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An enzyme hydrolysing beta-galactosides. In the lac operon system, its processing of lactose includes production of allolactose, which regulates LacI.

Inhibition of uptake of an inducing substrate by a preferred-carbon-source regulatory system. Glucose-dependent inhibition of lactose permease reduces formation of allolactose and reinforces lac operon repression.

An Escherichia coli transcription unit encoding lactose-use proteins. Expression integrates LacI-dependent repression, allolactose induction, catabolite activator protein activation and inducer exclusion.

The lac repressor, also called LacI, is the regulatory protein that reduces transcription of the lac operon by binding a lac operator in Escherichia coli. Binding of a small-molecule inducer changes the repressor's regulatory state through allostery. Allolactose connects this switch with lactose metabolism, while IPTG supplies an experimentally useful inducer. The lac repressor is distinct from the operator DNA and from the RNA polymerase whose transcriptional output is controlled.

Walter Gilbert and Benno Müller-Hill's 1966 isolation experiment gave the proposed regulator a biochemical measurement. Their equilibrium dialysis assay used radioactive IPTG: small free inducer could cross the membrane, while the macromolecular binding component was retained. Extra total labelled inducer on the protein side reported binding. The assay deliberately used inducer recognition rather than assuming that the exact mechanism of transcriptional repression was already established.^[ref]

An original one-site binding model explains that readout. If the free inducer concentration is $I$, the concentration of independent binding sites is $B_T$ and the dissociation constant is $K_I$, the bound concentration isAt equilibrium dialysis with matched solvent conditions, the protein side contains free plus bound inducer, $I+B$, while the opposite side contains free inducer $I$. Choosing $B_T=2\mu \mathrm{M}$ and $I=K_I=1\mu \mathrm{M}$ gives $B=1\mu \mathrm{M}$ and total concentrations $2$ versus $1\mu \mathrm{M}$. Equality of the free concentration does not require equality of the total concentration. The numbers are illustrative; the native lac repressor has a more detailed oligomeric and allosteric structure.

A separate one-operator model connects binding to expression. If a concentration $R$ of binding-competent repressor occupies the lac operator with probability $\theta =R/(K_O+R)$, and occupied DNA produces no transcripts in this model, thenReducing $R/K_O$ from $9$ to $1$ raises the model's transcription rate from $0.1r_0$ to $0.5r_0$. It does not follow that every measured cellular response obeys this one-site expression: operator arrangement, additional regulators and the later stages of gene expression affect the output. Measuring inducer binding and measuring repression therefore test related but different parts of the mechanism.

The repressor controlling the lac operon. Operator binding represses transcription, while inducer binding shifts the conformational equilibrium towards lower operator occupancy.

A disaccharide composed of glucose and galactose. Its uptake and conversion to allolactose connect substrate availability to lac operon regulation.

Strong lac expression requires relief of lactose-responsive repression together with a favourable glucose-responsive activation state. In Escherichia coli, the lac operon encodes beta-galactosidase, lactose permease and a transacetylase. LacI binds operator DNA and represses transcription; binding of the inducer allolactose shifts its conformation and reduces operator occupancy. Basal expression provides enough permease and beta-galactosidase to import and process some lactose, including formation of allolactose. This explains induction without requiring a completely silent system somehow to manufacture its own detector.

Glucose availability affects positive regulation. When glucose is scarce, the physiological state of the phosphotransferase system favours activation of adenylate cyclase and increased cyclic AMP. Binding of cyclic AMP activates catabolite activator protein, also called CRP, which binds near the lac promoter and helps recruit RNA polymerase. In glucose-rich conditions this activation is reduced. Operator repression and activator-dependent recruitment act at distinct sites, so relief of repression does not guarantee maximum expression. The promoter behaves approximately as a requirement for lactose availability AND glucose scarcity, but its quantitative output is graded rather than a perfect digital gate.

Glucose also regulates inducer entry. During glucose uptake through the phosphotransferase system, the glucose-specific EIIA glucose protein tends to be dephosphorylated. That form can bind and inhibit lactose permease, reducing lactose entry and hence allolactose formation. This inducer exclusion reinforces repression while a preferred substrate is being used. Mutations in the central cytoplasmic loop of the permease that abolish regulation and binding provide a way of separating transport inhibition from promoter regulation.^[ref] It is therefore incomplete to attribute every glucose effect to cyclic AMP alone.

The four limiting conditions make the integration clear. Without lactose, LacI represses whether glucose is high or low; an active CRP cannot simply substitute for inducer. With lactose and abundant glucose, induction is limited by weak activation and often by inducer exclusion. With lactose and little glucose, repression is relieved and CRP-dependent recruitment is favoured, giving the highest expression. With both sugars initially available, glucose consumption followed by adaptation to lactose can produce diauxic growth; the timing depends on concentrations, transport and culture conditions.

Genetic and physiological controls distinguish the mechanisms. A loss-of-function LacI mutation should remove inducer dependence and can be complemented by a functional repressor supplied in trans. An operator mutation acts primarily in cis, on the linked operon. A superrepressor that cannot respond appropriately to inducer can remain repressive despite lactose. Compare promoter reporters and lactose-uptake measurements separately, because an uptake defect and a transcription defect can give similar growth phenotypes. Adding cyclic AMP tests one activation arm, but cannot necessarily overcome a permease blocked by inducer exclusion. The cell combines a local substrate signal with a global carbon-use signal, acting through both transcription and transport.