Molecular Mechanism of Polarization and Piezoelectric Effect in Super

Article pubs.acs.org/journal/abseba

Molecular Mechanism of Polarization and Piezoelectric Effect in Super-Twisted Collagen Zhong Zhou,† Dong Qian,† and Majid Minary-Jolandan*,†,‡ †

Department of Mechanical Engineering, The University of Texas at Dallas, 800 W. Campbell Rd, Richardson, Texas 75080, United States ‡ Alan G. MacDiarmid NanoTech Institute, The University of Texas at Dallas, 800 W. Campbell Rd, Richardson, Texas 75080, United States ABSTRACT: It has been known for decades that bone exhibits piezoelectric behavior. In recent years, it was directly proved that this effect stems from a polymeric matrix in bone, i.e., collagen fibrils. This effect in collagen is distinctly different from organic piezoelectric crystals, given the semicrystalline molecular structure of the collagen biopolymer. As such, the molecular mechanism of this electromechanical coupling effect in a realistic “super-twisted” model of collagen has been elusive. Herein, we present an investigation on the molecular mechanism of piezoelectric effect in collagen using full atomistic simulation based on the experimentally verified “super-twisted” microstructure of collagen. Our results reveal that collagen exhibits a uniaxial polarization along the long axis of the collagen fibril. In addition, the piezoelectric effect in collagen originates at the collagen molecule level and is due to the mechanical stress-induced reorientation and magnitude change of the permanent dipoles of individual charged and polar residues. A piezoelectric constant in the range of 1−2 pm/V (pC/N) is obtained from the simulation, which agrees well with the experimental data. KEYWORDS: collagen piezoelectricity, atomistic simulation, molecular mechanism, bone piezoelectricity, molecular dynamics

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From a materials point of view, bone is a hierarchical composite with up to seven levels of hierarchy having collagen fibrils at the lowest level of hierarchy.11 Collagen fibril, in turn, has several levels of hierarchy, which includes collagen microfibril, collagen molecule, triple helix, single α-chain, and amino acids. In bone, the collagen template is impregnated by hydroxyapatite (HAP) nanocrystals. Direct experimental results have established that individual collagen fibrils exhibit polarization and piezoelectric effect.12−14 In addition, experimentally it is has been shown that collagen is not ferroelectric, in a sense that the orientation of its dipoles cannot be switched. Some biomaterials such as elastin have been shown to be ferroelectric.15 The HAP component of bone is also known to be piezoelectric.16−18 Hence, the piezoelectric effect in bone can be attributed to both the collagen and HAP components. The physiological relevance of piezoelectricity in vivo is largely unresolved, due to the complexity of biological processes and the simultaneous effects of several competing mechanisms such as streaming potential, flow-generated shear stress, and screening effect of ions, which combined with cellmediated processes may also have certain roles in bone remodeling.19−22 A new hypothesis based on the piezoelectric-

s a linear type of electromechanical coupling, piezoelectricity has long been proposed as one of the mechanisms underlying a wide range of biological processes.1−3 Upon application of a mechanical stress (σ) on a piezoelectric material, an electric potential or polarization (D) is generated in the material, D = d·σ, and conversely, an applied electric field (E) generates a mechanical deformation or strain (ε) in the material, ε = d·E, where d is the piezoelectric tensor.4 In 1957, Fukada and Yasuda reported the existence of a piezoelectric effect in bone.1 By discovery in other biological materials such as the tendon and tooth, piezoelectricity was proposed as a fundamental property of biological tissues.5 Today, it is known that piezoelectricity is ubiquitous in biological materials.1,2,5−8 Electrostatics is known to be present in almost all aspects of biology. There is abundant evidence in biological systems indicating that electrostatic interactions and surface charges play important roles in cellular function and regulation, for instance in voltage-gated ion channels, cardiac and muscular cell contraction, protein folding, interaction of charged biomolecules, diffusion limited processes, and pH-dependent properties.9 Similarly, the electrostatic charges generated by the piezoelectric effect are hypothesized to have potential roles in cell-extracellular matrix communications, repair of soft connective tissues during rehabilitation, and mineralization and remodeling of calcified tissues.5,10 © XXXX American Chemical Society

Received: January 14, 2016 Accepted: April 18, 2016

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DOI: 10.1021/acsbiomaterials.6b00021 ACS Biomater. Sci. Eng. XXXX, XXX, XXX−XXX

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ACS Biomaterials Science & Engineering

conducted on the hydrated collagen model inside water, to mimic a more realistic biological environment. Collagen Molecule Model. Figure 1a shows an atomistic model of a single collagen molecule, which is made of three α-

mediated streaming potential in bone has been proposed, in which it is suggested that piezoelectric-generated electric charges change the zeta potential on the bone surface and hence act in concert with the streaming potential mechanism.22 The possible role of collagen piezoelectricity in bone mineralization in vitro was recently demonstrated, where it was experimentally revealed that mineral nanocrystals were nucleated on demineralized bone surface stimulated by piezoelectric generated charges.23 Although it has been established that piezoelectric effect originates from the collagen in bone, the molecular mechanism of this electromechanical coupling effect in collagen is not yet clear. Several hypotheses exist in the literature on the origin of the piezoelectric effect in collagen and in bone. They include the absence of a center of symmetry because of the spiral shape at different levels of organization, noncentrosymmetric crystal structure of protein, simultaneous presence of polar bonds and optical activity that provides sufficient conditions for piezoelectricity at the molecular level, rotation of the CO−NH bond in the α-helix of collagen molecules, and polarization or displacement of hydrogen bonds formed in the polypeptide chains of collagen.7,24−26 However, none of these hypotheses have been directly verified on realistic collagen models. Piezoelectric effect in a short-length “collagen-like” molecule with a sequence of glycine, proline, and hydroxyproline amino acids was recently reported.27 However, the origin of the piezoelectric effect in the realistic “super-twisted” structure of native collagen has not yet been reported. Based on the experimentally verified “super-twisted” microstructure of collagen, herein we present an investigation on the molecular mechanism of piezoelectric effect in both the collagen molecule and microfibril using full atomistic simulations. The right-handed, super-twisted structure of collagen employed in our study is established based on the reported in situ X-ray fiber diffraction experiment,28 which enables us to also quantify the piezoelectric constant of the collagen molecule and microfibril. Our results reveal that collagen exhibits a uniaxial polarization along the long axis of the collagen fibril. Our computer simulations based on a supertwisted model of collagen provides the clear view on the origin of this effect on the molecular scale. Given the hierarchical structure of collagen and corresponding organizations at each level, the results obtained in this study can be employed to investigate the piezoelectric effect from molecule to microfibril, fibril, fiber, and bundles.

Figure 1. Atomistic models of collagen molecule and collagen microfibril. (a) A single collagen molecule model from homology modeling, ∼300 nm in length. The inset shows the triple-helical backbone of the molecule comprised of three α-helices. (b) Constructed collagen microfibril model with five D periods. Each D period ∼67 nm in length includes a gap region ∼0.54D, and an overlap region ∼0.46D. The gap region in a microfibril has four molecules, whereas the overlap region has five molecules. (c) Collagen molecule model with water solvent in a box of 5 nm × 5 nm × 10 nm. (d) One D-periodic collagen microfibril model with water solvent, in a box of 12 nm × 8 nm × 70 nm.

helices, as shown in the magnified view. The atomistic model of the collagen molecule was constructed via a homology modeling approach,30 by aligning the 3HR2 PDB structure28 with the primary sequence of human type I collagen (PubMed entry number NP_000079 is for the α1(I) chain and NP_000080 for the α2(I) chain). More details are provided in our previous work.31 For this study, we further truncated the collagen molecule to 30-amino-acid-long representative volume element (RVE) segments (∼10 nm) with a sequence of Glycine−X−Y in each of the three chains, which was embedded in the simulation box. Collagen Microfibril Model. A supermolecular model of collagen microfibril was generated by applying a fractional translational function to nine copies of the coordinates of a single collagen molecule. The molecular packing topology obtained by this periodic repetition was based on the naturally occurring quasi-hexagonally packed crystallographic unit cell (a ≈ 40.0 Å, b ≈ 27.0 Å, c ≈ 678 Å, α ≈ 89.2°, β ≈ 94.6°, γ ≈ 105.6°).28 This configuration results in a right-handed twisted structure and well-defined “gap” and “overlap” regions that are unique to collagen fibril. The microfibril shown in Figure 1b has five D periods. Each D period of ∼67 nm in length includes a gap region of ∼0.54D, and an overlap region of ∼0.46D. The gap region in a microfibril has four molecules, whereas the

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RESULTS AND DISCUSSION Atomistic models of collagen were built based on the X-ray crystallographic structure representing the unique right-handed “super-twisted” structure of collagen microfibril and fully resolved amino acid sequence.28 This model is significantly different than the commonly used Hodge−Petruska model of collagen that assumes “straight rod-shape” collagen molecules.29 In order to investigate the molecular origin of piezoelectric effect in collagen, we first developed and validated atomistic models of collagen molecule (also referred to as tropocollagen molecules) and collagen microfibril consisting of five super-twisted collagen molecules. The establishment of these models allows for the investigation of the important contributions to the piezoelectric effect on both the molecular and microfibril scales. In vivo, collagen is embedded in a hydrated environment. Therefore, all the simulations were B


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Figure 2. Piezoelectric properties of the collagen molecule and microfibril. Radial and axial polarization components of the collagen molecule (a) and collagen microfibril (b) under tension. 3D view of the total dipole moment vector of the collagen molecule (c) and collagen microfibril (d), at different tensile strains. The figure is compressed in the z direction for better visualization. (e and f) Angle between the axial polarization and the total radial polarization component vs applied strain, for molecule and microfibril, respectively. Calculation of the piezoelectric constant d33 of the collagen molecule (g) and collagen microfibril (h). The ordinate is the axial component of the increment of electric displacement (i.e., the polarization), and the abscissa is the axial component of applied stress. The squares show the simulation results for the corresponding stress level, and the dashed lines show the least-squares linear fit. The initial linear portion of axial polarization as marked in a and b is used in the calculation, which corresponds to σ ∼ 1.2 GPa and ε ∼ 20% for the molecule and σ ∼ 0.4 GPa and ε ∼ 5% for the microfibril.

overlap region has five molecules. In this study, a D-period unit cell of collagen microfibril was extracted for the simulations.

Analysis of Piezoelectric Effect. Experimentally, the piezoelectric effect on the nanoscale is measured by application C


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∼6° and ∼1.3° for the molecule and the microfibril, respectively. This shows that the total electric polarization in collagen is uniaxial and along the axis of the fibril. These results confirm the experimental finding of axial polarization in collagen fibrils.12,13 Considering this axial polarization, Figure 2g and h show the linear segment of the axial component ΔD3 of the total polarization vector ΔD under applied mechanical stress, based on the initial linear response shown in Figure 2a and b. For the collagen molecule, it corresponds to a tensile stress of ∼1.2 GPa and a tensile strain of ∼20%, as is consistent with our previous work that the linear mechanical response of the collagen molecule can extend up to 20% strain.31 For the collagen microfibril, the linear range is observed within a tensile stress of ∼0.4 GPa and a tensile strain of ∼5%. This strain is within the range reported in recent experimental studies for extracting mechanical properties of collagen microfibrils.32−34 The slope of the linear fit in Figure 2g and h defines the piezoelectric constant of collagen. For the simulated uniaxial tension, piezoelectric coefficient d33 can be calculated from ΔD3 = d33Δσ3. For the collagen molecule, this piezoelectric constant is obtained to be ∼1.1 pC/N (or pm/V), while for the collagen microfibril this constant is ∼2.6 pC/N. The obtained piezoelectric coefficients are within the range of 1−2 pC/N reported in experimental studies for D-periodic collagen fibrils.12,14,35 As mentioned, bone is a complex material including HAP, cells, and collagen. Given the piezoelectric effect in HAP, the overall piezoelectric effect in bone has been reported to be as large as 7.80−8.72 pC/N.36 The results show that the piezoelectric effect originates in the collagen molecule, and this effect is maintained at the microfibril level, with relatively the same order of magnitude. It is noted that in the calculation of the piezoelectric constant, the volume of the simulation box was used. The box volume is obviously larger than the actual volume occupied by collagen; therefore, the obtained piezoelectric constant of 1−2 pC/N is the lower bound. The piezoelectric constant can be increased if the actual “volume” occupied by all the collagen is used as V0. In such cases, the d33 value will be close to 8−10 pC/N as reported in recent literature for human bones.36 The Molecular Origin of the Piezoelectric Effect in Collagen. In order to elucidate the molecular origin of piezoelectricity in collagen, we investigated the evolution of the reorientation and magnitude change of the dipole moments in collagen molecules under mechanical stress. Arrows in Figure 3 show dipole moment vectors of individual amino acids in a collagen molecule, before (Figure 3a) and after (Figure 3b) application of 10% strain. The dipole moment vector of each individual amino acid residue is calculated by summing up the contributions from all the dipoles in that residue. We note that only those amino acid residues with nonzero charge contribute to the total dipole moment and hence to the overall polarization in the collagen molecule. Upon stretching, the initial triple-helical backbone structure, featuring both structural twist and local kinks, initially starts to uncoil, and then the twisted structure starts to disentangle. As such, the side chains of the collagen molecule become more aligned toward the long axis of the molecule. This alignment leads to the reorientation of the polar groups of the molecule as a response to the applied mechanical stress. As a result, the dipole moment vectors of these polar groups (arrows in the 3D view in Figure 3) change in magnitude and realign with the axis of the collagen molecule by rotation.

of an electric field on a sample and measurement of the induced mechanical strain (converse piezoelectric effect), for example using piezoresponse force microscopy.13 For atomistic simulation, this effect is quantified accordingly by monitoring the generated dipole moments under an applied mechanical stress (direct piezoelectric effect). The direct and converse effects are thermodynamically equivalent.4 While it is not the focus of the present work, it will be, however, interesting to investigate how collagen responds to an applied electric field and related deformation mechanisms. Since no external electric field was applied in the molecular dynamics (MD) simulations, piezoelectricity in collagen can be described through the constitutive equation ΔDi = diklΔσkl, in which Δ represents the increment from state t1 to state t2, resulting from the applied stress, i.e., ΔDi = (Di)t2 − (Di)t1 and Δσkl = (σkl)t2 − (σkl)t1. In the constitutive equation, dikl is the direct piezoelectric coefficient matrix, σkl is the stress tensor, and the subscript “i” denoting the ith component. In the absence of an externally applied field, the electric displacement vector Di can be approximated by the dipole moment density (polarization) Pi. Pi is obtained by summing over all the individual dipole moments in collagen followed by a volume average over the RVE, i.e., Di ≈ Pi = pi/V0 = Σαpiα/V0, in which Pi is the polarization, pi is the dipole moment of collagen, piα is the dipole moment of αth individual dipole, and V0 is the volume of RVE. Because of the asymmetric helical structure of collagen, the cross section area and the volume of the collagen RVE model are not well-defined. In the calculations, we used the volume of a simulation box as V0, to represent the RVE volume. For the collagen molecule, the box size was 5 nm × 5 nm × 25 nm. For collagen microfibril, the box size was 12 nm × 8 nm × 100 nm. The size of the simulation box was chosen to be as small as possible to fully enclose the collagen model during the axial loading, without any atoms crossing the boundary. Piezoelectric Effect in Collagen. Figure 2 shows the piezoelectric response of both the collagen molecule and the collagen microfibril under uniaxial tension. Electric polarization vectors vs axial stress are shown in Figure 2a and b, for the molecule and microfibril, respectively. Two components of polarization correspond to the radial direction (ΔD1 and ΔD2), and the third component corresponds to the axial direction (ΔD3). It is observed that the axial polarization along the long axis of the molecule and microfibril increases with increasing tensile stress (or tensile strain). In addition, the axial polarization component shows an initial linear trend, fitted with the dashed line. In both cases, the polarization increases by increasing the applied stress, beyond the initial linear segment. These nonlinear effects can be attributed to higher order electromechanical couplings.4 In addition, this nonlinear behavior could be partially due to the nonlinear stress−strain behavior of collagen in a large strain as shown in our previous work.31 In contrast, the radial polarizations show only oscillations and overall negligible changes. Figure 2c and d show the change in the total dipole moment vector vs tensile strains for the collagen molecule and microfibril, respectively. The total dipole moment was obtained from [(Δp1)2 + (Δp2)2 + (Δp3)2]1/2. The graphs are compressed in the z direction for better visualization, since the Δp3 component is much larger than the other two components. The angle between the total dipole moment and the long axis of the molecule and microfibril is shown in Figure 2e and f. The angle is less than D


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amino acid groups, reorients toward the axis of the molecule and fibril. As an example, the change of dipole moment of the aspartic acid, which is a polar charged residue, at different strains is shown in the bottom panel of Figure 4b. Note that both the magnitude and orientation of the dipole moment changes under mechanical strain. Since each molecule and microfibril has many residues, we analyze the statistical distribution of the changes in dipole moment both in the magnitude and in the orientation. Figure 5 shows these results for molecule and microfibril. Figure 5a and c show a comparison of the distribution of cos θ for all the dipoles in two different molecular segments between 0%, 5%, and 10% strains. The molecular segments were extracted at different locations of the 300-nm-long collagen molecule, and the cutting strategy is described in our previous paper.31 The charge of the molecular segments is determined by the residues included, so different molecular segments might have different numbers of charges. Without a loss of generality, we plot the results of two representative molecular segments in Figure 5. Angle θ is the angle between dipole moment vectors and the longitudinal axis of collagen. It can be seen that for the unstretched molecule, cos θ is rather uniformly distributed. With the increasing strains, the distribution shifts toward cos θ ∼ 1, since it is more aligned toward the axis of the fibril. Since both magnitude and direction of the dipole moment contribute to the overall polarization, we calculated the dipole moment change by considering the effect of the magnitude only and the same due to reorientation only. These two contributions are further compared with the total change of dipole moment due to both effects at 10% applied mechanical strain, as shown in Figure 5b and d. We examined several cases of electrically neutral and charged molecular segments. By summing up the dipole moment changes of all the residues within the system, for electrically charged molecular segments, the contributions to the change in total dipole moment from magnitude change and orientation change factors are comparable, and the overall polarization is a cooperation of both the magnitude and the orientation effects (Figure 5b). However, it turns out that for electrically neutral molecular segments, the contributions of the magnitude change are canceled out. In this case, we conclude that the total change in the dipole moment vector is dominated by the reorientation effect of the dipoles (Figure 5d). Figure 5e shows comparison of the distribution of cos θ for all the dipoles within a microfibril between 0%, 5%, and 10% strains. Similar to the molecular segments, cos θ shifts toward ∼1. Figure 5f compares the contribution of the magnitude change and orientation change for all the charged residues within a microfibril. The results show that in the microfibril, the majority of the polarization is due to a change in the magnitude of the dipole moments. From a total change of ∼6100 D in the dipole moment of a microfibril, 5300 D is caused by a change in magnitude, vs 850 D contributed by changes in orientation.

Figure 3. Molecular origin of the piezoelectric effect in collagen. Changes of dipole moment vectors in a collagen molecule, before (a) and after (b) uniaxial tension. Red and blue arrows indicate the magnitude and direction of the dipole moment vectors of each individual residue in a collagen molecule.

To further illustrate this point, the magnified views of a short piece of a collagen molecule at different levels of mechanical strain are shown in Figure 4. Figure 4a shows a short piece of

Figure 4. (a) A short piece of collagen molecule, displaying a 7residue-long amino acid sequence (Pro-Gly-Asn-Asp-Gly-Ala-Lys) in chain C. In this molecular short piece, proline, glycine, and alanine are nonpolar residues; asparagine is the polar uncharged residue; and aspartic acid and lysine are polar charged residues. (b) Magnified views of a short piece of collagen molecule. Chains A (α1(I)) and B (α2(I)) are depicted as ribbons. In chain C (α1(I)), nonpolar amino acids are represented in licorice, and the polar amino acids are shown in ballsand-sticks representation. Bottom panel shows the change of dipole moment (red arrow) of a polar charged residue, aspartic acid, at different strain levels.

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collagen α-chain with a 7-residue-long amino acid sequence (Pro-Gly-Asn-Asp-Gly-Ala-Lys). In this molecular short piece, proline, glycine, and alanine are nonpolar residues; asparagine is the polar uncharged residue; and aspartic acid and lysine are polar charged residues. Figure 4b shows this short molecular piece with two other α-chains. For clarity, two chains, A (α1(I)) and B (α2(I)), are depicted as ribbons. In chain C (α1(I)), nonpolar amino acids are represented in licorice, and the polar amino acids are shown in balls-and-sticks representation. Under mechanical stress, chain C, and hence the associated polar

CONCLUSIONS In conclusion, this work presents an atomistic simulation to investigate the molecular origin of the piezoelectric effect in collagen using an experimentally derived “super-twisted” model of collagen microfibril. Our results show that the piezoelectric effect originates from individual collagen molecules and is maintained in super-twisted collagen microfibril, which is the unit building block of collagen fibrils and fibers. The results of our atomistic simulation provide the proof that the overall E


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Figure 5. Mechanical stress induced redistribution of cos θ and change in dipole moment of collagen molecule and microfibril. Variation in the statistical distributions of cos θ upon the application of mechanical stress. (θ: the angle between dipole moment vector and the longitudinal axis of collagen). (a and c) For charged and zero-charged molecular segments, respectively, and (e) for microfibril. (b) Related to a, (d) related to c, and (f) related to e show the change in the dipole moment contributed by two different factors: the change in magnitude and the change in orientation for each charged residue.

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polarization effect in collagen stems from polar and charged groups in the molecule. Under mechanical stress, the dipole moments of these residues reorient toward the long axis of the collagen molecule. In addition, the magnitude of the dipole moments changes under mechanical stress. These two effects together result in overall polarization and piezoelectric effect in collagen. Furthermore, the results reveal that this polarization is uniaxial along the long axis of collagen molecule and microfibril. This study provides contributions to the long-debated piezoelectric effect in bone and collagen and its molecular mechanism. The results of this study may be applicable to other biopolymers and synthetic piezoelectric materials.

METHODS

Molecular Dynamics Simulations. Molecular dynamics (MD) simulations were performed in the GROMACS 4.5 package37 using the CHARMM force field.38 Periodic water boxes with size of 5 nm × 5 nm × 25 nm for the collagen molecule and 12 nm × 8 nm × 100 nm for the collagen microfibril were used to solvate the collagen using SPC water molecules. Counter Cl¯ or Na+ ions were added to neutralize the system. The molarity of ions is 0.016 molar for the collagen molecule model and 0.0064 molar for the collagen microfibril model. The total number of atoms was 61 847 and 961 271, for the solvated collagen molecule system and solvated collagen microfibril system, respectively. Nonbonded van der Waals interactions were computed using a cutoff for neighbor lists at 1.2 nm, with a switching function that decays the force smoothly to zero between 1.0 and 1.2 nm. The Particle-Mesh Ewald (PME) model was applied to compute F


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ACS Biomaterials Science & Engineering electrostatic interactions at a cutoff of 1.2 nm, while a periodic boundary condition was used. The collagen models were first geometrically optimized through energy minimization using a steepest descent algorithm. Then, the equilibration stage was obtained in three steps. First, a 1 ns NVT equilibration at a temperature of 310 K was performed with a velocityrescaling thermostat. Rigid bonds were used to constrain covalent bond length, allowing a time step of 2 fs. Second, a 2 ns NPT ensemble with a Berendsen barostat at 1 bar pressure was used to equilibrate the system, while keeping temperature at 310 K. In this step, position restraint was applied to the heavy atoms in the collagen, and other atoms were free to move. Last, a further NPT equilibration step was performed with a more accurate pressure coupling algorithm based on the Parrinello−Rahman barostat. The equilibration time was 2 ns for the molecule model and 1 ns for the microfibril model, respectively. Only the first and the last C-α atoms of each collagen chain were constrained. After the equilibration stage was performed, the mechanical loading stage was achieved using a steered molecular dynamics (SMD) simulation in the NPT ensemble. To apply uniaxial tensile loading, the N-terminal C-α atoms on the collagen were constrained using a stiff harmonic spring. The center of mass of the C-terminal C-α atoms was pulled along the axial direction of collagen, at a pulling velocity of 0.001 nm/ps for 5 ns for the collagen molecule and a pulling velocity of 0.014 nm/ps for 2 ns for the collagen microfibril, respectively. The time step in the SMD simulation was 0.5 fs. Decomposition of the Magnitude and Orientation Effects. In Figure 5, we have decomposed the total change of the dipole moment into two parts: one due to the magnitude change and the other due to the orientation change. This decomposition was realized in two steps, i.e., a virtual tension and a virtual compression step: In the virtual tension step, we made exact copies of the residues from the unstrained state to the strained state by ensuring that the mass centers coincide. We then calculated the dipole change between this “virtual tension state” and the “unstrained state.” Since this process does not alter the orientation of the residues, the dipole moment change is solely due to the elongation of the collagen or equivalently the magnitude change. In the virtual compression step, we made copies of the residues from the strained state back to its original unstrained state in a similar fashion to arrive at a virtual compression state. We then compared the dipole moments between this “virtual compression state” and the “unstrained state,” which provided us the effects of the orientation.

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(3) Fukada, E. Mechanical deformation and electrical polarization in biological substances. Biorheology 1968, 5, 199−208. (4) Newnham, R. E. Properties of Materials: Anisotropy, Symmetry, Structure; Oxford University Press: 2005. (5) Shamos, M. H.; Lavine, L. S. Piezoelectricity as a fundamental property of biological tissues. Nature 1967, 213, 267−269. (6) Marino, A. A.; Becker, R. O.; Soderholm, S. C. Origin of the piezoelectric effect in bone. Calcif. Tissue Res. 1971, 8, 177−180. (7) Bystrov, V.; Bdikin, I.; Heredia, A.; Pullar, R.; Mishina, E.; Sigov, A.; Kholkin, A. Piezoelectricity and Ferroelectricity in Biomaterials: From Proteins to Self-assembled Peptide Nanotubes. In Piezoelectric Nanomaterials for Biomedical Applications, Ciofani, G.; Menciassi, A., Eds., Springer: Berlin, 2012; pp 187−211. DOI: 10.1007/978-3-64228044-3_7. (8) Kryszewski, M. Fifty years of study of the piezoelectric properties of macromolecular structural biological materials. Acta Phys. Pol., A 2004, 105, 389−408. (9) Honig, B.; Nicholls, A. Classical electrostatics in biology and chemistry. Science 1995, 268 (5214), 1144−9. (10) Jin-qiang, Z.; Shi-you, D.; Zhen-hua, M.; Qi-liang, Z.; Ye, M.; Xue-ren, T.; Lu-ping, L. Early isokinetic training after repair of Achilles tendon ruptures: A rehabilitation efficiency evaluation. Journal of Clinical Rehabilitative Tissue Engineering Research 2010, 14, 3793− 3796. (11) Weiner, S.; Wagner, H. D. The Material Bone: StructureMechanical Function Relations. Annu. Rev. Mater. Sci. 1998, 28 (1), 271−298. (12) Minary-Jolandan, M.; Yu, M.-F. Nanoscale characterization of isolated individual type I collagen fibrils: polarization and piezoelectricity. Nanotechnology 2009, 20, 085706. (13) Minary-Jolandan, M.; Yu, M.-F. Uncovering Nanoscale Electromechanical Heterogeneity in the Subfibrillar Structure of Collagen Fibrils Responsible for the Piezoelectricity of Bone. ACS Nano 2009, 3 (7), 1859−1863. (14) Denning, D.; Paukshto, M. V.; Habelitz, S.; Rodriguez, B. J. Piezoelectric properties of aligned collagen membranes. J. Biomed. Mater. Res., Part B 2014, 102 (2), 284−292. (15) Liu, Y.; Cai, H.-L.; Zelisko, M.; Wang, Y.; Sun, J.; Yan, F.; Ma, F.; Wang, P.; Chen, Q. N.; Zheng, H.; Meng, X.; Sharma, P.; Zhang, Y.; Li, J. Ferroelectric switching of elastin. Proc. Natl. Acad. Sci. U. S. A. 2014, 111 (27), E2780−E2786. (16) Tofail, S. A. M.; Haverty, D.; Cox, F.; Erhart, J.; Hána, P.; Ryzhenko, V. Direct and ultrasonic measurements of macroscopic piezoelectricity in sintered hydroxyapatite. J. Appl. Phys. 2009, 105 (6), 064103. (17) Lang, S. B.; Tofail, S. A. M.; Gandhi, A. A.; Gregor, M.; WolfBrandstetter, C.; Kost, J.; Bauer, S.; Krause, M. Pyroelectric, piezoelectric, and photoeffects in hydroxyapatite thin films on silicon. Appl. Phys. Lett. 2011, 98 (12), 123703. (18) Lang, S. B.; Tofail, S. A. M.; Kholkin, A. L.; Wojtaś, M.; Gregor, M.; Gandhi, A. A.; Wang, Y.; Bauer, S.; Krause, M.; Plecenik, A. Ferroelectric Polarization in Nanocrystalline Hydroxyapatite Thin Films on Silicon. Sci. Rep. 2013, 3, 2215. (19) Walsh, W. R.; Guzelsu, N. Ion concentration effects on bone streaming potentials and zeta potentials. Biomaterials 1993, 14 (5), 331−336. (20) Kowalchuk, R. M.; Pollack, S. R. Stress-generated potentials in bone: effects of bone fluid composition and kinetics. J. Orthop. Res. 1993, 11, 874−883. (21) Bassett, C. A. L.; Pawluk, R. J.; Becker, R. O. Effects of electric currents on bone in vivo. Nature 1964, 204, 652−654. (22) Ahn, A. C.; Grodzinsky, A. J. Relevance of collagen piezoelectricity to ″Wolff’s Law″: a critical review. Medical Engineering and Physics 2009, 31, 733−741. (23) Noris-Suárez, K.; Lira-Olivares, J.; Ferreira, A. M.; Feijoo, J. L.; Suárez, N.; Hernández, M. C.; Barrios, E. In Vitro Deposition of Hydroxyapatite on Cortical Bone Collagen Stimulated by Deformation-Induced Piezoelectricity. Biomacromolecules 2007, 8 (3), 941− 948.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

M.M.-J., D.Q., and Z.Z. designed the research; Z.Z. established the model and carried out the simulation and collected data; M.M.-J, Z.Z., and D.Q. analyzed the data and wrote the paper. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.M.-J. acknowledges funding from Air Force Office of Scientific Research (Young Investigator Program, FA9550-141-0252, Program Manager Dr. B. L. Lee). M.M.-J. and D.Q. also gratefully acknowledge the support of this work from the start-up fund provided by the University of Texas at Dallas and allocation of the computing resources at the Texas Advance Computing Center (TACC).

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REFERENCES

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