Triangular core as a universal strategy for stiff nanostructures in biology and biologically inspired materials

a r t i c l e i n f o Recent findings in protein structure prediction have revealed a new class of fibrous proteins called beta-solenoids. In stark resemblance to amyloid structures and prion proteins, these self-assembling peptides feature a triangular cross-sectional structure with non-specific biological significance. Using basic geometric and mechanical arguments and finite element simulations, here we point out that the equilateral triangle, as the most anisotropic regular convex polytope, is an ideal shape that leads to a maximum bending stiffness at minimum material usage. Considering the mechanical stability of the cell-puncture needle of the bacteriophage T4 virus and the extreme efficiency of aggregation in amyloids and prion proteins, possibly due to their capacity of acting as rigid binding and nucleation sites, we propose that the triangular core may reflect a universal biological paradigm for achieving exceptionally stiff nanostructures, overcoming the limitations of the underlying weak molecular interactions such as hydrogen bonds. Stiff nanostructures employing a triangular core geometry may be particularly useful for nanomechanical applications such as puncture and cutting devices where maximum rigidity has to be achieved using a minimal cross-sectional area. Recent advances in protein structure prediction techniques such as solid-state nuclear magnetic resonance (ssNMR) [1–3] have yielded detailed insight into the molecular architecture of fibrous protein oligomers with sub nano-scale precision, revealing a universal motif that features a triangular shaped core for these self-assembling peptides. Some of these protein structures have physiological functions in biology, whereas others occur spontaneously as a result of prion diseases. Certain amyloid fibrils that are found in Alzheimer's Disease also employ a triangular core with 3-fold symmetry [4] (Fig. 1(a)). Experimental evidence suggests that amyloid filaments are stiff, resulting in a large bending rigidity [5]. The interaction of these relatively rigid filaments with the surrounding cells and extracellular matrix may cause mechanical disruption of tissue and play a role in pathological pathways of diseases [6,7]. Similarly, beta-solenoids, a recently discovered class of protein topologies with triangular cross-sections, have been linked to pathological building blocks of prion diseases as well as virulence factors [8,9]. The high mechanical stiffness is utilized in biology as part of viral infection mechanisms. For example, the cell-puncture device needle of the bacteriophage T4 virus, a beta-solenoid with a triangular core [10], has been identified as a stiff needle that facilitates the drilling through the cell membrane of bacteria as part of the infection process …