Entropic elasticity controls nanomechanics of single tropocollagen molecules

Abstract

We report molecular modeling of stretching single molecules of tropocollagen, the building block of collagen fibrils and fibers that provide mechanical support in connective tissues. For small deformation, we observe a dominance of entropic elasticity. At larger deformation, we find a transition to energetic elasticity, which is characterized by first stretching and breaking of hydrogen bonds, followed by deformation of covalent bonds in the protein backbone, eventually leading to molecular fracture. Our force-displacement curves at small forces show excellent quantitative agreement with optical tweezer experiments. Our model predicts a persistence length xi(p) approximately 16 nm, confirming experimental results suggesting that tropocollagen molecules are very flexible elastic entities. We demonstrate that assembly of single tropocollagen molecules into fibrils significantly decreases their bending flexibility, leading to decreased contributions of entropic effects during deformation. The molecular simulation results are used to develop a simple continuum model capable of describing an entire deformation range of tropocollagen molecules. Our molecular model is capable of describing different regimes of elastic and permanent deformation, without relying on empirical parameters, including a transition from entropic to energetic elasticity.

FIGURE 1

Force-displacement response of a single TC molecule with L ≈ 8.4 nm under tensile loading, showing results obtained using different methods (nonreactive CHARMM force field (A) (27), ReaxFF (B), and the reactive mesoscale model (C) (25)). We distinguish four regimes as the molecule undergoes deformation: Regime I is characterized by uncoiling of the triple helical structure, and Regime II with a larger tangent modulus corresponds to stretching of covalent bonds. In Regime III, we observe molecular fracture followed by rapid decay of the force in Regime IV.

FIGURE 2

Snapshots during deformation of a single tropocollagen molecule, for different levels of tensile strain ranging from 0% to 50%.

FIGURE 3

Dependence of bending stiffness EI of a single TC molecule on the deformation rate, L ≈ 8.4 nm, at T = 300 K. The results indicate that EI decreases linearly with decreasing loading rate. A linear fit to the data enables us to extrapolate to The resulting bending stiffness for vanishing deformation rate is used as input parameter for the mesoscale molecular model.

FIGURE 4

Schematic showing development of the coarse-grained molecular model from a full atomistic description. The full atomistic representation of the triple-helical TC structure is replaced by a collection of beads, each of which represents ≈10 protein atoms plus water molecules (25), with r₀ = 7 Å. The bottom subplot depicts how the load is applied to the long tropocollagen molecule. The outermost particle of the molecule is kept fixed during the simulation, and a slowly increasing force is applied on the right end.

FIGURE 5

Force-displacement (F(x)) curves of stretching a single TC molecule, L = 301.7 nm, at 300 K. Subplot (a): Force-displacement curve over the entire deformation range, covering four stages: (I) uncoiling of the entangled configuration, (II) uncurling of the triple helix, (III) stretching of covalent bonds in the individual polypeptides, and (IV) rupture of the TC molecule. The dashed line of indicates the contour length of the molecule. The inlay depicts dɛ/dx(x), showing that entropic contributions dominate for x < 280 nm. Subplot b depicts a subset of the results depicted in the previous figure, focusing on the small force, entropic response (F < 14 pN). This plot also depicts experimental results obtained for TC molecules with similar contour lengths (23,24), as well as the prediction of the WLC model with persistence length ξ_p ≈ 16 nm.

FIGURE 6

Increase in bending stiffness of a collagen fibril, as a function of number of TC molecules in the radial direction. The plot shows the bending stiffness normalized by the value for a single TC molecule. The results suggest a strong increase of the bending stiffness with number of molecules. A power-law fit suggests a scaling of EI ∼ n^2.5.

FIGURE 7

Numerical estimates of the functions f_WLC—f₁(x) and f₂(x). These functions describe the smooth transition from entropic elasticity to energetic elasticity. The results show that entropic forces reach a maximum when the molecule is stretched to its contour length, approaching 140 pN.