RESEARCH

Mathematical models reveal how cancers grow

University-led research team is using mathematical models to study the growth of certain types of cancer, including breast and prostate cancer, with an eventual goal of developing new drugs.

The researchers have been awarded a three-year grant of nearly $1.2 million from the U.S. Department of Energy to undertake the project, which could provide a key to understanding and eventually controlling these cancers.

The research involves multiscale modeling of protein interactions that result in interesting phenomena, such as receptor clustering.

The team is led by Dionisios Vlachos, UD professor of chemical engineering, and includes Jeremy Edwards, former UD assistant professor of chemical engineering who now is a member of the molecular genetics and microbiology faculty at the University of New Mexico Health Sciences Center. Also working with the research project are Markos Katsoulakis, professor of mathematics at the University of Massachusetts, and James Faeder of the Theoretical Biology and Biophysics Group at Los Alamos National Laboratory.

Multiscale modeling is the use of mathematical equations and powerful computers to gain an understanding of multidimensional, multilength scale and multitime scale complex systems and, in this case, the highly intricate systems found in molecular biology.

Vlachos says the project will target hormone-responsive forms of cancer, such as breast, ovarian, endometrial and prostate cancer.

There is a great deal of information and expertise on these types of cancers, Vlachos says, but “what we do not know is what goes wrong at the system level when the cancer starts at the molecular level.”

Through the use of biomathematical models, the researchers hope to develop tools to understand the process and turn that knowledge into the development of new drugs that can hold the cancers in check.

“Computational mathematics will provide the underpinnings, and then we will pull the information together and create models that will help us understand the underlying biological mechanisms and make predictions about the best means of controlling the cancers,” Vlachos says.

Hormone-responsive cancers develop via a multiple-step process that starts from a local benign hyperplasia, which is an abnormal increase in the number of cells, and ends with an invasive tumor able to metastasize to other organs, he says.

During this process, cells must acquire the ability to divide continuously, to circumvent signals that would ordinarily lead to their natural death, to stimulate angiogenesis in order to ensure a supply of nutrients and oxygen and to migrate and invade distant tissue.

Not surprisingly, Vlachos says, these tumors are genetically heterogeneous by the time their presence is discovered. That heterogeneity translates to complexity in selecting the proper treatments for specific patients and in predicting initial patient response and the likely characteristics of recurrent tumors.

As one of the few constant features of these complex cancers, dysregulated signaling though members of the ErbB receptor family is implicated at essentially every step from the initial hyperplasia to the final metastasis, Vlachos says.

“We plan to demonstrate our approach to modeling the activation of the ErbB family of receptors, also known as the epidermal growth factor receptors (EGFR),” he says.

Signaling through EGFR is a powerful inducer of gene transcription and cell growth, and dysregulated signaling through EGFR plays a central role in many forms of cancer, Vlachos says. As a result, selective inhibition of EGFR signaling is a prime target for chemotherapeutic intervention and is a system that has been widely studied.

An overarching objective of this proposal is to develop the necessary mathematical and computational framework that can handle the full range of time and length scales required to model complex biological systems, Vlachos says. He adds that the researchers are confident the framework they develop “will pave the way for the modeling of other spatially distributed systems in biology and nanotechnology.”

Vlachos received a bachelor’s degree from the National Technical University of Athens and master’s and doctoral degrees from the University of Minnesota. He has won the prestigious National Science Foundation Career Award and the Office of Naval Research Young Investigator Award.

Vlachos has spent the last decade working in multiscale modeling and recently became interested in its biological applications. 

— Neil Thomas, AS ’76