Entropic Elasticity Controls Nanomechanics of Single Tropocollagen Molecules
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Entropic Elasticity Controls Nanomechanics of Single Tropocollagen Molecules Markus J. Buehler1, and Sophie Wong2 1 Civil and Environmental Engrg, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA, 02139 2 Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, 02139 Corresponding author: [email protected] ABSTRACT We report molecular modeling of stretching single molecules of tropocollagen, the building block of collagen fibrils and fibers that provide mechanical support in connective tissues. For small deformation, we observe a dominance of entropic elasticity. At larger deformation, we find a transition to energetic elasticity, which is characterized by first stretching and breaking of hydrogen bonds, followed by deformation of covalent bonds in the protein backbone, eventually leading to molecular fracture. Our force-displacement curves show excellent quantitative agreement with optical tweezer experiments, suggesting a persistence length of approximately 16 nm. We demonstrate that assembly of single TC molecules into fibrils significantly decreases their flexibility, leading to decreased contributions of entropic effects during deformation. We develop a simple continuum model capable of describing the entire deformation range of TC molecules. INTRODUCTION Collagen, the most abundant protein on earth, is a fibrous structural protein with superior mechanical properties, and provides an intriguing example of a hierarchical biological nanomaterial. Collagen consists of triple helical tropocollagen (TC) molecules that have highly conserved lengths of approximately 300 nm, with roughly 1.5 nm diameter [3, 4]. Staggered arrays of TC molecules form fibrils, which arrange to form collagen fibers [5, 6]. Collagen plays an important role in many biological tissues, including tendon, bone, teeth, cartilage and in the cardiovascular system, where mechanical tensile load is critical under physiological conditions [6-8]. Due to lack of understanding of nanomechanical properties of collagen, the source of the elasticity of individual TC molecules, fibrils and collagen fibers remains controversial. No studies of the large deformation elastic and fracture mechanics of TC molecules with physiological lengths have been reported. Little understanding exists about the transition from entropic to energetic elasticity, under which conditions either one dominates, and how properties change when individual TC molecules assemble into collagen fibrils. Understanding the nanomechanical properties of single TC molecules is essential to develop theories that link molecular and tissue properties of collagen.
Early experiments suggested that TC molecules are rigid, rodshaped structures with extremely large persistence lengths [9, 10]. However, based on hydrodynamic methods and transmission electron microscopy (TEM) it was found that TC molecules feature some flexibility, which can be measured by the persistence length. Hydrodynamic methods
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