Local Frustration Determines Molecular and Macroscopic Helix Structures Christopher J. Forman,* ,† Szilard N. Fejer, ‡ Dwaipayan Chakrabarti, †,§ Paul D. Barker, † and David J. Wales † † Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K. ‡ Department of Chemical Informatics, Faculty of Education, University of Szeged, Boldogasszony sgt. 6, Szeged 6725, Hungary and Pro-Vitam Ltd., str. Muncitorilor nr. 16, Sf. Gheorghe 520032, Romania § Department of Chemistry, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India * S Supporting Information ABSTRACT: Decorative domains force amyloid fibers to adopt spiral ribbon morphologies, as opposed to the more common twisted ribbon. We model the effect of decorating domains as a perturbation to the relative orientation of β strands in a bilayered extended β-sheet. The model consists of minimal energy assemblies of rigid building blocks containing two anisotropic interacting ellipsoids. The relative orientation of the ellipsoids dictates the morphology of the resulting assembly. Amyloid structures derived from experiment are consistent with our model, and we use magnets to demonstrate that the frustration principle is scale and system independent. In contrast to other models of amyloid, our model isolates the effect of frustration from the fundamental interactions between building blocks to reveal the frustration rather than dependence of morphology on the physical interactions. Consequently, amyloid is viewed as a discrete molecular version of the more general macroscopic frustrated bilayer that is exemplified by Bauhinia seedpods. The model supports the idea that the interactions arising from an arbitrary peptide sequence can support an amyloid structure if a bilayer can form first, which suggests that supplementary protein sequences, such as chaperones or decorative domains, could play a significant role in stabilizing such bilayers and therefore in selecting morphology during nucleation. Our model provides a foundation for exploring the effects of frustration on higher-order superstructural polymorphic assemblies that may exhibit complex functional behavior. Two outstanding examples are the systematic kinking of decorated fibers and the nested frustration of the Bauhinia seedpod. ■ MOTIVATION AND INTRODUCTION Many materials involve frustration, where part of a system cannot relax into its local ground state because of external constraints. Such frustration may induce interesting long- or short-range properties, which often give rise to complex emergent behavior. For example, tensegrity structures, 1-3 multidomain peptide structures, 4 amyloid fibers, 5,6 liquid crystals, 7 creased plates, 8 and bimetallic strips all exhibit internal frustration, which drives more complex behavior than any single component can exhibit alone. In this work we use a well-known bilayer frustration principle, observed in Bauhinia seedpods, 9 to model an unexplained change in amyloid fiber morphology from a twisted to a spiral ribbon (see Figure 1). This transition was observed experimentally when a fiber-forming protein, SH3, was covalently linked to a second protein, cytochrome b 562 . 10 On their own the SH3 domains typically form twisted ribbon amyloid fibres. 11,12 When combined with a cytochrome, the SH3-cytochrome b 562 fusion proteins always formed fibers with a spiral ribbon morphology. 10,12 Helical symmetry is very common, so it may be a coincidence that the fiber’s morphological transition mimics the transition observed for the Bauhinia bilayers. 9 However, we note that known amyloid fiber structures in the literature, such as Aβ 13 and HET-s, 14 contain even numbers of β-sheets due to the hydrophobic inner surfaces packing against each other, 15 thus yielding a bilayered arrangement. In the Bauhinia seedpods, the bilayer arrangement is fundamentally responsible for the helical morphologies, which minimize frustration between two stressed sublayers, each mutually inhibiting the other’s relaxation. 9 Narrow strips cut from such frustrated bilayers, at specific angles relative to the internal stress, produce ribbons that adopt a helical morphology somewhere around the transition between twists and spirals (see Figure 1a-d). 9 Since the morphology depends on the cutting angle, the shape of the ribbon cannot be said to be a property of the material from which the bilayer is made. Received: April 30, 2013 Published: May 31, 2013 Article pubs.acs.org/JPCB © 2013 American Chemical Society 7918 dx.doi.org/10.1021/jp4040503 | J. Phys. Chem. B 2013, 117, 7918-7928