Computational Modeling of Microtubule Dynamic Instability

Microtubules are the major component of cytoskeleton. They are proteinaceous polymers which consist of αβ tubulin dimers. In microtubules, these tubulin subunits are assembled into thirteen linear polymers, called protofilaments. Microtubules play key roles in many cellular functions. One important feature of microtubules is the abrupt transition between polymerization and depolymerization, which is called dynamic instability. Dynamic instability allows microtubules to explore cellular space constantly and to respond changes of cellular environment quickly. Since experimental data is not available at the smallest scale, modeling is the only approach available at this time to make predictions about mechanisms of dynamic instability to be tested in future experimentally. We extended our previous computational model to simulate dynamics of microtubules after instantaneously changing the nucleotide state of subunits in microtubule structure. We showed that the neighboring protofilaments can be not totally laterally bonded. The region which does not have lateral bonds is called a 'crack'. The cracks correlate with dynamic instability in two aspects. First, the microtubules display shallower cracks in growth state than in shortening state. Second, when the cracks terminate in a GTP-rich (GDP-rich) region, microtubules are more likely to grow (shorten). We performed the multinomial logistic regression and showed that the subunits at the bottom of the cracks are statistically significant for dynamic instability. Given the importance of the lateral bonds, we used random walk model to analyze the dynamics of lateral bonds in microtubules. We showed that when the subunits at the bottom of the cracks (Gs) and the subunits just above Gs are all GTP-bound (GDP-bound), microtubules grow (shorten) almost surely. Furthermore, we studied the critical concentrations of two types of microtubule growth by using master equations for a simplified 2-protofilaments microtubule model. One type is the microtubule growth with dynamic instability, called bounded growth. Another type is the microtubule growth without dynamic instability, called persistent growth. We calculated these two critical concentrations by numerically solving the master equations. Moreover, we extended our computational model to include microtubule binding proteins (MTBPs) and studied the mechanism of a key MTBP, stathmin/Op18, which destabilizes microtubule structures. One well-studied mechanism of stathmin is to induce depolymerization by sequestering the free tubulin subunits in cells so that few tubulins are available for microtubule polymerization. However, we showed that, besides the sequestration activity, stathmin can induce depolymerization by direct binding on the laterally unbonded region of protofilaments in microtubules. Hence, we proposed that stathmin destabilizes microtubules by a combination of the sequestration and the direct binding activities.