Memory and fitness optimisation under fluctuating environments (lac operon)

Katz and Springer (2016) cite early theoretical work by Richard Levins (1968). In their account, Levins argued that the statistical relations between signals in a fluctuating environment are central to adaptation.⁶ They add that this holds whatever costs different strains pay in each environmental state. As an example they note that yeast strains differ in the preparation time needed to switch from glucose to galactose. Katz and Springer propose that adaptation to changing environments can be framed as inference under uncertainty.⁷ They illustrate this with glucose-galactose adaptation in yeast, not the lac operon, and say the framework applies to other fluctuating environments.

Kashiwagi, Urabe, Kaneko and Yomo (2006) studied a gene network that adapts to environmental change by fitness-driven selection of states. They concede that attractor selection, because it is stochastic, may be less efficient than ordinary signal transduction. They argue that it may still keep cells from dying in fluctuating environments.¹ They also suggest it could let a network respond to unknown changes without many specific sensors and transducers.² Their constructs used parts such as the lacI gene and the Ptrc promoter from pTrc99A.

Lambert and Kussell (2014) modelled lac induction in a population facing sudden environmental changes. They used an earlier model and added an equation for mRNA transcription.³ They then pulsed cells grown in glucose medium with the unmetabolizable inducer IPTG. The result was identical to induction by lactose. IPTG induces the operon directly, while lactose needs LacZ activity to make allolactose.⁴ From this the authors concluded that neither lactose metabolism nor changes in catabolite repression are required for the observed overshoot.⁵ They also report that the stringent response to carbon starvation does not significantly affect induction dynamics.

Schavemaker and Lynch (2025) review how the energetic cost of a cellular trait affects fitness. They say this should ideally be tested by adding nonfunctional proteins. One attempt used the lac operon, expressed artificially without lactose so that cells bore the burden and gained no benefit. Growth rate fell by more than a linear model predicted.⁸ The review notes that the defect may partly reflect chaperone burden or cross-reactivity of lac proteins with other cellular traits.