Catastrophe Frequency Research Articles

Kinetic Stabilization of Microtubule Dynamics at Steady State in Vitro by Substoichiometric Concentrations of Tubulin-Colchicine Complex

We have analyzed the effects of tubulin-colchicine (TC)-complex on the dynamic instability behavior of bovine brain microtubules at steady state in vitro using video microscopy. Incorporation of low numbers of TC-complexes per microtubule strongly suppressed dynamics at the plus ends by reducing the rate and extent of growing and shortening and by increasing the time microtubules spent in an attenuated state, neither growing nor shortening detectably. In addition, TC-complex strongly suppressed the catastrophe frequency and increased the rescue frequency. At low concentrations (0.02-0.05 microM), TC-complex suppressed dynamics without reducing the polymer mass or the mean microtubule length. Such strong suppression of microtubule dynamics by low TC-complex concentrations in the absence of polymer mass changes demonstrates that microtubule dynamics are more sensitive to the actions of TC-complex than the polymer mass. Significant reduction of polymer mass occurred at relatively high TC-complex concentration (> 0.05 microM). However, the surviving microtubules were extremely stable. Thus, TC-complex stabilizes microtubules even though the microtubules can transiently depolymerize when TC-complex is added. The data also directly establish that kinetic suppression of dynamics by colchicine at low concentrations is effected by a low number of TC-complexes at the microtubule ends.

Risks of Population Extinction from Demographic and Environmental Stochasticity and Random Catastrophes.

Stochastic factors affecting the demography of a single population are analyzed to determine the relative risks of extinction from demographic stochasticity, environmental stochasticity, and random catastrophes. Relative risks are assessed by comparing asymptotic scaling relationships describing how the average time to extinction, T, increases with the carrying capacity of a population, K, under each stochastic factor alone. Stochastic factors are added to a simple model of exponential growth up to K. A critical parameter affecting the extinction dynamics is $$\tilde r,$$ the long-run growth rate of a population below K, including stochastic factors. If r̃ is positive, with demographic stochasticity T increases asymptotically as a nearly exponential function of K, and with either environmental stochasticity or random catastrophes T increases asymptotically as a power of K. If r̃ is negative, under any stochastic demographic factor, T increases asymptotically with the logarithm of K. Thus, for sufficiently large populations, the risk of extinction from demographic stochasticity is less important than that from either environmental stochasticity or random catastrophes. The relative risks of extinction from environmental stochasticity and random catastrophes depend on the mean and environmental variance of population growth rate, and the magnitude and frequency of catastrophes. Contrary to previous assertions in the literature, a population of modest size subject to environmental stochasticity or random catastrophes can persist for a long time, if r̃ is substantially positive.

How the transition frequencies of microtubule dynamic instability (nucleation, catastrophe, and rescue) regulate microtubule dynamics in interphase and mitosis: analysis using a Monte Carlo computer simulation.

Microtubules (MTs) in newt mitotic spindles grow faster than MTs in the interphase cytoplasmic microtubule complex (CMTC), yet spindle MTs do not have the long lengths or lifetimes of the CMTC microtubules. Because MTs undergo dynamic instability, it is likely that changes in the durations of growth or shortening are responsible for this anomaly. We have used a Monte Carlo computer simulation to examine how changes in the number of MTs and changes in the catastrophe and rescue frequencies of dynamic instability may be responsible for the cell cycle dependent changes in MT characteristics. We used the computer simulations to model interphase-like or mitotic-like MT populations on the basis of the dynamic instability parameters available from newt lung epithelial cells in vivo. We started with parameters that produced MT populations similar to the interphase newt lung cell CMTC. In the simulation, increasing the number of MTs and either increasing the frequency of catastrophe or decreasing the frequency of rescue reproduced the changes in MT dynamics measured in vivo between interphase and mitosis.

Brain microtubule-associated proteins modulate microtubule dynamic instability in vitro. Real-time observations using video microscopy.

We used video assays to study the dynamic instability behavior of individual microtubules assembled in vitro with purified tau, purified MAP2 or a preparation of unfractionated heat-stable MAPs. Axoneme-nucleated microtubules were assembled from pure tubulin at concentrations between 4 and 9 microM in the presence of MAPs, and observed by video-differential interference contrast microscopy. Microtubules co-assembled with each MAP preparation exhibited the elongation and rapid shortening phases and the abrupt transitions (catastrophe and rescue) characteristic of dynamic instability. Each MAP preparation increased the microtubule elongation rate above that for purified tubulin alone by decreasing the tubulin subunit dissociation rate during elongation. The brain MAPs used in this study reduced the rate of microtubule rapid shortening, but allowed significant loss of polymer during the shortening phase. Purified tau and MAP2 decreased the frequency of catastrophe and increased the frequency of rescue, while the heat-stable MAPs suppressed catastrophe at all but the lowest tubulin concentrations. Thus, each of these MAPs modulates, but does not abolish, dynamic instability behavior of microtubules. We propose a model to explain how MAP2 and tau bind to the microtubule lattice at sites along protofilaments so that the MAPs promote polymerization, but do not significantly block the mechanism of rapid shortening inherent in the tubulin lattice. Rapid shortening, when it occurs, proceeds primarily by the dissociation of short fragments of protofilaments, which contain the bound MAPs.

Control of microtubule dynamics and length by cyclin A- and cyclin B-dependent kinases in Xenopus egg extracts.

In eukaryotic cells, the onset of mitosis involves cyclin molecules which interact with proteins of the cdc2 family to produce active kinases. In vertebrate cells, cyclin A dependent kinases become active in S- and pro-phases, whereas a cyclin B-dependent kinase is mostly active in metaphase. It has recently been shown that, when added to Xenopus egg extracts, bacterially produced A- and B-type cyclins associate predominantly with the same kinase catalytic subunit, namely p34cdc2, and induce its histone H1 kinase activity with different kinetics. Here, we show that in the same cell free system, both the addition of cyclin A and cyclin B changes microtubule behavior. However, the cyclin A-dependent kinase does not induce a dramatic shortening of centrosome-nucleated microtubules whereas the cyclin B-dependent kinase does, as previously reported. Analysis of the parameters of microtubule dynamics by fluorescence video microscopy shows that the dramatic shortening induced by the cyclin B-dependent kinase is correlated with a several fold increase in catastrophe frequency, an effect not observed with the cyclin A-dependent kinase. Using a simple mathematical model, we show how the length distributions of centrosome-nucleated microtubules relate to the four parameters that describe microtubule dynamics. These four parameters define a threshold between unlimited microtubule growth and the establishment of steady-state dynamics, which implies that well defined steady-state length distributions can be produced by regulating precisely the respective values of the dynamical parameters. Moreover, the dynamical model predicts that increasing catastrophe frequency is more efficient than decreasing the rescue frequency to reduce the average steady state length of microtubules. These theoretical results are quantitatively confirmed by the experimental data.

Buffer conditions and non-tubulin factors critically affect the microtubule dynamic instability of sea urchin egg tubulin.

The dynamic instability of individual microtubules (Mts) in cytoplasmic extracts or assembled from highly purified sea urchin egg tubulin was examined using video-enhanced, differential-interference contrast (VE-DIC) light microscopy. Extract Mts (endogenous tubulin = 12.1 microM) displayed only plus-ended growth. The elongation velocity was 7.8 microns/min for an average duration of 1.3 min before switching (catastrophe) to rapid shortening, which occurred at 13.0 microns/min for an average duration of 0.5 min before switching (rescue) back to the elongation phase. These parameters are typical of interphase Mt dynamic instability. Surprisingly, Mts assembled from purified urchin egg tubulin in standard buffers were less dynamic that those reported for purified brain tubulin or Mts in the extract. Buffer parameters were changed in an attempt to mimic the extract Mt results. The pH buffer itself, Hepes or Pipes, drastically altered Mt dynamics but could not achieve high elongation velocity with high catastrophe frequencies. Calcium at 1 microM had negligible effects, while increasing pH from 6.9 to 7.2 stimulated elongation velocity. Finally, Mt dynamics of purified egg tubulin (11.9 microM) were assayed in ultrafiltrates (MW cut-off less than 30 kD) of the cytoplasmic extracts. Mts elongated slowly at 1.2 microns/min for 26 min before a catastrophe and rapid shortening at 11.8 microns/min. Rescue was less frequent than unfiltered extracts, minus-ended growth was observed, and self-assembly occurred at slightly higher tubulin concentrations. Therefore, the egg extracts and cytoplasm must contain non-buffer factors which stimulate elongation velocity by 6.5-fold without self-assembly, increase catastrophe frequency by 20-fold, and block minus-ended growth.

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

Although the mechanism of microtubule dynamic instability is thought to involve the hydrolysis of tubulin-bound GTP, the mechanism of GTP hydrolysis and the basis of microtubule stability are controversial. Video microscopy of individual microtubules and dilution protocols were used to examine the size and lifetime of the stabilizing cap. Purified porcine brain tubulin (7-23 microM) was assembled at 37 degrees C onto both ends of isolated sea urchin axoneme fragments in a miniature flow cell to give a 10-fold variation in elongation rate. The tubulin concentration in the region of microtubule growth could be diluted rapidly (by 84% within 3 s of the onset of dilution). Upon perfusion with buffer containing no tubulin, microtubules experienced a catastrophe (conversion from elongation to rapid shortening) within 4-6 s on average after dilution to 16% of the initial concentration, independent of the predilution rate of elongation and length. Based on extrapolation of catastrophe frequency to zero tubulin concentration, the estimated lifetime of the stable cap after infinite dilution was less than 3-4 s for plus and minus ends, much shorter than the approximately 200 s observed at steady state (Walker, R. A., E. T. O'Brien, N. K. Pryer, M. Soboeiro, W. A. Voter, H. P. Erickson, and E. D. Salmon. 1988. J. Cell Biol. 107:1437-1448.). We conclude that during elongation, both plus and minus ends are stabilized by a short region (approximately 200 dimers or less) and that the size of the stable cap is independent of 10-fold variation in elongation rate. These results eliminate models of dynamic instability which predict extensive "build-up" stabilizing caps and support models which constrain the cap to the elongating tip. We propose that the cell may take advantage of such an assembly mechanism by using "catastrophe factors" that can promote frequent catastrophe even at high elongation rates by transiently binding to microtubule ends and briefly inhibiting GTP-tubulin association.

Real-time visualization of cell cycle-dependent changes in microtubule dynamics in cytoplasmic extracts

Using Xenopus egg extracts arrested in interphase or mitosis, we directly observed differences in microtubule dynamics at different stages of the cell cycle. Interphase extracts were prepared from eggs in the first interphase after meiosis. Mitotic extracts were prepared by addition of purified cyclin to interphase extracts. Microtubules were nucleated by the addition of centrosomes and visualized by fluorescence videomicroscopy in extracts to which rhodamine-labeled tubulin had been added. We found a striking difference in microtubule dynamics in mitotic versus interphase extracts. Quantitative analysis revealed that the rates of polymerization and depolymerization are similar in interphase and mitosis and that within the spatial and temporal resolution of our experiments the difference in dynamics is due almost entirely to an increase in the frequency of transition from growing to shrinking (catastrophe frequency) in the mitotic extracts.

Effects of magnesium on the dynamic instability of individual microtubules

We investigated the effect of magnesium ion (Mg) on the parameters of dynamic instability of individual porcine brain microtubules. Rates of elongation and rapid shortening were measured by using video-enhanced DIC light microscopy and evaluated by using computer-generated plots of microtubule length vs time. Increasing [Mg] from 0.25 to 6 mM increased the second-order association rate constant for elongation about 25% at each end. At plus ends, this resulted in a 1.5-2-fold increase in elongation rates over the tubulin concentrations explored. Rapid shortening rates were more dramatically affected by Mg. As [Mg] was increased from 0.25 to 6 mM, the average rate of rapid shortening increased about 3-fold at plus ends and 4-5-fold at minus ends. The ends had roughly equivalent average rates at low [Mg], of 30-45 microns/min. At any Mg concentration, rates of disassembly varied from one microtubule to another, and often an individual microtubule would exhibit more than one rate during a single shortening phase. Individual rates at 6 mM Mg varied from 12 to 250 microns/min. Over the concentration range explored, Mg affected the frequencies of transition from elongation to shortening and back only at minus ends. Minus ends were relatively stable at low [Mg], having 4 times the frequency of rescue than at high [Mg], and a lower frequency of catastrophe (particularly evident at low tubulin concentrations). Plus ends, surprisingly, were highly unstable at all Mg concentrations investigated, having about the same transition frequencies as did the least stable (high Mg) minus ends. Our results have implications for models of the GTP cap, again emphasizing that GTP caps cannot build up in proportion to elongation rate, and must be constrained to the tips of growing microtubules.

Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies.

We have developed video microscopy methods to visualize the assembly and disassembly of individual microtubules at 33-ms intervals. Porcine brain tubulin, free of microtubule-associated proteins, was assembled onto axoneme fragments at 37 degrees C, and the dynamic behavior of the plus and minus ends of microtubules was analyzed for tubulin concentrations between 7 and 15.5 microM. Elongation and rapid shortening were distinctly different phases. At each end, the elongation phase was characterized by a second order association and a substantial first order dissociation reaction. Association rate constants were 8.9 and 4.3 microM-1 s-1 for the plus and minus ends, respectively; and the corresponding dissociation rate constants were 44 and 23 s-1. For both ends, the rate of tubulin dissociation equaled the rate of tubulin association at 5 microM. The rate of rapid shortening was similar at the two ends (plus = 733 s-1; minus = 915 s-1), and did not vary with tubulin concentration. Transitions between phases were abrupt and stochastic. As the tubulin concentration was increased, catastrophe frequency decreased at both ends, and rescue frequency increased dramatically at the minus end. This resulted in fewer rapid shortening phases at higher tubulin concentrations for both ends and shorter rapid shortening phases at the minus end. At each concentration, the frequency of catastrophe was slightly greater at the plus end, and the frequency of rescue was greater at the minus end. Our data demonstrate that microtubules assembled from pure tubulin undergo dynamic instability over a twofold range of tubulin concentrations, and that the dynamic instability of the plus and minus ends of microtubules can be significantly different. Our analysis indicates that this difference could produce treadmilling, and establishes general limits on the effectiveness of length redistribution as a measure of dynamic instability. Our results are consistent with the existence of a GTP cap during elongation, but are not consistent with existing GTP cap models.

Analysis of the Mechanism of Microtubule Dynamic Instability Using a UV Microbeam to Sever Elongating Microtubules

Microtubules polymerized in vitro from tubulin purified free of microtubule-associated proteins exhibit dynamic instability (1,2,3). Free microtubule ends exist in persistent phases of elongation or rapid shortening with infrequent, but, abrupt transitions between these phases. The abrupt transition from elongation to rapid shortening is termed catastrophe and the abrupt transition from rapid shortening to elongation is termed rescue. A microtubule is an asymmetrical structure. The plus end grows faster than the minus end. The frequency of catastrophe of the plus end is somewhat greater than the minus end, while the frequency of rescue of the plus end in much lower than for the minus end (4).The mechanism of catastrophe is controversial, but for both the plus and minus microtubule ends, catastrophe is thought to be dependent on GTP hydrolysis. Microtubule elongation occurs by the association of tubulin-GTP subunits to the growing end. Sometime after incorporation into an elongating microtubule end, the GTP is hydrolyzed to GDP, yielding a core of tubulin-GDP capped by tubulin-GTP (“GTP-cap”).

Infection After Kidney Transplantation

The first decade of modern kidney transplantation (1962 to 1972) was initiated with vigorous immunosuppressive regimens and associated with a catastrophic frequency of severe, often lethal, infectious complications.¹Early transplant recipients often received high doses of glucocorticosteroids and azathioprine, plus thymectomy, splenectomy, antilymphocyte serum, and graft irradiation. More than half of all transplant recipients had clinically notable infections develop, often caused by opportunistic organisms. Most centers reported that 15% to 30% of all transplant recipients died because of infection, usually within three months of the procedure.² The alarming frequency of severe and lethal infections caused transplant centers to reduce their immunosuppressive regimens, since kidney transplant recipients, unlike other organ transplant recipients, had a satisfactory therapeutic alternative to transplantation, ie, dialysis. Immunosuppressive regimens were limited to lower doses of glucocorticosteroids and azathioprine, plus an antilymphocyte serum at some centers. Progress was made on other fronts. Technology provided more effective