Enhanced substrate stress relaxation promotes filopodia-mediated cell migration.

Cell migration on two-dimensional substrates is typically characterized by lamellipodia at the leading edge, mature focal adhesions and spread morphologies. These observations result from adherent cell migration studies on stiff, elastic substrates, because most cells do not migrate on soft, elastic substrates. However, many biological tissues are soft and viscoelastic, exhibiting stress relaxation over time in response to a deformation. Here, we have systematically investigated the impact of substrate stress relaxation on cell migration on soft substrates. We observed that cells migrate minimally on substrates with an elastic modulus of 2 kPa that are elastic or exhibit slow stress relaxation, but migrate robustly on 2-kPa substrates that exhibit fast stress relaxation. Strikingly, migrating cells were not spread out and did not extend lamellipodial protrusions, but were instead rounded, with filopodia protrusions extending at the leading edge, and exhibited small nascent adhesions. Computational models of cell migration based on a motor-clutch framework predict the observed impact of substrate stress relaxation on cell migration and filopodia dynamics. Our findings establish substrate stress relaxation as a key requirement for robust cell migration on soft substrates and uncover a mode of two-dimensional cell migration marked by round morphologies, filopodia protrusions and weak adhesions.

Finite Element Formulation of Multiphasic Shell Elements for Cell Mechanics Analyses in FEBio.

With the recent implementation of multiphasic materials in the open-source finite element (FE) software FEBio (febio.org), 3D models of cells embedded within the tissue may now be analyzed, accounting for porous solid matrix deformation, transport of interstitial fluid and solutes, membrane potential, and reactions. The cell membrane is a critical component in cell models, which selectively regulates the transport of fluid and solutes in the presence of large concentration and electric potential gradients, while also facilitating the transport of various proteins. The cell membrane is much thinner than the cell; therefore, in an FE environment, shell elements formulated as 2D surfaces in 3D space would be preferred for modeling the cell membrane, for the convenience of mesh generation from image-based data, especially for convoluted membranes. However, multiphasic shell elements are yet to be developed in the FE literature and commercial FE software. This study presents a novel formulation of multiphasic shell elements and its implementation in FEBio. The shell model includes front- and back-face nodal degrees of freedom for the solid displacement, effective fluid pressure and effective solute concentrations, and a linear interpolation of these variables across the shell thickness. This formulation was verified against classical models of cell physiology and validated against reported experimental measurements in chondrocytes. This implementation of passive transport of fluid and solutes across multiphasic membranes makes it possible to model the biomechanics of isolated cells or cells embedded in their extracellular matrix, accounting for solvent and solute transport.

A molecular clock controls periodically driven cell migration in confined spaces.

Navigation through a dense, physically confining extracellular matrix is common in invasive cell spread and tissue reorganization but is still poorly understood. Here, we show that this migration is mediated by cyclic changes in the activity of a small GTPase RhoA, which is dependent on the oscillatory changes in the activity and abundance of the RhoA guanine nucleotide exchange factor, GEF-H1, and triggered by a persistent increase in the intracellular Ca2+ levels. We show that the molecular clock driving these cyclic changes is mediated by two coupled negative feedback loops, dependent on the microtubule dynamics, with a frequency that can be experimentally modulated based on a predictive mathematical model. We further demonstrate that an increasing frequency of the clock translates into a faster cell migration within physically confining spaces. This work lays the foundation for a better understanding of the molecular mechanisms dynamically driving cell migration in complex environments.

Modeling distributed forces within cell adhesions of varying size on continuous substrates.

Cell migration and traction are essential to many biological phenomena, and one of their key features is sensitivity to substrate stiffness, which biophysical models, such as the motor-clutch model and the cell migration simulator can predict and explain. However, these models have not accounted for the finite size of adhesions, the spatial distribution of forces within adhesions. Here, we derive an expression that relates varying adhesion radius ( R) and spatial distribution of force within an adhesion (described by s) to the effective substrate stiffness ( κsub ), as a function of the Young's modulus of the substrate ( E Y ), which yields the relation, κsub=RsEY , for two-dimensional cell cultures. Experimentally, we found that a cone-shaped force distribution ( s = 1.05) can describe the observed displacements of hydrogels deformed by adherent U251 glioma cells. Also, we found that the experimentally observed adhesion radius increases linearly with the cell protrusion force, consistent with the predictions of the motor-clutch model with spatially distributed clutches. We also found that, theoretically, the influence of one protrusion on another through a continuous elastic environment is negligible. Overall, we conclude cells can potentially control their own interpretation of the mechanics of the environment by controlling adhesion size and spatial distribution of forces within an adhesion.