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property of MTs by MT associated proteins and might also help obtain a clear insight of the endurance and mechanical instability of MTs under appl...
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Biomolecular Motor Modulates Mechanical Property of Microtubule Arif Md. Rashedul Kabir,† Daisuke Inoue,‡ Yoshimi Hamano,‡ Hiroyuki Mayama,§ Kazuki Sada,†,‡ and Akira Kakugo*,†,‡ †

Faculty of Science and ‡Graduate School of Chemical Sciences and Engineering, Hokkaido University, Sapporo 060-0810, Japan § Department of Chemistry, Asahikawa Medical University, Asahikawa 078-8510, Japan S Supporting Information *

ABSTRACT: The microtubule (MT) is the stiffest cytoskeletal filamentous protein that takes part in a wide range of cellular activities where its mechanical property plays a crucially significant role. How a single biological entity plays multiple roles in cell has been a mystery for long time. Over the recent years, it has been known that modulation of the mechanical property of MT by different cellular agents is the key to performing manifold in vivo activities by MT. Studying the mechanical property of MT thus has been a prerequisite in understanding how MT plays such diversified in vivo roles. However, the anisotropic structure of MT has been an impediment in obtaining a precise description of the mechanical property of MT along its longitudinal and lateral directions that requires employment of distinct experimental approach and has not been demonstrated yet. In this work, we have developed an experimental system that enabled us to investigate the effect of tensile stress on MT. By using our newly developed system, (1) we have determined the Young’s modulus of MT considering its deformation under applied tensile stress and (2) a new role of MT associated motor protein kinesin in modulating the mechanical property of MT was revealed for the first time. Decrease in Young’s modulus of MT with the increase in interaction with kinesin suggests that kinesin has a softening effect on MT and thereby can modulate the rigidity of MT. This work will be an aid in understanding the modulation of mechanical property of MTs by MT associated proteins and might also help obtain a clear insight of the endurance and mechanical instability of MTs under applied stress.

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INTRODUCTION Microtubules (MTs), one of the major components of cytoskeleton, are composed of protofilaments of tubulins and play significant roles in a wide range of fundamental cellular processes such as cell division, cell shape determination, intracellular transport, and so on.1,2 High rigidity of MTs is desired for maintaining cell shape and for allowing long-range intracellular transport, but in some cases MTs are also found to be highly curved3−5 and this change in mechanical property perhaps depends on the functions in which MTs are engaged. These observations imply that mechanical property of MTs in cell is variable, but how the mechanical property of MTs is modulated to enable them perform such diverse activities in cell has been an open question. To clarify this, mechanical properties of MTs have been studied by employing various experimental approaches that involved deformation of MTs using optical tweezers,6 hydrodynamic flow,7 thermally induced vibrations or shape fluctuations,8 buckling in vesicles,9 and atomic force microscopy (AFM).10 It was proposed that some microtubule associated proteins (MAPs) including kinesin families can locally regulate the mechanical property of MTs thereby rendering them suitable for performing different in vivo roles.11−14 However, in these works, the Young’s and shear moduli of MT could not be independently evaluated since bending and indentation induced deformation of MT is always accompanied by both stretching and sliding of protofilaments © 2014 American Chemical Society

(with the only exception in the determination of Young’s modulus using optical tweezers).15 Elastic properties of MTs along the longitudinal (Young’s modulus) and lateral directions (shear modulus) were reported to largely differ from each other reflecting the anisotropic structure of MTs10,16,17 and hence it is significantly important to characterize the Young’s and shear moduli of MT separately. To experimentally determine the Young’s modulus of MT in an independent way we have established a method, mimicking the protocol of a conventional fragmentation test,18,19 that enabled us to perform pseudofragmentation test of MT. Using the newly developed experimental system we have investigated how binding of kinesin, that is one of the abundant MAPs inside cell, affects the Young’s modulus of MT. We have designed an experimental set up named “stretch chamber system” that allowed us to apply mechanical stress at MTs and at the same time permitted the in situ observation of response of MTs to the applied stress. To demonstrate the pseudofragmentation test, surface of a soft elastomer polydimethylsiloxane (PDMS) was first coated with kinesin (in the absence of any nucleotide) and MTs were applied on the kinesin coated surface. PDMS substrate was then extended Received: February 4, 2014 Revised: April 1, 2014 Published: April 3, 2014 1797

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Determination of Association Constant between PDMS and Anti-GFP Antibody. Gold-coated crystals of quartz crystal microbalance (QCM) were coated with a thin layer of PDMS. In brief, PDMS solution and cross-linker were mixed at a ratio of 10:3 (w/w) and the mixture was diluted to 1:100 (w/w) in hexane. The surface of QCM crystal was plasma treated for 30 s (10 Pa, 8 mA). The PDMS solution in hexane was then spin-coated on the plasma treated gold coated QCM crystals at 3000 rpm for 40 s. The crystals were then cured overnight at 60 °C to allow polymerization of PDMS and evaporation of hexane. Measurements of the resonant frequency of QCM crystals before and after PDMS coating were taken at air and change in frequency was used to determine the thickness of PDMS layer.24−26 Thickness of the PDMS layer on quartz crystal was found to be ∼382.80 nm as calculated by using the change in resonance frequency. The PDMS layer on the QCM sensor was then plasma treated (30 s), BRB80 run buffer was passed through the cell of QCM and the system was allowed to come to a stable state confirmed by a constant frequency over time. The reference electrode was coated with casein buffer (10 mg mL−1). A volume of 30 μL of anti-GFP antibody solution of different concentrations such as 173, 260, 433, 1300, 2600, and 6500 nM in BRB80 buffer was then passed through the flow cell at a rate of 5 μL/min. Change in resonance frequency of both the electrodes were measured with time and net change of frequency was then used to find the mass change by using the Sauerbrey equation and finally association constant between PDMS and anti-GFP was determined as reported in literature.27 Determination of Kinesin Density on PDMS Substrate of Fragmentation Test. First kinesin solutions of a wide range of concentrations were applied on gold-coated crystals of QCM, prior to which the surface of the QCM sensor was coated with anti-GFP antibody in each case. Using the Sauerbrey equation, the density of kinesin deposited on the gold coated QCM crystal was determined for respective kinesin concentration. Next, after applying anti-GFP antibody, kinesin solutions of the same concentrations were applied to the surface of a gold coated cover glass. From here, fluorescence intensity values of GFP-kinesins at different concentrations were obtained. Finally, a standard curve was prepared by correlating the fluorescence intensity of GFP-kinesin with the kinesin density. Using the standard curve and the fluorescence intensity, kinesin density on PDMS substrate of fragmentation test was determined. Microscopic Image Capture and Analyses. Samples were illuminated with a 100 W mercury lamp and visualized by using an epifluorescence microscope (Eclipse Ti; Nikon) using an oil-coupled Plan Apo 60 × 1.40 objective (Nikon). Filter blocks with UV-cut specification (TRITC: EX540/25, DM565, BA606/55; GFP-HQ: EX455-485, DM495, BA500-545; Nikon) were used in the optical path of the microscope that allowed the visualization of samples but eliminated the UV part of radiation and minimized the harmful effect of UV radiation on samples. Images were captured using a cooled CMOS camera (Neo sCMOS; Andor) connected to a PC. To capture a field of view for more than several minutes, ND filters (ND4, 25% transmittance) were inserted into the illuminating light path of the fluorescence microscope to avoid photobleaching. Images of microtubules captured by fluorescence microscope were analyzed using “ImageJ”. Length of MTs and MT fragments at different experimental conditions were measured manually using the image processing software and MTs aligned parallel to the stretching axis were considered for analyses.

uniaxially to develop mechanical stress at MTs, and the accumulated stress consequently resulted in mechanical failure, that is, fragmentation of MTs. Effects of different parameters such as extent of strain, strain rate and amount of kinesin on fragmentation of MTs were also investigated in detail. Finally, using our experimental results from the fragmentation test, we have evaluated the Young’s modulus of MT as ∼12 MPa, which is within the range of Young’s modulus of MT reported in literature.6,10,15,20 At the same time, our results revealed that kinesin has a strong effect in modulating the mechanical property of MT and increased interaction with kinesin can dramatically decrease the Young’s modulus of MT. This work offers a novel strategy to experimentally investigate the Young’s modulus of MT and role of MT associated proteins in altering the mechanical property of MTs. Response of MTs to tensile stress in a wide range of conditions is also understandable now. So far, kinesin has been known to work as a biomolecular motor protein participating in intracellular transport, cell division, and so forth, but our work will shed light on a new role of kinesin where it is found to work as a modulator of MT’s mechanical property.

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EXPERIMENTAL SECTION

Preparation of Tubulin and Kinesin. Tubulin was purified from porcine brain using a high-concentration PIPES buffer (1 M PIPES, 20 mM EGTA, 10 mM MgCl2; pH adjusted to 6.8 using KOH). Highmolarity PIPES buffer (HMPB) and brain reconstitution buffer 80 mM PIPES (BRB80) were prepared using PIPES from Sigma, and the pH was adjusted using KOH.21 GFP-fused kinesin-1 consisting of the first 560 amino acid residue (K560-GFP) was prepared by partially modifying previously reported expression and purification methods.22 Preparation of Labeled Tubulin and Microtubules. Rhodamine-labeled tubulin was prepared using 5/6-carboxytetramethylrhodamine succinimidyl ester (TAMRA-SE; Invitrogen) according to the standard technique23 and the labeling ratio was 1.0 as determined by measuring the absorbance of the protein at 280 nm and that of tetramethyl-rhodamine at 555 nm. Rhodamine-labeled microtubules were obtained by polymerizing a mixture of rhodamine tubulin (RT) and nonlabeled tubulin (WT) at 37 °C (RT/WT = 4:1; final tubulin concentration = 55.6 μM). The solution containing the microtubules was then diluted with motility buffer (80 mM PIPES, 1 mM EGTA, 2 mM MgCl2, 0.5 mg mL−1 casein, 1 mM DTT, 10 μM paclitaxel, and ∼1% DMSO; pH 6.8). Fragmentation Test. A piece of poly(dimethylsiloxane) (elastic modulus: ∼1.33 MPa; Fuso Rubber Industry Co. Ltd.) with dimension 7.0 × 5.0 × 0.2 mm3 (L × W × T) was fixed to the movable stretcher of the stretch chamber. For using as a flowcell a narrow region at the top surface of PDMS was plasma treated for 3 min (10 Pa, 8 mA) by a plasma etcher (SEDE-GE; Meiwafosis Co. Ltd.) in order to increase the hydrophilicity of the surface. Anti-GFP antibody (Invitrogen) at 0.1 mg mL−1 (10 μL) was applied to the plasma treated PDMS surface (flowcell). Then, 10 μL kinesin-1 solution (K560-GFP) of prescribed concentrations (∼80 mM PIPES, ∼40 mM NaCl, 1 mM EGTA, 1 mM MgCl2, 1 mM DTT, 10 μM paclitaxel; pH 6.8) was introduced and incubated for 3 min to bind the kinesin to the antibody. The flowcell was washed with 10 μL of motility buffer (∼80 mM PIPES, 1 mM EGTA, 1 mM MgCl2, 0.5 mg mL−1 casein, 1 mM DTT, 10 μM paclitaxel, ∼1% DMSO; pH 6.8). Next, 10 μL of 200 nM microtubule solution was introduced and incubated for 3 min, followed by washing with 20 μL of motility buffer. Then the stretch chamber was closed and humid nitrogen gas was kept passing through the chamber to remove oxygen from the chamber. After passing the nitrogen gas for 1 h, the chamber was mounted to the stage of the fluorescence microscope. Fragmentation test was performed by applying uniaxial extension to the PDMS using the computer controlled stretcher. All the aforementioned experiments were performed at room temperature.

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RESULTS AND DISCUSSION In a conventional fragmentation test, a dog-bone-shaped matrix containing a single fiber is subjected to uniaxial extension and the tension applied to the matrix is then transferred from matrix to the fiber. Based on this principle of the fragmentation test, we have developed a stretch chamber to investigate the effect of mechanical stress on MTs by performing a pseudofragmentation test. The stretch chamber allowed us for performing the pseudofragmentation test of MTs keeping the specimen in an inert atmosphere free of reactive oxygen species and ruled out 1798

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Figure 1. (a) Schematic diagram of the stretch chamber used to demonstrate the fragmentation test of MTs. Two computer controlled DC motors were used for applying uniaxial extension to the PDMS fixed at the stretcher. Fragmentation test was performed keeping the specimen in an inert atmosphere maintained by passing humid nitrogen gas through the chamber continuously. Representative fluorescence microscopy images show MTs before (b) and after (c) the uniaxial extension of PDMS substrate; fragmentation of MTs could be observed in image (c). In this experiment, kinesin concentration was 1300 nM and image (c) was captured after applying 21.5% strain at the PDMS substrate at a strain rate of 0.44% s−1. Scale bar: 10 μm.

any possibility of oxidative damage of MTs and kinesins.28 Figure 1a shows the schematic diagram of the stretch chamber. The stretch chamber consists of two main parts named baseplate and cover head; both are made of stainless steel. The baseplate contains a stretcher connected to two computer controlled DC motors (Supporting Information, Figure S1). First, a piece of PDMS with dimension 7.0 × 5.0 × 0.2 mm3 (L × W × T) was fixed horizontally at the stretcher, and a narrow region on the top surface of PDMS was plasma treated to increase its hydrophilicity so that it can be used as a flowcell. Next the plasma treated surface of PDMS was coated with antiGFP antibody, green fluorescent protein fused kinesin (GFPkinesin) and then MTs were deposited on the substrate via interaction with the kinesin in the absence of any nucleotide. During sample preparation, shear flow was used by applying MT solution from one end of flowcell to align MTs parallel to the stretch axis. In this work, MTs were labeled with a fluorescent dye in order to monitor the response of MTs to the applied stress under a fluorescence microscope. It is noteworthy that, unlike to the case of a conventional single fiber fragmentation test, MT filaments were not directly embedded at the PDMS substrate in this work. After preparation of the flowcell, the stretch chamber was closed and humid nitrogen gas was purged to remove away oxygen from the chamber. Finally mechanical stress was applied at MTs by elongating the

PDMS substrate using the computer controlled stretcher. All the above procedures were conducted at room temperature. Uniaxial extension of the PDMS substrate developed mechanical stress at the interface which in turn developed stress in the MTs. As the strain at PDMS substrate was increased by extension, the stress in MTs also increased for maintaining force equilibrium. Further increase of strain was then found to result in fragmentation of MTs as shown by the fluorescence microscopy images in Figure 1b and c. Generally, at the onset of MT fracture at relatively low level of strain a crack (dark line) on MT perpendicular to its axis was found to develop (confirmed by the inhomogeneity in fluorescence intensity along the MT). The strain at which the first crack appeared is termed hereafter as threshold strain. On increasing the strain further MTs were broken at the position where the crack was initially developed. Presence of the crack was confirmed by following the motility of MTs by supplying adenosine 5′-triphosphate (ATP) where MTs were readily split into motile MT fragments at the crack position (Supporting Information, Movie S1). As the strain on the substrate was increased further, the fragmentation process continued until the fragments became too short to develop additional stress needed to produce additional breaks. Strain at which the fragmentation of MTs stopped is termed as the critical strain and average length of MT fragments at this strain will be defined hereafter 1799

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Figure 2. Effect of mechanical stress on fragmentation of MTs: (a) Representative fluorescence microscopy images show gradual change in MT length with the increase in strain. Black arrows indicate the position of new breakage along MT. Scale bar: 10 μm. (b) Histograms describe the change of MT length and its distribution with the change of strain. Inset shows the enlarged view of histogram for the case of 0% strain. In these experiments, kinesin concentration was 900 nM and strain rate was 0.44% s−1. (See Supporting Information, Figure S2 for the enlarged view of the histograms.)

as the critical MT fragment length, a dependent variable in the fragmentation test. Monitoring the behavior of a single MT, detailed investigation on the mode of breakage was performed. As shown in Figure 2a, a MT filament underwent the first fragmentation producing two fragments of unequal length at the threshold strain. On increasing the strain gradually, those 2 MT fragments were further broken into 5 shorter fragments over time and finally 7 MT fragments were produced from the single MT. During this process, fragmentation was observed only at certain strain values as shown in the figure and this observation suggests that fragmentation of MTs under applied mechanical stress is a discrete phenomenon. Length distribution of MTs at different strains is shown in Figure 2b (number of MT considered for analysis, n = 40), and the result clearly reveals that on increasing the strain, distribution of MT length gradually became narrower and shifted toward lower values due to the fragmentation. The effect of strain on average length of MTs is shown in Figure 3 where fixing the strain rate at 0.44% s−1 we also varied the concentration of kinesin over a wide range such as 50, 100, 200, 600, 900, and 1300 nM considering that in eukaryotic cell kinesin concentration varies between 10 and 1000 nM.29 Kinesin concentration is the parameter that can modulate the extent of interaction between MTs and PDMS substrate. Consequently, tuning the kinesin concentration allowed us to alter the interfacial stress which might affect the extent of MT fragmentation. MT fragmentation manner was found strongly dependent on the extent of interaction between MT and kinesin or in other words MT and substrate. At the lowest kinesin concentration i.e., at 50 nM, MTs underwent first fragmentation at ∼4.28% strain and due to fragmentation average length of MTs dropped to 26.2 μm ± 8.7 from 36.4 μm ± 4.6. At this kinesin concentration, no additional breakage of MT fragments was observed at higher strains and average length of MTs remained constant. However, on increasing the kinesin concentration such as at the highest 1300 nM, the threshold strain decreased to ∼1.4% at which the average MT length was found to be 18.3 μm ± 8.4, which on increasing the strain further decreased gradually through several steps of breakage and attained a constant value of 4.7 μm ± 2.4 at ∼71.4% strain. From Figure 3, it could be observed that at

Figure 3. Effect of extent of strain on MT fragmentation at different kinesin concentrations: (a) 50 nM; (b) 100 nM; (c) 200 nM; (d) 600 nM; (e) 900 nM; and (f) 1300 nM kinesin. For making the figure clearly visible, strain only up to 28% was considered in each case. In these experiments, strain rate was 0.44% s−1. Number of specimens considered was 40 except for the case of the lowest kinesin concentration. MTs aligned parallel to the stretching axis were considered for analyses. Here average length of MTs at 0% strain, which is almost same for the cases of all kinesin concentrations, represents the average length of MTs just after the preparation by tubulin polymerization. Inset in (d) shows fragmentation scenario of MTs at 600 nM kinesin concentration as depicted theoretically (see the discussion). In this figure, average MT fragment lengths at different strains were normalized with respect to the average MT length at 0% strain.

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relatively high kinesin concentrations MTs underwent several breakages until the critical MT length is reached. The figure also clearly discloses that fragmentation of MTs is a stepwise and discrete phenomenon and there is a threshold strain that is required to cause the fragmentation of MTs below which no fragmentation of MTs could be observed. However, the effect of strain on MT fragmentation also depends on the interfacial interaction between MTs and substrate, that is, kinesin concentration. On increasing the kinesin concentration, the interfacial interaction became stronger and as a result the threshold strain and critical MT fragment length decreased but critical strain increased. From the wide distributions of MT fragment lengths observed in this work, it seemed that distribution of the anchoring complex of kinesin−antibody−casein on microtubules may not be even, which was also noticed from the fluorescence microscopy images (data not shown) where randomly distributed aggregates of kinesins were observed especially when high concentrations of kinesins were used. Therefore, apparently it seemed that strain exerted on microtubules was not even that resulted in unequal microtubule fragment lengths. However, in a conventional single fiber fragmentation test the lengths of all fiber fragments even at the saturation (at the critical strain) are also not identical, which is considered due to uneven distribution of the flaws in the fiber with respect to spacing or severity and a number of some other factors that can also influence the fragment lengths.30 On the other hand, a wide distribution of microtubule fragment lengths was also reported when microtubule filaments were exposed to shear flow that caused a reduction in the average microtubule length but failed to reduce the polydispersity index.31 Thus, at this stage, it appears difficult to conclude that uneven distribution of anchoring complex was the reason for unequal microtubule fragment lengths observed in this work and this will be investigated in future work. Although in our pseudofragmentation test of MTs, wide distributions in MT fragment lengths could be noticed at lower strains and lower kinesin concentrations, on gradually increasing the strain particularly at relatively higher kinesin concentrations MT fragments became almost identical in length which is evident from the histograms shown in Figure 2b (see also Supporting Information, Figure S2) and decrease in error bar shown in Figure 3. Also it is noteworthy that, in our analyses, we have considered the average length of microtubule fragments obtained through a statistical treatment. Figure 4 shows how increased kinesin concentration caused severe fragmentation of MTs and consequently resulted in dramatic decrease in critical MT fragment length (see also Supporting Information, Figure S3). In order to discuss the effect of interfacial interaction on MT fragmentation, we have determined the kinesin density on PDMS substrate using quartz crystal microbalance (QCM) following a conventional protocol. First we determined the amount of kinesin deposited on a QCM gold sensor surface when kinesin solutions of a wide range of concentrations were applied. We found deposition of kinesins on the QCM gold sensor surface followed Langmuir adsorption isotherm according to the equation ρ = KNC/(1 + KC); here ρ is kinesin density, K is the binding constant between kinesin and anti-GFP antibody where K = 0.66 × 106 M−1, N is the number of binding sites, and C is the concentration of applied kinesin. Next, we collected the fluorescence intensity of GFP-kinesins by applying kinesin solution of the same concentrations on a

Figure 4. Effect of kinesin concentration on MT fragmentation. “Critical MT fragment length” represents average length of MT fragments at critical strain. Applied mechanical stress caused severe fragmentation when the concentration of kinesin was increased. Curve fitting was performed by least-squares method and followed a power relation. Inset shows the plot of Lc vs 1/ρkin. Here Lc is the critical MT fragment length and ρkin is the kinesin density on the substrate. In this case, curve fitting was performed by least-squares method that followed a linear relation. Kinesin density determined for the cases of five kinesin concentrations such as 100, 200, 600, 900, and 1300 nM were considered for preparing this figure (inset), and the lowest kinesin concentration (50 nM) was not considered as in that case only a small number of MTs underwent fragmentation.

gold coated cover glass. Adsorption of kinesin on gold coated cover glass also followed Langmuir adsorption isotherm according to the equation I = KNC/(1 + KC); here I is the fluorescence intensity of GFP-kinesin, K is the binding constant between kinesin and anti-GFP antibody, N is the number of binding sites, and C is the concentration of applied kinesin. Finally, from these two results, we obtained a linear correlation factor between fluorescence intensity and kinesin density as (kinesin density)/(fluorescence intensity) = 27.4 molecule·μm−2·au−1 (au stands for arbitrary unit of fluorescence intensity). It is to mention that, while preparing the standard curve and also throughout this work, light intensity and exposure time of fluorescence microscope were kept constant. The reciprocal plot of critical MT fragment length and kinesin density shown in Figure 4 (inset) produced a straight line according to the Kelly−Tyson model32 which suggests that fragmentation of MTs under mechanical stress demonstrated in this work closely resembles the conventional fragmentation test. Strain rate is particularly one of the variables in a conventional fragmentation test; and also because of the fact that during deformation biopolymers are susceptible to respond to any change in strain rate due to their viscoelastic property, we also investigated the effect of strain rate on MT fragmentation. Fixing kinesin concentration at a relatively low value, for example, 100 nM, pseudofragmentation tests of MTs were conducted by varying strain rate over 1 order of magnitude such as from 0.14% s−1 to 2.85% s−1, that is the maximum range of strain rate that could be applied using the stretch chamber. Responses of critical MT fragment length to changes in the strain rate were determined. As shown in Figure 5, strain rate has almost no effect on the critical MT fragment length under the present experimental condition and similar insensitivity was reported in fragmentation tests of composite 1801

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UMT(N ) = (1/2)EMT, long ⋅εMT, long (N )2 ⋅VMT(N − 1) + (1/2)EMT, lat ⋅εMT, lat(N )2 ⋅VMT(N − 1)

(1)

Here, EMT, long and EMT, lat are the moduli of MT along its longitudinal and lateral direction respectively; εMT, long(N) and εMT, lat(N) are the strains at MT at Nth fragmentation along longitudinal and lateral direction respectively and VMT(N − 1) is the volume of MT before the Nth fragmentation which is the product of length of MT before Nth fragmentation, Lf (N − 1) and cross-sectional area of MT, SMT. The last term in eq 1, which is the deformation energy due to compression along lateral direction, can be neglected since we experimentally determined the ratio of the lateral strain to the longitudinal strain of PDMS in our work which was ca. 0.17 and its contribution in the deformation energy was ca. 3%. Therefore, we get

Figure 5. Effect of strain rate (rate of axial deformation of PDMS substrate) on fragmentation of MTs. MT fragment length was determined at the critical strain, and kinesin concentration used in these experiments was 100 nM.

UMT(N ) ≈ (1/2)EMT, long ⋅εMT, long (N )2 ⋅VMT(N − 1)

30,33,34

materials. The exact reason behind such strain rate independence is not clear but might have arisen due to following factors: PDMS is an elastomer whose deformation is insensitive to the deformation rate but kinesin is a biopolymer and might have failed to transmit the stress to MTs readily at high strain rates and thereby minimizing the strain rate effect on MT fragmentation. Moreover, interfacial debonding specially at high strain rate is likely to occur as reported in literature,30 although we observed no such debonding phenomenon from the fluorescence microscopy images. Now let us discuss the mechanism of MT fragmentation in the light of our experimental results considering the balance between deformation energy of MTs and surface energy of fractured surfaces. First we discuss the contribution of stress working on MTs in the form of shear and tensile stress. As discussed in the Supporting Information, the effect of shear stress on the deformation of MTs in the presented fragmentation test was found negligible compared to the tensile stress, especially when high strains were applied. Here we assume that one MT is divided into two MT fragments of equal length, where we define the fragment length at the Nth fragmentation as Lf(N). We also assume that MT follows the extension and compression of PDMS until fragmentation and the applied strain at MT at the Nth fragmentation, εMT(N) is equal to the strain at PDMS at the Nth fragmentation, εPDMS(N), that is, εMT(N) ~ εPDMS(N) (see the Supporting Information), where we have considered the elastic moduli of the participants and the range of interactions working at the attachments of participants. Elastic modulus of motor domain and coiled coil part of kinesin were reported to be fairly high (on the order of sub GPa),35 whereas that of PDMS was experimentally evaluated as ca. 1 MPa in our work. It was reported that potential energy curves for specific and nonspecific interactions are very steep and these interactions can actively work over a very small distance, that is, several nanometers.36,37 These ranges are, in fact, quite small compared to the deformation of the PDMS observed in our experiments. Collectively, considering such a big difference in elastic modulus of kinesin and PDMS and very small range of interactions working at the attachments we assumed that the influence of kinesin and attachments on the strain of PDMS and microtubule could be neglected. Therefore, the deformation energy of MT at the Nth fragmentation, UMT(N) is expressed as

(2)

On the other hand the surface energy, Usurf is the product of surface tension (γ) and cross sectional area of two newly generated surfaces on fragmentation, (SMT) where Usurf = 2γSMT

(3)

In our previous work, we reported that new surfaces are created when the energy of deformation equals to the surface energy of newly formed surfaces.38 Then from the balance of Usurf and UMT, we obtain EMT, long = 4γ /[εMT, long (N )2 ⋅Lf (N − 1)]

(4)

Equation 4 allowed us to determine the EMT, long directly from the applied strain and corresponding fragment length in the final fragmentation conditions under the assumption that a long MT is divided into two MT fragments of equal length and MTs interacted homogeneously with kinesins. Now, even in the region of relatively high stain values we observed a linear correlation between stress and strain of the PDMS substrate (Supporting Information, Figure S4) and a very good reproducibility of results of MT fragmentation test and hence critical MT fragment lengths and critical strains were used to determine the EMT, long. The strains in the final step of fragmentation, εMT, long(final), were 4.28, 7.10, 14.3, 14.3, 28.5, and 71.4%, and the final fragment lengths, Lf(final), were 26.1, 18.1, 11.8, 7.5, 5.5, and 4.7 μm for the 50, 100, 200, 600, 900, and 1300 nM kinesin concentration respectively, where we assumed Lf(N − 1) = 2Lf(final) in eq 4. By considering the value of surface tension, γ, to be ~0.1 J/m2,39 the EMT, long in each condition was determined as 4.19, 13.7, 3.35, 1.30 MPa and 447, and 83.8 KPa for the 50, 100, 200, 600, 900 and 1300 nM kinesin respectively. Figure 6 shows how EMT, long decreased with the increase in kinesin concentration. From this result, it is obvious that increased interaction with kinesin decreases the Young’s modulus of MT, which implies that kinesin can modulate the mechanical property of MT. This kind of modulation of MT’s mechanical property by kinesin was not clearly observed in the indentation test of kinesin decorated MT by using AFM.13 The intercept in Figure 6 provides EMT, long in the absence of kinesin which was evaluated to be ∼12 MPa and this value of Young’s modulus lies within the range reported in literature.6,10,15,20 Based on the EMT, long obtained here, theoretical εMT, long for MT fragmentation can be discussed by a simple scenario. Since we assume that a long MT is 1802

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be responsible for determining the binding energy of the system and at the same time may prevent possible bond breakage at the microtubule/antibody or microtubule/kinesin interface. Also from our experiments we noticed no detachment event of microtubules from the substrate surface even at high strain and high strain rates. In addition to this, a discrete mechanism of fragmentation of microtubules (stepwise breakage of microtubules) observed in our work also corroborate our statement and also the fragmentation models reported in literature. Hence, reasonably, we did not consider any possibility of catastrophic loss of adhesion of MTs in the discussion. Here it is to mention that we did not account the association constants under loading in consideration of our binding energy based argument where binding energy is not likely to change under loading as may happen to binding force. Employment of the association constants facilitates an easier approach based on the binding energy instead of binding force for constructing the model of microtubule fragmentation. Also we experimentally confirmed that strain rate has no significant effect on the mechanical stress induced fragmentation of microtubules in the given conditions. Then it is also reasonable to assume that strain rate has no effect on the binding energy of antibodies and kinesins to PDMS. Now, under two-dimensional consideration the number of interaction site on MT could be expressed as ρkin1/2Lf(N − 1) and the binding energy for one binding site, ub could be expressed as − kBT lnKb ∼ 4 × 10−20 J (Kb is the binding constant between PDMS and anti-GFP and is the weakest one among all the binding constants considered in our system), where ρkin is the density of kinesins on PDMS. Therefore, the binding energy between MT and kinesins to maintain the Nth fragmentation, Ub(N), is ρkin1/2Lf(N − 1)ub. From the energy balance between UMT(N) and Ub(N), we obtain

Figure 6. Kinesin’s softening effect on MT is revealed from the pseudofragmentation test of MT where decrease in Young’s modulus, EMT, long was observed with the increase in interaction with kinesin. The lowest kinesin concentration (50 nM) was not considered for analysis as in that case very small number of MTs underwent fragmentation. Young’s modulus of MT was determined based on the surface energy (square) and binding energy (circle) arguments.

divided into two MT fragments of equal length, therefore, the MT length at the Nth fragmentation, Lf(N), is defined as Lf(N) = Lf(N − 1)/2 = Lf(N = 0)/2N, where Lf(N = 0) is the initial MT length, L0. Substituting Lf(N) by Lf(N = 0) in eq 4, the theoretical εMT, long was obtained using the MT length at the (N − 1)th fragmentation, Lf(N − 1), as εMT, long (N ) =

2N + 1γ /(EMT, long ⋅L0)

(5)

Figure 3d (inset) shows that under an ideal condition MT fragmentation proceeds in a stepwise manner where the experimentally obtained initial length and Young’s modulus of MT were used to describe the ideal scenario. A difference could be observed in the experimentally observed and theoretically depicted fragmentation manner especially at the lower strain region. The experimental results show that at higher kinesin concentrations MTs were fragmented at relatively low strain, which is contrary to the ideal scenario. This discrepancy could be accounted for by probable inhomogeneous distribution of kinesin on the PDMS surface and defect in MT lattice structure. The first one can induce a difference in the mechanical property within a MT where MT segment with low elasticity (part of MT interacting with a small number of kinesin) might readily break at much lower strain. The second one, defect in MT lattice structure caused by the probable variation in protofilament number within a MT,40 could also induce such breakage. Furthermore, it is possible to determine the EMT, long theoretically by considering an interaction that is largely involved in MT fragmentation. First, we made a comparison among the association constants of microtubule/kinesin, kinesin (antigen)/anti-GFP (antibody), and anti-GFP (antibody)/PDMS. The association constant between microtubule and kinesin in the presence of ATP or ADP was reported to lie on the order of ∼106 which increases in the absence of nucleotide.41−43 On the other hand, the association constant between kinesin (antigen) and anti-GFP (antibody) is on the order of ∼109.44 Using QCM, we determined the association constant between anti-GFP (antibody) and PDMS that was found to lie within the order of ∼104−106. The weakest association constant among all these three was between the anti-GFP (antibody) and PDMS. This weakest interaction will

(1/2)EMT, long ·εMT, long (N )2 ⋅SMT = ρkin1/2 ⋅ub −16

Now, SMT = 4.9 × 10 eq 6, we get

(6)

2

m (diameter of MT is 25 nm). From

EMT, long = 2ρkin1/2 ⋅ub/[εMT, long(N )2 ⋅SMT]

(7)

Comparison between EMT, long obtained from binding and surface energy consideration is shown in Figure 6. The result unveils similar softening effect of kinesin, although the value of EMT, long was found to be slightly lowered by a factor of ∼1.5 which might have arisen from underestimation of the binding constant. Now we discuss how the stretch chamber system can be used for applying longitudinal strain at a stretchable substrate. It might be suspected that during axial elongation of the PDMS substrate lateral contraction also have occurred that might have affected the fragmentation of microtubules by providing restraints to the longitudinal strain. To clarify the point, we investigated how axial elongation of the substrate, which is firmly fixed at the stretcher of the stretch chamber, is correlated to the lateral and longitudinal strain. The result (Supporting Information, Figure S5) reveals that under-axial elongation of the substrate lateral strain was quite small compared to the longitudinal strain. In addition to this, deformation energy of PDMS (or microtubules) is proportional to the square of strain as described in our model. Thus, contribution from the lateral strain was quite small compared to that originating from the longitudinal strain. Therefore, we may conclude that predominant longitudinal strain applied along the microtubule length 1803

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was the major contributor in the mechanical stress induced fragmentation of microtubules. For this reason, although in our model of microtubule fragmentation we initially considered the lateral contraction of the substrate (eq 1), we discarded it later due to its negligible contribution compared to the longitudinal strain and also for the sake of simplicity of the model. Finally, we discuss the softening mechanism of MT by kinesin from the viewpoint of behavior of a charged polymer. In physiological buffer condition (pH ∼ 6.8), MT is negatively charged and like charge repulsion might play an important role in the high flexural rigidity of MT filament. It was reported that persistence length of MT, a measure of flexural rigidity, decreased on neutralizing the charges along MT surface.45 Electrostatic interaction is known to contribute in the binding of MT and kinesin42 and increased kinesin density thereby can neutralize the charges along MT significantly finally changing the rigidity of the polymer, that is, MT.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone/fax: +81-11-7063474. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank Mr. Yasutaka Sasaki for his cooperation in constructing the “Stretch Chamber.” This research was financially supported by Grant-in-Aid for Scientific Research on Innovative Areas (Grant Number 25114501 and 25104501) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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REFERENCES

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CONCLUSION In conclusion, using a newly developed and easy to use stretch chamber system, we demonstrated the ever first fragmentation test of MT and determined the Young’s modulus of MT in an independent way that was found to lie within the range reported in literature. Moreover, we found that kinesin has a softening effect on MT; crowding by kinesin dramatically decreases the Young’s modulus of MT and thus kinesin works as a modulator of MT’s mechanical property. Several studies provided evidence that binding of the motor protein myosin to its associated filamentous protein actin was associated with structural changes that lead to reduced flexural rigidity of the actin filament.46−50 However, no report was available so far that could clearly describe the role of kinesin in altering mechanical property of MT, although some MAPs and MT severing proteins were known to have similar effect.51,52 Our work is the first report that not only quantifies the Young’s modulus of MT employing an independent experimental approach, but also sheds light on the role of kinesin in modulating the mechanical property of MT. Mutated or defective MAPs have been suspected to be linked to diseases, such as Alzheimer’s disease and Parkinson’s disease, by altering property of MTs. Our work might be important in understanding role of different agents in altering stability or flexibility of MTs, mechanical failure of MTs during traumatic brain injury (TBI) or other stretch injury,53,54 and recently reported disruption of MTs by nanoparticles.55 Besides the newly developed experimental setup is expected to find application in assessing inhomogeneity, defects, or mechanically weak points in any biological specimen, which would be important from different perspectives such as nanotechnology or materials science.

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Article

ASSOCIATED CONTENT

S Supporting Information *

Figures of design and images of the stretch chamber, representative fluorescence microscopy images showing the effect of kinesin concentration on MT fragmentation, stress− strain curve for PDMS substrate, figure showing the correlation between applied and measured strain of PDMS, theoretical discussion on the contribution of tensile and shear stress in MT fragmentation, and movie of the motility of fragmented MTs as mentioned in the text. This material is available free of charge via the Internet at http://pubs.acs.org. 1804

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