Mathematical Modeling of Cell Processes Is Year-Long Focus at MBI

September 30, 2003

Each day the human body produces millions of cells. Each cell works like an exceedingly complex machine, converting fuel to energy and pumping out proteins and enzymes as directed by its DNA. At the same time, a cell uses a variety of modes to communicate with other cells in its vicinity or in distant locations. Because the vast majority of medical science relies on an understanding of the physiology of cells, it comes as no surprise that the mechanisms by which cells control their behavior and coordinate with other cells are among the most intensively studied in the biological sciences.

"In the last few years, the importance of mathematical models in the study of cellular processes has become widely accepted," says Avner Friedman, director of the Mathematical Biosciences Institute at Ohio State University. "There are already many instances of how experimentalists and theoreticians, working together, can make discoveries that would be difficult, if not impossible, for each working independently." Examples include studies of oscillations in the cell cycle that leads to regular cell division, intercellular calcium waves, which coordinate cellular response over large areas, and the response of tumor growth to chemotherapy.

During the 2003-04 year, scientists at MBI will explore a selection of topics ranging from cell growth and death, to intercellular communication, and to the behaviors of large populations of cells, such as those found in the immune system. During the autumn of 2003, the program will evolve around cell proliferation. "The cell cycle," says John Tyson, one of the organizers of the program, "is a sequence of events by which a growing cell replicates all its components and divides them between two daughter cells, so that each daughter receives all the information and machinery necessary to repeat the process." Because cell proliferation underlies all biological growth, development, and reproduction, Tyson explains, an understanding of the molecular machinery that controls cell growth and division is a fundamental goal of cell biology.

The year's first workshop, organized by Baltazar Aguda and Jessie Au, has the following goals: summarize current knowledge of the molecular controls of cell division, examine the state of the art in computational modeling of these controls, open a fruitful dialog between experimental cell biologists and theoreticians, define the next set of problems to be tackled through mathematical modeling, and recruit a new generation of collaborative experimentalists and theoreticians to work on these problems.

"The key factors that determine the outcome of chemotherapy of cancer," says Au, "are the delivery of therapy to target tumor cells, mechanisms of drug action, growth and differentiation of cell populations, development of resistance, and optimization of chemotherapy and protocols."

"Mathematical modeling of growth and differentiation of cell populations is one of the oldest and best-developed topics in bio-mathematics," says Marek Kimmel, also an organizer of the upcoming program. Among the challenges facing researchers, he cites the integration of newly described genetic and molecular mechanisms in models of proliferation and in models of geometric growth of tumors in various stages, such as prevascular, vascular, and anoxic.

Calcium has the key role in cell communication. Because calcium is toxic, cells store most of their calcium in vescicles. In response to special signals, calcium channels open and calcium flows out for a brief period, delivering messages both within the cell and to neighboring or even remote cells.

"The question of how cells respond to their environment and coordinate their behavior with that of other cells is one that can be naturally studied using mathematical models," says James Sneyd, who is organizing two workshops for the winter of 2004. To communicate with each other, or with the outside world, cells have developed a large number of transduction mechanisms whereby extracellular signals can be translated into intracellular signals, or a signal of one type can be changed into a signal of another type, Sneyd explains. "For example, muscle cells change an electrical signal into a force; photoreceptors change a light signal into an electrical signal; and neurosecretory cells change an electrical signal into a hormonal signal."

The spring 2004 MBI program will focus on immune models and host-pathogen dynamics. "After decades of research focusing on infected patients and experimental animals," says Denise Kirschner, an organizer of this program, "most modern research in microbial pathogenesis takes place at the level of cellular and biochemical mechanisms governing host-parasite interaction." Studies at multiple scales will undoubtedly be needed for deeper understanding of infectious diseases, she says. Linking pathogen-specific information to that regarding the immune system, for example, will be critical for understanding the dynamics of most bacterial infections. Components of host-pathogen systems are sufficiently numerous and their interactions sufficiently complex that intuition alone is insufficient to fully understand the dynamics of the interactions. Here, Kirschner says, mathematical modeling becomes an important tool. She expects that models developed for host-HIV interaction will also be useful in studying the immune system response to other viral infections as well as to diseases caused by bacteria and parasites.

"With the ever increasing levels of computing power available to modelers, collaborations between mathematicians and cell biologists will have ever increasing importance," Friedman says. Commenting on the program as a whole, he expresses his belief that new kinds of mathematics will be essential contributors to advances in biological knowledge. Sneyd concurs: "Indeed, it is no exaggeration to say that biology is the new frontier of mathematics; it will have profound effects on the kinds of mathematics that are studied one hundred years from now."

Information about all programs of the Mathematical Biosciences Institute can be found at

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