Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of α-helical and β-sheet protein domains

doi:10.1073/pnas.0705759104

Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of α-helical and β-sheet protein domains

*Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental Engineering, and
^†Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139

Edited by Shu Chien, University of California at San Diego, La Jolla, CA, and approved August 13, 2007 (received for review June 20, 2007)

Abstract

The fundamental fracture mechanisms of biological protein materials remain largely unknown, in part, because of a lack of understanding of how individual protein building blocks respond to mechanical load. For instance, it remains controversial whether the free energy landscape of the unfolding behavior of proteins consists of multiple, discrete transition states or the location of the transition state changes continuously with the pulling velocity. This lack in understanding has thus far prevented us from developing predictive strength models of protein materials. Here, we report direct atomistic simulation that over four orders of magnitude in time scales of the unfolding behavior of α-helical (AH) and β-sheet (BS) domains, the key building blocks of hair, hoof, and wool as well as spider silk, amyloids, and titin. We find that two discrete transition states corresponding to two fracture mechanisms exist. Whereas the unfolding mechanism at fast pulling rates is sequential rupture of individual hydrogen bonds (HBs), unfolding at slow pulling rates proceeds by simultaneous rupture of several HBs. We derive the hierarchical Bell model, a theory that explicitly considers the hierarchical architecture of proteins, providing a rigorous structure–property relationship. We exemplify our model in a study of AHs, and show that 3–4 parallel HBs per turn are favorable in light of the protein's mechanical and thermodynamical stability, in agreement with experimental findings that AHs feature 3.6 HBs per turn. Our results provide evidence that the molecular structure of AHs maximizes its robustness at minimal use of building materials.

Footnotes

^‡To whom correspondence should be addressed at:
Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 1–272, Cambridge, MA 02139.
E-mail: mbuehler{at}mit.edu
Author contributions: T.A. and M.J.B. designed research; T.A., X.C., and S.K. performed research; T.A., X.C., S.K., and M.J.B. analyzed data; and T.A. and M.J.B. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0705759104/DC1.
Abbreviations:

AH,

α-helical;

AP,

angular point;

BS,

β-sheet;

HB,

hydrogen bond;

FDM,

fast-deformation mode;

MD,

molecular dynamics;

SDM,

slow-deformation mode;

SMD,

steered molecular dynamics.