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Frontiers in Mathematical Oncology

Creating Personalized Mathematical Models of Gene Expression in Thyroid Carcinoma

Kaitlin Sundling

University of Wisconsin


In the molecular era, computational tools are needed to translate big data into better outcomes for individual cancer patients. Personalized, well-validated mathematical models may be helpful in understanding the sources of variation and commonality among carcinomas. Many papillary thyroid carcinomas (PTCs) have an indolent course; however, a subset metastasize or invade nearby tissues. Using mathematical methods and focusing on pathways involved in epithelial-to-mesenchymal transition (EMT) and cancer stem cells, we aim to uncover underlying mechanisms of invasion and metastasis. We present an analysis of a personalized mathematical model of thyroid carcinoma utilizing publicly-available gene expression data.

Our mathematical model of PTC, based on published molecular interactions, utilizes 30 ordinary differential equations. Gene expression data from patients with PTC (conventional type), including both tumor and normal tissue, are obtained from the National Cancer Institute’s Genomic Data Commons. Simulations are performed in Python with the SciPy stack. Normal tissue gene expression values (RNA-Seq) are used as the model baseline, and the rates of the molecular interactions are optimized to predict 27 tumor gene expression values, 2 epigenetic modification levels (H3 K27 acetyl and methyl) and one protein localization value (beta-catenin). The percent error [(actual value - simulated value)/actual value] for each gene expression value is calculated to compare simulated and patient tumor data.

The simulations reveal that, following fitting of the model parameters, the model fits gene expression data from both stage 1 and stage 4 patients. However, when those fitted models are initialized using normal thyroid gene expression from different patients, the model does not predict tumor gene expression well. The fitted model for a stage 4 patient does not predict gene expression in either other stage 4 PTCs or in stage 1 PTCs.

The results of this mathematical approach suggest that our proposed model including pathways involved in EMT does not yet account for individual variability in gene expression, either in comparing patients within the same stage or between low and high stage PTC. The variables with the largest contributions to the discrepancy will be further investigated through simulations and experiments with a goal of developing a model that can predict individual patient outcomes and response to therapy.