Homeostasis despite instability.
Abstract
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.
Type
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https://hdl.handle.net/10161/19424Published Version (Please cite this version)
10.1016/j.mbs.2018.03.025Publication Info
Reed, MC; Duncan, William; Nijhout, HF; 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.
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William Duncan
Student
H. Frederik Nijhout
John Franklin Crowell Distinguished 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 inse
Michael C. Reed
Arts & Sciences Distinguished 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 sites@duke.edu/metabolism.
Since 2003, Professor Reed has worked with Professor Fred Nijhout (Duke Biology) to
use mathematical methods to understan
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