Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation |
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Authors: | Brian Ingalls,Maya Mincheva,Marc R. Roussel author-information" > |
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Affiliation: | 1.Department of Applied Mathematics,University of Waterloo,Waterloo,Canada;2.Department of Mathematical Sciences,Northern Illinois University,DeKalb,USA;3.Alberta RNA Research and Training Institute, Department of Chemistry and Biochemistry,University of Lethbridge,Lethbridge,Canada |
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Abstract: | A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered. |
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