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The textbooks starts with the phenomena that double helix is an expression of the rules of chemistry.

Hydrogen bonds are important in determining the formation of specific base pairs in the double helix. However in single staranded DNA, the hydrogen bond donors and acceptors are exposed to solution and can form hydrogen bonds with water molecules. When two single strands come together, these hydrogen bonds with water are broken and new hydrogen bonds between the bases are formed. Because the number of hydrogen bonds broken is the same as the number formed, these hydrogen bonds do not contribute substantially to driving the overall process of double helix-formation. However, they contribute greately to the specificity of binding.

I see the point that some neucleotides which form stable links are the complimentary bases (purine and pyramidine). Some bases do not form stable links. I did search my question online, I am not able to get near anything that's directly related or comprehensible at my level. So following is what I do not understand.

Suppose two bases that cannot form Watson-Crick base pairs are brought together. Hydrogen bonds with water must be broken as the bases come into contact. Because the bases are not complementary in structure, not all of these bonds can be simultaneously replaced by hydrogen bonds between the bases. Thus, the formation of a double helix between noncomplementary sequences is disfavoured.

What's the specificity mentioned here? What does it mean by non complementary in structure? An example is appreciated.

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If you take a look at the base pairings, as shown below, you can see that adenine and thymine form two hydrogen bonds when they are matched, while guanine and cytosine form three hydrogen bonds when they are matched. If you try to match an adenine with cytosine or guanine with thymine, the orientation of hydrogens and lone pairs will not line up.

For example, guanine has two hydrogens and one lone pair available for hydrogen bonding, while cytosine has one hydrogen and two lone pairs available for hydrogen bonding. They fit! However, if you try to match adenine (with one hydrogen and one lone pair available for hydrogen bonding) with cytosine, the elements will not match or line up, resulting in an energetically less-favorable interaction.

Summary: A base on one strand of DNA requires another, specific base to complement the exposed hydrogens and lone pairs to form the most most energetically favorable interactions.

enter image description here

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    $\begingroup$ So (mis)matching a guanine to say thymine would result in one H bond on both G and T being unfulfilled. So forming this mismatch would require breaking three H bonds between G and water, and at least two H bonds between T and water. And the mismatched pair would only have four inter-base H bonds, tops. So the energetic penalty for the mismatch is one H bond lost. In contrast, when matching G to its cognate base C, there is no H bond penatly. $\endgroup$ – Curt F. Aug 3 '15 at 23:07
  • $\begingroup$ @CurtF. Excellent recap! $\endgroup$ – Dan Burden Aug 3 '15 at 23:52
  • $\begingroup$ @CurtF. This is great: guanine has two hydrogens and one lone pair available for hydrogen bonding, while cytosine has one hydrogen and two lone pairs available for hydrogen bonding. They fit! However I am still confused about specificity. $\endgroup$ – bonCodigo Aug 4 '15 at 6:20
  • $\begingroup$ @bonCodigo specificity is just a term meaning that each purine only has one complement pyrimadine. $\endgroup$ – Dan Burden Aug 4 '15 at 10:52
  • $\begingroup$ @DanBurden This is not fully true. There can be some non-canonical interactions $\endgroup$ – WYSIWYG Aug 19 '15 at 11:57
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Addition to Dan Burden's answer:

Guanine can form a base-pair with Thymine or Uracil (2 hydrogen bonds). This is not generally observed in the DNA but is quite common in RNA helices.

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The non-Watson-Crick (WC) type base pairs or wobble-base pairs introduce distortion in the helix; they are also thermodynamically weaker than the WC pairs. However the GU pair, especially in RNA has a thermodynamic stability comparable to the WC pairs [1]. The distortion that it imposes on the helix is also less than that of other wobble pairs. GT mismatch can actually be tolerated to some extent even in DNA in all its structural forms (A,B and Z) [2]. GU pairs are however stabler in RNA and allow structural flexibility. GU pairs introduce a high electrostatic potential into the major groove which in turns increases its propensity for divalent metal ion binding [1]. It is my guess that metal-binding may stabilize the structure. Water molecules are also shown to cluster around the GU pair and possible stabilize the it [3]. Again it is a guess that this may be a resultant of the higher electrostatic potential in case of the GU wobble.

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