The formation of double helix from two short single stranded DNA molecules CGCGA

Question

The formation of double helix from two short single stranded DNA molecules CGCGATAT and ATATCGCG is spontaneous in 1 M NaCl at pH 7.0 and 25 oC . The DG for the reaction is -54 kJ/mol and 251 kJ/mol of heat is released from the reaction. Please calculate the entropy change of this reaction and explain why it is negative. What kind of noncovalent interactions are involved in the formation of the double helix? You can break up the DNA double helix by heating the solution, at what temperature this double helical DNA will start to melt? (Hints: the DH of the reactions is -251 kJ/mol since heat is released rather that absorbed in the reaction. Use the free energy equation to do the calculations.)

Explanation / Answer

The interaction between bases on different strands depends on the neighboring bases. Therefore, the nearest-neighbor model treats a DNA helix as a string of interactions between 'neighboring' base pairs. The free energy for the reaction of formation of double helix from the given two short single stranded DNA molecules is 54.42 KJ/mol.

DG = (-9.07) + (-9.07) + (-9.36) + (-9.07) + (-5.51) + (-3.67) + (-2.50) + (-3.67) + (-2.50) = -54.42 KJ/mol.

The entropy change of this reaction is -885.4 J/(mol.K)

DS = (-113.8) + (-113.8) + (-102.1) + (-113.8) + (-92.9) + (-85.4) + (-89.1) + (-85.4) + (-89.1) = -885.4 J/(mol.K).

Formation of a double helix happens spontaneously only if there is net increase in entropy. The increase in entropy is indicated by the increase in the amount of heat released. The greater the increase in entropy, the greater will be the heat released, and more the stability of the double helix DNA will be. The double helix is stable only because its formation leads to an increase in entropy. Breaking the strand leads to a decrease in entropy as that process absorbs heat.

The entropy for formation of DNA helix is always negative, as it releases good amount of heat into its surroundings.

Hydrogen bonds are a type of non-covalent interactions that hold the two strands of DNA double helix together.

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