Cooperative deformation of hydrogen bonds in beta-strands and beta-sheet nanocrystals

Beta-sheet protein domains are stabilized by weak hydrogen bonds, yet materials such as silk--whose ultimate tensile strength is controlled primarily by this secondary structure--can exceed the ultimate tensile strength of steel. Earlier work has suggested that this is because hydrogen bonds deform cooperatively within small protein domains to reach the maximum strength. Here we study the atomistic mechanism of this concerted deformation mechanism by applying an elastic structural model, used to solve the deformation field of the chemical bonds in beta-sheet nanostructures under stretching and thereby identify the number of hydrogen bonds that deform cooperatively. Through this analysis, we predict the optimal beta-strand and beta-sheet nanocrystal size associated with reaching the maximum usage of hydrogen bonds under loading applied per unit material volume. Our results, albeit based on a simple model and analytical equations, quantitatively agree with results based on experimental and molecular-dynamics studies and provide physical insight into the underlying molecular mechanisms of weak bond cooperativity. A comparison with the size of hydrogen bond clusters in biology reveals excellent agreement with the cluster sizes predicted by our analysis, suggesting that perhaps the confinement of hydrogen bonds into nanoscale elements is a universal biological design paradigm that turns weakness to strength. The parameters used in this study could be modified and applied to other protein and polymer structures, which imply potential applications of our model in understanding the physics of deformation and failure in a broader range of biological and polymer materials, as well as in de novo biomaterial design.