A Modeling Study to Characterize Microtubule Mechanisms of Dynamic Instability: Connecting Micro-Level Tip Structures to Macro-Level Phases

Microtubules (MTs) are cytoplasmic biopolymers that are common in eukaryotic cells. The MT is assembled by αβ tubulin dimer subunits that can be in either a GTP- or GDP-bound nucleotide state. These dimer subunit connect with longitudinal bonds to form linear strands called protofilements (PFs). Lateral bonds connect 13 PFs together to form the tube-like structure of a MT. GTP-bound subunits collect near the MT tip region to form a GTP-cap, which helps maintain the bonds that hold the MT structure intact. Losing the GTP-cap exposes GDP-bound subunits which are more likely to break their bonds, and promote subunits to detach from the MT structure. The MT length changes in time by undergoing spontaneous switches between periods of sustained growth and rapid shortening, which characterize the behavior called dynamic instability (DI).

The molecular reactions that drive MT dynamics primarily affect the tip portion of the structure. Therefore, a study of the connection between MT tip structures and macro-level phases is needed to gain a better understanding of the mechanisms that drive phase changes in DI. Laboratory conditions limit the level of detail that can be experimentally collected from MT structures. Computational models are a vital tool that provide this level of information, and they have helped understand how molecular level reactions alter the micro-level MT structure, which drives the MT length changes observed at the macro-level. The detailed 13-PF MT model was capable of running long-time simulations that display DI behavior with a low com- putational cost, but it made use of an approximation that skips over MT structural states. This study first develops the extended 13-PF MT model in order to simu- late a biochemically exact trajectory of all the MT structural states resulting from possible reactions events. Then, the minimal MT structure that includes the lateral bond is considered to present the simplified 2-PF MT model, a novel consideration which helps make calculations of the MT tip structure features more feasible while successfully simulating DI behavior.

The high frequency and low amplitude fluctuations present in simulated MT length history data make it difficult to pinpoint where DI phases begin and end, and where phase transitions occur. To this end, an unsupervised machine learning method based on K-means clustering is presented to identify, classify, and analyze macro-level phases present in MT length history data. Application of this method revealed an intermediate phase called “stutters”, during which the rate of MT length change is smaller in magnitude compared to classically recognized growth and short- ening phases. Additionally, stutter phases commonly appeared as a transitional phase during catastrophe events, between growth and shortening phases. This indicated that before a catastrophe event takes place, a MT is likely to first undergo structural changes that do not alter the MT length, which result in structural configurations prone to entering a period of rapid depolymerization. The proposed DI phase clas- sification method now can identify these periods, which in past experimental studies have been observed, but not separately considered as a unique class of behavior [21]. Furthermore, the stutter events specifically provide a target region to study the mechanisms involved with catastrophe events.

Finally, a supervised machine learning approach called Random Forest was used to test the ability for micro-level tip structure features to predict their correspond- ing macro-level DI phases, and to forecast upcoming phase transitions. The results indicated that the GTP-cap size and it’s relative position to the cracked tip region are important factors in predicting which DI phase a MT is in. In addition to the GTP-cap size, information on the PF-tip lengths and the dispersion of GTP-bound subunits in the tip region were found to be important in forecasting upcoming phase transitions. Thus, specific MT tip structures and the reaction events that create them are identified as the mechanisms that drive respective transitions between DI phases.