A fully continuous individual-based model of tumor cell evolution.

The aim of this work is to develop and study a fully continuous individual-based model (IBM) for cancer tumor invasion into a spatial environment of surrounding tissue. The IBM improves previous spatially discrete models, because it is continuous in all variables (including spatial variables), and thus not constrained to lattice frameworks. The IBM includes four types of individual elements: tumor cells, extracellular macromolecules (MM), a matrix degradative enzyme (MDE), and oxygen. The algorithm underlying the IBM is based on the dynamic interaction of these four elements in the spatial environment, with special consideration of mutation phenotypes. A set of stochastic differential equations is formulated to describe the evolution of the IBM in an equivalent way. The IBM is scaled up to a system of partial differential equations (PDE) representing the limiting behavior of the IBM as the number of cells and molecules approaches infinity. Both models (IBM and PDE) are numerically simulated with two kinds of initial conditions: homogeneous MM distribution and heterogeneous MM distribution. With both kinds of initial MM distributions spatial fingering patterns appear in the tumor growth. The output of both simulations is quite similar.

Biodegradation of oxadiazon by a soil isolated Pseudomonas fluorescens strain CG5: Implementation in an herbicide removal reactor and modelling.

An oxadiazon-degrading bacterial, Pseudomonas strain CG5, was isolated from an agricultural contaminated soil. This strain CG5 was able to grow on 10mg of oxadiazon per l, yielding 5.18+/-0.2 mg of protein biomass mol(-1). GC-MS analyses of the metabolites from oxadiazon catabolism revealed its dehalogenation and degradation to form non-toxic end-products, cells were then immobilized by adsorption on a ceramic support to be used as biocatalysts in herbicide removal biofilm-reactor processes. Seventy-two per cent of the oxadiazon was removed, and the maximum specific substrate uptake rate was 10.63+/-0.5 microg h(-1) mg(-1) prot. A new mathematical model was developed to interpret and predict the behaviour of the bacteria and pollutants in a biofilm-reactor system, to consider biofilm structural and morphological properties.