Traction force microscopy on soft elastic substrates: a guide to recent computational advances

The measurement of cellular traction forces on soft elastic substrates has become a standard tool for many labs working on mechanobiology. Here we review the basic principles and different variants of this approach. In general, the extraction of the substrate displacement field from image data and the reconstruction procedure for the forces are closely linked to each other and limited by the presence of experimental noise. We discuss different strategies to reconstruct cellular forces as they follow from the foundations of elasticity theory, including two- versus three-dimensional, inverse versus direct and linear versus non-linear approaches. We also discuss how biophysical models can improve force reconstruction and comment on practical issues like substrate preparation, image processing and the availability of software for traction force microscopy.Comment: Revtex, 29 pages, 3 PDF figures, 2 tables. BBA - Molecular Cell Research, online since 27 May 2015, special issue on mechanobiolog

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

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

Quantifying cell-generated forces: Poisson's ratio matters

Quantifying mechanical forces generated by cellular systems has led to key insights into a broad range of biological phenomena from cell adhesion to immune cell activation. Traction force microscopy (TFM), the most widely employed force measurement methodology, fundamentally relies on knowledge of the force-displacement relationship and mechanical properties of the substrate. Together with the elastic modulus, the Poisson’s ratio is a basic material property that to date has largely been overlooked in TFM. Here, we evaluate the sensitivity of TFM to Poisson’s ratio by employing a series of computer simulations and experimental data analysis. We demonstrate how applying the correct Poisson’s ratio is important for accurate force reconstruction and develop a framework for the determination of error levels resulting from the misestimation of the Poisson’s ratio. In addition, we provide experimental estimation of the Poisson’s ratios of elastic substrates commonly applied in TFM. Our work thus highlights the role of Poisson’s ratio underpinning cellular force quantification studied across many biological systems

Focal adhesion mediated regulation of pluripotency : The role of focal adhesions and contractile forces in human pluripotent stem cells

Human pluripotent stem cells (hPSCs) hold great promise for future medicine. They can differentiate to all adult cell types and self-replicate virtually endlessly. These features would make hPSCs a valuable tool for applications of regenerative medicine. Pluripotency is controlled by extracellular cues which establish the correct culture conditions. Appropriate growth factors and extracellular matrix (ECM) composition must be provided for maintenance of viability, pluripotency and self-renewal in vitro. However, the stem cell field has overlooked many of the basic cell biological phenomena that could affect the regulation of pluripotency. Focal adhesions (FAs) connect the ECM via integrin receptors to the cellular cytoskeleton. They are dynamic protein complexes responsible for broadcasting the information of composition and mechanical properties of the ECM to biochemical intracellular signalling cascades. Furthermore, they provide the physical anchoring points needed for cell adherence and movement. FAs have not been studied in the context of human pluripotency before. In this thesis, I utilise high-resolution microscopy to describe for the first time the characteristics of FAs in hPSCs. We show that hPSCs have large cornerstone FAs connected via contractile actin stress fibres at colony periphery. We provide evidence that structures at the colony edge create traction forces needed for compaction of the cells. Also, we show that FAs function as signalling platforms. We employ 3D superresolution microscopy and unveil unique ultrastructural features of large FAs and show that perturbation of the structure accelerates hPSC differentiation. Finally, we introduce a versatile, easy access method for implementation of fluctuation based super-resolution microscopy to measure cellular forces in nanoscale. In summary, this thesis provides in detail characterisation of cornerstone FAs in hPSCs and highlights their role for morphological features of the colonies and pluripotency. In addition, it provides a new method for studying cellular forces exerted by the FAs

A practical review on the measurement tools for cellular adhesion force

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

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

Remodeling by fibroblasts alters the rate-dependent mechanical properties of collagen

The ways that fibroblasts remodel their environment are central to wound healing, development of musculoskeletal tissues, and progression of pathologies such as fibrosis. However, the changes that fibroblasts make to the material around them and the mechanical consequences of these changes have proven difficult to quantify, especially in realistic, viscoelastic three-dimensional culture environments, leaving a critical need for quantitative data. Here, we observed the mechanisms and quantified the mechanical effects of fibroblast remodeling in engineered tissue constructs (ETCs) comprised of reconstituted rat tail (type I) collagen and human fibroblast cells. To study the effects of remodeling on tissue mechanics, stress-relaxation tests were performed on ETCs cultured for 24, 48, and 72 h. ETCs were treated with deoxycholate and tested again to assess the ECM response. Viscoelastic relaxation spectra were obtained using the generalized Maxwell model. Cells exhibited viscoelastic damping at two finite time constants over which the ECM showed little damping, approximately 0.2 s and 10-30 s. Different finite time constants in the range of 1-7000 s were attributed to ECM relaxation. Cells remodeled the ECM to produce a relaxation time constant on the order of 7000 s, and to merge relaxation finite time constants in the 0.5-2 s range into a single time content in the 1 s range. Results shed light on hierarchical deformation mechanisms in tissues, and on pathologies related to collagen relaxation such as diastolic dysfunction. Statement of Significance As fibroblasts proliferate within and remodel a tissue, they change the tissue mechanically. Quantifying these changes is critical for understanding wound healing and the development of pathologies such as cardiac fibrosis. Here, we characterize for the first time the spectrum of viscoelastic (rate-dependent) changes arising from the remodeling of reconstituted collagen by fibroblasts. The method also provides estimates of the viscoelastic spectra of fibroblasts within a three-dimensional culture environment. Results are of particular interest because of the ways that fibroblasts alter the mechanical response of collagen at loading frequencies associated with cardiac contraction in humans. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

Leveraging elasticity theory to calculate cell forces: From analytical insights to machine learning

Living cells possess capabilities to detect and respond to mechanical features of their surroundings. In traction force microscopy, the traction of cells on an elastic substrate is made visible by observing substrate deformation as measured by the movement of embedded marker beads. Describing the substrates by means of elasticity theory, we can calculate the adhesive forces, improving our understanding of cellular function and behavior. In this dissertation, I combine analytical solutions with numerical methods and machine learning techniques to improve traction prediction in a range of experimental applications. I describe how to include the normal traction component in regularization-based Fourier approaches, which I apply to experimental data. I compare the dominant strategies for traction reconstruction, the direct method and inverse, regularization-based approaches and find, that the latter are more precise while the former is more stress resilient to noise. I find that a point-force based reconstruction can be used to study the force balance evolution in response to microneedle pulling showing a transition from a dipolar into a monopolar force arrangement. Finally, I show how a conditional invertible neural network not only reconstructs adhesive areas more localized, but also reveals spatial correlations and variations in reliability of traction reconstructions

The mechanobiology of kidney podocytes in health and disease

Funding: UK Biotechnology and Biological Sciences Research Council (BB/P027148/1).Chronic kidney disease (CKD) substantially reduces quality of life and leads to premature death for thousands of people each year. Dialysis and kidney organ transplants remain prevalent therapeutic avenues but carry significant medical, economic and social burden. Podocytes are responsible for blood filtration selectivity in the kidney, where they extend a network of foot processes (FPs) from their cell bodies which surround endothelial cells and interdigitate with those on neighbouring podocytes to form narrow slit diaphragms (SDs). During aging, some podocytes are lost naturally but accelerated podocyte loss is a hallmark of CKD. Insights into the origin of degenerative podocyte loss will help answer important questions about kidney function and lead to substantial health benefits. Here, approaches that uncover insights into podocyte mechanobiology are reviewed, both those that interrogate the biophysical properties of podocytes and how the external physical environment affects podocyte behaviour, and also those that interrogate the biophysical effects that podocytes exert on their surroundings.PostprintPeer reviewe

Creeping motion of a solid particle inside a spherical elastic cavity

On the basis of the linear hydrodynamic equations, we present an analytical theory for the low-Reynolds-number motion of a solid particle moving inside a larger spherical elastic cavity which can be seen as a model system for a fluid vesicle. In the particular situation where the particle is concentric with the cavity, we use the stream function technique to find exact analytical solutions of the fluid motion equations on both sides of the elastic cavity. In this particular situation, we find that the solution of the hydrodynamic equations is solely determined by membrane shear properties and that bending does not play a role. For an arbitrary position of the solid particle within the spherical cavity, we employ the image solution technique to compute the axisymmetric flow field induced by a point force (Stokeslet). We then obtain analytical expressions of the leading order mobility function describing the fluid-mediated hydrodynamic interactions between the particle and confining elastic cavity. In the quasi-steady limit of vanishing frequency, we find that the particle self-mobility function is higher than that predicted inside a rigid no-slip cavity. Considering the cavity motion, we find that the pair-mobility function is determined only by membrane shear properties. Our analytical predictions are supplemented and validated by fully-resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied forcing frequencies.Comment: 15 pages, 5 figures, 90 references. To appear in Eur. Phys. J.