  Switch-like motifs are among the basic building blocks of biochemical
networks. A common motif that can serve as an ultrasensitive switch consists of
two enzymes acting antagonistically on a substrate, one making and the other
removing a covalent modification. To work as a switch, such covalent
modification cycles must be held out of thermodynamic equilibrium by continuous
expenditure of energy. Here, we exploit the linear framework for timescale
separation to establish tight bounds on the performance of any
covalent-modification switch, in terms of the chemical potential difference
driving the cycle. The bounds apply to arbitrary enzyme mechanisms, not just
Michaelis-Menten, with arbitrary rate constants, and thereby reflect
fundamental physical constraints on covalent switching.
