Microtubule catastrophe from protofilament dynamics

Abstract

The disappearance of the guanosine triphosphate (GTP)-tubulin cap is widely believed to be the forerunner event for the growth-shrinkage transition ('catastrophe') in microtubule filaments in eukaryotic cells. We study a discrete version of a stochastic model of the GTP cap dynamics, originally proposed by Flyvbjerg, Holy andLeibler (Flyvbjerg, Holy and Leibler, Phys. Rev. Lett. 73, 2372, 1994). Our model includes both spontaneous and vectorial hydrolysis, as well as dissociation of a non-hydrolyzed dimer from the filament after incorporation. In the first part of the paper, we apply this model to a single protofilament of a microtubule. A catastrophe transition is defined for each protofilament, similar to the earlier one-dimensional models, the frequency of occurrence of which is then calculated under various conditions, but without explicit assumption of steady state conditions. Using a perturbative approach, we show that the leading asymptotic behavior of the prot ofilament catastrophe in the limit of large growth velocities is remarkably similar across different models. In the second part of the paper, we extend our analysis to the entire filament by making a conjecture that a minimum number of such transitions are required to occur for the onset of microtubule catastrophe. The frequency of microtubule catastrophe is then determined using numerical simulations, and compared with analytical/semi-analytical estimates made under steady state/quasi-steady state assumptions respectively for the protofilament dynamics. A few relevant experimental results are analyzed in detail, and compared with predictions from the model. Our results indicate that loss of GTP cap in 2-3 protofilaments is necessary to trigger catastrophe in a microtubule.

Signatures of a macroscopic switching transition for a dynamic microtubule

“…7(b), at C  = 11  μM ) are also comparable to the data from experiments9 in the concentration range C  = 10–12  μM . The f c data seem to saturate at times smaller than in experiments, but this feature is similar to another theoretical model based on a multi-step mechanism of catastrophe15. Earlier models of microtubules5 that assume a single-step catastrophe would imply a f c which is a constant, for all times .…”

“…7(c)) that such an analysis leads to n  ≈ 3 over a broader range of k ′/ k . Values of n  ≈ 3 were reported in experiments9 and also in a multi-protofilament based theoretical study15.…”

“…Later experiments revealed that catastrophe events are preceded by multiple kinetic events789, and hence necessitated a more microscopic approach to study the phenomenon. These microscopic models can be broadly categorised into two types: (i) models that account for details of structural and mechanical aspects of the protofilaments and the interactions between them1011121314151617, and (ii) models that use a coarse-grained approach as far as multi-protofilament nature and elastic interactions are concerned but explicitly account for detailed kinetic events such as polymerisation, depolymerisation and hydrolysis of subunits (refs 18, 19, 20, 21, 22, 23, 24 and this work).…”

Regulation of Microtubule Growth and Catastrophe: Unifying Theory and Experiment

“…Thus they can be ruled out. Mixed vectorial/random models can account for the dependence of catastrophe on tubulin concentration [76,77]. However, they cannot account for a second key experimental observation: namely that catastrophe is not a random, single-step process but rather is rather a multi-step process whose rate depends on how long a microtubule has been growing [29,78].…”

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population

“…Age is reset to zero at each catastrophe event, which again starts to grow linearly with time upon the rescue of the filament. Since our objective is to explore the consequences of age-dependent catastrophe on dynamic instability, we do not consider explicitly microscopic events such as addition/removal of monomers and hydrolysis; these enter the formalism implicitly through catastrophe and rescue rates [6,10,15,16].…”