A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy.

Tumor angiogenesis is the process by which new blood vessels are formed and enhance the oxygenation and growth of tumors. As angiogenesis is recognized as being a critical event in cancer development, considerable efforts have been made to identify inhibitors of this process. Cytostatic treatments that target the molecular events of the angiogenesis process have been developed, and have met with some success. However, it is usually difficult to preclinically assess the effectiveness of targeted therapies, and apparently promising compounds sometimes fail in clinical trials. We have developed a multiscale mathematical model of angiogenesis and tumor growth. At the molecular level, the model focuses on molecular competition between pro- and anti-angiogenic substances modeled on the basis of pharmacological laws. At the tissue scale, the model uses partial differential equations to describe the spatio-temporal changes in cancer cells during three stages of the cell cycle, as well as those of the endothelial cells that constitute the blood vessel walls. This model is used to qualitatively assess how efficient endostatin gene therapy is. Endostatin is an anti-angiogenic endogenous substance. The gene therapy entails overexpressing endostatin in the tumor and in the surrounding tissue. Simulations show that there is a critical treatment dose below which increasing the duration of treatment leads to a loss of efficacy. This theoretical model may be useful to evaluate the efficacy of therapies targeting angiogenesis, and could therefore contribute to designing prospective clinical trials.

Kinetic analysis of the accumulation of a half-sandwich organo-osmium pro-drug in cancer cells.

The organo-osmium half-sandwich complex [(η6-p-cymene)Os(Ph-azopyridine-NMe2)I]+ (FY26) exhibits potent antiproliferative activity towards cancer cells and is active in vivo. The complex is relatively inert, but rapidly activated in cells by displacement of coordinated iodide. Here, we study time-dependent accumulation of FY26 in A2780 human ovarian cancer cells at various temperatures in comparison with the chlorido metabolite [(η6-p-cymene)Os(Ph-azopyridine-NMe2)Cl]+ (FY25). Mathematical models described the time evolution of FY26 and FY25 intracellular and extracellular concentrations taking into account both cellular transport (influx and efflux) and the intracellular conversion of FY26 to FY25. Uptake of iodide complex FY26 at 37 °C was 17× faster than that of chloride complex FY25, and efflux 1.4× faster. Osmium accumulation decreased markedly after 24 h of exposure. Modelling revealed that this phenomenon could be explained by complex-induced reduction of osmium uptake, rather than by a model involving enhanced osmium efflux. The intracellular osmium concentration threshold above which reduction in drug uptake was triggered was estimated as 20.8 µM (95% confidence interval [16.5, 30]). These studies provide important new insight into the dynamics of transport of this organometallic anticancer drug candidate.

Age-structured cell population model to study the influence of growth factors on cell cycle dynamics.

Cell proliferation is controlled by many complex regulatory networks. Our purpose is to analyse, through mathematical modeling, the effects of growth factors on the dynamics of the division cycle in cell populations. Our work is based on an age-structured PDE model of the cell division cycle within a population of cells in a common tissue. Cell proliferation is at its first stages exponential and is thus characterised by its growth exponent, the first eigenvalue of the linear system we consider here, a growth exponent that we will explicitly evaluate from biological data. Moreover, this study relies on recent and innovative imaging data (fluorescence microscopy) that make us able to experimentally determine the parameters of the model and to validate numerical results. This model has allowed us to study the degree of simultaneity of phase transitions within a proliferating cell population and to analyse the role of an increased growth factor concentration in this process. This study thus aims at helping biologists to elicit the impact of growth factor concentration on cell cycle regulation, at making more precise the dynamics of key mechanisms controlling the division cycle in proliferating cell populations, and eventually at establishing theoretical bases for optimised combined anticancer treatments.

Applying ecological and evolutionary theory to cancer: a long and winding road.

Since the mid 1970s, cancer has been described as a process of Darwinian evolution, with somatic cellular selection and evolution being the fundamental processes leading to malignancy and its many manifestations (neoangiogenesis, evasion of the immune system, metastasis, and resistance to therapies). Historically, little attention has been placed on applications of evolutionary biology to understanding and controlling neoplastic progression and to prevent therapeutic failures. This is now beginning to change, and there is a growing international interest in the interface between cancer and evolutionary biology. The objective of this introduction is first to describe the basic ideas and concepts linking evolutionary biology to cancer. We then present four major fronts where the evolutionary perspective is most developed, namely laboratory and clinical models, mathematical models, databases, and techniques and assays. Finally, we discuss several of the most promising challenges and future prospects in this interdisciplinary research direction in the war against cancer.