1. Rapid Microtubule Self-Assembly Kinetics
Melissa K. Gardner, Blake D. Charlebois, Imre M. Jánosi, Jonathon Howard, Alan J. Hunt, David J. Odde 
Cell 
Volume 146, Issue 4, Pages (August 2011)
DOI: /j.cell
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2. Cell  , DOI: ( /j.cell )
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3. Figure 1
Direct Observation of Microtubule Assembly via TIRF Microscopy Reveals that the Tubulin Off Rate Increases at Higher Free-Tubulin Concentrations
(A) Elements of a “1D” model, initially described by Oosawa (1970) (left). Here, the number of tubulin subunits added to the microtubule tip (λ+) in a time interval Δt increases proportionately to the tubulin concentration, while the number of subunits lost from the tip (λ-) remains constant regardless of the free-tubulin concentration. Thus, large shortening events should decrease in frequency as the tubulin concentration is increased (i.e., as λ+ increases). Given the number of arrivals, λ+, and the number of departures, λ-, the resulting difference, (λ+-λ-), gives the distribution of incremental microtubule length changes (right). An untested prediction of the 1D model is that the likelihood of large microtubule shortening events will decrease as the subunit arrival rate (λ+) becomes larger. Therefore, the probability of a large shortening event (see dashed vertical line located at |λ+-λ-| = |-4| at right) decreases with increasing free-tubulin concentration.
(B) Microtubule length measured using TIRF microscopy. Microtubule extensions (green), grown from GMPCPP microtubule seeds (red), are visualized during growth at varying GMPCPP-Tubulin concentrations. Tip position (μtip) is measured by fitting the decay in fluorescence intensity to the error function.
(C) Typical microtubule growth traces at different free concentrations of GMPCPP-Tubulin. Growth rate variability appears higher at 1.5 μM GMPCPP-Tubulin (right) as compared to a dilution experiment (left), and the magnitude of shortening events increases at higher tubulin concentrations (blue arrows).
(D) Quantification of growth rate variability. Length increments over 1.4 s intervals are summarized for each concentration. The fixed microtubule increment distribution (gray dashed line) is narrower than the live increment distribution for both 0.8 and 1.5 μM (p = and p = by t test, respectively), and large negative (shortening) increments are more common at higher GMPCPP-tubulin concentrations. For example, shortening events that are less than −32 nm account for 1.8% of all length increments in the dilution experiments, while length increments that are less than −32 nm are 9.1% of all increments at a GMPCPP-tubulin concentration of 1.5 μM. The fraction of length change increments for fixed microtubules remains relatively unchanged (1.4% at a pre-fix tubulin concentration of 0.6 μM, and 1.8% at a pre-fix concentration of 1.5 μM).
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4. Figure 2
Nanoscale Optical Tweezers Experiments Confirm Increasing Growth Rate Variability and Frequency of Large Shortening Events at Higher Tubulin Concentrations
(A) In laser tweezer experiments, the position of a microtubule-attached bead is monitored as the microtubule tip grows against a microfabricated barrier.
(B) Net assembly rate variability is measured with increasing free GMPCPP-tubulin concentrations. The microtubule growth rate variability becomes larger (i.e., noisier) with increasing free-tubulin concentration.
(C) Histograms of microtubule length change increments at 0.1 s intervals show increased variability with increasing tubulin concentration, and large microtubule shortening events increase in frequency at higher free-tubulin concentrations (percentages of increments that are ≤ −8 nm shown in red), consistent with the TIRF measurements.
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5. Figure 3
A 2D Model Predicts that Tubulin Subunit Dissociation Rates Are Dependent on Free Subunit Concentration
(A) Microtubules grow and shorten via the addition and loss of αβ-tubulin subunits. A 2D model includes the effect of both lateral bond interactions between neighboring protofilaments and longitudinal bonds along the protofilament.
(B) The 2D model predicts that tubulin dissociation rates increase at higher tubulin concentrations (red). Thus, the net assembly rate (blue) is given by the small difference between the large on rate (green) and the large off rate (red).
(C) Left: Dissociation rates at growing microtubule tips vary for each protofilament based on the number of lateral neighbor interactions at the protofilament tip. Here, dissociation rates are high for tubulin subunits with fewer lateral neighbors, while more lateral neighbors results in reduced dissociation rates. Right: The 2D model predicts that 1-neighbor protofilament tip interactions increase in likelihood at higher free subunit concentrations, while 2-neighbor interactions decrease with increasing free subunit concentration.
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6. Figure 4
Lateral Neighbor Interactions Require Rapid On-Off Kinetics for Tubulin Subunits at the Microtubule Tip
(A) The 1D model of Oosawa (1970) was used to estimate αβ-tubulin association and dissociation rate constants for GMPCPP-tubulin microtubules.
(B) Similar to the 1D model, a 2D model also predicts a linear microtubule growth rate increase with increasing concentration, but with a rate constant that is an order of magnitude higher than in the 1D model.
(C) A 2D model with rapid kinetics predicts experimental microtubule growth variability in the TIRF assay, whereas a 1D model with low subunit association and dissociation rates fails to reproduce the experimentally observed microtubule growth rate variability.
(D) By analyzing the mean-squared displacement versus time-step data at different tubulin concentrations, the tubulin subunit on rates, off rates, and net rates can be estimated in each case, as summarized in Table S3 and (E).
(E) Experimental tubulin subunit on rates and off rates as a function of GMPCPP-tubulin concentration. Similar to the 2D model prediction (Figure 3B), the tubulin dissociation rate rises with increasing tubulin concentration (red). The net assembly rate (blue) is given by the small difference between the large on rate (green) and the large off rate (red).
(F) A 2D model with rapid assembly kinetics predicts experimental microtubule growth variability in the GMPCPP-tubulin nanoscale laser-tweezer assay, while a 1D model with slow kinetics fails to reproduce the experimentally observed microtubule growth rate variance at higher GMPCPP-tubulin concentrations.
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7. Figure 5
TIRF Microscopy Measurements Show that Microtubule Tip Structure Depends on Free GMPCPP-Tubulin Concentration
(A) A 2D model predicts that tip structures at higher free-tubulin concentrations will exhibit a greater disparity in protofilament length.
(B) The standard deviation of protofilament lengths for a given microtubule (σtip) provides a measure of the variability in protofilament lengths. The 2D model predicts that σtip will, on average, be large in 1.5 μM tubulin (blue) relative to 0.8 μM tubulin (red).
(C) By fitting the decay in fluorescence intensity at the microtubule end to an error function, the standard deviation (σtip) of the error function is estimated, which reflects the variability in protofilament lengths at the microtubule tip. A low σtip (left) suggests that microtubule tips are blunt, with low variation in protofilament length. Conversely, a high σtip (right) suggests that tips are extended, with a higher variation in protofilament length.
(D) In TIRF experiments, the tip standard deviation (σtip) increases with increasing free GMPCPP-tubulin concentration. The mean tip standard deviation, 〈 σtip 〉 , at a concentration of 0.8 μM GMPCPP-tubulin is 99 ± 22 nm (mean ± SD; n = 700), while 〈 σtip 〉 at 1.5 μM GMPCPP-tubulin is 140 ± 55 nm (mean ± SD; n = 1120; p < 10−15) for similar length microtubules at both concentrations. This experimental result shows that microtubule tips are relatively blunt with low protofilament length variation in 0.8 μM GMPCPP-Tubulin, while they are more extended, with a larger variation in protofilament lengths, at 1.5 μM.
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8. Figure 6
Physiological Tubulin Concentrations Result in Increased Growth Variability Both In Vitro and In Vivo
(A) A 2D model predicts that subunit association rates and subunit dissociation rates will continue to increase for GTP-tubulin at physiological free-tubulin concentrations.
(B) Because of rapid kinetics at higher free subunit concentrations, the microtubule growth rate variability continues to increase for higher GTP-tubulin concentrations (5 μM GTP-tubulin data from (Schek et al., 2007), downsampled to 0.5 s intervals).
(C) TIRF experiments with GTP-tubulin qualitatively show increasing growth variability at 12 μM tubulin as compared to 7 μM tubulin.
(D) By analyzing the mean-squared displacement versus time-step data at different GTP-tubulin concentrations, the tubulin subunit on rates, off rates, and net rates can be estimated in each case, as summarized in Table S3 and (E).
(E) Experimental tubulin subunit on rates and off rates are plotted as a function of GMPCPP-tubulin and GTP-tubulin concentration. Similar to the 2D model prediction (Figure 6A), the tubulin off rate rises with increasing tubulin concentration (red). The net assembly rate (blue) is given by the small difference between the large on rate (green) and the large off rate (red) (see also Table S3).
(F) Microtubule growth rates are measured near the cell periphery in both live and fixed LLC-PK1α cells to measure the variance in growth rate at 0.5 s intervals (green: GFP-tubulin).
(G) Microtubule length as a function of time for live and fixed microtubules. Growing microtubules frequently shift the net rate dramatically on a time scale of seconds. In this example, the net rate shifts from 600 s-1 to 110 s-1 in a period of a few seconds.
(H) In vivo microtubule growth rate variance is nearly 5-fold higher than GTP-tubulin in vitro data at 5 μM. In vivo growth rate variances are calculated by subtracting the fixed-cell measurement error variance from the live-cell data. Thus, the kinetic constants in vivo are at least as large as those estimated in vitro for GTP-tubulin at similar concentrations.
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9. Figure 7 Revised View of Microtubule Assembly Kinetics
By accounting for a non-homogeneous tip structure in a 2D model of microtubule assembly, we find that (1) the association rate constant for tubulin subunits during microtubule assembly is an order of magnitude higher than previously thought, (2) the tubulin subunit dissociation rate is not constant, as previously assumed, but rather increases at higher tubulin concentrations, and (3) microtubule assembly is driven by rapid on and off events of individual tubulin subunits. Under typical assembly conditions, ∼10 μM GTP-tubulin, the combined kinetic rates are estimated to occur at nearly 1000/s. At all tubulin concentrations the association and dissociation rates are nearly equal to each other.
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10. Figure S1
Constraint of kon,MT in 2D Model Simulations, Related to Figure 3
By quantifying the microtubule length change increment variance as a function of time step, kon,MT is constrained in the 2D model simulation. The range of tested values for kon,MT is 39-78 μM-1s-1, and values of kon,MT = 52 μM-1s-1 and kon,MT = 65 μM-1s-1 are consistent with experimental results.
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11. Figure S2
Estimation of Free-Tubulin Subunit Concentration in Live LLC-PK1α Cells, Related to Figure 6
(A) The free concentration of tubulin is estimated in live LLC-PK1α cells by comparing the GFP-Tubulin fluorescence in a standard box size which includes a single microtubule (box #1), to the fluorescence in a box that includes only background GFP-Tubulin fluorescence (box #2). Here, background fluorescence per unit length is first calculated along the length of the background fluorescence box (#2). Then, MT-associated GFP-tubulin fluorescence per unit length (Intensity per μm) is calculated by measuring the fluorescence per unit length in box #1, and then by subtracting the background fluorescence per unit length as calculated from box #2. The GFP-tubulin fluorescence intensity per subunit is then calculated according to: Intensity per subunit = (Intensity per μm)/1625, as there are ∼1625 subunits/μm of MT length. The number of fluorescent tubulin subunits in the background box (#2) are then calculated by dividing the total fluorescence intensity in box #2 by the calculated value for Intensity per subunit. The background GFP-tubulin concentration is then calculated by dividing the number of tubulin subunits in box #2 by the volume of box #2. The length and the width of box #2 are established during the initial computer program measurements, but the thickness of the cell in the periphery is unknown. However, by adjusting the focus with an axial stepper motor (50 nm step size), we determined that the periphery of LLC-PK1α cells is no more than 400 nm thick on average, and our best estimate of cell thickness is approximately 200 nm. As shown in (B), tubulin concentration estimates are provided for various cell periphery thickness values, and our best estimate based on cell periphery thickness measurements is 5-15 μM. These values are in approximate agreement with previous quantitative analyses of total tubulin expression and polymer/monomer ratio in tissue cells, including LLC-PK1 cells (Hiller and Weber, 1978; Zhai and Borisy, 1994).
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12. Figure S3
Comparison of Laser-Tweezer Data from Schek et al. (2007) and Kerssemakers et al. (2006), Related to Figure 2
(A) To resolve any apparent discrepancy between the laser-tweezer data from separate groups, we digitized the Kerssemakers et al. data shown in Figure 2A of (Kerssemakers et al., 2006) (left, typical) to directly compare this raw data to the GTP data in Schek et al. (2007) (right, typical, DIGITIZEIT; Köln, Germany). Here, the data from Kerssemakers et al. is downsampled to match the data sampling rate in Schek et al.
(B) When the digitized data from Kerssemakers et al. is processed as described in Schek et al., the addition/loss events in single time intervals are similar between the studies. (C) The variance present in the Kerssemakers et al. data is consistent with the observations from the 5 μM GTP-tubulin data in Schek et al. Here, all data is downsampled to 0.5 s intervals.
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13. Figure S4
XMAP215 Laser-Tweezer Data from (Kerssemakers et al., 2006), Related to Figure 6
(A) To test the hypothesis that a microtubule polymerase could work by suppressing a large tubulin subunit off-rate, we digitized the nanometer-scale laser-tweezer data of (Kerssemakers et al., 2006) that was collected in the presence of XMAP215 (DIGITIZEIT; Köln, Germany; the data of Kerssemakers et al. were used because, to our knowledge, it is the highest resolution data collected to date in the presence of XMAP215). Here, the data from Kerssemakers et al. is downsampled to match the data sampling rate in Schek et al. (as above), and the control Kerssemakers data (red) is directly compared to the XMAP215 data (blue). The net microtubule growth rate is faster in the presence of XMAP215 (∼13 nm/s) as compared to the control data (∼9 nm/s), consistent with previous reports (Brouhard et al., 2008; Charrasse et al., 1998; Gard and Kirschner, 1987; Vasquez et al., 1994).
(B) The digitized data from Kerssemakers et al. is processed as described in Schek et al., and the addition/loss events in single time intervals are compared between the control data and the data collected in the presence of XMAP215. Strikingly, the mean microtubule shortening (negative) increment size is significantly reduced in the presence of XMAP215 as compared to control microtubules (p = , by t test), while the mean positive growth increment size is unaffected by XMAP215 (p = 0.29, by t test). This result suggests that XMAP215 works by weakly suppressing a large tubulin subunit off rate. (C) The variance present in the Kerssemakers et al. data is consistent with the conclusion that XMAP215 increases the microtubule growth rate by weakly reducing the tubulin subunit off rate, as the observed growth rate variance is similar between controls and in XMAP215, regardless of the increased net growth rate.
Cell  , DOI: ( /j.cell )
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