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Applied Mathematics Colloquium

Friday, September 9,  2005, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Differential Penetrance and Biological Principles

Hillel J. Chiel

Biology, Neurosciences and Biomedical Engineering

Case Western Reserve University

Cleveland, OH

Abstract

Biological systems are difficult to understand because, in some contexts, small changes at one level (e.g., the molecular level) can have large effects at another level (e.g., the behavioral level), whereas in other contexts, large changes can have little effect. The differential penetrance of details requires a different approach to developing models of biological systems than has been classically used for uniform physical systems. Several case studies demonstrating this approach will be presented in this talk. A model system for studying locomotion demonstrated that if the underlying dynamics of a system were understood, large coordinated changes in parameters could have little effect on output, whereas small changes in a single synaptic weight could have large effects on output. A model system for studying bistable oscillations made it possible to predict when small changes in gain could cause large changes in oscillatory output, and when large changes in gain would have little effect. A model system for studying feeding movements made it possible to predict when small changes in neural activity could cause large changes in the mechanical output of the system, and when large changes would have little effect. These results suggest that general principles for biological systems require conceptual and mathematical tools that describe differential penetrance.