A study concerning homeostasis and population development of colagen fibers

Abstract

Collagen is a generic name for the group of the most common proteins in mammals. It confers mechanical stability, strength and toughness to the tissues, in a large number of species. In this work we investigate two properties of collagen that explain in part the choice by natural selection of this substance as an essential building material. In the first study the property under investigation is the homeostasis of a single fiber, i.e., the maintenance of its elastic properties under the action of collagen monomers that contribute to its stiffening and enzymes that digest it. The model used for this purpose is a onedimensional chain of linearly elastic springs in series coupled with layers of sites. Particles representing monomers and enzymes can diffuse along these layers and interact with the springs according to specified rules. The predicted lognormal distribution for the local stiffness is compared to experimental data from electronic microscopy images and a good concordance is found. The second part of this work deals with the distribution of sizes among multiple collagen fibers, which is found to be bimodal, hypothetically because it leads to a compromise between stiffness and toughness of the bundle of fibers. We propose a mechanism for the evolution of the fiber population which includes growth, fusion and birth of fibers and write a Population Balance Equation for that. By performing a parameter estimation over a set of Monte Carlo simulations, we determine the parameters that best fit the available data.