MODELLING THE INFLUENCE OF NUCLEUS ELASTICITY ON CELL INVASION IN FIBER NETWORKS AND MICROCHANNELS

Cell migration in highly constrained extracellular matrices is exploited in scaffold-based tissue engineering and is fundamental in a wide variety of physiological and pathological phenomena, among others in cancer invasion and development. Research into the critical processes involved in cell migration has mainly focused on cell adhesion and proteolytic degradation of the external environment. However, rising evidence has recently shown that a number of cell-derived biophysical and mechanical parameters, among others nucleus stiffness and cell deformability, plays a major role in cell motility, especially in the ameboid-like migration mode in 3D confined tissue structures. We here present an extended cellular Potts model (CPM) first used to simulate a micro-fabricated migration chip, which tests the active invasive behavior of cancer cells into narrow channels. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated in the nucleus and in the cytosolic region, while the migration chamber is composed of channels of different widths. We find that cell motile phenotype and velocity in open spaces (i.e., 2D flat surfaces or large channels) are not significantly influenced by cell elastic properties. On the contrary, the migratory behavior of cells within subcellular and subnuclear structures strongly relies on the deformability of the cytosol and of the nuclear cluster, respectively. Further, we characterize two migration dynamics: a stepwise way, characterized by fluctuations in cell length, within channels smaller than nucleus dimensions and a smooth sliding (i.e., maintaining constant cell length) behavior within channels larger than the nuclear cluster. These resulting observations are then extended looking at cell migration in an artificial fiber network, which mimics cell invasion in a 3D extracellular matrix. In particular, in this case, we analyze the effect of variations in elasticity of the nucleus on cell movement. In order to summarize, with our simulated migration assays, we demonstrate that the dimensionality of the environment strongly affects the migration phenotype and we suggest that the cytoskeletal and nuclear elastic characteristics correlate with the tumor cell's invasive potentia

A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features

Differentiated cell behavior: a multiscale approach using measure theory

This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving measures, rather than at individual cell paths, we obtain an ensemble representation stemming from the phenomenological behavior of the single component cells. In particular, as a key advantage of our approach, the scale of representation of the system, i.e., microscopic/discrete vs. macroscopic/continuous, can be chosen a posteriori according only to the spatial structure given to the aforesaid measures. The paper focuses in particular on the use of different scales based on the specific functions performed by cells. A two-population hybrid system is considered, where cells with a specialized/differentiated phenotype are treated as a discrete population of point masses while unspecialized/undifferentiated cell aggregates are represented with a continuous approximation. Numerical simulations and analytical investigations emphasize the role of some biologically relevant parameters in determining the specific evolution of such a hybrid cell system.Comment: 25 pages, 6 figure

Multiscale developments of cellular Potts models

Multiscale problems are ubiquitous and fundamental in all biological phenomena that emerge naturally from the complex interaction of processes which occur at various levels. A number of both discrete and continuous mathematical models and methods have been developed to address such an intricate network of organization. One of the most suitable individual cell-based model for this purpose is the well-known cellular Potts model (CPM). The CPM is a discrete, lattice-based, flexible technique that is able to accurately identify and describe the phenomenological mechanisms which are responsible for innumerable biological (and nonbiological) phenomena. In this work, we first give a brief overview of its biophysical basis and discuss its main limitations. We then propose some innovative extensions, focusing on ways of integrating the basic mesoscopic CPM with accurate continuous models of microscopic dynamics of individuals. The aim is to create a multiscale hybrid framework that is able to deal with the typical multilevel organization of biological development, where the behavior of the simulated individuals is realistically driven by their internal state. Our CPM extensions are then tested with sample applications that show a qualitative and quantitative agreement with experimental data. Finally, we conclude by discussing further possible developments of the metho

Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles

The description of the cell spatial pattern and characteristic distances is fundamental in a wide range of physio-pathological biological phenomena, from morphogenesis to cancer growth. Discrete particle models are widely used in this field, since they are focused on the cell-level of abstraction and are able to preserve the identity of single individuals reproducing their behavior. In particular, a fundamental role in determining the usefulness and the realism of a particle mathematical approach is played by the choice of the intercellular pairwise interaction kernel and by the estimate of its parameters. The aim of the paper is to demonstrate how the concept of H-stability, deriving from statistical mechanics, can have important implications in this respect. For any given interaction kernel, it in fact allows to a priori predict the regions of the free parameter space that result in stable configurations of the system characterized by a finite and strictly positive minimal interparticle distance, which is fundamental when dealing with biological phenomena. The proposed analytical arguments are indeed able to restrict the range of possible variations of selected model coefficients, whose exact estimate however requires further investigations (e.g., fitting with empirical data), as illustrated in this paper by series of representative simulations dealing with cell colony reorganization, sorting phenomena and zebrafish embryonic development

Un WEBGIS Open Source a supporto dei rilievi GPS in Sicilia

Con il rapido sviluppo di Internet, degli ultimi anni, i sistemi informativi geografici basati sull’utilizzo del Web sono diventati un argomento di forte interesse per il settore dei GIS. Il WEBGIS è uno strumento software, basato su sistemi di reti locali o geografiche e su un’interfaccia semplificata operante tramite browser Internet, che permette l’accesso a banche dati geografiche, anche a persone non esperte del settore. Tramite tale strumento è possibile visualizzare contestualmente informazioni geografiche organizzate su livelli informativi tematici, anche caratterizzati da diverso sistema di riferimento geografico ed eseguire, tramite un’interfaccia Web semplificata, parte delle operazioni che normalmente vengono eseguite con software GIS per desktopworkstation. Un WEBGIS permette quindi in modo efficiente ed a costi contenuti la condivisione di informazioni geografiche ad un più vasto pubblico non necessariamente limitato ai soli addetti ai lavori. I campi applicativi dei WEBGIS sono molteplici ed ancor più numerosi di quelli dei GIS (non dimenticando che dietro un WEBGIS c’è sempre un GIS messo a punto da esperti del settore). Di interesse è anche quello del rilievo tramite strumenti di posizionamento globale (GNSS); il WEBGIS, infatti, può anche essere un utile strumento a supporto dei rilievi condotti o da effettuarsi con ricevitori GNSS, permettendo la fornitura di informazioni utili per le fasi preliminari al rilievo (copertura rete telefonica, collegamento internet, monografie dei punti) e/o successive ad esso (download dati necessari al post processing, monografie stazioni permanenti e coordinate aggiornate). Sulla base di tali istanze e dell’esistenza di una rete di stazioni permanenti, a copertura della Sicilia occidentale, realizzata dal 2005 al 2007 per fini non soltanto scientifici, ma anche tecnici, presso il Dipartimento di Rappresentazione dell’Università di Palermo (oggi Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, DICA) si è ritenuta di interesse la realizzazione di uno strumento software (WEBGIS), tale da permettere la gestione della grande mole di dati geografici, giornalmente acquisiti, in modo da supportare ricercatori e tecnici durante le operazioni preliminari al rilievo ed al post-processing dei dati rilevati

Functional traits of two co-occurring sea urchins across a barren/forest patch system

Temperate rocky reefs may occur in two alternative states (coralline barrens and erect algal forests), whose formation and maintenance are often determined by sea urchin grazing. The two sea urchin species Paracentrotus lividus and Arbacia lixula are considered to play a similar ecological role despite their differing morphological traits and diets. The patchy mosaic areas of Ustica Island, Italy, offer an ideal environment in which to study differences in the performance of P. lividus and A. lixula in barren versus forest states. Results show that the two sea urchin species differ in diet, trophic position, grazing adaptation, movement ability and fitness in both barren and forest patches. We confirmed herbivory in P. lividus and omnivory with a strong tendency to carnivory in A. lixula. When the sea urchin escape response to a predator was triggered, P. lividus responded faster in barren and forest patches. Forest patch restricted movement, especially in A. lixula (velocity in barren ≈10-fold greater than in forest). A large Aristotle's lantern, indicative of durophagy, confirmed adaptation of A. lixula to barren state