Nonlinear Dynamics of Microtubules: Biophysical Implications

A recently developed model of nonlinear dynamics for microtubules is further expanded based on the biophysical arguments involving the secondary structure of the constitutive protein tubulin and on the ferroelectric properties of microtubules. It is demonstrated that kink excitations arise due to GTP hydrolysis that causes a dynamical transition in the structure of tubulin. The presence of an intrinsic electric field associated with the structure of a microtubule leads to unidirectional propagation of the kink excitation along the microtubule axis. This mechanism offers an explanation of the dynamic instability phenomenon in terms of the electric field effects. Moreover, a possible elucidation of the unidirectional transport of cargo via motor proteins such as kinesin and dynein is proposed within the model developed in this paper.     

Insight into the GTPase activity of tubulin from complexes with stathmin-like domains

Microtubules are dynamically unstable tubulin polymers that interconvert stochastically between growing and shrinking states, a property central to their cellular functions. Following its incorporation in microtubules, tubulin hydrolyzes one GTP molecule. Microtubule dynamic instability depends on GTP hydrolysis so that this activity is crucial to the regulation of microtubule assembly. Tubulin also has a much lower GTPase activity in solution. We have used ternary complexes made of two tubulin molecules and one stathmin-like domain to investigate the mechanism of the tubulin GTPase activity in solution. We show that whereas stathmin-like domains and colchicine enhance this activity, it is inhibited by vinblastine and by the N-terminal part of stathmin-like domains. Taken together with the structures of the tubulin-colchicine-stathmin-like domain-vinblastine complex and of microtubules, our results lead to the conclusions that the tubulin-colchicine GTPase activity in solution is caused by tubulin-tubulin associations and that the residues involved in catalysis comprise the beta tubulin GTP binding site and alpha tubulin residues that participate in intermolecular interactions in protofilaments. This site resembles the one that has been proposed to give rise to GTP hydrolysis in microtubules. The widely different hydrolysis rates in these two sites result at least in part from the curved and straight tubulin assemblies in solution and in microtubules, respectively.     

Role of GTP hydrolysis in microtubule dynamics: information from a slowly hydrolyzable analogue, GMPCPP.

The role of GTP hydrolysis in microtubule dynamics has been reinvestigated using an analogue of GTP, guanylyl-(alpha, beta)-methylene-diphosphonate (GMPCPP). This analogue binds to the tubulin exchangeable nucleotide binding site (E-site) with an affinity four to eightfold lower than GTP and promotes the polymerization of normal microtubules. The polymerization rate of microtubules with GMPCPP-tubulin is very similar to that of GTP-tubulin. However, in contrast to microtubules polymerized with GTP, GMPCPP-microtubules do not depolymerize rapidly after isothermal dilution. The depolymerization rate of GMPCPP-microtubules is 0.1 s-1 compared with 500 s-1 for GDP-microtubules. GMPCPP also completely suppresses dynamic instability. Contrary to previous work, we find that the beta--gamma bond of GMPCPP is hydrolyzed extremely slowly after incorporation into the microtubule lattice, with a rate constant of 4 x 10(-7) s-1. Because GMPCPP hydrolysis is negligible over the course of a polymerization experiment, it can be used to test the role of hydrolysis in microtubule dynamics. Our results provide strong new evidence for the idea that GTP hydrolysis by tubulin is not required for normal polymerization but is essential for depolymerization and thus for dynamic instability. Because GMPCPP strongly promotes spontaneous nucleation of microtubules, we propose that GTP hydrolysis by tubulin also plays the important biological role of inhibiting spontaneous microtubule nucleation.     

Taxol effect on tubulin polymerization and associated guanosine 5'-triphosphate hydrolysis

Taxol has been used as a tool to investigate the relationship between microtubule assembly and guanosine 5'-triphosphate (GTP) hydrolysis. The data support the model previously proposed [Carlier, M.-F., & Pantaloni, D. (1981) Biochemistry 20, 1918] that GTP hydrolysis is not tightly coupled to the polymerization process but takes place as a monomolecular process following polymerization. The results further indicate that the energy liberated by GTP hydrolysis is not responsible for the subsequent blockage of GDP on polymerized tubulin. When tubulin is polymerized in the presence of 10-100 microM taxol, the rapid formation of a large number of very short microtubules (l less than 1 micron) is accompanied by the development of turbidity to a lesser extent than what is observed when the same weight amount of longer microtubules (l = 5 microns) is formed. A slower subsequent turbidity increase corresponds to the length redistribution of these short microtubules into 3-5-fold longer ones without any change in the weight amount of polymer. The evolution of the rate of length redistribution with the concentration of taxol suggests a model within which taxol would bind to dimeric tubulin and to tubulin present at the ends of microtubules with a somewhat 10-fold lower affinity than to polymerized tubulin embedded in the bulk of microtubules. In agreement with this model, binding of taxol to the tubulin-colchicine complex in the dimeric form could be measured from the increase in the GTPase activity of the tubulin-colchicine complex accompanying taxol binding.     

Microtubules: dissipative structures formed by self-assembly

Microtubules are hollow fibres that form the track upon which chromosomes or proteins, such as kinesins, are transported in the cell. They are formed by the self-assembly of the protein tubulin both in vitro and in vivo. In the cell, their appearance in time and space is strictly controlled by the presence of nucleation centres. Microtubules are very dynamic structures, a property that is obtained by coupling the self-assembly process to the hydrolysis of the nucleotide, guanosine 5′-triphosphate, (GTP). After assembly, GTP is hydrolysed and guanosine 5′-diphosphate, (GDP)-microtubule structure is formed which, although intrinsically very unstable, is stabilised by a small remaining tubulin-GTP-cap at both ends. As such, the ends of microtubules can be considered as gates for entry into the polymeric state. These gates can be blocked by sub-stoichiometric amounts of drugs such as colchicine.

As biological devices, microtubules differ considerably from man-made devices: they are dynamic dissipative structures, made by spontaneous self-assembly. It has been suggested that microtubules could play a role in the conduction and dynamic storage of information. This implies the existence of different conformational states of tubulin.     

Rate-limiting guanosine 5'-triphosphate hydrolysis during nucleotide turnover by FtsZ, a prokaryotic tubulin homologue involved in bacterial cell division

FtsZ is a prokaryotic tubulin homologue that polymerizes into a dynamic ring during cell division. GTP binding and hydrolysis provide the energy for FtsZ dynamics. However, the precise role of hydrolysis in polymer assembly and turnover is not understood, limiting our understanding of how FtsZ functions in the cell. Here we investigate GTP hydrolysis during the FtsZ polymerization cycle using several complementary approaches that avoid technical caveats of previous studies. We find that at steady state approximately 80% of FtsZ polymer subunits are bound to GTP. In addition, we use pre-steady-state, single turnover assays to directly measure the rate of hydrolysis. Hydrolysis was found to occur at approximately 8/min and to be a rate-limiting step in GTP turnover; phosphate release rapidly followed. These results clarify previously conflicting results in the literature and suggest that pure FtsZ polymers, unlike microtubules, may not be able to undergo dynamic instability or to store energy in the polymer for force production.     

Microtubule elongation and guanosine 5'-triphosphate hydrolysis. Role of guanine nucleotides in microtubule dynamics

The tubulin concentration dependence of the rates of microtubule elongation and accompanying GTP hydrolysis has been studied over a large range of tubulin concentration. GTP hydrolysis followed the elongation process closely at low tubulin concentration and became gradually uncoupled at higher concentrations, reaching a limiting rate of 35-40 s-1. The kinetic parameters for microtubule growth were different at low and high tubulin concentrations. Elongation of microtubules has also been studied in solutions containing GDP and GTP in variable proportions. Only traces of GTP present in GDP were necessary to confer a high stability (low critical concentration) to microtubules. Pure GDP-tubulin was found unable to elongate microtubules in the absence of GTP but blocked microtubule ends with an equilibrium dissociation constant of 5-6 microM. These data were accounted for by a model within which, in the presence of GTP-tubulin at high concentration, microtubules grow at a fast rate with a large GTP cap; the GTP cap may be quite short in the region of the critical concentration; microtubule stability is linked to the strong interaction between GTP and GDP subunits at the elongating site; dimeric GDP-tubulin does not have the appropriate conformation to undergo reversible polymerization. These results are discussed with regard to possible role of GDP and GTP and of GTP hydrolysis in microtubule dynamics.     

Mechanism of the microtubule GTPase reaction

The rate of GTP hydrolysis by microtubules has been measured at tubulin subunit concentrations where microtubules undergo net disassembly. This was made possible by using microtubules stabilized against disassembly by reaction with ethylene glycol bis-(succinimidylsuccinate) (EGS) as sites for the addition of tubulin-GTP subunits. The tubulin subunit concentration was varied from 25 to 90% of the steady state concentration, and there was no net elongation of stabilized microtubule seeds. The GTPase rate with EGS microtubules was linearly proportional to the tubulin-GTP subunit concentration when this concentration was varied by dilution and by using GDP to compete with GTP for the tubulin E-site. The linear dependence of the rate is consistent with a GTP mechanism in which hydrolysis is coupled to the tubulin-GTP subunit addition to microtubule ends. It is inconsistent with reaction schemes in which: microtubules are capped by a single tubulin-GTP subunit, which hydrolyzes GTP when a tubulin-GTP subunit adds to the end; hydrolysis occurs primarily in subunits at the interface of a tubulin-GTP cap and the tubulin-GDP microtubule core; hydrolysis is not coupled to subunit addition and occurs randomly in subunits in a tubulin-GTP cap. It was also found that GDP inhibition of the microtubule GTPase rate results from GDP competition for GTP at the tubulin subunit E-site. There is no additional effect of GDP on the GTPase rate resulting from exchange into tubulin subunits at microtubule ends.     

Role of GTP hydrolysis in microtubule polymerization: evidence for a coupled hydrolysis mechanism

The relationship between GTP hydrolysis and microtubule assembly has been investigated by using a rapid filtration method. Microtubules assembled from phosphocellulose-purified tubulin, double-labeled with [gamma-32P]- and [3H]GTP, were trapped and washed free of unbound nucleotide on glass fiber filters. The transient accumulation of microtubule-bound GTP predicted by uncoupled GTP hydrolysis models [Carlier & Pantaloni (1981) Biochemistry 20, 1918-1924; Carlier et al. (1987) Biochemistry 26, 4428-4437] during the rapid assembly of microtubules was not detectable under our experimental conditions. By calculating hypothetical time courses for the transient accumulation of microtubule-bound GTP, we demonstrate that microtubule-bound GTP would have been detectable even if the first-order rate constant for GTP hydrolysis were 4-5 times greater than the pseudo-first-order rate constant for tubulin subunit addition to microtubules. In a similar manner, we demonstrate that if GTP hydrolysis were uncoupled from microtubule assembly but were limited to the interface between GTP subunits and GDP subunits (uncoupled vectorial hydrolysis), then microtubule-bound GTP would have been detectable if GTP hydrolysis became uncoupled from microtubule assembly at less than 50 microM free tubulin, 5 times the steady-state tubulin concentration of our experimental conditions. In addition, during rapid microtubule assembly, we have not detected any microtubule-bound Pi, which has been proposed to form a stabilizing cap at the ends of microtubules [Carlier et al. (1988) Biochemistry 27, 3555-3559]. Also, several conditions that could be expected to increase the degree of potential uncoupling between GTP hydrolysis and microtubule assembly were examined, and no evidence of uncoupling was found. Our results are consistent with models that propose cooperative mechanisms that limit GTP hydrolysis to the terminal ring of tubulin subunits [e.g., O'Brien et al. (1987) Biochemistry 26, 4148-4156]. The results are also consistent with the hypothesis that a slow conformational change in tubulin subunits after GTP hydrolysis and Pi release occurs that results in destabilized microtubule ends when such subunits become exposed at the ends.     

GTP hydrolysis during microtubule assembly

The GTP cap model of dynamic instability [Mitchison, T., & Kirschner, M.W. (1984) Nature (London) 312, 237] postulates that a GTP cap at the end of most microtubules stabilizes the polymer and allows continuing assembly of GTP-tubulin subunits while microtubules without a cap rapidly disassemble. This attractive explanation for observed microtubule behavior is based on the suggestion that hydrolysis of GTP is not coupled to assembly but rather takes place as a first-order reaction after a subunit is assembled onto a polymer end. Carlier and Pantaloni [Carlier, M., & Pantaloni, D. (1981) Biochemistry 20, 1918] reported a lag of hydrolysis behind microtubule assembly and a first-order rate constant for hydrolysis (kh) of 0.25/min. A lag has not been demonstrated by other investigators, and a kh value that specifies such a slow rate of hydrolysis is difficult to reconcile with reported steady-state microtubule growth rates and frequencies of disassembly. We have looked for a lag using tubulin free of microtubule-associated protein at concentrations of 18.5-74 microM, assembly with and without glycerol, and two independent assays of GTP hydrolysis. No lag was observed under any of the conditions employed, with initial rates of hydrolysis increasing in proportion to rates of assembly. If hydrolysis is uncoupled from assembly, we estimate that kh must be at least 2.5/min and could be much greater, a result that we argue may be advantageous to the GTP cap model. We also describe a preliminary model of assembly coupled to hydrolysis that specifies formation and loss of a GTP cap, thus allowing dynamic instability.     

Direct evidence for GTP and GDP-Pi intermediates in microtubule assembly

Identification of the kinetic intermediates in GTP hydrolysis on microtubules and characterization of their assembly properties is essential in understanding microtubule dynamics. By using an improved glass filter assay that selectively traps microtubules with a dead time of 2 s and monitoring taxol-induced rapid assembly of microtubules from [gamma-32P,3H]GTP-tubulin 1:1 complex, direct evidence has been obtained for GTP- and GDP-Pi-microtubule transient states in the early stages of the polymerization process. A simple kinetic analysis of GTP hydrolysis on microtubules within two sequential pseudo-first-order processes led to apparent first-order rate constants of 0.065 s-1 for the cleavage of the gamma-phosphate and 0.02 s-1 for the liberation of Pi, assuming a simple random model. Apparent rate constants for GTP hydrolysis and Pi release were independent of the composition of the buffer used to polymerize tubulin. The significance of these values with respect to those derived from previous studies from this and other laboratories and the possibility of a vectorial model for GTP hydrolysis are discussed.     

Tubulin rings: which way do they curve?

Tubulin is known to exist in at least two main conformations: straight when bound to GTP or buried within the microtubule lattice, and curved when bound to GDP. The latter is most obvious during microtubule depolymerization, when protofilaments bend and peel off from microtubule ends. The curved, low-energy subunits form tantalizing ring structures in the presence of stabilizing divalent cations. Interestingly, cellular factors and antimitotic agents that act by depolymerizing microtubules can induce the formation of rings. In these rings, tubulin dimers generally appear kinked at the monomer-monomer interface, either to the same or to a lesser extent than at the dimer-dimer interface, with each agent giving rise to particular subtleties in the structures of the rings and the tubulin dimer itself that may reflect their distinctive mechanisms of action. How these kinks relate to what happens when the stored energy of GTP hydrolysis is released, freeing GDP*tubulin into an unconstrained state, remains an open question.     

Mechanism of GTP hydrolysis at microtubule ends

The kinetics of tubulin subunits incorporation into microtubules and the kinetics of inorganic phosphate release have been measured in parallel. Correlation of the two measurements indicates that the tubulin GTPase activity is due to GTP hydrolysis and exchange at the end of the microtubules. In some cases where the free GTP available in the medium is in-sufficient the rate of GTP hydrolysis is limited by the rate of tubulin-GTP association at the end of the microtubules. The affinity constant of GTP for the microtubule end appears to be 100 times lower than the affinity constant of the tubulin-GTP complex.     

G protein alpha subunits activate tubulin GTPase and modulate microtubule polymerization dynamics

G proteins serve many functions involving the transfer of signals from cell surface receptors to intracellular effector molecules. Considerable evidence suggests that there is an interaction between G proteins and the cytoskeleton. In this report, G protein alpha subunits Gi1alpha, Gsalpha, and Goalpha are shown to activate the GTPase activity of tubulin, inhibit microtubule assembly, and accelerate microtubule dynamics. Gialpha inhibited polymerization of tubulin-GTP into microtubules by 80-90% in the absence of exogenous GTP. Addition of exogenous GTP, but not guanylylimidodiphosphate, which is resistant to hydrolysis, overcame the inhibition. Analysis of the dynamics of individual microtubules by video microscopy demonstrated that Gi1alpha increases the catastrophe frequency, the frequency of transition from growth to shortening. Thus, Galpha may play a role in modulating microtubule dynamic instability, providing a mechanism for the modification of the cytoskeleton by extracellular signals.     

Effects of organic acids on tubulin polymerization and associated guanosine 5'-triphosphate hydrolysis

We have examined the effects of a number of organic anions, which stabilize tubulin, on tubulin polymerization, associated GTP hydrolysis, and polymer morphology. While microtubule-associated proteins, as well as glycerol, induced formation of typical microtubules in a reaction coupled to GTP hydrolysis at an initial 1:1 stoichiometry, the organic anions had varying effects. Only 2-(N-morpholino)ethanesulfonate induced formation of structures with the morphology of microtubules. With glutamate, fructose 1,6-bisphosphate, piperazine-N-N'-bis(2-ethanesulfonate), glutarate, and glucose 1-phosphate, the predominant structures formed were sheets of parallel protofilaments rather than microtubules. Creatine phosphate induced the formation of clusters of rings. GTP hydrolysis was closely coupled to polymerization only with glutamate. With creatine phosphate, there was minimal GTP hydrolysis. With all other organic anions, GTP hydrolysis substantially exceeded polymerization at all time points, with the onset of hydrolysis significantly preceding the onset of turbidity development. Nevertheless, the rate of GTP hydrolysis was a sigmoidal function of tubulin concentration under all conditions examined, suggesting that tubulin-tubulin interactions are required for hydrolysis. All anion-induced reactions were temperature dependent and cold reversible, but only the creatine phosphate induced reaction was not inhibited by GDP, CA2+, or colchicine and did not require GTP.     

The minimum GTP cap required to stabilize microtubules

Background: Microtubules polymerized from pure tubulin show the unusual property of dynamic instability, in which both growing and shrinking polymers coexist at steady state. Shortly after its addition to a microtubule end, a tubulin subunit hydrolyzes its bound GTP. Studies with non-hydrolyzable analogs have shown that GTP hydrolysis is not required for microtubule assembly, but is essential for generating a dynamic polymer, in which the subunits at the growing tip have bound GTP and those in the bulk of the polymer have bound GDP. It has been suggested that loss of the ‘GTP cap’ through dissociation or hydrolysis exposes the unstable GDP core, leading to rapid depolymerization. However, evidence for a stabilizing cap has been very difficult to obtain.Results We developed an assay to determine the minimum GTP cap necessary to stabilize a microtubule from shrinking. Assembly of a small number of subunits containing a slowly hydrolyzed GTP analog (GMPCPP) onto the end of dynamic microtubules stabilized the polymer to dilution. By labeling the subunits with rhodamine, we measured the size of the cap and found that as few as 40 subunits were sufficient to stabilize a microtubule.Conclusion On the basis of statistical arguments, in which the proportion of stabilized microtubules is compared to the probability that when 40 GMPCPP-tubulin subunits have polymerized onto a microtubule end, all protofilaments have added at least one GMPCPP-tubulin subunit, our measurements of cap size support a model in which a single GTP subunit at the end of each of the 13 protofilaments of a microtubule is sufficient for stabilization. Depolymerization of a microtubule may be initiated by an exposed tubulin–GDP subunit at even a single position. These results have implications for the structure of microtubules and their means of regulation.     

Mechanochemical modeling of dynamic microtubule growth involving sheet-to-tube transition

Microtubule dynamics is largely influenced by nucleotide hydrolysis and the resultant tubulin configuration changes. The GTP cap model has been proposed to interpret the stabilizing mechanisms of microtubule growth from the view of hydrolysis effects. Besides, the growth of a microtubule involves the closure of a curved sheet at its growing end. The curvature conversion from the longitudinal direction to the circumferential direction also helps to stabilize the successive growth, and the curved sheet is referred to as the conformational cap. However, there still lacks theoretical investigation on the mechanical-chemical coupling growth process of microtubules. In this paper, we study the growth mechanisms of microtubules by using a coarse-grained molecular method. First, the closure process involving a sheet-to-tube transition is simulated. The results verify the stabilizing effect of the sheet structure and predict that the minimum conformational cap length that can stabilize the growth is two dimers. Then, we show that the conformational cap and the GTP cap can function independently and harmoniously, signifying the pivotal role of mechanical factors. Furthermore, based on our theoretical results, we describe a Tetris-like growth style of microtubules: the stochastic tubulin assembly is regulated by energy and harmonized with the seam zipping such that the sheet keeps a practically constant length during growth.     

Straight GDP-tubulin protofilaments form in the presence of taxol

Microtubules exist in dynamic equilibrium, growing and shrinking by the addition or loss of tubulin dimers from the ends of protofilaments. The hydrolysis of GTP in beta-tubulin destabilizes the microtubule lattice by increasing the curvature of protofilaments in the microtubule and putting strain on the lattice. The observation that protofilament curvature depends on GTP hydrolysis suggests that microtubule destabilizers and stabilizers work by modulating the curvature of the microtubule lattice itself. Indeed, the microtubule destabilizer MCAK has been shown to increase the curvature of protofilaments during depolymerization. Here, we show that the atomic force microscopy (AFM) of individual tubulin protofilaments provides sufficient resolution to allow the imaging of single protofilaments in their native environment. By using this assay, we confirm previous results for the effects of GTP hydrolysis and MCAK on the conformation of protofilaments. We go on to show that taxol stabilizes microtubules by straightening the GDP protofilament and slowing down the transition of protofilaments from straight to a curved configuration.     

Growth and shortening of microtubules: a two-state model approach

In this study, a two-state mechanochemical model is presented to describe the dynamic instability of microtubules (MTs) in cells. The MT switches between two states, the assembly and disassembly states. In assembly state, the growth of MTs includes two processes: free GTP-tubulin binding to the tip of protofilament (PF) and conformation change of PF, during which the first tubulin unit that curls outwards is rearranged onto the MT surface, using the energy released from the hydrolysis of GTP in the penultimate tubulin unit. In the disassembly state, the shortening of MTs also includes two processes, the release of GDP-tubulin from the tip of PF and the curling of one new tubulin unit out of the MT surface. Switches between these two states, which are usually called rescue and catastrophe, happen stochastically with external force-dependent rates. Using this two-state model with parameters obtained by fitting the recent experimental data, detailed properties of MT growth are obtained. I find that MT is mainly in the assembly state, its mean growth velocity increases with both the external force and the GTP-tubulin concentration, and an MT will shorten on average without an external force. To know more about the external force and GTP-tubulin concentration-dependent properties of MT growth, and for future experimental verification of this two-state model, 11 critical forces are defined and discussed numerically.     

Direct incorporation of guanosine 5'-diphosphate into microtubules without guanosine 5'-triphosphate hydrolysis

Using highly purified calf brain tubulin bearing [8-14C]guanosine 5'-diphosphate (GDP) in the exchangeable nucleotide site and heat-treated microtubule-associated proteins (both components containing negligible amounts of nucleoside diphosphate kinase and nonspecific phosphatase activities), we have found that a significant proportion of exchangeable-site GDP in microtubules can be incorporated directly during guanosine 5'-triphosphate (GTP) dependent polymerization of tubulin, without an initial exchange of GDP for GTP and subsequent GTP hydrolysis during assembly. The precise amount of GDP incorporated directly into microtubules is highly dependent on specific reaction conditions, being favored by high tubulin concentrations, low GTP and Mg2+ concentrations, and exogenous GDP in the reaction mixture. Minimum effects were observed with changes in reaction pH or temperature, changes in concentration of microtubule-associated proteins, alteration of the sulfonate buffer, or the presence of a calcium chelator in the reaction mixture. Under conditions most favorable for direct GDP incorporation, about one-third of the GDP in microtubules is incorporated directly (without GTP hydrolysis) and two-thirds is incorporated hydrolytically (as a consequence of GTP hydrolysis). Direct incorporation of GDP occurs in a constant proportion throughout elongation, and the amount of direct incorporation probably reflects the rapid equilibration of GDP and GTP at the exchangeable site that occurs before the onset of assembly.