A mathematical model for cell-induced gel contraction incorporating osmotic effects

Biological tissues are composed of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting as a natural scaffolding to provide mechanical support to the cells. Reciprocal mechanical and chemical interactions between the cells and the ECM are crucial in regulating the development of tissues and maintaining their functionality. Hence, to maintain in vivo-like behaviour when cells are cultured in vitro, they are often seeded in a gel, which aims to mimic the ECM. In this paper, we present a mathematical model that incorporate cell-gel interactions together with osmotic pressure to study the mechanical behaviour of biological gels. In particular, we consider an experiment where cells are seeded within a gel, which gradually compacts due to forces exerted on it by the cells. Adopting a one-dimensional Cartesian geometry for simplicity, we use a combination of analytical techniques and numerical simulations to investigate how cell traction forces interact with osmotic effects (which can lead to either gel swelling or contraction depending on the gel's composition). Our results show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e. the chemical potentials) and the strength of the cell traction forces. We observe an unusual case where the gel oscillates between swelling and contraction. We also consider on how physical parameters like drag and viscosity affect the manner in which the gel evolves.

Zyxin Is Involved in Fibroblast Rigidity Sensing and Durotaxis

Focal adhesions (FAs) are specialized structures that enable cells to sense their extracellular matrix rigidity and transmit these signals to the interior of the cells, bringing about actin cytoskeleton reorganization, FA maturation, and cell migration. It is known that cells migrate towards regions of higher substrate rigidity, a phenomenon known as durotaxis. However, the underlying molecular mechanism of durotaxis and how different proteins in the FA are involved remain unclear. Zyxin is a component of the FA that has been implicated in connecting the actin cytoskeleton to the FA. We have found that knocking down zyxin impaired NIH3T3 fibroblast’s ability to sense and respond to changes in extracellular matrix in terms of their FA sizes, cell traction stress magnitudes and F-actin organization. Cell migration speed of zyxin knockdown fibroblasts was also independent of the underlying substrate rigidity, unlike wild type fibroblasts which migrated fastest at an intermediate substrate rigidity of 14 kPa. Wild type fibroblasts exhibited durotaxis by migrating toward regions of increasing substrate rigidity on polyacrylamide gels with substrate rigidity gradient, while zyxin knockdown fibroblasts did not exhibit durotaxis. Therefore, we propose zyxin as an essential protein that is required for rigidity sensing and durotaxis through modulating FA sizes, cell traction stress and F-actin organization.

Abstract P318: Dna Tension Probes Show That Cardiomyocyte Maturation Is Sensitive To The Pico-Newton Traction Forces Transmitted By Integrins

Cardiac muscle cells (CMCs) are the unit cells that comprise the heart. CMCs go through different stages of differentiation and maturation pathways to fully mature into beating cells. These cells can sense and respond to mechanical cues through receptors such as integrins which influence maturation pathways. For example, cell traction forces are important for the differentiation and development of functional CMCs, as CMCs cultured on varying substrate stiffness function differently. Most work in this area has focused on understanding the role of bulk ECM (extracellular matrix) stiffness in mediating the functional fate of CMC. Given that stiffness sensing mechanisms are mediated by individual integrin receptors, an important question in this area pertains to the specific magnitude of integrin piconewton (pN) forces that can trigger CMC functional maturation. To address this knowledge gap, we used DNA adhesion tethers that rupture at specific thresholds of force (~12, ~56, and ~160 pN) to test whether capping peak integrin tension to specific magnitudes affects CMC function. The work shows that adhesion tethers with greater force tolerance lead to functionally mature CMCs as determined by morphology, twitching frequency, transient calcium flux measurements and protein expression (F-actin, vinculin, α-actinin, YAP and SERCA2). Additionally, sacromeric actinin alignment and multinucleation were significantly enhanced as the mechanical tolerance of integrin tethers was increased. Taken together, the results show that CMCs harness defined pN integrin forces to influence early stage development. This study represents an important step toward biophysical characterization of the contribution of pN forces in early stage cardiac differentiation.

Developing a multi-functional sensor for cell traction force, matrix remodeling and biomechanical assays in self-assembled 3D tissues in vitro

Cell-matrix interactions, mediated by cellular force and matrix remodeling, result in a dynamic reciprocity that drives numerous biological processes and disease progression. Currently, there is no available method for direct quantification cell traction force and matrix remodeling in 3D matrices as a function of time. To address this long-standing need, we recently developed a high-resolution microfabricated sensor1 that measures cell force, tissue-stiffness and can apply mechanical stimulation to the tissue. Here the tissue self-assembles and self-integrates with the sensor. With primary fibroblasts, cancer cells and neurons, we demonstrated the feasibility of the sensor by measuring single/multiple cell force with a resolution of 1 nN, and tissue stiffness1 due to matrix remodeling by the cells. The sensor can be translated into a high-throughput system for clinical assays such as patient-specific drug and phenotypic screening. In this paper, we present the detailed protocol for manufacturing the sensors, preparing experimental setup, developing assays with different tissues, and for imaging and analyzing the data.

Dynamic real-time imaging of living cell traction force by piezo-phototronic light nano-antenna array

Dynamic mapping of the cell-generated force of cardiomyocytes will help provide an intrinsic understanding of the heart. However, a real-time, dynamic, and high-resolution mapping of the force distribution across a single living cell remains a challenge. Here, we established a force mapping method based on a “light nano-antenna” array with the use of piezo-phototronic effect. A spatial resolution of 800 nm and a temporal resolution of 333 ms have been demonstrated for force mapping. The dynamic mapping of cell force of live cardiomyocytes was directly derived by locating the antennas’ positions and quantifying the light intensities of the piezo-phototronic light nano-antenna array. This study presents a rapid and ultrahigh-resolution methodology for the fundamental study of cardiomyocyte behavior at the cell or subcellular level. It can provide valuable information about disease detection, drug screening, and tissue engineering for heart-related studies.

Does cellular adaptation to force loading rate determine the biphasic vs monotonic response of actin retrograde flow with substrate rigidity?

The transmission of cytoskeletal forces to the extracellular matrix through focal adhesion complexes is essential for a multitude of biological processes such as cell migration, differentiation, tissue development, cancer progression, among others. During migration, focal adhesions arrest the actin retrograde flow towards the cell interior, allowing the cell front to move forward. Here, we address a puzzling observation of the existence of two distinct phenomena: a biphasic relationship of the retrograde flow and cell traction force with increasing substrate rigidity, with maximum traction force and minimum retrograde flow velocity being present at an optimal substrate stiffness; in contrast, a monotonic relationship between them where the retrograde flow decreases and traction force increases with substrate stiffness. We propose a theoretical model for cell-matrix adhesions at the leading edge of a migrating cell, incorporating a novel approach in force loading rate sensitive binding and reinforcement of focal adhesions assembly and the subsequent force-induced slowing down of actin flow. Our model unravels both biphasic and monotonic responses of the retrograde flow and cell traction force with increasing substrate rigidity, owing to the cell’s ability to sense and adapt to the fast-growing forces. Moreover, we also elucidate how the viscoelastic properties of the substrate regulate these nonlinear responses and alter cellular behaviours.

A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes

The phenomenological model for cell shape deformation and cell migration Chen (BMM 17:1429–1450, 2018), Vermolen and Gefen (BMM 12:301–323, 2012), is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et al. (LC 13:340–348, 2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.