Proline Ring Conformations Corresponding to a Bistable Jump Model from $^{13}C$ spin-Lattice Relaxation Times

A formalism for extracting the conformations of a proline ring based on the bistable jump model of R. E. London [(1978) J. Am. Chem. Soc. 100, 2678-2685] from $^{13}C$ spin-lattice relaxation times ($T_1$) is given. The method is such that the relaxation data are only partially used to generate the conformations; these conformations are constrained to satisfy the rest of the relaxation data and to yield acceptable ring geometry. An alternate equation for $T_1$ of $^{13}C$ nuclei to that of London is given. The formalism is illustrated through an example