Flexibility and rigidity of cross-linked Straight Fibrils under axial motion constraints

The Straight Fibrils are stiff rod-like filaments and play a significant role in cellular processes as structural stability and intracellular transport. Introducing a 3D mechanical model for the motion of braced cylindrical fibrils under axial motion constraint; we provide some mechanism and a graph theoretical model for fibril structures and give the characterization of the flexibility and the rigidity of this bar-and-joint spatial framework. The connectedness and the circuit of the bracing graph characterize the flexibility of these structures. In this paper, we focus on the kinematical properties of hierarchical levels of fibrils and evaluate the number of the bracing elements for the rigidity and its computational complexity. The presented model is a good characterization of the frameworks of bio-fibrils such as microtubules, cellulose, which inspired this work.