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

Multiscale regulation of cellular mechanical properties

Thesis (Ph.D.)--Boston UniversityIn vivo, cells routinely experience mechanical stresses and strains in the form of circulatory pressure and flow, peristalsis ofthe gut, and airway inflation and deflation. Even on the microscale, all adherent cells apply contractile force to the extracellular matrix and to neighboring cells. Cells respond to these external forces both passively and actively. Passively, cells need to deform in a way that is tissue and function appropriate. Actively, cells use local mechanoreceptors present on their surface to trigger changes in global cell behavior. Dysregulation of cell responses to force are hallmarks of diseases such as atherosclerosis, asthma and cancer. Given the pluripotent role of cell mechanics in both normal cell behavior and disease, cell regulation of mechanical properties has become a major area of focus in biology. In this dissertation, we explore passive mechanical properties and active mechanical responses of cells on the subcellular, single cell and multicellular length scales. In Aim 1, we developed a new tool, called cell biomechanical imaging, for mapping intracellular stiffness and prestress. We have demonstrated a linear relationship between these two quantities, both at the whole cell and subcellular levels, which suggests prestress may be a unifying mechanism by which cells and tissues tune their mechanical properties. In Aim 2, we investigated how coordinated changes in cytoskeletal tension lead to cell reorientation. Previous research has shown that in response to strain applied through focal adhesions, the actin cytoskeleton promptly fluidizes and then slowly resolidifies. Using both experiments and a mathematical model, we found that repeated interplay ofthese phenomena was a driving force behind cytoskeletal reorganization during cell reorientation. It was previously hypothesized that the purpose of cytoskeletal remodeling in response to strain was to minimize changes in intracellular mechanical tension and maintain it at a preferred level. This feedback control mechanism, which balances forces between the cell and its microenvironment, is termed "tensional homeostasis." The dominant paradigm in vascular biology is that tensional homeostasis exists across multiple length and time scales. However, our results from Aim 2 challenged this idea; reoriented cells did not maintain steady levels of contractile force. In Aim 3, we investigated tensional homeostasis and its existence at multiple length scales. We found that cells do not have a preferred level of tension at the subcellular or single cell levels. However, in a cluster of confluent cells, contractile tension is maintained, the more so as cluster size increases. Together, the results of this dissertation emphasize the importance ofa multiscale approach to mechanobiology. Cells and tissue are hierarchically ordered systems that use mechanical stress (prestress) to tune their mechanical properties and responses across lengthscales. Thus, it is important to consider not just the behavior of separate components of each of these systems, but the behaviors that emerge when they interact with one another

Anisotropy in cell mechanics

Mechanical interactions between cells and their environment play an important role in many biological processes. These interactions are often anisotropic in nature, but most mathematical models in the field of cell mechanics describe cells as isotropic entities. In this thesis we theoretically study the role of anisotropic forces in cell mechanics, and compare our predictions to experimental data. Analysis and Stochastic

Amoeboid Shape Dynamics on Flat and Topographically Modified Surfaces

I present an analysis of the shape dynamics of the amoeba Dictyostelium discoideum, a model system for the study of cellular migration. To better understand cellular migration in complicated 3-D environments, cell migration was studied on simple 3-D surfaces, such as cliffs and ridges. D. discoideum interact with surfaces without forming mature focal adhesion complexes. The cellular response to the surface topography was characterized by measuring and looking for patterns in cell shape. Dynamic cell shape is a measure of the interaction between the internal biochemical state of a cell and its external environment. For D. discoideum migrating on flat surfaces, waves of high boundary curvature were observed to travel from the cell front to the cell back. Curvature waves are also easily seen in cells that do not adhere to a surface, such as cells that are electrostatically repelled from the coverslip or cells that are extended over the edge of micro-fabricated cliffs. At the leading edge of adhered cells, these curvature waves are associated with protrusive activity, suggesting that protrusive motion can be thought of as a wave-like process. The wave-like character of protrusions provides a plausible mechanism for the ability of cells to swim in viscous fluids and to navigate complex 3-D topography. Patterning of focal adhesion complexes has previously been implicated in contact guidance (polarization or migration parallel to linear topographical structures). However, significant contact guidance is observed in D. discoideum, which lack focal adhesion complexes. Analyzing the migration of cells on nanogratings of ridges spaced various distances apart, ridges spaced about 1.5 micrometers apart were found to guide cells best. Contact guidance was modeled as an interaction between wave-like processes internal to the cell and the periodicity of the nanograting. The observed wavelength and speed of the oscillations that best couple to the surface are consistent with those of protrusive dynamics. Dynamic sensing via actin or protrusive dynamics might then play a role in contact guidance

On the theory of cell migration: durotaxis and chemotaxis

Cell migration is a fundamental element in a variety of physiological and pathological processes. Alteration of its regulatory mechanisms leads to loss of cellular adhesion and increased motility, which are critical steps in the initial stages of metastasis, before a malignant cell colonizes a distant tissue or organ. Consequently, cell migration has become the focus of intensive experimental and theoretical studies; however the understanding of many of its mechanism remains elusive. Cell migration is the result of a periodic sequence of protrusion, adhesion remodeling and contraction stages that leads to directed movement of cells towards external stimuli. The spatio-temporal coordination of these processes depends on the di erential activation of the signaling networks that regulate them at specific subcellular locations. Particularly, proteins from the family of small RhoGTPases play a central role in establishing cell polarization, setting the direction of migration, regulating the formation of adhesion sites and the generation of the forces that drive motion. Theoretical models based on an independent description of these processes have a limited capacity to predict cellular behavior observed in vitro, since their functionality depends intrinsically on the cross-regulation between their signaling pathways. This thesis presents a model of cell migration that integrates a description of force generation and cell deformation, adhesion site dynamics and RhoGTPases activation. The cell is modeled as a viscoelastic body capable of developing active traction and protrusion forces. The magnitude of stresses is determined by the activation level of the RhoGTPases, whose distribution in the cell body is described by a set of reaction-di usion equations. Adhesion sites are modeled as punctual clusters of transmembrane receptors that dynamically bind and unbind the extracellular matrix depending on the force transmitted to them and the distance with ligands on the substrate. Onthe theoretical level, the major findings concern the relationship between the topology of a crosstalk scheme and the properties, as defined in [1], inherited by the associated reaction network as a gradient sensing and regulatory system: persistent and transient polarization triggered by external gradients, adaptation to uniform stimulus, reversible polarization, multi-stimuli response and amplification. This leads to models that remain functional against the biological diversity associated to di erent cell types and matches the observed cell behaviour in Chemotaxis essays [2, 3, 4, 5]: the capacity of cells to amplify gradients, polarize without featuring Turing patterns of activation, and switch the polarization axis and the direction of migration after the source of the external stimulus is changed. The RhoGTPase model, derived on theoretical premises, challenges a long held view on the mechanisms of RhoGTPase crosstalk and suggests that the role of GDIs, GEFs and GAPs has to be revised. Recent experimental evidence supports this idea[6]. In addition, the model allows to recapitulate a continuous transition between the tear-like shape adopted by neutrophiles and the fan-like shape of keratocytes during migration [7] by varying the relative magnitudes of protrusion and contraction forces or, alternatively, the strength of RhoGTPase Crosstalk. The second mechanism represents a novel explanation of the di erent morphologies observed in migrating cells. Di erences in RhoGTPase crosstalk strength could be mediated by di erences between the activity or concentration of GEFs, GAPs and GDIs in di erent cell types; an idea that can be explored experimentally. On cell mechanosensing, a new hypothesis based on a simple physical principle is proposed as the mechanism that might explain the universal preference of cells (bar neurons) to migrate along sti ness gradients. The theory provides a simple unifying explanation to a number of recent observations on force development and growth in real time at cell Focal adhesions [8, 9, 10, 11]. The apparently conflicting results have been attributed to the di erences in experimental set-ups and cell types used, and have fueled a longstanding controversy on how cells prove the mechanical properties of the extra-cellular matrix. The predictions of the theory recapitulate these experimental observations, and its founding hypothesis can be tested experimentally. This hypothesis directly suggests the mechanism that could explain the preference of cells to migrate along sti ness gradients, and for the first time, a plausible biological function for its existence. This phenomenon is known as Durotaxis, and its abnormal regulation has been associated to the malignant behaviour of cancer cells. &nbsp

A biophysical evaluation of cell-substrate interactions during spreading, migration and neuron differentiation

The development of engineered scaffolds has become a popular current avenue to treat numerous traumas and disease. In order to optimize the efficiency of these treatments, it is necessary to have a more thorough understanding of how cells interact with their substrate and how these interactions directly affect cellular behavior. Cell spreading is a critical component of numerous biological phenomena, including embryonic development, cancer metastasis, immune response, and wound healing. Along with spreading, cell adhesion and migration are all strongly dependent on the interactions between the cell and its substrate. Cell-substrate interactions can affect critical cellular mechanisms including internal cellular signaling, protein synthesis, differentiation, and replication and also influence the magnitude of adherence and motility. In an effort to better understand cell-substrate interactions we characterize the initial stages of cell spreading and blebbing using cell-substrate specific microscopy techniques, and identify the effects of cytoskeletal disruption and membrane modification on surface interactions and spreading. We identify that blebs appear after a sharp change in cellular tension, such as following rapid cell-substrate detachment with trypsin. An increased lag phase of spreading appears with increased blebbing; however, blebbing can be tuned by supplying the cell with more time to perform plasma membrane recycling. We developed software algorithms to detect individual bleb dynamics from TIRF and IRM images, and characterize three types of bleb-adhesion behaviors. Overall, we show that blebs initially create the first adhesion sites for the cell during spreading; however, their continuous protrusion and retraction events contribute to the slow spreading period prior to fast growth. In addition, we identify the elastic modulus of the rat cortex and characterize a polyacrylamide gel system that evaluates the effects of substrate stiffness on cortical outgrowth. Remarkably, we illustrate that cortical neuron differentiation and outgrowth are insensitive to substrate stiffness, and observe only morphological differences between laminin versus PDL-coated substrates. Together, this research identifies cell-specific behaviors critical to spreading and migration. The thorough evaluations of spreading and migration behavior presented here contribute to the understanding of critical cellular phenomena and suggest potential therapeutic targets for treatment of cardiovascular disease and neurological disorders

Imaging for the evaluation of endometriosis and adenomyosis

Endometriosis affects between 5 and 45% of women in reproductive age, is associated with significant morbidity, and constitutes a major public health concern. The correct diagnosis is fundamental in defining the best treatment strategy for endometriosis. Therefore, non-invasive methods are required to obtain accurate diagnoses of the location and extent of endometriotic lesions. Transvaginal sonography and magnetic resonance imaging are used most frequently to identify and characterise lesions in endometriosis. Subjective impression by an experienced sonologist for identifying endometriomas by ultrasound showed a high accuracy. Adhesions can be evaluated by real-time dynamic transvaginal sonography, using the sliding sign technique, to determine whether the uterus and ovaries glide freely over the posterior and anterior organs and tissues. Diagnosis is difficult when ovarian endometriomas are absent and endometriosis causes adhesions and deep infiltrating nodules in the pelvic organs. Magnetic resonance imaging seems to be useful in diagnosing all locations of endometriosis, and its diagnostic accuracy is similar to those obtained using ultrasound. Transvaginal ultrasound has been proposed as first line-line imaging technique because it is well accepted and widely available. The main limitation of ultrasound concerns lesions located above the rectosigmoid junction owing to the limited field-of-view of the transvaginal approach and low accuracy in detecting upper bowel lesions by transabdominal ultrasound. A detailed non-invasive diagnosis of the extension in the pelvis of endometriosis can facilitate the choice of a safe and adequate surgical or medical treatment

Engineering patterned and dynamic surfaces for the spatio-temporal control of cell behaviour

Stem cell shape and mechanical properties in vitro can be directed by geometrically defined micropatterned adhesion substrates. However conventional methods are limited by the fixed micropattern design, which cannot recapitulate the dynamic changes of the natural cell microenvironment. Recent advancements in microfabrication technologies in combination with the use of light-responsive materials, allow to manipulate the shape of living cells in real-time in a non-invasive Spatio-temporal controlled way to introduce additional geometrically defined adhesion sites and to study relative cell behaviour. Here, the confocal laser technique is exploited for dynamically evaluate the variation over time of the tensional and morphological cell state. This method allows the precise control of specific actin structures that regulate cell architecture. Actin filament bundles, initially randomly organized in circular-shaped cells, are induced to align and distribute to form a rectangular-shaped cell in response to specific dynamic changes in the cell adhesion pattern. The changes in morphology also reflect dramatic changes in FAs distribution, cell mechanics, nuclear morphology, and chromatin conformation. The reported strategy is convenient to explore the cell-substrate interface and the mechanisms through which cell geometry regulates cell signalling in a facile and cost-effective manner and it open new routes to understand how the field of dynamic platforms should potentially contribute to unveil complex biological events such as the modulation of cell shape

Microscale Measurements of Cell and Tissue Mechanics in Three Dimensions

Two-dimensional (2D) studies have revealed that mechanical forces drive cell migration and can feedback to regulate proliferation, differentiation and the synthesis/remodeling of extracellular matrix (ECM) proteins. Whether these observations can be translated to clinical settings or be utilized for tissue engineering will depend critically on our ability to translate these findings into physiologically relevant three-dimensional (3D) environments. The general goal of this dissertation has been to develop and apply new technologies capable of extending studies of cell and tissue mechanics into 3D environments. In the first project, we measured both shear and normal traction forces exerted by cells cultured on planar substrates. We observed that focal adhesions serve as pivots about which cells generate rotational moments. In the second project, we combined enzymatically degradable synthetic hydrogels with finite element models to measure the mechanical tractions exerted by cells fully encapsulated within 3D matrices. We found that cells reach out thin protrusions and pull back inward towards the cell body with the highest forces at the tip. Cellular extensions that were invading into the surrounding matrix displayed a strong inward force 10-15 microns behind the leading tip, suggesting that growing extensions may establish a contractile waypoint, before invading further. To study the forces cells exert during tissue remodeling, we utilized photolithograpy to generate arrays of microtissues consisting of cells encapsulated in 3D collagen matrices. Microcantilevers were used to constrain the remodeling of the collagen gel and to report the forces generated during this process. We used this technique to explore the effects of boundary stiffness and matrix density within model tendon and cardiac tissues. Finally, we combined this system with a Foerster radius energy transfer (FRET) based biosensor of fibronectin conformation to reveal how tissue geometry and cell-genereated tractions cooperate to pattern matrix conformation during tissue remodeling. Together, these studies highlight novel approaches to understand the nature of cell-ECM interactions in 3D matrices. Such mechanical insights will help us to understand how physical forces drive cell migration and behavior within physiologically relevant environments