# Resolving emergent transient oscillations in gene circuits with a growth-coupled model

## TL;DR

This paper introduces a new model that explains unexpected oscillations in synthetic gene circuits by linking gene expression to cell growth and recycling processes.

## Contribution

The GEAGS model couples gene expression with population growth, resolving mismatches in predicting transient oscillations in synthetic circuits.

## Key findings

- GEAGS accurately reproduces transient oscillations in protein reporters.
- Amino acid recycling and growth-phase transitions drive the observed dynamics.
- The model resolves long-standing mismatches in layered feedback circuits.

## Abstract

Synthetic gene circuits often behave unpredictably in batch cultures, where shifting physiological states are rarely accounted for in conventional models. Here, we find that degradation-tagged protein reporters could exhibit transient oscillatory expression, which standard single-scale models do not capture. We resolve this discrepancy by developing Gene Expression Across Growth Stages (GEAGS), a dual-scale modeling framework that explicitly couples intracellular gene expression to logistic population growth. Using a chemical reaction network model with growth phase–dependent rate-modifying functions, GEAGS accurately reproduces the observed transient oscillations and identifies amino acid recycling and growth-phase transition as key drivers. We reduce the model to an effective form for practical use and demonstrate its adaptability by applying it to layered feedback circuits, resolving long-standing mismatches between model predictions and measured dynamics. These results establish GEAGS as a generalizable platform for predicting emergent behaviors in synthetic gene circuits and underscore the importance of multiscale modeling for robust circuit design in dynamic environments.

Multiscale modeling reveals how growth and proteolysis-linked recycling cause transient oscillations in synthetic gene circuits.