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Atomistic Simulation Approach to a Continuum Description of Self-Assembled ß-Sheet Filaments

Jiyong Park ^*, Byungnam Kahng ^*, Roger D. Kamm   and Wonmuk Hwang  

^* School of Physics and Center for Theoretical Physics, Seoul National University, Seoul, Korea; Biological Engineering Division, Center for Biomedical Engineering, and Department of Mechanical Engineering, and Biological Engineering Division and Center for Biomedical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts; and Department of Biomedical Engineering, Texas A&M University, College Station, Texas

Correspondence: Address reprint requests to W. Hwang, Tel.: 979-458-0178; E-mail: hwm{at}tamu.edu.

We investigated the supramolecular structure and continuum mechanical properties of a ß-sheet nanofiber comprised of a self-assembling peptide ac-[RARADADA]₂-am using computer simulations. The supramolecular structure was determined by constructing candidate filaments with dimensions compatible with those observed in atomic force microscopy and selecting the most stable ones after running molecular dynamics simulations on each of them. Four structures with different backbone hydrogen-bonding patterns were identified to be similarly stable. We then quantified the continuum mechanical properties of these identified structures by running three independent simulations: thermal motion analysis, normal mode analysis, and steered molecular dynamics. Within the range of deformations investigated, the filament showed linear elasticity in transverse directions with an estimated persistence length of 1.2–4.8 µm. Although side-chain interactions govern the propensity and energetics of filament self-assembly, we found that backbone hydrogen-bonding interactions are the primary determinant of filament elasticity, as demonstrated by its effective thickness, which is smaller than that estimated by atomic force microscopy or from the molecular geometry, as well as by the similar bending stiffness of a model filament without charged side chains. The generality of our approach suggests that it should be applicable to developing continuum elastic ribbon models of other ß-sheet filaments and amyloid fibrils.

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