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

Abstract

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.

Összekapcsolt, axiális irányban mozgó szál hálózatok merevségének jellemzése gráfokkal

“…A párhuzamos szálak esetétés a jelen cikkben tárgyaltáltalános esetet (nem ilyen részletességgel) a [17] dolgozat tárgyalja.Általános helyzetű szálakbólés rudakbólálló rendszer akkor lesz infinitezimálisan merev, ha a fentihez hasonló egyenletrendszernek csak az x = ⃗ 0 vektor a megoldása. Az egyenletrendszer együtthatóit a szálakés merevítő rúdjaik térbeli helyzete határozza meg.…”

Braced grid framework rigidity characterization

“…Thus, it is no coincidence that biological structures come into the field of vision of our architects, and this is now an area researched not only by architects and structural engineers but also in materials science. A new branch of science, structural biology, has emerged, which plays a significant role not only in organ tissues but also in the mechanical characterization of the more minor elements that make them up, such as collagens and associated calcites, as well as the cross-connections of microtubules and actin fibers found within cells [13,14].…”

“…The generalization in the other direction characterizes hierarchical structures, for which the sample is e.g. the location of the cellulose bundles located in wood and the location of collagen fibers can be found in bony tissues [14]. We will apply the results of rhombus tiling rigidity to the stiffening of planar scaffolding with cables and struts.…”

Braced twist-free Cubic Framework characterized as tensegrities structures

“…The symmetry of the bar-joint structure to determine its rigidity is a problem of long-standing interest in kinematics, statics, and optimization [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The rigidity and mobility of bar and joint framework have served as models of the structure of metals, crystal states of matter [5], and biological systems [19]. Lattices, and tesselations as repetitive objects, are helpful as preliminary design structures [1-4, 6, 7, 9-13, 17, 18].…”