Quantifying cellular traction forces in three dimensions

Tension directs cancer cell migration over fiber alignment through energy minimization

Cell migration during many fundamental biological processes including metastasis requires cells to traverse tissue with heterogeneous mechanical cues that direct migration as well as determine force and energy requirements for motility. However, the influence of discrete structural and mechanical cues on migration remains challenging to determine as they are often coupled. Here, we decouple the pro-invasive cues of collagen fiber alignment and tension to study their individual impact on migration. When presented with both cues, cells preferentially travel in the axis of tension against fiber alignment. Computational and experimental data show applying tension perpendicular to alignment increases potential energy stored within collagen fibers, lowering requirements for cell-induced matrix deformation and energy usage during migration compared to motility in the direction of fiber alignment. Energy minimization directs migration trajectory, and tension can facilitate migration against fiber alignment. These findings provide a conceptual understanding of bioenergetics during migration through a fibrous matrix.

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.

Myotube formation on micropatterns guiding by centripetal cellular motility and crowding

The physical microenvironment, including substrate rigidity and topology, impacts myoblast differentiation and myotube maturation. However, the interplay effect and physical mechanism of mechanical stimuli on myotube formation is poorly understood. In this study, we utilized elastic substrates, microcontact patterning technique, and particle image velocimetry to investigate the effect of substrate rigidity and topological constraints on myoblast behaviors. Our findings suggested the interplay of substrate stiffness and cellular confinement improved the myotube formation by inducing centripetal cellular motility. These results shed light on the impact of the topological substrate on myoblast differentiation and emphasize the critical role of asymmetrical cell motility during this process, which is highly correlated with cell movement and crowding. Our research provides insights into the intricate interplay between substrate properties, cell motility, and myotube formation during myogenesis. Understanding these mechanisms could trigger tissue engineering strategies and therapies to enhance muscle regeneration and function.

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.

Degradability tunes ECM stress relaxation and cellular mechanics

In native extracellular matrices (ECM), cells can use matrix metalloproteinases (MMPs) to degrade and remodel their surroundings. Likewise, synthetic matrices have been engineered to facilitate MMP-mediated cleavage that enables cell spreading, migration, and interactions. However, the intersection of matrix degradability and mechanical properties has not been fully considered. We hypothesized that immediate mechanical changes result from the action of MMPs on the ECM and that these changes are sensed by cells. Using atomic force microscopy (AFM) to measure cell-scale mechanical properties, we find that both fibrillar collagen and synthetic degradable matrices exhibit enhanced stress relaxation after MMP exposure. Cells respond to these relaxation differences by altering their spreading and focal adhesions. We demonstrate that stress relaxation can be tuned through the rational design of matrix degradability. These findings establish a fundamental link between matrix degradability and stress relaxation, which may impact a range of biological applications.

Tracking single hiPSC-derived cardiomyocyte contractile function using CONTRAX an efficient pipeline for traction force measurement

Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) are powerful in vitro models to study the mechanisms underlying cardiomyopathies and cardiotoxicity. Quantification of the contractile function in single hiPSC-CMs at high-throughput and over time is essential to disentangle how cellular mechanisms affect heart function. Here, we present CONTRAX, an open-access, versatile, and streamlined pipeline for quantitative tracking of the contractile dynamics of single hiPSC-CMs over time. Three software modules enable: parameter-based identification of single hiPSC-CMs; automated video acquisition of >200 cells/hour; and contractility measurements via traction force microscopy. We analyze >4,500 hiPSC-CMs over time in the same cells under orthogonal conditions of culture media and substrate stiffnesses; +/- drug treatment; +/- cardiac mutations. Using undirected clustering, we reveal converging maturation patterns, quantifiable drug response to Mavacamten and significant deficiencies in hiPSC-CMs with disease mutations. CONTRAX empowers researchers with a potent quantitative approach to develop cardiac therapies.

Molecular Force Sensors for Biological Application

The mechanical forces exerted by cells on their surrounding microenvironment are known as cellular traction forces. These forces play crucial roles in various biological processes, such as tissue development, wound healing and cell functions. However, it is hard for traditional techniques to measure cellular traction forces accurately because their magnitude (from pN to nN) and the length scales over which they occur (from nm to μm) are extremely small. In order to fully understand mechanotransduction, highly sensitive tools for measuring cellular forces are needed. Current powerful techniques for measuring traction forces include traction force microscopy (TFM) and fluorescent molecular force sensors (FMFS). In this review, we elucidate the force imaging principles of TFM and FMFS. Then we highlight the application of FMFS in a variety of biological processes and offer our perspectives and insights into the potential applications of FMFS.

Cellular Traction Force Holds the Potential as a Drug Testing Readout for In Vitro Cancer Metastasis

Introduction

Metastasis is responsible for 90% of cancer-related deaths worldwide. However, the potential inhibitory effects of metastasis by various anticancer drugs have been left largely unexplored. Existing preclinical models primarily focus on antiproliferative agents on the primary tumor to halt the cancer growth but not in metastasis. Unlike primary tumors, metastasis requires cancer cells to exert sufficient cellular traction force through the actomyosin machinery to migrate away from the primary tumor site. Therefore, we seek to explore the potential of cellular traction force as a novel readout for screening drugs that target cancer metastasis.

Methods

In vitro models of invasive and non-invasive breast cancer were first established using MDA-MB-231 and MCF-7 cell lines, respectively. Cellular morphology was characterized, revealing spindle-like morphology in MDA-MB-231 and spherical morphology in MCF-7 cells. The baseline cellular traction force was quantified using the Traction force Microscopy technique. Cisplatin, a paradigm antimetastatic drug, and 5-Fluorouracil (5FU), a non-antimetastatic drug, were selected to evaluate the potential of cellular traction force as a drug testing readout for the in vitro cancer metastasis.

Results

MDA-MB-231 cells exhibited significantly higher baseline cellular traction force compared to MCF-7 cells. Treatment with Cisplatin, an antimetastatic drug, and 5-Fluorouracil (5FU), a non-antimetastatic drug, demonstrated distinct effects on cellular traction force in MDA-MB-231 but not in MCF-7 cells. These findings correlate with the invasive potential observed in the two models.

Conclusion

Cellular traction force emerges as a promising metric for evaluating drug efficacy in inhibiting cancer metastasis using in vitro models. This approach could enhance the screening and development of novel anti-metastatic therapies, addressing a critical gap in current anticancer drug research.

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.

Gelatin-tyramine addition and low hydrogel density improves cell attachment, migration, and metabolic activity in vitro and tissue response in vivo in enzymatically crosslinkable dextran-hyaluronic acid hydrogels

Hydrogels are receiving increasing attention for their use in 3D cell culture, tissue engineering, and bioprinting applications. Each application places specific mechanical and biological demands on these hydrogels. We developed a hydrogel toolbox based on enzymatically crosslinkable polysaccharides via tyramine (TA) moieties, allowing for rapid and tunable crosslinking with well-defined stiffness and high cell viability. Including gelatin modified with TA moieties (Gel-TA) improved the hydrogels' biological properties; 3 T3 fibroblasts and HUVECs attached to and proliferated on the enriched hydrogels at minute Gel-TA concentrations, in contrast to bare or unmodified gelatin-enriched hydrogels. Moreover, we were able to switch HUVECs from a quiescent to a migratory phenotype simply by altering the ligand concentration, demonstrating the potential to easily control cell fate. In encapsulation studies, Gel-TA significantly improved the metabolic activity of 3 T3 fibroblasts in soft hydrogels. Furthermore, we showed rapid migration and network formation in Gel-TA enriched hydrogels in contrast to a non-migratory behavior in non-enriched polysaccharide hydrogels. Finally, low hydrogel density significantly improves tissue response in vivo with large infiltration and low fibrotic reaction. Further development by adding ECM proteins, peptides, and growth factor adhesion sites will lead to a toolbox for hydrogels tailored toward their desired application.

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.

Magnetically controlled cyclic microscale deformation of in vitro cancer invasion models

Mechanical cues play an important role in the metastatic cascade of cancer. Three-dimensional (3D) tissue matrices with tunable stiffness have been extensively used as model systems of the tumor microenvironment for physiologically relevant studies. Tumor-associated cells actively deform these matrices, providing mechanical cues to other cancer cells residing in the tissue. Mimicking such dynamic deformation in the surrounding tumor matrix may help clarify the effect of local strain on cancer cell invasion. Remotely controlled microscale magnetic actuation of such 3D in vitro systems is a promising approach, offering a non-invasive means for in situ interrogation. Here, we investigate the influence of cyclic deformation on tumor spheroids embedded in matrices, continuously exerted for days by cell-sized anisotropic magnetic probes, referred to as μRods. Particle velocimetry analysis revealed the spatial extent of matrix deformation produced in response to a magnetic field, which was found to be on the order of 200 μm, resembling strain fields reported to originate from contracting cells. Intracellular calcium influx was observed in response to cyclic actuation, as well as an influence on cancer cell invasion from 3D spheroids, as compared to unactuated controls. Furthermore, RNA sequencing revealed subtle upregulation of certain genes associated with migration and stress, such as induced through mechanical deformation, for spheroids exposed to actuation vs. controls. Localized actuation at one side of a tumor spheroid tended to result in anisotropic invasion toward the μRods causing the deformation. In summary, our approach offers a strategy to test and control the influence of non-invasive micromechanical cues on cancer cell invasion and metastasis.

Imaging cellular forces with photonic crystals

Current techniques for visualizing and quantifying cellular forces have limitations in live cell imaging, throughput, and multi-scale analysis, which impede progress in cell force research and its practical applications. We developed a photonic crystal cellular force microscopy (PCCFM) to image vertical cell forces over a wide field of view (1.3 mm ⨯ 1.0 mm, a 10 ⨯ objective image) at high speed (about 20 frames per second) without references. The photonic crystal hydrogel substrate (PCS) converts micro-nano deformations into perceivable color changes, enabling in situ visualization and quantification of tiny vertical cell forces with high throughput. It enabled long-term, cross-scale monitoring from subcellular focal adhesions to tissue-level cell sheets and aggregates.

Imaging and detecting intercellular tensile forces in spheroids and embryoid bodies using lipid-modified DNA probes

Cells continuously experience and respond to different physical forces that are used to regulate their physiology and functions. Our ability to measure these mechanical cues is essential for understanding the bases of various mechanosensing and mechanotransduction processes. While multiple strategies have been developed to study mechanical forces within two-dimensional (2D) cell culture monolayers, the force measurement at cell-cell junctions in real three-dimensional (3D) cell models is still pretty rare. Considering that in real biological systems, cells are exposed to forces from 3D directions, measuring these molecular forces in their native environment is thus highly critical for the better understanding of different development and disease processes. We have recently developed a type of DNA-based molecular probe for measuring intercellular tensile forces in 2D cell models. Herein, we will report the further development and first-time usage of these molecular tension probes to visualize and detect mechanical forces within 3D spheroids and embryoid bodies (EBs). These probes can spontaneously anchor onto live cell membranes via the attached lipid moieties. By varying the concentrations of these DNA probes and their incubation time, we have first characterized the kinetics and efficiency of probe penetration and loading onto tumor spheroids and stem cell EBs of different sizes. After optimization, we have further imaged and measured E-cadherin-mediated forces in these 3D spheroids and EBs for the first time. Our results indicated that these DNA-based molecular tension probes can be used to study the spatiotemporal distributions of target mechanotransduction processes. These powerful imaging tools may be potentially applied to fill the gap between ongoing research of biomechanics in 2D systems and that in real 3D cell complexes.

Computational mechanobiology model evaluating healing of postoperative cavities following breast-conserving surgery

Breast cancer is the most commonly diagnosed cancer type worldwide. Given high survivorship, increased focus has been placed on long-term treatment outcomes and patient quality of life. While breast-conserving surgery (BCS) is the preferred treatment strategy for early-stage breast cancer, anticipated healing and breast deformation (cosmetic) outcomes weigh heavily on surgeon and patient selection between BCS and more aggressive mastectomy procedures. Unfortunately, surgical outcomes following BCS are difficult to predict, owing to the complexity of the tissue repair process and significant patient-to-patient variability. To overcome this challenge, we developed a predictive computational mechanobiological model that simulates breast healing and deformation following BCS. The coupled biochemical-biomechanical model incorporates multi-scale cell and tissue mechanics, including collagen deposition and remodeling, collagen-dependent cell migration and contractility, and tissue plastic deformation. Available human clinical data evaluating cavity contraction and histopathological data from an experimental porcine lumpectomy study were used for model calibration. The computational model was successfully fit to data by optimizing biochemical and mechanobiological parameters through Gaussian process surrogates. The calibrated model was then applied to define key mechanobiological parameters and relationships influencing healing and breast deformation outcomes. Variability in patient characteristics including cavity-to-breast volume percentage and breast composition were further evaluated to determine effects on cavity contraction and breast cosmetic outcomes, with simulation outcomes aligning well with previously reported human studies. The proposed model has the potential to assist surgeons and their patients in developing and discussing individualized treatment plans that lead to more satisfying post-surgical outcomes and improved quality of life.

A machine learning approach to predict cellular mechanical stresses in response to chemical perturbation

Mechanical stresses generated at the cell-cell level and cell-substrate level have been suggested to be important in a host of physiological and pathological processes. However, the influence various chemical compounds have on the mechanical stresses mentioned above is poorly understood, hindering the discovery of novel therapeutics, and representing a barrier in the field. To overcome this barrier, we implemented two approaches: 1) monolayer boundary predictor and 2) discretized window predictor utilizing either stepwise linear regression or quadratic support vector machine machine learning model to predict the dose-dependent response of tractions and intercellular stresses to chemical perturbation. We used experimental traction and intercellular stress data gathered from samples subject to 0.2 or 2 μg/mL drug concentrations along with cell morphological properties extracted from the bright-field images as predictors to train our model. To demonstrate the predictive capability of our machine learning models, we predicted tractions and intercellular stresses in response to 0 and 1 μg/mL drug concentrations which were not utilized in the training sets. Results revealed the discretized window predictor trained just with four samples (292 images) to best predict both intercellular stresses and tractions using the quadratic support vector machine and stepwise linear regression models, respectively, for the unseen sample images.

Mechanomorphological Guidance of Colloidal Gel Regulates Cell Morphogenesis

Microstructural morphology of the extracellular matrix guides the organization of cells in 3D. However, current biomaterials-based matrices cannot provide distinct spatial cues through their microstructural morphology due to design constraints. To address this, colloidal gels are developed as 3D matrices with distinct microstructure by aggregating ionic polyurethane colloids via electrostatic screening. Due to the defined orientation of interconnected particles, positively charged colloids form extended strands resulting in a dense microstructure whereas negatively charged colloids form compact aggregates with localized large voids. Chondrogenesis of human mesenchymal stem cells (MSCs) and endothelial morphogenesis of human endothelial cells (ECs) are examined in these colloidal gels. MSCs show enhanced chondrogenic response in dense colloidal gel due to their spatial organization achieved by balancing the cell-cell and cell-matrix interactions compared to porous gels where cells are mainly clustered. ECs tend to form relatively elongated cellular networks in dense colloidal gel compared to porous gels. Additionally, the role of matrix stiffness and viscoelasticity in the morphogenesis of MSCs and ECs are analyzed with respect to microstructural morphology. Overall, these results demonstrate that colloidal gels can provide spatial cues through their microstructural morphology and in correlation with matrix mechanics for cell morphogenesis.

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.

Fungus-derived protein particles as cell-adhesive matrices for cell-cultivated food

Cell-adhesive factors mediate adhesion of cells to substrates via peptide motifs such as the Arg-Gly-Asp (RGD) sequence. With the onset of sustainability issues, there is a pressing need to find alternatives to animal-derived cell-adhesive factors, especially for cell-cultivated food applications. In this paper, we show how data mining can be a powerful approach toward identifying fungal-derived cell-adhesive proteins and present a method to isolate and utilize these proteins as extracellular matrices (ECM) to support cell adhesion and culture in 3D. Screening of a protein database for fungal and plant proteins uncovered that ~5.5% of the unique reported proteins contain RGD sequences. A plot of fungi species vs RGD percentage revealed that 98% of the species exhibited an RGD percentage > = 1%. We observed the formation of protein particles in crude extracts isolated from basidiomycete fungi, which could be correlated to their stability towards particle aggregation at different temperatures. These protein particles were incorporated in 3D fiber matrices encapsulating mouse myoblast cells, showing a positive effect on cell alignment. We demonstrated a cell traction stress on the protein particles (from Flammulina velutipes) that was comparable to cells on fibronectin. A snapshot of the RGD-containing proteins in the fungal extracts was obtained by combining SDS-PAGE and mass spectrometry of the peptide fragments obtained by enzymatic cleavage. Therefore, a sustainable source of cell-adhesive proteins is widely available in the fungi kingdom. A method has been developed to identify candidate species and produce cell-adhesive matrices, applicable to the cell-cultivated food and healthcare industries.

Mechanosensitive traction force generation is regulated by the neutrophil activation state

The generation of traction forces by neutrophils regulates many crucial effector functions responsible for host defense, such as attachment, spreading, migration, phagocytosis, and NETosis. The activation state of the cell is a strong determinant of the functional efficacy of the neutrophil; however, the effect of activation on traction force production has not yet been determined experimentally. Previously, the mapping of cellular-generated forces produced by human neutrophils via a Traction Force Microscopy (TFM) method has required a three-dimensional imaging modality to capture out-of-plane forces, such as confocal or multiphoton techniques. A method newly developed in our laboratories can capture out-of-plane forces using only a two-dimensional imaging modality. This novel technique-combined with a topology-based single particle tracking algorithm and finite element method calculations-can construct high spatial frequency three-dimensional traction fields, allowing for traction forces in-plane and out-of-plane to the substrate to now be differentially visualized and quantified with a standard epifluorescence microscope. Here we apply this technology to determine the effect of neutrophil activation on force generation. Sepsis is a systemic inflammatory response that causes dysregulated neutrophil activation in vivo. We found that neutrophils from septic patients produced greater total forces than neutrophils from healthy donors and that the majority of this dysregulation occurred in-plane to the substrate. Ex vivo activation of neutrophils from healthy donors showed differential consequences depending on activation stimuli with mechanosensitive force decreases observed in some cases. These findings demonstrate the feasibility of epifluorescence-based microscopy in mapping traction forces to ask biologically significant questions regarding neutrophil function.

Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates

Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model's predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell-substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies.

Generic stress rectification in nonlinear elastic media

Stress propagation in nonlinear media is crucial in cell biology, where molecular motors exert anisotropic force dipoles on the fibrous cytoskeleton. While the force dipoles can be either contractile or expansile, a medium made of fibers which buckle under compression rectifies these stresses towards a biologically crucial contraction. A general understanding of this rectification phenomenon as a function of the medium's elasticity is however lacking. Here we use theoretical continuum elasticity to show that rectification is actually a very general effect in nonlinear materials subjected to anisotropic internal stresses. We analytically show that both bucklable and constitutively linear materials subjected to geometrical nonlinearities rectify small forces towards contraction, while granular-like materials rectify towards expansion. Using simulations, we moreover show that these results extend to larger forces. Beyond fiber networks, these results could shed light on the propagation of stresses in brittle or granular materials following a local plastic rearrangement.

Mechanical basis and topological routes to cell elimination

Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces involved in cellular extrusion remains largely unexplored. Utilizing a phase-field model of a three-dimensional cell layer, we study the interplay of cell extrusion with cell-cell and cell-substrate interactions in a flat monolayer. Independent tuning of cell-cell versus cell-substrate adhesion forces reveals that extrusion events can be distinctly linked to defects in nematic and hexatic orders associated with cellular arrangements. Specifically, we show that by increasing relative cell-cell adhesion forces the cell monolayer can switch between the collective tendency towards fivefold, hexatic, disclinations relative to half-integer, nematic, defects for extruding a cell. We unify our findings by accessing three-dimensional mechanical stress fields to show that an extrusion event acts as a mechanism to relieve localized stress concentration.

Characterization of Biocompatibility of Functional Bioinks for 3D Bioprinting

Three-dimensional (3D) bioprinting with suitable bioinks has become a critical tool for fabricating 3D biomimetic complex structures mimicking physiological functions. While enormous efforts have been devoted to developing functional bioinks for 3D bioprinting, widely accepted bioinks have not yet been developed because they have to fulfill stringent requirements such as biocompatibility and printability simultaneously. To further advance our knowledge of the biocompatibility of bioinks, this review presents the evolving concept of the biocompatibility of bioinks and standardization efforts for biocompatibility characterization. This work also briefly reviews recent methodological advances in image analyses to characterize the biocompatibility of bioinks with regard to cell viability and cell-material interactions within 3D constructs. Finally, this review highlights a number of updated contemporary characterization technologies and future perspectives to further advance our understanding of the biocompatibility of functional bioinks for successful 3D bioprinting.

Stability of a two-dimensional biomorphoelastic model for post-burn contraction

We consider the stability analysis of a two-dimensional model for post-burn contraction. The model is based on morphoelasticity for permanent deformations and combined with a chemical-biological model that incorporates cellular densities, collagen density, and the concentration of chemoattractants. We formulate stability conditions depending on the decay rate of signaling molecules for both the continuous partial differential equations-based problem and the (semi-)discrete representation. We analyze the difference and convergence between the resulting spatial eigenvalues from the continuous and semi-discrete problems.

Quantifying stiffness and forces of tumor colonies and embryos using a magnetic microrobot

Stiffness and forces are two fundamental quantities essential to living cells and tissues. However, it has been a challenge to quantify both 3D traction forces and stiffness (or modulus) using the same probe in vivo. Here, we describe an approach that overcomes this challenge by creating a magnetic microrobot probe with controllable functionality. Biocompatible ferromagnetic cobalt-platinum microcrosses were fabricated, and each microcross (about 30 micrometers) was trapped inside an arginine-glycine-apartic acid-conjugated stiff poly(ethylene glycol) (PEG) round microgel (about 50 micrometers) using a microfluidic device. The stiff magnetic microrobot was seeded inside a cell colony and acted as a stiffness probe by rigidly rotating in response to an oscillatory magnetic field. Then, brief episodes of ultraviolet light exposure were applied to dynamically photodegrade and soften the fluorescent nanoparticle-embedded PEG microgel, whose deformation and 3D traction forces were quantified. Using the microrobot probe, we show that malignant tumor-repopulating cell colonies altered their modulus but not traction forces in response to different 3D substrate elasticities. Stiffness and 3D traction forces were measured, and both normal and shear traction force oscillations were observed in zebrafish embryos from blastula to gastrula. Mouse embryos generated larger tensile and compressive traction force oscillations than shear traction force oscillations during blastocyst. The microrobot probe with controllable functionality via magnetic fields could potentially be useful for studying the mechanoregulation of cells, tissues, and embryos.

Zyxin regulates embryonic stem cell fate by modulating mechanical and biochemical signaling interface

Biochemical signaling and mechano-transduction are both critical in regulating stem cell fate. How crosstalk between mechanical and biochemical cues influences embryonic development, however, is not extensively investigated. Using a comparative study of focal adhesion constituents between mouse embryonic stem cell (mESC) and their differentiated counterparts, we find while zyxin is lowly expressed in mESCs, its levels increase dramatically during early differentiation. Interestingly, overexpression of zyxin in mESCs suppresses Oct4 and Nanog. Using an integrative biochemical and biophysical approach, we demonstrate involvement of zyxin in regulating pluripotency through actin stress fibres and focal adhesions which are known to modulate cellular traction stress and facilitate substrate rigidity-sensing. YAP signaling is identified as an important biochemical effector of zyxin-induced mechanotransduction. These results provide insights into the role of zyxin in the integration of mechanical and biochemical cues for the regulation of embryonic stem cell fate.

Tracking Mechanical Stress and Cell Migration with Inexpensive Polymer Thin-Film Sensors

Polydiacetylene (PDA) Langmuir films are well known for their blue to red chromatic transitions in response to a variety of stimuli, including UV light, heat, bio-molecule bindings and mechanical stress. In this work, we detail the ability to tune PDA Langmuir films to exhibit discrete chromatic transitions in response to applied mechanical stress. Normal and shear-induced transitions were quantified using the Surface Forces Apparatus and established to be binary and tunable as a function of film formation conditions. Both monomer alkyl tail length and metal cations were used to manipulate the chromatic transition force threshold to enable discrete force sensing from ~50 to ~500 nN μm-2 for normal loading and ~2 to ~40 nN μm-2 for shear-induced transitions, which are appropriate for biological cells. The utility of PDA thin-film sensors was demonstrated with the slime mold Physarum polycephalum. The fluorescence readout of the films enabled: the area explored by Physarum to be visualized, the forces involved in locomotion to be quantified, and revealed novel puncta formation potentially associated with Physarum sampling its environment.

Sensitivity of a two-dimensional biomorphoelastic model for post-burn contraction

We consider a two-dimensional biomorphoelastic model describing post-burn scar contraction. This model describes skin displacement and the development of the effective Eulerian strain in the tissue. Besides these mechanical components, signaling molecules, fibroblasts, myofibroblasts, and collagen also play a significant role in the model. We perform a sensitivity analysis for the independent parameters of the model and focus on the effects on features of the relative surface area and the total strain energy density. We conclude that the most sensitive parameters are the Poisson's ratio, the equilibrium collagen concentration, the contraction inhibitor constant, and the myofibroblast apoptosis rate. Next to these insights, we perform a sensitivity analysis where the proliferation rates of fibroblasts and myofibroblasts are not the same. The impact of this model adaptation is significant.

The role of cellular traction forces in deciphering nuclear mechanics

Cellular forces exerted on the extracellular matrix (ECM) during adhesion and migration under physiological and pathological conditions regulate not only the overall cell morphology but also nuclear deformation. Nuclear deformation can alter gene expression, integrity of the nuclear envelope, nucleus-cytoskeletal connection, chromatin architecture, and, in some cases, DNA damage responses. Although nuclear deformation is caused by the transfer of forces from the ECM to the nucleus, the role of intracellular organelles in force transfer remains unclear and a challenging area of study. To elucidate nuclear mechanics, various factors such as appropriate biomaterial properties, processing route, cellular force measurement technique, and micromanipulation of nuclear forces must be understood. In the initial phase of this review, we focused on various engineered biomaterials (natural and synthetic extracellular matrices) and their manufacturing routes along with the properties required to mimic the tumor microenvironment. Furthermore, we discussed the principle of tools used to measure the cellular traction force generated during cell adhesion and migration, followed by recently developed techniques to gauge nuclear mechanics. In the last phase of this review, we outlined the principle of traction force microscopy (TFM), challenges in the remodeling of traction forces, microbead displacement tracking algorithm, data transformation from bead movement, and extension of 2-dimensional TFM to multiscale TFM.

Adhesive peptide and polymer density modulate 3D cell traction forces within synthetic hydrogels

Cell-extracellular matrix forces provide pivotal signals regulating diverse physiological and pathological processes. Although mechanobiology has been widely studied in two-dimensional configurations, limited research has been conducted in three-dimensional (3D) systems due to the complex nature of mechanics and cellular behaviors. In this study, we established a platform integrating a well-defined synthetic hydrogel system (PEG-4MAL) with 3D traction force microscopy (TFM) methodologies to evaluate deformation and force responses within synthetic microenvironments, providing insights that are not tractable using biological matrices because of the interdependence of biochemical and biophysical properties and complex mechanics. We dissected the contributions of adhesive peptide density and polymer density, which determines hydrogel stiffness, to 3D force generation for fibroblasts. A critical threshold of adhesive peptide density at a constant matrix elasticity is required for cells to generate 3D forces. Furthermore, matrix displacements and strains decreased with matrix stiffness whereas stresses, and tractions increased with matrix stiffness until reaching constant values at higher stiffness values. Finally, Rho-kinase-dependent contractility and vinculin expression are required to generate significant 3D forces in both collagen and synthetic hydrogels. This research establishes a tunable platform for the study of mechanobiology and provides new insights into how cells sense and transmit forces in 3D.

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.

Signaling Downstream of Focal Adhesions Regulates Stiffness-Dependent Differences in the TGF-β1-Mediated Myofibroblast Differentiation of Corneal Keratocytes

Following injury and refractive surgery, corneal wound healing can initiate a protracted fibrotic response that interferes with ocular function. This fibrosis is related, in part, to the myofibroblast differentiation of corneal keratocytes in response to transforming growth factor beta 1 (TGF-β1). Previous studies have shown that changes in the mechanical properties of the extracellular matrix (ECM) can regulate this process, but the mechanotransductive pathways that govern stiffness-dependent changes in keratocyte differentiation remain unclear. Here, we used a polyacrylamide (PA) gel system to investigate how mechanosensing via focal adhesions (FAs) regulates the stiffness-dependent myofibroblast differentiation of primary corneal keratocytes treated with TGF-β1. Soft (1 kPa) and stiff (10 kPa) PA substrata were fabricated on glass coverslips, plated with corneal keratocytes, and cultured in defined serum free media with or without exogenous TGF-β1. In some experiments, an inhibitor of focal adhesion kinase (FAK) activation was also added to the media. Cells were fixed and stained for F-actin, as well as markers for myofibroblast differentiation (α-SMA), actomyosin contractility phosphorylated myosin light chain (pMLC), focal adhesions (vinculin), or Smad activity (pSmad3). We also used traction force microscopy (TFM) to quantify cellular traction stresses. Treatment with TGF-β1 elicited stiffness-dependent differences in the number, size, and subcellular distribution of FAs, but not in the nuclear localization of pSmad3. On stiff substrata, cells exhibited large FAs distributed throughout the entire cell body, while on soft gels, the FAs were smaller, fewer in number, and localized primarily to the distal tips of thin cellular extensions. Larger and increased numbers of FAs correlated with elevated traction stresses, increased levels of α-SMA immunofluorescence, and more prominent and broadly distributed pMLC staining. Inhibition of FAK disrupted stiffness-dependent differences in keratocyte contractility, FA patterning, and myofibroblast differentiation in the presence of TGF-β1. Taken together, these data suggest that signaling downstream of FAs has important implications for the stiffness-dependent myofibroblast differentiation of corneal keratocytes.

Focal adhesion-mediated cell anchoring and migration: from in vitro to in vivo

Cell-extracellular matrix interactions have been studied extensively using cells cultured in vitro. These studies indicate that focal adhesion (FA)-based cell-extracellular matrix interactions are essential for cell anchoring and cell migration. Whether FAs play a similarly important role in vivo is less clear. Here, we summarize the formation and function of FAs in cultured cells and review how FAs transmit and sense force in vitro. Using examples from animal studies, we also describe the role of FAs in cell anchoring during morphogenetic movements and cell migration in vivo. Finally, we conclude by discussing similarities and differences in how FAs function in vitro and in vivo.

Deep learning-based 3D cellular force reconstruction directly from volumetric images

The forces exerted by single cells in the three-dimensional (3D) environments play a crucial role in modulating cellular functions and behaviors closely related to physiological and pathological processes. Cellular force microscopy (CFM) provides a feasible solution for quantifying the mechanical interactions, which usually regains cellular forces from deformation information of extracellular matrices embedded with fluorescent beads. Owing to computational complexity, the traditional 3D-CFM is usually extremely time-consuming, which makes it challenging for efficient force recovery and large-scale sample analysis. With the aid of deep neural networks, this study puts forward a novel data-driven 3D-CFM to reconstruct 3D cellular force fields directly from volumetric images with random fluorescence patterns. The deep learning (DL)-based network is established through stacking deep convolutional neural network (DCNN) and specific function layers. Some necessary physical information associated with constitutive relation of extracellular matrix material is coupled to the data-driven network. The mini-batch stochastic gradient descent and back-propagation algorithms are introduced to ensure its convergence and training efficiency. The network not only have good generalization ability and robustness, but also can recover 3D cellular forces directly from the input fluorescence image pairs. Particularly, the computational efficiency of the DL-based network is at least one to two orders of magnitude higher than that of the traditional 3D-CFM. This study provides a novel scheme for developing high-performance 3D cellular force microscopy to quantitatively characterize mechanical interactions between single cells and surrounding extracellular matrices, which is of vital importance for quantitative investigations in biomechanics and mechanobiology.

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.

Regulation of Tumor Invasion by the Physical Microenvironment: Lessons from Breast and Brain Cancer

The success of anticancer therapies is often limited by heterogeneity within and between tumors. While much attention has been devoted to understanding the intrinsic molecular diversity of tumor cells, the surrounding tissue microenvironment is also highly complex and coevolves with tumor cells to drive clinical outcomes. Here, we propose that diverse types of solid tumors share common physical motifs that change in time and space, serving as universal regulators of malignancy. We use breast cancer and glioblastoma as instructive examples and highlight how invasion in both diseases is driven by the appropriation of structural guidance cues, contact-dependent heterotypic interactions with stromal cells, and elevated interstitial fluid pressure and flow. We discuss how engineering strategies show increasing value for measuring and modeling these physical properties for mechanistic studies. Moreover, engineered systems offer great promise for developing and testing novel therapies that improve patient prognosis by normalizing the physical tumor microenvironment. Expected final online publication date for the Annual Review of Biomedical Engineering, Volume 24 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Biocompatible micro tweezers for 3D hydrogel organoid array mechanical characterization

This study presents novel biocompatible Polydimethylsiloxane (PDMS)-based micromechanical tweezers (μTweezers) capable of the stiffness characterization and manipulation of hydrogel-based organoids. The system showed great potential for complementing established mechanical characterization methods such as Atomic Force Microscopy (AFM), parallel plate compression (PPC), and nanoindentation, while significantly reducing the volume of valuable hydrogels used for testing. We achieved a volume reduction of ~0.22 μl/sample using the μTweezers vs. ~157 μl/sample using the PPC, while targeting high-throughput measurement of widely adopted micro-mesoscale (a few hundred μm-1500 μm) 3D cell cultures. The μTweezers applied and measured nano-millinewton forces through cantilever' deflection with high linearity and tunability for different applications; the assembly is compatible with typical inverted optical microscopes and fit on standard tissue culture Petri dishes, allowing mechanical compression characterization of arrayed 3D hydrogel-based organoids in a high throughput manner. The average achievable output per group was 40 tests per hour, where 20 organoids and 20 reference images in one 35 mm petri dish were tested, illustrating efficient productivity to match the increasing demand on 3D organoids' applications. The changes in stiffness of collagen I hydrogel organoids in four conditions were measured, with ovarian cancer cells (SKOV3) or without (control). The Young's modulus of the control group (Control-day 0, E = 407± 146, n = 4) measured by PPC was used as a reference modulus, where the relative elastic compressive modulus of the other groups based on the stiffness measurements was also calculated (control-day 0, E = 407 Pa), (SKOV3-day 0, E = 318 Pa), (control-day 5, E = 528 Pa), and (SKOV3-day 5, E = 376 Pa). The SKOV3-embedded hydrogel-based organoids had more shrinkage and lowered moduli on day 0 and day 5 than controls, consistently, while SKOV3 embedded organoids increased in stiffness in a similar trend to the collagen I control from day 0 to day 5. The proposed method can contribute to the biomedical, biochemical, and regenerative engineering fields, where bulk mechanical characterization is of interest. The μTweezers will also provide attractive design and application concepts to soft membrane-micro 3D robotics, sensors, and actuators.

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.

Fibrin prestress due to platelet aggregation and contraction increases clot stiffness

Efficient hemorrhagic control is attained through the formation of strong and stable blood clots at the site of injury. Although it is known that platelet-driven contraction can dramatically influence clot stiffness, the underlying mechanisms by which platelets assist fibrin in resisting external loads are not understood. In this study, we delineate the contribution of platelet-fibrin interactions to clot tensile mechanics using a combination of new mechanical measurements, image analysis, and structural mechanics simulation. Based on uniaxial tensile test data using custom-made microtensometer and fluorescence microscopy of platelet aggregation and platelet-fibrin interactions, we show that integrin-mediated platelet aggregation and actomyosin-driven platelet contraction synergistically increase the elastic modulus of the clots. We demonstrate that the mechanical and geometric response of an active contraction model of platelet aggregates compacting vicinal fibrin is consistent with the experimental data. The model suggests that platelet contraction induces prestress in fibrin fibers and increases the effective stiffness in both cross-linked and noncross-linked clots. Our results provide evidence for fibrin compaction at discrete nodes as a major determinant of mechanical response to applied loads.

Zyxin Is Involved in Fibroblast Rigidity Sensing and Durotaxis

Focal adhesions (FAs) are specialized structures that enable cells to sense their extracellular matrix rigidity and transmit these signals to the interior of the cells, bringing about actin cytoskeleton reorganization, FA maturation, and cell migration. It is known that cells migrate towards regions of higher substrate rigidity, a phenomenon known as durotaxis. However, the underlying molecular mechanism of durotaxis and how different proteins in the FA are involved remain unclear. Zyxin is a component of the FA that has been implicated in connecting the actin cytoskeleton to the FA. We have found that knocking down zyxin impaired NIH3T3 fibroblast's ability to sense and respond to changes in extracellular matrix in terms of their FA sizes, cell traction stress magnitudes and F-actin organization. Cell migration speed of zyxin knockdown fibroblasts was also independent of the underlying substrate rigidity, unlike wild type fibroblasts which migrated fastest at an intermediate substrate rigidity of 14 kPa. Wild type fibroblasts exhibited durotaxis by migrating toward regions of increasing substrate rigidity on polyacrylamide gels with substrate rigidity gradient, while zyxin knockdown fibroblasts did not exhibit durotaxis. Therefore, we propose zyxin as an essential protein that is required for rigidity sensing and durotaxis through modulating FA sizes, cell traction stress and F-actin organization.

Nonlinearity of the coefficient of thermal expansion in brain tissue

The coefficient of thermal expansion (CTE) in biological tissues is an integral parameter behind the application of electromagnetic energy to biomedical technologies; however, its behavior is far from being fully characterized. In this study, we apply digital image correlation (DIC) to non-invasively measure the microscale thermal expansions of recently excised embryonic E18 rodent brain tissue slices. Although the CTE has been measured previously in soft tissues, the literature surrounding the expansion of brain tissue remains sparse. Previous work in measuring the thermal expansion behavior of soft tissue often simplifies the results into a single measurement of a linear CTE parameter and fails to convey the temperature-dependent nonlinearity that exists. In this work, we demonstrate that: (1) the coefficient of brain tissue is more similar to fat than blood, and (2) there exists a significant nonlinear increase in CTE at physiologically-relevant temperatures. This suggests some limitations with the interpretation of previously reported values of the CTE, which are often measured at room temperature.

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.

Stability of a one-dimensional morphoelastic model for post-burn contraction

To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {O}}}(h^2)$$\end{document}O(h2). Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

Sensitivity and feasibility of a one-dimensional morphoelastic model for post-burn contraction

We consider a one-dimensional morphoelastic model describing post-burn scar contraction. Contraction can lead to a limited range of motion (contracture). Reported prevalence of burn scar contractures are 58.6% at 3-6 weeks and 20.9% at 12 months post-reconstructive surgery after burns. This model describes the displacement of the dermal layer of the skin and the development of the effective Eulerian strain in the tissue. Besides these components, the model also contains components that play a major role in the skin repair after trauma. These components are signaling molecules, fibroblasts, myofibroblasts, and collagen. We perform a sensitivity analysis for many parameters of the model and use the results for a feasibility study. In this study, we test whether the model is suitable for predicting the extent of contraction in different age groups. To this end, we conduct an extensive literature review to find parameter values. From the sensitivity analysis, we conclude that the most sensitive parameters are the equilibrium collagen concentration in the dermal layer, the apoptosis rate of fibroblasts and myofibroblasts, and the secretion rate of signaling molecules. Further, although we can use the model to simulate significant distinct contraction densities in different age groups, our results differ from what is seen in the clinic. This particularly concerns children and elderly patients. In children we see more intense contractures if the burn injury occurs near a joint, because the growth induces extra forces on the tissue. Elderly patients seem to suffer less from contractures, possibly because of excess skin.

Mechanical compartmentalization of the intestinal organoid enables crypt folding and collective cell migration

Intestinal organoids capture essential features of the intestinal epithelium such as crypt folding, cellular compartmentalization and collective movements. Each of these processes and their coordination require patterned forces that are at present unknown. Here we map three-dimensional cellular forces in mouse intestinal organoids grown on soft hydrogels. We show that these organoids exhibit a non-monotonic stress distribution that defines mechanical and functional compartments. The stem cell compartment pushes the extracellular matrix and folds through apical constriction, whereas the transit amplifying zone pulls the extracellular matrix and elongates through basal constriction. The size of the stem cell compartment depends on the extracellular-matrix stiffness and endogenous cellular forces. Computational modelling reveals that crypt shape and force distribution rely on cell surface tensions following cortical actomyosin density. Finally, cells are pulled out of the crypt along a gradient of increasing tension. Our study unveils how patterned forces enable compartmentalization, folding and collective migration in the intestinal epithelium.

pyTFM: A tool for traction force and monolayer stress microscopy

Cellular force generation and force transmission are of fundamental importance for numerous biological processes and can be studied with the methods of Traction Force Microscopy (TFM) and Monolayer Stress Microscopy. Traction Force Microscopy and Monolayer Stress Microscopy solve the inverse problem of reconstructing cell-matrix tractions and inter- and intra-cellular stresses from the measured cell force-induced deformations of an adhesive substrate with known elasticity. Although several laboratories have developed software for Traction Force Microscopy and Monolayer Stress Microscopy computations, there is currently no software package available that allows non-expert users to perform a full evaluation of such experiments. Here we present pyTFM, a tool to perform Traction Force Microscopy and Monolayer Stress Microscopy on cell patches and cell layers grown in a 2-dimensional environment. pyTFM was optimized for ease-of-use; it is open-source and well documented (hosted at https://pytfm.readthedocs.io/) including usage examples and explanations of the theoretical background. pyTFM can be used as a standalone Python package or as an add-on to the image annotation tool ClickPoints. In combination with the ClickPoints environment, pyTFM allows the user to set all necessary analysis parameters, select regions of interest, examine the input data and intermediary results, and calculate a wide range of parameters describing forces, stresses, and their distribution. In this work, we also thoroughly analyze the accuracy and performance of the Traction Force Microscopy and Monolayer Stress Microscopy algorithms of pyTFM using synthetic and experimental data from epithelial cell patches.

The analysis of cellular force generation and transmission is an increasingly important aspect in the field of biological research. However, most methods for studying cellular force generation or transmission require complex calculations and have not yet been implemented in comprehensive, easy-to-use software. This is a major hurdle preventing a wider application in the field. Here we present pyTFM, an open-source Python package with a graphical user interface that can be used to evaluate cellular force generation in cells and cell colonies and force transfer within small cell patches and larger cell layers grown on the surface of an elastic substrate. In combination with the image annotation and tool ClickPoints, pyTFM allows the user to set all necessary analysis parameters, select regions of interest, examine the input data and intermediary results, and calculate a wide range of parameters describing cellular forces, stresses, and their distribution. Additionally, pyTFM can be used as standalone python library. pyTFM comes with an extensive documentation (hosted at https://pytfm.readthedocs.io/) including usage examples and explanations of the theoretical background.

Cytoskeletal prestress: The cellular hallmark in mechanobiology and mechanomedicine

Increasing evidence demonstrates that mechanical forces, in addition to soluble molecules, impact cell and tissue functions in physiology and diseases. How living cells integrate mechanical signals to perform appropriate biological functions is an area of intense investigation. Here, we review the evidence of the central role of cytoskeletal prestress in mechanotransduction and mechanobiology. Elevating cytoskeletal prestress increases cell stiffness and reinforces cell stiffening, facilitates long-range cytoplasmic mechanotransduction via integrins, enables direct chromatin stretching and rapid gene expression, spurs embryonic development and stem cell differentiation, and boosts immune cell activation and killing of tumor cells whereas lowering cytoskeletal prestress maintains embryonic stem cell pluripotency, promotes tumorigenesis and metastasis of stem cell-like malignant tumor-repopulating cells, and elevates drug delivery efficiency of soft-tumor-cell-derived microparticles. The overwhelming evidence suggests that the cytoskeletal prestress is the governing principle and the cellular hallmark in mechanobiology. The application of mechanobiology to medicine (mechanomedicine) is rapidly emerging and may help advance human health and improve diagnostics, treatment, and therapeutics of diseases.

A new 3D finite element-based approach for computing cell surface tractions assuming nonlinear conditions

Advances in methods for determining the forces exerted by cells while they migrate are essential for attempting to understand important pathological processes, such as cancer or angiogenesis, among others. Precise data from three-dimensional conditions are both difficult to obtain and manipulate. For this purpose, it is critical to develop workflows in which the experiments are closely linked to the subsequent computational postprocessing. The work presented here starts from a traction force microscopy (TFM) experiment carried out on microfluidic chips, and this experiment is automatically joined to an inverse problem solver that allows us to extract the traction forces exerted by the cell from the displacements of fluorescent beads embedded in the extracellular matrix (ECM). Therefore, both the reconstruction of the cell geometry and the recovery of the ECM displacements are used to generate the inputs for the resolution of the inverse problem. The inverse problem is solved iteratively by using the finite element method under the hypothesis of finite deformations and nonlinear material formulation. Finally, after mathematical postprocessing is performed, the traction forces on the surface of the cell in the undeformed configuration are obtained. Therefore, in this work, we demonstrate the robustness of our computational-based methodology by testing it under different conditions in an extreme theoretical load problem and then by applying it to a real case based on experimental results. In summary, we have developed a new procedure that adds value to existing methodologies for solving inverse problems in 3D, mainly by allowing for large deformations and not being restricted to any particular material formulation. In addition, it automatically bridges the gap between experimental images and mechanical computations.