The growth biomachine: proteome partition, growth laws, and bet-hedging

Growth rate is set by the ribosome fraction and its speed. Then the population question: when the environment fluctuates, a population that hedges outgrows one that optimizes.

CCBS · EST 5053 · Fall 2026 · lecture 14 · core page · 2026-10-27 (Tue) 10:40–12:15 · students present, lecturer-backed

A cell that grows is a machine whose product is more of itself, and the constraint is that every protein it makes competes for the same ribosomes. That single constraint produces the growth laws, which predict how the proteome repartitions under nutrient shifts. Pugatch's formulation makes the growth rate the largest eigenvalue of the production network, which is the cleanest statement of the idea. The lecture then steps up to the population: heterogeneity is not noise to be cleaned up but a strategy, and a constant-rate transition between phenotypes is enough to explain a passive population-level decision.

1The growth law: λ = εφ_R

Bacterial growth measured across conditions collapses onto one line: λ = ε·φ_R — proteome partition as a flux balance on ribosomes.

Maaløe's growth-rate law, recast by Scott et al. (Science 2011, Terry Hwa's group) as a proteome-partition constraint: the proteome splits into a ribosomal sector φ_R (the "growth" machinery — translation capacity) and a metabolic sector φ_P, with φ_P + φ_{R ≈} 1. The growth rate is then

with ε the ribosome's protein-synthesis rate per unit ribosome. Everything follows: nutrient quality sets ε; the cell responds by allocation — buy ribosomes when growth is good, shift to transport/catabolism when the nutrient is poor; and the crossing of supply and demand fluxes decides the realized state. The growth law is the industry school at its best: a multivariate, messy machine, compressed to a two-variable accounting identity with one eigenvalue (the Jacobian of the allocation system is effectively λ = εf_R in the notes' linearization²).

2Chemostat, diauxie, up- and downshift

The controlled versions of the growth machine: Monod kinetics in a chemostat, the diauxic shift, and the measurements that reveal allocation.

Three experimental windows onto (1):²

• Chemostat. Dilution rate δ = v/V and Monod growth μ = μ_max c/(c + K_M): the steady state sets the nutrient concentration that a given dilution supports — a consumer–resource ODE pair with a sharp conclusion: the chemostat is where the growth law is measured, not assumed.
• Diauxie. Two sugars, one hierarchy: the cell burns the good one first, then switches — the allocation rule's most famous phenotype, and the canonical "industry" evidence that metabolic switching is a designed choice (a regulatory tradeoff by repression, not by mere depletion).
• Up-/downshift. Perturb a steady culture (add nutrient, starve it) and watch φ_R rebalance; the RNA/protein ratio vs λ plot is the classic readout of the growth law, and the perturbation's relaxation tells you the timescale of allocation — the "wide frontier" the notes flag: a cell that grows, decides, and considers (the notes end with the coupled system V̇ = λ(x)V — volume as a state, the cell as a growing reactor).

†References & note sources

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