Comparison of reaction-diffusion simulations with experiment in self-organised microtubule solutions

This article deals with the physical chemical processes underlying biological self-organization by which an initially homogenous solution of reacting chemicals spontaneously self-organizes so as to give rise to a preparation of macroscopic order and form. Theoreticians have predicted that self-organization can arise from a coupling of reactive processes with molecular diffusion. In addition, the presence or absence of an external field, such as gravity, at a critical moment early in the self-organizing process may determine the morphology that subsequently develops. We have found that the formation in vitro of microtubules, a major element of the cellular skeleton, show this type of behaviour. The microtubule preparations spontaneously self-organise by way of reaction and diffusion, and the morphology of the state that forms depends on the presence of gravity at a critical moment early in the process. We have developed a numerical reaction-diffusion scheme, based on the chemical dynamics of a population of microtubules, which simulates the experimental self-organisation. In this article we outline the main features of these simulations and discuss the manner by which a permanent dialogue with experiment has helped develop a microscopic understanding of the collective behaviour.     

Gravity dependence of microtubule preparations

The mechanisms by which biological processes are effected by gravity are not understood. Theoreticians have proposed that gravitational effects could come about from the bifurcation properties of certain types of non-linear chemical reactions that self-organise by reaction and diffusion. We have found that in-vitro preparations of microtubules, an important element of the cellular skeleton, show this type of behaviour. They self-organise by reaction and diffusion and the morphology that arises depend upon the presence of gravity, at a critical moment or bifurcation time, early in the process. At a molecular level this behaviour results from an interaction of gravity with macroscopic concentration and density fluctuations created by microtubule contraction and elongation. Numerical simulations predict macroscopic self-organisation in qualitative agreement with experiment. It is plausible that microtubule organisation by these processes occurs in-vivo.     

Microtubules viewed as molecular ant colonies

Populations of ants and other social insects self-organize and develop 'emergent' properties through stigmergy in which individual ants communicate with one another via chemical trails of pheromones that attract or repulse other ants. In this way, sophisticated properties and functions develop. Under appropriate conditions, in vitro microtubule preparations, initially comprised of only tubulin and GTP, behave in a similar manner. They self-organize and develop other higher-level emergent phenomena by a process where individual microtubules are coupled together by the chemical trails they produce by their own reactive growing and shrinking. This behaviour is described and compared with the behaviour of ant colonies. Viewing microtubules as populations of molecular ants may provide new insights as to how the cytoskeleton may spontaneously develop high-level functions. It is plausible that such processes occur during the early stages of embryogenesis and in cells.     

Effect of weightlessness on colloidal particle transport and segregation in self-organising microtubule preparations

Weightlessness is known to effect cellular functions by as yet undetermined processes. Many experiments indicate a role of the cytoskeleton and microtubules. Under appropriate conditions in vitro microtubule preparations behave as a complex system that self-organises by a combination of reaction and diffusion. This process also results in the collective transport and organisation of any colloidal particles present. In large centimetre-sized samples, self-organisation does not occur when samples are exposed to a brief early period of weightlessness. Here, we report both space-flight and ground-based (clinorotation) experiments on the effect of weightlessness on the transport and segregation of colloidal particles and chromosomes. In centimetre-sized containers, both methods show that a brief initial period of weightlessness strongly inhibits particle transport. In miniature cell-sized containers under normal gravity conditions, the particle transport that self-organisation causes results in their accumulation into segregated regions of high and low particle density. The gravity dependence of this behaviour is strongly shape dependent. In square wells, neither self-organisation nor particle transport and segregation occur under conditions of weightlessness. On the contrary, in rectangular canals, both phenomena are largely unaffected by weightlessness. These observations suggest, depending on factors such as cell and embryo shape, that major biological functions associated with microtubule driven particle transport and organisation might be strongly perturbed by weightlessness.     

Brief exposure to high magnetic fields determines microtubule self-organisation by reaction-diffusion processes

A frequent feature of microtubule organisation in living systems is that it can be triggered by a variety of biochemical or physical factors. Under appropriate conditions, in vitro microtubule preparations self-organise by a reaction-diffusion process in which self-organisation depends upon, and can be triggered by, weak external physical factors such as gravity. Here, we show that self-organisation is also strongly dependent upon the presence of a high magnetic field, for a brief critical period early in the process, and before any self-organised pattern is visible. These results provide evidence that external physical factors trigger self-organisation by way of an orientational bias that breaks the symmetry of the reaction-diffusion process. As microtubule organisation is central to many cell functions, this behaviour provides a mechanism by which strong magnetic fields can intervene in biological processes.     

Dynamic instability of native microtubules from squid axons is rare and independent of gliding and vesicle transport

Dynamic instability characterizes the steady-state behavior of microtubules in vitro whereby polymer mass remains constant, while individual microtubules in the population may either grow or shrink. Video-enhanced contrast light microscopy was used to directly observe dynamic length changes in native, MAP-containing microtubules from squid axoplasm. We wanted to determine whether dynamic instability characterizes the steady-state behavior of axoplasmic microtubules in vitro. The lengths of a representative population of over 400 microtubules were analyzed. "Dynamic" microtubules were found to represent about 2% of the population. This observation is different from that described for cultured cells or microtubules assembled from PC-purified tubulin where most microtubules were either growing or shrinking.     

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.     

Ground-based methods reproduce space-flight experiments and show that weak vibrations trigger microtubule self-organisation

The effect of weightlessness on physical and biological systems is frequently studied by experiments in space. However, on the ground, gravity effects may also be strongly attenuated using methods such as magnetic levitation and clinorotation. Under suitable conditions, in vitro preparations of microtubules, a major element of the cytoskeleton, self-organise by a process of reaction–diffusion: self-organisation is triggered by gravity and samples prepared in space do not self-organise. Here, we report experiments carried out with ground-based methods of clinorotation and magnetic levitation. The behaviour observed closely resembles that of the space-flight experiment and suggests that many space experiments could be carried out equally well on the ground. Using clinorotation, we find that weak vibrations also trigger microtubule self-organisation and have an effect similar to gravity. Thus, in some in vitro biological systems, vibrations are a countermeasure to weightlessness.     

Microtubule solutions display nematic liquid crystalline structure

We report a study of the spontaneous formation of ordered arrays of microtubules in solution. Form birefringence and anisotropic light-scattering appear rapidly and spontaneously when tubulin, initially present in homogeneous solution, self-assembles into microtubules. This phenomenon is reversible and occurs at protein concentrations of a few milligrams per ml, in the presence or absence of microtubule-associated proteins. Light and electron microscopic examination reveals that extensive regions of these birefringent solutions consist of nearly parallel microtubules. Measurement of the order parameter, S, yields a value of 0.81 +/- 0.05, indicating a high degree of alignment. Comparison of these observations to qualitative predictions developed from the theory of Onsager ((1949) Ann. N.Y. Acad. Sci. 51, 627-659) leads to the conclusion that microtubules form a nematic liquid crystalline phase in vitro under ordinary conditions. Simultaneous spectrophotometric observation of turbidity (a measure of microtubule assembly) and birefringence shows that the parallel ordering lags only slightly behind assembly, thus demonstrating that much microtubule growth must occur by addition of tubulin to the ends of microtubules that are already aligned. These observations of anisotropy are important to the understanding of microtubule dynamics in vitro.     

Tubulin and actin in paired nonneoplastic and spontaneously transformed neoplastic cell lines in vitro: fluorescent antibody studies.

Pairs of nonneoplastic and spontaneously transformed neoplastic cells were derived from rat, mouse and hamster embryos. The neoplastic cells of each pair had poorly spread cellular morphology, grew in agarose in vitro and produced invasive sarcomas in vivo; the nonneoplastic cells exhibited none of these properties. The distribution of microtubules and microfilament bundles (stress fibers or actin cables) was examined in five such paired lines and in 3T3 and SV40-transformed 3T3 cells by indirect immunofluorescent microscopy of fixed cells treated with rabbit antibody prepared against bovine brain tubulin or guinea pig smooth muscle actin, respectively. Actin cables in all the neoplastic cells appeared thinner and more sparse than in the paired nonneoplastic cells. These differences were also observed in living cells with polarization microscopy. In contrast, microtubules appeared similar in neoplastic and nonneoplastic cells, both in areas of thin peripheral lamellar cytoplasm which allowed a clear visualization of fine, curving microtubules and in regions of thick, central endoplasm which obsecured individual microtubules. In fact, the main morphological difference between neoplastic and nonneoplastic cells was the relative amount of lamellar cytoplasm or endoplasm, rather than the appearance of microtubles in either region. Thus the distinctive growth properties and retracted cellular morphology of neoplastic cells in this study did not correlate with decreased or disorganized microtubules, but with thin and sparse actin cables.     

Some thoughts on the partitioning of tubulin between monomer and polymer under conditions of dynamic instability

We have considered the partitioning of tubulin between monomer and polymer in the cell under conditions of dynamic instability. Dynamic instability adds to the on and off rate constant of steady-state dynamics’ new parameters: (1) the rate at which growing microtubules transit to a shrinking phase; and (2) the rate at which shrinking microtubules transit to the growing phase. Under these conditions the free-monomer concentration in the cell increases with total tubulin if the number of nucleating sites is fixed. If the number of nucleating sites increases at fixed total tubulin, subunits shift from the monomer to the polymer phase. These important properties deviate from the traditional equilibrium and steady-state theories and have important implications for the biosynthetic regulation of tubulin.     

Kinetic analysis of tubulin exchange at microtubule ends at low vinblastine concentrations

We have investigated the effects of vinblastine at micromolar concentrations and below on the dynamics of tubulin exchange at the ends of microtubule-associated-protein-rich bovine brain microtubules. The predominant behavior of these microtubules at polymer-mass steady state under the conditions examined was tubulin flux, i.e., net addition of tubulin at one end of each microtubule, operationally defined as the assembly or A end, and balanced net loss at the opposite (disassembly or D) end. No dynamic instability behavior could be detected by video-enhanced dark-field microscopy. Addition of vinblastine to the microtubules at polymer-mass steady state resulted in an initial concentration-dependent depolymerization predominantly at the A ends, until a new steady-state plateau at an elevated critical concentration was established. Microtubules ultimately attained the same stable polymer-mass plateau when vinblastine was added prior to initiation of polymerization as when the drug was added to already polymerized microtubules. Vinblastine inhibited tubulin exchange at the ends of the microtubules at polymer-mass steady state, as determined by using microtubules differentially radiolabeled at their opposite ends. Inhibition of tubulin exchange occurred at concentrations of vinblastine that had very little effect on polymer mass. Both the initial burst of incorporation that occurs in control microtubule suspensions following a pulse of labeled GTP and the relatively slower linear incorporation of label that follows the initial burst were inhibited in a concentration-dependent manner by vinblastine. Both processes were inhibited to the same extent at all vinblastine concentrations examined. If the initial burst of label incorporation represents a low degree of dynamic instability (very short excursions of growth and shortening of the microtubules at one or both ends), then vinblastine inhibits both dynamic instability and flux to similar extents. The ability of vinblastine to inhibit tubulin exchange at microtubule ends in the micromolar concentration range appeared to be mediated by the reversible binding of vinblastine to tubulin binding sites exposed at the polymer ends. Determination by dilution analysis of the effects of vinblastine on the apparent dissociation rate constants for tubulin loss at opposite microtubule ends indicated that a principal effect of vinblastine is to decrease the dissociation rate constant at A ends (i.e., it produces a kinetic cap at A ends), whereas it has no effect on the D-end dissociation rate constant.     

Insights into allosteric control of microtubule dynamics from a buried β‐tubulin mutation that causes faster growth and slower shrinkage

αβ‐tubulin subunits cycle through a series of different conformations in the polymer lattice during microtubule growing and shrinking. How these allosteric responses to different tubulin:tubulin contacts contribute to microtubule dynamics, and whether the contributions are evolutionarily conserved, remains poorly understood. Here, we sought to determine whether the microtubule‐stabilizing effects (slower shrinking) of the β:T238A mutation we previously observed using yeast αβ‐tubulin would generalize to mammalian microtubules. Using recombinant human microtubules as a model, we found that the mutation caused slow microtubule shrinking, indicating that this effect of the mutation is indeed conserved. However, unlike in yeast, β:T238A human microtubules grew faster than wild‐type and the mutation did not appear to attenuate the conformational change associated with guanosine 5′‐triphosphate (GTP) hydrolysis in the lattice. We conclude that the assembly‐dependent conformational change in αβ‐tubulin can contribute to determine the rates of microtubule growing as well as shrinking. Our results also suggest that an allosteric perturbation like the β:T238A mutation can alter the behavior of terminal subunits without accompanying changes in the conformation of fully surrounded subunits in the body of the microtubule.     

Cortical microtubules are responsible for gravity resistance in plants

Mechanical resistance to the gravitational force is a principal gravity response in plants distinct from gravitropism. In the final step of gravity resistance, plants increase the rigidity of their cell walls. Here we discuss the role of cortical microtubules, which sustain the function of the cell wall, in gravity resistance. Hypocotyls of Arabidopsis tubulin mutants were shorter and thicker than the wild-type, and showed either left-handed or right-handed helical growth at 1 g. The degree of twisting phenotype was intensified under hypergravity conditions. Hypergravity also induces reorientation of cortical microtubules from transverse to longitudinal directions in epidermal cells. In tubulin mutants, the percentage of cells with longitudinal microtubules was high even at 1 g, and it was further increased by hypergravity. The left-handed helical growth mutants had right-handed microtubule arrays, whereas the right-handed mutant had left-handed arrays. Moreover, blockers of mechanoreceptors suppressed both the twisting phenotype and reorientation of microtubules in tubulin mutants. These results support the hypothesis that cortical microtubules play an essential role in maintenance of normal growth phenotype against the gravitational force, and suggest that mechanoreceptors are involved in signal perception in gravity resistance. Space experiments will confirm whether this view is applicable to plant resistance to 1 g gravity, as to the resistance to hypergravity.Key words: cortical microtubules, gravity, gravity resistance, hypergravity, mechanoreceptor, microgravity, tubulin mutants     

Microtubule dynamics and microtubule caps: a time-resolved cryo- electron microscopy study

Microtubules display the unique property of dynamic instability characterized by phase changes between growth and shrinkage, even in constant environmental conditions. The phases can be synchronized, leading to bulk oscillations of microtubules. To study the structural basis of dynamic instability we have examined growing, shrinking, and oscillating microtubules by time-resolved cryo-EM. In particular we have addressed three questions which are currently a matter of debate: (a) What is the relationship between microtubules, tubulin subunits, and tubulin oligomers in microtubule dynamics?; (b) How do microtubules shrink? By release of subunits or via oligomers?; and (c) Is there a conformational change at microtubule ends during the transitions from growth to shrinkage and vice versa? The results show that (a) oscillating microtubules coexist with a substantial fraction of oligomers, even at a maximum of microtubule assembly; (b) microtubules disassemble primarily into oligomers; and (c) the ends of growing microtubules have straight protofilaments, shrinking microtubules have protofilaments coiled inside out. This is interpreted as a transition from a tense to a relaxed conformation which could be used to perform work, as suggested by some models of poleward chromosome movement during anaphase.     

Dynamic microtubules slow down during their shrinkage phase

Microtubules are dynamic polymers that undergo stochastic transitions between growing and shrinking phases. The structural and chemical properties of these phases remain poorly understood. The transition from growth to shrinkage, termed catastrophe, is not a first-order reaction but rather a multistep process whose frequency increases with the growth time: the microtubule ages as the older microtubule tip becomes more unstable. Aging shows that the growing phase is not a single state but comprises several substates of increasing instability. To investigate whether the shrinking phase is also multistate, we characterized the kinetics of microtubule shrinkage following catastrophe using an in vitro reconstitution assay with purified tubulins. We found that the shrinkage speed is highly variable across microtubules and that the shrinkage speed of individual microtubules slows down over time by as much as several fold. The shrinkage slowdown was observed in both fluorescently labeled and unlabeled microtubules as well as in microtubules polymerized from tubulin purified from different species, suggesting that the shrinkage slowdown is a general property of microtubules. These results indicate that microtubule shrinkage, like catastrophe, is time dependent and that the shrinking microtubule tip passes through a succession of states of increasing stability. We hypothesize that the shrinkage slowdown is due to destabilizing events that took place during growth, which led to multistep catastrophe. This suggests that the aging associated with growth is also manifested during shrinkage, with the older, more unstable growing tip being associated with a faster depolymerizing shrinking tip.     

Cooperative lattice dynamics and anomalous fluctuations of microtubules

Microtubules have been in the focus of biophysical research for several decades. However, the confusing and mutually contradictory results regarding their elasticity and fluctuations have cast doubt on their present understanding. In this paper, we present the empirical evidence for the existence of discrete guanosine diphosphate (GDP)–tubulin fluctuations between a curved and a straight configuration at room temperature as well as for conformational tubulin cooperativity. Guided by a number of experimental findings, we build the case for a novel microtubule model, with the principal result that microtubules can spontaneously form micron-sized cooperative helical states with unique elastic and dynamic features. The polymorphic dynamics of the microtubule lattice resulting from the tubulin bistability quantitatively explains several experimental puzzles, including anomalous scaling of dynamic fluctuations of grafted microtubules, their apparent length–stiffness relation, and their remarkable curved–helical appearance in general. We point out that the multistability and cooperative switching of tubulin dimers could participate in important cellular processes, and could in particular lead to efficient mechanochemical signaling along single microtubules.     

Structural changes accompanying GTP hydrolysis in microtubules: information from a slowly hydrolyzable analogue guanylyl-(alpha,beta)- methylene-diphosphonate

We have used cryoelectron microscopy to try to understand the structural basis for the role of GTP hydrolysis in destabilizing the microtubule lattice. We have measured a structural difference introduced into microtubules by replacing GTP with guanylyl- (alpha,beta)-methylene-diphosphonate (GMPCPP). In a stable GMPCPP microtubule lattice, the moire patterns change and the tubulin subunits increase in size by 1.5 A. This information provides a clue to the role of hydrolysis in inducing the structural change at the end of a microtubule during the transition from a growing to a shrinking phase.     

Exposure of beta-tubulin regions defined by antibodies on an <Emphasis Type="Italic">Arabidopsis thaliana</Emphasis>microtubule protofilament model and in the cells

Background  

The function of the cortical microtubules, composed of αβ-tubulin heterodimers, is linked to their organizational state which is subject to spatial and temporal modulation by environmental cues. The role of tubulin posttranslational modifications in these processes is largely unknown. Although antibodies against small tubulin regions represent useful tool for studying molecular configuration of microtubules, data on the exposure of tubulin epitopes on plant microtubules are still limited.     

The assembly of microtubule protein in vitro. The kinetic role in microtubule elongation of oligomeric fragments containing microtubule-associated proteins.

The kinetics of assembly were studied for bovine and pig microtubule protein in vitro over a range of conditions of pH, temperature, nucleotide and protein concentration. The kinetics are in general biphasic with two major processes of similar amplitude but separated in rate by one order of magnitude. Rates and amplitudes are complex functions of solution conditions. The rates of the fast phase and the slow phase attain limiting values as a function of increasing protein concentration, and are more stringently limited at pH 6.5 than pH 6.95. Such behaviour indicates that mechanisms other than the condensation polymerization of tubulin dimer become rate-limiting at higher protein concentration. The constancy of the wavelength-dependence of light-scattering and ultrastructural criteria indicate that microtubules of normal morphology are formed in both phases of the assembly process. Electrophoretic analysis of assembling microtubule protein shows that MAP- (microtubule-associated-protein-)rich microtubules are formed during the fast phase. The rate of dissociation of oligomeric species on dilution of microtubule protein closely parallels the fast-phase rate in magnitude and temperature-dependence. We propose that the rate of this process constitutes an upper limit to the rate of the fast phase of assembly. The kinetics of redistribution of MAPs from MAP-rich microtubules may be a factor limiting the slow-phase rate. A working model is derived for the self-assembly of microtubule protein incorporating the dissociation and redistribution mechanisms that impose upper limits to the rates of assembly attainable by bimolecular addition reactions. Key roles are assigned to MAP-containing fragments in both phases of microtubule elongation. Variations in kinetic behaviour with solution conditions are inferred to derive from the nature and properties of fragments formed from oligomeric species after the rapid temperature jump. The model accounts for the limiting rate behaviour and indicates experimental criteria to be applied in evaluating the relative contributions of alternative pathways.