Statistical mechanics of noncovalent bonds in polyamino acids. IV. Matrix treatment of hydrophobic bonds in the random coil and of the helix–coil transition for chains of arbitrary length

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Abstract
The Lifson‐Roig matrix theory of the helix–coil transition in polyglycine is extended to situations where side‐chain interactions (hydrophobic bonds) are present both in the helix and in the random coil, as discussed for short chains in paper II of this series. It is shown that the conditional probabilities of occurrence of any number and size of hydrophobic pockets in the random coil can be adequately described by a 2 × 2 matrix. This is combined with the Lifson‐Roig 3 × 3 matrix to produce a 4 × 4 matrix which represents all possible combinations of any amount and size sequence of α‐helix with random coil containing all possible types of hydrophobic pockets in molecules of any given chain length.