WebGL is not available in this browser. The numbers and charts below still run.
t 0 min Promoter OFF mRNA 0 Protein 0 TF 1.0 a.u.
Drag to orbit, wheel or pinch to zoom. Green dots: transcription factor. Purple clamp on the DNA: RNA polymerase (works only while the promoter is ON). Orange squiggles: mRNA, leaving through the nuclear pore to ribosomes (blue blobs). Glowing beads: new protein. Colours are illustrative, not real molecular colours.
Gene Expression Lab: Promoter Bursting, mRNA Decay and Protein Noise
One living cell (shown in 3D) plus 120 identical cells run in the background. Every molecule event is an exact Gillespie draw, so you see real cell-to-cell noise, not a smooth curve.
Induce (TF high) Remove inducer Pause Reset Quality: High
Whole cell DNA Ribosomes From above
Promoter
mRNA and protein
Speed
Readouts: theory vs measured (120 cells)
This cell over time Orange: mRNA copies (left axis). Cyan: protein copies (right axis). White dotted: deterministic mean-field ODE. Green strip: promoter ON.
Protein copies across 120 cells Bars: how many of the 120 cells hold each protein count. Dashed line: theoretical mean.
Experiment: does burst size make noise?
Keeps the average protein level fixed and trades many small bursts for few big ones (translation rate x b, transcription rate / b). Sampling error is about 5-8 %. Theory predicts Fano = 1 + ktl /(γm +γp ) for a constitutive promoter and more with a switching one.
Run experiment (600 cells per row, a few seconds)
Independent numerical checks (run in this page)
Legend and controls Drag / one finger: orbit; wheel / pinch: zoom; the four camera buttons jump to a view. TF level sets how often the promoter turns ON (Hill activation). Induce / Remove inducer jump it so you can watch the delay: mRNA follows within minutes, protein within tens of minutes. Time scale is simulated minutes per real second. If many molecules make the exact simulation too slow, the 3D cell stays exact and the ensemble briefly lags. When the protein count is large, one glowing dot stands for several copies (the HUD says how many). The science
Telegraph promoter. The gene flips between OFF and ON with rates kon and koff ; the transcription factor TF raises the on-rate by a Hill law: kon = kbasal + kmax TFn /(Kn +TFn ) with n = 2, K = 1 a.u. The ON probability is f = kon /(kon +koff ).
Reactions (exact Gillespie SSA). ON: mRNA made at ktx . Each mRNA decays at γm = ln2 / t1/2,m . Each mRNA is translated at ktl ; each protein decays (or is diluted by growth) at γp = ln2 / t1/2,p . The next event time is τ = -ln(u)/a0 and the event is picked in proportion to its propensity, which is exact for piecewise-constant rates.
Averages. <m> = ktx f / γm , <p> = ktl <m> / γp . Burst size b = ktl /γm proteins per mRNA lifetime.
Noise. The Fano factor (variance/mean) of a Poisson process is 1. For a constitutive promoter the protein Fano is 1 + ktl /(γm +γp ) (Thattai and van Oudenaarden 2001). A switching promoter adds more; the page uses the exact stationary second moments of the linear system (Peccoud and Ycart 1995 for the mRNA part) and compares them with the ensemble.
Mean-field ODE. d<m>/dt = ktx f - γm <m>, d<p>/dt = ktl <m> - γp <p> integrated with RK4; it tracks the ensemble average but never shows the noise.
Simplifications. No cell growth/division, no gene copy-number change, no translation or transcription delays, no ribosome or polymerase queueing, no feedback from the protein to its own promoter, and mRNA/protein degradation are single first-order steps. Rate values are round illustrative numbers in the realistic range for bacteria and yeast; they do not describe any specific gene. The 3D molecules are artistic, not to scale, and colours are not real. Models built with Blender, scene by Three.js.
Educational virtual model, not for lab or medical decisions.