Periodic enzyme activities can improve the metabolic performance of cells. As
an adaptation to periodic environments or by driving metabolic cycles that can
shift fluxes and rearrange metabolic processes in time to increase their
efficiency. To study what benefits can ensue from rhythmic gene expression or
posttranslational modification of enzymes, I propose a theory of optimal enzyme
rhythms in periodic or static environments. The theory is based on kinetic
metabolic models with predefined metabolic objectives, scores the effects of
harmonic enzyme oscillations, and determines amplitudes and phase shifts that
maximise cell fitness. In an expansion around optimal steady states, the
optimal enzyme profiles can be computed by solving a quadratic optimality
problem. The formulae show how enzymes can increase their efficiency by
oscillating in phase with their substrates and how cells can benefit from
adapting to external rhythms and from spontaneous, intrinsic enzyme rhythms.
Both types of behaviour may occur different parameter regions of the same
model. Optimal enzyme profiles are not passively adapted to existing substrate
rhythms, but shape them actively to create opportunities for further fitness
advantage: in doing so, they reflect the dynamic effects that enzymes can exert
in the network. The proposed theory combines the dynamics and economics of
metabolic systems and shows how optimal enzyme profiles are shaped by network
structure, dynamics, external rhythms, and metabolic objectives. It covers
static enzyme adaptation as a special case, reveals the conditions for
beneficial metabolic cycles, and predicts optimally combinations of gene
expression and posttranslational modification for creating enzyme rhythms