DNA Melting and Mathematics

Abstract

High resolution DNA melting is a simple closed-tube method of genotyping and variant scanning. However, advanced analysis methods are crucial for accurate design and interpretation. Mathematical modeling allows melting prediction by nearest neighbor thermodynamics. Analysis needs including background subtraction and variant clustering have led to new mathematical problems and solutions. Examples include quantification of allele fractions for both common and rare alleles in naturally mixed or intentionally pooled samples, detection of subtle target peaks using the deviation of the melting curve from exponential background, optimal mixing for genotyping nearest-neighbor-symmetric SNPs of various ploidy, and geometric combinatorial methods for thermodynamic parameter estimation.