Dipole-dipole interactions in microtubules.

Dimers in microtubules possess a dipole moment with components along three axes. The interaction energy among all dipole components in a microtubule was calculated for an un-deformed and an elliptically deformed microtubule in a "dry" condition. The interaction energy was found to increase with deformation. The total interaction energy among all dipoles is positive, which implies that the un-deformed cylindrical shape of a microtubule represents a condition of minimum energy. This suggests that the cylindrical shape of microtubules is a consequence of dipole-dipole interactions. There may be other causes as well but these are not discussed in this paper. From these results, the contributions of the dipole-dipole interaction energy to the microtubule longitudinal and transverse flexural rigidities were calculated. It is shown that the longitudinal contribution to the elastic modulus is approximately 50-60% of the total measured value while the calculated transverse contribution is smaller than the longitudinal contribution by a factor of approximately 3. The ratio of the measured axial to the measured transverse flexural rigidity is approximately 125, in agreement with recent observations. However, these values are uncertain for reasons discussed in the text.