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.

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.

Hypergravity affects Cell Traction Forces of Fibroblasts

ABSTRACTCells sense and react on changes of the mechanical properties of their environment, and likewise respond to external mechanical stress applied to them. Whether the gravitational field, as overall body force, modulates cellular behavior is however unclear. Different studies demonstrated that micro- and hypergravity influences the shape and elasticity of cells, initiate cytoskeleton reorganization, and influence cell motility. All these cellular properties are interconnected, and contribute to forces that cells apply on their surrounding microenvironment. Yet, studies that investigated changes of cell traction forces under hypergravity conditions are scarce. Here we performed hypergravity experiments on 3T3 fibroblast cells using the Large Diameter Centrifuge at the European Space and Technology Centre (ESA-ESTEC). cells were exposed to hypergravity of up to 19.5g for 16 h in both the upright and the inverted orientation with respect to the g-force vector. We observed a decrease in cellular traction forces when the gravitational field was increased up to 5.4g, followed by an increase of traction forces for higher gravity fields up to 19.5g independent of the orientation of the gravity vector. We attribute the switch in cellular response to shear-thinning at low g-forces, followed by significant rearrangement and enforcement of the cytoskeleton at high g-forces.SIGNIFICANCEThe behavior of cells critically depend on the mechanical properties of their environment. For example external stresses and strains lead to decisions in cell differentiation as well as to collective-migration in metastasis. Gravity, as a permanently acting body force, is one of those externs stresses. We demonstrate the impact of gravitational challenges on forces that cells apply to their environment. We observed a switch in cellular response with a decrease in cell traction forces for low bypgrarayiv. conditions, followed by a significant increase in cell traction forces at higher g-level. This particular cellular response reflects a switch in croskeletal organization, similar to that observed for cells in fluids where shear forces act.

Dissipation of contractile forces: the missing piece in cell mechanics

Mechanical forces are key regulators of cell and tissue physiology. The basic molecular mechanism of fiber contraction by the sliding of actin filament upon myosin leading to conformational change has been known for decades. The regulation of force generation at the level of the cell, however, is still far from elucidated. Indeed, the magnitude of cell traction forces on the underlying extracellular matrix in culture is almost impossible to predict or experimentally control. The considerable variability in measurements of cell-traction forces indicates that they may not be the optimal readout to properly characterize cell contractile state and that a significant part of the contractile energy is not transferred to cell anchorage but instead is involved in actin network dynamics. Here we discuss the experimental, numerical, and biological parameters that may be responsible for the variability in traction force production. We argue that limiting these sources of variability and investigating the dissipation of mechanical work that occurs with structural rearrangements and the disengagement of force transmission is key for further understanding of cell mechanics.