Modeling of protein networks reveals factors affecting stiffness, yield stress, and strain stiffening in silk fibers

Thanks to their high stiffness, tensile strength, and toughness, silk fibers generated significant interest and are being considered for many applications. The superior properties of these fibers stem from a unique microstructure, which comprises crystalline domains and polypeptide chains that interact through weak intermolecular interactions. Recent works show that these fibers can be engineered to achieve target mechanical properties and response. Specifically, the uniaxial stretching of silk fibers typically results in a linear response up to a yield point, after which the fiber can exhibit a plateau or strain stiffening up to failure. The response depends on the amino-acid sequence and the molecular weights (MWs) of the peptides, which determine the degree of crystallinity in the network. In this work, we employ statistical mechanics to develop a microscopically motivated framework that sheds light on the underlying mechanisms that govern the fiber response. We propose that upon the application of a tensile force, the linear deformation is enabled by the distortion of weak intermolecular interactions, up to their rupture at a yield stress. In fibers with low crystallinity, the chains are not interconnected and therefore carry minimal load due to potential weak intramolecular interactions, resulting in a plateau stress up to failure. In fibers with a high degree of crystallinity, the crystalline domains are stiff and therefore deformations are enabled through the entropic stretching of the chains in the amorphous region, leading to strain stiffening. Our framework is validated through a comparison to two sets of experiments: (1) fibers with the same MWs but different sequences and (2) fibers with the same sequence but different MWs. The findings from this work enable to compare between the microstructures of different protein-based fibers and pave the way to the design of novel fibers with target mechanical properties and response. Statement of Significance: Silk fibers have attracted significant interest due to their high stiffness, tensile strength, and toughness. These properties arise from a unique microstructure, comprising crystalline domains and polypeptide chains cross-linked by weak intermolecular interactions. In this work, we employ polymer physics and statistical mechanics to develop an energy-based, microscopically motivated model describing the mechanical response of protein fibers under extension. We validate the model using two experimental sets: (1) fibers with identical molecular weights (MWs) but different sequences, and (2) fibers with the same sequence but varying MWs. Our findings offer a framework to compare the microstructures of proteinbased fibers and support the design of new fibers with tailored mechanical properties.