Tuesday, March 14, 2006
Shlomo Ta’asan has teamed up with immunologists at UPMC to Discern Immune Response to Infectious Diseases, Vaccine Development
Someone inhales the influenza virus, and his body mounts a defense, marshalling immune cells to destroy the intruders. Dozens of cell types send thousands of molecular signals to coordinate an attack of staggering proportions. This complexity makes understanding the immune system mind numbing—except to a mathematician.
At Carnegie Mellon University, Shlomo Ta’asan, professor of mathematical sciences, has teamed up with immunologists at the University of Pittsburgh School of Medicine to develop sophisticated mathematical models for investigating how the immune system responds to tiny microbes that cause flu, tuberculosis (TB) and tularemia. In Fall 2005, Pitt was awarded a five-year, $9.1 million contract to establish an Immune Modeling Center, one of four supported by the NIH’s National Institute of Allergy and Infectious Diseases. As part of this award Ta’asan, co-principal investigator of the center, received $1.2 million to support his work on developing mathematical models. His computational modeling framework will give immunologists a global picture of what happens during an immune response to these pathogens.
But using mathematics to understand immune system dynamics is no easy task. Traditional modeling uses precise numbers to describe levels of secreted molecules or numbers of cells present at any given time. This freeze-frame approach poses a problem, according to Ta’asan, because animals and humans are very different both within individuals and between species. Measurements taken one day may vary dramatically just one day later. To cope with this unpredictability, Ta’asan has developed an approach that avoids using precise numbers. Instead he uses numbers that give him (and his model) a little wiggle room. His approach incorporates logical variables with limited values, such as 0, 1 and 2, where 1 describes a low level and 2 describes a high level of cells or secreted molecules. According to Ta’asan, this use of such nonstandard values is reflected in examples such as 1+1=1 (low + low = low) or 2+1=2 (high + low = high). Such a technique avoids the pitfalls of using precise numbers to describe a variable system.
Traditional modeling techniques also require construction of an inflexible edifice of equations, which are inscrutable to immunologists. But the field of immunology is itself dynamic and demands flexibility. New findings make rigid mathematical models obsolete. To circumvent this problem, Ta’asan developed a simple language that immunologists understand. This way, they can write their own models using the terms they already use to describe immunological processes. For example, a natural killer cell is abbreviated NK, an active natural killer cell is represented aNK, and a macrophage is denoted with an M. Ta’asan’s language, used by an immunologist, may look like this:
NK + IL-12 (signaling molecule) → aNK
aNK → IFNg (signaling molecule)
M + IFNg → aM
A computer program, written by Ta’asan, reads this language and builds a model using differential equations, stochastic models, and logical networks. Ta’asan’s program acts as an interpreter and a necessary bridge between traditional immunology and mathematical modeling.
Nonstandard arithmetic and a new modeling language are only two aspects of Ta’asan’s approach to modeling the immune system. Immunologists at UPMC will conduct experiments and gather data over the course of an initial immune response to a pathogen. Data will include levels of signaling molecules (cytokines) being secreted by cells, the number and type of cells present, and whether genes are being turned on and off in cells. Such vast amounts of data are impossible for humans to interpret. Ta’asan’s mathematical strategies should be able to make sense of it all. Although thousands of molecules are involved in an immune response, his conjecture is that the system can be described with far fewer variables.
To meet this challenge, Ta’asan developed a new algorithm to identify the complexity of an immune response based on experimental data provided by University of Pittsburgh immunologists. This algorithm builds models that use a small number of variables to capture the essence of the full immune system. Unlike traditional models, which describe the immune system on a molecular scale, Ta’asan’s models use abstract entities to represent fundamental processes underlying an immune response. The immune system is built upon these abstract entities, much like all atoms are built from varying combinations of protons and electrons.
Ta’asan’s approach will help modelers and immunologists look at the immune system from a new viewpoint, shifting the thinking from single molecules to more abstract concepts that govern the evolution of the entire immune system. This new model can then allow scientists to use it for practical testing in the lab such as designing a vaccine to boost immunity against an influenza virus. To find a solution to this complicated problem, Ta’asan will manipulate his model using various mathematical ideas while keeping specific biological constraints in mind, such as limiting damage to the lung and maintaining patient health and safety. The model will generate an answer in terms of abstract entities, but that answer translates into terms needed by an immunologist to design a vaccine that will tweak the immune system in specific ways to accomplish successful vaccinations. Ta’asan’s model is expected to enable the design of novel vaccine and/or drug cocktails with specific purposes and few, if any, undesirable side effects.
By: Amy Pavlak