β-Sheet protein structures and domains are widely found in biological materials such as silk. These assemblies play a major role in the extraordinary strength and unique properties of biomaterials. At the molecular level, the single β-sheet structure comprises polypeptide chains in zig-zag conformations that are held together by hydrogen bonds. β-sheet domains comprise multiple β-sheets that originate from hydrophobic interactions between sheets and are held together by van der Waals interactions. In this work, we introduce molecular models that capture the response of such domains upon mechanical loading and illustrate the mechanisms behind their collapse. We begin by modeling the force that is required to pull a chain out of a β-sheet. Next, we employ these models to study the behavior of β-sheets that are embedded into and connected to an amorphous protein matrix. We show that the collapse of a β-sheet occurs upon the application of a sufficiently high force that is transferred from the chains in the matrix to individual chains of the β-sheet structure and causes shear. With the aim of understanding the response of β-sheet domains, we derive models for the interactions between β-sheets. These enable the study of critical forces required to break such domains. As opposed to molecular dynamics simulations, the analysis in this work yields simple expressions that shed light on the relations between the nanostructure of β-sheet domains and their mechanical response. In addition, the findings of this work suggest how β-sheet domains can be strengthened.
Keywords: biological materials; microstructure; multiscale modeling; spider silk; β-sheet mechanics.