Cooperative motor action to regulate microtubule length dynamics.

Motivated by the recent experimental observations on motor induced cooperative mechanism controlling the length dynamics of microtubules (MTs), we examine how plus-end-targeted proteins of the kinesin family regulate MT polymerization and depolymerization routines. Here, we study a stochastic mathematical model capturing the unusual form of collective motor interaction on MT dynamics originating due to the molecular traffic near the MT tip. We provide an extensive analysis of the joint effect of motor impelled MT polymerization and complete depolymerization. The effect of the cooperative action is included by modifying the intrinsic depolymerization rate. We analyze the model within the framework of continuum mean-field theory and the resultant steady-state analytic solution is expressed in terms of Lambert W functions. Four distinct steady-state phases including a shock phase have been reported. The significant features of the shock including its position and height have been analyzed. Theoretical outcomes are supported by extensive Monte Carlo simulations. To explore the system alterations between the regime of growth and shrinkage phase, we consider kymographs of the microtubule along with the length distributions. Finally, we investigated the dependence of MT length kinetics both on modifying factor of depolymerization rate and motor concentration. The overall extensive study reveals that the flux of molecular traffic at the microtubule plus end initiates a cooperative mechanism, resulting in significant change in MT growth and shrinkage regime as also observed experimentally.

Monte Carlo simulations of microtubule arrays: The critical roles of rescue transitions, the cell boundary, and tubulin concentration in shaping microtubule distributions.

Microtubules are dynamic polymers required for a number of processes, including chromosome movement in mitosis. While regulators of microtubule dynamics have been well characterized, we lack a convenient way to predict how the measured dynamic parameters shape the entire microtubule system within a cell, or how the system responds when specific parameters change in response to internal or external signals. Here we describe a Monte Carlo model to simulate an array of dynamic microtubules from parameters including the cell radius, total tubulin concentration, microtubule nucleation rate from the centrosome, and plus end dynamic instability. The algorithm also allows dynamic instability or position of the cell edge to vary during the simulation. Outputs from simulations include free tubulin concentration, average microtubule lengths, length distributions, and individual length changes over time. Using this platform and reported parameters measured in interphase LLCPK1 epithelial cells, we predict that sequestering ~ 15-20% of total tubulin results in fewer microtubules, but promotes dynamic instability of those remaining. Simulations also predict that lowering nucleation rate will increase the stability and average length of the remaining microtubules. Allowing the position of the cell's edge to vary over time changed the average length but not the number of microtubules and generated length distributions consistent with experimental measurements. Simulating the switch from interphase to prophase demonstrated that decreased rescue frequency at prophase is the critical factor needed to rapidly clear the cell of interphase microtubules prior to mitotic spindle assembly. Finally, consistent with several previous simulations, our results demonstrate that microtubule nucleation and dynamic instability in a confined space determines the partitioning of tubulin between monomer and polymer pools. The model and simulations will be useful for predicting changes to the entire microtubule array after modification to one or more parameters, including predicting the effects of tubulin-targeted chemotherapies.

Example-Based Super-Resolution Fluorescence Microscopy.

Capturing biological dynamics with high spatiotemporal resolution demands the advancement in imaging technologies. Super-resolution fluorescence microscopy offers spatial resolution surpassing the diffraction limit to resolve near-molecular-level details. While various strategies have been reported to improve the temporal resolution of super-resolution imaging, all super-resolution techniques are still fundamentally limited by the trade-off associated with the longer image acquisition time that is needed to achieve higher spatial information. Here, we demonstrated an example-based, computational method that aims to obtain super-resolution images using conventional imaging without increasing the imaging time. With a low-resolution image input, the method provides an estimate of its super-resolution image based on an example database that contains super- and low-resolution image pairs of biological structures of interest. The computational imaging of cellular microtubules agrees approximately with the experimental super-resolution STORM results. This new approach may offer potential improvements in temporal resolution for experimental super-resolution fluorescence microscopy and provide a new path for large-data aided biomedical imaging.

Signatures of a macroscopic switching transition for a dynamic microtubule.

Characterising complex kinetics of non-equilibrium self-assembly of bio-filaments is of general interest. Dynamic instability in microtubules, consisting of successive catastrophes and rescues, is observed to occur as a result of the non-equilibrium conversion of GTP-tubulin to GDP-tubulin. We study this phenomenon using a model for microtubule kinetics with GTP/GDP state-dependent polymerisation, depolymerisation and hydrolysis of subunits. Our results reveal a sharp switch-like transition in the mean velocity of the filaments, from a growth phase to a shrinkage phase, with an associated co-existence of the two phases. This transition is reminiscent of the discontinuous phase transition across the liquid-gas boundary. We probe the extent of discontinuity in the transition quantitatively using characteristic signatures such as bimodality in velocity distribution, variance and Binder cumulant, and also hysteresis behaviour of the system. We further investigate ageing behaviour in catastrophes of the filament, and find that the multi-step nature of catastrophes is intensified in the vicinity of the switching transition. This assumes importance in the context of Microtubule Associated Proteins which have the potential of altering kinetic parameter values.

Single-molecule tracking of tau reveals fast kiss-and-hop interaction with microtubules in living neurons.

The microtubule-associated phosphoprotein tau regulates microtubule dynamics and is involved in neurodegenerative diseases collectively called tauopathies. It is generally believed that the vast majority of tau molecules decorate axonal microtubules, thereby stabilizing them. However, it is an open question how tau can regulate microtubule dynamics without impeding microtubule-dependent transport and how tau is also available for interactions other than those with microtubules. Here we address this apparent paradox by fast single-molecule tracking of tau in living neurons and Monte Carlo simulations of tau dynamics. We find that tau dwells on a single microtubule for an unexpectedly short time of ∼40 ms before it hops to the next. This dwell time is 100-fold shorter than previously reported by ensemble measurements. Furthermore, we observed by quantitative imaging using fluorescence decay after photoactivation recordings of photoactivatable GFP-tagged tubulin that, despite this rapid dynamics, tau is capable of regulating the tubulin-microtubule balance. This indicates that tau's dwell time on microtubules is sufficiently long to influence the lifetime of a tubulin subunit in a GTP cap. Our data imply a novel kiss-and-hop mechanism by which tau promotes neuronal microtubule assembly. The rapid kiss-and-hop interaction explains why tau, although binding to microtubules, does not interfere with axonal transport.

Macroscopic simulations of microtubule dynamics predict two steady-state processes governing array morphology.

Microtubule polymers typically function through their collective organization into a patterned array. The formation of the pattern, whether it is a relatively simple astral array or a highly complex mitotic spindle, relies on controlled microtubule nucleation and the basal dynamics parameters governing polymer growth and shortening. We have investigated the interaction between the microtubule nucleation and dynamics parameters, using macroscopic Monte Carlo simulations, to determine how these parameters contribute to the underlying microtubule array morphology (i.e. polymer density and length distribution). In addition to the well-characterized steady state achieved between free tubulin subunits and microtubule polymer, we propose that microtubule nucleation and extinction constitute a second, interdependent steady state process. Our simulation studies show that the magnitude of both nucleation and extinction additively impacts the final steady state free subunit concentration. We systematically varied individual microtubule dynamics parameters to survey the effects on array morphology and find specific sensitivity to perturbations of catastrophe frequency. Altering the cellular context for the microtubule array, we find that nucleation template number plays a defining role in shaping the microtubule length distribution and polymer density.

Intrabundle microtubule dynamics in the Arabidopsis cortical array.

We tested the general hypothesis that bundling stabilizes the dynamic properties of the constituent microtubules (MTs) in vivo. We quantified the assembly dynamics of bundled and unbundled MTs in the interphase cortical array of Arabidopsis hypocotyl cells using high dynamic range spinning disk confocal microscopy. We find no evidence that bundled MTs are stabilized against depolymerization through changes to their dynamic properties. Our observations of MT plus and minus ends indicate that both bundled and unbundled polymers undergo persistent treadmilling in this system. We conclude that the temporal persistence of MT subassemblies in the Arabidopsis cortical array is largely dependent upon recruitment or nucleation of new treadmilling MTs and not on polymer stabilization. Monte Carlo simulations suggest that small differences discovered in the dynamic properties between bundled and unbundled polymers would produce relatively small macroscopic effects on the larger MT array.

Microtubule depolymerization by the Kinesin-8 motor Kip3p: a mathematical model.

Proteins from the kinesin-8 family promote microtubule (MT) depolymerization, a process thought to be important for the control of microtubule length in living cells. In addition to this MT shortening activity, kinesin 8s are motors that show plus-end directed motility on MTs. Here we describe a simple model that incorporates directional motion and destabilization of the MT plus-end by kinesin 8. Our model quantitatively reproduces the key features of length-versus-time traces for stabilized MTs in the presence of purified kinesin 8, including length-dependent depolymerization. Comparison of model predictions with experiments suggests that kinesin 8 depolymerizes processively, i.e., one motor can remove multiple tubulin dimers from a stabilized MT. Fluctuations in MT length as a function of time are related to depolymerization processivity. We have also determined the parameter regime in which the rate of MT depolymerization is length dependent: length-dependent depolymerization occurs only when MTs are sufficiently short; this crossover is sensitive to the bulk motor concentration.

Detection of GTP-tubulin conformation in vivo reveals a role for GTP remnants in microtubule rescues.

Microtubules display dynamic instability, with alternating phases of growth and shrinkage separated by catastrophe and rescue events. The guanosine triphosphate (GTP) cap at the growing end of microtubules, whose presence is essential to prevent microtubule catastrophes in vitro, has been difficult to observe in vivo. We selected a recombinant antibody that specifically recognizes GTP-bound tubulin in microtubules and found that GTP-tubulin was indeed present at the plus end of growing microtubules. Unexpectedly, GTP-tubulin remnants were also present in older parts of microtubules, which suggests that GTP hydrolysis is sometimes incomplete during polymerization. Observations in living cells suggested that these GTP remnants may be responsible for the rescue events in which microtubules recover from catastrophe.

A novel approach to determine water content in DMSO for a compound collection repository.

The quality of a corporate compound collection can be significantly affected by a complex combination of storage and operational processing factors. Water content in DMSO solutions is one factor that is of great interest as it can affect solubility, degradation, and freeze-thaw cycle parameters. To the authors' knowledge, this is the first report of using near-infrared (NIR) spectroscopy to assess water content in DMSO compound stock solutions within the common storage vessel format of polypropylene microtubes. The precision and accuracy of the NIR technique was benchmarked against a Karl Fisher titration method, and a correlation coefficient was determined to be 0.985 over a range of 1% to 10% water in DMSO by weight. The advantages of the NIR technique include accuracy, precision, speed, nondestructiveness, and the capability of assessing compounds under in situ storage conditions within microtubes. In this report, the authors demonstrate the accuracy and precision of using NIR to assess water content in DMSO solutions and present a case study to demonstrate the utility of the technique to aid in assessing a pharmaceutical compound collection.

Encounters between dynamic cortical microtubules promote ordering of the cortical array through angle-dependent modifications of microtubule behavior.

Ordered cortical microtubule arrays are essential for normal plant morphogenesis, but how these arrays form is unclear. The dynamics of individual cortical microtubules are stochastic and cannot fully account for the observed order; however, using tobacco (Nicotiana tabacum) cells expressing either the MBD-DsRed (microtubule binding domain of the mammalian MAP4 fused to the Discosoma sp red fluorescent protein) or YFP-TUA6 (yellow fluorescent protein fused to the Arabidopsis alpha-tubulin 6 isoform) microtubule markers, we identified intermicrotubule interactions that modify their stochastic behaviors. The intermicrotubule interactions occur when the growing plus-ends of cortical microtubules encounter previously existing cortical microtubules. Importantly, the outcome of such encounters depends on the angle at which they occur: steep-angle collisions are characterized by approximately sevenfold shorter microtubule contact times compared with shallow-angle encounters, and steep-angle collisions are twice as likely to result in microtubule depolymerization. Hence, steep-angle collisions promote microtubule destabilization, whereas shallow-angle encounters promote both microtubule stabilization and coalignment. Monte Carlo modeling of the behavior of simulated microtubules, according to the observed behavior of transverse and longitudinally oriented cortical microtubules in cells, reveals that these simple rules for intermicrotubule interactions are necessary and sufficient to facilitate the self-organization of dynamic microtubules into a parallel configuration.

The importance of lattice defects in katanin-mediated microtubule severing in vitro.

The microtubule-severing enzyme katanin uses ATP hydrolysis to disrupt noncovalent bonds between tubulin dimers within the microtubule lattice. Although its microtubule severing activity is likely important for fundamental processes including mitosis and axonal outgrowth, its mechanism of action is poorly understood. To better understand this activity, an in vitro assay was developed to enable the real-time observation of katanin-mediated severing of individual, mechanically unconstrained microtubules. To interpret the experimental observations, a number of theoretical models were developed and compared quantitatively to the experimental data via Monte Carlo simulation. Models that assumed that katanin acts on a uniform microtubule lattice were incompatible with the in vitro data, whereas a model that assumed that katanin acts preferentially on spatially infrequent microtubule lattice defects was found to correctly predict the experimentally observed breaking rates, number and spatial frequency of severing events, final levels of severing, and sensitivity to katanin concentration over the range 6-300 nM. As a result of our analysis, we propose that defects in the microtubule lattice, which are known to exist but previously not known to have any biological function, serve as sites for katanin activity.

Thermodynamic and structural analysis of microtubule assembly: the role of GTP hydrolysis.

Different models have been proposed that link the tubulin heterodimer nucleotide content and the role of GTP hydrolysis with microtubule assembly and dynamics. Here we compare the thermodynamics of microtubule assembly as a function of nucleotide content by van't Hoff analysis. The thermodynamic parameters of tubulin assembly in 30-100 mM piperazine-N,N'-bis(2-ethanesulfonic acid), 1 mM MgSO4, 2 mM EGTA, pH 6.9, in the presence of a weakly hydrolyzable analog, GMPCPP, the dinucleotide analog GMPCP plus 2 M glycerol, and GTP plus 2 M glycerol were obtained together with data for taxol-GTP/GDP tubulin assembly (GMPCPP and GMPCP are the GTP and GDP nucleotide analogs where the alpha beta oxygen has been replaced by a methylene, -CH2-). All of the processes studied are characterized by a positive enthalpy, a positive entropy, and a large, negative heat capacity change. GMPCP-induced assembly has the largest negative heat capacity change and GMPCPP has the second largest, whereas GTP/2 M glycerol- and taxol-induced assembly have more positive values, respectively. A large, negative heat capacity is most consistent with the burial of water-accessible hydrophobic surface area, which gives rise to the release of bound water. The heat capacity changes observed with GTP/2 M glycerol-induced and with taxol-induced assembly are very similar, -790 +/- 190 cal/mol/k, and correspond to the burial of 3330 +/- 820 A2 of nonpolar surface area. This value is shown to be very similar to an estimate of the buried nonpolar surface in a reconstructed microtubule lattice. Polymerization data from GMPCP- and GMPCPP-induced assembly are consistent with buried nonpolar surface areas that are 3 and 6 times larger. A linear enthalpy-entropy and enthalpy-free energy plot for tubulin polymerization reactions verifies that enthalpy-entropy compensation for this system is based upon true biochemical correlation, most likely corresponding to a dominant hydrophobic effect. Entropy analysis suggests that assembly with GTP/2 M glycerol and with taxol is consistent with conformational rearrangements in 3-6% of the total amino acids in the heterodimer. In addition, taxol binding contributes to the thermodynamics of the overall process by reducing the delta H degree and delta S degree for microtubule assembly. In the presence of GMPCPP or GMPCP, tubulin subunits associate with extensive conformational rearrangement, corresponding to 10% and 26% of the total amino acids in the heterodimer, respectively, which gives rise to a large loss of configurational entropy. An alternative, and probably preferable, interpretation of these data is that, especially with GMPCP-tubulin, additional isomerization or protonation events are induced by the presence of the methylene moiety and linked to microtubule assembly. Structural analysis shows that GTP hydrolysis is not required for sheet closure into a microtubule cylinder, but only increases the probability of this event occurring. Sheet extensions and sheet polymers appear to have a similar average length under various conditions, suggesting that the minimum cooperative unit for closure of sheets into a microtubule cylinder is approximately 400 nm long. Because of their low level of occurrence, sheets are not expected to significantly affect the thermodynamics of assembly.

Diffusion and formation of microtubule asters: physical processes versus biochemical regulation.

Microtubule asters forming the mitotic spindle are assembled around two centrosomes through the process of dynamic instability in which microtubules alternate between growing and shrinking states. By modifying the dynamics of this assembly process, cell cycle enzymes, such as cdc2 cyclin kinases, regulate length distributions in the asters. It is believed that the same enzymes control the number of assembled microtubules by changing the "nucleating activity" of the centrosomes. Here we show that assembly of microtubule asters may be strongly altered by effects connected with diffusion of tubulin monomers. Theoretical analysis of a simple model describing assembly of microtubule asters clearly shows the existence of a region surrounding the centrosome depleted in GTP tubulin. The number of assembled microtubules may in some cases be limited by this depletion effect rather than by the number of available nucleation sites on the centrosome.

Dynamic instability of microtubules: Monte Carlo simulation and application to different types of microtubule lattice.

Dynamic instability is the term used to describe the transition of an individual microtubule, apparently at random, between extended periods of slow growth and brief periods of rapid shortening. The typical sawtooth growth and shortening transition behavior has been successfully simulated numerically for the 13-protofilament microtubule A-lattice by a lateral cap model (Bayley, P. M., M. J. Schilstra, and S. R. Martin. 1990. J. Cell Sci. 95:33-48). This kinetic model is now extended systematically to other related lattice geometries, namely the 13-protofilament B-lattice and the 14-protofilament A-lattice, which contain structural "seams". The treatment requires the assignment of the free energies of specific protein-protein interactions in terms of the basic microtubule lattice. It is seen that dynamic instability is not restricted to the helically symmetric 13-protofilament A-lattice but is potentially a feature of all A- and B-lattices, irrespective of protofilament number. The advantages of this general energetic approach are that it allows a consistent treatment to be made for both ends of any microtubule lattice. Important features are the predominance of longitudinal interactions between tubulin molecules within the same protofilament and the implication of a relatively favorable interaction of tubulin-GDP with the growing microtubule end. For the three lattices specifically considered, the treatment predicts the dependence of the transition behavior upon tubulin concentration as a cooperative process, in good agreement with recent experimental observations. The model rationalizes the dynamic properties in terms of a metastable microtubule lattice of tubulin-GDP, stabilized by the kinetic process of tubulin-GTP addition. It provides a quantitative basis for the consideration of in vitro microtubule behaviour under both steady-state and non-steady-state conditions, for comparison with experimental data on the dilution-induced disassembly of microtubules. Similarly, the effects of small tubulin-binding molecules such as GDP and nonhydrolyzable GTP analogues are readily treated. An extension of the model allows a detailed quantitative examination of possible modes of substoichiometric action of a number of antimitotic drugs relevant to cancer chemotherapy.

A morphological control for ventricular pathology in man: a morphometric and morphologic assessment of LV myofibres in secundum ASD.

Ethical considerations preclude the biopsy of normal human myocardium. As a consequence, morphological investigations of diseased human heart muscle are hampered by a lack of suitable normal control tissue. The left ventricular (LV) myocardium of patients with isolated secundum atrial septal defect (ASD) is considered to be normal. This study was designed to investigate the possibility that the fine-structure of LV myofibres in hearts with ASD could be used as normal controls for myofibre pathomorphology. Wedge biopsies from the LV of four adults undergoing elective surgery for the repair of ASD were examined by light and electron microscopy. Bivariant myofibre morphometry showed that the LV myocardium of one specimen was 'normal' while three specimens exhibited varying degrees of hypertrophy. There was a correlation between the diameter (FD) and morphology of individual myofibres within and between specimens. In general, myofibres with FD less than 25 microns were similar in fine-structural appearance to those described as morphologically normal in animal models whereas those with FD greater than 25 microns exhibited hypertrophic features that increased in 'severity' with increase in myofibre size. It is proposed that although the LV myocardium in ASD may be mildly hypertrophied, myofibres with FD less than 25 microns are probably normal and may be used as fine-structural controls for myofibre pathomorphology in hearts suspected of disease.

Mechanical effects on endothelial cell morphology: in vitro assessment.

Endothelial cells are subjected to fluid mechanical forces which accompany blood flow. These cells become elongated and orient their long axes parallel to the direction of shear stress when the cultured cells are subjected to flow in an in vitro circulatory system. When the substrate is compliant and cyclically deformed, to simulate effects of pressure in the vasculature, the cells elongate an orient perpendicular to the axis of deformation. Cell shape changes are reflected in the alignment of microtubule networks. The systems described provide tools for assessing the individual roles of shear stress, pressure, and mechanical strain on vascular cell structure and function.

The distribution and assessment of electron-microscopic abnormalities of human cilia.

The aim of this study was to overcome difficulties of assessing the true incidence of electromicroscopic abnormalities of microtubular structure of cilia by examining large numbers of cilia from each case. The effects of different fixatives on the appearances of cilia were also studied. Bronchial biopsies were examined from 35 subjects who were being investigated for various lung diseases and nasal biopsies from 12 subjects (7 with retinitis pigmentosa (R.P.), and 5 healthy controls). Numerous pieces of normal looking bronchial wall from a lobectomy specimen were used to examine the effect of six different fixatives. 2.9% of bronchial cilia (mean of 890 cilia examined) and 2.4% of nasal cilia (mean of 808 cilia examined) showed microtubular abnormalities. Examining large numbers of cilia established that increased microtubular abnormalities were associated with smoking, chronic pulmonary infection and carcinoma of the lung. There was a significant increase (p less than 0.001) in microtubular abnormalities in nasal cilia in R.P. The appearances of cilia varied considerably with different fixatives. The numbers of dynein arms seen and the ease of recognising radial spokes and microtubules was particularly effected by fixation. The true incidence of microtubular abnormalities can only be ascertained by examining large numbers of cilia.