From DNA to Protein
Gene expression is the fundamental process that converts genetic information into functional molecules. RNA polymerase reads the DNA template and synthesizes messenger RNA (transcription), which ribosomes then decode into protein chains (translation). The rates of these processes and the stability of their products determine how much of each protein a cell contains — from a handful of transcription factors to millions of copies of structural proteins. This simulation models the coupled dynamics of mRNA and protein production in a single gene.
Two-Stage Model
The simplest useful model of gene expression tracks two molecules: mRNA and protein. mRNA is produced at rate kTx (determined by promoter strength and transcription factor binding) and degraded at rate δm. Protein is synthesized from mRNA at rate kTl (ribosome loading and elongation speed) and degraded at rate δp (protease activity and dilution). These four parameters fully determine the steady-state expression level and the dynamics of how the system responds to perturbations.
Timescales & Response
A key insight from the two-stage model is that the response time to a change in transcription is set by the slower degradation rate — typically protein degradation. If protein half-life is 30 minutes, it takes about 2 hours to reach 90% of the new steady state after turning on a gene. This fundamental constraint shapes cellular signaling: fast responses require rapid protein turnover (or post-translational modification), while stable housekeeping proteins change slowly. The simulation shows these timescales visually as the system approaches steady state.
Noise in Gene Expression
At the molecular level, gene expression is inherently stochastic. Transcription occurs in bursts as RNA polymerase binds, transcribes, and dissociates from the promoter. Translation produces varying numbers of proteins from each mRNA. These random fluctuations mean genetically identical cells in identical environments express different protein levels — a phenomenon called gene expression noise. The simulation captures this stochasticity through fluctuating molecule counts, demonstrating how promoter architecture and degradation rates affect noise levels.