Surface effects on the mechanical characteristics of microtubule networks in living cells

• A new persistence length relation is presented for microtubules.
• Surface effects are taken into consideration using a modified Timoshenko beam theory.
• Buckling behavior of microtubule systems in viscoelastic surrounding cytoplasm is investigated.
• Buckling solutions are intensely sensitive to surface parameters.

In this article, a new explicit formula is presented for the length-dependent persistence length of microtubules with consideration of surface effects. Further, surface effects on the buckling characteristics of microtubule systems in viscoelastic surrounding cytoplasm are investigated using a modified Timoshenko beam model. Closed-form solutions are presented for the buckling growth rates of double-microtubule systems. Both normal and shearing behaviors of microtubule associated proteins are taken into consideration. The comparison of present results with the available experimental data in the open literature shows that the present formulation provides more accurate results than those obtained by the classical beam theory. It is observed that the surface effect plays a prominent role in the bending and buckling behaviors of microtubules. Further, surface effects are more significant at higher buckling modes.