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Summary: Protein concentration gradients encode spatial information across cells and tissues and often depend on spatially localized protein synthesis. Here, we report that a different mechanism underlies the MEX-5 gradient. MEX-5 is an RNA-binding protein that becomes distributed in a cytoplasmic gradient along the anterior-to-posterior axis of the one-cell C. elegans embryo. We demonstrate that the MEX-5 gradient is a direct consequence of an underlying gradient in MEX-5 diffusivity. The MEX-5 diffusion gradient arises when the PAR-1 kinase stimulates the release of MEX-5 from slow-diffusive, RNA-containing complexes in the posterior cytoplasm. PAR-1 directly phosphorylates MEX-5 and is antagonized by the spatially uniform phosphatase PP2A. Mathematical modeling and in vivo observations demonstrate that spatially segregated phosphorylation and dephosphorylation reactions are sufficient to generate stable protein concentration gradients in the cytoplasm. The principles demonstrated here apply to any spatially segregated modification cycle that affects protein diffusion and do not require protein synthesis or degradation. [Copyright &y& Elsevier]

Summary: Background: Breaking cell symmetry, known as polarization, requires dynamic reorganization of microtubules (MTs) and is essential to many cellular processes, including axon formation in neurons. A critical step in polarization is believed to be the “selective stabilization” of MTs, which hypothesizes a spatial and/or temporal shift toward net MT assembly in a preferred direction of growth. Results: We now find that a simpler “length-dependent” model, in which MT assembly parameters are spatially and temporally constant, predicts MT accumulation in the direction of growth because of longer mean first passage times in the longer direction. We experimentally tested both models by tracking MT assembly dynamics in polarizing embryonic chick forebrain neurons, and we confirmed that assembly is spatially and temporally constant during axon formation. Conclusion: Cell polarization occurs most simply through cell-length-dependent accumulation of MTs without MT stabilization or capture. In this way, F-actin-mediated cell shape and size changes can be read out by dynamic MTs undergoing simple dynamic instability to ultimately break cell symmetry. [Copyright &y& Elsevier]

Small molecule inhibitors of microtubule dynamics are widely used as cell biology research tools and clinically as cancer chemotherapeutics. By slight modification to the chemical structure of a known microtubule inhibitor, combretastatin A-4, Borowiak et al. develop a photoswitchable derivative that can be turned “on” and “off” with low-intensity light to spatially and temporally control microtubule dynamics. [ABSTRACT FROM AUTHOR]

During mitosis, molecular motors hydrolyze ATP to generate sliding forces between adjacent microtubules and form the bipolar mitotic spindle. Lansky et al. now show that the diffusible microtubule crosslinker Ase1p can generate sliding forces between adjacent microtubules, and it does so without ATP hydrolysis. [ABSTRACT FROM AUTHOR]

A new study shows that an antagonistic force model can explain a number of complex mitotic spindle movements in the first mitosis of the Caenorhabditis elegans embryo by simply assuming that cortical force generators become increasingly persistent in their interaction with microtubules during mitosis. [Copyright &y& Elsevier]

Mitotic spindles maintain a roughly constant length in metaphase, so the forces between the spindle poles are balanced. A new study involving screening molecules believed to mediate this force balance has found that spindle length is relatively insensitive to perturbations of molecular motor force-generating activities, but more sensitive to perturbation of microtubule assembly regulators and chromosome cohesion. [Copyright &y& Elsevier]

To form a proper mitotic spindle, all kinetochores must capture at least one microtubule plus end. A new computational modeling study shows that a search-and-capture mechanism based on spatially unbiased microtubule dynamic instability is too slow to account for the experimentally observed rate of chromosome capture. [Copyright &y& Elsevier]

Summary: Background: In order for signals generated at the plasma membrane to reach intracellular targets, activated messengers, such as G proteins and phosphoproteins, must diffuse through the cytoplasm. If the deactivators of these messengers, GTPase activating proteins (GAPs) and phosphatases, respectively, are sufficiently active in the cytoplasm, then the signal could in principle decay before reaching the target and a stable spatial gradient in phosphostate would be generated. Recent experiments document the existence of such gradients in living cells and suggest a role for them in mitotic spindle morphogenesis and cell migration. However, how such systems behave theoretically when embedded in a cell of varying size or shape has not been considered. Results: Here we use a simple mathematical model to explore the theoretical consequences of a plasma membrane bound activator (i.e., guanine nucleotide exchange factor, GEF, or kinase) and a cytoplasmic deactivator (i.e., GAP or phosphatase), and we find that as a model cell grows, the substrate becomes progressively dephosphorylated as a result of decreased proximity to the activator. Conversely, as a cell spreads and flattens, the substrate becomes globally phosphorylated because of increased proximity of the substrate to the activator. Similarly, in the leading edge of polarized cells and in protrusions such as lamellipodia or filopodia, the substrate is highly phosphorylated. As a specific test of the model, we found that the experimentally observed preferential activation of the G protein Cdc42 in the periphery of fibroblasts that was recently reported is consistent with model predictions. Conclusions: We conclude that cell-signaling pathways can theoretically be turned on and off, both locally and globally, in response to alterations in cell size and shape. [Copyright &y& Elsevier]

Summary: Microtubules are key structural and transport elements in cells. The dynamics at microtubule ends are characterized by periods of slow growth, followed by stochastic switching events termed “catastrophes,” in which microtubules suddenly undergo rapid shortening [1]. Growing microtubules are thought to be protected from catastrophe by a GTP-tubulin “cap”: GTP-tubulin subunits add to the tips of growing microtubules but are subsequently hydrolyzed to GDP-tubulin subunits once they are incorporated into the microtubule lattice [2–4]. Loss of the GTP-tubulin cap exposes GDP-tubulin subunits at the microtubule tip, resulting in a catastrophe event [5–9]. However, the mechanistic basis for sudden loss of the GTP cap, leading to catastrophe, is not known. To investigate microtubule catastrophe events, we performed 3D mechanochemical simulations that account for interactions between neighboring protofilaments [10–12]. We found that there are two separate factors that contribute to catastrophe events in the 3D simulation: the GTP-tubulin cap size, which settles into a steady-state value that depends on the free tubulin concentration during microtubule growth, and the structure of the microtubule tip. Importantly, 3D simulations predict, and both fluorescence and electron microscopy experiments confirm, that microtubule tips become more tapered as the microtubule grows. This effect destabilizes the tip and ultimately contributes to microtubule catastrophe. Thus, the likelihood of a catastrophe event may be intimately linked to the aging physical structure of the growing microtubule tip. These results have important consequences for catastrophe regulation in cells, as microtubule-associated proteins could promote catastrophe events in part by modifying microtubule tip structures. [Copyright &y& Elsevier]

Summary: Microtubules (MTs) polymerize via net addition of GTP-tubulin subunits to the MT plus end, which subsequently hydrolyze to GDP-tubulin in the MT lattice. Relatively stable GTP-tubulin subunits create a “GTP cap” at the growing MT plus end that suppresses catastrophe. To understand MT assembly regulation, we need to understand GTP hydrolysis reaction kinetics and the GTP cap size. In vitro, the GTP cap has been estimated to be as small as one layer [1–3] (13 subunits) or as large as 100–200 subunits [4]. GTP cap size estimates in vivo have not yet been reported. Using EB1-EGFP as a marker for GTP-tubulin in epithelial cells, we find on average (1) 270 EB1 dimers bound to growing MT plus ends, and (2) a GTP cap size of ∼750 tubulin subunits. Thus, in vivo, the GTP cap is far larger than previous estimates in vitro, and ∼60-fold larger than a single layer cap. We also find that the tail of a large GTP cap promotes MT rescue and suppresses shortening. We speculate that a large GTP cap provides a locally concentrated scaffold for tip-tracking proteins and confers persistence to assembly in the face of physical barriers such as the cell cortex. [ABSTRACT FROM AUTHOR]

Summary: Microtubules undergo alternating periods of growth and shortening, known as dynamic instability. These dynamics allow microtubule plus ends to explore cellular space. The “search and capture” model posits that selective anchoring of microtubule plus ends at the cell cortex may contribute to cell polarization, spindle orientation, or targeted trafficking to specific cellular domains []. Whereas cytoplasmic dynein is primarily known as a minus-end-directed microtubule motor for organelle transport, cortically localized dynein has been shown to capture and tether microtubules at the cell periphery in both dividing and interphase cells []. To explore the mechanism involved, we developed a minimal in vitro system, with dynein-bound beads positioned near microtubule plus ends using an optical trap. Dynein induced a significant reduction in the lateral diffusion of microtubule ends, distinct from the effects of other microtubule-associated proteins such as kinesin-1 and EB1. In assays with dynamic microtubules, dynein delayed barrier-induced catastrophe of microtubules. This effect was ATP dependent, indicating that dynein motor activity was required. Computational modeling suggests that dynein delays catastrophe by exerting tension on individual protofilaments, leading to microtubule stabilization. Thus, dynein-mediated capture and tethering of microtubules at the cortex can lead to enhanced stability of dynamic plus ends. [ABSTRACT FROM AUTHOR]

Summary: Microtubule assembly is vital for many fundamental cellular processes. Current models for microtubule assembly kinetics assume that the subunit dissociation rate from a microtubule tip is independent of free subunit concentration. Total-Internal-Reflection-Fluorescence (TIRF) microscopy experiments and data from a laser tweezers assay that measures in vitro microtubule assembly with nanometer resolution, provides evidence that the subunit dissociation rate from a microtubule tip increases as the free subunit concentration increases. These data are consistent with a two-dimensional model for microtubule assembly, and are explained by a shift in microtubule tip structure from a relatively blunt shape at low free concentrations to relatively tapered at high free concentrations. We find that because both the association and the dissociation rates increase at higher free subunit concentrations, the kinetics of microtubule assembly are an order-of-magnitude higher than currently estimated in the literature. [ABSTRACT FROM AUTHOR]

Summary: During mitosis, sister chromatids congress to the spindle equator and are subsequently segregated via attachment to dynamic kinetochore microtubule (kMT) plus ends. A major question is how kMT plus-end assembly is spatially regulated to achieve chromosome congression. Here we find in budding yeast that the widely conserved kinesin-5 sliding motor proteins, Cin8p and Kip1p, mediate chromosome congression by suppressing kMT plus-end assembly of longer kMTs. Of the two, Cin8p is the major effector and its activity requires a functional motor domain. In contrast, the depolymerizing kinesin-8 motor Kip3p plays a minor role in spatial regulation of yeast kMT assembly. Our analysis identified a model where kinesin-5 motors bind to kMTs, move to kMT plus ends, and upon arrival at a growing plus end promote net kMT plus-end disassembly. In conclusion, we find that length-dependent control of net kMT assembly by kinesin-5 motors yields a simple and stable self-organizing mechanism for chromosome congression. [Copyright &y& Elsevier]

Summary: Background: The labile nature of microtubules is critical for establishing cellular morphology and motility, yet the molecular basis of assembly remains unclear. Here we use optical tweezers to track microtubule polymerization against microfabricated barriers, permitting unprecedented spatial resolution. Results: We find that microtubules exhibit extensive nanometer-scale variability in growth rate and often undergo shortening excursions, in some cases exceeding five tubulin layers, during periods of overall net growth. This result indicates that the guanosine triphosphate (GTP) cap does not exist as a single layer as previously proposed. We also find that length increments (over 100 ms time intervals, n = 16,762) are small, 0.81 ± 6.60 nm (mean ± standard deviation), and very rarely exceed 16 nm (about two dimer lengths), indicating that assembly occurs almost exclusively via single-subunit addition rather than via oligomers as was recently suggested. Finally, the assembly rate depends only weakly on load, with the average growth rate decreasing only 2-fold as the force increases 7-fold from 0.4 pN to 2.8 pN. Conclusions: The data are consistent with a mechanochemical model in which a spatially extended GTP cap allows substantial shortening on the nanoscale, while still preventing complete catastrophe in most cases. [Copyright &y& Elsevier]

Summary: Background: Duplicated chromosomes are equally segregated to daughter cells by a bipolar mitotic spindle during cell division. By metaphase, sister chromatids are coupled to microtubule (MT) plus ends from opposite poles of the bipolar spindle via kinetochores. Here we describe a phosphorylation event that promotes the coupling of kinetochores to microtubule plus ends. Results: Dam1 is a kinetochore component that directly binds to microtubules. We identified DAM1-765, a dominant allele of DAM1, in a genetic screen for mutations that increase stress on the spindle pole body (SPB) in Saccharomyces cerevisiae. DAM1-765 contains the single mutation S221F. We show that S221 is one of six Dam1 serines (S13, S49, S217, S218, S221, and S232) phosphorylated by Mps1 in vitro. In cells with single mutations S221F, S218A, or S221A, kinetochores in the metaphase spindle form tight clusters that are closer to the SPBs than in a wild-type cell. Five lines of experimental evidence, including localization of spindle components by fluorescence microscopy, measurement of microtubule dynamics by fluorescence redistribution after photobleaching, and reconstructions of three-dimensional structure by electron tomography, combined with computational modeling of microtubule behavior strongly indicate that, unlike wild-type kinetochores, Dam1-765 kinetochores do not colocalize with an equal number of plus ends. Despite the uncoupling of the kinetochores from the plus ends of MTs, the DAM1-765 cells are viable, complete the cell cycle with the same kinetics as wild-type cells, and biorient their chromosomes as efficiently as wild-type cells. Conclusions: We conclude that phosphorylation of Dam1 residues S218 and S221 by Mps1 is required for efficient coupling of kinetochores to MT plus ends. We find that efficient plus-end coupling is not required for (1) maintenance of chromosome biorientation, (2) maintenance of tension between sister kinetochores, or (3) chromosome segregation. [Copyright &y& Elsevier]

Cells exert forces on mechanically compliant environments to sense stiffness, migrate, and remodel tissue. Cells can sense environmental stiffness via myosin-generated pulling forces acting on F-actin, which is in turn mechanically coupled to the environment via adhesive proteins, akin to a clutch in a drivetrain. In this "motor-clutch" framework, the force transmitted depends on the complex interplay of motor, clutch, and environmental properties. Previous mean-field analysis of the motor-clutch model identified the conditions for optimal stiffness for maximal force transmission via a dimensionless number that combines motor-clutch parameters. However, in this and other previous mean-field analyses, the motor-clutch system is assumed to have balanced motors and clutches and did not consider force-dependent clutch reinforcement and catch bond behavior. Here, we generalize the motor-clutch analytical framework to include imbalanced motor-clutch regimes, with clutch reinforcement and catch bonding, and investigate optimality with respect to all parameters. We found that traction force is strongly influenced by clutch stiffness, and we discovered an optimal clutch stiffness that maximizes traction force, suggesting that cells could tune their clutch mechanical properties to perform a specific function. The results provide guidance for maximizing the accuracy of cell-generated force measurements via molecular tension sensors by designing their mechanosensitive linker peptide to be as stiff as possible. In addition, we found that, on rigid substrates, the mean-field analysis identifies optimal motor properties, suggesting that cells could regulate their myosin repertoire and activity to maximize force transmission. Finally, we found that clutch reinforcement shifts the optimum substrate stiffness to larger values, whereas the optimum substrate stiffness is insensitive to clutch catch bond properties. Overall, our work reveals novel features of the motor-clutch model that can affect the design of molecular tension sensors and provide a generalized analytical framework for predicting and controlling cell adhesion and migration in immunotherapy and cancer., Competing Interests: Declaration of interests P.P.P. is a member of the Scientific Advisory Board for Parthenon Therapeutics., (Copyright © 2023 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Navigation through a dense, physically confining extracellular matrix is common in invasive cell spread and tissue reorganization but is still poorly understood. Here, we show that this migration is mediated by cyclic changes in the activity of a small GTPase RhoA, which is dependent on the oscillatory changes in the activity and abundance of the RhoA guanine nucleotide exchange factor, GEF-H1, and triggered by a persistent increase in the intracellular Ca 2+ levels. We show that the molecular clock driving these cyclic changes is mediated by two coupled negative feedback loops, dependent on the microtubule dynamics, with a frequency that can be experimentally modulated based on a predictive mathematical model. We further demonstrate that an increasing frequency of the clock translates into a faster cell migration within physically confining spaces. This work lays the foundation for a better understanding of the molecular mechanisms dynamically driving cell migration in complex environments., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2022 Elsevier Inc. All rights reserved.)

Plus-end tracking proteins (+TIPs) associate with the growing end of microtubules and mediate important cellular functions. The majority of +TIPs are directed to the plus-end through a family of end-binding proteins (EBs), which preferentially bind the stabilizing cap of GTP-tubulin present during microtubule growth. One outstanding question is whether there may exist other microtubule-associated proteins (MAPs) that preferentially bind specific nucleotide states of tubulin. Here, we report that the neuronal MAP tau preferentially binds GDP-tubulin ( K D  = 0.26 μM) over GMPCPP-tubulin ( K D  = 1.1 μM) in vitro, as well as GTP-tubulin at the tips of growing microtubules, causing tau binding to lag behind the plus-end both in vitro and in live cells. Thus, tau is a microtubule tip avoiding protein, establishing the framework for a possible new class of tip avoiding MAPs. We speculate that disease-relevant tau mutations may exert their phenotype by their failure to properly recognize GDP-tubulin., Competing Interests: The authors declare no competing interests., (© 2020 The Authors.)

Biological tissues contain micrometer-scale gaps and pores, including those found within extracellular matrix fiber networks, between tightly packed cells, and between blood vessels or nerve bundles and their associated basement membranes. These spaces restrict cell motion to a single-spatial dimension (1D), a feature that is not captured in traditional in vitro cell migration assays performed on flat, unconfined two-dimensional (2D) substrates. Mechanical confinement can variably influence cell migration behaviors, and it is presently unclear whether the mechanisms used for migration in 2D unconfined environments are relevant in 1D confined environments. Here, we assessed whether a cell migration simulator and associated parameters previously measured for cells on 2D unconfined compliant hydrogels could predict 1D confined cell migration in microfluidic channels. We manufactured microfluidic devices with narrow channels (60-μm 2 rectangular cross-sectional area) and tracked human glioma cells that spontaneously migrated within channels. Cell velocities (v exp  = 0.51 ± 0.02 μm min -1 ) were comparable to brain tumor expansion rates measured in the clinic. Using motor-clutch model parameters estimated from cells on unconfined 2D planar hydrogel substrates, simulations predicted similar migration velocities (v sim  = 0.37 ± 0.04 μm min -1 ) and also predicted the effects of drugs targeting the motor-clutch system or cytoskeletal assembly. These results are consistent with glioma cells utilizing a motor-clutch system to migrate in confined environments., (Copyright © 2020 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Glioblastoma is a primary malignant brain tumor characterized by highly infiltrative glioma cells. Vasculature and white matter tracts are considered to be the preferred and fastest routes for glioma invasion through brain tissue. In this study, we systematically quantified the routes and motility of the U251 human glioblastoma cell line in mouse brain slices by multimodal imaging. Specifically, we used polarization-sensitive optical coherence tomography to delineate nerve fiber tracts while confocal fluorescence microscopy was used to image cell migration and brain vasculature. Somewhat surprisingly, we found that in mouse brain slices, U251 glioma cells do not follow white matter tracts but rather preferentially migrate along vasculature in both gray and white matter. In addition, U251 cell motility is ∼2-fold higher in gray matter than in white matter (91 vs. 43 μm 2 /h), with a substantial fraction (44%) of cells in both regions invading without close association with vasculature. Interestingly, within both regions, the rates of migration for the perivascular and televascular routes of invasion were indistinguishable. Furthermore, by imaging of local vasculature deformation dynamics during cell migration, we found that U251 cells are capable of exerting traction forces that locally pull on their environment, suggesting the applicability of a "motor-clutch"-based model for migration in vivo. Overall, by quantitatively analyzing the migration dynamics along the diverse pathways followed by invading U251 glioma cells as observed by our multimodal imaging approach, our studies suggest that effective antiinvasive strategies will need to simultaneously limit parallel routes of both perivascular and televascular invasion through both gray and white matter., (Copyright © 2019 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Microtubules are multistranded polymers in eukaryotic cells that support key cellular functions such as chromosome segregation, motor-based cargo transport, and maintenance of cell polarity. Microtubules self-assemble via "dynamic instability," in which the dynamic plus ends switch stochastically between alternating phases of polymerization and depolymerization. A key question in the field is what are the atomistic origins of this switching, i.e., what is different between the GTP- and GDP-tubulin states that enables microtubule growth and shortening, respectively? More generally, a major challenge in biology is how to connect theoretical frameworks across length- and timescales, from atoms to cellular behavior. In this study, we describe a multiscale model by linking atomistic molecular dynamics (MD), molecular Brownian dynamics (BD), and cellular-level thermokinetic modeling of microtubules. Here, we investigated the underlying interaction energy when tubulin dimers associate laterally by performing all-atom MD simulations. We found that the lateral potential energy is not significantly different among three nucleotide states of tubulin, GTP, GDP, and GMPCPP and is estimated to be ≅ -11 k B T. Furthermore, using MD potential energy in our BD simulations of tubulin dimers confirms that the lateral bond is weak on its own, with a mean lifetime of ∼0.1 μs, implying that the longitudinal bond is required for microtubule assembly. We conclude that nucleotide-dependent lateral-bond strength is not the key mediator microtubule dynamic instability, implying that GTP acts elsewhere to exert its stabilizing influence on microtubule polymer. Furthermore, the estimated lateral-bond strength (ΔG lat 0 ≅ -5 k B T) is well-aligned with earlier estimates based on thermokinetic modeling and light microscopy measurements. Thus, we have computationally connected atomistic-level structural information, obtained by cryo-electron microscopy, to cellular-scale microtubule assembly dynamics using a combination of MD, BD, and thermokinetic models to bridge from Ångstroms to micrometers and from femtoseconds to minutes., (Copyright © 2019. Published by Elsevier Inc.)

Microtubule-targeting agents (MTAs) are widely used chemotherapy drugs capable of disrupting microtubule-dependent cellular functions, such as division and migration. We show that two clinically approved MTAs, paclitaxel and vinblastine, each suppress stiffness-sensitive migration and polarization characteristic of human glioma cells on compliant hydrogels. MTAs influence microtubule dynamics and cell traction forces by nearly opposite mechanisms, the latter of which can be explained by a combination of changes in myosin motor and adhesion clutch number. Our results support a microtubule-dependent signaling-based model for controlling traction forces through a motor-clutch mechanism, rather than microtubules directly relieving tension within F-actin and adhesions. Computational simulations of cell migration suggest that increasing protrusion number also impairs stiffness-sensitive migration, consistent with experimental MTA effects. These results provide a theoretical basis for the role of microtubules and mechanisms of MTAs in controlling cell migration., (Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.)

Proper segregation of the replicated genome requires that kinetochores form and maintain bioriented, amphitelic attachments to microtubules from opposite spindle poles and eliminate erroneous, syntelic attachments to microtubules from the same spindle pole. Phosphorylation of kinetochore proteins destabilizes low-tension kinetochore-microtubule attachments, yet tension stabilizes bioriented attachments. This conundrum for forming high-tension amphitelic attachments is recognized as the "initiation problem of biorientation (IPBO)." A delay before kinetochore-microtubule detachment solves the IPBO, but it lacks a mechanistic framework. We developed a stochastic mathematical model for kinetochore-microtubule error correction in yeast that reveals: (1) under low chromatin tension, requiring a large number of phosphorylation events at multiple sites to achieve detachment provides the necessary delay; and (2) kinetochore-induced microtubule depolymerization generates tension in amphitelic, but not syntelic, attachments. With these requirements, the model provides a mechanistic framework for the delay before detachment to solve the IPBO and demonstrates the high degree of amphitely observed experimentally for wild-type spindles under optimal conditions., (Copyright © 2017 Elsevier Inc. All rights reserved.)

During cell division, a microtubule-based mitotic spindle mediates the faithful segregation of duplicated chromosomes into daughter cells. Proper length control of the metaphase mitotic spindle is critical to this process and is thought to be achieved through a mechanism in which spindle pole separation forces from plus-end-directed motors are balanced by forces from minus-end-directed motors that pull spindle poles together. However, in contrast to this model, metaphase mitotic spindles with inactive kinesin-14 minus-end-directed motors often have shorter spindle lengths, along with poorly aligned spindle microtubules. A mechanistic explanation for this paradox is unknown. Using computational modeling, in vitro reconstitution, live-cell fluorescence microscopy, and electron microscopy, we now find that the budding yeast kinesin-14 molecular motor Kar3-Cik1 can efficiently align spindle microtubules along the spindle axis. This then allows plus-end-directed kinesin-5 motors to efficiently exert the outward microtubule sliding forces needed for proper spindle bipolarity., (Copyright © 2014 Elsevier Inc. All rights reserved.)

The structure and free energy of multistranded linear polymer ends evolves as individual subunits are added and lost. Thus, the energetic state of the polymer end is not constant, as assembly theory has assumed. Here we utilize a Brownian dynamics approach to simulate the addition and loss of individual subunits at the polymer tip. Using the microtubule as a primary example, we examined how the structure of the polymer tip dictates the rate at which units are added to and lost from individual protofilaments. We find that freely diffusing subunits arrive less frequently to lagging protofilaments but bind more efficiently, such that there is no kinetic difference between leading and lagging protofilaments within a tapered tip. However, local structure at the nanoscale has up to an order-of-magnitude effect on the rate of addition. Thus, the kinetic on-rate constant, integrated across the microtubule tip (kon,MT), is an ensemble average of the varying individual protofilament on-rate constants (kon,PF). Our findings have implications for both catastrophe and rescue of the dynamic microtubule end, and provide a subnanoscale framework for understanding the mechanism of action of microtubule-associated proteins and microtubule-directed drugs. Although we utilize the specific example of the microtubule here, the findings are applicable to multistranded polymers generally., (Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The mechanical stiffness of a cell's environment exerts a strong, but variable, influence on cell behavior and fate. For example, different cell types cultured on compliant substrates have opposite trends of cell migration and traction as a function of substrate stiffness. Here, we describe how a motor-clutch model of cell traction, which exhibits a maximum in traction force with respect to substrate stiffness, may provide a mechanistic basis for understanding how cells are tuned to sense the stiffness of specific microenvironments. We find that the optimal stiffness is generally more sensitive to clutch parameters than to motor parameters, but that single parameter changes are generally only effective over a small range of values. By contrast, dual parameter changes, such as coordinately increasing the numbers of both motors and clutches offer a larger dynamic range for tuning the optimum. The model exhibits distinct regimes: at high substrate stiffness, clutches quickly build force and fail (so-called frictional slippage), whereas at low substrate stiffness, clutches fail spontaneously before the motors can load the substrate appreciably (a second regime of frictional slippage). Between the two extremes, we find the maximum traction force, which occurs when the substrate load-and-fail cycle time equals the expected time for all clutches to bind. At this stiffness, clutches are used to their fullest extent, and motors are therefore resisted to their fullest extent. The analysis suggests that coordinate parameter shifts, such as increasing the numbers of motors and clutches, could underlie tumor progression and collective cell migration., (Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Microtubule self-assembly is largely governed by the chemical kinetics and thermodynamics of tubulin-tubulin interactions. An important aspect of microtubule assembly is that hydrolysis of the beta-tubulin-associated GTP promotes protofilament curling. Protofilament curling presumably drives the transition from tip structures associated with growth (sheetlike projections and blunt ends) to those associated with shortening (rams' horns and frayed ends), and transitions between these structures have been proposed to be important for growth-shortening transitions. However, previous models for microtubule dynamic instability have not considered such structures or mechanics explicitly. Here we present a three-dimensional model that explicitly incorporates mechanical stress and strain within the microtubule lattice. First, we found that the model recapitulates three-dimensional tip structures and rates of assembly and disassembly for microtubules grown under standard conditions, and we propose that taxol may stabilize microtubule growth by reducing flexural rigidity. Second, in contrast to recent suggestions, it was determined that sheetlike tips are more likely to undergo catastrophe than blunt tips. Third, partial uncapping of the tubulin-GTP cap provides a possible mechanism for microtubule pause events. Finally, simulations of the binding and structural effects of XMAP215 produced the experimentally observed growth and shortening rates, and tip structure.

Previous work using glass microneedles to apply calibrated, localized force to neurons showed that tensile force is a sufficient signal for neurite initiation and elongation. However, previous studies did not examine the kinetics or probability of neurite initiation as a function of force or the rate of force application. Here we report the use of a new technique-magnetic bead force application-to systematically investigate the role of force in these phenomena with better ease of use and control over force than glass microneedles. Force-induced neurite initiation from embryonic chick forebrain neurons appeared to be a first-order random process whose rate increased with increasing force, and required the presence of peripheral microtubules. In addition, the probability of initiation was more than twofold lower for neurons exposed to rapid initial force ramps (450 pN/s) than for neurons exposed to slower ramps (1.5 and 11 pN/s). We observed a low force threshold for elongation (15-100 pN), which was not previously detected in chick forebrain neurites elongated by glass microneedles. Finally, neurites subjected to constant force elongated at variable instantaneous rates, and switched abruptly between elongation and retraction, similar to spontaneous, growth-cone-mediated outgrowth and microtubule dynamic instability.

It has been hypothesized that spatial gradients in kMT dynamic instability facilitate mitotic spindle formation and chromosome movement. To test this hypothesis requires the analysis of kMT dynamics, which have not been resolved at the single kMT level in living cells. The budding yeast spindle offers an attractive system in which to study kMT dynamics because, in contrast to animal cells, there is only one kMT per kinetochore. To visualize metaphase kMT plus-end dynamics in yeast, a strain containing a green fluorescent protein fusion to the kinetochore protein, Cse4, was imaged by fluorescence microscopy. Although individual kinetochores were not resolvable, we found that models of kMT dynamics could be evaluated by simulating the stochastic kMT dynamics and then simulating the fluorescence imaging of kMT plus-end-associated kinetochores. Statistical comparison of model-predicted images to experimentally observed images demonstrated that a pure dynamic instability model for kMT dynamics in the yeast metaphase spindle was unacceptable. However, when a temporally stable spatial gradient in the catastrophe or rescue frequency was added to the model, there was reasonable agreement between the model and the experiment. These results provide the first evidence of temporally stable spatial gradients of kMT catastrophe and/or rescue frequency in living cells.

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.