Traction force microscopy in physics and biology

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.

Drop impact dynamics of complex fluids: a review

The impact of fluid drops on solid substrates has widespread interest in many industrial coating and spraying applications, such as ink-jet printing and agricultural pesticide sprays. Many of the fluids used in these applications are non-Newtonian, that is they contain particulate or polymeric additives that strongly modify their flow behaviour. While a large body of experimental and theoretical work has been done to understand the impact dynamics of Newtonian fluids, we as a community have much progress to make to understand how these dynamics are modified when the impact fluid has non-Newtonian rheology. In this review, we outline recent experimental, theoretical, and computational advances in the study of impact dynamics of complex fluids on solid surfaces. Here, we provide an overview of this field that is geared towards a multidisciplinary audience. Our discussion is segmented by two principal material constitutions: polymeric fluids and particulate suspensions. Throughout, we highlight promising future directions, as well as ongoing experimental and theoretical challenges in the field.

Red blood cell flickering activity locally controlled by holographic optical tweezers

Red blood cells possess a singular mechanobiology, enabling efficient navigation through capillaries smaller than their own size. Their plasma membrane exhibits non-equilibrium shape fluctuation, often reported as enhanced flickering activity. Such active membrane motion is propelled by motor proteins that mediate interactions between the spectrin skeleton and the lipid bilayer. However, modulating the flickering in living red blood cells without permanently altering their mechanical properties represents a significant challenge. In this study, we developed holographic optical tweezers to generate a force field distributed along the equatorial membrane contour of individual red blood cells. In free-standing red blood cells, we observed heterogeneous flickering activity, attributed to localized membrane kickers. By employing holographic optical forces, these active kickers can be selectively halted under minimal invasion. Our findings shed light on the dynamics of membrane flickering and established a manipulation tool that could open new avenues for investigating mechanotransduction processes in living cells.

Label-Free Optical Mapping for Large-Area Biomechanical Dynamics of Multicellular Systems

Mapping cellular activities over large areas is crucial for understanding the collective behaviors of multicellular systems. Biomechanical properties, such as cellular traction force, serve as critical regulators of physiological states and molecular configurations. However, existing technologies for mapping large-area biomechanical dynamics are limited by the small field of view and scanning nature. To address this, we propose a novel platform that utilizes a vast number of optical diffractive elements for mapping large-area biomechanical dynamics. This platform achieves a field-of-view of 10.6 mm X 10.6 mm, a three-orders-of-magnitude improvement over traditional traction force microscopy. Transient mechanical waves generated by monolayer neonatal rat ventricular myocytes were captured with high spatiotemporal resolution (130 fps and 20 µm for temporal and spatial resolution, respectively). Furthermore, its label-free nature allows for long-term observations extended to a week, with minimal disruption of cellular functions. Finally, simultaneous measurements of calcium ions concentrations and biomechanical dynamics are demonstrated.

Ultrasoft silicone gels with tunable refractive index for traction force microscopy

We formulate and characterize silicone gels near the gelation threshold with tunable refractive index, 1.4 < n < 1.49, and small viscoelastic moduli, G'∼1 Pa, for use in traction force microscopy. The near-critical gels have low-frequency storage plateau moduli between 50 Pa and 1 Pa, with loss moduli that are more than fifty times lower at low frequencies. The gels are linearly elastic up to strains of at least 50%. The refractive index of the gel is tuned to eliminate spherical aberrations during confocal imaging thereby minimizing signal loss when imaging through thick gel substrates. We also develop an index-matched colloidal particle, stabilized by a silicone brush, that can be dispersed throughout the gel. These particles can be used to determine the deformation of the gel. The combination of mechanical and optical properties of these near-critical gels extends the lower limit of stresses that can be measured with traction force microscopy to single mPa values, while minimizing optical aberrations.

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.

How cytoskeletal crosstalk makes cells move: Bridging cell-free and cell studies

Cell migration is a fundamental process for life and is highly dependent on the dynamical and mechanical properties of the cytoskeleton. Intensive physical and biochemical crosstalk among actin, microtubules, and intermediate filaments ensures their coordination to facilitate and enable migration. In this review, we discuss the different mechanical aspects that govern cell migration and provide, for each mechanical aspect, a novel perspective by juxtaposing two complementary approaches to the biophysical study of cytoskeletal crosstalk: live-cell studies (often referred to as top-down studies) and cell-free studies (often referred to as bottom-up studies). We summarize the main findings from both experimental approaches, and we provide our perspective on bridging the two perspectives to address the open questions of how cytoskeletal crosstalk governs cell migration and makes cells move.

Cell Migration Assays and Their Application to Wound Healing Assays-A Critical Review

In recent years, cell migration assays (CMAs) have emerged as a tool to study the migration of cells along with their physiological responses under various stimuli, including both mechanical and bio-chemical properties. CMAs are a generic system in that they support various biological applications, such as wound healing assays. In this paper, we review the development of the CMA in the context of its application to wound healing assays. As such, the wound healing assay will be used to derive the requirements on CMAs. This paper will provide a comprehensive and critical review of the development of CMAs along with their application to wound healing assays. One salient feature of our methodology in this paper is the application of the so-called design thinking; namely we define the requirements of CMAs first and then take them as a benchmark for various developments of CMAs in the literature. The state-of-the-art CMAs are compared with this benchmark to derive the knowledge and technological gap with CMAs in the literature. We will also discuss future research directions for the CMA together with its application to wound healing assays.

Investigation of the surface mechanical properties of functionalized single-walled carbon nanotube (SWCNT) reinforced PDMS nanocomposites using nanoindentation analysis

Functionalizing single-walled carbon nanotubes (SWCNT) with different chemical functional groups directly enhances their chemical adhesion and dispersion in viscous polymeric resins such as polydimethylsiloxane (PDMS). Nevertheless, the ideal surface polarity (hydrophilic or hydrophobic) for SWCNT to foster stronger chemical bonding with PDMS remains uncertain. This investigation delves into the impact of enhanced SWCNT dispersion within PDMS on the surface mechanical characteristics of this flexible composite system. We use carboxylic acid-functionalized SWCNT (COOH-SWCNT) and silane-functionalized SWCNT (sily-SWCNT), recognized for their hydrophilic and hydrophobic surface polarities, respectively, as reinforcing agents at ultra-low weight percentage loadings: 0.05 wt%, 0.5 wt%, and 1 wt%. We perform quasi-static nanoindentation analysis employing a Berkovich tip to probe the localized mechanical behavior of PDMS-SWCNT films at an indentation depth of 1 μm. Plastic deformation within the samples, denoted as plastic work (Wp), as well as the elastic modulus (E), hardness (H), and contact stiffness (Sc) of the composites are examined from the force-displacement curves to elucidate the enhancement in the surface mechanical attributes of the composite films.

Dynamics of centipede locomotion revealed by large-scale traction force microscopy

We present a novel approach to traction force microscopy (TFM) for studying the locomotion of 10 cm long walking centipedes on soft substrates. Leveraging the remarkable elasticity and ductility of kudzu starch gels, we use them as a deformable gel substrate, providing resilience against the centipedes' sharp leg tips. By optimizing fiducial marker size and density and fine-tuning imaging conditions, we enhance measurement accuracy. Our TFM investigation reveals traction forces along the centipede's longitudinal axis that effectively counterbalance inertial forces within the 0-10 mN range, providing the first report of non-vanishing inertia forces in TFM studies. Interestingly, we observe waves of forces propagating from the head to the tail of the centipede, corresponding to its locomotion speed. Furthermore, we discover a characteristic cycle of leg clusters engaging with the substrate: forward force (friction) upon leg tip contact, backward force (traction) as the leg pulls the substrate while stationary, and subsequent forward force as the leg tip detaches to reposition itself in the anterior direction. This work opens perspectives for TFM applications in ethology, tribology and robotics.

Field Guide to Traction Force Microscopy

Introduction

Traction force microscopy (TFM) is a widely used technique to measure cell contractility on compliant substrates that mimic the stiffness of human tissues. For every step in a TFM workflow, users make choices which impact the quantitative results, yet many times the rationales and consequences for making these decisions are unclear. We have found few papers which show the complete experimental and mathematical steps of TFM, thus obfuscating the full effects of these decisions on the final output.

Methods

Therefore, we present this "Field Guide" with the goal to explain the mathematical basis of common TFM methods to practitioners in an accessible way. We specifically focus on how errors propagate in TFM workflows given specific experimental design and analytical choices.

Results

We cover important assumptions and considerations in TFM substrate manufacturing, substrate mechanical properties, imaging techniques, image processing methods, approaches and parameters used in calculating traction stress, and data-reporting strategies.

Conclusions

By presenting a conceptual review and analysis of TFM-focused research articles published over the last two decades, we provide researchers in the field with a better understanding of their options to make more informed choices when creating TFM workflows depending on the type of cell being studied. With this review, we aim to empower experimentalists to quantify cell contractility with confidence.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00801-6.

Selective Suppression of Integrin-Ligand Binding by Single Molecular Tension Probes Mediates Directional Cell Migration

Cell migration interacting with continuously changing microenvironment, is one of the most essential cellular functions, participating in embryonic development, wound repair, immune response, and cancer metastasis. The migration process is finely tuned by integrin-mediated binding to ligand molecules. Although numerous biochemical pathways orchestrating cell adhesion and motility are identified, how subcellular forces between the cell and extracellular matrix regulate intracellular signaling for cell migration remains unclear. Here, it is showed that a molecular binding force across integrin subunits determines directional migration by regulating tension-dependent focal contact formation and focal adhesion kinase phosphorylation. Molecular binding strength between integrin αvβ3 and fibronectin is precisely manipulated by developing molecular tension probes that control the mechanical tolerance applied to cell-substrate interfaces. This data reveals that integrin-mediated molecular binding force reduction suppresses cell spreading and focal adhesion formation, attenuating the focal adhesion kinase (FAK) phosphorylation that regulates the persistence of cell migration. These results further demonstrate that manipulating subcellular binding forces at the molecular level can recapitulate differential cell migration in response to changes of substrate rigidity that determines the physical condition of extracellular microenvironment. Novel insights is provided into the subcellular mechanics behind global mechanical adaptation of the cell to surrounding tissue environments featuring distinct biophysical signatures.

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

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

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.

Quantifying local stiffness and forces in soft biological tissues using droplet optical microcavities

Mechanical properties of biological tissues fundamentally underlie various biological processes and noncontact, local, and microscopic methods can provide fundamental insights. Here, we present an approach for quantifying the local mechanical properties of biological materials at the microscale, based on measuring the spectral shifts of the optical resonances in droplet microcavities. Specifically, the developed method allows for measurements of deformations in dye-doped oil droplets embedded in soft materials or biological tissues with an error of only 1 nm, which in turn enables measurements of anisotropic stress inside tissues as small as a few pN/μm2. Furthermore, by applying an external strain, Young's modulus can be measured in the range from 1 Pa to 35 kPa, which covers most human soft tissues. Using multiple droplet microcavities, our approach could enable mapping of stiffness and forces in inhomogeneous soft tissues and could also be applied to in vivo and single-cell experiments. The developed method can potentially lead to insights into the mechanics of biological tissues.

Electrochemical DNA-based sensors for measuring cell-generated forces

Mechanical forces play an important role in cellular communication and signaling. We developed in this study novel electrochemical DNA-based force sensors for measuring cell-generated adhesion forces. Two types of DNA probes, i.e., tension gauge tether and DNA hairpin, were constructed on the surface of a smartphone-based electrochemical device to detect piconewton-scale cellular forces at tunable levels. Upon experiencing cellular tension, the unfolding of DNA probes induces the separation of redox reporters from the surface of the electrode, which results in detectable electrochemical signals. Using integrin-mediated cell adhesion as an example, our results indicated that these electrochemical sensors can be used for highly sensitive, robust, simple, and portable measurement of cell-generated forces.

Viscoelastic confinement induces periodic flow reversals in active nematics

We use linear stability analysis and hybrid lattice Boltzmann simulations to study the dynamical behavior of an active nematic confined in a channel made of viscoelastic material. We find that the quiescent, ordered active nematic is unstable above a critical activity. The transition is to a steady flow state for high elasticity of the channel surroundings. However, below a threshold elastic modulus, the system produces spontaneous oscillations with periodic flow reversals. We provide a phase diagram that highlights the region where time-periodic oscillations are observed and explain how they are produced by the interplay of activity and viscoelasticity. Our results suggest experiments to study the role of viscoelastic confinement in the spatiotemporal organization and control of active matter.

Polycrystallinity Enhances Stress Buildup around Ice

Damage caused by freezing wet, porous materials is a widespread problem but is hard to predict or control. Here, we show that polycrystallinity significantly speeds up the stress buildup process that underpins this damage. Unfrozen water in grain-boundary grooves feeds ice growth at temperatures below the freezing temperature, leading to fast stress buildup. These stresses can build up to levels that can easily break many brittle materials. The dynamics of the process are very variable, which we ascribe to local differences in ice-grain orientation and to the surprising mobility of many grooves-which further accelerates stress buildup. Our Letter will help understand how freezing damage occurs and in developing accurate models and effective damage-mitigation strategies.

Using Biosensors to Study Organoids, Spheroids and Organs-on-a-Chip: A Mechanobiology Perspective

The increasing popularity of 3D cell culture models is being driven by the demand for more in vivo-like conditions with which to study the biochemistry and biomechanics of numerous biological processes in health and disease. Spheroids and organoids are 3D culture platforms that self-assemble and regenerate from stem cells, tissue progenitor cells or cell lines, and that show great potential for studying tissue development and regeneration. Organ-on-a-chip approaches can be used to achieve spatiotemporal control over the biochemical and biomechanical signals that promote tissue growth and differentiation. These 3D model systems can be engineered to serve as disease models and used for drug screens. While culture methods have been developed to support these 3D structures, challenges remain to completely recapitulate the cell-cell and cell-matrix biomechanical interactions occurring in vivo. Understanding how forces influence the functions of cells in these 3D systems will require precise tools to measure such forces, as well as a better understanding of the mechanobiology of cell-cell and cell-matrix interactions. Biosensors will prove powerful for measuring forces in both of these contexts, thereby leading to a better understanding of how mechanical forces influence biological systems at the cellular and tissue levels. Here, we discussed how biosensors and mechanobiological research can be coupled to develop accurate, physiologically relevant 3D tissue models to study tissue development, function, malfunction in disease, and avenues for disease intervention.

In situ measurement of viscoelastic properties of cellular monolayers via graphene strain sensing of elastohydrodynamic phenomena

Recent advances recognize that the viscoelastic properties of epithelial structures play important roles in biology and disease modeling. However, accessing the viscoelastic properties of multicellular structures in mechanistic or drug-screening applications has challenges in repeatability, accuracy, and practical implementation. Here, we present a microfluidic platform that leverages elastohydrodynamic phenomena, sensed by strain sensors made from graphene decorated with palladium nanoislands, to measure the viscoelasticity of cellular monolayers in situ, without using chemical labels or specialized equipment. We demonstrate platform utility with two systems: cell dissociation following trypsinization, where viscoelastic properties change over minutes, and epithelial-to-mesenchymal transition, where changes occur over days. These cellular events could only be resolved with our platform's higher resolution: viscoelastic relaxation time constants of λ = 14.5 ± 0.4 s-1 for intact epithelial monolayers, compared to λ = 13.4 ± 15.0 s-1 in other platforms, which represents a 30-fold improvement. By rapidly assessing combined contributions from cell stiffness and intercellular interactions, we anticipate that the platform will hasten the translation of new mechanical biomarkers.

Enhancing robustness, precision, and speed of traction force microscopy with machine learning

Traction patterns of adherent cells provide important information on their interaction with the environment, cell migration, or tissue patterns and morphogenesis. Traction force microscopy is a method aimed at revealing these traction patterns for adherent cells on engineered substrates with known constitutive elastic properties from deformation information obtained from substrate images. Conventionally, the substrate deformation information is processed by numerical algorithms of varying complexity to give the corresponding traction field via solution of an ill-posed inverse elastic problem. We explore the capabilities of a deep convolutional neural network as a computationally more efficient and robust approach to solve this inversion problem. We develop a general purpose training process based on collections of circular force patches as synthetic training data, which can be subjected to different noise levels for additional robustness. The performance and the robustness of our approach against noise is systematically characterized for synthetic data, artificial cell models, and real cell images, which are subjected to different noise levels. A comparison with state-of-the-art Bayesian Fourier transform traction cytometry reveals the precision, robustness, and speed improvements achieved by our approach, leading to an acceleration of traction force microscopy methods in practical applications.

Mechanical control of the mammalian circadian clock via YAP/TAZ and TEAD

Autonomous circadian clocks exist in nearly every mammalian cell type. These cellular clocks are subjected to a multilayered regulation sensitive to the mechanochemical cell microenvironment. Whereas the biochemical signaling that controls the cellular circadian clock is increasingly well understood, mechanisms underlying regulation by mechanical cues are largely unknown. Here we show that the fibroblast circadian clock is mechanically regulated through YAP/TAZ nuclear levels. We use high-throughput analysis of single-cell circadian rhythms and apply controlled mechanical, biochemical, and genetic perturbations to study the expression of the clock gene Rev-erbα. We observe that Rev-erbα circadian oscillations are disrupted with YAP/TAZ nuclear translocation. By targeted mutations and overexpression of YAP/TAZ, we show that this mechanobiological regulation, which also impacts core components of the clock such as Bmal1 and Cry1, depends on the binding of YAP/TAZ to the transcriptional effector TEAD. This mechanism could explain the impairment of circadian rhythms observed when YAP/TAZ activity is upregulated, as in cancer and aging.

Biomembrane force probe (BFP): Design, advancements, and recent applications to live-cell mechanobiology

Mechanical forces play a vital role in biological processes at molecular and cellular levels, significantly impacting various diseases such as cancer, cardiovascular disease, and COVID-19. Recent advancements in dynamic force spectroscopy (DFS) techniques have enabled the application and measurement of forces and displacements with high resolutions, providing crucial insights into the mechanical pathways underlying these diseases. Among DFS techniques, the biomembrane force probe (BFP) stands out for its ability to measure bond kinetics and cellular mechanosensing with pico-newton and nano-meter resolutions. Here, a comprehensive overview of the classical BFP-DFS setup is presented and key advancements are emphasized, including the development of dual biomembrane force probe (dBFP) and fluorescence biomembrane force probe (fBFP). BFP-DFS allows us to investigate dynamic bond behaviors on living cells and significantly enhances the understanding of specific ligand-receptor axes mediated cell mechanosensing. The contributions of BFP-DFS to the fields of cancer biology, thrombosis, and inflammation are delved into, exploring its potential to elucidate novel therapeutic discoveries. Furthermore, future BFP upgrades aimed at improving output and feasibility are anticipated, emphasizing its growing importance in the field of cell mechanobiology. Although BFP-DFS remains a niche research modality, its impact on the expanding field of cell mechanobiology is immense.

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.

Mapping mechanical stress in curved epithelia of designed size and shape

The function of organs such as lungs, kidneys and mammary glands relies on the three-dimensional geometry of their epithelium. To adopt shapes such as spheres, tubes and ellipsoids, epithelia generate mechanical stresses that are generally unknown. Here we engineer curved epithelial monolayers of controlled size and shape and map their state of stress. We design pressurized epithelia with circular, rectangular and ellipsoidal footprints. We develop a computational method, called curved monolayer stress microscopy, to map the stress tensor in these epithelia. This method establishes a correspondence between epithelial shape and mechanical stress without assumptions of material properties. In epithelia with spherical geometry we show that stress weakly increases with areal strain in a size-independent manner. In epithelia with rectangular and ellipsoidal cross-section we find pronounced stress anisotropies that impact cell alignment. Our approach enables a systematic study of how geometry and stress influence epithelial fate and function in three-dimensions.

Contact Guidance Drives Upward Cellular Migration at the Mesoscopic Scale

Introduction

Cancer metastasis is associated with increased cancer incidence, recurrence, and mortality. The role of cell contact guidance behaviors in cancer metastasis has been recognized but has not been elucidated yet.

Methods

The contact guidance behavior of cancer cells in response to topographical constraints is identified using microgrooved substrates with varying dimensions at the mesoscopic scale. Then, the cell morphology is determined to quantitatively analyze the effects of substrate dimensions on cells contact guidance. Cell density and migrate velocity signatures within the cellular population are determined using time-lapse phase-contrast microscopy. The effect of soluble factors concentration is determined by culturing cells upside down. Then, the effect of cell-substrate interaction on cell migration is investigated using traction force microscopy.

Results

With increasing depth and decreasing groove width, cell elongation and alignment are enhanced, while cell spreading is inhibited. Moreover, cells display preferential distribution on the ridges, which is found to be more pronounced with increasing depth and groove width. Determinations of cell density and migration velocity signatures reveal that the preferential distribution on ridges is caused by cell upward migration. Combined with traction force measurement, we find that migration toward ridges is governed by different cell-substrate interactions between grooves and ridges caused by geometrical constraints. Interestingly, the upward migration of cells at the mesoscopic scale is driven by entropic maximization.

Conclusions

The mesoscopic cell contact guidance mechanism based on the entropic force driven theory provides basic support for the study of cell alignment and migration along healthy tissues with varying size, thereby aiding in the prediction of cancer metastasis.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-023-00766-y.

Reformulating Optical Flow to Solve Image-Based Inverse Problems and Quantify Uncertainty

From meteorology to medical imaging and cell mechanics, many scientific domains use inverse problems (IPs) to extract physical measurements from image movement. To this end, motion estimation methods such as optical flow (OF) pre-process images into motion data to feed the IP, which then inverts for the measurements through a physical model. However, this combined OFIP pipeline exacerbates the ill-posedness inherent to each technique, propagating errors and preventing uncertainty quantification. We introduce a Bayesian PDE-constrained framework that transforms visual information directly into physical measurements in the context of probability distributions. The posterior mean is a constrained IP that tracks brightness while satisfying the physical model, thereby translating the aperture problem from the motion to the underlying physics; whereas the posterior covariance derives measurement error out of image noise. As we illustrate with traction force microscopy, our approach offers several advantages: more accurate reconstructions; unprecedented flexibility in experiment design (e.g., arbitrary boundary conditions); and the exclusivity of measurement error, central to empirical science, yet still unavailable under the OFIP strategy.

4D Force Detection of Cell Adhesion and Contractility

Mechanical signals establish two-way communication between mammalian cells and their environment. Cells contacting a surface exert forces via contractility and transmit them at the areas of focal adhesions. External stimuli, such as compressive and pulling forces, typically affect the adhesion-free cell surface. Here, we demonstrate the collaborative employment of Fluidic Force Microscopy and confocal Traction Force Microscopy supported by the Cellogram solver to enable a powerful integrated force probing approach, where controlled vertical forces are applied to the free surface of individual cells, while the concomitant deformations are used to map their transmission to the substrate. Force transmission across human cells is measured with unprecedented temporal and spatial resolution, enabling the investigation of the cellular mechanisms involved in the adaptation, or maladaptation, to external mechanical stimuli. Altogether, the system enables facile and precise force interrogation of individual cells, with the capacity to perform population-based analysis.

Automated, high temporal resolution mechanics measurements during incubation of contractile tissues

Muscle tissue mechanics and contractility measurements have a great advantage over cultured cell level experiments as their mechanical and contractile properties are much closer to in vivo tissue properties. However, tissue level experiments cannot be combined with incubation with the same time resolution and consistency as cell culture studies. Here we present a system in which contractile tissues can be incubated for days while intermittently being tested for their mechanical and contractile properties. A two-chamber system was developed with control of temperature in the outer chamber and CO₂ and humidity control in the inner, sterile chamber. Incubation medium, to which biologically active components may be added, is reused after each mechanics test to preserve both added and released components. Mechanics and contractility are measured in a different medium to which, through a high accuracy syringe pump, up to 6 different agonists in a 100-fold dose range can be added. The whole system can be operated through fully automated protocols from a personal computer. Testing data shows accurate maintenance of temperature, CO₂ and relative humidity at pre-set levels. Equine trachealis smooth muscle tissues tested in the system showed no signs of infection after 72 h with incubation medium replacement every 24 h. Methacholine dosing and electrical field stimulation every 4 h showed consistent responses. In conclusion, the developed system is a great improvement on the manual incubation techniques being used thus far, improving on time resolution, repeatability and robustness, while reducing contamination risk and tissue damage from repeated handling.

In vitro human cell-based models to study airway remodeling in asthma

Airway remodeling, as a predominant characteristic of asthma, refers to the structural changes that occurred both in the large and small airways. These pathological changes not only contribute to airway hyperresponsiveness and airway obstruction, but also predict poor outcomes of patients. In vitro models are the alternatives to animal models that facilitate airway remodeling research. Current approaches to mimic airway remodeling in vitro include mono cultures of cell lines and primary cells that are derived from the respiratory tract, and co-culture systems that consist of different cell subpopulations. Moreover, recent advances in microfluid chips and organoids show promise in simulating the complex architecture and functionality of native organs. According, they enable highly physiological-relevant investigations of human diseases in vitro. Here we aim to detail the current human cell-based models regarding their key pros and cons, and to discuss how they may be used to facilitate our understanding of airway remodeling in asthma.

Single-Cell Quantification of the Mechanical Stability of Cell-Cell Adherens Junction Using Glass Micropipettes

Micropipette-based methods have been widely used for the manipulation of cells and characterization of the mechanical properties at the cell or tissue level. Here, we introduce the glass micropipette-based mechanical assays for the stability of cell-cell adhesion. A probing microbead coated with specific adhesion ligands, captured by a glass micropipette, is manipulated to form the adhesion complexes with the corresponding receptors on a single cell. Once the cell is moving away from the micropipette, forces are generated from 20 pN to 100 nN to the adhesion complexes, which are quantified in real-time based on the bending of the glass micropipette. We specifically emphasize the principle and method to probe the rupturing forces of the adhesion complexes at controlled force loading rates, the ligand coating on the probe microbeads, the force calibration of the glass micropipette, and the applications of the method to probe the E-cadherin-based cell-cell adhesions. The principles can be broadly applied to other cell adhesions such as cell-matrix adhesions, neuronal synapses, and bacterial-cell adhesions.

Mechanochemical subcellular-element model of crawling cells

Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.

Trans-epithelial fluid flow and mechanics of epithelial morphogenesis

Active fluid transport across epithelial monolayers is emerging as a major driving force of tissue morphogenesis in a variety of healthy and diseased systems, as well as during embryonic development. Cells use directional transport of ions and osmotic gradients to drive fluid flow across the cell surface, in the process also building up fluid pressure. The basic physics of this process is described by the osmotic engine model, which also underlies actin-independent cell migration. Recently, the trans-epithelial fluid flux and the hydraulic pressure gradient have been explicitly measured for a variety of cellular and tissue model systems across various species. For the kidney, it was shown that tubular epithelial cells behave as active mechanical fluid pumps: the trans-epithelial fluid flux depends on the hydraulic pressure difference across the epithelial layer. When a stall pressure is reached, the fluid flux vanishes. Hydraulic forces generated from active fluid pumping are important in tissue morphogenesis and homeostasis, and could also underlie multiple morphogenic events seen in other developmental contexts. In this review, we highlight findings that examined the role of trans-epithelial fluid flux and hydraulic pressure gradient in driving tissue-scale morphogenesis. We also review organ pathophysiology due to impaired fluid pumping and the loss of hydraulic pressure sensing at the cellular scale. Finally, we draw an analogy between cellular fluidic pumps and a connected network of water pumps in a city. The dynamics of fluid transport in an active and adaptive network is determined globally at the systemic level, and transport in such a network is best when each pump is operating at its optimal efficiency.

Hydrostatic pressure as a driver of cell and tissue morphogenesis

Morphogenesis, the process by which tissues develop into functional shapes, requires coordinated mechanical forces. Most current literature ascribes contractile forces derived from actomyosin networks as the major driver of tissue morphogenesis. Recent works from diverse species have shown that pressure derived from fluids can generate deformations necessary for tissue morphogenesis. In this review, we discuss how hydrostatic pressure is generated at the cellular and tissue level and how the pressure can cause deformations. We highlight and review findings demonstrating the mechanical roles of pressures from fluid-filled lumens and viscous gel-like components of the extracellular matrix. We also emphasise the interactions and mechanochemical feedbacks between extracellular pressures and tissue behaviour in driving tissue remodelling. Lastly, we offer perspectives on the open questions in the field that will further our understanding to uncover new principles of tissue organisation during development.

Unraveling the Mechanobiology Underlying Traumatic Brain Injury with Advanced Technologies and Biomaterials

Traumatic brain injury (TBI) is a worldwide health and socioeconomic problem, associated with prolonged and complex neurological aftermaths, including a variety of functional deficits and neurodegenerative disorders. Research on the long-term effects has highlighted that TBI shall be regarded as a chronic health condition. The initiation and exacerbation of TBI involve a series of mechanical stimulations and perturbations, accompanied by mechanotransduction events within the brain tissues. Mechanobiology thus offers a unique perspective and likely promising approach to unravel the underlying molecular and biochemical mechanisms leading to neural cells dysfunction after TBI, which may contribute to the discovery of novel targets for future clinical treatment. This article investigates TBI and the subsequent brain dysfunction from a lens of neuromechanobiology. Following an introduction, the mechanobiological insights are examined into the molecular pathology of TBI, and then an overview is given of the latest research technologies to explore neuromechanobiology, with particular focus on microfluidics and biomaterials. Challenges and prospects in the current field are also discussed. Through this article, it is hoped that extensive technical innovation in biomedical devices and materials can be encouraged to advance the field of neuromechanobiology, paving potential ways for the research and rehabilitation of neurotrauma and neurological diseases.

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.

Capillary pressure mediated long-term dynamics of thin soft films

HYPOTHESIS

The conventional solid-solid contact is well studied in the literature. However, a number of practical applications, such as adhesive patches and biomimetic surfaces, require a much deeper understanding of soft contact where there is a distinct time-dependent adhesion behavior due to the dual-phase structure (solids and liquids). To understand this, currently existing solid-solid contact behavior is extrapolated to soft contact, wherein the size-effect of the gel film and the preload are typically neglected. When introducing the finite-size effect and preload, gels could experience distinctive long-term contact dynamics in contact with another material.

EXPERIMENTS

We reconstruct the evolving surface profile of the gel films intercalated between a glass sphere and glass slide using dual wavelength-reflection interference contrast microscopy. The macro-sized glass sphere compresses the gel. The indentation depth is comparable to the gel film thickness, wherein the conventional contact theories are inapplicable.

FINDINGS

The gel surface experiences two deformation stages. The natural preload and elastic force develop the contact area in the early state. In the later state, the viscous free molecules of the gel develop the ridge. We discover that the residual surface stress relaxes over 85 hr. Our findings on the long-term gel deformation provide a new perspective on soft adhesion, from developing soft adhesives to understanding biological tissues.

Structure of propagating high-stress fronts in a shear-thickening suspension

We report direct measurements of spatially resolved stress at the boundary of a shear-thickening cornstarch suspension revealing persistent regions of high local stress propagating in the flow direction at the speed of the top boundary. The persistence of these propagating fronts enables precise measurements of their structure, including the profile of boundary stress measured by boundary stress microscopy (BSM) and the nonaffine velocity of particles at the bottom boundary of the suspension measured by particle image velocimetry (PIV). In addition, we directly measure the relative flow between the particle phase and the suspending fluid (fluid migration) and find the migration is highly localized to the fronts and changes direction across the front, indicating that the fronts are composed of a localized region of high dilatant pressure and low particle concentration. The magnitude of the flow indicates that the pore pressure difference driving the fluid migration is comparable to the critical shear stress for the onset of shear thickening. The propagating fronts fully account for the increase in viscosity with applied stress reported by the rheometer and are consistent with the existence of a stable jammed region in contact with one boundary of the system that generates a propagating network of percolated frictional contacts spanning the gap between the rheometer plates and producing strong localized dilatant pressure.

Stress accumulation by confined ice in a temperature gradient

When materials freeze, they often undergo damage due to ice growth. Although this damage is commonly ascribed to the volumetric expansion of water upon freezing, it is usually driven by the flow of water toward growing ice crystals that feeds their growth. The freezing of this additional water can cause a large buildup of stress. Here, we demonstrate a technique for characterizing this stress buildup with unprecedented spatial resolution. We create a stable ice-water interface in a controlled temperature gradient and measure the deformation of the confining boundary. Analysis of the deformation field reveals stresses applied to the boundary with [Formula: see text](micrometers) spatial resolution. Globally, stresses increase steadily over time as liquid water is transported to more deeply undercooled regions. Locally, stresses increase until ice growth is stalled by the confining stresses. Importantly, we find a strong localization of stresses, which significantly increases the likelihood of damage caused by the presence of ice, even in apparently benign freezing situations. Ultimately, the limiting stress that the ice exerts is proportional to the local undercooling, in accordance with the Clapeyron equation, which describes the equilibrium between a stressed solid and its melt. Our results are closely connected to the condensation pressure during liquid-liquid phase separation and the crystallization pressure for growing crystals. Thus, they are highly relevant in fields ranging from cryopreservation and frost heave to food science, rock weathering, and art conservation.

May the force be with your (immune) cells: an introduction to traction force microscopy in Immunology

For more than a couple of decades now, “force” has been recognized as an important physical parameter that cells employ to adapt to their microenvironment. Whether it is externally applied, or internally generated, cells use force to modulate their various actions, from adhesion and migration to differentiation and immune function. T lymphocytes use such mechano-sensitivity to decipher signals when recognizing cognate antigens presented on the surface of antigen presenting cells (APCs), a critical process in the adaptive immune response. As such, many techniques have been developed and used to measure the forces felt/exerted by these small, solitary and extremely reactive cells to decipher their influence on diverse T cell functions, primarily activation. Here, we focus on traction force microscopy (TFM), in which a deformable substrate, coated with the appropriate molecules, acts as a force sensor on the cellular scale. This technique has recently become a center of interest for many groups in the “ImmunoBiophysics” community and, as a consequence, has been subjected to refinements for its application to immune cells. Here, we present an overview of TFM, the precautions and pitfalls, and the most recent developments in the context of T cell immunology.

Cell-Matrix Elastocapillary Interactions Drive Pressure-based Wetting of Cell Aggregates

Cell-matrix interfacial energies and the energies of matrix deformations may be comparable on cellular length-scales, yet how capillary effects influence tis sue shape and motion are unknown. In this work, we induce wetting (spreading and migration) of cell aggregates, as models of active droplets onto adhesive substrates of varying elasticity and correlate the dynamics of wetting to the balance of interfacial tensions. Upon wetting rigid substrates, cell-substrate tension drives outward expansion of the monolayer. By contrast, upon wetting compliant substrates, cell substrate tension is attenuated and aggregate capillary forces contribute to internal pressures that drive expansion. Thus, we show by experiments, data-driven modeling and computational simulations that myosin-driven 'active elasto-capillary' effects enable adaptation of wetting mechanisms to substrate rigidity and introduce a novel, pressure-based mechanism for guiding collective cell motion.

Epithelial Cell-Like Elasticity Modulates Actin-Dependent E-Cadherin Adhesion Organization

E-cadherin adhesions are essential for cell-to-cell cohesion and mechanical coupling between epithelial cells and reside in a microenvironment that comprises the adjoining epithelial cells. While E-cadherin has been shown to be a mechanosensor, it is unknown if E-cadherin adhesions can differentially sense stiffness within the range of that of epithelial cells. A survey of literature shows that epithelial cells' Young's moduli of elasticity lie predominantly in the sub-kPa to few-kPa range, with cancer cells often being softer than noncancerous ones. Here, we devised oriented E-cadherin-coated soft silicone substrates with sub-kPa or few-kPa elasticity but with similar viscous moduli and found that E-cadherin adhesions differentially organize depending on the magnitude of epithelial cell-like elasticity. Our results show that the actin cytoskeleton organizes E-cadherin adhesions in two ways─by supporting irregularly shaped adhesions at localized regions of high actin density and linear shaped adhesions at the end of linear actin bundles. Linearly shaped E-cadherin adhesions associated with radially oriented actin─but not irregularly shaped E-cadherin adhesions associated with circumferential actin foci─were much more numerous on 2.4 kPa E-cadherin substrates compared to 0.3 kPa E-cadherin substrates. However, the total amount of E-cadherin in both types of adhesions taken together was similar on the 0.3 and 2.4 kPa E-cadherin substrates across many cells. Our results show how the distribution of E-cadherin adhesions, supported by actin density and architecture, is modulated by epithelial cell-like elasticity and have significant implications for disease states like carcinomas characterized by altered epithelial cell elasticity.

Integrin molecular tension required for focal adhesion maturation and YAP nuclear translocation

Focal adhesions (FAs) provide the cells linkages to extracellular matrix (ECM) at sites of integrins binding and transmit mechanical forces between the ECM and the actin cytoskeleton. Cells sense and respond to physical stimuli from their surrounding environment through the activation of mechanosensitive signaling pathways, a process called mechanotransduction. In this study, we used RGD-peptide conjugated DNA tension gauge tethers (TGTs) with different tension tolerance (T_tol) to determine the molecular forces required for FA maturation in different sizes and YAP nuclear translocation. We found that the limitation of FA sizes in cells seeded on TGTs with different T_tol were less than 1 μm, 2 μm, 3 μm, and 6 μm for T_tol values of 43 pN, 50 pN, 54 pN, and 56 pN, respectively. This suggests that the molecular tension across integrins increases gradually as FA size increases throughout FA maturation. For YAP nuclear translocation, significant YAP nuclear localization was observed only in the cells seeded on the TGTs with T_tol ≥ 54 pN, but not on TGTs with T_tol ≤ 50 pN, suggesting a threshold of molecular force across integrins for YAP nuclear translocation lies in the range of 50 pN–54 pN.

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Defining forces required for FA maturation and YAP nuclear translocation.

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Integrin tension enhances gradually with the increase of FA size.

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Forces required for YAP nuclear translocation lies in the range of 50–54 pN.

Effective Force Generation During Mammalian Cell Migration Under Different Molecular and Physical Mechanisms

We have developed much understanding of actin-driven cell migration and the forces that propel cell motility. However, fewer studies focused on estimating the effective forces generated by migrating cells. Since cells in vivo are exposed to complex physical environments with various barriers, understanding the forces generated by cells will provide insights into how cells manage to navigate challenging environments. In this work, we use theoretical models to discuss actin-driven and water-driven cell migration and the effect of cell shapes on force generation. The results show that the effective force generated by actin-driven cell migration is proportional to the rate of actin polymerization and the strength of focal adhesion; the energy source comes from the actin polymerization against the actin network pressure. The effective force generated by water-driven cell migration is proportional to the rate of active solute flux and the coefficient of external hydraulic resistance; the energy sources come from active solute pumping against the solute concentration gradient. The model further predicts that the actin network distribution is mechanosensitive and the presence of globular actin helps to establish a biphasic cell velocity in the strength of focal adhesion. The cell velocity and effective force generation also depend on the cell shape through the intracellular actin flow field.

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.

A primer to traction force microscopy

Traction force microscopy (TFM) has emerged as a versatile technique for the measurement of single-cell-generated forces. TFM has gained wide use among mechanobiology laboratories, and several variants of the original methodology have been proposed. However, issues related to the experimental setup and, most importantly, data analysis of cell traction datasets may restrain the adoption of TFM by a wider community. In this review, we summarize the state of the art in TFM-related research, with a focus on the analytical methods underlying data analysis. We aim to provide the reader with a friendly compendium underlying the potential of TFM and emphasizing the methodological framework required for a thorough understanding of experimental data. We also compile a list of data analytics tools freely available to the scientific community for the furtherance of knowledge on this powerful technique.

Biophysical Approaches for Applying and Measuring Biological Forces

Over the past decades, increasing evidence has indicated that mechanical loads can regulate the morphogenesis, proliferation, migration, and apoptosis of living cells. Investigations of how cells sense mechanical stimuli or the mechanotransduction mechanism is an active field of biomaterials and biophysics. Gaining a further understanding of mechanical regulation and depicting the mechanotransduction network inside cells require advanced experimental techniques and new theories. In this review, the fundamental principles of various experimental approaches that have been developed to characterize various types and magnitudes of forces experienced at the cellular and subcellular levels are summarized. The broad applications of these techniques are introduced with an emphasis on the difficulties in implementing these techniques in special biological systems. The advantages and disadvantages of each technique are discussed, which can guide readers to choose the most suitable technique for their questions. A perspective on future directions in this field is also provided. It is anticipated that technical advancement can be a driving force for the development of mechanobiology.

Molecular Tension Probes to Quantify Cell-Generated Mechanical Forces

Living cells generate, sense, and respond to mechanical forces through their interaction with neighboring cells or extracellular matrix, thereby regulating diverse cellular processes such as growth, motility, differentiation, and immune responses. Dysregulation of mechanosensitive signaling pathways is found associated with the development and progression of various diseases such as cancer. Yet, little is known about the mechanisms behind mechano-regulation, largely due to the limited availability of tools to study it at the molecular level. The recent development of molecular tension probes allows measurement of cellular forces exerted by single ligandreceptor interaction, which has helped in revealing the hitherto unknown mechanistic details of various mechanosensitive processes in living cells. Here, we provide an introductory overview of two methods based on molecular tension probes, tension gauge tether (TGT), and molecular tension fluorescence microscopy (MTFM). TGT utilizes the irreversible rupture of double-stranded DNA tether upon application of force in the piconewton (pN) range, whereas MTFM utilizes the reversible extension of molecular springs such as polymer or single-stranded DNA hairpin under applied pN forces. Specifically, the underlying principle of how molecular tension probes measure cell-generated mechanical forces and their applications to mechanosensitive biological processes are described.

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.

Coupling traction force patterns and actomyosin wave dynamics reveals mechanics of cell motion

Motile cells can use and switch between different modes of migration. Here, we use traction force microscopy and fluorescent labeling of actin and myosin to quantify and correlate traction force patterns and cytoskeletal distributions in Dictyostelium discoideum cells that move and switch between keratocyte-like fan-shaped, oscillatory, and amoeboid modes. We find that the wave dynamics of the cytoskeletal components critically determine the traction force pattern, cell morphology, and migration mode. Furthermore, we find that fan-shaped cells can exhibit two different propulsion mechanisms, each with a distinct traction force pattern. Finally, the traction force patterns can be recapitulated using a computational model, which uses the experimentally determined spatiotemporal distributions of actin and myosin forces and a viscous cytoskeletal network. Our results suggest that cell motion can be generated by friction between the flow of this network and the substrate.