NDLI: Biochemical oscillator sensitivity analysis in the presence of conservation constraints

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Biochemical oscillator sensitivity analysis in the presence of conservation constraints

Content Provider	ACM Digital Library
Author	Castillo, Anya Tidor, Bruce Toettcher, Jared White, Jacob
Abstract	Computing parametric sensitivities for oscillators has a now well-understood subtlety associated with the indeterminacy of phase. A less universal, but still vexing, subtlety arises when an oscillator is described by a system of differential equations with "hidden" conservation constraints (HCC's); defined as weighted sums of state variables that are time-invariant. If there are HCC's, as is commonly the case for models of biochemical oscillators but rarely the case for practical circuit oscillators, the now-standard approach to computing parametric sensitivities can yield incorrect results. In addition, the monodromy matrix (the matrix of state sensitivities over one oscillation period), is often defective in a way that interferes with the usual approach to computing oscillator phase noise. In this paper we analyze the HCC case, and show that by augmenting the standard sensitivity approach with explicit HCC's, one can recover the correct parametric sensitivities. In addition, we prove that there is a typically satisfied condition that guarantees that a system with HCCs will have a defective monodromy matrix. A deliberately "flawed" ring oscillator circuit and a cyanobacterial circadian clock biochemical oscillator are used to demonstrate the parametric sensitivity problem and its resolution, and to show the issue of the defective monodromy matrix.
Starting Page	806
Ending Page	811
Page Count	6
File Format	PDF
ISBN	9781450306362
ISSN	85644924
DOI	10.1145/2024724.2024905
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-06-05
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Sensitivity analysis Biochemical kinetics Periodic steady-state
Content Type	Text
Resource Type	Article

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