I know, for instance, that RNA is much more succetible to alkaline hydrolysis than DNA and this difference is determined by the presence of 2'-hydroxyl group in ribose. I have also heard that "DNA is more stable" and thus was selected as the repository of genetic information. Though, I still haven't understood why the lack of just one hydroxyl would lead to more stability...
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@Chris ok, I will actually delete the other because something similar has already been asked – El Cid Feb 24 '15 at 21:35
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My answer to this question may interest you, specifically the part about sugar pucker: http://biology.stackexchange.com/questions/19115/what-makes-dna-helical – canadianer Feb 24 '15 at 23:12
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From a chemical point of view, the phosphate can form a bond with the 2' hydroxyl, forming a cyclic structure and breaking the bond with the next nucleotide, thus breaking the RNA backbone. – user137 Feb 25 '15 at 03:07
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As user137 said, the general base abstracts a proton from the 2'OH and subsequently the 2'O- renders a nucleophilic attack on the δ+ Phosphorous, leading to the hydrolysis of the phosphodiester bond. There can be slight variations in the mechanism and the intermediates; for details see this review.

After hydrolysis both 2'- and 3'- phosphates can form.
RNA is not thermodynamically unstable; apart from being unstable in the presence of a strong base RNA is biochemically unstable too. This is because there are several RNAses and most of them degrade RNA by a mechanism similar to alkaline hydrolysis (they cannot act on DNA). Also see this post.