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What are the algorithms / methods in use for the calculation of primer dimers and hairpins?

As an example, IDT's OligoAnalyzer tool will generate these analysis given particular sequences.

The homo-dimer analysis seems to me to just be a sliding scan of two sequences across each other. I assume this doesn't take into account possible hairpin issues? or are such structures less likely compared to the myriad of other more common problems. In addition, how are the ΔG values calculated given a particular dimerization pattern?

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It is important visualize more faces to design primer or oligo and PCR experiments:

- calculate thermodynamic parameters of DNA Hybridization (Oligo/Template)

  • compute hairpin-loop, dimer, bases penality and melting temperature about primer or pair primer

  • calculate statistics about melting temperature with the change in composition and mix PCR concentration

with google you could find more tools but you must choose a tool of a sequencing team. almost all tools use mfold algorithm, it's simple and effective:

M. Zuker, D. H. Mathews & D. H. Turner. Algorithms and Thermodynamics for RNA Secondary Structure Prediction: A Practical Guide In A Biochemistry and Biotechnology, 11-43, J. Barciszewski and B. F. C. Clark, eds. , NATO ASI Series, Kluwer Academic Publishers, Dordrecht, NL, 1999.

I worked in a sequencing team and there was a programmer. he developed a fantastic tools. he is a little english, but he could support you: http://promix.cribi.unipd.it/cgi-bin/promix/melting/melting_main.exe

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