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Does the pH influence the stability of double stranded DNA?

Yes. The pH of the environment influences the stability of double-stranded oligonucleotides profoundly. Therefore most hybridization reactions are conducted at near neutral pH. Alkaline buffers promote duplex dissociation and therefore inhibit hybridization.

For example, siRNA and aptamers are less stable at lower pH because of depurination of bases that can lead to abasic sites.

In the pH range around the neutral pH, from pH 5 to 9, common nucleic acid duplexes are quite stable. None of the functional groups present in typical nucleic acids titrate between pH 5 to 9. However, modified bases may differ.

Below pH 5 and above pH 9, standard duplexes are destabilized because of titration of the polar groups on the bases.  Polar groups are involved in hydrogen bonding between base pairs. Ionization adds a net charge to polar bonds.

Low pH decreases the solubility and can cause depurination and strand breakage.

Low pH also stabilizes triple helices that contain pyrimidine-purine-pyrimidine and cytosine residues.

High pH, up to 13, is less damaging and is used to denature nucleic acids. However, depurination and strand breakage can still happen. 

Reference

Creighton, T. E. (2010); The biophysical chemistry of nucleic acids and proteins. Helvetian Press.

Farrell, R. E. Jr.; RNA methodologies. 5th Edition. Academic Press. 2017.

Roberts RW, Crothers DM. Stability and properties of double and triple helices: dramatic effects of RNA or DNA backbone composition. Science. 1992;258:1463–6. [PubMed]