Characterization of bending stiffness and spontaneous buckling of alpha-helices and coiled coils

Abstract

Elasticity of α-helices and coiled coils have often been described by a linear response to local bending with bending stiffness (Kb) and persistence length (Lp) describing their flexibility. However, we observed that the non-bonded forces along the length of these structures are not screened at physiological conditions and introduce a buckling instability. For α-helical systems of same composition, but different lengths, this is identified by a drop in Kb for longer helices and the length where this drop is triggered is referred to as the critical buckling length. When shorter than their critical buckling length they behave linearly, and Kb calculated using normal mode analysis in this regime is about (3.0−3.4)×10-28 Nm2 for α-helices with varying compositions, and about (1.9 − 2.1) × 10−27 Nm2 for coiled coils with leucine zipper periodicity. Beyond the critical buckling length, normal mode solutions turn imaginary, leading to an eventual disappearance of bending modes. Investigations with one dimensional (1-D) linear chains of beads (a simplistic representation of bio-filaments) show that non-bonded forces have a reciprocal relation with the critical buckling length (no buckling instability existed in the absence of non-bonded forces). Critical buckling length is 115.3 ± 2.9 °A for α-helices and 695.1 ± 44.8 Å for coiled coils with leucine zipper periodicity, which is much smaller than their Lp (~ 800 Å for α-helices and ~ 3000 Å for coiled coils).