Real PCR Shortfall Grows Across Further Cycles - Physics for Biophysics Step by Step

The same real lmsim PCR run continues past the earlier lesson's checked cycles. By real cycle 6, the real amplified count (383) against the deterministic formula's 512 gives real ratio 383/512, lower than the earlier cycles' ratios. By real cycle 10, the real count (4936) against the deterministic formula's 8192 gives real ratio 617/1024, the lowest of the four real cycles checked across both lessons — because the real sub-unity efficiency compounds cycle after cycle, the real shortfall only grows, never shrinks.

The same real lmsim PCR run's ratio of real amplified count to the deterministic doubling formula, shrinking at every later cited cycle as the real sub-unity efficiency compounds. 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 keeps compounding at cycle six

By real cycle 6, the real amplified count is 383 against the deterministic formula's 512 — real ratio 383/512, lower still than the earlier cited cycles.

383/512=\frac{383}{512}

The real ratio is lowest at the last cited cycle

By real cycle 10, the real amplified count is only 4936 against the deterministic formula's 8192 — real ratio 617/1024, the lowest of the four real cycles checked, because the real sub-unity efficiency compounds cycle after cycle.

\frac{383}{512}>\frac{617}{1024}