Mechanical model for a collagen fibril pair in extracellular matrix

TL;DR

This paper develops a physical and mathematical model of collagen fibril pairs in extracellular matrix, highlighting the role of glycosaminoglycans in force transmission and tissue structure, with implications for tissue mechanics.

Contribution

It introduces a quantitative model combining Hooke's law and worm-like chain theory to describe collagen and glycosaminoglycan interactions in connective tissue.

Findings

Fibril growth is linked to glycosaminoglycan length and fibril displacement.

Glycosaminoglycans are crucial for force transmission and tissue shape.

Macroscopic tissue properties relate to microscopic molecular characteristics.

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 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 find that the growth of fibrils is intimately related to the maximum length of the anionic glycosaminoglycan and the relative displacement of two adjacent fibrils, which in return is 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 find that some macroscopic properties, like the maximum molecular energy and the breaking fraction of the collagen, are also related to the microscopic characteristics of the anionic glycosaminoglycan.