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Gene Expression Explorer

Explore how genes are turned on and off at the molecular level. Toggle lac and trp operon regulators, control eukaryotic enhancers and chromatin state, or trace a signal from receptor to protein output with real-time dose-response curves.

Operon Diagram

CAPCAPPromoterOperatorlacIRNAPlacZlacYlacAlac OperonRepressor: Bound (blocking)CAP-cAMP: Active (enhancing)Transcription: Off

Controls

Lactose Present
Glucose Present

Results

Transcription Rate=0.010\text{Transcription Rate} = 0.010
Repressor State
Bound
CAP-cAMP
Active
Transcription Rate
1.0%
mRNA Level (rel)
0.010

Dose-Response (Hill Function)

Reference Guide

lac Operon Regulation

The lac operon encodes enzymes for lactose metabolism in E. coli. It is controlled by two signals: lactose availability and glucose levels.

Negative control by the lac repressor (lacI). Without lactose, the repressor binds the operator and blocks RNA polymerase. Allolactose (from lactose) binds the repressor and releases it from the operator.

Positive control by CAP-cAMP. When glucose is absent, cAMP levels rise and activate CAP, which enhances transcription. This is catabolite repression.

Maximum expression: lactose present + glucose absent\text{Maximum expression: lactose present + glucose absent}

trp Operon (Repressible)

The trp operon encodes enzymes for tryptophan biosynthesis. Unlike the lac operon, it is a repressible system.

The trp aporepressor alone cannot bind the operator. When tryptophan (the corepressor) is abundant, it binds the aporepressor, which then binds the operator and blocks transcription.

When tryptophan is scarce, the repressor cannot bind, and the operon is transcribed to make more tryptophan.

High Trp⇒Repressor binds⇒OFF\text{High Trp} \Rightarrow \text{Repressor binds} \Rightarrow \text{OFF}

Hill Equation and Cooperativity

The Hill equation models cooperative binding of ligands to receptors or transcription factors to DNA.

θ=[L]nKdn+[L]n\theta = \frac{[L]^n}{K_d^n + [L]^n}

At [L] = Kd, occupancy is exactly 50%. The Hill coefficient n controls steepness: n = 1 is hyperbolic, n > 1 shows positive cooperativity (sigmoidal curve), and n < 1 shows negative cooperativity.

Gene Expression Kinetics

mRNA and protein levels follow first-order kinetics with constant production and degradation rates.

mRNA(t)=ktxnδ(1−e−δt)\text{mRNA}(t) = \frac{k_{txn}}{\delta}\left(1 - e^{-\delta t}\right)

At steady state, mRNA = transcription rate / degradation rate. The half-life to reach steady state is ln(2) / degradation rate.

Protein levels lag behind mRNA because translation depends on mRNA availability, creating a delayed response to transcriptional changes.