Length and Sequence Dependence of the Elasticity of Alpha Helices and Coiled-Coils

Fibrous proteins made by α-helices, one of the most elementary protein secondary structures, have various mechanical roles in a sub cellular environment. An α-helix is wound in a right-handed fashion due to hydrogen bonding between the C=O and the N-H atoms across every i and i+4^th residues in the polypeptide chain. Previous approaches characterizing mechanical properties of α-helices treated them as homogenous and linear elastic rods. Stiffness is typically expressed in terms of persistence length l_p (∼100nm from K_b∼3×10⁻²⁸ Nm², l_p = K_b/kT: K_b, the bending stiffness, k the Boltzmann constant and T = 300 K, the temperature) [1–3]. In this study, we show that bending stiffness depends on the length of the filament, due to inherent non-bonded attractions. In particular, non-bonded attraction introduces a new length scale, critical buckling length, beyond which the filament can no longer remain linearly elastic. These results suggest that non-bonded attractions can significantly affect elastic properties of biofilament systems such as the cytoskeleton. Furthermore, we find that while elasticity of a single α-helix is largely independent of its amino acid sequence, α-helical coiled-coils have stronger sequence dependence, and in the case of tropomyosin molecule, we find regional variations in the flexibility which may have functional implications in its actin binding properties and muscle contraction.