Schoutens Jacques E
665 Shaw Street, PO Box 634, Los Alamos, CA 93440 U.S.A.
J Biol Phys. 2005 Jan;31(1):35-55. doi: 10.1007/s10867-005-3886-1.
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.
微管中的二聚体具有沿三个轴的偶极矩分量。计算了在“干燥”条件下未变形和椭圆变形微管中微管内所有偶极分量之间的相互作用能。发现相互作用能随变形而增加。所有偶极之间的总相互作用能为正,这意味着微管未变形的圆柱形代表了能量最小的状态。这表明微管的圆柱形是偶极 - 偶极相互作用的结果。可能还有其他原因,但本文未作讨论。根据这些结果,计算了偶极 - 偶极相互作用能对微管纵向和横向弯曲刚度的贡献。结果表明,对弹性模量的纵向贡献约为总测量值的50 - 60%,而计算出的横向贡献比纵向贡献小约3倍。测量的轴向与横向弯曲刚度之比约为125,与最近的观测结果一致。然而,由于文中讨论的原因,这些值并不确定。