Collagen is a basic biopolymer usually found in animal bodies, but its mechanical property and behavior are not sufficiently understood so as to apply to effective regenerative medicine and so on. Since the collagen material is composed of many hierarchical structures from atomistic level to tissue or organ level, we need to well understand fundamental and atomistic mechanism of the collagen in mechanical response. First, we approach at exactly atomistic level by using all-atom modeling of tropocollagen (TC) molecule, which is a basic structural unit of the collagen. We perform molecular dynamics (MD) simulations concerning tensile loading of a single TC model. The main nature of elastic (often superelastic) behavior and the dependency on temperature and size are discussed. Then, to aim at coarse-graining of atomic configuration into some bundle structure of TC molecules (TC fibril), as a model of higher collagen structure, we construct a kind of mesoscopic model by adopting a simulation framework of beads-spring model which is ordinarily used in polymer simulation. Tensile or compression simulation to the fibril model reveals that the dependency of yield or buckling limit on the number of TCs in the model. Also, we compare the models with various molecular orientations in winding process of initial spiral of TC. The results are analyzed geometrically and it shows that characteristic orientational change of molecules increases or decreases depending on the direction and magnitude of longitudinal strain.
References
[1]
Callister Jr., W.D. and Rethwisch, D.G. (2014) Materials Science and Engineering. John Wiley & Sons Inc., Hoboken, NJ.
[2]
Agrawal, C.M., Ong, J.L., Appleford, M.R. and Mani, G. (2013) Introduction to Biomaterials: Basic Theory with Engineering Applications. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9781139035545
[3]
Balasubramanian, P., Prabhakaran, M.P., Sieesha, M. and Ramakrishna, S. (2013) Collagen in Human Tissues: Structure, Function, and Biomedical Implications from a Tissue Engineering Perspective. Advances in Polymer Science, 251, 173-206.
https://doi.org/10.1007/12_2012_176
[4]
Sherman, V.R., Yang, W. and Meyers, M.A. (2015) The Materials Science of Collagen. Journal of the Mechanical Behavior of Biomedical Materials, 52, 22-50.
https://doi.org/10.1016/j.jmbbm.2015.05.023
[5]
Vesentini, S., Redaelli, A. and Gautieri, A. (2013) Nanomechanics of Collagen Microfibrils. Muscles Ligaments Tendons Journal, 3, 23-34.
https://doi.org/10.32098/mltj.01.2013.05
[6]
Hamed, E. and Jasiuk, I. (2012) Elastic Modeling of Bone at Nanostructural Level. Materials Science and Engineering R, 73, 27-49.
https://doi.org/10.1016/j.mser.2012.04.001
[7]
Orgel, J.P.R., Irving, T.C., Miller, A. and Wess, T.J. (2006) Microfibrillar Structure of Type I Collagen in Situ. PNAS (Proceedings of the National Academy of Sciences of the United States of America), 103, 9001-9005.
https://doi.org/10.1073/pnas.0502718103
[8]
Shen, Z.L., Dodge, M.R., Khan, H., Ballarini, R. and Eppell, S.J. (2008) Stress-Strain Experiments on Individual Collagen Fibrils. Biophysical Journal, 95, 3956-3963.
https://doi.org/10.1529/biophysj.107.124602
[9]
Epell, S.J., Smith, B.N., Kahn, H. and Ballarini, R. (2006) Nano Measurements with Micro-Devices: Mechanical Properties of Hydrated Collagen Fibrils. Journal of the Royal Society Interface, 3, 117-121. https://doi.org/10.1098/rsif.2005.0100
[10]
Van der Rijt, J.A.J., Van der Werf, K.O., Bennink, M.L., Dijkstra, P.J. and Feijen, J. (2006) Micromechanical Testing of Individual Collagen Fibrils. Macromolecular Bioscience, 6, 697-702. https://doi.org/10.1002/mabi.200600063
[11]
Peacock, C.J. and Kreplak, L. (2019) Nanomechanical Mapping of Single Collagen Fibrils under Tension. Nanoscale, 11, 14417-14425.
https://doi.org/10.1039/C9NR02644D
[12]
Gao, H., Ji, B., Jager, I.L., Arzt, E. and Fratzl, P. (2003) Materials Become Insensitive to Flaws at Nanoscale: Lessons from Nature. PNAS (Proceedings of the National Academy of Sciences of the United States of America), 100, 5597-5600.
https://doi.org/10.1073/pnas.0631609100
[13]
Nitta, N., Kuramae, H., Morita, Y. and Nakamachi, E. (2012) Multi-Scale and Multi-Physics Finite Element Analyses of Articular Cartilage and Chondrocyte. Proceedings of the Conference of Kansai Branch (The Japan Society of Mechanical Engineers), 124, 4-19. (In Japanese)
[14]
Saitoh, K., Sato, T., Takuma, M., Takahashi, Y. and Imanishi, T. (2016) Molecular Dynamics Study of Collagen Fibrils: Relation between Mechanical Properties and Molecular Chirality. 10th International Conference on Fracture and Strength of Solids (FEOFS2016), Tokyo, Japan, 28 August-1 September 2016.
[15]
Okuyama, K. and Kawaguchi, T. (2010) Molecular and Fibrillar Structures of Collagen. Kobunshi Ronbunshu, 67, 229-247. (In Japanese)
[16]
Osaki, S. (2005) Fiber Orientation of Collagens Determines the Motional Functions in Biological Tissues: Application of a New Method using Microwaves. Journal of Nara Medical Association, 56, 205-224. (In Japanese)
[17]
Phillips, J.C., Braun, R., Wang, W., Gumbart, J., Tajkhorshid, E., Villa, E., Chipot, C., Skeel, R.D., Kale, L. and Schulten, K. (2005) Scalable Molecular Dynamics with NAMD. Journal of Computational Chemistry, 26, 1781-802.
https://doi.org/10.1002/jcc.20289
http://www.ks.uiuc.edu/Research/namd
[18]
Monti, S., Bronco, S. and Cappelli, C. (2005) Toward the Supramolecular Structure of Collagen: A Molecular Dynamics Approach. Physical Chemistry B, 109, 11389-11398. https://doi.org/10.1021/jp0440941
[19]
Buehler, M.J. (2006) Atomistic and Continuum Modeling of Mechanical Properties of Collagen: Elasticity, Fracture and Self-assembly. Journal of Materials Research, 21, 1947-1961. https://doi.org/10.1557/jmr.2006.0236
[20]
Buehler, M.J. (2006) Mesoscale Modeling of Mechanics of Carbon Nanotubes: Self-Assembly, Self-folding, and Fracture. Journal of Materials Research, 21, 2855-2869.
https://doi.org/10.1557/jmr.2006.0347
[21]
Buehler, M.J. (2006) Nature Designs Tough Collagen: Explaining the Nanostructure of Collagen Fibrils. PNAS (Proceedings of the National Academy of Sciences of the United States of America), 103, 12285-12290.
https://doi.org/10.1073/pnas.0603216103
[22]
Buehler, M.J. (2007) Molecular Nanomechanics of Nascent Bone: Fibrillar Toughening by Mineralization. Nanotechnology, 18, 295102.
https://doi.org/10.1088/0957-4484/18/29/295102
[23]
Nair, A.K., Gautieri, A., Chang, S.-W. and Buehler, M.J. (2012) Molecular Mechanics of Mineralized Collagen Fibrils in Bone. Nature Communications, 4, Article number: 1724. https://doi.org/10.1038/ncomms2720
[24]
Buehler, M.J. (2008) Nanomechanics of Collagen Fibrils under Varying Cross-link Densities: Atomistic and Continuum Studies. Journal of the Mechanical Behavior of Biomedical Materials, 1, 59-67. https://doi.org/10.1016/j.jmbbm.2007.04.001
[25]
Depalle, B., Qin, Z., Shefelbine, S.J. and Buheler, M.J. (2015) Influence of Cross-Link Structure, Density and Mechanical Properties in the Mesoscale Deformation Mechanisms of Collagen Fibrils. Journal of the Mechanical Behavior of Biomedical Materials, 52, 1-13. https://doi.org/10.1016/j.jmbbm.2014.07.008
[26]
Malaspina, D.C., Szleifer, I. and Dhaher, Y. (2017) Mechanical Properties of a Collagen Fibril under Simulated Degradation. Journal of the Mechanical Behavior of Biomedical Materials, 75, 549-557. https://doi.org/10.1016/j.jmbbm.2017.08.020
[27]
Saitoh, K., Suzuki, R., Takuma, M., Takahashi, Y. and Sato, T. (2019) Atomistic Simulation for Mechanical Property of Collagen Nanostructures: The Effect of Molecular Crosslink and Triple Helix on Mechanical Properties. The Asian Pacific Congress on Computational Mechanics (APCOM2019), Taipei, 17-21 December 2019, 0478.
[28]
In’tVeld, P.J. and Stevens, M.J. (2008) Simulation of the Mechanical Strength of a Single Collagen Molecule. Biophysical Journal, 95, 33-39.
https://doi.org/10.1529/biophysj.107.120659
[29]
Dubey, D.K. and Tomar, V. (2010) Role of Molecular Level Interfacial Forces in Hard Biomaterial Mechanics: A Review. Annals Biomedical Engineering, 38, 2040-2055.
https://doi.org/10.1007/s10439-010-9988-3
[30]
Tang, Y., Ballarini, R., Buehler,M.J. and Eppell, S.J. (2010) Deformation Micromechanisms of Collagen Fibrils under Uniaxial Tension. Journal of the Royal Society Interface, 7, 839-850. https://doi.org/10.1098/rsif.2009.0390
[31]
Pradhan, S.M., Katti, D.R., ASCE, M. and Katti, K.S. (2011) Steered Molecular Dynamics Study of Mechanical Response of Full Length and Short Collagen Molecules. Journal of Nanomechanics and Micromechanics, 1, 104-110.
https://doi.org/10.1061/(ASCE)NM.2153-5477.0000035
[32]
Gautieri, A., Vesentini, S., Redaelli, A. and Buehler, M.J. (2011) Hierarchical Structure and Nanomechanics of Collagen Microfibrils from the Atomistic Scale up. Nano Letters, 11, 757-766. https://doi.org/10.1021/nl103943u
[33]
Marlowe, A.E., Singh, A. and Yingling, Y.G. (2012) The Effect of Point Mutations on Structure and Mechanical Properties of Collagen-like Fibril: A Molecular Dynamics Study. Materials Science and Engineering C, 32, 2583-2588.
https://doi.org/10.1016/j.msec.2012.07.044
[34]
Marino, M. and Vairo, G. (2014) Influence of Inter-Molecular Interactions on the Elast-Damage Mechanics of Collagen Fibrils: A Bottom-Up Approach towards Macroscopic Tissue Modeling. Journal of the Mechanics and Physics of Solids, 73, 38-54. https://doi.org/10.1016/j.jmps.2014.08.009
[35]
Fielder, M. and Nair, A.K. (2019) Effects of Hydration and Mineralization on the Deformation Mechanisms of Collagen Fibrils in Bone at the Nanoscale. Biomechanics and Modeling in Mechanobiology, 18, 57-68.
https://doi.org/10.1007/s10237-018-1067-y
[36]
Morsali, R., Dai, Z., Wang, Y., Qian, D. and Minary-Jolandan, M. (2019) Deformation Mechanisms of “Two-Part” Natural Adhesive in Bone Interfibrillar Nano-interfaces. ACS Biomaterials Science and Engineering, 5, 5916-5924.
https://doi.org/10.1021/acsbiomaterials.9b00588
[37]
Tang, M., Li, T., Pickering, E., Gandhi, N.S., Burrage, K. and Gu, Y.T. (2018) Steered Molecular Dynamics Characterization of the Elastic Modulus and Deformation Mechanism of Single Natural Tropocollagen Molecules. Journal of the Mechanical Behavior of Biomedical Materials, 86, 359-367.
https://doi.org/10.1016/j.jmbbm.2018.07.009
[38]
Ghanaeian, A. and Soheilifard, R. (2018) Mechanical Elasticity of Proline-Rich and Hydroxyproline-Rich Collagen-Like Triple-helices Studied Using Steered Molecular Dynamics. Journal of the Mechanical Behavior of Biomedical Materials, 86, 105-112. https://doi.org/10.1016/j.jmbbm.2018.06.021
[39]
Yeo, J., Jung, G.S., Trakanova, A., Martin-Martinez, F.J, Qin, Z., Cheng, Y., Zhang, Y.-W. and Buehler, M.J. (2018) Multiscale Modeling of Keratin, Collagen, Elastin and Related Human Diseases: Perspectives from Atomistic to Coarse-Grained Molecular Dynamics Simulations. Extreme Mechanics Letters, 20, 112-124.
https://doi.org/10.1016/j.eml.2018.01.009
[40]
Suzuki, T. (2016) Molecular Dynamics Modeling of Tropocollagen: Molecular Structure and Mechanical Properties. Graduation Thesis, Faculty of Engineering Science, Kansai University. (In Japanese)
[41]
Mackerell, A.D., Bashford, D., Bellontt, M., Dunbrack, R.L., Evanseck, J.D., Field, M.J., Fischer, S.,M., Gao, J., Guo, H., Ha, S., Joseph-McCarthy, D., Kuchnir, L., Kuczera, K., Lau, F.T.K., Mattos, C., Michnick, S., Ngo, T., Nguyen, D.T., Prodhom, B., Reiher, W.E., Roux, B., Schlenkrich, M., Smith, J.C., Stote, R., Straub, J., Watanabe, M., Wiorkiewicz-Kuczera, J., Yin, D. and Karplus, M. (1998) All-Atom Empirical Potential for Molecular Modeling Dynamics Studies of Proteins. Journal of Physical Chemistry B, 102, 3586-3616. https://doi.org/10.1021/jp973084f
[42]
Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N. and Bourne, P.E. (2000) The Protein Data Bank. Nucleic Acids Research, 28, 235-242. https://doi.org/10.1093/nar/28.1.235
[43]
Protein Data Bank Japan (PDBj). https://pdbj.org/mine/summary/1cag
[44]
Bella, J., Eaton, M., Brodsky, B. and Berman, H.M. (1994) Crystal and Molecular Structure of a Collagen-Like Peptide at 1.9 A Resolution. Science, 266, 75-81.
https://doi.org/10.1126/science.7695699
[45]
CHARMM Force Field (That Used in the Present Study Is Named
“par_all27_prot_lipid.inp”). https://www.charmm.org/
Rudd, R.E. and Broughton, Q. (1998) Coarse-Grained Molecular Dynamics and the Atomic Limit of Finite Elements. Physical Review B, 58, R5893.
https://doi.org/10.1103/PhysRevB.58.R5893
[48]
Hoogerbrugge, P.J. and Koelman, J.M.V.A. (1992) Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics. Europhysics Letters, 19, 155-160. https://doi.org/10.1209/0295-5075/19/3/001
[49]
Greenspan, D. (1997) Particle Modeling, Birkhäuser, Boston.
https://doi.org/10.1007/978-1-4612-1992-7
[50]
Kremer, K. and Grest, G.S. (1990) Dynamics of Entangled Linear Polymer Melts: A Molecular-Dynamics Simulation. Journal of Chemical Physics, 92, 5057-5086.
https://doi.org/10.1063/1.458541
[51]
Shirahana, T. (2015) Molecular Dynamics Modeling of Collagen Fibril: Evaluation of Mechanical Properties. Master’s Thesis. Graduate School of Science and Engineering, Kansai University. (In Japanese)
[52]
Hsu, H.P. (1969) Vector Analysis. Simon and Schuster, New York.
