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PCR converts a selected DNA sequence into a detectable and manipulable quantity; different downstream measurements give it different uses. A pair of PCR primers defines the interval amplified by DNA polymerase. Repeated denaturation, annealing and extension produce approximately $N_n=N_0(1+E{)}^n$ copies while PCR efficiency $E$ remains constant. At ideal efficiency, twenty cycles give about a millionfold amplification; depletion and accumulating products eventually cause a PCR plateau. Specificity derives from both primer-binding sites and their orientation, and should be checked by product size, melting behaviour or sequencing.

One application is genotyping. A disease-associated substitution can be detected by amplifying the surrounding region and reading the sequence, probing with an allele-specific oligonucleotide, or digesting a restriction site changed by the variant. An early demonstration amplified the human beta-globin region for restriction-based diagnosis of sickle cell disease. Amplification increased sensitivity; the restriction pattern supplied the allele information.^[ref] A negative disease-specific signal is interpretable only if a control locus amplifies, because poor extraction or an inhibitor can mimic absence of an allele. In forensic DNA profiling, several short tandem repeat loci are amplified and fragment lengths compared. A multilocus match supports identity statistically; it does not eliminate contamination, mixtures, allelic dropout or the need for appropriate population-frequency estimates.

For infectious agents, primers can detect a pathogen-specific DNA sequence. An RNA virus first requires reverse transcription, followed by polymerase chain reaction. In RT-qPCR, fluorescence is monitored during amplification, and a threshold cycle is related to starting RNA using calibrated standards and efficiency measurements. This also measures changes in cellular gene expression: compare a target transcript between conditions after suitable normalization. Include extraction controls, a no-template reaction and, for RNA measurements, a no-reverse-transcriptase control to detect genomic DNA contamination. A positive pathogen signal establishes the presence of target nucleic acid, not necessarily a viable organism or infectious virus. Likewise, RNA abundance is not a direct measurement of protein abundance or transcription rate, since RNA degradation also matters.

PCR is also a preparative method. Amplified coding sequences can be assembled into expression vectors; primer tails can add restriction sites, assembly overlaps, sequencing adaptors or an affinity tag. High-fidelity polymerase reduces unwanted substitutions, but the final clone should still be sequenced. Site-directed mutagenesis introduces a specified substitution using mutagenic primers, whereas error-prone PCR creates a library for directed evolution. Sequencing after selection distinguishes the intended change from other mutations. In chromatin immunoprecipitation, quantitative amplification of recovered loci can test enrichment of a DNA-associated protein, with input DNA and immunoprecipitation controls needed to interpret it.

These examples separate presence, identity, quantity and construction. Endpoint band intensity is a poor substitute for quantitative amplification measured before the PCR plateau; multiplex assays can also suffer unequal amplification. The appropriate answer therefore identifies what is amplified, what is measured, and which alternative explanation each control excludes.

For a stipulated population of amplifiable copies, let $N_n$ be the amount after cycle $n$ and define PCR efficiency by the fractional new yieldHere $E_n=1$ means one additional copy per existing copy, hence ideal doubling. If every cycle has the same PCR efficiency $E$, the exponential growth model gives $N_n=N_0(1+E{)}^n$. Starting with $N_0=100$ copies, twenty ideal cycles give $104857600$ copies; the stipulated value $E=0.8$ gives about $12748236$. An efficiency of 80 percent therefore means multiplication by 1.8 each cycle, not retention of 80 percent of the final ideal yield.

In the ideal strand-counting example, all duplex-equivalent material doubles, but exact-length amplicons lag initially. Starting from one longer duplex and retaining its two original strands, cycle $n\ge 1$ contains $2(2^n-n-1)$ exact-length strands out of $2^{n+1}$ total strands. Thus their fraction is $1-(n+1)/2^n$: zero after cycle 1, one quarter after cycle 2 and one half after cycle 3. This counts strands rather than assuming every strand immediately finds an exact-length partner. The generic yield model above ignores this early distinction.

A PCR plateau is the late phase in which further cycles add little product. Depletion of substrates and accumulation of reaction by-products can reduce PCR efficiency. Consequently, similar final amplicon amounts need not mean similar initial template amounts. In the stipulated green model, $0<N_n<K$ implies $N_n<N_{n+1}<K$, and growth approaches the imposed ceiling. That illustrates loss of starting-amount information without claiming to identify the limiting chemical process in an actual tube.^[ref]