SALT LAKE CITY — A University of Utah professor is taking mathematics further into real-world applications, taking a step closer to understanding cancer.
Fred Adler, professor of mathematics and chair of the Department of Biological Sciences, recently published a paper presenting a mathematical model of how cancer develops.
in Article from the Faculty of ScienceAdler said he has been working for years on models that explain the complexities of cancer development.
“While traveling on an airplane, I came up with a very complicated approximation method, and then I realized, on solid grounds, that the exact method was quite simple,” he said.
Adler used differential equations to think about individual cells and how they compete for resources and space, a framework that takes into account evolution, stochasticity (a measure of how random something is), and control and the breakdown of control.
His model helps explain some mysteries about cancer, including why most cancers develop late in life.
The conventional explanation for this question is that six mutations in one cell are enough to induce cancer, increasing the likelihood of cancer over time.
Adler disputes that explanation, saying his model casts doubt on the importance of individual cells. His model, like other studies that look at mutations in tissues, suggests that cancer development depends on interactions with neighboring tissues.
“Detailed studies of adults reveal that very few of their cells are ‘normal.’ … Their tissues are made up of lineages with an increasing number of abnormal traits, many of which promote excessive growth,” Adler said.
His paper explains that aging has two effects that increase the chances of developing cancer: increased mutations and a breakdown in regulation. Humans have systems that keep mutated cells from multiplying, such as cell-cell communication, but these systems weaken with age.
To grow, cancer must circumvent control and repair systems and “escape regulation at many internal and tissue-level hierarchies,” Adler’s paper states.
This model helps explain why cancer-associated mutations exist in healthy tissue that are not associated with future cancers.
“[This model]recapitulates the rapid increase in cancer incidence with age and complements our focus on mutations that may identify key aspects of regulation and lead to new therapeutic strategies,” Adler said.
The hope is that this understanding will help doctors and researchers find additional ways to treat and prevent cancer.
Adler’s paper, “A Modeling Framework for Cancer Biology and Evolution,” Royal Society Interface.
Fix: In previous versions, Adler’s name was incorrectly spelled Alder.
