A Versatile Mathematical Work-Flow to Explore How Cancer Stem Cell Fate Influences Tumor Progression.

BACKGROUND:Nowadays multidisciplinary approaches combining mathematical models with experimental assays are becoming relevant for the study of biological systems. Indeed, in cancer research multidisciplinary approaches are successfully used to understand the crucial aspects implicated in tumor growth. In particular, the Cancer Stem Cell (CSC) biology represents an area particularly suited to be studied through multidisciplinary approaches, and modeling has significantly contributed to pinpoint the crucial aspects implicated in this theory. More generally, to acquire new insights on a biological system it is necessary to have an accurate description of the phenomenon, such that making accurate predictions on its future behaviors becomes more likely. In this context, the identification of the parameters influencing model dynamics can be advantageous to increase model accuracy and to provide hints in designing wet experiments. Different techniques, ranging from statistical methods to analytical studies, have been developed. Their applications depend on case-specific aspects, such as the availability and quality of experimental data, and the dimension of the parameter space.RESULTS:The study of a new model on the CSC-based tumor progression has been the motivation to design a new work-flow that helps to characterize possible system dynamics and to identify those parameters influencing such behaviors. In detail, we extended our recent model on CSC-dynamics creating a new system capable of describing tumor growth during the different stages of cancer progression. Indeed, tumor cells appear to progress through lineage stages like those of normal tissues, being their division auto-regulated by internal feedback mechanisms. These new features have introduced some non-linearities in the model, making it more difficult to be studied by solely analytical techniques. Our new work-flow, based on statistical methods, was used to identify the parameters which influence the tumor growth. The effectiveness of the presented work-flow was firstly verified on two well known models and then applied to investigate our extended CSC model.CONCLUSIONS:We propose a new work-flow to study in a practical and informative way complex systems, allowing an easy identification, interpretation, and visualization of the key model parameters. Our methodology is useful to investigate possible model behaviors and to establish factors driving model dynamics. Analyzing our new CSC model guided by the proposed work-flow, we found that the deregulation of CSC asymmetric proliferation contributes to cancer initiation, in accordance with several experimental evidences. Specifically, model results indicated that the probability of CSC symmetric proliferation is responsible of a switching-like behavior which discriminates between tumorigenesis and unsustainable tumor growth.