Maximizing average throughput in oscillatory biochemical synthesis systems: An optimal control approach

M. Ali Al-Radhawi, Michael Margaliot, Eduardo D. Sontag*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A dynamical system entrains to a periodic input if its state converges globally to an attractor with the same period. In particular, for a constant input, the state converges to a unique equilibrium point for any initial condition. We consider the problem of maximizing a weighted average of the system's output along the periodic attractor. The gain of entrainment is the benefit achieved by using a non-constant periodic input relative to a constant input with the same time average. Such a problem amounts to optimal allocation of resources in a periodic manner. We formulate this problem as a periodic optimal control problem, which can be analysed by means of the Pontryagin maximum principle or solved numerically via powerful software packages. We then apply our framework to a class of nonlinear occupancy models that appear frequently in biological synthesis systems and other applications. We show that, perhaps surprisingly, constant inputs are optimal for various architectures. This suggests that the presence of non-constant periodic signals, which frequently appear in biological occupancy systems, is a signature of an underlying time-varying objective functional being optimized.

Original languageEnglish
Article number210878
JournalRoyal Society Open Science
Issue number9
StatePublished - 22 Sep 2021


FundersFunder number
National Science Foundation1817936, 2052455
Office of Naval ResearchN00014-21-1-2431
Air Force Office of Scientific ResearchFA9550-21-1-0289
United States-Israel Binational Science Foundation
Israel Science Foundation


    • contractive systems
    • entrainment
    • gene expression
    • optimal control theory
    • ribosome flow model
    • systems biology


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