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Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation
- Source :
- Bulletin of Mathematical Biology. 79:1539-1563
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
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.
- Subjects :
- 0301 basic medicine
General Mathematics
Immunology
Evolutionary landscape
Phase (waves)
General Biochemistry, Genetics and Molecular Biology
03 medical and health sciences
0302 clinical medicine
Control theory
Applied mathematics
Gene Regulatory Networks
Sensitivity (control systems)
General Environmental Science
Parametric statistics
Mathematics
Pharmacology
General Neuroscience
Delay differential equation
Maxima and minima
030104 developmental biology
Amplitude
Gene Expression Regulation
Computational Theory and Mathematics
RNA Interference
General Agricultural and Biological Sciences
Focus (optics)
030217 neurology & neurosurgery
Subjects
Details
- ISSN :
- 15229602 and 00928240
- Volume :
- 79
- Database :
- OpenAIRE
- Journal :
- Bulletin of Mathematical Biology
- Accession number :
- edsair.doi.dedup.....50aea92c067189abdbc45bafa2f11ad8