# Tunability of the Dual Feedback Genetic Oscillator Modeled by the Asymmetry in Transcription and Translation

## TL;DR

This paper presents a simplified delay differential equation model of a dual feedback genetic oscillator, revealing how asymmetries in gene expression parameters can tune and improve its robustness and tunability.

## Contribution

The authors develop a reduced DDE model that captures oscillator tunability and predict how asymmetries in gene expression affect its dynamics, guiding experimental redesign.

## Key findings

- Oscillator period is sensitive to DNA copy number asymmetry.
- Translation rate asymmetry mimics effects of plasmid copy number differences.
- Modulating mRNA degradation asymmetry enhances tunability and robustness.

## Abstract

Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits have been increasingly used to test fundamental principles of genetic network dynamics. A recently developed fast, tunable genetic oscillator by Stricker et al.[23] has demonstrated robustness and tunability of oscillatory behavior by combining positive and negative feedback loops. This oscillator combining lacI (negative) and araC (positive) feedback loops, was however modeled using multiple layers of differential equations to capture the molecular complexity of regulation, in order to explain the experimentally measured oscillations. We have developed a reduced model based on delay differential equations (DDEs) of this dual feedback loop oscillator, that reproduces the tunability of oscillator period and amplitude based on the concentration of the two inducers isopropyl b-D-1-thiogalactopyranoside (IPTG) and arabinose. Previous work had predicted a need for an asymmetry in copy numbers of activator (araC) and repressor (lacI) genes encoded on plasmids. We use our reduced model to redesign the network by comparing the effect of asymmetry in gene expression at the level of (a) DNA copy numbers and the rates of (b) mRNA translation and (c) degradation. We find the minimal period of the oscillator is sensitive to DNA copy number asymmetry, but translation rate asymmetry has an identical effect as plasmid copy numbers, while modulating the asymmetry in mRNA degradation can improve the tunability of period of the oscillator, together with increased robustness to replication 'noise' and influence of the host cell cycle. Thus, our model predicts experimentally testable principles to redesign a potentially more robust oscillatory genetic network.