Effects of elastic medium on buckling of microtubules due to bending and torsion

Microtubules buckle under bending and torsion and this property has been studied for free microtubules before using orthotropic elastic shell model. But as microtubules are embedded in other elastic filaments and it is experimentally showed that these elastic filaments affect the critical buckling moment and critical buckling torque of the microtubules. To prove that, we developed orthotropic Winkler like model and demonstrated that the critical buckling moment and critical buckling torque of the microtubules are orders of higher magnitude than those found for free microtubules. Our results show that Critical buckling moment is about 6.04 nNnm for which the corresponding curvature is about o=1.33 rad /um for embedded MTs, and critical buckling torque is 0.9 nNnm for the angle of 1.33 rad/um. Our results well proved the experimental findings.