A continuum mechanical model of cell motion driven by a biphasic traction stress.

The aim of this paper is to place the cell locomotion problem within the general framework of classical continuum mechanics, and while doing so, to account for the deformation of the actin network in the cytoskeleton; the myosin activity on the lamellum including its effect on depolymerization at the trailing edge; model the stress-dependent driving forces and kinetic laws controlling polymerization at the leading edge, depolymerization at the trailing edge and ATP hydrolysis consistently with the dissipation inequality; and, based on the observations in Gardel (Gardel 2008 , 999-1005 (doi:10.1083/jcb.200810060)), include a biphasic velocity-dependent traction stress acting on the actin network.

A computational modeling of invadopodia protrusion into an extracellular matrix fiber network.

Invadopodia are dynamic actin-rich membrane protrusions that have been implicated in cancer cell invasion and metastasis. In addition, invasiveness of cancer cells is strongly correlated with invadopodia formation, which are observed during extravasation and colonization of metastatic cancer cells at secondary sites. However, quantitative understanding of the interaction of invadopodia with extracellular matrix (ECM) is lacking, and how invadopodia protrusion speed is associated with the frequency of protrusion-retraction cycles remains unknown.

Configurational fingerprints of multicellular living systems.

Cells cooperate as groups to achieve structure and function at the tissue level, during which specific material characteristics emerge. Analogous to phase transitions in classical physics, transformations in the material characteristics of multicellular assemblies are essential for a variety of vital processes including morphogenesis, wound healing, and cancer. In this work, we develop configurational fingerprints of particulate and multicellular assemblies and extract volumetric and shear order parameters based on this fingerprint to quantify the system disorder.

A continuum model for the growth of dendritic actin networks.

Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechano-chemical models of actin polymerization; most models are focused on single growing filaments, and only a few address polymerization of filament networks through simulations. Here, we propose a continuum model of surface growth and filament nucleation to describe polymerization of dendritic actin networks.

Kinetics of surface growth with coupled diffusion and the emergence of a universal growth path.

Surface growth by association or dissociation of material on the boundary of a body is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a single cell, and is increasingly applied in engineering processes for fabrication and self-assembly. A significant challenge in modelling such processes arises due to the inherent coupled interaction between the growth kinetics, the local stresses and the diffusing constituents needed to sustain the growth.

Computational modeling of three-dimensional ECM-rigidity sensing to guide directed cell migration.

Filopodia have a key role in sensing both chemical and mechanical cues in surrounding extracellular matrix (ECM). However, quantitative understanding is still missing in the filopodial mechanosensing of local ECM stiffness, resulting from dynamic interactions between filopodia and the surrounding 3D ECM fibers. Here we present a method for characterizing the stiffness of ECM that is sensed by filopodia based on the theory of elasticity and discrete ECM fiber.

Fringe instability in constrained soft elastic layers.

Soft elastic layers with top and bottom surfaces adhered to rigid bodies are abundant in biological organisms and engineering applications. As the rigid bodies are pulled apart, the stressed layer can exhibit various modes of mechanical instabilities. In cases where the layer's thickness is much smaller than its length and width, the dominant modes that have been studied are the cavitation, interfacial and fingering instabilities.