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

Area of Science:

• Dynamical systems theory
• Optimal control
• Systems biology

Background:

• Dynamical systems entrain to periodic inputs, converging to attractors with the same period.
• Entrainment implies that for constant inputs, systems reach a unique equilibrium.
• The gain of entrainment quantifies benefits of periodic over constant inputs.

Purpose of the Study:

• To maximize the weighted average output of a dynamical system along its periodic attractor.
• To analyze resource allocation problems using periodic optimal control.
• To investigate optimality of constant versus periodic inputs in entraining systems.

Main Methods:

• Formulation as a periodic optimal control problem.
• Analysis using the Pontryagin maximum principle.
• Numerical solutions via specialized software packages.
• Application to nonlinear occupancy models in biological synthesis.

Main Results:

• Constant inputs were found to be optimal for various nonlinear occupancy model architectures.
• The gain of entrainment was not always positive, challenging intuitive expectations.
• Optimality of constant inputs suggests underlying time-varying objectives when periodic signals are observed.

Conclusions:

• Constant inputs can be optimal for maximizing system output in entraining dynamical systems.
• The prevalence of non-constant periodic signals in biological systems may signal optimization of time-varying objectives.
• This framework provides insights into resource allocation and signal processing in biological and engineered systems.