Study Of Mechanical Properties Of F-actin Bundles

As a class of complex sub-cellular structures, the mechanical properties of F-actin bundles plays a crucial role in many fundamental cellular processes, such as cell migration, intracellular transport, regulation of cell adhesion and maintenance of cell morphology and so on. Multiple skeletal substructure cells, such as microvilli, stress fibers, stereocilia, filopodia, etc., are formed by F-actin bundles. These sub-frame structures have respective different properties since different number of fibers, the length of fibers and different types of actin binding proteins. Currently, people tend to study the mechanical properties of F-actin bundles from a single continuum mechanics or statistical thermodynamics. However F-actin bundle is extremely flexible in the microscale and effected easily by thermal disturbance, so they have the characteristcs of polymer. At the same time, F-actin bundles have complex composite bundle structures which differ from classic polymer molecule. So in order to achieve the precise quantitative description of F-actin bundle’s mechanical properties, we first established new model which combine the statistical thermodynamic theory and continuum structural mechanics theory to realize this goal in this paper.In general solution environment, F-actin bundle not only has low modes of whole bundle’s deformation, but also has each fiber’s high modes of deformation. Firstly, we obtain the equivalent Young’s modulus of F-actin bundle which based on confined space polymer theory by considering the impact of a single fiber’s tiny fluctuation. Meanwhile we study the tensile behavior of statistical thermodynamics of F-actin bundle packing with chains squarely and hexagonally. Through these calculation, we find the tiny fluctuation of single fiber have great impact on stretching stiffness of F-actin bundle which reflect strong nonlinear hyper-elastic properties. Secondly, through the establishment of theoretical model of coupled statistical thermodynamic theory and continuum structural mechanics theory, we get the nonlinear singular quantitative dependencies of persistence length which describe statistical thermodynamic bending stiffness and contour length, persistence length and tensile force. These properties show that the persistence length increases with the contour length increasing and tensile force increasing. Namely, when bundle’s contour length and tension increase, F-actin bundle can harden. While, for the usual micro-mechanical structures or polymer chain, the persistence length is a constant. Finally, we consider F-actin bundle as a complex microstructure’s bunchy polymer molecule chain and study the mechanical properties by means of statistical thermodynamics. We obtain quantitative dependency between tensile force and displacement and equivalent tensile stiffness. Ewin Frey professor with the German team to ignore a single high-order mode fiber thermal disturbance to the conclusion compare hair:When large shear stiffness between the fibers are basically the same conclusion when the shear stiffness is smaller exhibit when loose fibers combined the differences. Therefore, a single fiber for small perturbations combined looser mechanical properties of the fiber bundle has a great impact. Through comparison with German’s Ewin Frey professor’s team’s conclusion in which ignore a high-order mode’s fluctuation of single fiber, we find that these two conclusions are basically same when shear stiffness is large, while when shear stiffness is small, namely, when F-actin bundle is loose, they have large difference. Therefore, tiny fluctuation of single fiber has a great impact on mechanical properties of F-actin bundle.