Session F26: Mechanics of Cells and Tissues Across Scales IV

Vimentin intermediate filament biomechanics in 3D cell motility

The migration of cells through confining spaces in tissues is important for many biological processes and depends on the mechanical properties of a cytoskeleton made up of three different filaments: F-actin, microtubules, and intermediate filaments. The signaling pathways and cytoskeletal structures that control cell motility on 2D are often very different from those that control motility in 3D. Previous studies have shown that intermediate filaments can promote actin-driven protrusions at the cell edge, but have little effect on overall motility of cells on flat surfaces. They are however important for cells to maintain resistance to repeated compressive stresses that are expected to occur in vivo. Using mouse embryonic fibroblasts derived from wild-type and vimentin-null mice, we find that loss of vimentin increases motility in 3D micro-channels even though on flat surfaces it has the opposite effect. Atomic force microscopy and traction force microscopy experiments reveal that vimentin enhances perinuclear cell stiffness while maintaining the same level of acto-myosin contractility in cells. We propose a minimal model in which a perinuclear vimentin cage constricts along with the nucleus during motility through confining spaces, providing mechanical resistance against large strains that can damage the structural integrity of cells and their nuclei.   

Confined cell migration - a dynamical systems perspective

In many biological phenomena, cells migrate through confining environments. However, a quantitative conceptual framework for confined migration has remained elusive. To provide such a framework, we employ a data-driven approach to infer the dynamics of cell movement, morphology and interactions of cells confined in two-state micropatterns. In this confinement, cells stochastically migrate back and forth between two square adhesion sites connected by a thin bridge. By inferring a stochastic equation of motion directly from the experimentally determined short time-scale dynamics, we show that cells exhibit intricate non-linear deterministic dynamics that adapt to the geometry of confinement. This approach reveals that different cell lines exhibit distinct classes of dynamical systems, ranging from bistable to limit cycle behavior. To connect these findings to underlying migratory mechanisms, we track the evolution of cell shape and develop a framework for the dynamics of cell morphology in confinement. Our approach yields a conceptual framework for the motility and morphology of confined cells which can be generalized to more complex environments including multiple interacting confined cells.   

Finite element simulation of a cell entering a pipette: Effects of large deformation and frictional contact

The process of single cells entering a confined channel under pressure is widely seen in cell mechanics experiments (e.g., micropipette aspiration) and biological process (e.g., tumor cell migration in capillaries). Finite element method that models the cell as a continuum solid has been extensively used to study this process. However, most previous modeling studies suffered from limitations including inaccurate pressure and frictional boundary conditions, therefore making it challenging to simulate the complete entry process involving large deformation of the cell. Here we present a simulation approach that can continuously update the boundary condition according to the contact status as the cell enters the channel, thus enabling more accurate description of the pressure and frictional conditions. Using a quasi-linear viscoelastic solid model for the cell, we show that the detailed pressure boundary condition and interface friction coefficients can significantly affect the cell entry process.   

Modeling the effect of vimentin on confined cell motility.

As a cell moves in a strongly confined geometry, its cytoskeleton undergoes changes as does the peri-nuclear cage. How do these changes affect cell motility? The cytoskeleton is made up of three different semi-flexible polymers: actin, microtubules, and intermediate filaments, such as vimentin. Recent studies demonstrate that the loss of vimentin enhances cell motility through micro-channels and confining spaces, though it has the opposite effect in 2D. We are, therefore, modeling the effects of intermediate filaments on cell motility in confinement to understand these latest experiments. We have developed a biophysical model for a cell moving through various confined geometries based on Brownian dynamics. It includes an intracellular network along with a peri-nuclear cage, both of which involve vimentin. We explore a possible mechanism behind the enhanced motility of vimentin-null cells, irrespective of channel width, in comparison to wild-type. We also characterize the increased speed of vimentin-null cells with increasing confinement and the minimal effect on the speed of wild-type cells under the same conditions. We also investigate the effects of flexible confinement walls on cell motility to better mimic the physiological conditions.   

Regulation of nuclear architecture, mechanics, and nucleocytoplasmic shuttling of epigenetic factors by cell geometric constraints

Cells sense mechanical signals from their microenvironment and transduce them to the nucleus to regulate gene expression programs. To elucidate the physical mechanisms involved in this regulation, we developed an active 3D chemomechanical model to describe the three-way feedback between the adhesions, the cytoskeleton, and the nucleus. The model shows local tensile stresses generated at the interface of the cell and the extracellular matrix regulate the properties of the nucleus, including nuclear morphology, levels of lamin A,C, and histone deacetylation, as these tensile stresses 1) are transmitted to the nucleus through cytoskeletal physical links and 2) trigger an actomyosin-dependent shuttling of epigenetic factors. We then show how cell geometric constraints affect the local tensile stresses and subsequently the three-way feedback and induce cytoskeleton-mediated alterations in the properties of the nucleus such as nuclear lamina softening, chromatin stiffening, nuclear lamina invaginations, increase in nuclear height, and shrinkage of nuclear volume. We predict a phase diagram that describes how the disruption of cytoskeletal components impacts the feedback and subsequently induce contractility-dependent alterations in the properties of the nucleus. Our simulations show that these changes in contractility levels can be also used as predictors of nucleocytoplasmic shuttling of transcription factors and the level of chromatin condensation. The predictions are experimentally validated by studying the properties of nuclei of fibroblasts on micropatterned substrates with different shapes and areas.   

Effective pressure in a dense cell monolayer and collective cell migration

A system of dividing and growing cells provides an intriguing example of active matter far from equilibrium. Living cells in a dense system are all in contact with each other. The common assumption is that such cells stop dividing due to a lack of space. Recent experimental observations have shown, however, that cells continue dividing for some time, even after a dense cell monolayer is formed. Effective pressure is introduced in order to model the experimentally observed phenomenon in which the average cell size dramatically decreases over time, and cell area distribution becomes narrower. For a non-uniform system, I will consider the cell shift due to the gradient of the effective pressure and examine its effect on the average cell area profiles. Then I will discuss collective cell migration where cells maintain contact with their neighbors. This migration can be described in terms of a novel front propagation phenomenon; the front speed and effective pressure profile are found both numerically and analytically.   

Effects of cell-cell adhesion on collective migration of multicellular clusters

Collections of cells exhibit directional coherent migration during morphogenesis, cancer-metastasis, and wound healing. Often during migration, bigger clusters split, smaller sub-clusters collide and reassemble, and gaps continually emerge. This leads to the formation of protrusions by some inner cells which eventually act as “leaders", along with the cells at the leading edge, pulling the cluster towards the favorable direction. Large populations like neural crest cells are known to exhibit such phenomena. We hypothesize that the cells may have an optimal adhesion among themselves, rather than very strong or weak, to favor the formation of gaps and achieve an effective faster migration. We test this hypothesis for one- and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We develop both a minimal framework based on the lattice gas model of statistical physics, as well as a more realistic framework based on the cellular Potts model. Results from both frameworks support our hypothesis, suggesting that intermediate adhesion leads to optimal migration. We discuss the mechanisms behind this optimum and relate our results to specific cellular systems.   

Plasticity of cell migration resulting from mechanochemical coupling

Eukaryotic cells can migrate using different modes, ranging from amoeboid-like, during which actin filled protrusions come and go, to keratocyte-like, characterized by a stable actin wave at the front of the cell and persistent motion. How cells can switch between these modes is not well understood but waves of signaling events that lead to actin waves propagation are thought to play an important role in these transitions. Our experiments, performed with Dictyostelium discoideum, show that systematically reducing the protrusion force of the actin network using a drug, latrunculin B, leads to different migration modes including amoeboid-like and keratocyte-like. We find that a sufficient decrease of the protrusion force can destabilize keratocyte-like cells, resulting in cells that employ amoeboid-like migration. We then present a simple two-component biochemical reaction-diffusion model based on relaxation oscillators and couple this to a model for the mechanics of cell deformations. Predictions of the model are in good agreement with the experiments. Our results indicate the importance of coupling signaling events to cell mechanics and morphology and may be applicable in a wide variety of cell motility systems.   

Collective Cell Migration in Wound Healing

Following a wound, epithelial cells migrate collectively to heal. During healing, “leader cells” begin to form at the free edge and migrate as finger-like, multi-cellular protrusions into the wound boundary. While the presence of leader cells is well documented, factors contributing to their formation is not well understood. Standard wound healing assays often culture cells against a physical barrier, and cells migrate to the free space once the barrier is removed. However, the role of time in culture against a barrier in leader cell formation has not been studied. To address this, a monolayer of Human Keratinocytes (HaCaTs) is seeded against PDMS barriers. The time in culture is varied to study its effect on cell force, motion, wound closure, distribution of actin, and the presence of leader cells following barrier removal by using traction force microscopy and fluorescent imaging. With increased time against a barrier, the number of leader cells increased, a multi-cellular actin cable was formed at the leading edge, and cell migration speeds decreased. The resulting data point to the importance of time in culture in altering cellular mechanics to affect wound healing and add new understanding of factors affecting formation of leader cells in collective cell migration.   

Traction dynamics in collective cell migration

Recent theoretical models have emphasized cell motility force as a key driver of collective cell migration. In experiments, the equivalent to the motility force is traction applied by each cell to the substrate, which can be measured by traction force microscopy. Previous experiments have measured tractions in groups of cells but have not tracked tractions applied by individual cells. As a result, there is a lack of information on single-cell tractions over time, which makes it difficult to bridge the gap between single cell and collective cell dynamics. Here, we designed experiments to follow cells in a Lagrangian frame of reference, tracking each cell using fluorescent imaging of its nucleus. To investigate the evolution of traction of each cell over time, we built a Voronoi tessellation based on the centroids of cell nuclei and mapped tractions obtained from traction force microscopy onto each cell’s Voronoi-based polygon. The resulting data can be used to compute different metrics of traction dynamics of each cell such as the persistence of both direction and magnitude of traction. This new approach helps to investigate theoretical predictions of cell motility force on collective cell migration, thus bridging the gap between single cell and collective cell dynamics.