PIk SOO21-9290(96)00151-O THE MECHANICAL PROPERTIES OF SIMULATED COLLAGEN FIBRILS John Parkinson,* Andy Brass,* Giles Canova? and Yves Brechetf * School of Biological Sciences, 2.205 Stopford Building, University of Manchester, Oxford Road, Manchester Ml3 9PT, U.K.; and 7 Laboratoire de Thermodynamique et Physico-Chimie Metallurgiques, ENSEEG, 1130 Rue de la Piscine, Domaine Universitaire, BP 75, 38402 Saint-martind’heres Cedex, France Abstract-Previous theoretical studies of the mechanical properties of tissues such as skin, bone and tendon, have used approaches based on composite materials and have tended to neglect the contribution of individual microscopic components. In this paper, we examine the relationship between the fine structure of a collagen fibril and its relative tensile strength. Collagen is a fibrous protein which provides associated tissues with the majority of their tensile strength. It is present in the form of elongated structures termed fibrils which are created by the self-assembly of rod-like collagen molecules in an entropy-driven process termed fibrillogenesis. Mutations that alter the primary structure of the collagen molecule, interfere with this assembly process and can lead to the potentially fatal brittle bone disease, osteogenesfs imperjecta. Here we investigate the mechanical properties of a range of computer-generated aggregates. The aggregates, created by the diffusion limited aggregation of rods, were subjected to a simple tensile test based on local rules of damage accumulation. In the test, core samples are ‘extracted’ from the aggregates, and the network of particles involved in the transmission of stress resolved. Increasing stress applied to the core leads to the removal of individual rods from this network the tensile strength is determined from the force necessary to form a discontinuous network. Using this approach, we have shown that collagen fibril morphology is critical in determining its tensile strength. We suggest a possible mechanism to account for the increasing severity of osteogenesis imperfecru associated with the distance of mutation from the N-terminal of the collagen molecule. $3 1997 Elsevier Science Ltd Keywords: Collagen; Mechanical properties; Computer modeling. INTRODUCTION Type I collagen is a fibrous protein which forms a major part of the extracellular matrix, providing a structural scaffold for other components. It is present in the form of elongated fibres (termed fibrils) in tissues such as skin, bone and tendon. Individual fibrils can be greater than 500 ,um in length, 500 nm in diameter and contain more than 107 molecules (Parry and Craig 1984). They form by the self-assembly of rod-like collagen molecules (-300 nm in length by 1.5 nm in diameter) in an entropy driven process termed fibrillogenesis (Kadler et uL, 1987). Mutations in the primary sequence of collagen mole- cules, are linked with a variety of heritable diseases including Ehlers Danlos syndrome and osteogenesis im- perfectu (01). 01 is typically characterised by brittle bones but may also involve other tissues rich in type1 collagen to produce blue sclera, abnormal teeth, thin skin and weak tendons (Prockop and Kivirikko, 1995). These characteristics arise from mutations leading to changes in the structural characteristics of the collagen molecules. Interestingly, the severity of the disease phenotype ap- pears to be related to the position of the mutation in Received in&al form 8 August 1996. Address correspondence to: Andy Brass, School of Biological Sciences, 2.205 Stopford Building, University of Manchester, Oxford Road, Manchester Ml3 9PT, U.K. relation to the amino-terminal of the molecule (Byers and Steiner, 1992). What is not known is how these changes alter the mechanical properties of collagenous tissues. Although collagen fibrils have little strength in either bending or torsion, the presence of covalent cross-links results in an ability to resist high tensile stresses (Parry, 1988). This allows them to act as reinforcing fibres in bone and to transmit stress in tissues such as skin and tendon. A number of experimental and theoretical stud- ies of the mechanical properties of these tissues have already been undertaken (e.g. Katz, 1980; Okada et al., 1992; Woo et ul., 1993). Such approaches have tended to treat the tissue as a homogenous composite in which the mechanical interactions between the matrix components and collagen fibrils at a microstructural level are neglect- ed. Studies of cancellous bone, for example, have tended to model the tissue as a porous cellular composite mater- ial (Katz, 1980; Mammone and Hudson, 1993; Martin, 1991). In an attempt to determine how microscopic cha- nges in tissue components may affect mechanical strength, this paper presents an investigation into the role of collagen fibril morphology. Due to their relatively small size, it has not been possible to investigate the mechanical properties of indi- vidual collagen fibrils. Recently, however, a computer model of collagen fibril formation has been proposed which realistically simulates the formation of a range of different fibril morphologies (Parkinson et ul., 1995). By applying ideas based on the fracture of disordered media, 549