Nematode movement along a chemical gradient in a structurally heterogeneous environment : 2. Theory

L'influence de l'hétérogénéité sur la diffusion chimique et le déplacement des nématodes est étudiée par le biais d'un modèle théorique. Ce modèle prend en compte trois facteurs influant sur le déplacement des nématodes : la structure du sol, la stratégie de recherche de nourriture et la chémotaxie. Utilisant un modèle continu, nous avons mis au point un système discret permettant de simuler les traces des nématodes dans chacune des quatre situations définies par Anderson et al. (1997). Nous avons montré que l'hétérogénéité structurale provoque aussi bien des taux variables de concentrations du composé attractif dans des aires réduites que la reconnaissance de ce composé. L'hétérogénéité structurale du sol limite également la stratégie de recherche de nourriture du nématode lequel adopte alors une stratégie permettant d'éviter les pièges structuraux. Il est démontré que des augmentations localisées de la densité structurale accroissent significativement la reconnaissance du composé attractif. (Résumé d'auteur

Nematode movement along a chemical gradient in a structurally heterogeneous environment : 1 . Experiment

L'interaction entre l'hétérogénéité structurale et les gradients chimiques, ainsi que leur influence sur le déplacement des nématodes, ont été étudiées. Trois dispositifs expérimentaux ont été utilisés qui comprennent un nématode (#Caenorhabditis elegans) placé sur une couche homogène de milieu nutritif gélosé dans une boîte de Petri avec ou sans présence d'une source bactérienne de nourriture (#Escherichia coli) utilisée comme attractif. L'hétérogénéité structurale est réalisée en ajoutant des grains de sable en une seule épaisseur dans chacun des traitements homologues. Toutes les traces ont été relevées à l'aide d'un dispositif de vidéo à séquences temporelles et les données digitalisées avant analyse. Les répartitions des angles de changement de direction et les dimensions fractales des traces sont calculées pour chaque traitement. Il se révèle un effet statistiquement significatif (P inférieur ou égal à 0,01) de tous les traitements sur le déplacement des nématodes. En présence d'un produit attractif, le déplacement du nématode est plus linéaire et dirigé vers la source bactérienne. L'hétérogénéité structurale provoque un déplacement plus linéaire que dans le cas d'un milieu homogène. La dimension fractale des traces du nématode est significativement (P inférieur ou égal à 0,01) plus élevée pour les traitements sans sable ni bactéries que pour les autres traitements. Ces résultats permettent, pour la première fois, de quantifier le degré auquel les nématodes utilisent un comportement de recherche de nourriture au hasard dans un milieu homogène et adoptent un déplacement mieux orienté en présence d'un produit attractif. Finalement, lorsqu'une hétérogénéité est présente, la stratégie de recherche de nourriture devient plutôt une stratégie d'évitement permettant au nématode d'échapper aux "pièges" structuraux, tels les pores en cul-de-sac, et de pouvoir ainsi continuer à réagir à l'attraction. (Résumé d'auteur

Inferring tumour proliferative organisation from phylogenetic tree measures in a computational model

We use a computational modelling approach to explore whether it is possible to infer a solid tumour’s cellular proliferative hierarchy under the assumptions of the cancer stem cell hypothesis and neutral evolution. We focus on inferring the symmetric division probability for cancer stem cells, since this is believed to be a key driver of progression and therapeutic response. Motivated by the advent of multi-region sampling and resulting opportunities to infer tumour evolutionary history, we focus on a suite of statistical measures of the phylogenetic trees resulting from the tumour’s evolution in different regions of parameter space and through time. We find strikingly different patterns in these measures for changing symmetric division probability which hinge on the inclusion of spatial constraints. These results give us a starting point to begin stratifying tumours by this biological parameter and also generate a number of actionable clinical and biological hypotheses including changes during therapy, and through tumour evolution

Long-time behavior of an angiogenesis model with flux at the tumor boundary

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behaviour of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.Comment: 17 page

Inferring tumour proliferative organisation from phylogenetic tree measures in a computational model

We use a computational modelling approach to explore whether it is possible to infer a tumour's cell proliferative hierarchy, under the assumptions of the cancer stem cell hypothesis and neutral evolution. We focus on inferring the symmetric division probability for cancer stem cells in our model, as this is believed to be a key driving parameter of tumour progression and therapeutic response. Given the advent of multi-region sampling, and the opportunities offered by them to understand tumour evolutionary history, we focus on a suite of statistical measures of the phylogenetic trees resulting from the tumour's evolution in different regions of parameter space and through time. We find strikingly different patterns in these measures for changing symmetric division probability which hinge on the inclusion of spatial constraints. These results give us a starting point to begin stratifying tumours by this biological parameter and also generate a number of actionable clinical and biological hypotheses including changes during therapy, and through tumour evolution

Oscillatory wave fronts in chains of coupled nonlinear oscillators

Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress $F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate, for $F_{cd} < |F| < F_{cs}$ stable static and moving wave fronts coexist, and for $|F| > F_{cs}$ (static Peierls stress) there are only stable moving wave fronts. For piecewise linear models, extending an exact method of Atkinson and Cabrera's to chains with damped dynamics corroborates this description. For smooth nonlinearities, an approximate analytical description is found by means of the active point theory. Generically for small or zero damping, stable wave front profiles are non-monotone and become wavy (oscillatory) in one of their tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.

A new ghost cell/level set method for moving boundary problems:application to tumor growth

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth

MultiCellDS : a community-developed standard for curating microenvironment-dependent multicellular data

Exchanging and understanding scientific data and their context represents a significant barrier to advancing research, especially with respect to information siloing. Maintaining information provenance and providing data curation and quality control help overcome common concerns and barriers to the effective sharing of scientific data. To address these problems in and the unique challenges of multicellular systems, we assembled a panel composed of investigators from several disciplines to create the MultiCellular Data Standard (MultiCellDS) with a use-case driven development process. The standard includes (1) digital cell lines, which are analogous to traditional biological cell lines, to record metadata, cellular microenvironment, and cellular phenotype variables of a biological cell line, (2) digital snapshots to consistently record simulation, experimental, and clinical data for multicellular systems, and (3) collections that can logically group digital cell lines and snapshots. We have created a MultiCellular DataBase (MultiCellDB) to store digital snapshots and the 200+ digital cell lines we have generated. MultiCellDS, by having a fixed standard, enables discoverability, extensibility, maintainability, searchability, and sustainability of data, creating biological applicability and clinical utility that permits us to identify upcoming challenges to uplift biology and strategies and therapies for improving human health

MultiCellDS: a community-developed standard for curating microenvironment-dependent multicellular data

Exchanging and understanding scientific data and their context represents a significant barrier to advancing research, especially with respect to information siloing. Maintaining information provenance and providing data curation and quality control help overcome common concerns and barriers to the effective sharing of scientific data. To address these problems in and the unique challenges of multicellular systems, we assembled a panel composed of investigators from several disciplines to create the MultiCellular Data Standard (MultiCellDS) with a use-case driven development process. The standard includes (1) digital cell lines, which are analogous to traditional biological cell lines, to record metadata, cellular microenvironment, and cellular phenotype variables of a biological cell line, (2) digital snapshots to consistently record simulation, experimental, and clinical data for multicellular systems, and (3) collections that can logically group digital cell lines and snapshots. We have created a MultiCellular DataBase (MultiCellDB) to store digital snapshots and the 200+ digital cell lines we have generated. MultiCellDS, by having a fixed standard, enables discoverability, extensibility, maintainability, searchability, and sustainability of data, creating biological applicability and clinical utility that permits us to identify upcoming challenges to uplift biology and strategies and therapies for improving human health