Dilution of individual microtubules observed in real time in vitro: evidence that cap size is small and independent of elongation rate

On the critical concentration for net assembly of dynamically unstable polymers

Cytoskeletal and cytomotive filaments are protein polymers that move molecular cargo and organize cellular contents in all domains of life. A key parameter describing the self-assembly of many of these polymers -including actin filaments and microtubules- is the minimum concentration required for polymer formation. This 'critical concentration for net assembly' (cc N ) is easy to calculate for eukaryotic actins but more difficult for dynamically unstable filaments such as microtubules and some bacterial polymers. To better understand how cells (especially bacteria) regulate assembly of dynamically unstable polymers I investigate the microscopic parameters that influence their critical concentrations. Assuming simple models for spontaneous nucleation and catastrophe I derive expressions for the monomer-polymer balance. In the absence of concentration-dependent rescue, fixed catastrophe rates do not produce clear critical concentrations. In contrast, simple ATP-/GTP-cap models with concentration-dependent catastrophe rates, generate phenomenological critical concentrations that increase linearly with the rate of nucleotide hydrolysis and decrease logarithmically with the rate of spontaneous nucleation.

CLASPs stabilize the pre-catastrophe intermediate state between microtubule growth and shrinkage

Cytoplasmic linker-associated proteins (CLASPs) regulate microtubules in fundamental cellular processes. CLASPs stabilize dynamic microtubules by suppressing microtubule catastrophe and promoting rescue, the switch-like transitions between growth and shrinkage. How CLASPs specifically modulate microtubule transitions is not understood. Here, we investigate the effects of CLASPs on the pre-catastrophe intermediate state of microtubule dynamics, employing distinct microtubule substrates to mimic the intermediate state. Surprisingly, we find that CLASP1 promotes the depolymerization of stabilized microtubules in the presence of GTP, but not in the absence of nucleotide. This activity is also observed for CLASP2 family members and a minimal TOG2-domain construct. Conversely, we find that CLASP1 stabilizes unstable microtubules upon tubulin dilution in the presence of GTP. Strikingly, our results reveal that CLASP1 drives microtubule substrates with vastly different inherent stabilities into the same slowly depolymerizing state in a nucleotide-dependent manner. We interpret this state as the pre-catastrophe intermediate state. Therefore, we conclude that CLASPs suppress microtubule catastrophe by stabilizing the intermediate state between growth and shrinkage.

Effect of tubulin self-association on GTP hydrolysis and nucleotide exchange reactions

We investigated how the self-association of isolated tubulin dimers affects the rate of GTP hydrolysis and the equilibrium of nucleotide exchange. Both reactions are relevant for microtubule (MT) dynamics. We used HPLC to determine the concentrations of GDP and GTP and thereby the GTPase activity of SEC-eluted tubulin dimers in assembly buffer solution, free of glycerol and tubulin aggregates. When GTP hydrolysis was negligible, the nucleotide exchange mechanism was studied by determining the concentrations of tubulin-free and tubulin-bound GTP and GDP. We observed no GTP hydrolysis below the critical conditions for MT assembly (either below the critical tubulin concentration and/or at low temperature), despite the assembly of tubulin 1D curved oligomers and single-rings, showing that their assembly did not involve GTP hydrolysis. Under conditions enabling spontaneous slow MT assembly, a slow pseudo-first-order GTP hydrolysis kinetics was detected, limited by the rate of MT assembly. Cryo-TEM images showed that GTP-tubulin 1D oligomers were curved also at 36 °C. Nucleotide exchange depended on the total tubulin concentration and the molar ratio between tubulin-free GDP and GTP. We used a thermodynamic model of isodesmic tubulin self-association, terminated by the formation of tubulin single-rings to determine the molar fractions of dimers with exposed and buried nucleotide exchangeable sites (E-sites). Our analysis shows that the GDP to GTP exchange reaction equilibrium constant was an order-of-magnitude larger for tubulin dimers with exposed E-sites than for assembled dimers with buried E-sites. This conclusion may have implications on the dynamics at the tip of the MT plus end.

Regulation of microtubule dynamics, mechanics and function through the growing tip

Microtubule dynamics and their control are essential for the normal function and division of all eukaryotic cells. This plethora of functions is, in large part, supported by dynamic microtubule tips, which can bind to various intracellular targets, generate mechanical forces and couple with actin microfilaments. Here, we review progress in the understanding of microtubule assembly and dynamics, focusing on new information about the structure of microtubule tips. First, we discuss evidence for the widely accepted GTP cap model of microtubule dynamics. Next, we address microtubule dynamic instability in the context of structural information about assembly intermediates at microtubule tips. Three currently discussed models of microtubule assembly and dynamics are reviewed. These are considered in the context of established facts and recent data, which suggest that some long-held views must be re-evaluated. Finally, we review structural observations about the tips of microtubules in cells and describe their implications for understanding the mechanisms of microtubule regulation by associated proteins, by mechanical forces and by microtubule-targeting drugs, prominently including cancer chemotherapeutics.

Dynamic Instability from Non-equilibrium Structural Transitions on the Energy Landscape of Microtubule

Microtubules are the backbone of the cytoskeleton and vital to numerous cellular processes. The central dogma of microtubules is that all their functions are driven by dynamic instability, but its mechanism has remained unresolved for over 30 years because of conceptual difficulties inherent in the dominant GTP-cap framework. We present a physically rigorous structural mechanochemical model: dynamic instability is driven by non-equilibrium transitions between the bent (B), straight (S), and curved (C) forms of tubulin monomers and longitudinal interfaces in the two-dimensional lattice of microtubule. All the different phenomena (growth, shortening, catastrophe, rescue, and pausing) are controlled by the kinetic pathways for B↔S↔C transitions and corresponding energy landscapes. Different kinetics at minus end are due to different B↔S↔C pathways imposed by the polarity of microtubule lattice. This model enables us to reproduce all the observed phenomena of dynamic instability of purified tubulins in kinetic simulations.

Microtubule catastrophe under force: mathematical and computational results from a Brownian ratchet model

In the intracellular environment, the intrinsic dynamics of microtubule filaments is often hindered by the presence of barriers of various kind, such as kinetochore complexes and cell cortex, which impact their polymerisation force and dynamical properties such as catastrophe frequency. We present a theoretical study of the effect of a forced barrier, also subjected to thermal noise, on the statistics of catastrophe events in a single microtubule as well as a 'bundle' of two parallel microtubules. For microtubule dynamics, which includes growth, detachment, hydrolysis and the consequent dynamic instability, we employ a one-dimensional discrete stochastic model. The dynamics of the barrier is captured by over-damped Langevin equation, while its interaction with a growing filament is assumed to be hard-core repulsion. A unified treatment of the continuum dynamics of the barrier and the discrete dynamics of the filament is realized using a hybrid Fokker-Planck equation. An explicit mathematical formula for the force-dependent catastrophe frequency of a single microtubule is obtained by solving the above equation, under some assumptions. The prediction agrees well with results of numerical simulations in the appropriate parameter regime. More general situations are studied via numerical simulations. To investigate the extent of 'load-sharing' in a microtubule bundle, and its impact on the frequency of catastrophes, the dynamics of a two-filament bundle is also studied. Here, two parallel, non-interacting microtubules interact with a common, forced barrier. The equations for the two-filament model, when solved using a mean-field assumption, predicts equal sharing of load between the filaments. However, numerical results indicate the existence of a wide spectrum of load-sharing behaviour, which is characterized using a dimensionless parameter.

Pseudo-repeats in doublecortin make distinct mechanistic contributions to microtubule regulation

Doublecortin (DCX) is a neuronal microtubule-associated protein (MAP) indispensable for brain development. Its flexibly linked doublecortin (DC) domains-NDC and CDC-mediate microtubule (MT) nucleation and stabilization, but it is unclear how. Using high-resolution time-resolved cryo-EM, we mapped NDC and CDC interactions with tubulin at different MT polymerization stages and studied their functional effects on MT dynamics using TIRF microscopy. Although coupled, each DC repeat within DCX appears to have a distinct role in MT nucleation and stabilization: CDC is a conformationally plastic module that appears to facilitate MT nucleation and stabilize tubulin-tubulin contacts in the nascent MT lattice, while NDC appears to be favored along the mature lattice, providing MT stabilization. Our structures of MT-bound DC domains also explain in unprecedented detail the DCX mutation-related brain defects observed in the clinic. This modular composition of DCX reflects a common design principle among MAPs where pseudo-repeats of tubulin/MT binding elements chaperone or stabilize distinct conformational transitions to regulate distinct stages of MT dynamic instability.

The Progress of the Anticancer Agents Related to the Microtubules Target

Anticancer drugs based on the microtubules target are potent mitotic spindle poison agents, which interact directly with the microtubules, and were classified as microtubule-stabilizing agents and microtubule-destabilizing agents. Researchers have worked tremendously towards the improvements of anticancer drugs, in terms of improving the efficacy, solubility and reducing the side effects, which brought about advancement in chemotherapy. In this review, we focused on describing the discovery, structures and functions of the microtubules as well as the progress of anticancer agents related to the microtubules, which will provide adequate references for researchers.

Mechanisms of microtubule dynamics and force generation examined with computational modeling and electron cryotomography

Microtubules are dynamic tubulin polymers responsible for many cellular processes, including the capture and segregation of chromosomes during mitosis. In contrast to textbook models of tubulin self-assembly, we have recently demonstrated that microtubules elongate by addition of bent guanosine triphosphate tubulin to the tips of curving protofilaments. Here we explore this mechanism of microtubule growth using Brownian dynamics modeling and electron cryotomography. The previously described flaring shapes of growing microtubule tips are remarkably consistent under various assembly conditions, including different tubulin concentrations, the presence or absence of a polymerization catalyst or tubulin-binding drugs. Simulations indicate that development of substantial forces during microtubule growth and shortening requires a high activation energy barrier in lateral tubulin-tubulin interactions. Modeling offers a mechanism to explain kinetochore coupling to growing microtubule tips under assisting force, and it predicts a load-dependent acceleration of microtubule assembly, providing a role for the flared morphology of growing microtubule ends.

Structural model for differential cap maturation at growing microtubule ends

Microtubules (MTs) are hollow cylinders made of tubulin, a GTPase responsible for essential functions during cell growth and division, and thus, key target for anti-tumor drugs. In MTs, GTP hydrolysis triggers structural changes in the lattice, which are responsible for interaction with regulatory factors. The stabilizing GTP-cap is a hallmark of MTs and the mechanism of the chemical-structural link between the GTP hydrolysis site and the MT lattice is a matter of debate. We have analyzed the structure of tubulin and MTs assembled in the presence of fluoride salts that mimic the GTP-bound and GDP•P_i transition states. Our results challenge current models because tubulin does not change axial length upon GTP hydrolysis. Moreover, analysis of the structure of MTs assembled in the presence of several nucleotide analogues and of taxol allows us to propose that previously described lattice expansion could be a post-hydrolysis stage involved in P_i release.

Microtubule minus-end stability is dictated by the tubulin off-rate

Dynamic organization of microtubule minus ends is vital for the formation and maintenance of acentrosomal microtubule arrays. In vitro, both microtubule ends switch between phases of assembly and disassembly, a behavior called dynamic instability. Although minus ends grow slower, their lifetimes are similar to those of plus ends. The mechanisms underlying these distinct dynamics remain unknown. Here, we use an in vitro reconstitution approach to investigate minus-end dynamics. We find that minus-end lifetimes are not defined by the mean size of the protective GTP-tubulin cap. Rather, we conclude that the distinct tubulin off-rate is the primary determinant of the difference between plus- and minus-end dynamics. Further, our results show that the minus-end-directed kinesin-14 HSET/KIFC1 suppresses tubulin off-rate to specifically suppress minus-end catastrophe. HSET maintains its protective minus-end activity even when challenged by a known microtubule depolymerase, kinesin-13 MCAK. Our results provide novel insight into the mechanisms of minus-end dynamics, essential for our understanding of microtubule minus-end regulation in cells.

Measuring microtubule dynamics

Microtubules are key players in cellular self-organization, acting as structural scaffolds, cellular highways, force generators and signalling platforms. Microtubules are polar filaments that undergo dynamic instability, i.e. transition between phases of growth and shrinkage. This allows microtubules to explore the inner space of the cell, generate pushing and pulling forces and remodel themselves into arrays with different geometry and function such as the mitotic spindle. To do this, eukaryotic cells employ an arsenal of regulatory proteins to control microtubule dynamics spatially and temporally. Plants and microorganisms have developed secondary metabolites that perturb microtubule dynamics, many of which are in active use as cancer chemotherapeutics and anti-inflammatory drugs. Here, we summarize the methods used to visualize microtubules and to measure the parameters of dynamic instability to study both microtubule regulatory proteins and the action of small molecules interfering with microtubule assembly and/or disassembly.

Microtubules and Microtubule-Associated Proteins

Microtubules act as "railways" for motor-driven intracellular transport, interact with accessory proteins to assemble into larger structures such as the mitotic spindle, and provide an organizational framework to the rest of the cell. Key to these functions is the fact that microtubules are "dynamic." As with actin, the polymer dynamics are driven by nucleotide hydrolysis and influenced by a host of specialized regulatory proteins, including microtubule-associated proteins. However, microtubule turnover involves a surprising behavior-termed dynamic instability-in which individual polymers switch stochastically between growth and depolymerization. Dynamic instability allows microtubules to explore intracellular space and remodel in response to intracellular and extracellular cues. Here, we review how such instability is central to the assembly of many microtubule-based structures and to the robust functioning of the microtubule cytoskeleton.

Microtubule assembly governed by tubulin allosteric gain in flexibility and lattice induced fit

Microtubules (MTs) are key components of the cytoskeleton and play a central role in cell division and development. MT assembly is known to be associated with a structural change in αβ-tubulin dimers from kinked to straight conformations. How GTP binding renders individual dimers polymerization-competent, however, is still unclear. Here, we have characterized the conformational dynamics and energetics of unassembled tubulin using atomistic molecular dynamics and free energy calculations. Contrary to existing allosteric and lattice models, we find that GTP-tubulin favors a broad range of almost isoenergetic curvatures, whereas GDP-tubulin has a much lower bending flexibility. Moreover, irrespective of the bound nucleotide and curvature, two conformational states exist differing in location of the anchor point connecting the monomers that affects tubulin bending, with one state being strongly favored in solution. Our findings suggest a new combined model in which MTs incorporate and stabilize flexible GTP-dimers with a specific anchor point state.

Cell Biology: Microtubule Collisions to the Rescue

The proper regulation of microtubule lengths is fundamental to their cellular function. New work now reports that the collision of a growing microtubule end with another object, such as a microtubule, can contribute to the regulation of microtubule lengths by leaving behind damage that ultimately acts to stabilize the microtubule network.

The Roles of β-Tubulin Mutations and Isotype Expression in Acquired Drug Resistance

The antitumor drug paclitaxel stabilizes microtubules and reduces their dynamicity, promoting mitotic arrest and eventually apoptosis. Upon assembly of the α/β-tubulin heterodimer, GTP becomes bound to both the α and β-tubulin monomers. During microtubule assembly, the GTP bound to β-tubulin is hydrolyzed to GDP, eventually reaching steady-state equilibrium between free tubulin dimers and those polymerized into microtubules. Tubulin-binding drugs such as paclitaxel interact with β-tubulin, resulting in the disruption of this equilibrium. In spite of several crystal structures of tubulin, there is little biochemical insight into the mechanism by which anti-tubulin drugs target microtubules and alter their normal behavior. The mechanism of drug action is further complicated, as the description of altered β-tubulin isotype expression and/or mutations in tubulin genes may lead to drug resistance as has been described in the literature. Because of the relationship between β-tubulin isotype expression and mutations within β-tubulin, both leading to resistance, we examined the properties of altered residues within the taxane, colchicine and Vinca binding sites. The amount of data now available, allows us to investigate common patterns that lead to microtubule disruption and may provide a guide to the rational design of novel compounds that can inhibit microtubule dynamics for specific tubulin isotypes or, indeed resistant cell lines. Because of the vast amount of data published to date, we will only provide a broad overview of the mutational results and how these correlate with differences between tubulin isotypes. We also note that clinical studies describe a number of predictive factors for the response to anti-tubulin drugs and attempt to develop an understanding of the features within tubulin that may help explain how they may affect both microtubule assembly and stability.

Understanding force-generating microtubule systems through in vitro reconstitution

Microtubules switch between growing and shrinking states, a feature known as dynamic instability. The biochemical parameters underlying dynamic instability are modulated by a wide variety of microtubule-associated proteins that enable the strict control of microtubule dynamics in cells. The forces generated by controlled growth and shrinkage of microtubules drive a large range of processes, including organelle positioning, mitotic spindle assembly, and chromosome segregation. In the past decade, our understanding of microtubule dynamics and microtubule force generation has progressed significantly. Here, we review the microtubule-intrinsic process of dynamic instability, the effect of external factors on this process, and how the resulting forces act on various biological systems. Recently, reconstitution-based approaches have strongly benefited from extensive biochemical and biophysical characterization of individual components that are involved in regulating or transmitting microtubule-driven forces. We will focus on the current state of reconstituting increasingly complex biological systems and provide new directions for future developments.

Mechanisms of kinetic stabilization by the drugs paclitaxel and vinblastine

Chemotherapeutic agents that target microtubule dynamics promote a universal phenotype of kinetic stabilization. Integrated computational modeling and fluorescence microscopy identify the fundamental kinetic and thermodynamic mechanisms that result in kinetic stabilization, specifically by the drugs paclitaxel and vinblastine.

Microtubule-targeting agents (MTAs), widely used as biological probes and chemotherapeutic drugs, bind directly to tubulin subunits and “kinetically stabilize” microtubules, suppressing the characteristic self-assembly process of dynamic instability. However, the molecular-level mechanisms of kinetic stabilization are unclear, and the fundamental thermodynamic and kinetic requirements for dynamic instability and its elimination by MTAs have yet to be defined. Here we integrate a computational model for microtubule assembly with nanometer-scale fluorescence microscopy measurements to identify the kinetic and thermodynamic basis of kinetic stabilization by the MTAs paclitaxel, an assembly promoter, and vinblastine, a disassembly promoter. We identify two distinct modes of kinetic stabilization in live cells, one that truly suppresses on-off kinetics, characteristic of vinblastine, and the other a “pseudo” kinetic stabilization, characteristic of paclitaxel, that nearly eliminates the energy difference between the GTP- and GDP-tubulin thermodynamic states. By either mechanism, the main effect of both MTAs is to effectively stabilize the microtubule against disassembly in the absence of a robust GTP cap.

Molecular and Mechanical Causes of Microtubule Catastrophe and Aging

Tubulin polymers, microtubules, can switch abruptly from the assembly to shortening. These infrequent transitions, termed "catastrophes", affect numerous cellular processes but the underlying mechanisms are elusive. We approached this complex stochastic system using advanced coarse-grained molecular dynamics modeling of tubulin-tubulin interactions. Unlike in previous simplified models of dynamic microtubules, the catastrophes in this model arise owing to fluctuations in the composition and conformation of a growing microtubule tip, most notably in the number of protofilament curls. In our model, dynamic evolution of the stochastic microtubule tip configurations over a long timescale, known as the system's "aging", gives rise to the nonexponential distribution of microtubule lifetimes, consistent with experiment. We show that aging takes place in the absence of visible changes in the microtubule wall or tip, as this complex molecular-mechanical system evolves slowly and asymptotically toward the steady-state level of the catastrophe-promoting configurations. This new, to our knowledge, theoretical basis will assist detailed mechanistic investigations of the mechanisms of action of different microtubule-binding proteins and drugs, thereby enabling accurate control over the microtubule dynamics to treat various pathologies.

Regulation of Microtubule Growth and Catastrophe: Unifying Theory and Experiment

Recent studies have found that microtubule-associated proteins (MAPs) can regulate the dynamical properties of microtubules in unexpected ways. For most MAPs, there is an inverse relationship between their effects on the speed of growth and the frequency of catastrophe, the conversion of a growing microtubule to a shrinking one. Such a negative correlation is predicted by the standard GTP-cap model, which posits that catastrophe is due to loss of a stabilizing cap of GTP-tubulin at the end of a growing microtubule. However, many other MAPs, notably Kinesin-4 and combinations of EB1 with XMAP215, contradict this general rule. In this review, we show that a more nuanced, but still simple, GTP-cap model, can account for the diverse regulatory activities of MAPs.

Microtubule aging probed by microfluidics-assisted tubulin washout

Microtubule aging—the decrease of stability with age—is an interesting but mechanistically not understood property of microtubules. It constrains possible mechanisms of catastrophe induction and is believed to be crucial for length regulation. New in vitro experiments and model fits provide insight into the origin of microtubule aging.

Microtubules switch stochastically between phases of growth and shrinkage. The molecular mechanism responsible for the end of a growth phase, an event called catastrophe, is still not understood. The probability for a catastrophe to occur increases with microtubule age, putting constraints on the possible molecular mechanism of catastrophe induction. Here we used microfluidics-assisted fast tubulin washout experiments to induce microtubule depolymerization in a controlled manner at different times after the start of growth. We found that aging can also be observed in this assay, providing valuable new constraints against which theoretical models of catastrophe induction can be tested. We found that the data can be quantitatively well explained by a simple kinetic threshold model that assumes an age-dependent broadening of the protective cap at the microtubule end as a result of an evolving tapered end structure; this leads to a decrease of the cap density and its stability. This analysis suggests an intuitive picture of the role of morphological changes of the protective cap for the age dependence of microtubule stability.

The size of the EB cap determines instantaneous microtubule stability

The function of microtubules relies on their ability to switch between phases of growth and shrinkage. A nucleotide-dependent stabilising cap at microtubule ends is thought to be lost before this switch can occur; however, the nature and size of this protective cap are unknown. Using a microfluidics-assisted multi-colour TIRF microscopy assay with close-to-nm and sub-second precision, we measured the sizes of the stabilizing cap of individual microtubules. We find that the protective caps are formed by the extended binding regions of EB proteins. Cap lengths vary considerably and longer caps are more stable. Nevertheless, the trigger of instability lies in a short region at the end of the cap, as a quantitative model of cap stability demonstrates. Our study establishes the spatial and kinetic characteristics of the protective cap and provides an insight into the molecular mechanism by which its loss leads to the switch from microtubule growth to shrinkage.

DOI:http://dx.doi.org/10.7554/eLife.13470.001

Much like the skeleton supports the human body, a structure called the cytoskeleton provides support and structure to cells. Part of this cytoskeleton is made up of small tubes called microtubules that – unlike bones – can shrink and grow very quickly. This allows the cell to change shape, move and split into two new cells.

Exactly how the microtubules switch between growing and shrinking was not clear. One suggestion is that a protective cap at the end of microtubule allows it to keep growing and prevents it from shrinking. However, the nature and size of this cap have been debated.

Now, Duellberg et al. have measured the caps of microtubules with high precision by combining the techniques of microfluidics, TIRF microscopy and recently developed image analysis tools. This revealed that the cap sizes change, with longer caps being more stable. In addition, proteins called end-binding proteins can destabilize the cap by binding to it. This allows microtubules to switch from a growing to a shrinking state more often.

Future work could now investigate how changes in cap length cause the microtubules to switch from growing to shrinking. It also remains to be seen whether other proteins also influence the cap to control this switching behaviour.

DOI:http://dx.doi.org/10.7554/eLife.13470.002

May I check your cap?

Modernizing a classic technique to study microtubules has revealed that the stability of a microtubule is related to its growth rate.

Mutations in Human Tubulin Proximal to the Kinesin-Binding Site Alter Dynamic Instability at Microtubule Plus- and Minus-Ends

The assembly of microtubule-based cellular structures depends on regulated tubulin polymerization and directional transport. Here, we purify and characterize tubulin heterodimers that have human β-tubulin isotype III (TUBB3), as well as heterodimers with one of two β-tubulin mutations (D417H or R262H). Both point mutations are proximal to the kinesin-binding site and have been linked to an ocular motility disorder in humans. Compared to wild-type, microtubules with these mutations have decreased catastrophe frequencies and increased average lifetimes of plus- and minus-end-stabilizing caps. Importantly, the D417H mutation does not alter microtubule lattice structure or Mal3 binding to growing filaments. Instead, this mutation reduces the affinity of tubulin for TOG domains and colchicine, suggesting that the distribution of tubulin heterodimer conformations is changed. Together, our findings reveal how residues on the surface of microtubules, distal from the GTP-hydrolysis site and inter-subunit contacts, can alter polymerization dynamics at the plus- and minus-ends of microtubules.

Ectopic A-lattice seams destabilize microtubules

Natural microtubules typically include one A-lattice seam within an otherwise helically symmetric B-lattice tube. It is currently unclear how A-lattice seams influence microtubule dynamic instability. Here we find that including extra A-lattice seams in GMPCPP microtubules, structural analogues of the GTP caps of dynamic microtubules, destabilizes them, enhancing their median shrinkage rate by >20-fold. Dynamic microtubules nucleated by seeds containing extra A-lattice seams have growth rates similar to microtubules nucleated by B-lattice seeds, yet have increased catastrophe frequencies at both ends. Furthermore, binding B-lattice GDP microtubules to a rigor kinesin surface stabilizes them against shrinkage, whereas microtubules with extra A-lattice seams are stabilized only slightly. Our data suggest that introducing extra A-lattice seams into dynamic microtubules destabilizes them by destabilizing their GTP caps. On this basis, we propose that the single A-lattice seam of natural B-lattice MTs may act as a trigger point, and potentially a regulation point, for catastrophe.

The contribution of αβ-tubulin curvature to microtubule dynamics

Microtubules are dynamic polymers of αβ-tubulin that form diverse cellular structures, such as the mitotic spindle for cell division, the backbone of neurons, and axonemes. To control the architecture of microtubule networks, microtubule-associated proteins (MAPs) and motor proteins regulate microtubule growth, shrinkage, and the transitions between these states. Recent evidence shows that many MAPs exert their effects by selectively binding to distinct conformations of polymerized or unpolymerized αβ-tubulin. The ability of αβ-tubulin to adopt distinct conformations contributes to the intrinsic polymerization dynamics of microtubules. αβ-Tubulin conformation is a fundamental property that MAPs monitor and control to build proper microtubule networks.

Microtubule plus-end tracking proteins and their roles in cell division

Microtubules are cellular components that are required for a variety of essential processes such as cell motility, mitosis, and intracellular transport. This is possible because of the inherent dynamic properties of microtubules. Many of these properties are tightly regulated by a number of microtubule plus-end-binding proteins or +TIPs. These proteins recognize the distal end of microtubules and are thus in the right context to control microtubule dynamics. In this review, we address how microtubule dynamics are regulated by different +TIP families, focusing on how functionally diverse +TIPs spatially and temporally regulate microtubule dynamics during animal cell division.

Evolving tip structures can explain age-dependent microtubule catastrophe

Microtubules are key structural and transport elements in cells. The dynamics at microtubule ends are characterized by periods of slow growth, followed by stochastic switching events termed "catastrophes," in which microtubules suddenly undergo rapid shortening. Growing microtubules are thought to be protected from catastrophe by a GTP-tubulin "cap": GTP-tubulin subunits add to the tips of growing microtubules but are subsequently hydrolyzed to GDP-tubulin subunits once they are incorporated into the microtubule lattice. Loss of the GTP-tubulin cap exposes GDP-tubulin subunits at the microtubule tip, resulting in a catastrophe event. However, the mechanistic basis for sudden loss of the GTP cap, leading to catastrophe, is not known. To investigate microtubule catastrophe events, we performed 3D mechanochemical simulations that account for interactions between neighboring protofilaments. We found that there are two separate factors that contribute to catastrophe events in the 3D simulation: the GTP-tubulin cap size, which settles into a steady-state value that depends on the free tubulin concentration during microtubule growth, and the structure of the microtubule tip. Importantly, 3D simulations predict, and both fluorescence and electron microscopy experiments confirm, that microtubule tips become more tapered as the microtubule grows. This effect destabilizes the tip and ultimately contributes to microtubule catastrophe. Thus, the likelihood of a catastrophe event may be intimately linked to the aging physical structure of the growing microtubule tip. These results have important consequences for catastrophe regulation in cells, as microtubule-associated proteins could promote catastrophe events in part by modifying microtubule tip structures.

Microtubule dynamic instability: a new model with coupled GTP hydrolysis and multistep catastrophe

A key question in understanding microtubule dynamics is how GTP hydrolysis leads to catastrophe, the switch from slow growth to rapid shrinkage. We first provide a review of the experimental and modeling literature, and then present a new model of microtubule dynamics. We demonstrate that vectorial, random, and coupled hydrolysis mechanisms are not consistent with the dependence of catastrophe on tubulin concentration and show that, although single-protofilament models can explain many features of dynamics, they do not describe catastrophe as a multistep process. Finally, we present a new combined (coupled plus random hydrolysis) multiple-protofilament model that is a simple, analytically solvable generalization of a single-protofilament model. This model accounts for the observed lifetimes of growing microtubules, the delay to catastrophe following dilution and describes catastrophe as a multistep process.

Models of assembly and disassembly of individual microtubules: stochastic and averaged equations

In this paper we present solutions of the master equations for the microtubule length and show that the local probability for rescues or catastrophes can lead to bell-shaped length histograms. Conversely, as already known, non-local probabilities for these events result in exponential length histograms. We also derive master equations for a stabilizing cap and obtain a new boundary condition which provides an explanation of the results obtained in dilution and cutting experiments.

Microtubule catastrophe and rescue

Microtubules are long cylindrical polymers composed of tubulin subunits. In cells, microtubules play an essential role in architecture and motility. For example, microtubules give shape to cells, serve as intracellular transport tracks, and act as key elements in important cellular structures such as axonemes and mitotic spindles. To accomplish these varied functions, networks of microtubules in cells are very dynamic, continuously remodeling through stochastic length fluctuations at the ends of individual microtubules. The dynamic behavior at the end of an individual microtubule is termed 'dynamic instability'. This behavior manifests itself by periods of persistent microtubule growth interrupted by occasional switching to rapid shrinkage (called microtubule 'catastrophe'), and then by switching back from shrinkage to growth (called microtubule 'rescue'). In this review, we summarize recent findings which provide new insights into the mechanisms of microtubule catastrophe and rescue, and discuss the impact of these findings in regards to the role of microtubule dynamics inside of cells.

Dynamics and length distribution of microtubules under force and confinement

We investigate the microtubule polymerization dynamics with catastrophe and rescue events for three different confinement scenarios, which mimic typical cellular environments: (i) The microtubule is confined by rigid and fixed walls, (ii) it grows under constant force, and (iii) it grows against an elastic obstacle with a linearly increasing force. We use realistic catastrophe models and analyze the microtubule dynamics, the resulting microtubule length distributions, and force generation by stochastic and mean field calculations; in addition, we perform stochastic simulations. Freely growing microtubules exhibit a phase of bounded growth with finite microtubule length and a phase of unbounded growth. The main results for the three confinement scenarios are as follows: (i) In confinement by fixed rigid walls, we find exponentially decreasing or increasing stationary microtubule length distributions instead of bounded or unbounded phases, respectively. We introduce a realistic model for wall-induced catastrophes and investigate the behavior of the average length as a function of microtubule growth parameters. (ii) Under a constant force, the boundary between bounded and unbounded growth is shifted to higher tubulin concentrations and rescue rates. The critical force f(c) for the transition from unbounded to bounded growth increases logarithmically with tubulin concentration and the rescue rate, and it is smaller than the stall force. (iii) For microtubule growth against an elastic obstacle, the microtubule length and polymerization force can be regulated by microtubule growth parameters. For zero rescue rate, we find that the average polymerization force depends logarithmically on the tubulin concentration and is always smaller than the stall force in the absence of catastrophes and rescues. For a nonzero rescue rate, we find a sharply peaked steady-state length distribution, which is tightly controlled by microtubule growth parameters. The corresponding average microtubule length self-organizes such that the average polymerization force equals the critical force f(c) for the transition from unbounded to bounded growth. We also investigate the force dynamics if growth parameters are perturbed in dilution experiments. Finally, we show the robustness of our results against changes of catastrophe models and load distribution factors.

Estimating the microtubule GTP cap size in vivo

Microtubules (MTs) polymerize via net addition of GTP-tubulin subunits to the MT plus end, which subsequently hydrolyze to GDP-tubulin in the MT lattice. Relatively stable GTP-tubulin subunits create a "GTP cap" at the growing MT plus end that suppresses catastrophe. To understand MT assembly regulation, we need to understand GTP hydrolysis reaction kinetics and the GTP cap size. In vitro, the GTP cap has been estimated to be as small as one layer (13 subunits) or as large as 100-200 subunits. GTP cap size estimates in vivo have not yet been reported. Using EB1-EGFP as a marker for GTP-tubulin in epithelial cells, we find on average (1) 270 EB1 dimers bound to growing MT plus ends, and (2) a GTP cap size of ∼750 tubulin subunits. Thus, in vivo, the GTP cap is far larger than previous estimates in vitro, and ∼60-fold larger than a single layer cap. We also find that the tail of a large GTP cap promotes MT rescue and suppresses shortening. We speculate that a large GTP cap provides a locally concentrated scaffold for tip-tracking proteins and confers persistence to assembly in the face of physical barriers such as the cell cortex.

Random hydrolysis controls the dynamic instability of microtubules

Uncovering mechanisms that control the dynamics of microtubules is fundamental for our understanding of multiple cellular processes such as chromosome separation and cell motility. Building on previous theoretical work on the dynamic instability of microtubules, we propose here a stochastic model that includes all relevant biochemical processes that affect the dynamics of microtubule plus-end, namely, the binding of GTP-bound monomers, unbinding of GTP- and GDP-bound monomers, and hydrolysis of GTP monomers. The inclusion of dissociation processes, present in our approach but absent from many previous studies, is essential to guarantee the thermodynamic consistency of the model. Our theoretical method allows us to compute all dynamic properties of microtubules explicitly. Using experimentally determined rates, it is found that the cap size is ∼3.6 layers, an estimate that is compatible with several experimental observations. In the end, our model provides a comprehensive description of the dynamic instability of microtubules that includes not only the statistics of catastrophes but also the statistics of rescues.

Depolymerizing kinesins Kip3 and MCAK shape cellular microtubule architecture by differential control of catastrophe

Microtubules are dynamic filaments whose ends alternate between periods of slow growth and rapid shortening as they explore intracellular space and move organelles. A key question is how regulatory proteins modulate catastrophe, the conversion from growth to shortening. To study this process, we reconstituted microtubule dynamics in the absence and presence of the kinesin-8 Kip3 and the kinesin-13 MCAK. Surprisingly, we found that, even in the absence of the kinesins, the microtubule catastrophe frequency depends on the age of the microtubule, indicating that catastrophe is a multistep process. Kip3 slowed microtubule growth in a length-dependent manner and increased the rate of aging. In contrast, MCAK eliminated the aging process. Thus, both kinesins are catastrophe factors; Kip3 mediates fine control of microtubule length by narrowing the distribution of maximum lengths prior to catastrophe, whereas MCAK promotes rapid restructuring of the microtubule cytoskeleton by making catastrophe a first-order random process.

The mechanisms of microtubule catastrophe and rescue: implications from analysis of a dimer-scale computational model

ETOC: The behavior of a dimer-scale computational model predicts that short interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks govern both catastrophe and rescue.

Microtubule (MT) dynamic instability is fundamental to many cell functions, but its mechanism remains poorly understood, in part because it is difficult to gain information about the dimer-scale events at the MT tip. To address this issue, we used a dimer-scale computational model of MT assembly that is consistent with tubulin structure and biochemistry, displays dynamic instability, and covers experimentally relevant spans of time. It allows us to correlate macroscopic behaviors (dynamic instability parameters) with microscopic structures (tip conformations) and examine protofilament structure as the tip spontaneously progresses through both catastrophe and rescue. The model's behavior suggests that several commonly held assumptions about MT dynamics should be reconsidered. Moreover, it predicts that short, interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks influence both catastrophe and rescue. We conclude that experimentally observed microtubule behavior can best be explained by a “stochastic cap” model in which tubulin subunits hydrolyze GTP according to a first-order reaction after they are incorporated into the lattice; catastrophe and rescue result from stochastic fluctuations in the size, shape, and extent of lateral bonding of the cap.

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.

Macroscopic simulations of microtubule dynamics predict two steady-state processes governing array morphology

Microtubule polymers typically function through their collective organization into a patterned array. The formation of the pattern, whether it is a relatively simple astral array or a highly complex mitotic spindle, relies on controlled microtubule nucleation and the basal dynamics parameters governing polymer growth and shortening. We have investigated the interaction between the microtubule nucleation and dynamics parameters, using macroscopic Monte Carlo simulations, to determine how these parameters contribute to the underlying microtubule array morphology (i.e. polymer density and length distribution). In addition to the well-characterized steady state achieved between free tubulin subunits and microtubule polymer, we propose that microtubule nucleation and extinction constitute a second, interdependent steady state process. Our simulation studies show that the magnitude of both nucleation and extinction additively impacts the final steady state free subunit concentration. We systematically varied individual microtubule dynamics parameters to survey the effects on array morphology and find specific sensitivity to perturbations of catastrophe frequency. Altering the cellular context for the microtubule array, we find that nucleation template number plays a defining role in shaping the microtubule length distribution and polymer density.

How to measure microtubule dynamics?

Microtubules are one of the most spectacular features in the cell: long, fairly rigid tubules that provide physical strength while at the same time serving as tracks of the intracellular transport network. In addition, they are the main constituents of the cell division machinery, and guide axonal growth and the direction of cell migration. To be able to fulfil such diverse functions, microtubules have to be arranged into suitable patterns and remodelled according to extra- and intracellular cues. Moreover, the delicate regulation of microtubule dynamics and the dynamic interactions with subcellular structures, such as kinetochores or cell adhesion sites, appear to be of crucial importance to microtubule functions. It is, therefore, important to understand microtubule dynamics and its spatiotemporal regulation at the molecular level. In this chapter, I introduce the concept of microtubule dynamics and discuss the techniques that can be employed to study microtubule dynamics in vitro and in cells, for many of which detailed protocols can be found in this volume. Microtubule dynamics is traditionally assessed by the four parameters of dynamic instability: growth and shrinkage rates, rescue and catastrophe frequencies, sometimes supplemented by pause duration. I discuss emerging issues with and alternatives to this parameter description of microtubule dynamics.

Structure-specific recognition protein 1 facilitates microtubule growth and bundling required for mitosis

Tight regulation of microtubule (MT) dynamics is essential for proper chromosome movement during mitosis. Here we show, using mammalian cells, that structure-specific recognition protein 1 (SSRP1) is a novel regulator of MT dynamics. SSRP1 colocalizes with the spindle and midbody MTs, and associates with MTs both in vitro and in vivo. Purified SSRP1 facilitates tubulin polymerization and MT bundling in vitro. Knockdown of SSRP1 inhibits the growth of MTs and leads to disorganized spindle structures, reduction of K-fibers and midbody fibers, disrupted chromosome movement, and attenuated cytokinesis in vivo. These results demonstrate that SSRP1 is crucial for MT growth and spindle assembly during mitosis.

A theory of microtubule catastrophes and their regulation

Dynamic instability, in which abrupt transitions occur between growing and shrinking states, is an intrinsic property of microtubules that is regulated by both mechanics and specialized proteins. We discuss a model of dynamic instability based on the popular idea that growth is maintained by a cap at the tip of the fiber. The loss of this cap is thought to trigger the transition from growth to shrinkage, called a catastrophe. The model includes longitudinal interactions between the terminal tubulins of each protofilament and "gating rescues" between neighboring protofilaments. These interactions allow individual protofilaments to transiently shorten during a phase of overall microtubule growth. The model reproduces the reported dependency of the catastrophe rate on tubulin concentration, the time between tubulin dilution and catastrophe, and the induction of microtubule catastrophes by walking depolymerases. The model also reproduces the comet tail distribution that is characteristic of proteins that bind to the tips of growing microtubules.

A protein diffusion model of the sealing effect

Water transport across the arterial endothelium is believed primarily to occur through breaks in the tight junction strands at the cell periphery between neighboring cells. Additional proteins arriving at the tight junction can close these breaks, thereby attenuating this water flux. Motivated by evidence that the diffusion of presynthesized protein from the interior of the cell to and incorporation into the cell border is the mechanism of endothelial tight junctional sealing, we develop a diffusion-limited mathematical model of intercellular gap sealing. A single endothelial cell is represented as a thin, axisymmetric disk, initially containing a uniform distribution of junctional protein that does not interact with the apical or basal cell surfaces. Upon application of a transmural pressure gradient, water flows through the junctional cleft, and tight junction remodeling begins. We assume that proteins at the junction are instantaneously incorporated into its strand, dropping the free protein concentration at the cell periphery to zero. This sets the diffusion of intracellular proteins toward the junction in motion. The solution of this one-dimensional initial value problem provides excellent fits to current and previously published experimental data over a wide variety of conditions. It yields three physically meaningful parameters for each fit, including a protein diffusivity in the cytoplasm that varies little within experimental treatments. Statistical variation of these parameters allows rational comparison of experimental runs and identification of outlier runs.

A thermodynamic model of microtubule assembly and disassembly

Microtubules are self-assembling polymers whose dynamics are essential for the normal function of cellular processes including chromosome separation and cytokinesis. Therefore understanding what factors effect microtubule growth is fundamental to our understanding of the control of microtubule based processes. An important factor that determines the status of a microtubule, whether it is growing or shrinking, is the length of the GTP tubulin microtubule cap. Here, we derive a Monte Carlo model of the assembly and disassembly of microtubules. We use thermodynamic laws to reduce the number of parameters of our model and, in particular, we take into account the contribution of water to the entropy of the system. We fit all parameters of the model from published experimental data using the GTP tubulin dimer attachment rate and the lateral and longitudinal binding energies of GTP and GDP tubulin dimers at both ends. Also we calculate and incorporate the GTP hydrolysis rate. We have applied our model and can mimic published experimental data, which formerly suggested a single layer GTP tubulin dimer microtubule cap, to show that these data demonstrate that the GTP cap can fluctuate and can be several microns long.

Polyamine sharing between tubulin dimers favours microtubule nucleation and elongation via facilitated diffusion

We suggest for the first time that the action of multivalent cations on microtubule dynamics can result from facilitated diffusion of GTP-tubulin to the microtubule ends. Facilitated diffusion can promote microtubule assembly, because, upon encountering a growing nucleus or the microtubule wall, random GTP-tubulin sliding on their surfaces will increase the probability of association to the target sites (nucleation sites or MT ends). This is an original explanation for understanding the apparent discrepancy between the high rate of microtubule elongation and the low rate of tubulin association at the microtubule ends in the viscous cytoplasm. The mechanism of facilitated diffusion requires an attraction force between two tubulins, which can result from the sharing of multivalent counterions. Natural polyamines (putrescine, spermidine, and spermine) are present in all living cells and are potent agents to trigger tubulin self-attraction. By using an analytical model, we analyze the implication of facilitated diffusion mediated by polyamines on nucleation and elongation of microtubules. In vitro experiments using pure tubulin indicate that the promotion of microtubule assembly by polyamines is typical of facilitated diffusion. The results presented here show that polyamines can be of particular importance for the regulation of the microtubule network in vivo and provide the basis for further investigations into the effects of facilitated diffusion on cytoskeleton dynamics.

The formin mDia2 stabilizes microtubules independently of its actin nucleation activity

A critical microtubule (MT) polarization event in cell migration is the Rho/mDia-dependent stabilization of a subset of MTs oriented toward the direction of migration. Although mDia nucleates actin filaments, it is unclear whether this or a separate activity of mDia underlies MT stabilization. We generated two actin mutants (K853A and I704A) in a constitutively active version of mDia2 containing formin homology domains 1 and 2 (FH1FH2) and found that they still induced stable MTs and bound to the MT TIP proteins EB1 and APC, which have also been implicated in MT stabilization. A dimerization-impaired mutant of mDia2 (W630A) also generated stable MTs in cells. We examined whether FH1FH2mDia2 had direct activity on MTs in vitro and found that it bound directly to MTs, stabilized MTs against cold- and dilution-induced disassembly, and reduced the rates of growth and shortening during MT assembly and disassembly, respectively. These results indicate that mDia2 has a novel MT stabilization activity that is separate from its actin nucleation activity.

Microtubule assembly of isotypically purified tubulin and its mixtures

Numerous isotypes of the structural protein tubulin have now been characterized in various organisms and their expression offers a plausible explanation for observed differences affecting microtubule function in vivo. While this is an attractive hypothesis, there are only a handful of studies demonstrating a direct influence of tubulin isotype composition on the dynamic properties of microtubules. Here, we present the results of experimental assays on the assembly of microtubules from bovine brain tubulin using purified isotypes at various controlled relative concentrations. A novel data analysis is developed using recursive maps which are shown to be related to the master equation formalism. We have found striking similarities between the three isotypes of bovine tubulin studied in regard to their dynamic instability properties, except for subtle differences in their catastrophe frequencies. When mixtures of tubulin isotypes are analyzed, their nonlinear concentration dependence is modeled and interpreted in terms of lower affinities of tubulin dimers belonging to the same isotype than those that represent different isotypes indicating hitherto unsuspected influences of tubulin dimers on each other within a microtubule. Finally, we investigate the fluctuations in microtubule assembly and disassembly rates and conclude that the inherent rate variability may signify differences in the guanosine-5'-triphosphate composition of the growing and shortening microtubule tips. It is the main objective of this article to develop a quantitative model of tubulin polymerization for individual isotypes and their mixtures. The possible biological significance of the observed differences is addressed.

Three-dimensional microtubule behavior in Xenopus egg extracts reveals four dynamic states and state-dependent elastic properties

Although microtubules are key players in many cellular processes, very little is known about their dynamic and mechanical properties in physiological three-dimensional environments. The conventional model of microtubule dynamic instability postulates two dynamic microtubule states, growth and shrinkage. However, several studies have indicated that such a model does not provide a comprehensive quantitative and qualitative description of microtubule behavior. Using three-dimensional laser light-sheet fluorescence microscopy and a three-dimensional sample preparation in spacious Teflon cylinders, we measured microtubule dynamic instability and elasticity in interphase Xenopus laevis egg extracts. Our data are inconsistent with a two-state model of microtubule dynamic instability and favor an extended four-state model with two independent metastable pause states over a three-state model with a single pause state. Moreover, our data on kinetic state transitions rule out a simple GTP cap model as the driving force of microtubule stabilization in egg extracts on timescales of a few seconds or longer. We determined the three-dimensional elastic properties of microtubules as a function of both the contour length and the dynamic state. Our results indicate that pausing microtubules are less flexible than growing microtubules and suggest a growth-speed-dependent persistence length. These data might hint toward mechanisms that enable microtubules to efficiently perform multiple different tasks in the cell and suggest the development of a unified model of microtubule dynamics and microtubule mechanics.

TheDrosophilaCLASP homologue, Mast/Orbit regulates the dynamic behaviour of interphase microtubules by promoting the pause state

An important group of microtubule associated proteins are the plus-end tracking proteins which includes the Mast/Orbit/CLASPs family amongst others. Several of these proteins have important functions during interphase and mitosis in the modulation of the dynamic properties of microtubules, however, the precise mechanism remains to be elucidated. To investigate the role of Mast in the regulation of microtubule behaviour during interphase, we used RNAi in Drosophila S2 culture cells stably expressing GFP-alpha-tubulin and followed the behaviour of microtubules in vivo. Mast depleted cells show a significant reduction of microtubule density and an abnormal interphase microtubule array that rarely reaches the cell cortex. Analysis of the dynamic parameters revealed that in the absence of Mast, microtubules are highly dynamic, constantly growing or shrinking. These alterations are characterized by a severe reduction in the transition frequencies to and from the pause state. Moreover, analysis of de novo microtubule polymerization after cold treatment showed that Mast is not required for nucleation since Mast depleted cells nucleate microtubules soon after return to normal temperature. Taken together these results suggest that Mast plays an essential role in reducing the dynamic behaviour of microtubules by specifically promoting the pause state.

The roles of beta-tubulin mutations and isotype expression in acquired drug resistance

The antitumor drug paclitaxel stabilizes microtubules and reduces their dynamicity, promoting mitotic arrest and eventually apoptosis. Upon assembly of the alpha/beta-tubulin heterodimer, GTP becomes bound to both the alpha and beta-tubulin monomers. During microtubule assembly, the GTP bound to beta-tubulin is hydrolyzed to GDP, eventually reaching steady-state equilibrium between free tubulin dimers and those polymerized into microtubules. Tubulin-binding drugs such as paclitaxel interact with beta-tubulin, resulting in the disruption of this equilibrium. In spite of several crystal structures of tubulin, there is little biochemical insight into the mechanism by which anti-tubulin drugs target microtubules and alter their normal behavior. The mechanism of drug action is further complicated, as the description of altered beta-tubulin isotype expression and/or mutations in tubulin genes may lead to drug resistance as has been described in the literature. Because of the relationship between beta-tubulin isotype expression and mutations within beta-tubulin, both leading to resistance, we examined the properties of altered residues within the taxane, colchicine and Vinca binding sites. The amount of data now available, allows us to investigate common patterns that lead to microtubule disruption and may provide a guide to the rational design of novel compounds that can inhibit microtubule dynamics for specific tubulin isotypes or, indeed resistant cell lines. Because of the vast amount of data published to date, we will only provide a broad overview of the mutational results and how these correlate with differences between tubulin isotypes. We also note that clinical studies describe a number of predictive factors for the response to anti-tubulin drugs and attempt to develop an understanding of the features within tubulin that may help explain how they may affect both microtubule assembly and stability.

Analysis of a mesoscopic stochastic model of microtubule dynamic instability

A theoretical model of dynamic instability of a system of linear one-dimensional microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single-mesoscopic-unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates and frequencies of larger-scale macroscopic changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady-state concentration of free tubulin and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between mesoscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Last, we provide an explanation for nonexponential MT length distributions observed in experiments. In particular, we show that the appearance of such nonexponential distributions in the experiments can occur because a true steady state has not been reached and/or due to the presence of a cell edge.