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Abstract

This work is devoted to mathematical modeling of deregulation of the Wnt/β-catenin signaling pathway in medulloblastoma resulting in abnormal dynamics of target genes. Medulloblastoma is a brain tumor, mostly diagnosed in children. It is associated with several molecular genetic alterations. Specific aberrations of chromosome 6q, leading either to the chromosome copy-number loss (monosomy 6) or gain (trisomy 6), occur in two different subtypes of the tumor. The model is a nine-dimensional system of ordinary differential equations and describes nonlinear dynamics of the key ingredients of the signaling process. The model is based on the law of mass action and accounts for a two-compartment architecture of a cell consisting of the nucleus and cytoplasm. The model helps to understand molecular differences between the two medulloblastoma mutation subtypes that are associated with different patient prognosis. Our studies are based on a collaboration with the group of Prof. Dr. med. Stefan Pfister at the Division of Pediatric Neuro-oncology Research Group of the German Cancer Research Center (DKFZ). The model is used to evaluate data from the gene expression microarray data from the clinics in Heidelberg, Boston and Amsterdam. Numerical simulations lead to new biological hypotheses related to a significant role of the regulatory loop SGK1-GSK3β-MYC, a part of the Wnt/β-catenin signaling pathway. Simulations indicate the advantage of using the pharmacological inhibitor of SGK1 in patients with copy-number gain of chromosome 6q. Finally, the simulation results suggest a beneficial use of an adjuvant therapy in a trisomy 6 treatment. Mathematical analysis of the ordinary differential equations system confirms the wellposedness of the model and provides basic properties of the solutions. Supported by numerical analysis, we conclude about global stability of a unique positive equilibrium corresponding to the homeostasis of the system. We also tackle the parameter estimation problem using statistical assessment of the results and Gauss-Newton method. Sensitivity analysis provides insight into the role of model parameters. In particular, it confirms the sensitivity of the system to the parameter of SGK1 degradation. The model provides a powerful tool to study mechanistically the underlying process and to support the experiments.