Sensitivity analysis of oscillating dynamical systems with applications to the mammalian circadian clock

The work presented in this thesis consists of two major parts. In Chapter 2, the theory for sensitivity analysis of oscillatory systems is developed and discussed. Several contributions are made, in particular in the precise definition of phase sensitivities and in the generalization of the theory to all types of autonomous oscillators. All methods rely on the solution of a boundary value problem, which identifies the periodic orbit. The choice of initial condition on the limit cycle has important consequences for phase sensitivity analysis, and its influence is quantified and discussed in detail. The results are exact and efficient to compute compared to existing partial methods. The theory is then applied to different models of the mammalian circadian clock system in the following chapters. First, different types of sensitivities in a pair of smaller models are analyzed. The models have slightly different architectures, with one having an additional negative feedback loop compared to the other. The differences in their behavior with respect to phases, the period and amplitude are discussed in the context of their network architecture. It is found that, contrary to previous assumptions in the literature, the additional negative feedback loop makes the model less "flexible" in at least one sense that was studied here. The theory was also applied to larger, more detailed models of the mammalian circadian clock, based on the original model of Forger and Peskin. Between the original model's publication in 2003 and the present time, several key advances were made in understanding the mechanistic detail of the mammalian circadian clock, and at least one additional clock gene was identified. These advances are incorporated in an extended model, which is then studied using sensitivity analysis. Period sensitivity analysis is performed first and it was found that only one negative feedback loop dominates the setting of the period.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Chemical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Wilkins, Anna Katharina

Advisor dc:contributor.advisor

• Paul I. Barton and Bruce Tidor.

• Chemical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/42944

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/42944