response to mechanical stress in ECs.

Dissecting cellular mechanics: Implications for aging, cancer, and immunity

Cells are dynamic structures that must respond to complex physical and chemical signals from their surrounding environment. The cytoskeleton is a key mediator of a cell's response to the signals of both the extracellular matrix and other cells present in the local microenvironment and allows it to tune its own mechanical properties in response to these cues. A growing body of evidence suggests that altered cellular viscoelasticity is a strong indicator of disease state; including cancer, laminopathy (genetic disorders of the nuclear lamina), infection, and aging. Here, we review recent work on the characterization of cell mechanics in disease and discuss the implications of altered viscoelasticity in regulation of immune responses. Finally, we provide an overview of techniques for measuring the mechanical properties of cells deeply embedded within tissues.

Investigating the interplay between substrate stiffness and ligand chemistry in directing mesenchymal stem cell differentiation within 3D macro-porous substrates

Dimensionality can have a profound impact on stiffness-mediated differentiation of mesenchymal stem cells (MSCs). However, while we have begun to understand cellular response when encapsulated within 3D substrates, the behavior of cells within macro-porous substrates is relatively underexplored. The goal of this study was to determine the influence of macro-porous topographies on stiffness-mediated differentiation of MSCs. We developed macro-porous recombinant elastin-like protein (ELP) substrates that allow independent control of mechanical properties and ligand chemistry. We then used computational modeling to probe the impact of pore topography on the mechanical stimulus that cells are exposed to within these substrates, and finally we investigated stiffness induced biases towards adipogenic and osteogenic differentiation of MSCs within macro-porous substrates. Computational modeling revealed that there is significant heterogeneity in the mechanical stimuli that cells are exposed to within porous substrates and that this heterogeneity is predominantly due to the wide range of possible cellular orientations within the pores. Surprisingly, MSCs grown within 3D porous substrates respond to increasing substrate stiffness by up-regulating both osteogenesis and adipogenesis. These results demonstrate that within porous substrates the behavior of MSCs diverges from previously observed responses to substrate stiffness, emphasizing the importance of topography as a determinant of cellular behavior.

Traction cytometry: regularization in the Fourier approach and comparisons with finite element method

Traction forces exerted by adherent cells are quantified using displacements of embedded markers on polyacrylamide substrates due to cell contractility. Fourier Transform Traction Cytometry (FTTC) is widely used to calculate tractions but has inherent limitations due to errors in the displacement fields; these are mitigated through a regularization parameter (γ) in the Reg-FTTC method. An alternate finite element (FE) approach computes tractions on a domain using known boundary conditions. Robust verification and recovery studies are lacking but essential in assessing the accuracy and noise sensitivity of the traction solutions from the different methods. We implemented the L2 regularization method and defined a maximum curvature point in the traction with γ plot as the optimal regularization parameter (γ*) in the Reg-FTTC approach. Traction reconstructions using γ* yield accurate values of low and maximum tractions (Tmax) in the presence of up to 5% noise. Reg-FTTC is hence a clear improvement over the FTTC method but is inadequate to reconstruct low stresses such as those at nascent focal adhesions. FE, implemented using a node-by-node comparison, showed an intermediate reconstruction compared to Reg-FTTC. We performed experiments using mouse embryonic fibroblast (MEF) and compared results between these approaches. Tractions from FTTC and FE showed differences of ∼92% and 22% as compared to Reg-FTTC. Selection of an optimum value of γ for each cell reduced variability in the computed tractions as compared to using a single value of γ for all the MEF cells in this study.

Collective Cell Behavior in Mechanosensing of Substrate Thickness

Extracellular matrix stiffness has a profound effect on the behavior of many cell types. Adherent cells apply contractile forces to the material on which they adhere and sense the resistance of the material to deformation-its stiffness. This is dependent on both the elastic modulus and the thickness of the material, with the corollary that single cells are able to sense underlying stiff materials through soft hydrogel materials at low (<10 μm) thicknesses. Here, we hypothesized that cohesive colonies of cells exert more force and create more hydrogel deformation than single cells, therefore enabling them to mechanosense more deeply into underlying materials than single cells. To test this, we modulated the thickness of soft (1 kPa) elastic extracellular-matrix-functionalized polyacrylamide hydrogels adhered to glass substrates and allowed colonies of MG63 cells to form on their surfaces. Cell morphology and deformations of fluorescent fiducial-marker-labeled hydrogels were quantified by time-lapse fluorescence microscopy imaging. Single-cell spreading increased with respect to decreasing hydrogel thickness, with data fitting to an exponential model with half-maximal response at a thickness of 3.2 μm. By quantifying cell area within colonies of defined area, we similarly found that colony-cell spreading increased with decreasing hydrogel thickness but with a greater half-maximal response at 54 μm. Depth-sensing was dependent on Rho-associated protein kinase-mediated cellular contractility. Surface hydrogel deformations were significantly greater on thick hydrogels compared to thin hydrogels. In addition, deformations extended greater distances from the periphery of colonies on thick hydrogels compared to thin hydrogels. Our data suggest that by acting collectively, cells mechanosense rigid materials beneath elastic hydrogels at greater depths than individual cells. This raises the possibility that the collective action of cells in colonies or sheets may allow cells to sense structures of differing material properties at comparatively large distances.

Quantification of focal adhesion dynamics of cell movement based on cell-induced collagen matrix deformation using second-harmonic generation microscopy

Mechanical interactions of living cells with the surrounding environment via focal adhesion (FA) in three dimensions (3-D) play a key role in dynamic biological events, such as tissue regeneration, wound healing, and cancer invasion. Recently, several methods for observing 3-D cell-extracellular matrix (ECM) interactions have been reported, lacking solid and quantitative analysis on the dynamics of the physical interaction between the cell and the ECM. We measured the submicron displacements of ECM deformation in 3-D due to protrusion-retraction dynamics during cell migration, using second-harmonic generation without labeling the matrix structures. We then quantitatively analyzed the mechanical deformation between the ECM and the cells based on spatiotemporal volumetric correlations. The greatest deformations within the collagen matrix were found to occur at sites of colocalization of the FA site-related proteins vinculin and actin, which confirms that FA sites play a critical role in living cells within the ECM as a point for adhesion, traction, and migration. We believe that this modality can be used in studies of cell-ECM interaction during angiogenesis, wound healing, and metastasis.

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.

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.

Substrate stiffness and VE-cadherin mechano-transduction coordinate to regulate endothelial monolayer integrity

The vascular endothelium is subject to diverse mechanical cues that regulate vascular endothelial barrier function. In addition to rigidity sensing through integrin adhesions, mechanical perturbations such as changes in fluid shear stress can also activate force transduction signals at intercellular junctions. This study investigated how extracellular matrix rigidity and intercellular force transduction, activated by vascular endothelial cadherin, coordinate to regulate the integrity of endothelial monolayers. Studies used complementary mechanical measurements of endothelial monolayers grown on patterned substrates of variable stiffness. Specifically perturbing VE-cadherin receptors activated intercellular force transduction signals that increased integrin-dependent cell contractility and disrupted cell-cell and cell-matrix adhesions. Further investigations of the impact of substrate rigidity on force transduction signaling demonstrated how cells integrate extracellular mechanics cues and intercellular force transduction signals, to regulate endothelial integrity and global tissue mechanics. VE-cadherin specific signaling increased focal adhesion remodeling and cell contractility, while sustaining the overall mechanical equilibrium at the mesoscale. Conversely, increased substrate rigidity exacerbates the disruptive effects of intercellular force transduction signals, by increasing heterogeneity in monolayer stress distributions. The results provide new insights into how substrate stiffness and intercellular force transduction coordinate to regulate endothelial monolayer integrity.