  It has long been hypothesized that futile cycles in cellular metabolism are
involved in the regulation of biochemical pathways. Following the work of
Newsholme and Crabtree, we develop a quantitative theory for this idea based on
open-system thermodynamics and metabolic control analysis. It is shown that the
{\it stoichiometric sensitivity} of an intermediary metabolite concentration
with respect to changes in steady-state flux is governed by the effective
equilibrium constant of the intermediate formation, and the equilibrium can be
regulated by a futile cycle. The direction of the shift in the effective
equilibrium constant depends on the direction of operation of the futile cycle.
High stoichiometric sensitivity corresponds to ultrasensitivity of an
intermediate concentration to net flow through a pathway; low stoichiometric
sensitivity corresponds to super-robustness of concentration with respect to
changes in flux. Both cases potentially play important roles in metabolic
regulation. Futile cycles actively shift the effective equilibrium by expending
energy; the magnitude of changes in effective equilibria and sensitivities is a
function of the amount of energy used by a futile cycle. This proposed
mechanism for control by futile cycles works remarkably similarly to kinetic
proofreading in biosynthesis. The sensitivity of the system is also intimately
related to the rate of concentration fluctuations of intermediate metabolites.
The possibly different roles of the two major mechanisms for cellular
biochemical regulation, namely reversible chemical modifications via futile
cycles and shifting equilibrium by macromolecular binding, are discussed.
