Traction force microscopy by deep learning

Inferring cellular contractile forces and work using deep morphology traction microscopy

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

3D Traction Force Microscopy in Biological Gels: From Single Cells to Multicellular Spheroids

Cell traction force plays a critical role in directing cellular functions, such as proliferation, migration, and differentiation. Current understanding of cell traction force is largely derived from 2D measurements where cells are plated on 2D substrates. However, 2D measurements do not recapitulate a vital aspect of living systems; that is, cells actively remodel their surrounding extracellular matrix (ECM), and the remodeled ECM, in return, can have a profound impact on cell phenotype and traction force generation. This reciprocal adaptivity of living systems is encoded in the material properties of biological gels. In this review, we summarize recent progress in measuring cell traction force for cells embedded within 3D biological gels, with an emphasis on cell-ECM cross talk. We also provide perspectives on tools and techniques that could be adapted to measure cell traction force in complex biochemical and biophysical environments.

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.

Natural Killer Cell Mechanosensing in Solid Tumors

Natural killer (NK) cells, which are an exciting alternative cell source for cancer immunotherapies, must sense and respond to their physical environment to traffic to and eliminate cancer cells. Herein, we review the mechanisms by which NK cells receive mechanical signals and explore recent key findings regarding the impact of the physical characteristics of solid tumors on NK cell functions. Data suggest that different mechanical stresses present in solid tumors facilitate NK cell functions, especially infiltration and degranulation. Moreover, we review recent engineering advances that can be used to systemically study the role of mechanical forces on NK cell activity. Understanding the mechanisms by which NK cells interpret their environment presents potential targets to enhance NK cell immunotherapies for the treatment of solid tumors.

High-resolution assessment of multidimensional cellular mechanics using label-free refractive-index traction force microscopy

A critical requirement for studying cell mechanics is three-dimensional assessment of cellular shapes and forces with high spatiotemporal resolution. Traction force microscopy with fluorescence imaging enables the measurement of cellular forces, but it is limited by photobleaching and a slow acquisition speed. Here, we present refractive-index traction force microscopy (RI-TFM), which simultaneously quantifies the volumetric morphology and traction force of cells using a high-speed illumination scheme with 0.5-Hz temporal resolution. Without labelling, our method enables quantitative analyses of dry-mass distributions and shear (in-plane) and normal (out-of-plane) tractions of single cells on the extracellular matrix. When combined with a constrained total variation-based deconvolution algorithm, it provides 0.55-Pa shear and 1.59-Pa normal traction sensitivity for a 1-kPa hydrogel substrate. We demonstrate its utility by assessing the effects of compromised intracellular stress and capturing the rapid dynamics of cellular junction formation in the spatiotemporal changes in non-planar traction components.

Machine learning interpretable models of cell mechanics from protein images

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. Currently, no systematic strategy exists to infer large-scale physical properties of a cell from its molecular components. This is an obstacle to understanding processes such as cell adhesion and migration. Here, we develop a data-driven modeling pipeline to learn the mechanical behavior of adherent cells. We first train neural networks to predict cellular forces from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion (FA) protein, such as zyxin, are sufficient to predict forces and can generalize to unseen biological regimes. Using this observation, we develop two approaches-one constrained by physics and the other agnostic-to construct data-driven continuum models of cellular forces. Both reveal how cellular forces are encoded by two distinct length scales. Beyond adherent cell mechanics, our work serves as a case study for integrating neural networks into predictive models for cell biology.

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.

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.

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.

Functions and clinical significance of mechanical tumor microenvironment: cancer cell sensing, mechanobiology and metastasis

Dynamic and heterogeneous interaction between tumor cells and the surrounding microenvironment fuels the occurrence, progression, invasion, and metastasis of solid tumors. In this process, the tumor microenvironment (TME) fractures cellular and matrix architecture normality through biochemical and mechanical means, abetting tumorigenesis and treatment resistance. Tumor cells sense and respond to the strength, direction, and duration of mechanical cues in the TME by various mechanotransduction pathways. However, far less understood is the comprehensive perspective of the functions and mechanisms of mechanotransduction. Due to the great therapeutic difficulties brought by the mechanical changes in the TME, emerging studies have focused on targeting the adverse mechanical factors in the TME to attenuate disease rather than conventionally targeting tumor cells themselves, which has been proven to be a potential therapeutic approach. In this review, we discussed the origins and roles of mechanical factors in the TME, cell sensing, mechano‐biological coupling and signal transduction, in vitro construction of the tumor mechanical microenvironment, applications and clinical significance in the TME.