Quantifying Biological Performance in System Design Space

Michael A. Savageau (University of California, Davis)

Abstract

Locating the representation of a biological system as a point in its multi-dimensional parameter space is seldom useful because of the high dimensionality and the lack of physiological context within such a space. Its system design space, by contrast, is a highly compressed space in which the parameters are represented not in isolation but in constellations defining geometrical relationships that reflect physical limits, physiological considerations, dynamical constraints, equivalence classes, etc. It would be desirable to have a tractable method for partitioning design space into a set of regions within which the system behavior could be efficiently characterized and within which distances to the boundaries between regions could be well defined.

My colleagues and I have developed such an approach. Inspired by classical Bode analysis of the rational functions encountered in the frequency analysis of electronic circuits, we have previously developed an analogous method of analysis for the rational functions encountered in enzyme kinetics. When used to analyze intact systems, this approach partitions the design space into regions based on the “break-points” of the system’s rate laws. The distances from a given physiological position in system design space to the nearby regions provide measures of global tolerance. Global tolerance, defined in this manner, applies to large changes in parameter values and complements local robustness, defined as parameter insensitivity, which applies to small changes in parameter values. This talk will illustrate the application of this approach in the context of biological systems representing different levels of organization.

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