Skip to main content
Open Access Publications from the University of California

UC Irvine

UC Irvine Electronic Theses and Dissertations bannerUC Irvine

Mathematical Modeling of Tumor Growth and Metabolism


The objective of this work is to use mathematical modeling to understand the mechanisms that regulate tumor growth and metabolism. A hallmark of cancer is cell-intrinsic metabolic reprogramming that enhances anabolic support of cell proliferation and leads to metabolic heterogeneity in tumors at larger scales. Here we report a self-organizing pattern of metabolism in xenograft colon tumors, where Pyruvate Dehydrogenase Kinase (PDK1), a negative regulator of oxidative phosphorylation, is highly active in clusters of cells arranged in a spotted array. To explore the basis for this pattern, we developed reaction-diffusion models describing the interactions between two different metabolic cell types, nutrients, and growth factors. Our first model is based on Gierer-Meinhardt's activator-depleted substrate model and characterizes the relationship between cells, glucose, and lactate. In the other mathematical models reported here, we incorporated Wnt, a signal known to upregulate PDK1 and Warburg metabolism, so that Wnt promotes a metabolic switch to glycolysis. Diffusive instability analysis, or classic Turing analysis, is used to determine parameter sets in which patterns are expected to form and is found to be in good agreement with numerical simulations. Partial inhibition of Wnt alters the pattern in tumors and in the model, which also predicts that inhibition of Wnt alters the expression of proteins that increase the range of Wnt ligand diffusion. This prediction is validated in xenograft tumors and is consistent with expression data in primary human colon cancer. The model also predicts that inhibitors that target glycolysis or Wnt signaling are not so effective as single therapies for cancer as they are in combination for synergistic reduction of tumor growth. We present another mathematical model similar to the Wnt signaling model, but which includes other factors known to be involved in cancer metabolism. This larger mathematical model and numerical results demonstrate good agreement with the Wnt signaling model, and we therefore conclude that the smaller model contains all essential elements necessary to capture the effects we observe, to make predictions for the mechanisms that cause the altered metabolic pattern in Wnt-inhibited tumors, and to investigate treatment programs in silico. It is hoped that these mathematical models will be useful in informing researchers and collaborators about cancer and metabolism.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View