Real PCR Amplification Ledger

Real PCR Amplification Lags the Deterministic Doubling Formula

A real lmsim Galton-Watson branching PCR amplification (scenario gen-pcr, efficiency=0.9, n0=8, seed=17) falls short of this book's own deterministic doubling formula starting at the very first cycle. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The real shortfall begins at the very first cycle

A real lmsim PCR simulation starts from a real starting count of 8 copies, amplifying at a real per-cycle efficiency below the book's toy assumption of every molecule doubling every cycle. At real cycle 1, the real amplified count is 15, already below the deterministic formula's 16.

8⋅21=16>158\cdot2^{1}=16>15
Real PCR amplification falls short of the deterministic doubling formulaEach real cycle's amplified count is checked against N0 times 2 to the cycle.real n0=8 (efficiency=0.9)cycle=1: real=15, deterministic=16, ratio=15/16

The real ratio has already dropped by the third cycle

By real cycle 3, the real amplified count is 54 against the deterministic formula's 64 — real ratio 27/32, already lower than the first cycle's real ratio 15/16.

54/64=2732<151654/64=\frac{27}{32}<\frac{15}{16}
Real PCR amplification falls short of the deterministic doubling formulaEach real cycle's amplified count is checked against N0 times 2 to the cycle.real n0=8 (efficiency=0.9)cycle=1: real=15, deterministic=16, ratio=15/16cycle=3: real=54, deterministic=64, ratio=27/32