# Methods and formula provenance

All calculator code in this directory is an independent implementation. No Primer3 source code, interface, or parameter files are included.

OD→ng/µL conversion is not included in this version; the suite does not infer nucleic-acid concentration from absorbance.

## qPCR relative expression

For equal target/reference amplification factors, `ΔCq = mean(target Cq) − mean(reference Cq)`, `ΔΔCq = ΔCq(sample) − ΔCq(control)`, and relative expression is `E^(−ΔΔCq)` (normally `E = 2`). Differing efficiencies use the ratio `E_target^(Cq control − Cq sample) / E_reference^(Cq control − Cq sample)`. Replicate means and sample standard deviations are shown; an SD above 0.5 Cq is flagged. “Undetermined” is rejected rather than converted to a number.

The integrated CSV workflow groups rows by sample and group, propagates independent standard errors, flags replicate SD above 0.5 Ct and Ct above 35, and supports both Livak and Pfaffl output. Flags prompt review and do not automatically exclude data.

- Livak KJ, Schmittgen TD (2001), *Methods* 25:402–408. [doi:10.1006/meth.2001.1262](https://doi.org/10.1006/meth.2001.1262)
- Bustin SA et al. (2009), MIQE guidelines, *Clinical Chemistry* 55:611–622. [doi:10.1373/clinchem.2008.112797](https://doi.org/10.1373/clinchem.2008.112797)
- Pfaffl MW (2001), efficiency-corrected relative quantification, *Nucleic Acids Research* 29:e45. [doi:10.1093/nar/29.9.e45](https://doi.org/10.1093/nar/29.9.e45)

## Dilution and molarity

Single dilutions use conservation of solute, `C₁V₁ = C₂V₂`. Exactly one of C₁, V₁, C₂ or V₂ is solved. Units are normalized within compatible molar or mass-concentration families; conversion between those families is rejected because it requires molecular weight. Diluent is `V₂ − V₁`. Serial plans use `transfer = final volume / factor` and apply the same factor at every step. Molarity is `moles / litres`; moles from mass are `mass × purity / effective formula weight`. The user supplies molecular weight and hydrate factor.

## Sequence transformations and GC content

DNA and RNA complement maps cover the IUPAC symbols A, C, G, T/U, R, Y, S, W, K, M, B, V, D, H and N. FASTA records are processed independently. Reverse, complement and reverse-complement operations preserve ambiguity codes. Transcription swaps T and U. GC% is the count of literal G and C bases divided by total sequence length; ambiguous positions remain in the denominator.

## Primer melting temperature

Wallace mode uses `2(A+T) + 4(G+C)` °C as a rough short-primer screen. Nearest-neighbor mode transcribes the unified DNA/DNA ΔH/ΔS table from SantaLucia (1998), includes terminal AT initiation corrections and optional symmetry entropy, then evaluates `Tm = ΔH/(ΔS + R ln(Ct/F)) − 273.15 + 16.6 log10([Na+])`, with `F=4` for non-self-complementary and `F=1` for self-complementary sequences. It models monovalent salt only.

- Wallace RB et al. (1979), *Nucleic Acids Research* 6:3543–3557. [doi:10.1093/nar/6.11.3543](https://doi.org/10.1093/nar/6.11.3543)
- SantaLucia J Jr (1998), *PNAS* 95:1460–1465. [doi:10.1073/pnas.95.4.1460](https://doi.org/10.1073/pnas.95.4.1460)

These calculations support research planning, not validated diagnostic use. Dilution, molarity, qPCR and sequence transformations incorporate the audited standalone implementations and are no longer labelled Experimental. Primer Tm is not a specificity, structure, dimer, or primer-design assessment; numerical and domain review by a molecular biologist remains required before removing its Experimental label.