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J. theor. Biol. (2000) 203, 117}133
doi:10.1006/jtbi.2000.1068, available online at http://www.idealibrary.com on
How to make a Biological Switch
JOSHUA L. CHERRY*- AND FREDERICK R. ADLER*?
*Department of Biology and ?Department of Mathematics, ;niversity of ;tah, Salt žake City,
;¹ 84112, ;.S.A.
(Received on 30 March 1999, Accepted in revised form on 20 December 1999)
Some biological regulatory systems must &&remember'' a state for long periods of time. A simple
type of system that can accomplish this task is one in which two regulatory elements negatively
regulate one another. For example, two repressor proteins might control one another's
synthesis. Qualitative reasoning suggests that such a system will have two stable states, one in
which the "rst element is &&on'' and the second &&o!'', and another in which these states are
reversed. Quantitative analysis shows that the existence of two stable steady states depends on
the details of the system. Among other things, the shapes of functions describing the e!ect of
one regulatory element on the other must meet certain criteria in order for two steady states to
exist. Many biologically reasonable functions do not meet these criteria. In particular,
repression that is well described by a Michaelis}Menten-type equation cannot lead to
a working switch. However, functions describing positive cooperativity of binding, non-