Cellular Tango: how extracellular matrix adhesion choreographs Rac-Rho signaling and cell movement.

The small GTPases Rac and Rho are known to regulate eukaryotic cell shape, promoting front protrusion (Rac) or rear retraction (Rho) of the cell edge. Such cell deformation changes the contact and adhesion of cell to the extracellular matrix (ECM), while ECM signaling through integrin receptors also affects GTPase activity. We develop and investigate a model for this three-way feedback loop in 1D and 2D spatial domains, as well as in a fully deforming 2D cell shapes with detailed adhesion-bond biophysics. The model consists of reaction-diffusion equations solved numerically with open-source software, Morpheus, and with custom-built cellular Potts model simulations. We find a variety of patterns and cell behaviors, including persistent polarity, flipped front-back cell polarity oscillations, spiral waves, and random protrusion-retraction. We show that the observed spatial patterns depend on the cell shape, and vice versa.

Symmetry and fluctuation of cell movements in neural crest-derived facial mesenchyme.

In the face, symmetry is established when bilateral streams of neural crest cells leave the neural tube at the same time, follow identical migration routes and then give rise to the facial prominences. However, developmental instability exists, particularly surrounding the steps of lip fusion. The causes of instability are unknown but inability to cope with developmental fluctuations are a likely cause of congenital malformations, such as non-syndromic orofacial clefts. Here, we tracked cell movements over time in the frontonasal mass, which forms the facial midline and participates in lip fusion, using live-cell imaging of chick embryos. Our mathematical examination of cell velocity vectors uncovered temporal fluctuations in several parameters, including order/disorder, symmetry/asymmetry and divergence/convergence. We found that treatment with a Rho GTPase inhibitor completely disrupted the temporal fluctuations in all measures and blocked morphogenesis. Thus, we discovered that genetic control of symmetry extends to mesenchymal cell movements and that these movements are of the type that could be perturbed in asymmetrical malformations, such as non-syndromic cleft lip. This article has an associated 'The people behind the papers' interview.

Spots, stripes, and spiral waves in models for static and motile cells : GTPase patterns in cells.

The polarization and motility of eukaryotic cells depends on assembly and contraction of the actin cytoskeleton and its regulation by proteins called GTPases. The activity of GTPases causes assembly of filamentous actin (by GTPases Cdc42, Rac), resulting in protrusion of the cell edge. Mathematical models for GTPase dynamics address the spontaneous formation of patterns and nonuniform spatial distributions of such proteins in the cell. Here we revisit the wave-pinning model for GTPase-induced cell polarization, together with a number of extensions proposed in the literature. These include introduction of sources and sinks of active and inactive GTPase (by the group of A. Champneys), and negative feedback from F-actin to GTPase activity. We discuss these extensions singly and in combination, in 1D, and 2D static domains. We then show how the patterns that form (spots, waves, and spirals) interact with cell boundaries to create a variety of interesting and dynamic cell shapes and motion.

Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics.

Many cells are small and rounded on soft extracellular matrices (ECM), elongated on stiffer ECMs, and flattened on hard ECMs. Cells also migrate up stiffness gradients (durotaxis). Using a hybrid cellular Potts and finite-element model extended with ODE-based models of focal adhesion (FA) turnover, we show that the full range of cell shape and durotaxis can be explained in unison from dynamics of FAs, in contrast to previous mathematical models. In our 2D cell-shape model, FAs grow due to cell traction forces. Forces develop faster on stiff ECMs, causing FAs to stabilize and, consequently, cells to spread on stiff ECMs. If ECM stress further stabilizes FAs, cells elongate on substrates of intermediate stiffness. We show that durotaxis follows from the same set of assumptions. Our model contributes to the understanding of the basic responses of cells to ECM stiffness, paving the way for future modeling of more complex cell-ECM interactions.

Autocrine inhibition of cell motility can drive epithelial branching morphogenesis in the absence of growth.

Epithelial branching morphogenesis drives the development of organs such as the lung, salivary gland, kidney and the mammary gland. It involves cell proliferation, cell differentiation and cell migration. An elaborate network of chemical and mechanical signals between the epithelium and the surrounding mesenchymal tissues regulates the formation and growth of branching organs. Surprisingly, when cultured in isolation from mesenchymal tissues, many epithelial tissues retain the ability to exhibit branching morphogenesis even in the absence of proliferation. In this work, we propose a simple, experimentally plausible mechanism that can drive branching morphogenesis in the absence of proliferation and cross-talk with the surrounding mesenchymal tissue. The assumptions of our mathematical model derive from in vitro observations of the behaviour of mammary epithelial cells. These data show that autocrine secretion of the growth factor TGF[Formula: see text]1 inhibits the formation of cell protrusions, leading to curvature-dependent inhibition of sprouting. Our hybrid cellular Potts and partial-differential equation model correctly reproduces the experimentally observed tissue-geometry-dependent determination of the sites of branching, and it suffices for the formation of self-avoiding branching structures in the absence and also in the presence of cell proliferation. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

From energy to cellular forces in the Cellular Potts Model: An algorithmic approach.

Single and collective cell dynamics, cell shape changes, and cell migration can be conveniently represented by the Cellular Potts Model, a computational platform based on minimization of a Hamiltonian. Using the fact that a force field is easily derived from a scalar energy (F = -∇H), we develop a simple algorithm to associate effective forces with cell shapes in the CPM. We predict the traction forces exerted by single cells of various shapes and sizes on a 2D substrate. While CPM forces are specified directly from the Hamiltonian on the cell perimeter, we approximate the force field inside the cell domain using interpolation, and refine the results with smoothing. Predicted forces compare favorably with experimentally measured cellular traction forces. We show that a CPM model with internal signaling (such as Rho-GTPase-related contractility) can be associated with retraction-protrusion forces that accompany cell shape changes and migration. We adapt the computations to multicellular systems, showing, for example, the forces that a pair of swirling cells exert on one another, demonstrating that our algorithm works equally well for interacting cells. Finally, we show forces exerted by cells on one another in classic cell-sorting experiments.

Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis.

Mathematical modeling is an essential approach for the understanding of complex multicellular behaviors in tissue morphogenesis. Here, we review the cellular Potts model (CPM; also known as the Glazier-Graner-Hogeweg model), an effective computational modeling framework. We discuss its usability for modeling complex developmental phenomena by examining four fundamental examples of tissue morphogenesis: (i) cell sorting, (ii) cyst formation, (iii) tube morphogenesis in kidney development, and (iv) blood vessel formation. The review provides an introduction for biologists for starting simulation analysis using the CPM framework.

Cell Contractility Facilitates Alignment of Cells and Tissues to Static Uniaxial Stretch.

During animal development and homeostasis, the structure of tissues, including muscles, blood vessels, and connective tissues, adapts to mechanical strains in the extracellular matrix (ECM). These strains originate from the differential growth of tissues or forces due to muscle contraction or gravity. Here we show using a computational model that by amplifying local strain cues, active cell contractility can facilitate and accelerate the reorientation of single cells to static strains. At the collective cell level, the model simulations show that active cell contractility can facilitate the formation of strings along the orientation of stretch. The computational model is based on a hybrid cellular Potts and finite-element simulation framework describing a mechanical cell-substrate feedback, where: 1) cells apply forces on the ECM, such that 2) local strains are generated in the ECM and 3) cells preferentially extend protrusions along the strain orientation. In accordance with experimental observations, simulated cells align and form stringlike structures parallel to static uniaxial stretch. Our model simulations predict that the magnitude of the uniaxial stretch and the strength of the contractile forces regulate a gradual transition between stringlike patterns and vascular networklike patterns. Our simulations also suggest that at high population densities, less cell cohesion promotes string formation.

Association with pathogenic bacteria affects life-history traits and population growth in Caenorhabditis elegans.

Determining the relationship between individual life-history traits and population dynamics is an essential step to understand and predict natural selection. Model organisms that can be conveniently studied experimentally at both levels are invaluable to test the rich body of theoretical literature in this area. The nematode Caenorhabditis elegans, despite being a well-established workhorse in genetics, has only recently received attention from ecologists and evolutionary biologists, especially with respect to its association with pathogenic bacteria. In order to start filling the gap between the two areas, we conducted a series of experiments aiming at measuring life-history traits as well as population growth of C. elegans in response to three different bacterial strains: Escherichia coli OP50, Salmonella enterica Typhimurium, and Pseudomonas aeruginosa PAO1. Whereas previous studies had established that the latter two reduced the survival of nematodes feeding on them compared to E. coli OP50, we report for the first time an enhancement in reproductive success and population growth for worms feeding on S. enterica Typhimurium. Furthermore, we used an age-specific population dynamic model, parameterized using individual life-history assays, to successfully predict the growth of populations over three generations. This study paves the way for more detailed and quantitative experimental investigation of the ecology and evolution of C. elegans and the bacteria it interacts with, which could improve our understanding of the fate of opportunistic pathogens in the environment.

Nodal signaling range is regulated by proprotein convertase-mediated maturation.

Tissue patterning is established by extracellular growth factors or morphogens. Although different theoretical models explaining specific patterns have been proposed, our understanding of tissue pattern establishment in vivo remains limited. In many animal species, left-right patterning is governed by a reaction-diffusion system relying on the different diffusivity of an activator, Nodal, and an inhibitor, Lefty. In a genetic screen, we identified a zebrafish loss-of-function mutant for the proprotein convertase FurinA. Embryological and biochemical experiments demonstrate that cleavage of the Nodal-related Spaw proprotein into a mature form by FurinA is required for Spaw gradient formation and activation of Nodal signaling. We demonstrate that FurinA is required cell-autonomously for the long-range signaling activity of Spaw and no other Nodal-related factors. Combined in silico and in vivo approaches support a model in which FurinA controls the signaling range of Spaw by cleaving its proprotein into a mature, extracellular form, consequently regulating left-right patterning.

Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro.

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.