Variance-Component Decomposition of E. coli Adder — DnaA Counting Dominant at Fast Growth

Bacteria like E. coli face a surprisingly tricky problem: how do they make sure each new cell is roughly the same size as its parent? Scientists have discovered they follow something called the 'adder' rule — each cell simply adds a fixed amount of size before dividing, regardless of how big it started out. It's an elegant self-correcting trick. But the machinery behind it is noisy, and understanding *where* that noise comes from has been an open question. This hypothesis proposes that the answer depends on how fast the bacteria are growing. At fast growth rates, the dominant source of size variability is a molecular counting process — a protein called DnaA accumulates until it hits a threshold that triggers DNA copying, and the randomness in counting those molecules is the main thing making cell sizes vary. At slow growth, a different source of noise takes over: the variable time it takes to actually copy and divide the DNA (called the C and D periods). The hypothesis even identifies a specific growth rate — around 0.8 to 1.0 doublings per hour — where the system transitions between these two regimes. A set of mathematical tools from physics called the Thermodynamic Uncertainty Relation is used to put rigorous bounds on how much each noise source can contribute. In plain terms: the 'wobbly ruler' a bacterium uses to measure its size isn't always the same ruler. Fast-growing cells are limited by how precisely they can count a key protein; slow-growing cells are limited by timing variability in DNA replication. It's like discovering that a factory's quality control bottleneck shifts depending on production speed.

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