scholarly journals Predicted effects of severing enzymes on the length distribution and total mass of microtubules

2019 ◽  
Author(s):  
Y.-W. Kuo ◽  
O. Trottier ◽  
J. Howard
Keyword(s):  
Steady State ◽  
Numerical Solutions ◽  
Dynamic Instability ◽  
Computational Simulation ◽  
Length Distribution ◽  
Microtubule Dynamics ◽  
Microtubule Dynamic ◽  
Cytoskeletal Network ◽  
Hydrolyzing Enzymes ◽  
In Cells

AbstractMicrotubules are dynamic cytoskeletal polymers whose growth and shrinkage are highly regulated as eukaryotic cells change shape, move and divide. One family of microtubule regulators includes the ATP-hydrolyzing enzymes spastin, katanin and fidgetin, which sever microtubule polymers into shorter fragments. Paradoxically, severases can increase microtubule number and mass in cells. Recent work with purified spastin and katanin accounts for this phenotype by showing that, in addition to severing, these enzymes modulate microtubule dynamics by accelerating the conversion of microtubules to the growing state and thereby promoting their regrowth. This leads to the observed exponential increase in microtubule mass. Spastin also influences the steady-state distribution of microtubule lengths, changing it from an exponential, as predicted by models of microtubule dynamic instability, to a peaked distribution. This effect of severing and regrowth by spastin on the microtubule length distribution has not been explained theoretically. To solve this problem, we formulated and solved a master equation for the time evolution of microtubule lengths in the presence of severing and microtubule dynamic instability. We then obtained numerical solutions to the steady-state length distribution and showed that the rate of severing and the speed of microtubule growth are the dominant parameters determining the steady-state length distribution. Furthermore, we found that the amplification rate is predicted to increase with severing, which is a new result. Our results establish a theoretical basis for how severing and dynamics together can serve to nucleate new microtubules, constituting a versatile mechanism to regulate microtubule length and mass.SignificanceThe numbers and lengths of microtubules are tightly regulated in cells. Severing enzymes fragment microtubules into shorter filaments and are important for cell division and tissue development. Previous work has shown that severing can lead to an increase in total microtubule number and mass, but the effect of severing on microtubule length is not understood quantitatively. Combining mathematical modeling and computational simulation, we solve the microtubule length distribution in the presence of severing enzymes and explore how severing activity and microtubule dynamics collectively control microtubule number and length. These results advance our understanding of the physical basis of severing as a regulatory mechanism shaping the cellular cytoskeletal network.

scholarly journals Phase dynamics at microtubule ends: the coexistence of microtubule length changes and treadmilling

1987 ◽  
Vol 104 (4) ◽  
pp. 1035-1046 ◽  
Author(s):  
KW Farrell ◽  
MA Jordan ◽  
HP Miller ◽  
L Wilson
Keyword(s):  
Steady State ◽  
Length Distribution ◽  
Bovine Brain ◽  
Phase Dynamics ◽  
Protein Map ◽  
Length Changes ◽  
Brain Microtubules ◽  
Inherent Tendency ◽  
In Cells

The length dynamics both of microtubule-associated protein (MAP)-rich and MAP-depleted bovine brain microtubules were examined at polymer mass steady state. In both preparations, the microtubules exhibited length redistributions shortly after polymer mass steady state was attained. With time, however, both populations relaxed to a state in which no further changes in length distributions could be detected. Shearing the microtubules or diluting the microtubule suspensions transiently increased the extent to which microtubule length redistributions occurred, but again the microtubules relaxed to a state in which changes in the polymer length distributions were not detected. Under steady-state conditions of constant polymer mass and stable microtubule length distribution, both MAP-rich and MAP-depleted microtubules exhibited behavior consistent with treadmilling. MAPs strongly suppressed the magnitude of length redistributions and the steady-state treadmilling rates. These data indicate that the inherent tendency of microtubules in vitro is to relax to a steady state in which net changes in the microtubule length distributions are zero. If the basis of the observed length redistributions is the spontaneous loss and regain of GTP-tubulin ("GTP caps") at microtubule ends, then in order to account for stable length distributions the microtubule ends must reside in the capped state far longer than in the uncapped state, and uncapped microtubule ends must be rapidly recapped. The data suggest that microtubules in cells may have an inherent tendency to remain in the polymerized state, and that microtubule disassembly must be induced actively.

Target finding time for microtubules in a confined geometry

2009 ◽  
Vol 87 (6) ◽  
pp. 691-694 ◽  
Author(s):  
Mitra Shojania Feizabadi
Keyword(s):  
Steady State ◽  
Cell Shape ◽  
Dynamic Instability ◽  
Length Distribution ◽  
Biological Role ◽  
Cell Cortex ◽  
Cell Periphery ◽  
Confined Geometry ◽  
A Cell ◽  
Motile Activity

Dynamic instability of microtubules may reach the steady state with exponentially growing or decaying length distribution in a confined geometry such as a cell-like environment. In this brief communication, the target finding time for these microtubules with the stochastic polymerization in a confined geometry is compared with the reversible polymerization. It is shown that the efficiency of microtubules with increasing length distribution at the steady state depends on the location of a target. They are very efficient in finding a target located at the cell cortex, which confirms the significant biological role they play in rapidly reaching the cell cortex to change the cell shape and to coordinate a motile activity around the cell periphery.

scholarly journals Okadaic acid induces interphase to mitotic-like microtubule dynamic instability by inactivating rescue.

1992 ◽  
Vol 119 (5) ◽  
pp. 1271-1276 ◽  
Author(s):  
N R Gliksman ◽  
S F Parsons ◽  
E D Salmon
Keyword(s):  
High Resolution ◽  
Sea Urchin ◽  
Okadaic Acid ◽  
Dynamic Instability ◽  
Major Change ◽  
Microtubule Dynamics ◽  
Regulatory Pathway ◽  
Microtubule Dynamic ◽  
Interphase Cells ◽  
Frequent Switching

We used high-resolution video microscopy to visualize microtubule dynamic instability in extracts of interphase sea urchin eggs and to analyze the changes that occur upon addition of 0.8-2.5 microM okadaic acid, an inhibitor of phosphatase 1 and 2A (PP1, PP2a) (Bialojan, D., and A. Takai. 1988. Biochem. J. 256:283-290). Microtubule plus-ends in these extracts oscillated between the elongation and shortening phases of dynamic instability at frequencies typical for interphase cells. Switching from elongation to shortening (catastrophe) was frequent, but microtubules persisted and grew long because of frequent switching back to elongation (rescue). Addition of okadaic acid to the extract induced rapid (< 5 min) conversion to short, dynamic microtubules typical of mitosis. The frequency of catastrophe doubled and the velocities of elongation and shortening increased slightly; however, the major change was an elimination of rescue. Thus, modulation of the rescue frequency by phosphorylation-dependent mechanisms may be a major regulatory pathway for selectively controlling microtubule dynamics without dramatically changing velocities of microtubule elongation and shortening.

scholarly journals A mutation uncouples the tubulin conformational and GTPase cycles, revealing allosteric control of microtubule dynamics

eLife ◽  
2015 ◽  
Vol 4 ◽  
Author(s):  
Elisabeth A Geyer ◽  
Alexander Burns ◽  
Beth A Lalonde ◽  
Xuecheng Ye ◽  
Felipe-Andres Piedra ◽  
...  
Keyword(s):  
Conformational Change ◽  
Dynamic Instability ◽  
Dynamic Properties ◽  
Microtubule Dynamics ◽  
Gtpase Activity ◽  
Microtubule Dynamic ◽  
Gtp Hydrolysis ◽  
Allosteric Control

Microtubule dynamic instability depends on the GTPase activity of the polymerizing αβ-tubulin subunits, which cycle through at least three distinct conformations as they move into and out of microtubules. How this conformational cycle contributes to microtubule growing, shrinking, and switching remains unknown. Here, we report that a buried mutation in αβ-tubulin yields microtubules with dramatically reduced shrinking rate and catastrophe frequency. The mutation causes these effects by suppressing a conformational change that normally occurs in response to GTP hydrolysis in the lattice, without detectably changing the conformation of unpolymerized αβ-tubulin. Thus, the mutation weakens the coupling between the conformational and GTPase cycles of αβ-tubulin. By showing that the mutation predominantly affects post-GTPase conformational and dynamic properties of microtubules, our data reveal that the strength of the allosteric response to GDP in the lattice dictates the frequency of catastrophe and the severity of rapid shrinking.

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

1988 ◽  
Vol 46 ◽  
pp. 122-123
Author(s):  
R.A Walker ◽  
S. Inoue ◽  
E.D. Salmon
Keyword(s):  
Dynamic Instability ◽  
Microtubule Dynamic ◽  
Gtp Hydrolysis ◽  
Abrupt Transition ◽  
Microtubule Associated Proteins ◽  
Asymmetrical Structure ◽  
Associated Proteins

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”).

scholarly journals Temperature-jump studies of microtubule dynamic instability.

1988 ◽  
Vol 263 (21) ◽  
pp. 10344-10352
Author(s):  
M Caplow ◽  
J Shanks ◽  
R L Ruhlen
Keyword(s):  
Temperature Jump ◽  
Dynamic Instability ◽  
Microtubule Dynamic

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

scholarly journals Motile kinetochores and polar ejection forces dictate chromosome position on the vertebrate mitotic spindle

1994 ◽  
Vol 124 (3) ◽  
pp. 223-233 ◽  
Author(s):  
CL Rieder ◽  
ED Salmon
Keyword(s):  
Mitotic Spindle ◽  
Constant Velocity ◽  
Molecular Mechanisms ◽  
Dynamic Instability ◽  
Microtubule Dynamic ◽  
Pole Motion ◽  
Microtubule Motors ◽  
Chromosome Position ◽  
Pulling Forces

We argue that hypotheses for how chromosomes achieve a metaphase alignment, that are based solely on a tug-of-war between poleward pulling forces produced along the length of opposing kinetochore fibers, are no longer tenable for vertebrates. Instead, kinetochores move themselves and their attached chromosomes, poleward and away from the pole, on the ends of relatively stationary but shortening/elongating kinetochore fiber microtubules. Kinetochores are also "smart" in that they switch between persistent constant-velocity phases of poleward and away from the pole motion, both autonomously and in response to information within the spindle. Several molecular mechanisms may contribute to this directional instability including kinetochore-associated microtubule motors and kinetochore microtubule dynamic instability. The control of kinetochore directional instability, to allow for congression and anaphase, is likely mediated by a vectorial mechanism whose magnitude and orientation depend on the density and orientation or growth of polar microtubules. Polar microtubule arrays have been shown to resist chromosome poleward motion and to push chromosomes away from the pole. These "polar ejection forces" appear to play a key role in regulating kinetochore directional instability, and hence, positions achieved by chromosomes on the spindle.

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