A beam element is constructed for microtubules based upon data reduction of the results from atomistic simulation of the carbon backbone chain of αβ-tubulin dimers. The database of mechanical responses to various types of loads from atomistic simulation is reduced to dominant modes. The dominant modes are subsequently used to construct the stiffness matrix of a beam element that captures the anisotropic behavior and deformation mode coupling that arises from a microtubule’s spiral structure.
In contrast to standard Euler-Bernoulli or Timoshenko beam elements, the link between forces and node displacements results not from hypothesized deformation behavior, but directly from the data obtained by molecular scale simulation. Researchers from the Mitran Group present differences between the resulting microtubule data-driven beam model, MTDDBM, and standard beam elements with a focus on coupling of bending, stretch, shear deformations. The MTDDBM is just as economical to use as a standard beam element, and allows accurate reconstruction of the mechanical behavior of structures within a cell as exemplified in a simple model of a component element of the mitotic spindle.
A model reduction approach is introduced that processes a large database of atomistic-level mechanical responses into an efficient reduced model for microtubules, similar in simplicity to Euler–Bernoulli beam models, but capturing the effects of the microtubule spiral dimer structure. The resulting MTDDBM can readily be used as a building block for more complicated cell structures such as a cilium axoneme or the mitotic spindle constituent element considered in this paper. It also offers a more accurate methodology for extraction of effective mechanical moduli from experimental results.