Article pubs.acs.org/Biomac
Role of Intrafibrillar Collagen Mineralization in Defining the Compressive Properties of Nascent Bone Arun K. Nair,†,⊥ Alfonso Gautieri,†,‡ and Markus J. Buehler*,†,§,∥ †
Laboratory for Atomistic and Molecular Mechanics (LAMM), Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 1-235 A&B, Cambridge, Massachusetts 02139, United States ‡ Biomechanics Group, Department of Electronics, Information and Bioengineering, Politecnico di Milano, Via Golgi 39, 20133 Milan, Italy § Center for Computational Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States ∥ Center for Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States ABSTRACT: Bone is the sole biological material found in the human body that is able to sustain compressive loads. However, although the structure of bone is well-known (it is a natural composite of collagen protein and hydroxyapatite mineral with a complex hierarchical organization), the details about the mechanisms that govern deformation at the molecular scale under compressive loading are still not completely understood. To investigate the molecular origins of bone’s unique compressive properties, we perform full atomistic simulations of the three-dimensional molecular structure of a mineralized collagen fibril, focusing on the role of intrafibrillar mineral densities in dictating the mechanical performance under compressive loading. We find that as the mineral density increases, the compressive modulus of the mineralized collagen increases monotonically and well beyond that of pure collagen fibrils. These findings reveal the mechanism by which bone is able to achieve superior load bearing characteristics beyond its individual constituents. Moreover, we find that intrafibrillar mineralization leads to compressive moduli that are one order of magnitude lower than the macroscale modulus of bone, indicating that extrafibrillar mineralization is mandatory for providing the load bearing properties of bone, consistent with recent experimental observations.
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INTRODUCTION Bone is a hierarchical biocomposite with a primary physiological role to carry compressive and tensile loads (Figure 1a). Apart from water, bone is composed of soft organic material such as collagen and much stiffer apatite at the nanoscale.1,2 During the complex phenomena of bone formation, collagen molecules assemble into fibrils, which are mineralized via the formation of apatite crystals.3 The organic component of bone (i.e., collagen) is able to sustain considerable tensile loads but does not have high compressive load bearing capacity; hence, the investigation of the role of apatite in compressive loading is very relevant to bone nanomechanics. Also, understanding the deformation of bone at the nanoscale is very useful for developing new biocomposities.4,5 Moreover, various diseases associated with bone such as brittle bone disease can cause deterioration of bone strength, and the origin of such diseases typically involves mutation of the collagen structure or variation of apatite crystal sizes. Thus, the loss of macroscale strength in bone due to diseases is directly related to the nanoscale mechanics of bone structure. In this paper, we focus on the mechanics of mineralized collagen fibrils under compressive loading, which is a predominant function of bone. © 2014 American Chemical Society
The structure of bone at the nanoscale and its associated mechanical properties have been studied; however, our knowledge of how collagen fibrils and hydroxyapatite crystals interact at the molecular scale and how they deform as an integrated system under compressive stress are not well understood. Furthermore, it has long been believed that mineral crystals that form within the collagen fibrils are the key structures that provide bone its compressive modulus. However, recent work6 has suggested that intrafibrillar mineral alone is not able to provide the required bone mechanical properties and thus extrafibrillar mineralization is mandatory. These findings highlight the need for a deeper understanding of the properties of bone from the level of its building blocks, which requires a thorough investigation of the interplay of the organic protein molecules with the mineral crystals. This, in turn, requires an atomistic-level investigation of the properties of the organic−inorganic interfaces7,8 and their correlation with overall mechanical behavior. The recent success in developing Received: March 5, 2014 Revised: May 26, 2014 Published: June 3, 2014 2494
dx.doi.org/10.1021/bm5003416 | Biomacromolecules 2014, 15, 2494−2500
Biomacromolecules
Article
Figure 1. Bone structure at multiple scales, and loading condition considered in this analysis. Hierarchical structure of bone ranging from the (a) macroscale skeleton (image reproduced from ref 41 with permission. Copyright 2010 Annual Reviews) to (b) nanoscale collagen fibril (green) and hydroxyapatite platelets (red) and (c) atomistic scale interface consisting of collagen and hydroxyapatite.
Figure 2. Collagen microfibril model at different mineralization stages. Collagen microfibril models with 0% mineralization (the inset shows the collagen triple-helix structure), 20% mineral content (the inset shows a hydroxyapatite unit cell), and 40% mineral content. The hydroxyapatite crystals are arranged such that the c axis of the crystal aligns with the fibril axis. Ca atoms are colored green. OH groups are colored red and white, and the tetrahedron structure visualizes the PO4 group. Images reprinted from ref 10 with permission. Copyright 2013 MacMillan Publishers Ltd.
fully atomistic models for pure collagen9 and mineralized collagen fibrils10 has shown that the nanoscale study of bone can be conducted to uncover nanoscale deformation mechanisms. In this paper, we utilize a three-dimensional fully atomistic model of an unmineralized collagen microfibril (representing tendon-like microstructure) and a mineralized collagen microfibril (representing bone microstructure) to perform compressive tests at various stress levels, with the goal of identifying key deformation mechanisms and assessing the role of intrafibrillar mineralization. The use of molecular dynamics allows us to ask fundamental questions about the relationship among the chemical composition, distribution of minerals, and associated mechanical properties11 and can be used in systematic design.12,13
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different mineral concentrations in the bone collagen microfibril. The model used in this study accounts for the complexity of the chemical interactions14−16 as described in the earlier model.10 Collagen Protein Force Field Parametrization. All atomistic simulations are conducted using the CHARMM force field.17 However, a relevant building block of collagen sequence is hydroxyproline (HYP), a nonstandard amino acid resulting from the post-translational hydroxylation of proline. HYP is not parametrized in common biomolecular force fields; hence, we used a parameter set for HYP18 that has been developed on the basis of quantum mechanical models and have been subsequently used to derive the atomistic parameters that best match the quantum mechanics calculation. These parameters have been included in an extended CHARMM force field, similar to previous works.19−22 Crystal Geometry and Hydroxyapatite Force Field Parametrization. The hexagonal hydroxyapatite crystal unit cell is generated using Material Studio 4.4 (Accelrys, Inc.), with the following lattice parameters: a = 9.4214 Å, b = 9.4214 Å, c = 6.8814 Å, α = 90°, β = 90°, and γ = 120°. As was done for HYP, we extended the CHARMM force field because it does not include parameters for mineral crystal such as hydroxyapatite. All parameters for mineral (bond, angle, dihedral, and nonbond parameters) are reported in ref 23 and are based on both quantum mechanical calculations and empirical data. For nonbonded terms, we use data from ref 24 in which the authors fit the Born−Mayer−Huggins potential23 with a LennardJones potential.
MATERIALS AND METHODS
Here we use the full-atomistic model developed in previous works9,10 to perform a systematic study of bone nanomechanics. The geometry and composition of the model are summarized in Figure 2, indicating varied levels of mineral content. The 0% case corresponds to a nonmineralized collagen microfibril, mimicking tendon fibrils (Figure 2). The 20% and 40% mineral density cases correspond to the two 2495
dx.doi.org/10.1021/bm5003416 | Biomacromolecules 2014, 15, 2494−2500
Biomacromolecules
Article
Mineralized Collagen Microfibril Model: In Silico Mineralization. The bone microfibril model used here is based on Protein Data Bank entry 3HR2 that was used as a basis for the nonmineralized collagen fibril model reported previously.9,10 The model represents a unit cell of the collagen fibril, simulated using periodic boundary conditions (i.e., modeling an infinitely large fibril), and thus, it is not subject to buckling, which may occur in a fibrous structure subjected to compression. For further information, we refer the reader to a previous paper with the details on the development of the collagen fibril atomistic model9 and to the work that describes the details of the Xray crystallography.25 The mineralized models are built starting from the nonmineralized model by filling the model’s periodic box of HAP unit cells.10 We stress that the mineralization modeled in this work refers only to the intrafibrillar component. Indeed, in addition to the crystallites located within the collagen fibrils, a significant amount of mineral is believed to be located in the spaces between the fibrils (extrafibrillar mineralization). The amount of mineral outside the fibril is estimated to as much as 75% of the total mineral in bone tissues.26−28 Therefore, in our models, which account only for intrafibrillar mineralization, we consider degrees of mineralization of up to 40% by weight, which allows us to study moderately to highly mineralized fibrils. Finally, in our model, the mineral crystals are oriented such that orientation of OH groups of the crystal is parallel to the collagen fibril axis. This is because the orientation and surface of hydroxyapatite crystals have been shown to produce a significant effect in controlling the collagen−mineral interactions: recent works have shown that the mineral crystal surface (i.e., either a OH or a Caterminated surface) plays a significant role in controlling the interaction between collagen and hydroxyapatite.29 Fibril Equilibration. For fibril equilibration, we use molecular dynamics as implemented in LAMMPS code30 and the modified CHARMM force field described above. The collagen−hydroxyapatite model is first geometrically optimized through energy minimization, and then an NVT equilibration is performed for 2 ns. The system temperature is maintained at 300 K (room temperature). The unit cell that comprises collagen and hydroxyapatite has triclinic symmetry as described previously.25 We use a time step of 2 fs by constraining the rigid covalent bond lengths. Nonbonding interactions are computed using a switching function between 0.8 and 1.0 nm for van Der Waals interactions, while the Ewald summation method31 is applied to describe electrostatic interactions. We confirmed that the root-meansquare deviation (rmsd) of the mineralized collagen is stable. In Silico Mechanical Testing. We perform stress-controlled (NPijT) molecular dynamics simulations with increasing compressive stress applied along the X axis of the unit cell as depicted in Figure 3a to assess the mechanical properties of mineralized collagen fibrils, the loading along the X axis is held constant until the samples attains equilibrium. The unit cell is under constant atmospheric pressure along other two axes (Y and Z). We use an NPijT ensemble30 for loading the samples with different stress states σ = Pij: (i) atmospheric pressure, (ii) −20 MPa, (iii) −60 MPa, and (iv) −100 MPa. We observe that samples reached equilibration under an applied load at approximately 6 ns. The strain is computed as ε = (L − Lo)/Lo, where Lo is the equilibrium length identified at atmospheric pressure. We monitor the pressure at equilibrium and rmsd to confirm that the size of the simulation cell reaches a steady-state value. Using the fibril strain ε associated with each applied stress σ, we obtain the stress−strain behavior for each case by plotting σ over ε. We use a linear function to fit the stress−strain data for both nonmineralized and mineralized data sets. The general form of the equation is σ = a1 + a2ε. The modulus is computed from the first derivative of the linear function that is fit to the stress−strain data. The computational time requirement for equilibration is 0.2 ns/week using 24 processors for the 40% mineral density case.
Figure 3. Mechanical properties of collagen fibrils under compressive loading at different mineralization stages. (a) Fibril unit cell with mineral content used to perform the compression test by measuring stress vs strain. (b) Stress−strain plots for nonmineralized collagen fibril (0%), 20% mineral density, and 40% mineral density cases. For the 0% case, the modulus decreases as the stress increases, while for 20 and 40% mineral densities, an increase in the modulus is observed as the stress increases. The error bars in panel b are computed from the maximal and minimal values of the periodic box length along the X direction at equilibrium.
implemented in VMD. This approach of computing the strain in a collagen molecule is different from the approach discussed in earlier work33 and is due to the fact that under compressive stress, the distance between glycine residues on the collagen triple helix varies significantly through the collagen microfibril length.
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RESULTS AND DISCUSSION We use previously developed atomistic models of collagen fibrils to study the compressive behavior at different mineral densities, from 0% tendon-like collagen microfibril (see Figure 2 for model details) to 40% mineral density (highly mineralized bone-like collagen fibril). When present, the mineral is deposited predominantly in the gap region along the fibril axis, with sparse deposition in the overlap region. This observation is consistent with the experimental findings.3 We conduct compressive tests on nonmineralized (0%) and 20% and 40% mineral density samples (Figure 3a). We observe that as the mineral content increases, the stress−strain behavior of the mineralized collagen microfibril also changes compared to that of pure collagen fibrils (see Figure 3b). The tendon-like collagen fibrils show an initial high modulus (E ≈ 1.2 GPa) for low stresses (
