Phase-change kinetics for a microtubule with two free ends

Polymerization kinetics of tubulin from mung seedlings modeled as a competition between nucleation and GTP-hydrolysis rates

Microtubules (MTs) form physiologically important cytoskeletal structures that assemble by tubulin polymerization in a nucleation- and GTP-dependent manner. GTP-hydrolysis competes with the addition of monomers, to determine the GTP-cap size, and onset of shrinkage, which alternates with growth. Multiple theoretical models of MT polymerization dynamics have been reconciled to the kinetics of animal brain tubulins, but more recently rapid kinetics seen in Arabidopsis tubulin polymerization suggest the need to sample a wider diversity in tubulin polymerization kinetics and reconcile it to theory. Here, we have isolated tubulin from seedlings of Vigna sp. (mung bean), compared polymerization kinetics to animal brain tubulin and used a computational model to understand the di_erences. We _nd that activity isolated mung tubulin polymerizes in a nucleation-dependent manner, based on turbidimetry, qualitatively similar to brain tubulin, but with a ten-fold smaller critical critical concentration. GTP-dependent polymerization kinetics also appear to be transient, indicative of high rates of GTP-hydrolysis. Computational modeling of tubulin nucleation and vectorial GTP-hydrolysis to examine the e_ect of high nucleation and GTP-hydrolysis rates predicts a dominance of the latter in determining MT lengths and numbers. Microscopy of mung tubulin _laments stabilized by GMPCPP or taxol result in few and short MTs, compared to the many long MTs arising from goat tubulin, qualitatively matching the model predictions. We _nd GTP-hydrolysis outcompetes nucleation rates in determining MT lengths and numbers. This article is protected by copyright. All rights reserved.

Effect of tubulin diffusion on polymerization of microtubules

The dynamics of microtubules (MT's) growing from a nucleation center is simulated with a kinetic Monte Carlo model that includes tubulin diffusion. In the limit of fast diffusion (homogeneous tubulin concentration), MT growth is synchronous and bounded. The microtubules form an aster with a monotonously decreasing long-time distribution of lengths. Slow tubulin diffusion leads to rapid dephasing in the growth dynamics, unbounded growth of some MT's, spatial inhomogeneities, and morphological change toward a morphology with bounded short MT's located in the nucleation center and unbounded long MT's with narrowly distributed lengths. The transition from unbounded to bounded growth is driven by the competition between the reaction rate of the tubulin assembly and the tubulin's diffusion rate. While the present study reports the effect of the tubulin diffusion coefficient on the transition, the results of the simulations are qualitatively comparable to the morphological and dynamical changes of centrosome-nucleated MT's from interphase to mitosis in cellular systems where the transition is regulated by the reaction rates.

Assembly of chick brain MAP2-tubulin microtubule protein. Analysis of tubulin subunit flux rates by immunofluorescence microscopy

A filter-based immunofluorescence-microscopy method for obtaining microtubule lengths has been developed and evaluated. Kinetic constants and mean lengths obtained show close agreement with those obtained by complementary methods applied to chick brain MAP2-tubulin microtubule protein in NaCl-supplemented buffer. The filter-based method has been used to estimate tubulin subunit flux (Jon) resulting from isothermal dilution of microtubule populations to various free tubulin concentrations, (c). This experimental Jon(c) plot is significantly different from that predicted by a variety of theoretical models, but is consistent with a 'lateral cap' model of dynamic instability [Bayley, Schilstra & Martin (1990) J. Cell. Sci. 95, 33-48] adapted to accommodate the observed vectorial GTP hydrolysis.

Characteristics of microtubules at the different stages of neuronal differentiation and maturation

The developing nervous system has proved to be a very powerful tool to analyze how MT are involved in basic biological processes such as cell proliferation, cell migration, cell shaping, and transport. A better knowledge of the basic events occurring during neurogenesis also affords us the possibility of establishing the basis of experiments and trying to solve unanswered and important questions. Despite the considerable value of cell culture, we need to use more discrete regions of the developing brain in situ in order to analyze the MT and their modifications into cells developing their "natural" environment. One major problem remains the question of the mode of assembly and disassembly, that is, the behavior of MT in living cells. Dynamic instability and/or treadmilling are accurate interpretations of the dynamics of MT at least in vitro or in cell culture, but we do need more information on what happens in situ and in vitro. One of the main tasks of cell biologists is to devise satisfactory tests to approach this fundamental question. In this view, pharmacological manipulation of embryos treated in whole-embryo culture systems might be a possible way. Microtubules are ubiquitous cell components. However, the extensive heterogeneity of MAP and tubulin in the CNS confers on the neurons a wide range of capabilities of assembly of these proteins and suggests that the neuron has a unique potential of a relation between MT composition and cell function. We have seen that each major event during neurogenesis is related to a specific series of modifications of the MT components. It remains to be determined if there is a causal or just a correlative relationship between the appearance of specific isotypes and the occurrence of specific events and/or functions. We have also to determine the exact spatial and temporal relations among the different isotypes of MT proteins, tubulin, and MAP. Is there a close correspondence between a tubulin and a MAP isotype? Can the appearance of one isotype of tubulin influence the appearance and the assembly of a specific MAP, or vice versa? Recent results obtained with the Tyr- and Glu-MT shed light on these questions and suggest a whole series of possibilities for cells to modulate the structure, behavior, and function of MT in specific domains of the neuron or in specific regions of the brain, by only a minute modification of the molecule of tubulin. Microtubule protein heterogeneity raises also a number of questions.(ABSTRACT TRUNCATED AT 400 WORDS)

Theoretical study of a model for the ATP cap at the end of an actin filament

The model used successfully by Pantaloni et al. to fit experimental data on steady-state actin polymerization is investigated theoretically. Many properties are deduced, as functions of the free subunit concentration. The model is simple enough so that one can examine analytically the question of whether actin shows the same dramatic phase changes associated with the GTP cap in microtubules. The answer is negative, judging from this model. However, it is possible to obtain such phase changes using the same model but with quite different, hypothetical choices of parameters. Thus, aside from its application to actin, this model is useful pedagogically to illustrate the nature of phase changes that may occur at the end of a steady-state polymer.

Direct observation of steady-state microtubule dynamics

Different types of unusual dynamic behavior have been reported for steady-state microtubules. While almost all earlier reports relied on kinetic measurements of bulk polymerization, we have directly visualized the steady-state addition of subunits to individual microtubules through the use of tubulin derivitized with biotin. Biotinylated tubulin was used both as an internal "seed" for polymerization and as a marker for assembly onto the ends of microtubules composed of purified tubulin. Biotinylated segments were distinguished from unmodified tubulin by double-label immunofluorescence. Microtubule lengths, number concentrations, and segment lengths have been monitored with time at steady state under two buffer conditions. The results indicate that the microtubule steady state under these conditions is a balance between a majority of slowly growing microtubules and a minority of rapidly depolymerizing ones as described by the "dynamic instability" model (Mitchison T., and M. Kirschner, 1984, Nature (Lond.)., 312:232-242). Microtubules show no evidence of treadmilling; instead most show progressive growth off both ends at steady state. Although solvent conditions markedly influence the growth rates, qualitatively the behavior is unchanged.

A model for actin polymerization and the kinetic effects of ATP hydrolysis

A model for actin polymerization is proposed in which the rate of elongation of actin filaments depends on whether adenosine 5'-triphosphate or adenosine 5'-diphosphate is bound to the two terminal subunits of the filament. This model accounts quantitatively for the experimental data on the kinetics of filament elongation and explains the effect of ATP hydrolysis on actin polymerization.

Theoretical problems related to the attachment of microtubules to kinetochores

A possible model is analyzed for the maintenance of attachment of a shortening microtubule (MT) to a kinetochore. In this model it is assumed that a MT is inserted and held in a sleeve or channel of the outer layer of a kinetochore while subunits are lost from the MT tip through the central layer of the kinetochore. A second problem considered is the elementary bioenergetics of MT growth and shortening, as associated with the presence or absence of a GTP cap on the MT ends. The free-energy source is the hydrolysis of GTP in solution. The third problem discussed is the kinetics of capture of a centrosomal MT by a target (e.g., a kinetochore).

Theoretical treatment of microtubules disappearing in solution

The origin of the two-phase (cap, no cap) macroscopic kinetic model of the end of a microtubule is reviewed. The model is then applied to a new theoretical problem, namely, the Mitchison-Kirschner [Mitchison, T. & Kirschner, M. W. (1984) Nature (London) 312, 237-242] experiment in which aggregated microtubules in solution spontaneously decrease in number (shorten to disappearance) while the surviving microtubules increase in length. The model fits the experiments without difficulty.