Traction Force Microscopy Methods Research Articles

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.

Extended mechanical force measurements using structured illumination microscopy.

Quantifying cell generated mechanical forces is key to furthering our understanding of mechanobiology. Traction force microscopy (TFM) is one of the most broadly applied force probing technologies, but its sensitivity is strictly dependent on the spatio-temporal resolution of the underlying imaging system. In previous works, it was demonstrated that increased sampling densities of cell derived forces permitted by super-resolution fluorescence imaging enhanced the sensitivity of the TFM method. However, these recent advances to TFM based on super-resolution techniques were limited to slow acquisition speeds and high illumination powers. Here, we present three novel TFM approaches that, in combination with total internal reflection, structured illumination microscopy and astigmatism, improve the spatial and temporal performance in either two-dimensional or three-dimensional mechanical force quantification, while maintaining low illumination powers. These three techniques can be straightforwardly implemented on a single optical set-up offering a powerful platform to provide new insights into the physiological force generation in a wide range of biological studies. This article is part of the Theo Murphy meeting issue 'Super-resolution structured illumination microscopy (part 1)'.

Computational 4D-OCM for label-free imaging of collective cell invasion and force-mediated deformations in collagen

Traction force microscopy (TFM) is an important family of techniques used to measure and study the role of cellular traction forces (CTFs) associated with many biological processes. However, current standard TFM methods rely on imaging techniques that do not provide the experimental capabilities necessary to study CTFs within 3D collective and dynamic systems embedded within optically scattering media. Traction force optical coherence microscopy (TF-OCM) was developed to address these needs, but has only been demonstrated for the study of isolated cells embedded within optically clear media. Here, we present computational 4D-OCM methods that enable the study of dynamic invasion behavior of large tumor spheroids embedded in collagen. Our multi-day, time-lapse imaging data provided detailed visualizations of evolving spheroid morphology, collagen degradation, and collagen deformation, all using label-free scattering contrast. These capabilities, which provided insights into how stromal cells affect cancer progression, significantly expand access to critical data about biophysical interactions of cells with their environment, and lay the foundation for future efforts toward volumetric, time-lapse reconstructions of collective CTFs with TF-OCM.

Focus on time: dynamic imaging reveals stretch-dependent cell relaxation and nuclear deformation

Among the stimuli to which cells are exposed in vivo, it has been shown that tensile deformations induce specific cellular responses in musculoskeletal, cardiovascular, and stromal tissues. However, the early response of cells to sustained substrate-based stretch has remained elusive because of the short timescale at which it occurs. To measure the tensile mechanical properties of adherent cells immediately after the application of substrate deformations, we have developed a dynamic traction force microscopy method that enables subsecond temporal resolution imaging of transient subcellular events. The system employs a novel, to our knowledge, tracking approach with minimal computational overhead to compensate substrate-based, stretch-induced motion/drift of stretched single cells in real time, allowing capture of biophysical phenomena on multiple channels by fluorescent multichannel imaging on a single camera, thus avoiding the need for beam splitting with the associated loss of light. Using this tool, we have characterized the transient subcellular forces and nuclear deformations of single cells immediately after the application of equibiaxial strain. Our experiments reveal significant differences in the cell relaxation dynamics and in the intracellular propagation of force to the nuclear compartment in cells stretched at different strain rates and exposes the need for time control for the correct interpretation of dynamic cell mechanics experiments.

A Bayesian traction force microscopy method with automated denoising in a user-friendly software package

Adherent biological cells generate traction forces on a substrate that play a central role for migration, mechanosensing, differentiation, and collective behavior. The established method for quantifying this cell–substrate interaction is traction force microscopy (TFM). In spite of recent advancements, inference of the traction forces from measurements remains very sensitive to noise. However, suppression of the noise reduces the measurement accuracy and the spatial resolution, which makes it crucial to select an optimal level of noise reduction. Here, we present a fully automated method for noise reduction and robust, standardized traction-force reconstruction. The method, termed Bayesian Fourier transform traction cytometry, combines the robustness of Bayesian L2 regularization with the computation speed of Fourier transform traction cytometry. We validate the performance of the method with synthetic and real data. The method is made freely available as a software package with a graphical user-interface for intuitive usage. Program summaryProgram Title: Easy-to-use TFM softwareProgram Files doi:http://dx.doi.org/10.17632/229bnpp8rb.1Licensing provisions: GNU General Public License v3.0Programming language: Matlab version R2010b or higherSupplementary material: A user manual for the software and a test data set.Nature of problem: Calculation of the traction forces on the surface of an elastic material from observed displacements.Solution method: Traction forces are efficiently calculated by combining L2 regularization in Fourier space with Bayesian inference of the regularization parameter.

Quantitative reconstruction of time-varying 3D cell forces with traction force optical coherence microscopy

Cellular traction forces (CTFs) play an integral role in both physiological processes and disease, and are a topic of interest in mechanobiology. Traction force microscopy (TFM) is a family of methods used to quantify CTFs in a variety of settings. State-of-the-art 3D TFM methods typically rely on confocal fluorescence microscopy, which can impose limitations on acquisition speed, volumetric coverage, and temporal sampling or coverage. In this report, we present the first quantitative implementation of a new TFM technique: traction force optical coherence microscopy (TF-OCM). TF-OCM leverages the capabilities of optical coherence microscopy and computational adaptive optics (CAO) to enable the quantitative reconstruction of 3D CTFs in scattering media with minute-scale temporal sampling. We applied TF-OCM to quantify CTFs exerted by isolated NIH-3T3 fibroblasts embedded in Matrigel, with five-minute temporal sampling, using images spanning a 500 × 500 × 500 μm3 field-of-view. Due to the reliance of TF-OCM on computational imaging methods, we have provided extensive discussion of the equations, assumptions, and failure modes of these methods. By providing high-throughput, label-free, volumetric imaging in scattering media, TF-OCM is well-suited to the study of 3D CTF dynamics, and may prove advantageous for the study of large cell collectives, such as the spheroid models prevalent in mechanobiology.

Confocal reference free traction force microscopy.

The mechanical wiring between cells and their surroundings is fundamental to the regulation of complex biological processes during tissue development, repair or pathology. Traction force microscopy (TFM) enables determination of the actuating forces. Despite progress, important limitations with intrusion effects in low resolution 2D pillar-based methods or disruptive intermediate steps of cell removal and substrate relaxation in high-resolution continuum TFM methods need to be overcome. Here we introduce a novel method allowing a one-shot (live) acquisition of continuous in- and out-of-plane traction fields with high sensitivity. The method is based on electrohydrodynamic nanodrip-printing of quantum dots into confocal monocrystalline arrays, rendering individually identifiable point light sources on compliant substrates. We demonstrate the undisrupted reference-free acquisition and quantification of high-resolution continuous force fields, and the simultaneous capability of this method to correlatively overlap traction forces with spatial localization of proteins revealed using immunofluorescence methods.

Abstract 18251: Establishment of an in vitro Platform, the Hydrogel Mattress, to Enhance Maturation and Evaluate Contractile Function of Individual hiPSC-CMs

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) have great potential as tools for cell based therapy, disease modeling and drug discovery. However, their contractile properties have not been routinely evaluated; as methods to do so are cumbersome and not easily translated to standard laboratories. We sought to develop a more efficient protocol to evaluate hiPSC-CM mechanical properties, at the single cell level. Individual hiPSC-CMs were cultured on a hydrogel based platform, termed the hydrogel mattress, and their cellular contractile properties were evaluated using video based edge detection (Figure A). We found individual hiPSC-CMs maintained for 5 days on the mattress assumed an elongated shape (Figure B) and exhibited robust, reproducible cell shortening (~10% versus <1% for standard culture). We further found hiPSC-CM cellular contraction and peak cell shortening amplitude was comparable to that of freshly isolated adult rabbit and mouse ventricular CMs (Figure C). In addition, hiPSC-CMs maintained on the mattress exhibited characteristics of mature CMs including action potential waveform, calcium handling and pharmacological response to myofilament calcium sensitizers. We further show a positive correlation with the established traction force microscopy method. We demonstrate the hydrogel mattress platform enables routine characterization and quantification of contractile performance of isolated hiPSC-CMs. This platform can be extended to in vitro disease modeling, drug discovery and drug induced cardiotoxicity testing. Further, the mattress can be easily adapted to virtually any laboratory, thus streamlining cellular mechanical evaluation of individual hiPSC-CMs in vitro.

Three-Dimensional Fourier Monolayer Stress Microscopy

Many important biological processes, such as endothelial mechanotransduction of hemodynamic forces and neutrophil extravasation, involve the transmission of stresses across a cell monolayer. During these processes, the monolayer undergoes both lateral distortion due to the in-plane traction forces generated by the cells, and bending due to the out-of-plane component of the traction forces. However, the contribution of this bending to the monolayer stresses has been neglected in the literature. Here, we present a novel technique to determine monolayer stresses that considers both lateral distortion and bending. To illustrate the method, and to quantify the relative importance of the lateral and bending stresses, we measure the monolayer stresses in micropatterned endothelial cell islands of varying sizes and shapes. The cell islands are cultured on flexible polyacrylamide gels embedded with fluorescent beads, which deform due to traction forces exerted by the cells. We measure the three-dimensional gel deformation using previously established 3D Traction Force Microscopy methods, and recover the monolayer stresses from the measured deformation using Kirchoff-Love thin plate theory. The equations are solved numerically in an efficient manner using a Fourier pseudo-spectral method. The boundary conditions corresponding to the geometry of the cell islands are enforced within the Fourier framework using a relaxation iterative method. Our results indicate that, regardless of island shape, the three-dimensional bending stresses are dominant at the center of the island while the lateral stresses are more important near the island edge. Also, comparing the results from islands of different sizes shows that the relative importance of the bending stresses decreases with island size. These results suggest that it is necessary to resolve bending stresses to accurately determine the monolayer stresses, and reveal that the transmission of forces across cell junctions is three-dimensional and more complex than previously believed.

Cytoskeletal Mechanics Regulating Amoeboid Cell Locomotion.

Migrating cells exert traction forces when moving. Amoeboid cell migration is a common type of cell migration that appears in many physiological and pathological processes and is performed by a wide variety of cell types. Understanding the coupling of the biochemistry and mechanics underlying the process of migration has the potential to guide the development of pharmacological treatment or genetic manipulations to treat a wide range of diseases. The measurement of the spatiotemporal evolution of the traction forces that produce the movement is an important aspect for the characterization of the locomotion mechanics. There are several methods to calculate the traction forces exerted by the cells. Currently the most commonly used ones are traction force microscopy methods based on the measurement of the deformation induced by the cells on elastic substrate on which they are moving. Amoeboid cells migrate by implementing a motility cycle based on the sequential repetition of four phases. In this paper we review the role that specific cytoskeletal components play in the regulation of the cell migration mechanics. We investigate the role of specific cytoskeletal components regarding the ability of the cells to perform the motility cycle effectively and the generation of traction forces. The actin nucleation in the leading edge of the cell, carried by the ARP2/3 complex activated through the SCAR/WAVE complex, has shown to be fundamental to the execution of the cyclic movement and to the generation of the traction forces. The protein PIR121, a member of the SCAR/WAVE complex, is essential to the proper regulation of the periodic movement and the protein SCAR, also included in the SCAR/WAVE complex, is necessary for the generation of the traction forces during migration. The protein Myosin II, an important F-actin cross-linker and motor protein, is essential to cytoskeletal contractility and to the generation and proper organization of the traction forces during migration.

Three-dimensional quantification of cellular traction forces and mechanosensing of thin substrata by fourier traction force microscopy.

We introduce a novel three-dimensional (3D) traction force microscopy (TFM) method motivated by the recent discovery that cells adhering on plane surfaces exert both in-plane and out-of-plane traction stresses. We measure the 3D deformation of the substratum on a thin layer near its surface, and input this information into an exact analytical solution of the elastic equilibrium equation. These operations are performed in the Fourier domain with high computational efficiency, allowing to obtain the 3D traction stresses from raw microscopy images virtually in real time. We also characterize the error of previous two-dimensional (2D) TFM methods that neglect the out-of-plane component of the traction stresses. This analysis reveals that, under certain combinations of experimental parameters (cell size, substratums' thickness and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by neglecting the out-of-plane component of the traction stresses. Finally, we consider the cell's mechanosensing of substratum thickness by 3D traction stresses, finding that, when cells adhere on thin substrata, their out-of-plane traction stresses can reach four times deeper into the substratum than their in-plane traction stresses. It is also found that the substratum stiffness sensed by applying out-of-plane traction stresses may be up to 10 times larger than the stiffness sensed by applying in-plane traction stresses.

Improved-Throughput Traction Microscopy Based on Fluorescence Micropattern for Manual Microscopy

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

Validation of the Boussinesq equation for use in traction field determination

Cell traction force plays an important role in many biological processes. Several traction force microscopy methods have been developed to determine cell traction forces based on the Boussinesq solution. This approach, however, is rooted in a half-space assumption. The purpose of this study was to determine the error induced in the half-space assumption using a finite element method (FEM). It demonstrates that displacement error between the FEM and the Boussinesq equation can be used to measure the accuracy of the Boussinesq equation, although singularity exists in the loading point. For one concentrated force, significant difference between the FEM and the Boussinesq equation occurs in the whole field; this difference decreases with an increase in the plate thickness. However, in the case of the balanced forces, the offset of the balanced forces decreases the errors in the middle area. Overall, this study demonstrates that increasing the thickness of the polyacrylamide gel is important for reducing the error of the Boussinesq equation when determining the displacement field of the gel under loads.

Determining substrate displacement and cell traction fields—a new approach

This paper presents a new approach for the traction force microscopy (TFM) method which determines traction forces exerted by adherent cells on a thin, elastic polyacrylamide gel embedded with fluorescent microbeads. In this enhanced TFM method, a pattern recognition technique is first applied to match the pair of microbead embedded images before and after deformation, which subsequently provides the displacement field of the elastic substrate. Once the displacement field is obtained, the 3-D finite element method (FEM) is used to compute cell traction forces. The new TFM has been applied to determine traction forces of human tendon fibroblasts. Compared to existing TFM methods, the present method has the following advantages: (1) its displacement field obtained is associated with microbead movements; (2) it considers the finite thickness of the thin polyacrylamide gel and is therefore free from the infinite half-space approximation adopted by existing TFM methods; and (3) its computation procedure for determining cell traction forces is fast.