Homeostasis despite instability.
Repository Usage Stats
We have shown previously that different homeostatic mechanisms in biochemistry create input-output curves with a "chair" shape. At equilibrium, for intermediate values of a parameter (often an input), a variable, Z, changes very little (the homeostatic plateau), but for low and high values of the parameter, Z changes rapidly (escape from homeostasis). In all cases previously studied, the steady state was stable for each value of the input parameter. Here we show that, for the feedback inhibition motif, stability may be lost through a Hopf bifurcation on the homeostatic plateau and then regained by another Hopf bifurcation. If the limit cycle oscillations are relatively small in the unstable interval, then the variable Z maintains homeostasis despite the instability. We show that the existence of an input interval in which there are oscillations, the length of the interval, and the size of the oscillations depend in interesting and complicated ways on the properties of the inhibition function, f, the length of the chain, and the size of a leakage parameter.
Published Version (Please cite this version)10.1016/j.mbs.2018.03.025
Publication InfoReed, Michael; Duncan, William; Nijhout, Frederik; Best, J; & Golubitsky, M (2018). Homeostasis despite instability. Mathematical biosciences, 300. pp. 130-137. 10.1016/j.mbs.2018.03.025. Retrieved from https://hdl.handle.net/10161/19424.
This is constructed from limited available data and may be imprecise. To cite this article, please review & use the official citation provided by the journal.
More InfoShow full item record
John Franklin Crowell Professor of Biology
Fred Nijhout is broadly interested in developmental physiology and in the interactions between development and evolution. He has several lines of research ongoing in his laboratory that on the surface may look independent from one another, but all share a conceptual interest in understanding how complex traits arise through, and are affected by, the interaction of genetic and environmental factors. 1) The control of polyphenic development in insects. This work attempts to understand how the
Professor of Mathematics
Professor Reed is engaged in a large number of research projects that involve the application of mathematics to questions in physiology and medicine. He also works on questions in analysis that are stimulated by biological questions. For recent work on cell metabolism and public health, go to email@example.com/metabolism. Since 2003, Professor Reed has worked with Professor Fred Nijhout (Duke Biology) to use mathematical methods to understan
Alphabetical list of authors with Scholars@Duke profiles.