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Collagen Network Fracture Connectivity and plasticity determine collagen network fracture Federica Burlaa,1, Simone Dussib,1, Cristina Martinez-Torresa,c, Justin Tauberb, Jasper van der Guchtb,2, and Gijsje H. Koenderinka,c,2 aBiological Soft Matter Group, Department of Living Matter, AMOLF, 1098 XG Amsterdam, The Netherlands; bPhysical Chemistry and Soft Matter, Wageningen University and Research, 6708 WE Wageningen, The Netherlands; and cDepartment of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, 2629 HZ Delft, The Netherlands Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved February 28, 2020 (received for review November 15, 2019) Collagen forms the structural scaffold of connective tissues in all during diseases (18). However, collagen in many other connec- mammals. Tissues are remarkably resistant against mechanical tive tissues assembles in disordered networks that lack a pref- deformations because collagen molecules hierarchically self- erential orientation. Examples are skin (19), cartilage (20), assemble in fibrous networks that stiffen with increasing strain. vitreous humor (21), and the aortae (22). Interestingly, research Nevertheless, collagen networks do fracture when tissues are on aortae fracture in the context of aneurysms (9) as well as overloaded or subject to pathological conditions such as aneu- studies using tissue models (23–26) have revealed that isotropic rysms. Prior studies of the role of collagen in tissue fracture have tissues fracture at higher strain than aligned tissues like tendon. mainly focused on tendons, which contain highly aligned bun- This observation suggests that isotropic networks might be dles of collagen. By contrast, little is known about fracture of the optimized to withstand larger strains, because disorder delays orientationally more disordered collagen networks present in fracture by facilitating stress delocalization (27–31). However, a many other tissues such as skin and cartilage. Here, we combine mechanistic understanding of the role of network architecture shear rheology of reconstituted collagen networks with com- and plasticity in tissue fracture has so far been lacking, due to the puter simulations to investigate the primary determinants of complexity of living tissues. fracture in disordered collagen networks. We show that the Here, we investigate the mechanisms that protect isotropic fracture strain is controlled by the coordination number of the collagen networks from fracture by performing quantitative network junctions, with less connected networks fracturing at measurements of shear-induced fracture of reconstituted colla- BIOPHYSICS AND COMPUTATIONAL BIOLOGY larger strains. The hierarchical structure of collagen fine-tunes gen networks, both experimentally and computationally. Exper- the fracture strain by providing structural plasticity at the imentally, we control the collagen structure from the network network and fiber level. Our findings imply that low connectivity level (mesh size and connectivity) down to the fiber level (di- and plasticity provide protective mechanisms against network fracture that can optimize the strength of biological tissues. ameter and intrafibrillar cross-linking) by reconstituting net- works of collagen purified from different animal and tissue collagen | fracture | network | connectivity sources and by exploiting the known sensitivity of collagen self- assembly to the polymerization temperature (32, 33). By com- paring our results against a computational model of network ollagen is the most abundant protein in the human body. fracture, we find that the connectivity of the network, defined as CSecreted in the extracellular space by cells, collagen assem- bles in networks of thick rope-like fibrils that shape and reinforce tissues and provide a scaffold for cell growth and movement (1). Significance The spatial organization of these networks varies widely among tissues, from aligned bundles in tendons to randomly oriented Collagen fibers are the main components of the extracellular (isotropic) networks in skin. Isotropic collagen networks tend to matrix, a fibrous scaffold that sets the shape and stiffness of have a low connectivity, because the fibrils are mainly joined in tissues in the human body and protects them from mechanical threefold junctions by branches and in fourfold junctions by failure. The relation between the hierarchical and heteroge- cross-links. As a result, the network connectivity is below the neous structure of collagen networks and their fracture be- Maxwell criterion of six required for mechanical stability of havior is still missing. Prior studies focused on tendons, where random networks of springs (2, 3). Collagen networks never- collagen forms highly aligned bundles, but many tissues such theless possess a finite elasticity below the percolation threshold as skin contain disordered collagen networks. Here, we show because the fibers have a finite bending rigidity. It was recently that fracture of disordered collagen networks is controlled by their connectivity rather than by the single-fiber properties. shown that the subisostatic architecture offers a great mechanical We further show that structural plasticity can delay network advantage for collagen networks, because it causes them to be failure. Our findings are useful in understanding how tissues soft at small deformations, primarily due to fibril bending, yet fail and in the design of stronger network-based materials. stiff at large deformations, due to fibril alignment and a corre- – sponding transition from fibril bending to stretching (3 5). Author contributions: F.B., S.D., J.v.d.G., and G.H.K. designed research; F.B., S.D., C.M.-T., Nevertheless, tissues still fracture when exposed to large defor- and J.T. performed research; F.B., S.D., C.M.-T., J.T., J.v.d.G., and G.H.K. analyzed data; and mations, especially in pathological conditions such as injuries (6), F.B., S.D., C.M.-T., J.T., J.v.d.G., and G.H.K. wrote the paper. surgical interventions (7), aneurysms (8, 9), and hydraulic frac- The authors declare no competing interest. ture of tumors (10, 11). This article is a PNAS Direct Submission. Fracture of collagen has so far mainly been investigated in Published under the PNAS license. tendons (12, 13), where collagen fibrils organize in long cable- 1F.B. and S.D. contributed equally to this work. like structures optimized to withstand large axial loads (14, 15). 2To whom correspondence may be addressed. Email: [email protected] or Because of the unidirectional fiber orientations, the fracture of [email protected]. tendons is mainly governed by molecular properties of the fibrils, This article contains supporting information online at https://www.pnas.org/lookup/suppl/ which vary among functionally distinct tendons (13) and change doi:10.1073/pnas.1920062117/-/DCSupplemental. upon age-related enzymatic cross-linking reactions (16, 17) and www.pnas.org/cgi/doi/10.1073/pnas.1920062117 PNAS Latest Articles | 1of9 Downloaded by guest on September 23, 2021 the mean number of fibers meeting at a junction, is the main order to assess collagen fracture, we apply a linear strain ramp γ determinant of collagen fracture. We can explain almost all of on the networks by rotating the top plate and measuring the our findings by using a threshold strain for fiber fracture in the resulting shear stress σ. As illustrated in Fig. 1B and SI Appendix, range of 10 to 20%, a value that is consistent with prior tensile Fig. S1, the stress initially increases linearly with strain, as expected tests on single collagen fibrils (34, 35). Furthermore, the com- for the linear elastic regime. However, above a threshold strain of 4 putational model enables us to assess the contributions of system to 5%, the stress starts to deviate from this linear behavior and size and detailed network and fiber properties on the fracture shows an upturn indicative of network stiffening. The stress even- behavior. Molecular effects, such as intrafibrillar cross-linking, tually reaches a maximum value, which we call the peak stress σp, and network properties, such as branching, modulate the frac- associated to a peak strain γp. Beyond the stress peak, the shear ture strain by setting the degree of plasticity. Our results are im- stress decreases, which is symptomatic of fracture. Images taken portant not only for understanding how disorder protects collagen during the strain ramp at a fixed height of 20 μmabovethebottom networks—and therefore, living tissues—from fracture but also for plate of the rheometer indeed reveal network fracture, as signaled the rational design of synthetic fibrillar materials resistant to by the onset of fibril motion, breakage of connections, and a de- strain-induced breakage. crease in fluorescence intensity in the imaging plane that signals the appearance of a crack coming from outside the field of view (Fig. Results 1C, Movie S1,andSI Appendix,Fig.S2). However, fracture is al- To test the mechanical resistance of collagen networks against ways first observed at strains beyond γp (SI Appendix,Figs.S3and fracture, we perform rheology experiments on reconstituted S4). This may be partly explained from the fact that the macroscopic collagen networks polymerized between the plates of a custom- strain we report here corresponds to the strain at the edge of the built confocal rheometer. The bottom plate of the rheometer is sample, while our imaging area is located at a radial distance stationary and optically
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