Surface deflection of a microtubule loaded by a concentrated radial force

Microtubules are hollow cylindrical filaments of a eukaryotic cytoskeleton which are sensitive to externally applied radial forces due to their low circumferential elastic modulus. In this work, an orthotropic elastic shell model for microtubules is used to study the surface radial deflection of a microtubule loaded by a concentrated radial force generated by either a single molecular motor or a radial indentation tip. Our results show that the maximum surface radial deflection of a microtubule generated by a concentrated radial force of a few pN can be as large as a few nanometers ( a significant fraction of the radius of microtubules), which could cause significant surface morphological non-uniformity of the microtubule. In contrast, radial indentation under a much larger compressive force, which can be as large as a few hundreds of pN, will cause hardening of the circumferential elastic modulus almost equal to the longitudinal modulus of microtubules. In this case, our results show that a microtubule can withstand a concentrated radial compressive force as large as a few hundreds of pN, with a maximum radial deflection not more than a few nanometers, in good agreement with recent experiments on radial indentation of microtubules. These results offer useful data and new insights into the basic understanding of elastic interaction between microtubules and molecular motors and radial indentation of microtubules.