Kinetics of the Helix—Coil Transition in Polyamino Acids

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Abstract
The matrix theory of the helix—coil transition in polyamino acids is extended to give the initial rate of change of helical content when the system is suddenly perturbed from equilibrium. Using the matrix to treat chains of arbitrary length, it is possible to assign not only the equilibrium statistical weights for the initial probability of occurrence of each species but also the rate constants for all possible initial reactions involving the formation and breakdown of helical states. It is shown that all the rate constants can be related to the equilibrium statistical weights and to only one rate constant. It is found that reactions at helical ends dominate the initial rate, even though there are many more interior sites than there are ends. As a result, the initial rate of change of helical content goes through a maximum at the transition temperature. With the aid of some approximate expressions for the number of helical ends, it is possible to discuss the initial rate for all ranges of chain length. The technique used to compute the initial rate can also be applied to calculate the moments of the equilibrium distribution of lengths of helical sequences; this calculation is given in the Appendix.