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. 2006 Aug 15;103(33):12285-90.
doi: 10.1073/pnas.0603216103. Epub 2006 Aug 8.

Nature designs tough collagen: explaining the nanostructure of collagen fibrils

Markus J Buehler  1
Affiliations

Nature designs tough collagen: explaining the nanostructure of collagen fibrils

Markus J Buehler. Proc Natl Acad Sci U S A. .

Abstract

Collagen is a protein material with superior mechanical properties. It consists of collagen fibrils composed of a staggered array of ultra-long tropocollagen (TC) molecules. Theoretical and molecular modeling suggests that this natural design of collagen fibrils maximizes the strength and provides large energy dissipation during deformation, thus creating a tough and robust material. We find that the mechanics of collagen fibrils can be understood quantitatively in terms of two critical molecular length scales chi(S) and chi(R) that characterize when (i) deformation changes from homogeneous intermolecular shear to propagation of slip pulses and when (ii) covalent bonds within TC molecules begin to fracture, leading to brittle-like failure. The ratio chi(S)/chi(R) indicates which mechanism dominates deformation. Our modeling rigorously links the chemical properties of individual TC molecules to the macroscopic mechanical response of fibrils. The results help to explain why collagen fibers found in nature consist of TC molecules with lengths in the proximity of 300 nm and advance the understanding how collagen diseases that change intermolecular adhesion properties influence mechanical properties.

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Conflict of interest statement

Conflict of interest statement: No conflicts declared.

Figures

Fig. 1.
Fig. 1.
Schematic view of some of the hierarchical features of collagen, ranging from the amino acid sequence level at nanoscale up to the scale of collagen fibers with lengths on the order of 10 μm. Here we focus on the mechanical properties of collagen fibrils consisting of a staggered array of TC molecules.
Fig. 2.
Fig. 2.
Study of a BM assembly of TC molecules. (a) Simplistic model of a collagen fibril used to study the dependence of the BM fibril tensile strength FF on molecular length and adhesion strength. (b) The variation of FF due to changes of the adhesion strength [tensile strength normalized by FF(τshear) and adhesion strength normalized by τshear, considering fully hydrated TC molecules without cross-links, χS/χR < 1]. (c) FF as a function of molecular length [normalized by its maximum value FF(L/χS = 1), for χS/χR < 1]. At the critical molecular length (L/χS = 1), the tensile force saturates, corresponding to a change from homogeneous shear to propagation of slip pulses. (d) The transition from homogeneous shear to brittle-like rupture of TC molecules, depicting FF and the dissipated energy (both normalized by reference values for χS/χR > 1). Energy dissipation is maximized when L/χR = 1, when the transition from shear to molecular rupture occurs. (e) The effects for variations in cross-link density on the BM fibril strength (normalized by the strength of the cross-link-free BM fibril) for a collagen molecule with a length of 840 Å, assuming a regular distribution of cross-links. The BM fibril strength approaches a finite value for large cross-link densities.
Fig. 3.
Fig. 3.
Stress versus strain of a collagen fibril for different molecular lengths (model for cross-link-deficient collagen, because no covalent cross-links are present in the collagen fibril). The longer the molecular length, the stronger the fibril. The maximum elastic strength achieved by collagen fibrils approaches ≈0.3 GPa, with the largest stress at ≈0.5 GPa. The onset of intermolecular shear can be recognized by the deviation of the stress–strain behavior from a linear elastic relationship.
Fig. 4.
Fig. 4.
Elastic strength and energy dissipation of the collagen fibril. (a) The critical stress at the onset of plastic shear between TC molecules. An initial regime of linear increase of strength with molecular length is followed by a regime of finite strength at a plateau value. (b) The dissipated energy during deformation per unit volume in a collagen fibril as a function of molecular length normalized by the maximum value. An initial steep increase is followed by a plateau regime, with a local maximum of ≈220 nm. The smooth curve is a fit of a third-order expansion to the simulation data.
Fig. 5.
Fig. 5.
Deformation map of collagen fibrils. The mechanical response is controlled by two length scales, χS and χR. Intermolecular shear governs deformation for small molecular lengths, leading to a relatively small strength of the collagen fibril. For large molecular lengths, either intermolecular slip pulses (χS/χR < 1) or rupture of individual TC molecules (χS/χR > 1) dominate. The maximum strength and maximum energy dissipation of the collagen fibril is reached at a critical molecular length scale Lχ that is defined as the minimum χS and χR. The regime χS/χR > 1 refers to the case of strong intermolecular interactions (e.g., increased cross-link densities or due to the effects of solvants that effectively increase molecular adhesion). Physiological collagen typically features long molecules with variations in molecular interaction so that either intermolecular shear (e.g., slip pulses) or molecular fracture are expected to dominate.
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