A Physically-Based Machine Learning Approach Inspires an Analytical Model for Spider Silk Supercontraction

Scientific and industrial interest in spider silk stems from its remarkable properties, including supercontraction-an activation effect induced by wetting. Understanding the underlying molecular scale mechanisms is then also crucial for biomimetic applications. In this study, it is illustrated how the effective integration of physically-based machine learning with scientific interpretations can lead to significant physical insights and enhance the predictive power of an existing microstructure-inspired model. A symbolic data modeling technique, known as Evolutionary Polynomial Regression (EPR), is employed, which integrates regression capabilities with the genetic programming paradigm, enabling the derivation of explicit analytical formulas for deducing structure-function relationships emerging across different scales, to investigate the impact of protein primary structures on supercontraction. This analysis is based on recent multiscale experimental data encompassing a diverse range of scales and a wide variety of different spider silks. Specifically, this analysis reveals a correlation between supercontraction and the repeat length of the MaSp2 protein as well as the polyalanine region of MaSp1. Straightforward microstructural interpretations that align with experimental observations are proposed. The MaSp2 repeat length governs the cross-links that stabilize amorphous chains in dry conditions. When hydrated, these cross-links are disrupted, leading to entropic coiling and fiber contraction. Furthermore, the length of the polyalanine region in MaSp1 plays a critical role in supercontraction by restricting the extent of crystal misalignment necessary to accommodate the shortening of the soft regions. The validation of the model is accomplished by comparing experimental data from the Silkome database with theoretical predictions derived from both the machine learning and the proposed model. The enhanced model offers a more comprehensive understanding of supercontraction and establishes a link between the primary structure of silk proteins and their macroscopic behavior, thereby advancing the field of biomimetic applications.