2D companion to the 3D qPCR scene: the same efficiency-limited logistic amplification model, read off three live panels instead of a rendered reaction tube. Each PCR cycle roughly doubles the number of double-stranded DNA copies, but the reaction saturates as primers and polymerase run out:
N(n+1) = N(n) + E·N(n)·(1 − N(n)/K)
F(n) = F0 + (1 − F0)·N(n)/K (SYBR-Green fluorescence ∝ dsDNA mass)
Ct = cycle where F(n) first crosses the detection threshold Ft
N(n) is the copy number after n cycles, E is the per-cycle amplification efficiency (1.0 = perfect doubling), K is the plateau capacity where reagents are exhausted, and F0 is background fluorescence. In the early exponential phase (N ≪ K) this reduces to the textbook relation used to back-calculate starting quantity from a measured Ct:
Ct ≈ log(Nt / N0) / log(1 + E)
- Starting template — the initial copy number N0 loaded into the tube; lower N0 needs more cycles to reach threshold, which is exactly how qPCR quantifies an unknown sample against a standard curve.
- Amplification efficiency — how close each cycle gets to a perfect doubling (100%); poor primer design or inhibitors lower it and delay Ct.
- Detection threshold — the fluorescence level the instrument's optics must clear above background noise before a Ct is called.
- Run speed — animation pace only; the underlying cycle-by-cycle math is unaffected.
- Log-scale copy plot — the amplification-plot panel plots log10(copies) against cycle, the standard view a real thermocycler reports: a straight line in the exponential phase, flattening at plateau.
Real-world relevance: this is the core readout behind viral load testing, gene-expression quantification and pathogen detection assays used throughout the genomic diagnostics pipelines described in medical bioinformatics.