Structural distributions from single-molecule measurements as a tool for molecular mechanics

A mechanical view provides an attractive alternative for predicting the behavior of complex systems since it circumvents the resource-intensive requirements of atomistic models; however, it remains extremely challenging to characterize the mechanical responses of a system at the molecular level. Here, the structural distribution is proposed to be an effective means to extracting the molecular mechanical properties. End-to-end distance distributions for a series of short poly-l-proline peptides with the sequence P _nCG ₃K-biotin (n = 8, 12, 15 and 24) were used to experimentally illustrate this new approach. High-resolution single-molecule Förster-type resonance energy transfer (FRET) experiments were carried out and the conformation-resolving power was characterized and discussed in the context of the conventional constant-time binning procedure for FRET data analysis. It was shown that the commonly adopted theoretical polymer models - including the worm-like chain, the freely jointed chain, and the self-avoiding chain - could not be distinguished by the averaged end-to-end distances, but could be ruled out using the molecular details gained by conformational distribution analysis because similar polymers of different sizes could respond to external forces differently. Specifically, by fitting the molecular conformational distribution to a semi-flexible polymer model, the effective persistence lengths for the series of short poly-l-proline peptides were found to be size-dependent with values of ∼190 , ∼67 , ∼51 , and ∼76 for n = 8, 12, 15, and 24, respectively. A comprehensive computational modeling was carried out to gain further insights for this surprising discovery. It was found that P ₈ exists as the extended all-trans isomaer whereas P ₁₂ and P ₁₅ predominantly contained one proline residue in the cis conformation. P ₂₄ exists as a mixture of one-cis (75%) and two-cis (25%) isomers where each isomer contributes to an experimentally resolvable conformational mode. This work demonstrates the resolving power of the distribution-based approach, and the capacity of integrating high-resolution single-molecule FRET experiments with molecular modeling to reveal detailed structural information about the conformation of molecules on the length scales relevant to the study of biological molecules.