One-dimensional modeling of the self-assembly of complex elastic particles

Self-assembly is a spontaneous aggregation of small subunits into a larger structure. We focus on a specific kind of self-assembly phenomenon in cells where protein molecules aggregate into finite-size fibers. This phenomenon involves deformations and elastic properties of the protein molecules. However, this behavior has been shown to be generic beyond any specific types of proteins. Currently, the exact mathematical descriptions of the deformation are known only for a one-dimensional aggregate model consisting of simple subunits. Real-world protein molecules, on the other hand, pose more complexity -- both in terms of their shapes and their elastic properties -- and a more complex model is required. In this work, we attempt to narrow down the difference between real-world systems and the existing mathematical models by introducing complexity via randomness of the positions of protein binding sites. Our model displays a novel oscillatory deformation mode that has not been previously observed. We offer a quantitative explanation of this kind of deformation mode. Moreover, our findings suggest a universality in aggregate size independent of the elastic properties of the subunits.