Effects of microtubule mechanics on hydrolysis and catastrophes

Abstract

Abstract. We introduce a model for microtubule mechanics containing lateral bonds between dimers in neighboring protofilaments, bending rigidity of dimers, and repulsive interactions between protofilaments modeling steric constraints to investigate the influence of mechanical forces on hydrolysis and catastrophes. We use the allosteric dimer model, where tubulin dimers are characterized by an equilibrium bending angle, which changes from 0• to 22• by hydrolysis of a dimer. This also affects the lateral interaction and bending energies and, thus, the mechanical equilibrium state of the microtubule. As hydrolysis gives rise to conformational changes in dimers, mechanical forces also influence the hydrolysis rates by mechanical energy changes modulating the hydrolysis rate. The interaction via the microtubule mechanics then gives rise to correlation effects in the hydrolysis dynamics, which have not been taken into account before. Assuming a dominant influence of mechanical energies on hydrolysis rates, we investigate the most probable hydrolysis pathways both for vectorial and random hydrolysis. Investigating the stability with respect to lateral bond rupture, we identify initiation configurations for catastrophes along the hydrolysis pathways and values for a lateral bond rupture force. If we allow for rupturing of lateral bonds between dimers in neighboring protofilaments above this threshold force, our model exhibits avalanche-like catastrophe events.

Chemomechanical Simulation of Microtubule Dynamics With Explicit Lateral Bond Dynamics

“…Hydrolysis of tubulin dimers embedded in a straight MT causes mechanical strain in the tubular structure because the surrounding MT lattice prevents these GDP-tubulin dimers from assuming their preferred bent conformation. This model was employed in almost all previous MT simulation models that consider MT mechanics [14][15][16][17][18][19]. The lattice model, on the other hand, is based on evidence from X-ray and cryo-EM structures [20][21][22][23] and simulations [24,25] that also GTP-tubulin dimers assume a bent conformation and that hydrolysis rather affects the lateral and longitudinal dimer interaction energies.…”

“…Therefore, chemomechanical MT models with explicit bond rupture are a necessity to reproduce catastrophes. We build on existing modeling approaches based on the allosteric model [14][15][16][17][18][19] and include lateral bond rupture as explicit stochastic events with force-dependent rates, which can give important clues about how catastrophes are triggered in the MT structure.…”

“…The influence of tubulin dimer hydrolysis onto the mechanics of the MT lattice suggests that, vice versa, mechanical forces and torques acting on tubulin dimers via strains in the tubular structure could also affect hydrolysis rates, an effect which has been explored only in reference [17] previously. Although this interplay is plausible from a mechanochemistry point of view, experimental verification on the dimer level is extremely difficult and not possible yet, but we can employ chemomechanical MT models to explore and suggest possible implications for the dynamic instability.…”

Mathematical modeling of the microtubule dynamic instability: a new approch of GTP-tubulin hydrolysis

“…This new variable "age" will allow us to take into account the age-dependance of the hydrolysis. Note that the mecanism of hydrolysis has not been fully elucidated, Through many computational and analytical models of MT dynamic instability, it emerges different ideas on mechanism of hydrolysis : random, vectorial or coupled random hydrolysis ( [MK14], [HRT09], [HRL+11]). Since hydrolysis leads to catastrophe, choice of the mechanism of hydrolysis is one of the crucial points to simulate dynamic instability.…”

Mathematical modeling of microtubule dynamic instability: new insight into the link between gtp-hydrolysis and microtubule aging

“…Many computational and analytical models of MT dynamic instability have been developed to describe how the hydrolysis process might work. Some examples include: random hydrolysis, vectorial hydrolysis, or a combination of both random and vectorial hydrolysis [4,16,17,32,33]. To complement our continuous modeling approach, we choose a vectorial description of GTP-tubulin hydrolysis.…”