scholarly journals Behaviors of individual microtubules and microtubule populations relative to critical concentrations: Dynamic instability occurs when critical concentrations are driven apart by nucleotide hydrolysis

2018 ◽  
Author(s):  
Erin M. Jonasson ◽  
Ava J. Mauro ◽  
Chunlei Li ◽  
Ellen C. Norby ◽  
Shant M. Mahserejian ◽  
...  
Keyword(s):  
Steady State ◽  
Dynamic Instability ◽  
Critical Concentration ◽  
Growth Phases ◽  
Nucleotide Hydrolysis ◽  
Critical Concentrations ◽  
Degree Of Separation ◽  
Polymer Assembly

ABSTRACTThe concept of critical concentration (CC) is central to understanding behaviors of microtubules and other cytoskeletal polymers. Traditionally, these polymers are understood to have one CC, measured multiple ways and assumed to be the subunit concentration necessary for polymer assembly. However, this framework does not incorporate dynamic instability (DI), and there is work indicating that microtubules have two CCs. We use our previously established simulations to confirm that microtubules have (at least) two experimentally relevant CCs and to clarify the behaviors of individuals and populations relative to the CCs. At free subunit concentrations above the lower CC (CCIndGrow), growth phases of individual filaments can occur transiently; above the higher CC (CCPopGrow), the population’s polymer mass will increase persistently. Our results demonstrate that most experimental CC measurements correspond to CCPopGrow, meaning “typical” DI occurs below the concentration traditionally considered necessary for polymer assembly. We report that [free tubulin] at steady state does not equal CCPopGrow, but instead approaches CCPopGrow asymptotically as [total tubulin] increases and depends on the number of stable microtubule seeds. We show that the degree of separation between CCIndGrow and CCPopGrow depends on the rate of nucleotide hydrolysis. This clarified framework helps explain and unify many experimental observations.

scholarly journals Behaviors of individual microtubules and microtubule populations relative to critical concentrations: dynamic instability occurs when critical concentrations are driven apart by nucleotide hydrolysis

2020 ◽  
Vol 31 (7) ◽  
pp. 589-618 ◽  
Author(s):  
Erin M. Jonasson ◽  
Ava J. Mauro ◽  
Chunlei Li ◽  
Ellen C. Labuz ◽  
Shant M. Mahserejian ◽  
...  
Keyword(s):  
Dynamic Instability ◽  
Hydrolysis Rate ◽  
Nucleotide Hydrolysis ◽  
Critical Concentrations

We show that polymers displaying dynamic instability (DI) have at least two experimentally distinguishable critical concentrations (CCs), typical DI occurs between these two CCs, and the separation between the CCs depends on the NTP hydrolysis rate. We demonstrate how these CCs relate to various existing experimental and theoretical definitions of CC.

scholarly journals Polymerization of FtsZ, a Bacterial Homolog of Tubulin

2001 ◽  
Vol 276 (15) ◽  
pp. 11743-11753 ◽  
Author(s):  
Laura Romberg ◽  
Martha Simon ◽  
Harold P. Erickson
Keyword(s):  
Steady State ◽  
Critical Concentration ◽  
Gtp Hydrolysis ◽  
Nucleotide Hydrolysis ◽  
High Affinity ◽  
Hydrolysis Rates ◽  
Bacterial Homolog ◽  
Nucleation Phase ◽  
Maximum Steady State

FtsZ is a bacterial homolog of tubulin that is essential for prokaryotic cytokinesis.In vitro, GTP induces FtsZ to assemble into straight, 5-nm-wide polymers. Here we show that the polymerization of these FtsZ filaments most closely resembles noncooperative (or “isodesmic”) assembly; the polymers are single-stranded and assemble with no evidence of a nucleation phase and without a critical concentration. We have developed a model for the isodesmic polymerization that includes GTP hydrolysis in the scheme. The model can account for the lengths of the FtsZ polymers and their maximum steady state nucleotide hydrolysis rates. It predicts that unlike microtubules, FtsZ protofilaments consist of GTP-bound FtsZ subunits that hydrolyze their nucleotide only slowly and are connected by high affinity longitudinal bonds with a nanomolarKD.

Dynamic Instability in Quartering Seas: The Behavior of a Ship During Broaching

1996 ◽  
Vol 40 (01) ◽  
pp. 46-59 ◽  
Author(s):  
K. J. Spyrou
Keyword(s):  
Steady State ◽  
Transient Analysis ◽  
Dynamic Instability ◽  
Dynamical Analysis ◽  
Wave Excitation ◽  
Periodic Motions ◽  
Regular Waves ◽  
Limit Sets ◽  
Diffraction Wave ◽  
Surf Riding

The dynamic stability of ships encountering large regular waves from astern is analyzed, with focus on delineating the specific conditions leading to the uncontrolled turn identified as broaching. The problem's formulation takes into account motions of the actively steered or controls-fixed vessel in surge-sway-yaw-roll with consideration of Froude-Krylov and diffraction wave excitation. Dynamical analysis of surf-riding is carried out for the general case of quartering waves, exploring the route periodic motions—surf riding, loss of stationary stability, turn, capsize. Steady-state and transient analysis is carried out in the system's multidimensional state-space in order to identify all existing limit sets and locate attracting domains. Broaching from periodic motions is also a part of the investigation.

Electrical and Rheological Properties of Double Percolated Poly(methyl methacrylate)/Multiwalled Carbon Nanotube Nanocomposites

2007 ◽  
Vol 7 (11) ◽  
pp. 3847-3851 ◽  
Author(s):  
Sung-Hun Jin ◽  
Dai-Soo Lee
Keyword(s):  
Carbon Nanotube ◽  
Methyl Methacrylate ◽  
Rheological Properties ◽  
Critical Concentration ◽  
Threshold Concentration ◽  
Multiwalled Carbon Nanotube ◽  
Multiwalled Carbon ◽  
Poly Methyl Methacrylate ◽  
Critical Concentrations ◽  
Double Percolation

Electrical and rheological properties of nanocomposites based on poly(methyl methacrylate) (PMMA) and multiwalled carbon nanotube (MWCNT) were studied from view points of double percolation by adding crosslinked methyl methacrylate-butadiene-styrene (MBS) copolymer particles to lower percolation threshold concentration of MWCNTs. It was found that the critical concentrations of MWCNTs for the percolation in the nanocomposites decrease and then increase with increasing the MBS contents of the nanocomposites. It is postulated that the addition of MBS at low concentrations results in double percolation of MWCNT and the significant decrease of critical concentration for the percolations. However, adding MBS particles in large amounts results in limited space for the distribution of MWCNTs and less efficient dispersion of the MWCNTs and the increase of the critical concentrations of MWCNTs for the percolations. Rheological properties and change of Tgs reflect large interfacial areas in the well dispersed nanocomposite and were also interpreted to support the speculations for the effects of MBS contents and MWCNT concentrations of PMMA/MWCNT nanocomposites.

scholarly journals Dynamics of microtubules from erythrocyte marginal bands.

1993 ◽  
Vol 4 (3) ◽  
pp. 323-335 ◽  
Author(s):  
B Trinczek ◽  
A Marx ◽  
E M Mandelkow ◽  
D B Murphy ◽  
E Mandelkow
Keyword(s):  
Phosphate Buffer ◽  
Dynamic Instability ◽  
Critical Concentration ◽  
Mammalian Brain ◽  
Tubulin Isoforms ◽  
Marginal Band ◽  
Associated Proteins ◽  
Free Microtubules ◽  
The Difference ◽  
Brain Microtubules

Microtubules can adjust their length by the mechanism of dynamic instability, that is by switching between phases of growth and shrinkage. Thus far this phenomenon has been studied with microtubules that contain several components, that is, a mixture of tubulin isoforms, with or without a mixture of microtubule-associated proteins (MAPs), which can act as regulators of dynamic instability. Here we concentrate on the influence of the tubulin component. We have studied MAP-free microtubules from the marginal band of avian erythrocytes and compared them with mammalian brain microtubules. The erythrocyte system was selected because it represents a naturally stable aggregate of microtubules; second, the tubulin is largely homogeneous, in contrast to brain tubulin. Qualitatively, erythrocyte microtubules show similar features as brain microtubules, but they were found to be much less dynamic. The critical concentration of elongation, and the rates of association and dissociation of tubulin are all lower than with brain microtubules. Catastrophes are rare, rescues frequent, and shrinkage slow. This means that dynamic instability can be controlled by the tubulin isotype, independently of MAPs. Moreover, the extent of dynamic behavior is highly dependent on buffer conditions. In particular, dynamic instability is strongly enhanced in phosphate buffer, both for erythrocyte marginal band and brain microtubules. The lower stability in phosphate buffer argues against the hypothesis that a cap of tubulin.GDP.Pi subunits stabilizes microtubules. The difference in dynamics between tubulin isotypes and between the two ends of microtubules is preserved in the different buffer systems.

scholarly journals Proteolytic removal of three C-terminal residues of actin alters the monomer-monomer interactions

1993 ◽  
Vol 289 (3) ◽  
pp. 897-902 ◽  
Author(s):  
M Mossakowska ◽  
J Moraczewska ◽  
S Khaitlina ◽  
H Strzelecka-Golaszewska
Keyword(s):  
Electron Microscopy ◽  
Steady State ◽  
Ionic Strength ◽  
Rate Constants ◽  
Initial Rate ◽  
Critical Concentration ◽  
Rate Of Polymerization ◽  
Low Ionic Strength ◽  
Hydrolysis Of

Homogeneous preparations of actin devoid of the three C-terminal residues were obtained by digestion of G-actin with trypsin after blocking proteolysis at other sites by substitution of Mg2+ for the tightly bound Ca2+. Removal of the C-terminal residues resulted in the following: an enhancement of the Mg(2+)-induced hydrolysis of ATP in low-ionic-strength solutions of actin; an increase in the critical concentration for polymerization; a decrease in the initial rate of polymerization; and an enhancement of the steady-state exchange of subunits in the polymer. Electron microscopy indicated an increased fragility of the filaments assembled from truncated actin. The results suggest that removal of the C-terminal residues increases the rate constants for monomer dissociation from the polymer ends and from the oligomeric species.

CRITICAL CONCENTRATION EFFECTS IN POLYMER–POLYMER–SOLVENT SYSTEMS

1958 ◽  
Vol 36 (1) ◽  
pp. 199-205 ◽  
Author(s):  
C. C. Bigelow ◽  
L. H. Cragg
Keyword(s):  
Polymethyl Methacrylate ◽  
Intrinsic Viscosity ◽  
Polyvinyl Acetate ◽  
Mixed Solvent ◽  
Critical Concentration ◽  
Ternary Systems ◽  
Concentration Effects ◽  
Critical Concentrations ◽  
Solvent Systems ◽  
Good Agreement

In various ternary systems of the type polymer A – polymer B – solvent S, a dip or peak has been observed in the [η] – cB curve at the critical concentration of polymer B. ([η] is the intrinsic viscosity of A in mixed solvent consisting of B and S, and cB is the concentration of B in this mixed solvent.) It is shown that such a critical concentration effect is most likely to occur when the solvent is poor for polymer B, and will be the larger the poorer the solvent.Evidence is also presented in support of the hypothesis that if, as is usual, the two polymers repel each other, the effect is a dip if the solvent is good for polymer A and is a peak if the solvent is sufficiently poor for polymer A.Critical concentrations of polystyrene, polyvinyl acetate, and polymethyl methacrylate (five different samples) have been measured in this way in 12 different ternary systems. These observed critical concentrations are in good agreement with values calculated using the equation previously described, according to which the critical concentration of a polymer is inversely proportional to its intrinsic viscosity in the solution.

scholarly journals Relationship between Dynamic Instability of Individual Microtubules and Flux of Subunits into and out of Polymer

2019 ◽  
Author(s):  
Ava J. Mauro ◽  
Erin M. Jonasson ◽  
Holly V. Goodson
Keyword(s):  
Steady State ◽  
Computer Simulations ◽  
Dynamic Instability ◽  
Rate Of Change ◽  
Bulk Polymer ◽  
Multi Scale ◽  
Experimental Approaches ◽  
Short Time ◽  
Individual Filament

ABSTRACTBehaviors of dynamic polymers such as microtubules and actin are frequently assessed at one or both of two scales: (i) net assembly or disassembly of bulk polymer, (ii) growth and shortening of individual filaments. Previous work has derived various forms of an equation to relate the rate of change in bulk polymer mass (i.e., flux of subunits into and out of polymer, often abbreviated as “J”) to individual filament behaviors. However, these versions of this “J equation” differ in the variables used to quantify individual filament behavior, which correspond to different experimental approaches. For example, some variants of the J equation use dynamic instability parameters, obtained by following particular individuals for long periods of time. Another form of the equation uses measurements from many individuals followed over short time steps. We use a combination of derivations and computer simulations that mimic experiments to (i) relate the various forms of the J equation to each other; (ii) determine conditions under which these J equation forms are and are not equivalent; and (iii) identify aspects of the measurements that can affect the accuracy of each form of the J equation. Improved understanding of the J equation and its connections to experimentally measurable quantities will contribute to efforts to build a multi-scale understanding of steady-state polymer behavior.

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