Deciphering the Replication-Division Coordination in E. coli: A Unified Mathematical framework for Systematic Model Comparison

Abstract

Despite extensive research, the quantitative principles that govern the coordination between DNA replication and cell division in bacteria remain debated. Multiple theoretical models have been proposed, some postulating that a single regulatory process is sufficient to ensure replication-division coordination, while others argue that two concurrent processes are required for robust control. In this work, we develop a unifying mathematical framework within which models can be consistently formulated, qualitatively analysed and quantitatively compared. This framework also allows us to propose a new double-process model. Through theoretical analysis, we establish the necessary and sufficient conditions under which single-process models can reproduce physiological cell behaviours. Beyond the correlation-based analyses extensively used to date, we further demonstrate within a comprehensive statistical framework that double-process models more accurately recapitulate experimental data across all growth conditions. Specifically, the new model we propose robustly captures the replication-division coordination in every growth regime, thereby providing a foundation for future mechanistic studies. Author SummaryHow bacteria regulate their cell size and ensure complete chromosome replication before division remains only partly understood, posing a fundamental question. A key challenge is understanding how bacterial cells reliably distribute their genetic material to daughter cells while managing randomness in division timing, especially since DNA replication is often initiated in earlier generations. Over the past decade, several models have been developed to describe the coordination of DNA replication and cell division in Escherichia coli, combining different mechanisms and levels of complexity. These models have mainly been evaluated through correlation analysis between cell cycle parameters, such as the size at which bacteria divide or initiate DNA replication. However, such analyses depend on strong underlying assumptions that are not always met by the experimental data. Here, we present a general framework that systematically integrates multiple models, allowing both qualitative analysis and quantitative comparison without relying on correlations. Our work concludes that under all growth conditions, E. coli cells most likely divide only after meeting two combined requirements: adding a critical size since birth and a critical size since the initiation of DNA replication.