Mathematical Models of Biochemical Oscillations

The goal of this paper is to explain the mathematics involved in modeling biochemical oscillations. We first discuss several important biochemical concepts fundamental to the construction of descriptive mathematical models. We review the basic theory of differential equations and stability analysis as it relates to two-variable models exhibiting oscillatory behavior. The importance of the Hopf Bifurcation will be discussed in detail for the central role it plays in limit cycle behavior and instability. Once we have exposed the necessary mathematical framework, we consider several specific models of biochemical oscillators in three or more variables. This will include a detailed analysis of Goodwin's equations and their modification first studied by Painter. Additionally, we consider the consequences of introducing both distributed and discrete time delay into Goodwin's model. We will show that the presence of distributed time lag modifies Goodwin's model in no significant way. The final section of the paper will discuss discrete time lag in the context of a minimal model of the circadian rhythm. In the main, this paper will address mathematical, as opposed to biochemical, issues. Nevertheless, the significance of the mathematics to the biochemistry will be considered throughout.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1999

Author dc:creator

• Conrad, Emery David

Chair dc:contributor.committeechair

• Tyson, John J.

Committee members dc:contributor.committeemember

• Day, Martin V.
• Rogers, Robert C.

• Oscillation
• Feedback
• Routh-Hurwitz

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-051499-113229

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32781