First-Order Phase Transitions in Multistranded Macromolecules

The theory of the helix–coil equilibrium in an n‐stranded macromolecule is investigated under restrictions analogous to the matching case discussed in the preceding paper for two‐stranded molecules. The problem is found to be formally identical to the two‐strand case by showing that the probability of a looped state is proportional to $k^{\mathrm{-a}}$ , where $k$ is the number of links in each branch of the loop and $\text{a\hspace{0.17em}=\hspace{0.17em}3(n\hspace{0.17em}−\hspace{0.17em}1)\hspace{0.17em}/\hspace{0.17em}2}$ for Gaussian chains. It follows that a first‐order phase transition occurs at a critical value of the stability constant for $\text{n\hspace{0.17em}≥\hspace{0.17em}3}$ . Data bearing on the helix–coil transition in the three‐stranded protein collagen are examined and found to suggest that a first‐order phase transition would indeed occur under equilibrium conditions. The three‐stranded polynucleotide complex formed from one stand of polyriboadenylic acid and two strands of polyribouridylic acid shows an apparent second‐order transition. This is interpreted to mean that mismatching of strands occurs in this material.