Mechanical model for a collagen fibril pair in extracellular matrix |
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Authors: | Yue Chan Grant M Cox Richard G Haverkamp James M Hill |
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Institution: | (1) Present address: Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia;(2) School of Engineering and Advanced Technology, Massey University, Private Bag 11222, Palmerston North, 4442, New Zealand |
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Abstract: | In this paper, we model the mechanics of a collagen pair in the connective tissue extracellular matrix that exists in abundance
throughout animals, including the human body. This connective tissue comprises repeated units of two main structures, namely
collagens as well as axial, parallel and regular anionic glycosaminoglycan between collagens. The collagen fibril can be modeled
by Hooke’s law whereas anionic glycosaminoglycan behaves more like a rubber-band rod and as such can be better modeled by
the worm-like chain model. While both computer simulations and continuum mechanics models have been investigated for the behavior
of this connective tissue typically, authors either assume a simple form of the molecular potential energy or entirely ignore
the microscopic structure of the connective tissue. Here, we apply basic physical methodologies and simple applied mathematical
modeling techniques to describe the collagen pair quantitatively. We found that the growth of fibrils was intimately related
to the maximum length of the anionic glycosaminoglycan and the relative displacement of two adjacent fibrils, which in return
was closely related to the effectiveness of anionic glycosaminoglycan in transmitting forces between fibrils. These reveal
the importance of the anionic glycosaminoglycan in maintaining the structural shape of the connective tissue extracellular
matrix and eventually the shape modulus of human tissues. We also found that some macroscopic properties, like the maximum
molecular energy and the breaking fraction of the collagen, were also related to the microscopic characteristics of the anionic
glycosaminoglycan. |
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Keywords: | Mathematical modeling Connective tissue extracellular matrix Hooke’ s law Worm-like chain model Molecular potential energy |
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