Oscillator Model Reduction Preserving the Phase Response: Application to the Circadian Clock

¹ University of California Santa Barbara

^* To whom correspondence should be addressed. E-mail: petzold{at}cs.ucsb.edu.

Submitted on January 2, 2008
Revised on February 10, 2008
Accepted on 18 April 2008

	Abstract

Mathematical model reduction is a long-standing technique used both to gain insight into model sub-processes and to reduce the computational costs of simulation and analysis. A reduced model must retain essential features of the full model, which, traditionally, have been the trajectories of certain state variables. For biological clocks, timing, or phase, characteristics must be preserved. A key performance criterion for a clock is the ability to adjust its phase correctly in response to external signals. We present a novel model reduction technique that removes components from a single-oscillator clock model and discover that four feedback loops are redundant with respect to its phase response behavior. Using a coupled multi-oscillator model of a circadian clock, we demonstrate that by preserving the phase response behavior of a single oscillator, we preserve timing behavior at the multi-oscillator level.

Key Words: coupled oscillators, genetic algorithm, limit cycle oscillator, phase response curve (PRC), sensitivity analysis

This article has been cited by other articles:

				S. Hildebrandt, D. Raden, L. Petzold, A. S. Robinson, and F. J. Doyle III A Top-Down Approach to Mechanistic Biological Modeling: Application to the Single-Chain Antibody Folding Pathway Biophys. J., October 15, 2008; 95(8): 3535 - 3558. [Abstract] [Full Text] [PDF]