Mathematical Modelling of Molecular Pathways Enabling Tumour Cell Invasion and Migration

Abstract

Understanding the etiology of metastasis is very important in clinical perspective, since it is estimated that metastasis accounts for 90% of cancer patient mortality. Metastasis results from a sequence of multiple steps including invasion and migration. The early stages of metastasis are tightly controlled in normal cells and can be drastically affected by malignant mutations; therefore, they might constitute the principal determinants of the overall metastatic rate even if the later stages take long to occur. To elucidate the role of individual mutations or their combinations affecting the metastatic development, a logical model has been constructed that recapitulates published experimental results of known gene perturbations on local invasion and migration processes, and predict the effect of not yet experimentally assessed mutations. The model has been validated using experimental data on transcriptome dynamics following TGF-β-dependent induction of Epithelial to Mesenchymal Transition in lung cancer cell lines. A method to associate gene expression profiles with different stable state solutions of the logical model has been developed for that purpose. In addition, we have systematically predicted alleviating (masking) and synergistic pairwise genetic interactions between the genes composing the model with respect to the probability of acquiring the metastatic phenotype. We focused on several unexpected synergistic genetic interactions leading to theoretically very high metastasis probability. Among them, the synergistic combination of Notch overexpression and p53 deletion shows one of the strongest effects, which is in agreement with a recent published experiment in a mouse model of gut cancer. The mathematical model can recapitulate experimental mutations in both cell line and mouse models. Furthermore, the model predicts new gene perturbations that affect the early steps of metastasis underlying potential intervention points for innovative therapeutic strategies in oncology.

Fig 1. Regulatory networks of mechanisms leading to EMT, invasion, migration and metastasis.

A. Detailed network of the pathways involved in metastasis. B. Modular network derived from network in A.

Fig 2. A. Genetic interactions between two mutants leading to the masking or the antagonism of a phenotype (metastasis).

Application of non-linear dimension reduction for visualising the distribution of phenotype probabilities, computed with MaBoSS for all single and double mutants of the model. The grading in the background shows the density of points (mutants) projections. Six clusters are distinguished based on this grading. Wild-type model, all single over-expression and knockout mutants and the NICD GoF / p53 LoF mutant are labelled. Note that each gene pair in this plot is represented by four different double mutants (small red points) corresponding to LoF/LoF, LoF/GoF, GoF/LoF, GoF/GoF combinations. B. Genetic interaction network showing the most significant synergistic (shown in green) and alleviating (masking, showing in red) interactions between GoF and LoF mutants with respect to the probability of having metastasis. The size of the node reflects the metastasis probability for individual mutation. The thickness of the edge reflects the absolute value of epistasis measure (see Methods).

Fig 3. MaBoSS simulation of wild type, of individual mutations of p53 and NICD and of the double mutant.

The probabilities associated with each phenotype represent the number of stochastic simulations leading to each phenotype from pre-defined initial conditions. A. Wild type, see text. B. p53 LoF, same phenotypes found in (A) are reachable but with different probabilities than wild type conditions. C. NICD GoF, apoptosis is no longer reachable. D. p53 LoF and NICD GoF, only metastasis is observed. Note that HS stands for “Homeostatic State” and CCA for “CellCycleArrest.”