title: A fractional programming approach to efficient DNA melting temperature calculation.
abstract: BACKGROUND
  In a wide range of experimental techniques in biology, there is a need for an efficient method to calculate the melting temperature of pairings of two single DNA strands. Avoiding cross-hybridization when choosing primers for the polymerase chain reaction or selecting probes for large-scale DNA assays are examples where the exact determination of melting temperatures is important. Beyond being exact, the method has to be efficient, as these techniques often require the simultaneous calculation of melting temperatures of up to millions of possible pairings. The problem is to simultaneously determine the most stable alignment of two sequences, including potential loops and bulges, and calculate the corresponding melting temperature.
  
  
  RESULTS
  As the melting temperature can be expressed as a fraction in terms of enthalpy and entropy differences of the corresponding annealing reaction, we propose to use a fractional programming algorithm, the Dinkelbach algorithm, to solve the problem. To calculate the required differences of enthalpy and entropy, the Nearest Neighbor model is applied. Using this model, the substeps of the Dinkelbach algorithm in our problem setting turn out to be calculations of alignments which optimize an additive score function. Thus, the usual dynamic programming techniques can be applied. The result is an efficient algorithm to determine melting temperatures of two DNA strands, suitable for large-scale applications such as primer or probe design.
  
  
  BACKGROUND
  The software is available for academic purposes from the authors. A web interface is provided at http://www.zaik.uni-koeln.de/bioinformatik/fptm.html
authors.affiliation: Institute for Biochemistry, University of Cologne, Zülpicher Strasse 47, Köln, D-50674, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Leber
authors.forename: Lars
authors.initials: L
authors.lastname: Kaderali
authors.forename: Alexander
authors.initials: A
authors.lastname: Schönhuth
authors.forename: Rainer
authors.initials: R
authors.lastname: Schrader
mesh_terms: D000465:Algorithms; D001483:Base Sequence; D003198:Computer Simulation; D004247:DNA / Q000032:analysis* / Q000737:chemistry*; D008956:Models, Chemical; D008958:Models, Molecular; D008969:Molecular Sequence Data; D009690:Nucleic Acid Conformation; D009691:Nucleic Acid Denaturation; D016415:Sequence Alignment / Q000379:methods; D017422:Sequence Analysis, DNA / Q000379:methods*; D012984:Software; D013696:Temperature; D044366:Transition Temperature
chemical_list: D004247:DNA