A Model for Membrane Degradation Using a Gelatin Invadopodia Assay.

One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells.

Modeling ATP-mediated endothelial cell elongation on line patterns.

Endothelial cell (EC) migration is crucial for a wide range of processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. We have previously demonstrated that ECs cultured on 15-μm wide adhesive line patterns exhibit three distinct migration phenotypes: (a) "running" cells that are polarized and migrate continuously and persistently on the adhesive lines with possible spontaneous directional changes, (b) "undecided" cells that are highly elongated and exhibit periodic changes in the direction of their polarization while maintaining minimal net migration, and (c) "tumbling-like" cells that migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. Importantly, the three migration patterns are associated with distinct profiles of cell length.

Numerical optimization of plasmid DNA delivery combined with hyaluronidase injection for electroporation protocol.

Background And Objective: The paper focuses on the numerical strategies to optimize a plasmid DNA delivery protocol, which combines hyaluronidase and electroporation.

Methods: A well-defined continuum mechanics model of muscle porosity and advanced numerical optimization strategies have been used, to propose a substantial improvement of a pre-existing experimental protocol of DNA transfer in mice. Our work suggests that a computational model might help in the definition of innovative therapeutic procedures, thanks to the fine tuning of all the involved experimental steps.

A Continuum Mechanics Model of Enzyme-Based Tissue Degradation in Cancer Therapies.

We propose a mathematical model to describe enzyme-based tissue degradation in cancer therapies. The proposed model combines the poroelastic theory of mixtures with the transport of enzymes or drugs in the extracellular space. The effect of the matrix-degrading enzymes on the tissue composition and its mechanical response are accounted for.

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres).

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes.

A Macroscopic Mathematical Model for Cell Migration Assays Using a Real-Time Cell Analysis.

Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This technology measures impedance changes caused by the gradual increase of electrode surface occupation by cells during the course of time and provide a Cell Index which is proportional to cellular morphology, spreading, ruffling and adhesion quality as well as cell number.

The dynamics of p53 in single cells: physiologically based ODE and reaction-diffusion PDE models.

The intracellular signalling network of the p53 protein plays important roles in genome protection and the control of cell cycle phase transitions. Recently observed oscillatory behaviour in single cells under stress conditions has inspired several research groups to simulate and study the dynamics of the protein with the aim of gaining a proper understanding of the physiological meanings of the oscillations. We propose compartmental ODE and PDE models of p53 activation and regulation in single cells following DNA damage and we show that the p53 oscillations can be retrieved by plainly involving p53-Mdm2 and ATM-p53-Wip1 negative feedbacks, which are sufficient for oscillations experimentally, with no further need to introduce any delays into the protein responses and without considering additional positive feedback.

Gene therapy: the role of cytoskeleton in gene transfer studies based on biology and mathematics.

Gene therapy is a promising approach for treating a wide range of human pathologies such as genetic disorders as well as diseases acquired over time. Viral and non-viral vectors are used to convey sequences of genes that can be expressed for therapeutic purposes. Plasmid DNA is receiving considerable attention for intramuscular gene transfer due to its safety, simplicity and low cost of production.

The p53 protein and its molecular network: modelling a missing link between DNA damage and cell fate.

Various molecular pharmacokinetic-pharmacodynamic (PK-PD) models have been proposed in the last decades to represent and predict drug effects in anticancer chemotherapies. Most of these models are cell population based since clearly measurable effects of drugs can be seen much more easily on populations of cells, healthy and tumour, than in individual cells. The actual targets of drugs are, however, cells themselves.

Design and optimization of reaction chamber and detection system in dynamic labs-on-chip for proteins detection.

In this paper, the lab-on-chip section for a protein assay is designed and optimized. To avoid severe reliability problems related to activated surface stability, a dynamic assay approach is adopted: protein-to-protein neutralization is performed while proteins diffuse freely in the reaction chamber. The related refraction index change is detected via an integrated interferometer.

A spatial physiological model for p53 intracellular dynamics.

In this paper we design and analyse a physiologically based model representing the accumulation of protein p53 in the nucleus after triggering of ATM by DNA damage. The p53 protein is known to have a central role in the response of the cell to cytotoxic or radiotoxic insults resulting in DNA damage. A reasonable requirement for a model describing intracellular signalling pathways is taking into account the basic feature of eukaryotic cells: the distinction between nucleus and cytoplasm.

A pressure model of immune response to mycobacterium tuberculosis infection in several space dimensions.

Mycobacterium tuberculosis (Mtb) is a widely diffused infection. However, in general, the human immune system is able to contain it. In this work, we propose a mathematical model which describes the early immune response to the Mtb infection in the lungs, also including the possible evolution of the infection in the formation of a granuloma.

A model of ischemia-induced neuroblast activation in the adult subventricular zone.

We have developed a rat brain organotypic culture model, in which tissue slices contain cortex-subventricular zone-striatum regions, to model neuroblast activity in response to in vitro ischemia. Neuroblast activation has been described in terms of two main parameters, proliferation and migration from the subventricular zone into the injured cortex. We observed distinct phases of neuroblast activation as is known to occur after in vivo ischemia.