This image simulates mathematically a pattern formed when Dictyostelium cells, in the face of starvation, abandon their existence as free-living amoebas and aggregate. The model that produced such images captures the combined effect of subcellular processes and self-organizing behavior. Red represents the highest cell density, blue the lowest. Images courtesy of John C. Dallon, Brigham Young University.

# Multiscale modeling in biology

### Abstract

The 1966 science-fiction film Fantastic Voyage captured the public imagination with a clever idea: What fantastic things might we see and do if we could miniaturize ourselves and travel through the bloodstream as corpuscles do? (This being Hollywood, the answer was that we’d save a fellow scientist from evildoers.) A generation later, many wonder why we’d go to the trouble of shrinking ourselves. Now we can easily see″ into blood vessels, into cells themselves, with nanosize detectors, DNA assays, digital imaging tools and advanced microscopes. We have only to turn on the television to take a digitally simulated voyage deep into the body of a crime victim. And scientists have the tools to examine life at almost any scale imaginable-to scan the solar system for biomolecules., monitor changes in global vegetation from satellites, watch blood flow inside the brain or locate a point mutation in a chromosome. But that’s the problem with biology. Life has so many scales, each rich and complex, that progress has required the field to be sliced up. Some scientists are molecular biologists, others cellular, organismic or population biologists; still others study broad issues emerging from the perspectives of evolution, ecology or bioinformatics. Biology at each level incorporates information from strata above and below. With tools and resources ample enough to parse whole genomes, our view of life is no longer limited by our instruments. But information can easily outrace the theory needed to understand it. As each layer of life becomes more transparent, what is revealed is more complexity than could have been imagined. Consider the brain, astoundingly complex from its convoluted outer folds right down to the intricate chemistry and nanosecond networking capabilities of its neurons. Ponder malaria, a disease involving the complex life cycles, behavior and genetics of host, pathogen and vector, not to mention climate and evolutionary factors, predators, coinfection and the like. Or, finally, cancer, a destructive disorder arising over time and space from the complex genetics and environmental interactions of animal cells. Firmly rooted in observation and experiment, biology for decades had little use for mathematical modeling, which was, in any event, a slow business until computers made it possible to simulate large complex systems of nonlinear equations. Today biologists and mathematicians desperately need each other-not just to find structure in the vast quantities of data flowing from experiment but also to integrate this information into models that explain at multiple scales of time and space how life works. Trees branch, fish grow scales, bacterial colonies form dendritic patterns, birds flock, tumors invade organs, grasses colonize a bare riverbank. Much of life is emergent, a complex system growing out of the interaction of simple elements. New tools are helping us see the regulatory and adaptive properties that characterize all biological phenomena. With the computing power to harness some of the data now available, and with insights offered from old and new mathematics, modelers are making progress on many fronts.

Publication
AMERICAN SCIENTIST 95, 134-142