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Research Papers

Critical Scales Govern the Mechanical Fragmentation Mechanisms of Biomolecular Assemblies

[+] Author and Article Information
Sinan Keten

e-mail: s-keten@northwestern.edu
Civil & Environmental Engineering
and Mechanical Engineering,
Northwestern University,
2145 Sheridan Rd., Room A133,
Evanston, IL 60208

1Corresponding author.

Manuscript received November 7, 2012; final manuscript received December 26, 2012; accepted manuscript posted February 14, 2013; published online August 19, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061010 (Aug 19, 2013) (8 pages) Paper No: JAM-12-1507; doi: 10.1115/1.4023681 History: Received November 07, 2012; Revised December 26, 2012; Accepted February 14, 2013

Fragmentation mechanisms of peptide assemblies under shock deformation are studied using molecular dynamics simulations and are found to depend strongly on the relative magnitude of the shock front radius to the fibril length and the ratio of the impact energy to the fibril cohesive energy. The competition between size scaling of curvature and impact energy leads to a mechanism change at a critical impact velocity, developing a stark contrast in the size scaling of fragmentation at low and high strain rates. We show that the fragmentation mechanisms can be classified on the basis of the length and time scales of deformation and relaxation to provide new insight into experimental observations.

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Figures

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Fig. 1

(a) Self-assembling, hydrogen-bonded biomolecular materials are observed in the amyloids found in Alzheimer's disease, designer peptide fibers and nanotubes, and β-sheet nanocrystals in materials like silk. (b) Supramolecular assemblies can be broken by force through the impact of a sonication-induced water hammer or collision with a solid. (c) A cylindrical rod (circular in 2D) of radius R moving with constant velocity impacts a fibril of length L modeled here as a network of linkages (bonds) using a Morse potential to allow breaking between.

Grahic Jump Location
Fig. 2

Number of fragments as a function of impact velocity and shock front radius are shown. Here, the number of fragments observed after the impact are plotted as a function of impact velocity (v) and the ratio of shock front radius to the fibril length (R/L). It is observed that the number of fragments increases with the impact velocity ((a)–(d)). Likewise, the number of fragments increases with the size of the impact region (indenter) up to 2 RL. Beyond this point, further increasing the shock front radius ceases to increase fragmentation at fast rates ((a) and (c)). More interestingly, at slow rates, this leads to reduction of the total number of fragments ((b) and (d)) subunits.

Grahic Jump Location
Fig. 3

Classification of fragmentation mechanisms. The layers that are below the bond breaking threshold are displayed as cylinders. The radius of the cylinder depicts the strain on each segment. At fast impact velocities, the molecules break by stripping along the shock front boundary, and fragmentation is maximized as the shock front diameter approaches fibril length ((a) and (b)). For small shock front radii and slow rates, the fibril breaks locally in a burst type of mechanism that causes fragmentation by local penetration, bending, and buckling mechanisms induced by the curvature of the shock front (c). As the shock front radius exceeds the end-to-end length of the fibril, curvature diminishes significantly, and the total impact energy ceases to increase due to saturation of the contact area. The fibril breaks in tension upon impact due to axial stresses and elongational vibrations along the fibril, leading to rupture at one or more points near the center of the fibril (d). These results suggest that a smaller fibril size relative to the shock front radius will be more robust under mechanical agitation if the fragmentation mechanism is dominated by curvature rather than initial impact energy.

Grahic Jump Location
Fig. 4

Velocity dependence of fragmentation mechanisms. Plots show that, for both fibril sizes studies, the number of fragments formed increase with increasing impact velocity ((a) and (b)) but reach a diminishing rate at very high velocities. A semilog plot of the number of fragments and impact velocities reveal a critical transition velocity v*, above which the number of fragments increase multifold ((c) and (d)). As a visual aid, the region where the critical velocity is located has been shaded for 10.0 R/L. The mechanisms and size-scaling of the number of fragments are evidently different below and above the critical velocity.

Grahic Jump Location
Fig. 5

Sensitivity to bending rigidity and binding energy. By increasing the bending rigidity of the fibril, the critical velocity increases (a). At an intermediate velocity (b), the softer fibrils display a positive trend as the indenter size increases, while the stiffer fibrils display a negative trend as the indenter size increases. These trends imply that v = 200 m/s is above the critical velocity for the softer fibrils but not the stiffer fibrils. By altering the cohesive energy per layer of the model, the lower energy fibrils produce more fragments. As a result, a similar shift in the velocity dependence curves is observed (c). At v = 350 m/s, the strongly cohesive fibril is below the critical velocity, whereas the weakly cohesive fibril is above the critical velocity.

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