Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics.

We here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states.

Modelling Cell Orientation Under Stretch: The Effect of Substrate Elasticity.

When cells are seeded on a cyclically deformed substrate like silicon, they tend to reorient their major axis in two ways: either perpendicular to the main stretching direction, or forming an oblique angle with it. However, when the substrate is very soft such as a collagen gel, the oblique orientation is no longer observed, and the cells align either along the stretching direction, or perpendicularly to it. To explain this switch, we propose a simplified model of the cell, consisting of two elastic elements representing the stress fiber/focal adhesion complexes in the main and transverse directions.

Modeling hypoxia-related inflammation scenarios.

Cells respond to hypoxia via the activation of three isoforms of Hypoxia Inducible Factors (HIFs), that are characterized by different activation times. HIF overexpression has many effects on cell behavior, such as change in metabolism, promotion of angiogenic processes and elicitation of a pro-inflammatory response. These effects are driving forces of malignant progression in cancer cells.

A phenotype-structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment.

We here propose a one-dimensional spatially explicit phenotype-structured model to analyze selected aspects of avascular tumor progression. In particular, our approach distinguishes viable and necrotic cell fractions. The metabolically active part of the disease is, in turn, differentiated according to a continuous trait, that identifies cell variants with different degrees of motility and proliferation potential.

A hybrid integro-differential model for the early development of the zebrafish posterior lateral line.

The aim of this work is to provide a mathematical model to describe the early stages of the embryonic development of zebrafish posterior lateral line (PLL). In particular, we focus on evolution of PLL proto-organ (said primordium), from its formation to the beginning of the cyclical behavior that amounts in the assembly of immature proto-neuromasts towards its caudal edge accompanied by the deposition of mature proto-neuromasts at its rostral region. Our approach has an hybrid integro-differential nature, since it integrates a microscopic/discrete particle-based description for cell dynamics and a continuous description for the evolution of the spatial distribution of chemical substances (i.

Collective migration and patterning during early development of zebrafish posterior lateral line.

The morphogenesis of zebrafish posterior lateral line (PLL) is a good predictive model largely used in biology to study cell coordinated reorganization and collective migration regulating pathologies and human embryonic processes. PLL development involves the formation of a placode formed by epithelial cells with mesenchymal characteristics which migrates within the animal myoseptum while cyclically assembling and depositing rosette-like clusters (progenitors of neuromast structures). The overall process mainly relies on the activity of specific diffusive chemicals, which trigger collective directional migration and patterning.

An agent-based approach for modelling collective dynamics in animal groups distinguishing individual speed and orientation.

Collective dynamics in animal groups is a challenging theme for the modelling community, being treated with a wide range of approaches. This topic is here tackled by a discrete model. Entering in more details, each agent, represented by a material point, is assumed to move following a first-order Newtonian law, which distinguishes speed and orientation.

Modelling chase-and-run migration in heterogeneous populations.

Cell migration is crucial for many physiological and pathological processes. During embryogenesis, neural crest cells undergo coordinated epithelial to mesenchymal transformations and migrate towards various forming organs. Here we develop a computational model to understand how mutual interactions between migrating neural crest cells (NCs) and the surrounding population of placode cells (PCs) generate coordinated migration.

Kinesin-2 Controls the Motility of RAB5 Endosomes and Their Association with the Spindle in Mitosis.

RAB5 is a small GTPase that belongs to the wide family of Rab proteins and localizes on early endosomes. In its active GTP-bound form, RAB5 recruits downstream effectors that, in turn, are responsible for distinct aspects of early endosome function, including their movement along microtubules. We previously reported that, at the onset of mitosis, RAB5positive vesicles cluster around the spindle poles and, during metaphase, move along spindle microtubules.

A particle model analysing the behavioural rules underlying the collective flight of a bee swarm towards the new nest.

The swarming of a bee colony is guided by a small group of scout individuals, which are informed of the target destination (the new nest). However, little is known on the underlying mechanisms, i.e.

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.

A discrete particle model reproducing collective dynamics of a bee swarm.

In this article, we present a microscopic discrete mathematical model describing collective dynamics of a bee swarm. More specifically, each bee is set to move according to individual strategies and social interactions, the former involving the desire to reach a target destination, the latter accounting for repulsive/attractive stimuli and for alignment processes. The insects tend in fact to remain sufficiently close to the rest of the population, while avoiding collisions, and they are able to track and synchronize their movement to the flight of a given set of neighbors within their visual field.

TRPM8 inhibits endothelial cell migration via a non-channel function by trapping the small GTPase Rap1.

Endothelial cell adhesion and migration are critical steps of the angiogenic process, whose dysfunction is associated with tumor growth and metastasis. The TRPM8 channel has recently been proposed to play a protective role in prostate cancer by impairing cell motility. However, the mechanisms by which it could influence vascular behavior are unknown.

Modelling human perception processes in pedestrian dynamics: a hybrid approach.

In this paper, we present a hybrid mathematical model describing crowd dynamics. More specifically, our approach is based on the well-established Helbing-like discrete model, where each pedestrian is individually represented as a dimensionless point and set to move in order to reach a target destination, with deviations deriving from both physical and social forces. In particular, physical forces account for interpersonal collisions, whereas social components include the individual desire to remain sufficiently far from other walkers (the so-called territorial effect).

An Innovative Assay for the Analysis of In Vitro Endothelial Remodeling: Experimental and Computational Evidence.

The molecular and cellular mechanisms underlying vascular remodeling are currently investigated by experimental strategies which aim to mimic the complex environmental conditions found in vivo. Some of them focus on the tubulogenic activity of dispersed endothelial cell populations, while others evaluate vascular sprouting. Here we propose a new method to assess matrigel invasion starting from confluent or subconfluent monolayers of human microvascular ECs (HMVEC) seeded on different substrates.

Computational Approaches for Translational Oncology: Concepts and Patents.

Background: Cancer is a heterogeneous disease, which is based on an intricate network of processes at different spatiotemporal scales, from the genome to the tissue level. Hence the necessity for the biomedical and pharmaceutical research to work in a multiscale fashion. In this respect, a significant help derives from the collaboration with theoretical sciences.

Coherent modelling switch between pointwise and distributed representations of cell aggregates.

Biological systems are typically formed by different cell phenotypes, characterized by specific biophysical properties and behaviors. Moreover, cells are able to undergo differentiation or phenotypic transitions upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cells can be described either as pointwise/concentrated particles or as distributed masses, according to their biological determinants.

A node-based version of the cellular Potts model.

The cellular Potts model (CPM) is a lattice-based Monte Carlo method that uses an energetic formalism to describe the phenomenological mechanisms underlying the biophysical problem of interest. We here propose a CPM-derived framework that relies on a node-based representation of cell-scale elements. This feature has relevant consequences on the overall simulation environment.

A Cellular Potts Model of single cell migration in presence of durotaxis.

Cell migration is a fundamental biological phenomenon during which cells sense their surroundings and respond to different types of signals. In presence of durotaxis, cells preferentially crawl from soft to stiff substrates by reorganizing their cytoskeleton from an isotropic to an anisotropic distribution of actin filaments. In the present paper, we propose a Cellular Potts Model to simulate single cell migration over flat substrates with variable stiffness.

A cellular Potts model analyzing differentiated cell behavior during in vivo vascularization of a hypoxic tissue.

Angiogenesis, the formation of new blood vessel networks from existing capillary or post-capillary venules, is an intrinsically multiscale process occurring in several physio-pathological conditions. In particular, hypoxic tissue cells activate downstream cascades culminating in the secretion of a wide range of angiogenic factors, including VEGF isoforms. Such diffusive chemicals activate the endothelial cells (ECs) forming the external walls of the nearby vessels that chemotactically migrate toward the hypoxic areas of the tissue as multicellular sprouts.

An extended Cellular Potts Model analyzing a wound healing assay.

A suitable Cellular Potts Model is developed to reproduce and analyze an in vitro wound-healing assay. The proposed approach is able both to quantify the invasive capacity of the overall cell population and to evaluate selected determinants of single cell movement (velocity, directional movement, and final displacement). In this respect, the present CPM allows us to capture differences and correlations in the migratory behavior of cells initially located at different distances from the wound edge.

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.

A review of mathematical models for the formation of vascular networks.

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes 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 term describes the sprouting of new vessels from an existing capillary or post-capillary venule.

A Cellular Potts Model simulating cell migration on and in matrix environments.

Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence.

Modeling 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.