Single Filament Behavior of Microtubules in the Presence of Added

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Single Filament Behavior of Microtubules in the Presence of Added Divalent Counterions Nathan F. Bouxsein and George D. Bachand* Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185 United States S Supporting Information *

ABSTRACT: Microtubules (MTs) are hollow biopolymeric filaments that function to define the shape of eukaryotic cells, serve as a platform for intracellular vesicular transport, and separate chromosomes during mitosis. One means of physiological regulation of MT mechanics and dynamics, critical to their adaptability in such processes, is through electrostatics due to the strong polyelectrolyte nature of MTs. Here, we show that in the presence of physiologically relevant amounts of divalent salts, MTs experience a dramatic increase in persistence length or stiffness, which is counter to theoretical expectations and experimental observations in similar systems (e.g., DNA). Divalent salt-dependent effects on MT dynamics were also observed with respect to suppressing depolymerization as well as reducing dispersion in kinesin-driven molecular motor transport assays. These results establish a novel mechanism by which MT dynamics, mechanics, and interaction with molecular motors may be regulated by physiologically relevant concentrations of divalent salts.

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INTRODUCTION Microtubule filaments (MTs) are a critical component of the cytoskeleton in eukaryotic cells and are involved in a range of physiological process including cell motility, cell mechanical stability, and organelle transport. MTs are comprised of heterodimers of α and β tubulin that assemble into a hollow filament structure with a large diameter (∼25 nm) and large aspect ratios.1 As a polymer filament, MTs are unique in a number of ways, but primarily in its highly dynamic in vivo behavior. Because the mature MT is fully self-assembled, it undergoes cycles of polymerization and rapid depolymerization, called dynamic instability, that allow the filaments to reconfigure based on changes in the cell cycle. Mature MT filaments are also exceedingly rigid and act as highways for the binding of motor proteins and resulting transport of macromolecules and organelles. Due to the importance of these dynamic and mechanical properties, cells rely on a number of accessory proteins to regulate MT dynamics and behaviors. Some of the more common examples are microtubule associated proteins (MAPs) such as MAP2 and tau, both of which have been shown to facilitate MT polymerization, increase stability of the mature MT, and significantly lower the MT flexibility.2,3 Additionally, MTs are highly charged structures and thus may be classified as a biological polyelecrotyle (PE). PEs readily dissociate in water into a two-component system consisting of charged polymer chains and associated mobile counterions. The charged groups on the backbone of PEs are responsible for intermolecular electrostatic repulsion, as well as intramolecular repulsion between adjacent charged groups, which tend to © XXXX American Chemical Society

extend the conformation of PEs. When the spacing between the adjacent charged groups is shorter than the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy scale (i.e., the Bjerrum length), a fraction of the counterions will condense into the immediate vicinity of the PE surface. 4 The conformation and association of PEs is thus strongly dependent on the dissolving solvent and on the nature of the counterions (e.g., valence, size, etc.). For example, DNA, a relatively stiff biological PE, collapses into a highly compact state in the presence of trivalent ions, while other truly rod-like biological PEs, such as the filamentous bacteriophage fd, form bundles in the presence of divalent ions.5,6 Many cationic divalent ions and polyvalent molecules have been shown to either stimulate MT assembly or to strongly promote its disassembly. Here, our work draws inspiration from the numerous studies on the effects of dilute concentrations of cationic ions on the bulk polymerization and structural behavior of MT filaments. For example, MT sheets and rings form, rather than hollow filaments, when tubulin is polymerized in the presence of Zn2+ or Mn2+, respectively;7,8 in contrast, Ca2+ strongly stimulates the depolymerization of MT filaments.9 Some alkali metal chlorides and oligocations also promote tubulin polymerization.10,11 Further, the addition of certain divalent and polyvalent cations induces self-assembly of mature MTs into “living necklaces” and hexagonal bundles.12 These effects have Received: July 7, 2014 Revised: August 22, 2014

A

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Lp Measurements of Freely Suspended MTs. MTs were further diluted to 0.05 μM in 80 mM PIPES, 2 mM MgCl2, 1 mM EDTA containing 5 mg mL−1 casein, 0.25 μM glucose oxidase, 0.064 μM catalase, 1 mM dithiothreitol, and 40 mM D-glucose. The ionic strength of the solution (control measurements) was calculated using I = 1/2∑CiZ2i , where Ci and Zi indicate the molar concentration and charge valence of the ion species i, except in the case of PIPES, where I was calculated following the methods of Hatae et al.23 I = 176 mM, with 130 mM monovalent species. Additional monovalent or divalent salts were added to this solution at the indicated concentrations. A total of 2 μL of the diluted MT solution was placed between a glass slide and coverslip. The edges of the coverslip were sealed to the slide with mineral oil to prevent fluid flow. The sample was placed in a thermal controlled microscope stage and held at 23 °C for the duration of the experiment. The fluorescent MTs were observed with a 100×, 1.4 NA oil immersion objective (Olympus) using appropriate filter sets. Images were captured on an ORCA-Flash4.0 digital sCMOS camera (Hamamatsu) with 10 ms exposure taken every 12 s for 20 min. Images were filtered using a real-space band-pass to suppress pixel noise and long-wavelength image variations.24 The fluorescent filaments shapes were traced into digitized x and y pixel coordinates flowing an open active contours method using ImageJ (NIH).25 The digitized filament shapes were parametrized by a tangent angle as a function of arc length. The parametrized shape was decomposed into a set of Fourier modes determined numerically in Matlab and Lp calculated as described in the text. The MT shape can be reconstructed from a complete set of mode amplitudes. The shape reconstructions in Figure 1a,b are representative of 10 frames from the set of 120, which were reparameterized into x and y pixel values, converted into microns based on the microscopes calibration (0.1997 μm/pixel), and rotated by an angle such that the reconstructed filament origin and filament end coincided with the x-axis. The Fourier sums used only the first 3 modes, corrected for the filament intrinsic shape (by subtracting the mean mode amplitudes) for the reconstruction. Control experiments performed on MTs containing 5 mM PMSF but not treated with subtilisin showed no difference in the measured Lp, as compared with control, paclitaxel-stabilized MTs. ⟨Lp,surf⟩ and Trajectory Measurements. A capillary flow chamber was constructed on a glass slide using double sided tape and a coverslip. The average dimensions of the flow chamber were 22 mm × 3 mm × 40 μm. A total of 5 mg mL−1 casein protein diluted in 80 mM PIPES was added to fill the flow chamber and incubated for 5 min. Kinesin was diluted to 325 nM in 80 mM PIPES with 5 mg mL−1 casein and 1 mM ATP and then added to the flow chamber and incubated for 5 min. Paclitaxel-stabilized MTs were diluted to 0.05 μM in 80 mM PIPES containing 5 mg mL−1 casein, 3 mM ATP, 0.045 mg mL−1 glucose oxidase, 0.0165 mg mL−1 catalase, 1 mM DTT, and 40 mM D-glucose and added to the flow chamber. After 5 min, the flow chamber was imaged using fluorescent microscopy as described above. Instantaneous images were capture at 50 ms exposure where each exposure corresponded to a nonoverlapping image frame. Roughly 100 individual MTs were imaged (control). Using the same sample, the flow chamber was washed with the above solution containing added monovalent or divalent salts as described in the text. After 5 min, an additional 100 individual MT were imaged (added salt). Sample temperature held at 23 °C for the duration of the experiment. Images were filter and digitized as above. The average cosine correlation (for control or added salt) was calculated in Matlab to determine ⟨Lp,surf⟩. Trajectory measurements followed a similar protocol except the sample position was held fixed and images were capture sequentially every 250 ms with 10 ms exposure for 30 s. The leading tip position of each MT in the sequential image frame was tracked using ImageJ. The initial tip position for an individual filament was set as a reference at the origin and each subsequent point from that filament was plotted with respect to this origin. In this configuration every filament appears to originate from the position x = 0 μm and y = 0 μm. MT Stability. MTs were polymerized as above except stabilized in 25 nM paclitaxel. A total of 5 mg mL−1 casein diluted in 80 mM PIPES was added to fill a flow chamber and incubated for 5 min. Kinesin was diluted to 325 nM in 80 mM PIPES with 1 mg mL−1 casein and 1 mM

been primarily described for in vitro reconstituted MTs but provide invaluable information relevant to understanding MT polymerization and assembly in varying cytoskeletal architectures (e.g., axonal MT bundles). In addition, understanding the behavior of MTs in the presence of divalent metal ions has important implications for in vitro kinesin−MT systems that have been used to study the biophysical mechanisms of active transport as well as to engineer integrated nanomaterials and devices.13,14 We report on the effects of counterions at concentrations below the like-charge bundling phase boundary for noncovalently assembled MT filaments. We observe significant increases in the flexural rigidity of freely suspended MT filaments in the presence of physiological concentrations of divalent ions (Mg2+, Sr2+, and Ba2+), a behavior that is unique to MTs as many other common rod-like PE are reported to present lower bulk rigidity in the presence of similar counterions.15−17 Moreover, we demonstrate a correlation between structural stability and mechanical rigidity, consistent with prior work with MAPs, 3 where the addition of physiologically relevant concentrations of Ba2+ stabilizes MT filaments against depolymerization. Lastly, the changes in biomechanical properties in turn affect kinesin-transport of MTs, whereby the path trajectories of MTs undergo a transition from highly dispersed transport to deterministic transport in the presence of divalent ions.18,19 Our findings provide new insights to the continued understanding of MT dynamic instability where divalent ions have been shown to enhance the exchange rate between tubulin dimers and steadystate MTs.20 The variation in the MT conformation in motilitybased assays in the presence of multivalent ions also adds new tools for engineering nanodevice applications for surface-based nanofluidic transport.

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METHODS

All chemicals were purchased from Sigma-Aldrich unless indicated otherwise. Lyophilized unlabeled tubulin and HiLyte 488 (Anaspec Inc., CA, U.S.A.) labeled tubulin from porcine brain were purchased from Cytoskeleton Inc. (Denver, CO, U.S.A.) and used without further purification and modification. Kinesin. Full-length Drosophila melanogaster kinesin-1 was expressed in Escherichia coli from the recombinant kinesin heavy chain expression vector pPK113 (http://www.ncbi.nlm.nih.gov/protein/ AAD13351.1) and purified by Ni-NTA chromatography (Invitrogen).21 Protein concentration was determined by standard Bradford assay to be 1.08 μM. Aliquots of the protein were snap frozen in liquid nitrogen and stored at −80 °C. Microtubule Polymerization. An ice cold solution of 1 mM GTP and 15% glycerol dissolved in 80 mM piperazine-N,N′-bis(2ethanesulfonic acid) (PIPES), 2 mM MgCl2, and 1 mM EDTA with pH set to 6.9 by KOH (BRB80) was used to suspend the tubulin proteins to a concentration of 22 μM. Hilyte 488 tubulin and unlabeled tubulin were mixed at a molar ratio of 15:85, respectively, and polymerized at 37 °C for 20 min. The polymerized MTs were then diluted to 0.5 μM and stabilized against depolymerization by using a solution of BRB80 containing 10 μM paclitaxel (Taxol) and stored at room temperature. Subtilisin Digestion of MT. Paclitaxel-stabilized MTs were incubated in 100 μg/mL of subtilisin (Sigma) for 60 min at 37 °C, which has been shown previously to completely digest the C-terminal tubulin tails.22 The enzymatic activity was quenched with the addition of 5 mM phenylmethylsulfonyl fluoride (PMSF), and the resulting samples were centrifuged at 190000 × g for 20 min over a warm 30% sucrose cushion. The MT pellet was suspended in BRB80 containing 10 μM paclitaxel. B

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mM D-glucose and either added directly to the flow chamber (control) or incubated in additional 5 mM BaCl2 for 5 min before being added to the flow chamber. Sequential fluorescent images were captured every second at 10 ms exposure for 60 s. No postprocessing was performed on these images. Each end of a filament was tracked in ImageJ to determine disassembly rates.

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RESULTS Properties of Freely Suspended MT in the Presence of Additional Counterions. The mechanical rigidity of MTs was measured from observations of the thermal fluctuation of filaments confined in a pseudo two-dimensional space between coverslips with no motors present, as previously described by Gittes et al.26 MT filaments were incubated for 5 min in motility solution with 5 mM CsCl, MgCl2, SrCl2, BaCl2, or no added salts before confinement in the observation chamber. The digitized positions of 20 individual fluorescent MT filaments from each salt sample and control sample were recorded every 12 s for 20 min. The shapes of the digitized positions were parametrized by tangent angle, θt, as a function of arc length, S , and decomposed into a series of Fourier modes each with an amplitude an given by an =

2 L

∫0

L

⎛ nπ S ⎞ ⎟ d Sθt cos⎜ ⎝ L ⎠

where L is the filament contour length and n is the mode number. Lp is determined by measuring the variance of the mode amplitudes, var(an) var(an) = (an − ano)2 =

L2 n2π 2Lp

where aon is the mean of the nth mode describing the intrinsic shape of the filament. It is important to note that Lp  κ/kBT is the ratio of the flexural rigidity, κ, to thermal energy and is considered as a measurement of flexibility for freely suspended macromolecules. A total of 10 modes at each time point were calculated numerically and var(an) for each mode was measured for the entire time series. The variance in the lowest order modes best represents fluctuations due to thermal bending, while higher order modes are predominantly influenced by measurement errors.3,27 Reconstruction of filament shapes using only the first three modes (corrected for a no ) demonstrated the effect of divalent ions on the flexural rigidity (Figure 1a and b, control and added 5 mM BaCl2, respectively). Even in this simple reconstruction, different shape fluctuations between the two samples are readily observable. Movies highlighting these types of thermal fluctuations are included in the Supporting Information (Supplementary Movie 1 and Movie 2). The calculated persistence lengths and corresponding flexural rigidities are shown in Figure 1c. No statistical difference (P = 0.135) was observed between the control (Lp = 2067 ± 1081 μm) and the monovalent salt (Lp = 2480 ± 570 μm). Significant increases in Lp, however, were observed in the presence of MgCl2 (Lp = 3040 ± 720 μm, P = 0.003), SrCl2 (Lp = 3567 ± 508 μm, P < 0.001), and BaCl2 (Lp = 5108 ± 784 μm, P < 0.001). Of the divalent salts tested, Ba2+ ions more than double the experimentally determined Lp of MTs. The effect is fully reversible when a solution of MTs in added divalent salts is dialyzed against the control buffer; the Lp is reduced to the control values (Lp = 1859 ± 935 μm). In samples with only monovalent counterion species, the fraction of charge neutralization on the MT surface due to

Figure 1. Persistence length of MT filaments increases in the presence of divalent salts as a function of hydrated ion size but requires tubulin C-terminal tails. Fluorescent MT filaments were incubated in control ionic strength motility solution or in motility solution with added salts (5 mM) and confined between two glass coverslips. Coverslips were passivized with casein to prevent surface absorption by the MTs. An image was taken every 12 s for 20 min: example fluorescent images from the control population (A-bottom) or in added 5 mM BaCl2 (Bbottom) are shown. The contours from the filaments were digitized and decomposed into a series of Fourier modes as described in the text. Example reconstructions of the filament shapes using only the first three modes, corrected for the mean mode amplitude, are shown for the control (A-top) and with added 5 mM BaCl2 (B-top). The horizontal scale bars are 20 μm. The vertical axis in A-top and B-top have been expanded for clarity (as shown). Lp and flexural rigidity for the indicated added salts are shown in (C). Control (SubA) and BaCl2 (SubA) are the Lp for MTs pretreated with subtilisin (to remove Cterminal tails) prior to Lp characterization. adenosine 5′-(β,γ-imido)triphosphate lithium salt hydrate (AMPPNP) and then added to the flow chamber and incubated for 5 min. A total of 25 nM paclitaxel-stabilized MTs were diluted to 0.05 μM in 80 mM PIPES containing 5 mg mL−1 casein, 3 mM AMP-PNP, 0.045 mg mL−1 glucose oxidase, 0.0165 mg mL−1 catalase, 1 mM DTT, and 40 C

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Figure 2. BaCl2 (5 mM) stabilizes low paclitaxel MTs. Fluorescent MTs were immobilized on a kinesin surface with AMP-PNP and time lapse images were taken every 1 min at 50 ms exposure. MTs in 25 nM paclitaxel are susceptible to characteristic patterns of depolymerization (top row). MTs in 25 nM paclitaxel and 5 mM BaCl2 show longer term stability (bottom row). Scale bar is 20 μm, and the time each image was captured is shown in the upper left (min).

counterion condensation can be estimated by (1 − lo/lb), where lo = 4.0 Å is the linear charge density of the MT and lb = 7.1 Å is the Bjerrum length in water at room temperature (further details are given in the Supporting Information).28,29 For the control solution (only monovalent counterions), charge neutralization is ∼44%. As divalent salts are added to the control solution, charge neutralization of the MT increases as the divalent counterions compete for condensation with the monovalent species. We estimated the charge neutralization fraction of MTs as a function of divalent ion concentration using Manning’s two variable theory (further details are given in Supporting Information).30 In the case of added 5 mM BaCl2, the charge neutralization fraction was estimated to be 57.5% and the measured Lp was 5108 ± 784 μm. In contrast, charge neutralization fraction and Lp for MTs in the control solutions were ∼44% and 2067 ± 802 μm, respectively. For polyelectrolyte rod-like molecules, Lp is a sum of a finite intrinsic persistence length and an electrostatic persistence length, le, where le is proportional to the linear charge density of the rod.31,32 As the MT surface charge is increasingly neutralized through the addition of the divalent salt, a decrease in le and, therefore, Lp would be expected. Thus, the data suggest a correlation between charge neutralization and an increase in Lp as opposed to an electrostatic neutralization of le resulting in a decreased Lp for MTs. The outer surface of MTs contain highly charged unstructured C-terminal tails on both the α and β tubulin subunits and are composed primarily of acidic groups.33 Proteolytic digestion of these tails using subtilisin has been shown to reduce the bare MT charge per dimer by 36%.22,34 The persistence length of subtilisin-treated MT was measured as above for control and BaCl2 MTs (Figure 1c). Subtilisin treatment did not affect the measured Lp for control samples (2007 ± 471 μm), but eliminated the observed increase in Lp for BaCl2 MTs (2315 ± 471 μm for subtilisin treated MTs in the presence of 5 mM BaCl2). Reconstructions of filament shapes (similar to those presented in Figure 1a,b) for subtilisintreated microtubules are included in the Supporting Information, S.1.5. MTs Stabilized by Divalent Salts. Previous works have shown that agents such as tau protein and guanylyl-(a,b)methylene-diphosphonate (GMPCPP) stabilize MTs against depolymerization while also increasing the Lp of the filament. Thus, we hypothesized that the increased Lp in the presence of added Ba2+ ions would correlate with enhanced stabilization of MTs against depolymerization. Freshly polymerized MTs stabilized in substoichiometric paclitaxel concentrations (25 nM) were prepared to suppresses but not inhibit MT depolymerization.35 These MTs were added to kinesin prepared flow cells along with a nonhydrolyzable analog of

ATP, AMP-PNP, which facilitates binding of motors and MTs but prevents enzymatic catalysis and associated motility.36,37 After MTs bound to the surface-adhered kinesin, the flow cell was washed with a paclitaxel-free buffer with or without added 5 mM BaCl2. Characteristic disassembly of the control MTs was observed with shortening rates of 30 μm min−1 at the minus end and 10 μm min−1 at the plus end (Figure 2, top row), consistent with previously published data.38,39 In contrast, only a very minimal loss of tubulin subunits was observed at initial time points in the presences of Ba2+, while subsequent time points confirmed no significant change in MT length (Figure 2, bottom row). Movies of the disassembly for control and for Ba2+ MTs can be found in the Supporting Information (Supplementary Movies 3 and 4). Freshly polymerized substoichiometric paclitaxel MTs were also stored at room temperature either with or without added 5 mM BaCl2 and checked after 7 days for the presence of MTs. Here, only samples stored in the added divalent salt contained mature MT filaments, as was expected based on the above results. MT Conformation During Active Transport. Based by our results on freely suspended MT stiffening induced by divalent counterions, we next characterized conformational changes during active MTs transport by surface bound kinesin motors. Paclitaxel (10 μM) stabilized fluorescent MT filaments processed by surface bound kinesin in motility solution (i.e., control, no added salts) were captured by fluorescent microscopy (Figure 3a,b). The motility solution was replaced with equivalent motility solution containing additional divalent or monovalent salt. Instantaneous images of the fluorescent MTs were captured at various locations throughout the observation chamber to ensure that the sampled data was measured from unique MTs and not from the same MT at different time points. This approach was used to prevent the influence of filaments shape history on the conformation analysis described below. The fluorescent images of these filaments were filtered and binarized to reduce background noise and the filaments were then fit using an open active contour method to determine the instantaneous pixel conformation of the MTs.24,25 The correlation persistence length for each surface bound filament was determined by measuring the mean of the angular cosine difference between sequential unit tangent vectors (Δθ) along the digitized MT length, L. Generally, for semiflexible polymers such as MTs, where L ≫ the monomer length, correlation between these cosines falls off exponentially as ⎛ Δs ⎞ ⎟⎟ ⟨cos(Δθ ), Δs⟩ = exp⎜⎜ − ⎝ 2Lp ⎠ D

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Table 1. Correlation Length of MTs Undergoing Active Surface Transport (⟨Lp,surf⟩) as a Function of Different Added Counterion Species added salt

concn (mM)

⟨Lp,surf⟩ (μm)

BaCl2

0.005 0.01 0.050 0.5 1.0 5.0 10.0 5.0 5.0 50.0 50.0 0

57.5 ± 6.9 74.6 ± 8.0 98.2 ± 8.6 220.8 ± 23.3 356.8 ± 19.5 558.2 ± 31.2 741.6 ± 46.9 285.0 ± 36.8 150.8 ± 20.3 63.9 ± 8.5 41.9 ± 8.6 69.0 ± 5.6

SrCl2 MgCl2 CsCl NaCl control

CsCl or NaCl. The effect was visible in the single-frame images of control MTs (Figure 3a, ⟨Lp,surf⟩ = 69.0 ± 5.6 μm) and with added 5 mM BaCl2 (Figure 3b, ⟨Lp,surf⟩ = 558.2 ± 31.2 μm). As an additional comparison, ⟨Lp,surf⟩ was plotted as a function of BaCl2 concentration (Figure 4, filled circles) alongside

Figure 4. Charge neutralization of MTs leads to straighter surface conformations. ⟨Lp,surf⟩ for various concentrations of added BaCl2 to motility solution (closed circles) were determined as described in the text and in Figure 3. The corresponding charge neutralization fraction of the MT surface (dashed line) was estimated using Manning’s two variable method as described in the text and in the Supporting Information. Charge neutralization calculation does not take into account ion size, and thus, the dashed line is representative of mixed monovalent and divalent ion solution and is not specific to BaCl2.

Figure 3. Effect of added divalent salts on MT motility. Selected images from a time lapsed video of fluorescently labeled MT during active transport by surface kinesin motors. The control sample in normal ionic strength motility solution is shown in (a) and with 5 mM added BaCl2 washed into the motility chamber in (b). Scale bar is 20 μm. Filament contours for MT > 50 μm were used to construct the average cosine regression plot in (c). Solid lines indicate the nonlinear least-squares fit to ⟨cos(Δθ),Δs⟩ = exp(−Δs/(2⟨Lp,surf⟩)). Values for ⟨Lp,surf⟩ can be found in Table 1.

Manning’s prediction (Figure 4, dashed line), showing the existence of a direct correlation between charge neutralization and straighter surface conformation, as was discussed above for freely suspended behavior. Approximately 1 mM divalent salt was required to significantly influence charge neutralization, which is concurrent with a large increase in ⟨Lp,surf⟩ observed for this concentration of added BaCl2.The path trajectory of MTs transported in the motility assay depends on both thermal motion of the leading MT tip and the availability of free surface motors.43 As the MT tip advances a distance r away from the most recently bound motor, the tip thermally fluctuates through an angle ∝ (r/Lp)1/2 and continues to do so until it contacts another motor. The configuration of the filament contour, thus, becomes a good measure of the history of these tip fluctuations coupled with the frequency of new motor protein interaction in the case where motors continually process MTs.44,45 The addition of a small amount of divalent salt acts to straighten the conformation of MTs in motility based on the size of the divalent ion and is in agreement with

where Δs is the contour length between tangent vectors and Lp is the persistence length.40−42 Because the MT conformation is influenced by the interaction with surface confined motors, Lp = ⟨Lp,surf⟩ was used to describe the correlation length of MTs undergoing active surface transport. The weighted average cosine correlation was calculated for 100 filaments and shown in Figure 3c, where the effect of adding 5 mM BaCl2, SrCl2, or MgCl2 to MTs during transport may be observed, as compared to no added salts (control). The surface concentration of kinesin was held constant for all assays and only filaments longer than 50 μm were considered in the weighted average. A nonlinear least-squares fit using the above equation was used to estimate ⟨Lp,surf⟩ from the data (Table 1). The filaments decay away from perfectly straight rods, ⟨cos(Δθ),Δs⟩ = 1, at significantly longer lengths in the presence of added divalent salt when compared against the control or added monovalent E

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Figure 5. Divalent salts eliminate dispersion in MT path trajectories. The leading tip of actively transported MTs was tracked for a period of 60 s. Examples tracks after 5 s and after 30 s are shown for control (a, 5 s; c, 30 s) and for added 5 mM BaCl2 (b, 5 s; d, 30 s). The initial tip position for each filament was normalized to (x = 0, y = 0) and used as a reference for subsequent tip positions at later times. In this way, each filament appears to be traveling away from a common origin. A total of 25 path trajectories for MT in control motility solution (e) or in motility solution with added 5 mM BaCl2 (f) are shown following the referenced construction.

the results we have presented for Lp of free MTs. Interestingly, the conformation change is reversible, by simply washing divalent salt treated MTs with the standard control motility solution, ⟨Lp,surf⟩ returns to the control value (i.e., ∼70 μm). Path Trajectories of Transported MTs. The effects of added counterions on the transport and trajectory of MTs in the inverted motility geometry were then characterized. Here, paclitaxel (10 μM) stabilized fluorescent MT filaments processed by surface bound kinesin in standard motility solution or with added 5 mM BaCl2 were captured in sequential fluorescent images with a 1 s time interval at a fixed location in the observation chamber. The leading tip position for 100 individual MTs was tracked over a time (t) of 60 s. Examples of five MTs tracked after 5 s and after 30 s are shown for control samples (Figure 5a,c) and for added 5 mM BaCl2 (Figure 5b,d). Cumulative track plots were created with the initial tip location for a filament at t = 0 set to the coordinate position (x0 = 0 μm, y0 = 0 μm) and subsequent tip positions were then recorded with respect to x0,y0 such that all filament trajectories appear to be traveling away from a common origin (Figure 5e,f).46 In the absence of added salt (Figure 5a,c,e), MT trajectories show significant dispersion, where the starting trajectory angle was not correlated with the trajectory angle after 60 s (Pearson correlation, r = 0.186). In the case of added salt (Figure 5b,d,f), MTs appear to follow straight line trajectories with little dispersion between the starting trajectory angle and the trajectory angle after 60 s (r = 0.938). A comparison of two isolated filaments (Supporting Information, Figure 1) highlighted the drastic change in the path profile for the control MTs. Movies of these two sample types are included in the Supporting Information (Supplementary Movies 5−7). Electrostatic Screening Effects on Inactive Molecular Motors. MTs actively transported by kinesin motors show

additional behavior modification due to the counterioncondensation charge neutralization effect. Divalent salts weaken the binding interaction between MTs and kinesin motors as well as increase the mechanical rigidity of the filaments, resulting in significantly increased correlation lengths and a reduction in trajectory dispersion. The conformation of MT in motility assays, ⟨Lp,surf⟩, depends on the surface concentration of motors and on the free MT Lp. Theoretical predictions indicate that filament contours for high motor densities should be on the order of Lp.43,47 However, the surface conformation, ⟨Lp,surf⟩, for both control and added divalent salt MTs was observed to be significantly lower than the corresponding measured Lp (Table 1 and Figure 1c). Previous observations have measured decreased Lp of MTs over short length scales impacting the flexibility of the leading MT tip during transport.48,49 Interestingly, ⟨Lp,surf⟩ increases by a magnitude that far surpassed the increase in Lp when divalent salts are added into the system. We quantified this magnitude by examining the fractional increase [fc = Lp (added salt)/Lp (control); = ⟨Lp,surf⟩ (added salt)/⟨Lp,surf⟩ (control)] in Lp or ⟨Lp,surf⟩ with respect to the control (Figure 6). From this comparison we conclude that, while added divalent salts do increase the flexural rigidity of unbound MT, the effect is predominantly observed through an increase in the correlation length of actively transported filaments. During in vitro active transport, a fraction of motors are enzymatically inactive yet retain the ability to bind MTs and affect the transport characteristics. For example, interactions between filaments and such motors lead to pinning events that can affect MT conformation by inducing the formation of loops, spirals and rings.50−53 Additionally, temporary pinning by inactive motors has been shown to cause significant dispersion in the path trajectory of MTs.54 Temporary pinning events were responsible for the wide degree of dispersion but F

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tubule associated proteins (MAPs), which have been reported to increase the stiffness and stability of MTs, and can limit kinesin binding to the MT surface. We therefore hypothesized that these two entities (i.e., MAPs and divalent salts) share a common mechanism in observed function that is related to their interaction with the C-terminal tails in tubulin; further discussion of this mechanism is presented in the following paragraphs. To address point (i) from above, it is important to first discuss the change in mechanical properties of MTs upon the addition of paclitaxel. Addition of paclitaxel to MTs increases lateral protofilament interactions within the filament allowing for enhanced MT stability. The paclitaxel-induced conformational changes to tubulin necessary to maintain these lateral contacts, however, also result in increased flexibility at the interdimer α- and β-tubulin interface.60,64 The change in flexibility at the interface between tubulin dimers is proposed, mechanistically, to be the explanation for the many experimental observations of an increase in overall MT flexibility after paclitaxel addition.65−67 In contrast, the addition of MAPs MAP2 or tau, to MT after paclitaxel stabilization results in a significant increase in the flexural rigidity of the filament, which is similar to the observed effects of divalent salts reported in the present work.68,69 MAPs interact with MTs by binding to the C-terminal projections of α- and β- tubulin. The interaction between MAPs and the C-terminal domains are likely driven by electrostatic attraction between oppositely charged amino acids at the binding interface.70−72 Once bound, MAPs play a regulatory role in both microtubule stability and kinesin motor binding frequency. The stabilization and stiffening effect imparted on MTs by MAPs is proposed to occur through bridging tubulin along an individual protofilament, as well as through conformational changes to the Cterminal domain.73 Additionally, MAPs can shield kinesin motors from the C-terminal domains and limit the attachment frequency and processivity.72,74 These effects are directly comparable with observations (ii) and (iii) above for divalent ions. Collectively the similarities between MAP-MT behavior and the effects of divalent salts reported here support an argument by which the observed changes in the mechanical properties and stability of MTs are driven by the condensation of oppositely charged divalent ions on to the C-terminal domain. The high density of charge in the tail region of the MT is well suited for exchange of 1+ counterions with the added 2+ counterions (driven by solution entropy). Divalent cations also have been demonstrated to strongly associate to carboxylate sites on biopolymer side chains with varying degrees of strength that order from Ba2+ > Sr2+ > Mg2+, which is in agreement with data presented here.75 Similarly, removal of the C-terminal tails from tubulin severely limits the impact of cationic ions and polyvalent macro-ions in facilitating MT assembly indicating the importance of the interaction of this unstructured motif with oppositely charged ions in solution.10,11,76 In the present work, we demonstrated that removal of the C-terminal domains from tubulin dimers eliminates the observed increase in Lp for added BaCl2 (Figure 1c and Supporting Information, S.1.5). Therefore, we conclude that added divalent ions interact with the C-terminal tails of tubulin dimers, and induce changes in the conformation of these domains that in turn drive the observed changes in MT mechanics and dynamics. In their native state, the C-terminal tails prefer to orient away and extend from the MT surface due to the negative charge density on the C-terminal tails and at the surface of the MT

Figure 6. ⟨Lp,surf⟩ strongly depends on the presence of divalent salts. The fractional increase in ⟨Lp,surf⟩ (solid bars) or Lp (hashed bars) is plotted for various motility solution conditions. The x-axis describes the formulation of the motility solution containing 5 mM of the indicated salt. fc is the ratio between ⟨Lp,surf⟩ (added salts)/⟨Lp,surf⟩ (control) or Lp (added salts)/Lp (control).

smaller fluctuations in trajectory were also common (Figure 5a,c,e). Both of these events were highly suppressed when divalent salts were present (Figure 5b,d,f). These results are consistent with those reported by Nitta and Hess54 and are compared in greater detail in Supporting Information, S.1.4.

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DISCUSSION Based on their intrinsic properties, the observed counterioninduced behaviors of MTs presented in this paper may be compared with experimentally observed polyelectrolyte (PE) behaviors of much simpler systems.55−59 The outer surface of a MT has a net negative charge while the individual building blocks (i.e., αβ tubulin) possess a heterogeneous distribution of amino acids with cationic and anionic side chains and are held together through noncovalent interactions. Importantly, a Cterminal region also extends from the outer surface of both subunits of the tubulin dimer, these “tails” are unstructured and confer a majority of negative charges (net charge of ∼11e−)60,61 Thus, we consider the PE behavior of MTs in the presence of additional divalent salts, demonstrating significant increases in the Lp of freely suspended MTs and in the conformation of MT undergoing active transport (⟨Lp,surf⟩). Due to the complex charge nature of MT assemblies, it is not surprising that the mechanical behavior presented in our work does not follow previous observations on similar biological PEs, such as DNA, where the addition of divalent ions decreases Lp.15 It should be noted that a wide range of values have been reported for MT Lp (∼1−10 mm),3,26,27,62,63 as factors such as polymerization conditions, buffer compositions, and MT binding proteins impact the flexural rigidity. Realizing these effects, all experiments in the present work were performed using the same MT polymerization protocol, ionic strength buffer, and paclitaxel concentrations (unless specifically indicated otherwise). Additional monovalent or divalent counterions were always added to the buffer in excess at the indicated concentrations. The concentrations of divalent ions used in this study were also below that required for transitional (i.e., bundling) phase behavior. Three important observations should be noted from the current work: (i) divalent counterions decrease the flexibility of paclitaxel-stabilized MTs with varying degrees of effectiveness following Ba2+ > Sr2+ > Mg2+, but requires the C-terminal tails of αβ tubulin dimers; (ii) added Ba2+ enhances the stability of mature MT filaments in the presence of substoichiometric paclitaxel; and (iii) added Sr2+ and Ba2+ weakens interactions between MTs and kinesin motors. Collectively, these observations follow characteristics that are similar to microG

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suggested for F-actin in which filament stiffness is regulated through a specific Ca2+ binding site between the DB-loop and SD3 of adjacent actin subunits.83 However, two critical observations from our work support a counterion-condensation exchange hypothesis. First, there is a clear ion size effect at fixed ion concentrations (Figure 1 and Table 1), consistent with previously published works that indicate ions with larger hydrated sizes (Mg2+ > Sr2+ > Ba2+) require higher bulk concentrations for significant condensation.84,85 Second, diluting the added divalent ion concentration (via dialysis or washing) with monovalent control ionic strength solutions reversibly restores the filament conformation back to control values, which is unlikely to occur in the absence of a chelator, if ion binding was in fact coordinated in a specific site. In addition to changes in the mechanical properties of the MTs, counterion-screening effects also weaken the binding between MT and kinesin motors, which contributes to a reduction in the impact of pinning events on MT conformation and trajectory dispersion. During gliding motility, a MT is bound by multiple motors simultaneously. When one bound motor becomes pinned, the local transport motion of the filament at the pinned motor stops. The remaining active motors still transport the MT but at the cost of MT buckling and intermittent MT gliding (see Supporting Information, Supplementary Movie 7). The pinned motor eventually unbinds due to the force generated by the actively bound motors, which lead to deflections in both the surface conformation, ⟨Lp,surf⟩, and in the trajectory angle of the MT (Figure 5e). Electrostatic cooperativity between the negative Cterminal tails of the MT and positive regions of the kinesin head is known to play an important role in the binding of kinesin to MTs, particularly with regard to the stepping mechanism.86,87 Therefore, we conclude that reduced surface charge density weakens the binding of all motors to MTs but, importantly, also limits the attachment lifetime of pinning motors, resulting in straighter filaments and trajectories. This effect was only observed in added divalent salt solutions, which suggests that a threshold level of charge neutralization (or binding strength) is required to achieve this effect. This argument is further supported by the observation of significant detachment of MTs from the surface at BaCl 2 salt concentrations ≳10 mM due to further charge neutralization of the filament.

(Figure 7a).77 Thermal fluctuations, however, can occasionally drive a tail into a down configuration where it may interact with

Figure 7. Conformational changes to tubulin C-terminal tails. Added divalent ions replace condensed monovalent ions on the highly negatively charged C-terminal tail of tubulin, which reduces the charge repulsion between the tails and the surface of the MT. The screened coulomb interactions in turn promote tail−body interactions and bias the configuration of the tails from up and noninteracting (a) to down and body interacting (b).

positive pockets of charge on the MT surface (Figure 7b). Screening due to the presence of additional divalent counterions can bias the system toward the down state as coulomb repulsion would drive tend to drive the tails away from the MT surface. In bovine brain tubulin, such a secondary structure has been proposed where negatively charged residues on the Cterminal tail can interact with a proximal highly reactive surface lysine (Lys-394) resulting in a down tail configuration.78 Similarly, Mg2+ and Mn2+ also have been implicated in facilitating tail-MT surface interactions. In light of the previous discussion of divalent ion binding efficiencies to carboxylate sites on biopolymers, it is reasonable to conclude that Ba2+ and Sr2+ would have a similar effect.79 Herein we propose that the down C-terminal tail state is facilitated by screened coulomb interactions between the tail and the MT surface related to divalent counterions interaction with the tails. In turn, the conformational changes and screened coulomb interactions are responsible for the presented global effects of increased MT stability, reduced flexibility of paclitaxel stabilized MTs and weaker interactions between MTs and kinesin motors. AFM experiments provide evidence for a conformational change in the C-terminal tail induced by tau; simulations of this interaction also confirm that the tail exists in the down configuration.80,81 Because tau functions to stabilize MT and reduce the flexibility of paclitaxel-MTs, it may be rationalized that tail−MT surface interactions play a role in these observations for tau, as well as the observations in our current work. We also note that it is unlikely for the divalent counterions used at the concentrations in this study (≤5 mM) to effect lateral or longitudinal interactions between and within MT protofilaments. Screening of these interfaces would weaken the electrostatic contacts between them leading to an increase in the flexibility (longitudinal) or a decrease in stability (lateral). To this point, divalent ion concentrations, at high concentrations (i.e., ≥ 50 mM), have been shown to depolymerize paclitaxel-stabilized MTs in the absence of bundle formation.82 While, to our knowledge, no specific binding sites for Sr2+ or Ba2+ have been reported in tubulin, one may argue that coordinated ion binding could modulate the mechanical properties of MT filaments independently from nonspecific charge−charge interactions. Such a mechanism has been

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CONCLUSION Electrostatics, in addition to protein conformation changes, are important mediators for interactions between MAPs with MT filaments. Here we have described how screened coulomb interactions between the MT surface and C-terminal tails may drive significant increases in the rigidity and stability of MTs, as well as affect interactions with kinesin motor proteins. These unique behaviors are likely specific to the complex nature of the charge distribution within MTs, and are predominantly driven by interactions with the highly charged C-terminal regions of tubulin. Changes in the structure of the C-terminal tails have been correlated with similar changes in the mechanical properties and stability induced by MAP binding to MTs, which supports this hypothesis. Further investigation of counterion-induced changes in the C-terminal tails and their relationship to increased stability may provide valuable insights with respect to the role of electrostatics in MT dynamics and the regulation of binding between motor proteins and other MAPs with the MT surface. H

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ASSOCIATED CONTENT

S Supporting Information *

Solution to the two variable Manning condensation. Description and movies of MT thermal fluctuations in monovalent and divalent solutions, motility in monovalent and divalent solutions, and stability in control and divalent solutions. Figure highlighting path trajectories of MT. Comparison between path persistence with previously reported values. Reconstruction of subtilisin-treated microtubule shapes. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +1 (505) 844-5164. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We sincerely thank Drs. Susan Rempe, Cecilia Leal, and Mark Stevens for their critical review and comments on this manuscript and Dr. Virginia VanDelinder for preparing the graphical image of divalent effects on the configuration of tubulin’s C-terminal tails. This work was supported from the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, Project KC0203010. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.

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