Jain Ishutesh, Inamdar Mandar M, Padinhateeri Ranjith
Department of Biosciences and Bioengineering, Indian Institute of Technology Bombay, Mumbai, India.
Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India.
PLoS Comput Biol. 2015 Feb 18;11(2):e1004099. doi: 10.1371/journal.pcbi.1004099. eCollection 2015 Feb.
Microtubules are nano-machines that grow and shrink stochastically, making use of the coupling between chemical kinetics and mechanics of its constituent protofilaments (PFs). We investigate the stability and shrinkage of microtubules taking into account inter-protofilament interactions and bending interactions of intrinsically curved PFs. Computing the free energy as a function of PF tip position, we show that the competition between curvature energy, inter-PF interaction energy and entropy leads to a rich landscape with a series of minima that repeat over a length-scale determined by the intrinsic curvature. Computing Langevin dynamics of the tip through the landscape and accounting for depolymerization, we calculate the average unzippering and shrinkage velocities of GDP protofilaments and compare them with the experimentally known results. Our analysis predicts that the strength of the inter-PF interaction (E(s)(m)) has to be comparable to the strength of the curvature energy (E(b)(m)) such that E(s)(m) - E(b)(m) ≈ 1kBT, and questions the prevalent notion that unzippering results from the domination of bending energy of curved GDP PFs. Our work demonstrates how the shape of the free energy landscape is crucial in explaining the mechanism of MT shrinkage where the unzippered PFs will fluctuate in a set of partially peeled off states and subunit dissociation will reduce the length.
微管是利用其组成原丝（PFs）的化学动力学与力学之间的耦合随机生长和收缩的纳米机器。我们在考虑原丝间相互作用以及固有弯曲原丝的弯曲相互作用的情况下，研究微管的稳定性和收缩情况。通过计算作为PF尖端位置函数的自由能，我们表明曲率能量、原丝间相互作用能量和熵之间的竞争导致了一个丰富的能量景观，其中有一系列最小值，这些最小值在由固有曲率决定的长度尺度上重复出现。通过该能量景观计算尖端的朗之万动力学并考虑解聚过程，我们计算了GDP原丝的平均解链和收缩速度，并将其与实验已知结果进行比较。我们的分析预测，原丝间相互作用强度（E(s)(m)）必须与曲率能量强度（E(b)(m)）相当，使得E(s)(m) - E(b)(m) ≈ 1kBT，并且对普遍认为解链是由弯曲的GDP原丝的弯曲能量主导这一观点提出了质疑。我们的工作展示了自由能景观的形状在解释微管收缩机制方面是如何至关重要的，在该机制中，解链的原丝将在一组部分剥离状态中波动，并且亚基解离将缩短长度。
