Aranson Igor S, Tsimring Lev S
Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 1):031915. doi: 10.1103/PhysRevE.74.031915. Epub 2006 Sep 26.
We derive a model describing spatiotemporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel, we obtain a set of equations for the local rods concentration and orientation. At large enough mean density of rods and concentration of motors, the model describes an orientational instability. We demonstrate that the orientational instability leads to the formation of vortices and (for large density and/or kernel anisotropy) asters seen in recent experiments. We derive the specific form of the interaction kernel from the detailed analysis of microscopic interaction of two filaments mediated by a moving molecular motor and extend our results to include variable motor density and motor attachment to the substrate.
我们推导了一个描述通过分子马达相互作用的微管阵列时空组织的模型。从具有一般各向异性相互作用核的非弹性极性杆的随机模型出发，我们得到了局部杆浓度和方向的一组方程。在杆的平均密度和马达浓度足够大时，该模型描述了一种取向不稳定性。我们证明，取向不稳定性会导致形成涡旋以及（对于高密度和/或核各向异性）在最近的实验中观察到的星状体。我们通过对由移动分子马达介导的两根细丝微观相互作用的详细分析，推导出相互作用核的具体形式，并将我们的结果扩展到包括可变的马达密度和马达与底物的附着。
