Water water everywhere (9.5.2)

Alpha-helix formation is another phenomenon that can be explained by the ‘hydrophillic effect’. As it seems water prefers water over amino acids. The hydrophilic interactions can drive the apparently energetically unfavourable formation of an amino acid alpha-helix.

∆E(bond) : the energy change for DNA when moving from a random coil formation to an alpha-helix. The helix has higher energy as ∆E(bond) > 0.
∆S(conf) : the entropy change from restricting the movements of the DNA monomers. This is usually < 0.
∆S(bond) : the entropy of redistributing hydrogen bonds interacting with the environment to interacting with other monomers to create helix. Can be > 0 depending on the environment.

∆S(tot) = ∆S(bond) + ∆S(conf)

If ∆S(bond) is larger enough it can overcome the entropy decrease of ∆S(conf). Which can then overcome the effect of the energy difference ∆E(bond) creating a favourable reaction.

∆G(bond) = ∆E(bond) - T∆S(tot)

Nelson defines a parameter
α = [∆E(bond) - T∆S(tot)]/[-2k(b)T]
Where if α is positive, extension of the DNA helix is favourable in the current environment.

α=((∆E-T∆S))⁄(-2kT)
α= 1/2×((T∆S-∆E)∆E/∆S)/(kT ∆E/∆S)
α= 1/2×∆E/k×(T-∆E/∆S)/(T ∆E/∆S)
α= 1/2×∆E/k×(T-Tm)/TTm
T= ∆E/∆S (Eq 6.9)

When T = Tm, α = 0 Therefore at Tm there is no free energy cost of extending the alpha-helix.