# Robustness of a Biomolecular Oscillator to Pulse Perturbations

## TL;DR

This paper investigates the robustness of a biomolecular oscillator, specifically the repressilator, to pulse perturbations using computational and Floquet theory, revealing that increased delay enhances robustness.

## Contribution

It introduces a combined computational and analytical approach to assess pulse robustness and identifies delay-related design principles for robust oscillators.

## Key findings

- Delay increases robustness to pulse perturbations.
- Adding proteins or positive feedback enhances delay and robustness.
- Floquet theory correlates well with direct settling time measurements.

## Abstract

Biomolecular oscillators can function robustly in the presence of environmental perturbations, which can either be static or dynamic. While the effect of different circuit parameters and mechanisms on the robustness to steady perturbations has been investigated, the scenario for dynamic perturbations is relatively unclear. To address this we use a benchmark three protein oscillator design - the repressilator - and investigate its robustness to pulse perturbations, computationally as well as using analytical tools of Floquet theory. We find that the metric provided by direct computations of the time it takes for the oscillator to settle after a pulse perturbation is applied, correlates well with the metric provided by Floquet theory. We investigate the parametric dependence of the Floquet metric, finding that the parameters that increase the effective delay enhance robustness to pulse perturbation. We find that the structural changes such as increasing the number of proteins in a ring oscillator as well as adding positive feedback, both of which increase effective delay, facilitates such robustness. These results highlight such design principles, especially the role of delay, for designing an oscillator that is robust to pulse perturbation.