Asymptotic Strength Limit of Hydrogen Bond Assemblies in Proteins at Vanishing Pulling Rates
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1062-NN05-08
Asymptotic Strength Limit of Hydrogen Bond Assemblies in Proteins at Vanishing Pulling Rates Sinan Keten, and Markus J. Buehler Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139 ABSTRACT Experimental and computational studies on mechanical unfolding of proteins suggest that rupture forces approach a limiting value of a few hundred pN at vanishing pulling velocities. We develop a fracture mechanics based theoretical framework that considers the free energy competition between entropic elasticity of polypeptide chains and rupture of peptide hydrogen bonds, which we use here to provide an explanation for the intrinsic strength limit of proteins. Our analysis predicts that individual protein domains stabilized by hydrogen bonds can not exhibit rupture forces larger than ≈ 200 pN, regardless of the presence of a large number of hydrogen bonds. This result explains a wide range of experimental and computational observations. INTRODUCTION Rupture of parallel inter-strand hydrogen bonds controls the mechanical unfolding pathway of protein structures, governing the strength of peptide based materials such as silks. Atomistic simulation [1, 2] and single-molecule force microscopy studies [3, 4] have shown that beta-sheet rich proteins exhibit higher rupture forces, since they employ parallel strands with numerous hydrogen bonds that act as mechanical clamps under shear loading [6-9]. In both experiment and simulation of mechanically resistant proteins, the maximum force peak observed is linked to an individual event corresponding to the unravelling of a single beta-sheet in the protein. It is astonishing to see that regardless of the variation in topology and size of structures studied, almost all so called ‘mechanical’ proteins (e.g. fibronectin and titin domains) examined so far exhibit a rupture force of a few hundred piconewtons (pN) at experimental pulling rates[10, 11]. Earlier experimental and computational results with different deformation rates are summarized in Figure 1, where the rupture forces of predominantly beta structured proteins are plotted against the pulling velocities (v) on a log (v) scale. The asymptotical limit at vanishing rates can be inferred from the overall behaviour as well as from the power law fit to data based on unfolding force data corresponding to the Ig27 domain in titin (data adapted from [10, 11]). This observation suggests that the strength of individual protein domains asymptotically approaches a limiting strength. Thus far, no theoretical basis or prediction has been proposed for such an intrinsic strength limit; most earlier analyses have been focused on the rate dependent behavior in order to explain the increase in unfolding forces with increasing pulling speed (see Figure 1).
Strength of β - domains 4500
Rupture Force (pN)
4000 3500 3000 2500 2000 1500 1000 500 0 1.00E-10
1.00E-08
1.00E-06
1.00E-04
1.00E-02
Pulling Velocity, v (m/s)
1.00E+00
1.00E+02
Figure 1. Earlier s
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