Label Structured Cell Proliferation Models.

International audienceWe present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation

Recasting the cancer stem cell hypothesis: Unification using a continuum model of microenvironmental forces

Purpose of review Here, we identify shortcomings of standard compartment-based mathematical models of cancer stem-cells, and propose a continuous formalism which includes the tumor microenvironment. Recent findings Stem-cell models of tumor growth have provided explanations for various phenomena in oncology including, metastasis, drug- and radio-resistance, and functional heterogeneity in the face of genetic homogeneity. While some of the newer models allow for plasticity, or de-differentiation, there is no consensus on the mechanisms driving this. Recent experimental evidence suggests that tumor microenvironment factors like hypoxia, acidosis, and nutrient deprivation have causative roles. Summary To settle the dissonance between the mounting experimental evidence surrounding the effects of the microenvironment on tumor stemness, we propose a continuous mathematical model where we model microenvironmental perturbations like forces, which then shape the distribution of stemness within the tumor. We propose methods by which to systematically measure and characterize these forces, and show results of a simple experiment which support our claims

Deterministic mathematical modelling for cancer chronotherapeutics: cell population dynamics and treatment optimisation

Chronotherapeutics has been designed and used for more than twenty years as an effective treatment against cancer by a few teams around the world, among whom one of the first is Francis Lévi's at Paul-Brousse hospital (Villejuif, France), in application of circadian clock physiology to determine best infusion times within the 24-hour span for anticancer drug delivery. Mathematical models have been called in the last ten years to give a rational basis to such optimised treatments, for use in the laboratory and ultimately in the clinic. While actual clinical applications of the theoretical optimisation principles found have remained elusive so far to improve chronotherapeutic treatments in use, mathematical models provide proofs of concepts and tracks to be explored experimentally, to progress from theory to bedside. Starting from a simple ordinary differential equation model that allowed setting and numerically solving a drug delivery optimisation problem with toxicity constraints, this modelling enterprise has been extended to represent the division cycle in proliferating cell populations with different molecular targets, to allow for the representation of anticancer drug combinations that are used in clinical oncology. The main point to be made precise in such a therapeutic optimisation problem is to establish, here in the frame of circadian chronobiology, physiologically based differences between healthy and cancer cell populations in their responses to drugs. To this aim, clear biological evidence at the molecular level is still lacking, so that, starting from indirect observations at the experimental and clinical levels and from theoretical considerations on the model, speculations have been made, that will be exposed in this review of cancer chronotherapeutics models with the corresponding optimisation problems and their numerical solutions, to represent these differences between the two cell populations, with regard to circadian clock control