The aim of this study was to describe and analyze the regulation and spatio-temporal dynamics of melanocyte migration in vitro and its coupling to cell division and interaction with the matrix. The melanocyte lineage is particularly interesting because it is involved in both embryonic development and oncogenesis/metastasis (melanoma). Biological experiments were performed on two melanocyte cell lines established from wild-type and β-catenin-transgenic mice (bcat*). The multi-functional β-catenin molecule is known to be able to regulate the transcription of various genes involved in cell proliferation and migration, particularly in the melanocyte lineage. We also investigated fibronectin, an extra-cellular matrix protein that binds integrins, thereby providing adhesion points for cells and encouraging migration. As the migration of individual cells were followed, automated methods were required for processing the large amount of data generated by the time-lapse video-microscopy. A model-based approach for automated cell tracking was evaluated on a sample by comparison with manual tracking. This method was found reliable in studying overall cell behaviour. Its application to all the observed sequences provided insight into the factors affecting melanocyte migration in vitro: melanocytes of mutated form of β-catenin showed higher division rates and no contact inhibition of growth was induced by the resulting increase in cell density. However, cell density limited the amplitude of cell displacements, although their motility was less affected. The high fibronectin concentration bound to substratum promoted cell migration and motility, the effect being more intense for wild-type cells than for cells with β-catenin over-expression. During the division process, cell migration speed increased rapidly then decreased slowly. Analyses of such data is expected to lead both to biological answers and to a framework for a better modeling processes in the future.

Cell motility is an integral part of a diverse set of biological processes. The quest for mathematical models of cell motility has prompted the development of automated approaches for gathering quantitative data on cell morphology, and the distribution of molecular players involved in cell motility. Here we review recent approaches for quantifying cell motility, including automated cell segmentation and tracking. Secondly, we present our own novel method for tracking cell boundaries of moving cells, the Electrostatic Contour Migration Method (ECMM), as an alternative to the generally accepted level set method (LSM). ECMM smoothly tracks regions of the cell boundary over time to compute local membrane displacements using the simple underlying concept of electrostatics. It offers substantial speed increases and reduced computational overheads in comparison to the LSM. We conclude with general considerations regarding boundary tracking in the context of mathematical modelling.

In this paper, we propose a computational model to investigate the coupling between cell’s adhesions and actin fibres and how this coupling affects cell shape and stability. To accomplish that, we take into account the successive stages of adhesion maturation from adhesion precursors to focal complexes and ultimately to focal adhesions, as well as the actin fibres evolution from growing filaments, to bundles and finally contractile stress fibres.

We use substrates with discrete patterns of adhesive patches, whose inter-patches distance can be modulated in order to control the location of the adhesions and the resulting fibres architecture. We then investigate the emergence of stable cell morphologies as a function of the inter-patches distance, for two different cell phenotypes generated from the model. Force generated by the stress fibres on the focal adhesions and specifically the influence of the cell contractility are also investigated.

Our results suggest that adhesion lifetime and fibre growing rate are the key parameters in the emergence of stable cell morphologies and the limiting factors for the magnitude of the mean tension force from the fibres on the focal adhesions.

We present a simple mechanism of cell motility in a confined geometry, inspired by recent motility assays in microfabricated channels. This mechanism relies mainly on the coupling of actin polymerisation at the cell membrane to geometric confinement. We first show analytically using a minimal model of polymerising viscoelastic gel confined in a narrow channel that spontaneous motion occurs due to polymerisation alone. Interestingly, this mechanism does not require specific adhesion with the channel walls, and yields velocities potentially larger than the polymerisation velocity of the gel. We then study the effect of the contractile activity of myosin motors, and show that whilst it is not necessary to induce motion, it quantitatively increases the velocity of motion in the polymerisation mechanism we describe. Our model qualitatively accounts for recent experiments which show that cells without specific adhesion proteins are motile only in confined environments while they are unable to move on a flat surface. It also constitutes a first step in the study of cell migration in more complex confined geometries such as living tissues.

Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated analogy between surface tension and cell-cell adhesion, we demonstrate that such a mechanism is unable to recruit cells to the sprout. Moreover, the expansion of such hypothetical sprouts is limited by a form of the Plateau-Taylor instability. In contrast, actively moving cells – guided by cell-cell contacts – can readily populate and expand linear sprouts. We argue that preferential attraction to the surfaces of elongated cells can provide a generic mechanism, shared by several cell types, for multicellular sprout formation.

The oriented movement of biological cells or organisms in response to a chemical gradient is called chemotaxis. The most interesting situation related to self-organization phenomenon takes place when the cells detect and response to a chemical which is secreted by themselves. Since pioneering works of Patlak (1953) and Keller and Segel (1970) many particularized models have been proposed to describe the aggregation phase of this process. Most of efforts were concentrated, so far, on mathematical models in which the formation of aggregate is interpreted as finite time blow-up of cell density. In recently proposed models cells are no more treated as point masses and their finite volume is accounted for. Thus, arbitrary high cell densities are precluded in such description and a threshold value for cells density is a priori assumed. Different modeling approaches based on this assumption lead to a class of quasilinear parabolic systems with strong nonlinearities including degenerate or singular diffusion. We give a survey of analytical results on the existence and uniqueness of global-in-time solutions, their convergence to stationary states and on a possibility of reaching the density threshold by a solution. Unsolved problems are pointed as well.

Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare them to relevant experimental data together with a critical analysis of the validity of the models based on recent observations of the swarming bacteria which show that nutrients are not limitating but distinct subpopulations growing at different rates are likely present.

Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels — a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour growth and wound healing. However, relatively few studies have examined the important role played by blood perfusion during angiogenesis and fewer still have explored the ways in which a dynamically evolving vascular bed architecture can affect the distribution of flow within it. From the perspective of solid tumour growth and, perhaps more importantly, its treatment (e.g. chemotherapy), it would clearly be of some benefit to understand this coupling between vascular structure and perfusion more fully. This paper focuses on the implications of such a coupling upon chemotherapeutic, anti-angiogenic, and anti-vascular treatments.

In an extension to previous work by the authors, the issue of pericyte recruitment during vessel maturation is considered in order to study the effects of different anti-vascular and anti-angiogenic therapies from a more rigorous modelling standpoint. Pericytes are a prime target for new vascular disrupting agents (VDAs) currently in clinical trials. However, different compounds attack different components of the vascular network and the implications of targeting only certain elements of the capillary bed are not immediately clear. In light of these uncertainties, the effects of anti-angiogenic and anti-vascular drugs are re-examined by using an extended model that includes an interdependency between vessel remodelling potential and local pericyte density. Two- and three-dimensional simulation results are presented and suggest that it may be possible to identify a VDA-specific “plasticity window” (a time period corresponding to low pericyte density), within which a given VDA would be most effective.

In vitro transmesothelial migration assays of ovarian cancer cells, isolated or aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts Models (CPM). We show that the simulations are in good agreement with the experimental evidence and that the overall process is regulated by the activity of matrix metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells with the extracellular matrix and between cells, both of the same type and of different types. In particular, the process depends on the ability of the cell to induce the loosening of cadherin-mediated junctions. Coherently with experiments, it is found that single cell invasion is more conservative with a crucial role played by MMPs. A similar important role is played in cell spheroid invasion, which in comparison is more disruptive. It achieves monofocal or multifocal characteristics according to the relative adhesion affinity among cells or between them and the mesothelial layer.

In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –, distinguished by specific interaction potentials and, eventually, also by the use of modified interaction criteria. For example, membrane sub-particles may interact only on a two-dimensional surface embedded on three-dimensional space, described via a restricted Delaunay triangulation. The model can be used not only to study cell shape and movement, but also has the potential to investigate the coupling between internal space-resolved movement of molecules and determined cell behaviors.