Nanowire-Imposed Geometrical Control in Studies of ... - IEEE Xplore

IEEE TRANSACTIONS ON NANOBIOSCIENCE, VOL. 14, NO. 3, APRIL 2015

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Nanowire-Imposed Geometrical Control in Studies of Actomyosin Motor Function Mercy Lard, Lasse ten Siethoff, Johanna Generosi, Malin Persson, Heiner Linke, and Alf Månsson*

Abstract—Recently, molecular motor gliding assays with actin and myosin from muscle have been realized on semiconductor nanowires coated with Al O . This opens for unique nanotechnological applications and novel fundamental studies of actomyosin motor function. Here, we provide a comparison of myosin-driven actin filament motility on Al O to both nitrocellulose and trimethylchlorosilane derivatized surfaces. We also show that actomyosin motility on the less than 200 nm wide tips of arrays of Al O -coated nanowires can be used to control the number, and density, of myosin-actin attachment points. Results obtained using nanowire arrays with different inter-wire spacing are consistent with the idea that the actin filament sliding velocity is determined both by the total number and the average density of attached myosin heads along the actin filament. Further, the results are consistent with buckling of long myosin-free segments of the filaments as a factor underlying reduced velocity. On the other hand, the findings do not support a mechanistic role in decreasing velocity, of increased nearest neighbor distance between available myosin heads. Our results open up for more advanced studies that may use nanowire-based structures for fundamental investigations of molecular motors, including the possibility to create a nanowire-templated bottom-up assembly of 3D, muscle-like structures. Index Terms—Actin, aluminum oxide, in vitro motility assay, myosin, oxide-coated nanowire, sarcomere.

I. INTRODUCTION

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USCLE contraction relies on ATP-driven cyclical interactions between myosin II motors and actin filaments. In vitro assays where myosin molecules, or rather their proteolytic motor fragments such as heavy meromyosin (HMM), are adsorbed to surfaces and propel actin filaments in the presence of ATP [1] have given important insights into molecular physiology and pathology [2]–[8] and inspired nanotechnological applications [8]–[18]. In most efforts towards applications using actomyosin, HMM has been adsorbed to chemically and/or topographically defined micro-, to nano-sized tracks [9], [19]–[23] and the actin filaments have been engineered to carry diverse cargoes [24]–[26].

Manuscript received October 15, 2014; revised February 03, 2015, February 26, 2015; accepted March 04, 2015. Date of publication March 24, 2015; date of current version May 29, 2015. Asterisk indicates corresponding author. M. Lard, J. Generosi, and H. Linke are with the Nanometer Structure Consortium (nmC@LU) and Division of Solid State Physics, Lund University, SE-221 00 Lund, Sweden. L. ten Siethoff and M. Persson are with the Department of Chemistry and Biomedical Sciences, Linnaeus University, SE-391 82 Kalmar, Sweden. *A. Månsson is with the Department of Chemistry and Biomedical Sciences, Linnaeus University, SE-391 82 Kalmar, Sweden (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNB.2015.2412036

Previously, no efforts had been made to produce three-dimensional (3D) motility on the nanometer length scale, e.g., between different parallel surface levels, or to enable plane-separated crossings. Such 3D spatial control is of interest for different bio-nanodevices, e.g., in biosensing [13], [21] and biocomputation [27], [28]. Recently [29], we took initial steps in this direction, showing that actomyosin motility is feasible both vertically, along m long Al O -coated nanowires, and horizontally between the 175 nm wide tips of several such nanowires in ordered arrays. Later, we demonstrated truly one-dimensional motility of actin filaments through hollow Al O nanowires, functionalized on their interior surface with HMM [30]. The realization of actomyosin motility on nanowire scaffolds also opens for novel types of fundamental studies. In the long term, it may be feasible, combining protein components and nanometer-scale engineering, to achieve bottom-up reconstruction of the 3D arrangement of the contractile proteins actin and myosin in the myofilament lattice of muscle (Fig. 1(A), (B)). Thus, the ability to use arrays of nanowires for guiding of actin filaments would be an interesting engineering challenge opening for a range of applications both in fundamental studies of actomyosin and for novel motor driven bio-nano devices. An interesting application of motility between nanowire tips, is studies to elucidate the intriguing finding [31] of a lower saturation sliding speed of long actin filaments at low compared to high myosin head densities on a surface. Here, we first compare the actomyosin motility quality on Al O to conventional substrates, such as trimethylchlorosilane (TMCS)-derivatized glass/SiO [32]–[34] and nitrocellulose [35]. We then use different nanowire-array geometries to impose geometrical constraints on motility between the tips of Al O -coated nanowires. Particularly, we investigated the use of densely packed and sparse square arrays of nanowires to test hypotheses about the basis for the reduction in actin filament velocity at low myosin head density [31]. Our results show comparable motility on Al O and conventional substrates but with room for improvement. Then, studies, using square nanowire-arrays with different inter-wire distances provide evidence consistent with views similar to those put forward previously [31], [36] that the actin filament sliding velocity is determined both by the total number and the density of attached myosin heads independent of the detailed spatial distribution of these heads. Our findings are also consistent with the idea [31] that long myosin-free segments of the filaments reduce velocity by filament buckling. We discuss our results in relation to previous studies using other methods to vary the myosin distribution along actin filaments. Finally, we consider the findings in relation to central phenomena in muscle physiology and

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Fig. 1. Three-dimensional order between contractile proteins in the muscle sarcomere in relation to the current experimental system. (A) Schematic illustrations of the actin and myosin filaments in the sarcomere. Actin: green (light gray). Myosin: purple (dark gray). (B) Nanowire array dimensions approaching those of the sarcomere as illustrated by scanning electron micrograph. (C) Nanowires are grown from gold seed (yellow (light gray)) particles (I) by metal organic vapor phase epitaxy (II) and coated with Al O (blue (dark gray)) by atomic layer deposition (III). (D) Nanowire surfaces are placed inverted on top of a glass surface with double-sided tape as spacers. A flow of assay solutions through the flow cell is generated by applying a filter paper to one end. (E) Schematic illustration of fluorescently labeled actin filaments that are propelled by HMM motors adsorbed to the Al O surface, vertically along the nanowires and on top of the nanowires. Note, illustration not to scale. Further, note, that top is defined as in (E) irrespective of actually being downwards with the arrangement in (D).

the possibility for future developments of nanowire enhanced motility assays. II. METHOD A. Nanowire Fabrication Nanowires were fabricated and coated with oxide as previously described [29], [37], [38]. Gallium phosphide (GaP (111)B; Girmet Ltd, Moscow, Russia) substrates were spin coated at 5000 RPM with a polymer layer, either polymethylmetacrylate (PMMA 950A5; Microchem Corporation, Newton, MA, USA) or ZEP (520A5; Zeon Chemicals L.P., Louisville, KY USA) for 60 seconds. The resists were baked on a hot plate at 160 C for 15 min (PMMA) and 180 C for 2 min (ZEP).

Samples were then exposed with electron beam lithography (EBL, Raith 150, Dortmund, Germany) with an accelerating voltage of 20 kV at a single-pixel dose of 0.022 pAs (PMMA) or 0.002–0.01 pAs (ZEP) to produce nanometer-sized openings in the resist [29]. The samples were then submerged in a developer solution to remove the exposed regions. For PMMA, resist development was done in methyl isobutyl ketone and isopropanol (MIBK:IPA; Merck KGaA, Darmstadt, Germany) at a ratio of 1:3 for 1 min, followed by rinsing with IPA for 30 s and blowing dry with nitrogen. For ZEP, resist development samples were placed in o-xylene for 5 min, rinsed in IPA for 30 s and blown dry with nitrogen. The surface was next coated with approximately 20 nm of thermally evaporated gold using physical vapor deposition (AVAC, Teknikbyn Valla, Linköping, Sweden). Unwanted resist and excess gold was lifted off in a remover solution (Microposit Remover 1165, Rohm and Haas Electronic Materials, Coventry, U.K.) at 60 C on a hotplate, leaving gold seed particles 30–80 nm in diameter, on the GaP surface in EBL-defined patterns (Fig. 1(C(i))). The samples were then subjected to metal organic vapor phase epitaxy [39], [40] (MOVPE; Aix 200/4, Aixtron, Herzogenrath, Germany) whereby precursor gases, introduced into the growth chamber, accumulate in the gold particles on the sample's surface, causing nanowires to assemble underneath them [41] (Fig. 1(C(ii))). Initially, the samples were annealed at 470 C for 5 min under a constant flow of a phosphine precursor (PH , molar fraction 1.2 10 ) supplied by H carrier gas at 6 l min . Thereafter, the growth process was initiated when the second precursor, trimethylgallium (TMGa, molar fraction 4.3 10 ), was introduced into the growth chamber, while the substrate is held at a temperature of 470 C. Under these conditions, the growth rate is approximately 1 m min . The lengths of the wires were therefore varied, by changing the growth time (between 1–5 min), depending on the desired length (in the range 1–5 m). Next, GaP substrates with and without nanowires were covered with 60 or 50–100 nm thick Al O layer, respectively, (Fig. 1(C(iii))) using atomic layer deposition (ALD, Savannah 100, Cambridge Nanotech Inc., Cambridge, Massachusetts, USA). During the self-terminating layer-by-layer deposition, alternating 15 ms pulses of water and trimethylaluminum (TMAl) were introduced to the sample chamber, while the substrate was kept at 250 C. The number of cycles of water and TMAl used, (500–1000 cycles) determines the final thickness of the Al O layer (50–100 nm). The final diameter of the nanowires (150–200 nm; average 175 nm) depends on the diameter of the gold particles and the thickness of the Al O layer used for coating. The inter-nanowire distance was either 1000 50 nm or 250 50 nm unless otherwise stated. B. In Vitro Motility Assay Actin and HMM were prepared from rabbit skeletal muscle [26], and flow cells were constructed [29] by connecting two surfaces using double-sided sticky tape as spacers (Fig. 1(D)). The bottom surface was a silanized or un-silanized glass cover-slip, whereas the top surface was an Al O -coated GaP-chip with or without nanowires but otherwise treated as described above. In

LARD et al.: NANOWIRE-IMPOSED GEOMETRICAL CONTROL IN STUDIES OF ACTOMYOSIN MOTOR FUNCTION

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the presence of nanowires, motility could be observed both on the floor between nanowires, vertically along nanowires and on the top of the nanowire array (Fig. 1(E)). We consequently define the “top” as in Fig. 1(E) even though this was physically oriented downward in the motility assay. All motility and wash solutions were based on buffer A containing 1 mM MgCl , 0.1 mM EGTA, 1 mM DTT, and 10 mM MOPS, pH 7.4. The flow cell was incubated according to standard procedures [21], [26], [29], [42] with i) HMM (120 g/ml), ii) BSA, iii) block actin (when required for improved motility), iv) wash buffer (buffer A with 45 mM KCl) with 1 mM MgATP, v) wash buffer, vi) actin filaments fluorescently labeled with Alexa 488® phalloidin, vii) wash buffer, and finally viii) assay solution, i.e., buffer A with 1 mM MgATP, 10 mM DTT, and an ionic strength between 60 and 130 mM (see further [29]). The experiments were performed at room temperature (22–25 C) unless otherwise stated. Filaments were observed using a Nikon Eclipse TE300 inverted fluorescent microscope equipped with a Nikon (100x, 1.4 NA) oil immersion objective, FITC (Ex. 465–495, DM 505, and BA 515–555) filter set, and a Hamamatsu EMCCD camera. C. Image Processing Sliding filament velocity was calculated using algorithms developed in Matlab [29]. The fraction of motile filaments was calculated by manual counting of stationary and motile filaments (see further [29]). Image stacks were made in Image J and statistical analyses and representations were made using Graph Pad Prism 6.0. III. RESULTS AND DISCUSSION A. Motility on Al O Compared to Traditional Surface Substrates Recent studies of actomyosin motility on nanowires [29], [30] used Al O as an HMM-adsorbing substrate instead of trimethylchlorosilane derivatized SiO , previously demonstrated [32], [34], [43] to be optimal for motor function. This was largely for practical reasons: 1. Nanowire coating with Al O rather than SiO was standard in the nanofabrication procedure, e.g., for producing hollow nanowires [30], [38] and 2. pure Al O was found to support satisfactory actomyosin motility [29]. Whereas the motility appeared comparable to that on TMCS-derivatized SiO or glass, the difference in motility quality from these substrates was not analyzed in detail previously. We therefore first investigated the motility on flat Al O substrates without nanowires. As demonstrated in Fig. 2, the velocity of smoothly sliding filaments was similar to that on flat TMCS-derivatized and nitrocellulose-coated glass surfaces. This applied both at ionic strengths of 60 and 130 mM (Fig. 2(A)), in the latter case with methylcellulose (0.6%) in the assay solution (solution denoted aMC130). It also applied at both 29 C and at 22–25 C (Fig. 2(A)–(B); see Fig. 5(A) for one further surface). In contrast to the sliding velocity, the fraction of motile filaments tended to be lower on Al O than on TMCS. Nevertheless, considering the similarity in velocities, we regard the motility on Al O as satisfactory. Contact angle measurements on flat surfaces [29] have suggested that the contact angle on non-treated Al O is higher

Fig. 2. Motility differences between Al O and traditional surface substrates. (A) Sliding velocity and fraction of motile filaments on Al O coated flat surfaces at ionic strength 60 mM (a60; pair of left-most bars) and 130 mM (second left-most pair of bars) compared to data obtained under similar conditions ([MgATP], temperature) on TMCS-derivatized and nitrocellulose coated glass surfaces (not same HMM preparations) in aMC130 solution. All experiments at 29 C. (B) Similar data as in (A), but all data obtained in a60 solution at room temperature (22–25 C), using a given HMM preparation and given experimental occasion for TMCS derivatized SiO . In addition to TMCS derivatized SiO surfaces and flat Al O coated surfaces, velocity and fraction of motile filaments are shown for motility on top of dense nanowire arrays (250 nm inter-wire spacing). Number of filaments as basis for the measurements indicated within parentheses. Error bars represent standard error of the mean. Note, that the small difference in fraction of motile filaments between A and B for Al O coated flat surfaces is not statistically significant. The velocity-differences between (A) and (B) are explained by the temperature difference.

(about 90 degrees) than the range 70–80 degrees believed to give optimal motility on silanized silicon-oxide like surfaces. The optimal motility under the latter conditions has been attributed to appropriate surface adsorption of HMM with little head-surface interactions [12], [32], [44]. It is demonstrated in Fig. 3 that acetone cleaning reduced the contact angle from about 90 degrees to a range that is optimal for silanized SiO . However, attempts to silanize Al O , following mild cleaning procedures so as to not damage the nanowires, resulted in too low surface contact angle for good motility [32] (see Fig. 3). On the other hand, further improved function might be achieved by including acetone treatment in future studies, or alternatively, one may consider switching from Al O to TMCS-derivatized SiO -coated nanowires. However, the following points must then be considered. First, whereas contact angles on flat surfaces

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The focus of the present paper is the nature of the motility on nanowire tips, and what can be concluded about actomyosin physiology, as discussed in the next section. B. Mechanisms Affecting Velocity at Low Myosin Surface Densities—Study Using Al O Coated Nanowires in Ordered Square Arrays

Fig. 3. Contact angle of flat Al O surfaces Black bar: Without cleaning or other treatment subsequent to atomic layer deposition of Al O (5 surfaces 9 measurements for each surface). Light grey bar: After acetone cleaning for 30 min (2 surfaces 9 measurements for each surface). Dark grey bar: After acid cleaning and attempted silanization with TMCS (3 surfaces, 6 measurements for each surface). Error bars represent standard deviation.

In addition to motility between nanowire tips in arrays with short ( 250 nm) inter-wire spacing (Fig. 4), motility was studied on square arrays with inter-nanowire separations of either 250 nm or 1 m. As described in the following, this opens for important fundamental insights into actomyosin interaction mechanisms. A quantitative analysis (Fig. 5(A)) showed that the fraction of motile filaments on the top of an array was higher than on flat Al O surfaces but that the velocity was reduced with increased inter-wire separation. Interestingly, a similar reduction in velocity was observed by lowering the number of actin-interacting HMM molecules by means of reduced HMM incubation concentration [31]. In order to account for the relationship between HMM propelled filament sliding velocity and the number of myosin heads that interact with the actin filament, Uyeda et al. [31] used the relationship (see also Fig. 6): (1)

Fig. 4. Actin filament guiding on top of circular nanowire array. (A) Scanning electron micrograph (SEM) of arrays of nanowires in spiraling configuration connected to a straight array. The array is composed of three nanowires across the width, with 300 nm center-to-center spacing. Inset: Fluorescence micrograph illustrating several filament trajectories (manually tracked) on nanowire array similar to that in the main figure. An Image J routine is used to obtain the fluorescence micrograph by taking average pixel grey scale intensity values from a sequence of images (frame rate 0.4 s/frame) obtained over 1.4 min and projecting them into a single frame. Each filament traveled on top of the array for short time spans, of a few seconds each. Scale bar: 5 m. (B)–(C) Fluorescence micrographs of a single filament (black arrows indicate trailing end) on nanowire array similar to that in (A), tracked at a later time than those on the inset to (A). The filament moved for approximately 3 s before detaching from the array.

may be used to conclude whether a substrate (e.g., Al O with or without acetone cleaning) is appropriate based on its chemical properties it is not self-evident that contact angles measured on flat surfaces directly reflect the surface properties of the nanowire tips. Second, SiO -coating followed by TMCS-derivatization of nanowires for high-quality motility is unlikely to be straightforward, as suggested by our previous experience with different flat SiO -substrates, such as glass cover-slips, Si-SiO wafers and fused silica slides for fluorescence spectroscopy [33]. Thus, further improvements of the assays are likely to require extensive testing of a range of conditions and are therefore outside the scope of the present study. Accordingly, the studies described below were performed with HMM adsorption to Al O coated nanowires without prior acetone cleaning. Satisfactory motility on Al O is not only limited to flat surfaces but can also be observed inside hollow Al O nanowires [30], vertically along Al O coated nanowires grown on a surface and between the tips of such wires [29]. It is interesting to note, that, using motility on the tips of nanowires, some degree of guiding can be achieved on top of nanowire arrays (Fig. 4). However, the guiding is not very good as filaments follow the curved boundary of an array only for a while before detaching.

where is an efficiency factor for force transmission (see further below), is the velocity for infinitely long filaments, is the myosin duty ratio (ratio of force-producing attachment time to ATPase cycle time), is the length of the filament in contact with a myosin coated surface with active head density . Finally, is the width of a band around the filament where myosin heads may reach their attachment sites on actin. In our analyses, we assumed that the myosin duty ratio is 0.05. That this applies approximately both on TMCS and Al O at the temperatures used, follows from the velocities in the range of 5–10 m/s which gives an average on-time for the myosin heads in strongly attached states of ms, assuming a myosin power-stroke distance of 8 nm [45]. With an ATP cycle time of 32 ms [46], this gives a duty ratio of . On TMCS-derivatized surfaces, the HMM density after incubation at 120 g/ml has been estimated [33], [44], [47] to be about 6000 m . Here we assume an active myosin head density, , of 4 000 m on Al O after incubation with HMM at a concentration of 120 g/ml, based on the following considerations: 1) only one of the two heads in a pair is likely to attach to the same actin filament, 2) 70% of the heads are active on TMCS [44], [47], and 3) the sliding speed after HMM incubation with 120 g/ml HMM is similar on flat Al O and TMCS surfaces. We assume a comparable value for the myosin head density on nanowire tips, consistent with comparison between experimental data and theoretical velocity vs. filamentlength plots in Fig. 6 (the latter based on (1)). The theoretical curves predict that the mean velocity would vary with filament length according to the full or dashed line in Fig. 6, if the active myosin head density on the nanowire tips is 10 000 m or 2500 m , respectively. In the experiments, the mean velocity saturates at filament lengths shorter than expected (dashed


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Fig. 6. Sliding velocity on top of dense nanowire array plotted against filament length with bound HMM molecules. Experimental data from two different experiments (filled black circles and open black squares, respectively). In both experiments the average inter-nanowire spacing was 250 nm (centercenter), whereas nanowire diameter was either 170 nm (full circles) or 150 nm (open squares). Grey symbols represent average value 95% confidence interval for data within range of filament lengths indicated by horizontal bars. ,v m/s, f=0.05, d=0.03 m, and Lines represent (1) with m (full line) or m (dashed line). Note that the lines are not fits to the data but have been obtained by inserting data from the literature (see further text).

Fig. 5. Effects on motility of reducing the number of available HMM molecules through increased lateral spacing between 175 nm wide nanowires in square lattice. A. Effects of increased inter-wire distance from 0 m (flat Al O surface) to 1 m on the sliding speed and the fraction of motile actin filaments. Other surface than in Fig. 2. A60 assay solution used. Error bars represent standard error of the mean. B-C. Schematic illustration showing that increased inter-wire distance at maintained HMM incubation concentration of 120 g/ml 1. reduces the total number of HMM molecules available for interaction per m of the actin filament approximately as much as reduction of the HMM incubation concentration indicated, 2. does not change the nearest neighbor distance between HMM molecules in contrast to reduced incubation concentration and 3. increases the myosin-free actin filament length more than reduced HMM incubation concentration.

line) for the density of 2500 m . This is clear from the velocity distribution among individual data points at these filament

lengths as well as from the mean velocity values which are similar to that at saturation (grey symbols in Fig. 6). Particularly, for one of the experiments in Fig. 6, the 95% confidence interval of the mean value, only just reaches the dashed line for myosin head density of 2500 m . These findings are consistent with a myosin head density on the nanowire tips similar to the value of 4000 m for TMCS-derivatized surfaces. For the plots in Fig. 6 we used 30 nm for the band-width d (1), as proposed by Uyeda et al. [31], on the basis of electron microscopic observations and consistent with the flexibility of surface adsorbed HMM molecules on TMCS [44]. Based on the above assumptions, one predicts that an actin filament, which is longer than the nanowire diameter of approximately 0.175 m, will be within reach of myosin heads per nanowire. With a duty ratio of 0.05, this corresponds to one actin-attached head per nanowire tip, on average, at each given point in time. In the experiments of Uyeda et al. [31], where myosin heads were randomly adsorbed to flat surfaces, the velocity at saturating filament length was lower at low than at high myosin head density. This was somewhat unexpected, because at least one myosin head is believed to act on the actin filament all the time under saturating conditions both at low and high myosin density. The result was attributed to poor propagation of force along the actin filament in the case of low myosin density, and was taken into account in the theoretical treatment (1) by introducing the efficiency factor . However, alternative explanations are possible, e.g., that a long distance between the nearest neighbor myosin heads prevents cooperative interactions between closely spaced binding sites on the actin filament [48], [49], or that the surface between the myosin heads produces a drag force that resists filament sliding. It is important to consider these possibilities, since the studies at different myosin densities and filament lengths are useful for mechanistic insights into several aspects of actomyosin function [50], [51].

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NUMBER OF MYOSIN HEADS PER


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TABLE I WITH NANOWIRE ARRAY AND 120 G/ML HMM INCUBATION CONCENTRATION (PRESENT WORK) COMPARED TO FLAT SURFACE WITH DIFFERENT INCUBATION CONCENTRATIONS

Moreover, the condition with large distances between myosin heads exists physiologically at low activation levels in muscle cells when only a fraction of the binding sites on actin is available for myosin interaction (cf. [52]). Motility between nanowire tips allows the total number of myosin heads available for interaction with an actin filament to be reduced without lowering the HMM incubation concentration, i.e., simply by increasing the distance between the wires (Fig. 5(B)–(C)). Whereas both this approach, and lowered HMM incubation concentration, reduce the average distance between subsequent HMM attachment points along an actin filament (see Table I), there are two important differences. First, lowering of the HMM density by increased nanowire separation virtually eliminates any drag forces between the actin filament and the underlying surface (or with BSA) that may result at low HMM densities on a flat surface. Second, increased nanowire separation, as opposed to reduced HMM incubation concentration, does not affect the nearest neighbor distance of HMM molecules close to an attached myosin head. Therefore, if myosin head attachment cooperatively increases the probability of attachment of additional heads at neighboring actin sites [48], this effect would be maintained also at increased inter-nanowire distance. However, the effect would be eliminated by a reduced HMM incubation concentration due to appreciably increased nearest neighbor distance between HMM molecules (Fig. 5(C); Table I).

Clearly, our new approach for reducing the number of HMMactin interactions reduces rather than increases actin-surface interactions and it does not compromise actin-myosin cooperativity. Therefore, if such cooperativity or actin-surface interaction were important in determining the sliding speed, a lower reduction in speed would be expected when reducing the number of available HMM molecules by increased inter-wire distance than when reducing them by lowered HMM incubation concentration. In contrast we found a greater reduction in velocity with the nanowire approach (Table I). Related to this finding, we could not detect any runs with periods of continuous filament sliding at velocity similar to that on flat surfaces at high HMM density. Whereas such periods if brief, may be difficult to detect with our limited temporal and spatial resolution, the fact that we cannot observe them argues against ideas that myosin head attachment is appreciably enhanced at sites close to already attached heads. Our findings argue against inhibition of velocity at low myosin head densities due to: 1) surface-actin interactions and 2) lack of cooperative enhancement of myosin head binding at neighboring sites due to myosin induced structural changes in actin filaments. Instead, the results are consistent with ideas put forward previously that the actin filament sliding velocity is reduced by reduced number of attached cross-bridges [31], [36]. This accounts for the reduction in velocity with reduced filament length at a given surface density of myosin heads.


However, both our study and that of Uyeda et al. [31] suggest that also the average density ( m ) of attached myosin heads along the filament is important. Thus, if only the total number of heads had been important, the velocity on the dense (250 nm inter-wire distance) nanowire array (Figs. 5–6) would have increased towards the velocity on a flat surface when the length of the filament in contact with the nanowires is increased. This is in contrast to our findings (Fig. 6) where velocity reached saturation if less than 1 m of the filament was in contact with the nanowire tip. No increase in average velocity was observed for further increased length. To conclude, our findings are consistent with ideas that both the total number of attached myosin heads and the average density of attached heads along the filament determine velocity. Further, the results are consistent with buckling of long myosin-free segments of the filaments as a possible factor underlying reduced velocity at reduced myosin head density [31]. The idea that buckling is important for reduced velocity is consistent with the expected critical buckling force of actin filaments in the range 0.4–6 pN, on our nanowire arrays (Table I), considerably less than the maximal force (10 pN [53]) developed by an actomyosin cross-bridge. We observed a somewhat larger reduction in velocity for a given increase in the average free filament length (Table I) than Uyeda et al. [31]. Whereas we cannot fully exclude that the difference is within the experimental uncertainty, a remaining real difference may be attributed to differences in experimental conditions in addition to those considered above. First, we used an assay solution without methylcellulose because the effects of methylcellulose on motility between nanowire tips is unpredictable and expected to be very different from the effect of methylcellulose close to a surface, studied in detail by Uyeda et al. [31]. Second, we used room temperature in our experiments with nanowire arrays in order to keep velocities low to facilitate the rather difficult imaging conditions. Whereas we cannot exclude that the presence of methylcellulose in the study of Uyeda et al. [31] may lead to smaller effects on velocity with increased average free filament length it is unlikely that this would be due to effects of methylcellulose on the buckling tendency. First, the viscosity of the medium does not appear in the equation for the critical buckling force. Second, effects that rely on thermal bending motion of HMM propelled actin filaments on a surface were not affected by the presence of methylcellulose [54]. A mechanistic importance of buckling, may seem confusing in relation to the model of Uyeda et al. [31] (see further [55], [56]). At saturating motor number along the filament, the model thus assumes that there is always at least one myosin head attached to the actin filament and the filament therefore moves at maximum speed past each nanowire. If this is the case, there would be no buckling, regardless of the spacing between the nanowire tips. Yet Uyeda et al. [31] introduced the efficiency factor to take into account effects of possible buckling. This can be understood as follows. First, the Uyeda et al. [31] model only considers average actomyosin cross-bridge properties and second, it does not take into account that cross-bridges may execute forces that either promote or resist muscle shortening (filament sliding). In contrast, most models of muscle contraction (e.g., [57], [58]) predict that the maximum velocity of shortening is attained when forces due to cross-bridges that promote and resist shortening

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outbalance [56]. In the present case, such models would instead predict stochastic variation in number of actin-attached heads1 as well as force per attached head [59]. Therefore, the force developed on the actin filament varies stochastically with time at each nanowire and is rarely the same on neighboring wires. Under these conditions, buckling would occur if the compressive forces between the actin-attached heads on neighboring wires are greater than the critical buckling force. The present results are of physiological interest because the large distance between attached heads along the actin filaments is likely to correspond to the situation in the filament lattice of the muscle sarcomere at low level of calcium-activation, e.g., in heart muscle [52], when only few actin sites are available for actomyosin cross-bridge formation. In this connection it is of great interest to note striking conceptual similarities between our approach to reduce myosin head density and previous studies [36] of the effects of calcium activation using flat motility assay surfaces. Thus, prevention of actin activation at some regulatory units along the thin filament, as in the study of Liang et al. [36], increases the average length of filament regions that are inaccessible to myosin binding. This is analogous to the inter-wire distances in our study where no myosin head binding is possible. In further analogy to our work, the accessible nearest neighbor distance is not altered in the study of Liang et al. [36]. This is due to 10–12 neighboring actin monomers in a regulatory unit [60] that are all exposed upon binding of Ca to this regulatory unit. The filament lattice in muscle has similarities to the present system without direct surface interactions. However, in reality the situation is more complex in muscle with a very narrow lattice (Fig. 1(A)), additional thick-thin filament cross-links (e.g., myosin binding protein C [61]); and a range of physical-chemical interaction forces between the actin-containing thin and myosin-containing thick filaments [62]. Nevertheless, interestingly, Liang et al. [36] found a correspondence between their results from studies of calcium-activation (see above) in muscle fibers and in vitro motility assays. One interpretation of this finding in the context of our results is that there may be buckling of the thin filaments also in the ordered filament lattice of muscle at low levels of activation or in other conditions with low number of attached cross-bridges. If this hypothesis can be corroborated it would have important implications for the mechanisms of regulation and force transmission as well as for the use of stiffness measurements to estimate the number of attached cross-bridges (cf. [63]). It is of great relevance that the minimal dimensions of the currently produced nanowire arrays achieve wall-to-wall spacings of less than 100 nm (e.g., Fig. 1(B)). Thus, together with the presently described good actomyosin motility quality, this opens for interesting future developments for studies of actomyosin in more complex arrangements. Particularly, it may be feasible to use nanowires as 3D scaffolds for reproducing key aspects of the three-dimensional order of the muscle sarcomere system in the near future. 1With

n being approximately 20 on each nanowire and the duty ratio , the number of attached heads would vary according to a binomial distribution around a mean value of 1 (20 0.05). Only occasionally the number of attached heads would be the same on all wires.

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ACKNOWLEDGMENT This work was funded by the European Union Seventh Framework Programme (FP7/2007-2011) under grant agreement number 228971 (MONAD) and from the Future and Emerging Technologies (FET) program under grant agreement number 613044 (ABACUS), The Swedish Research Council (Projects # 621-2010-5146 and 621-2010-4527), The Carl Trygger Foundation, the Faculty of Natural Sciences and Engineering and the Faculty of Health and Life Sciences at Linnaeus University, the Nanometer Structure Consortium (nmC@LU), and the Knut and Alice Wallenberg Foundation. REFERENCES [1] S. J. Kron and J. A. Spudich, “Fluorescent actin-filaments move on myosin fixed to a glass-surface,” Proc. Natl. Acad. Sci. USA, vol. 83, no. 17, pp. 6272–6276, Sep. 1986. [2] J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: Piconewton forces and nanometre steps,” Nature, vol. 368, no. 6467, pp. 113–119, Mar. 10, 1994. [3] T. Q. Uyeda, P. D. Abramson, and J. A. Spudich, “The neck region of the myosin motor domain acts as a lever arm to generate movement,” Proc. Natl. Acad. Sci. USA, vol. 93, no. 9, pp. 4459–4464, Apr. 1996. [4] A. Kishino and T. Yanagida, “Force measurements by micromanipulation of a single actin filament by glass needles,” Nature, vol. 334, no. 6177, pp. 74–76, 1988. [5] Y. Y. Toyoshima, S. J. Kron, E. M. McNally, K. R. Niebling, C. Toyoshima, and J. A. Spudich, “Myosin subfragment-1 is sufficient to move actin filaments in vitro,” Nature, vol. 328, no. 6130, pp. 536–539, 1987. [6] Y. Y. Toyoshima, C. Toyoshima, and J. A. Spudich, “Bidirectional movement of actin filaments along tracks of myosin heads,” Nature, vol. 341, no. 6238, pp. 154–156, 1989. [7] R. F. Sommese, J. Sung, S. Nag, S. Sutton, J. C. Deacon, E. Choe, L. A. Leinwand, K. Ruppel, and J. A. Spudich, “Molecular consequences of the R453C hypertrophic cardiomyopathy mutation on human betacardiac myosin motor function,” Proc. Natl. Acad. Sci. USA, vol. 110, no. 31, pp. 12607–12612, Jul. 2013. [8] N. M. Brunet, G. Mihajlovic, K. Aledealat, F. Wang, P. Xiong, S. von Molnar, and P. B. Chase, “Micromechanical thermal assays of Ca2 -regulated thin-filament function and modulation by hypertrophic cardiomyopathy mutants of human cardiac troponin,” J. Biomed. Biotechnol., vol. 2012, p. 657523, 2012. [9] H. Suzuki, A. Yamada, K. Oiwa, H. Nakayama, and S. Mashiko, “Control of actin moving trajectory by patterned poly(methylmethacrylate) tracks,” Biophys. J., vol. 72, no. 5, pp. 1997–2001, May 1997. [10] P. Manandhar, L. Huang, J. R. Grubich, J. W. Hutchinson, P. B. Chase, and S. H. Hong, “Highly selective directed assembly of functional actomyosin on Au surfaces,” Langmuir, vol. 21, no. 8, pp. 3213–3216, Apr. 12, 2005. [11] M. G. L. van den Heuvel and C. Dekker, “Motor proteins at work for nanotechnology,” Science, vol. 317, no. 5836, pp. 333–336, Jul. 2007. [12] A. Månsson, “Translational actomyosin research: Fundamental insights and applications hand in hand,” J. Muscle Res. Cell Motil., vol. 33, no. 3–4, pp. 219–233, Aug. 2012. [13] T. Korten, A. Mansson, and S. Diez, “Towards the application of cytoskeletal motor proteins in molecular detection and diagnostic devices,” Curr. Opin. Biotechnol., vol. 21, no. 4, pp. 477–488, Aug. 2010. [14] A. Agarwal and H. Hess, “Biomolecular motors at the intersection of nanotechnology and polymer science,” Prog. Polym. Sci., vol. 35, no. 1–2, pp. 252–277, Jan. 2010. [15] A. Goel and V. Vogel, “Harnessing biological motors to engineer systems for nanoscale transport and assembly,” Nat. Nanotechnol., vol. 3, no. 8, pp. 465–475, Aug. 2008. [16] D. J. G. Bakewell and D. V. Nicolau, “Protein linear molecular motorpowered nanodevices,” Aust. J. Chem., vol. 60, pp. 314–332, Aug. 2007. [17] G. D. Bachand, N. F. Bouxsein, V. VanDelinder, and M. Bachand, “Biomolecular motors in nanoscale materials, devices, and systems,” Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol., vol. 6, no. 2, pp. 163–177, 2014.

[18] G. Mihajlovic, N. M. Brunet, J. Trbovic, P. Xiong, S. von Molnar, and P. B. Chase, “All-electrical switching and control mechanism for actomyosin-powered nanoactuators,” Appl. Phys. Lett., vol. 85, no. 6, pp. 1060–1062, Aug. 9, 2004. [19] R. Bunk, M. Sundberg, I. A. Nicholls, P. Omling, S. Tågerud, A. Månsson, and L. Montelius, “Guiding motor-propelled molecules with nanoscale precision through silanized bi-channel structures,” Nanotechnology, vol. 16, pp. 710–717, Jun. 2005. [20] M. Sundberg, R. Bunk, N. Albet-Torres, A. Kvennefors, F. Persson, L. Montelius, I. A. Nicholls, S. Ghatnekar-Nilsson, P. Omling, S. Tagerud, and A. Mansson, “Actin filament guidance on a chip: Toward high-throughput assays and lab-on-a-chip applications,” Langmuir, vol. 22, no. 17, pp. 7286–7295, Aug. 15, 2006. [21] M. Lard, L. ten Siethoff, S. Kumar, M. Persson, G. te Kronnie, H. Linke, and A. Månsson, “Ultrafast molecular motor driven nanoseparation and biosensing,” Biosens. Bioelectron., vol. 48, pp. 145–152, Apr. 2013. [22] D. V. Nicolau, H. Suzuki, S. Mashiko, T. Taguchi, and S. Yoshikawa, “Actin motion on microlithographically functionalized myosin surfaces and tracks,” Biophys. J., vol. 77, no. 2, pp. 1126–1134, Nov. 1999. [23] K. E. Byun, M. G. Kim, P. B. Chase, and S. H. Hong, “Selective assembly and guiding of actomyosin using carbon nanotube network monolayer patterns,” Langmuir, vol. 23, no. 19, pp. 9535–9539, Sept. 11, 2007. [24] M. Persson, M. Gullberg, C. Tolf, A. M. Lindberg, A. Mansson, and A. Kocer, “Transportation of nanoscale cargoes by Myosin propelled actin filaments,” PloS One, vol. 8, no. 2, p. e55931, 2013. [25] S. Kumar, L. ten Siethoff, and A. Månsson, “Magnetic separation alleviates deleterious effects of blood serum on actomyosin based diagnostics device.,” J. Nanobiotechnol., vol. 11, p. 14, May 2013. [26] S. Kumar, L. ten Siethoff, M. Persson, M. Lard, G. te Kronnie, H. Linke, and A. Månsson, “Antibodies covalently immobilized on actin filaments for fast myosin driven analyte transport,” PLoS One, vol. 7, no. 10, p. e46298, Oct. 2012. [27] D. V. Nicolau, D. V. Nicolau, G. Solana, K. L. Hanson, L. Filipponi, L. S. Wang, and A. P. Lee, “Molecular motors-based micro- and nanobiocomputation devices,” Microelectron. Eng., vol. 83, no. 4–9, pp. 1582–1588, Apr.–Sep. 2006. [28] D. V. J. Nicolau, M. Lard, T. Korten, F. van Delft, M. Persson, E. Bengtsson, A. Månsson, S. Diez, H. Linke, and D. V. Nicolau, “Massively-parallel computation with molecular motor-propelled agents in nanofabricated networks,” 2014. [29] L. Ten Siethoff, M. Lard, J. Generosi, H. S. Andersson, H. Linke, and A. Mansson, “Molecular motor propelled filaments reveal lightguiding in nanowire arrays for enhanced biosensing,” Nano Lett., vol. 14, no. 2, pp. 737–742, Feb. 2014. [30] M. Lard, L. Ten Siethoff, J. Generosi, A. Månsson, and H. Linke, “Molecular motor transport through hollow nanowires,” Nano Lett., vol. 14, no. 6, pp. 3041–3046, Jun. 2014. [31] T. Q. Uyeda, S. J. Kron, and J. A. Spudich, “Myosin step size. Estimation from slow sliding movement of actin over low densities of heavy meromyosin,” J. Mol. Biol., vol. 214, no. 3, pp. 699–710, 1990. [32] N. Albet-Torres, J. O'Mahony, C. Charlton, M. Balaz, P. Lisboa, T. Aastrup, A. Mansson, and I. A. Nicholls, “Mode of heavy meromyosin adsorption and motor function correlated with surface hydrophobicity and charge,” Langmuir, vol. 23, no. 22, pp. 11147–11156, Oct. 23, 2007. [33] M. Sundberg, M. Balaz, R. Bunk, J. P. Rosengren-Holmberg, L. Montelius, I. A. Nicholls, P. Omling, S. Tagerud, and A. Mansson, “Selective spatial localization of actomyosin motor function by chemical surface patterning,” Langmuir, vol. 22, no. 17, pp. 7302–7312, Aug. 15, 2006. [34] M. Sundberg, J. P. Rosengren, R. Bunk, J. Lindahl, I. A. Nicholls, S. Tagerud, P. Omling, L. Montelius, and A. Mansson, “Silanized surfaces for in vitro studies of actomyosin function and nanotechnology applications,” Anal. Biochem., vol. 323, no. 1, pp. 127–138, Dec. 2003. [35] S. J. Kron, Y. Y. Toyoshima, T. Q. Uyeda, and J. A. Spudich, “Assays for actin sliding movement over myosin-coated surfaces,” Methods Enzymol., vol. 196, pp. 399–416, 1991. [36] B. Liang, Y. Chen, C. K. Wang, Z. Luo, M. Regnier, A. M. Gordon, and P. B. Chase, “Ca2 regulation of rabbit skeletal muscle thin filament sliding: Role of cross-bridge number,” Biophys. J., vol. 85, no. 3, pp. 1775–1786, Sep. 2003. [37] D. B. Suyatin, W. Hallstram, L. Samuelson, L. Montelius, C. N. Prinz, and M. Kanje, “Gallium phosphide nanowire arrays and their possible application in cellular force investigations,” J. Vac. Sci. Technol. B, vol. 27, no. 6, pp. 3092–3094, Nov. 2009.


[38] H. Persson, J. P. Beech, L. Samuelson, S. Oredsson, C. N. Prinz, and J. Tegenfeldt, “Vertical oxide nanotubes connected by subsurface microchannels,” Nano Res., vol. 5, pp. 190–198, Mar. 2012. [39] K. A. Dick, P. Caroff, J. Bolinsson, M. E. Messing, J. Johansson, K. Deppert, L. R. Wallenberg, and L. Samuelson, “Control of III-V nanowire crystal structure by growth parameter tuning,” Semiconduct. Sci. Technol., vol. 25, no. 2, Feb. 2010. [40] W. Seifert, M. Borgstrom, K. Deppert, K. A. Dick, J. Johansson, M. W. Larsson, T. Martensson, N. Skold, C. P. T. Svensson, B. A. Wacaser, L. R. Wallenberg, and L. Samuelson, “Growth of one-dimensional nanostructures in MOVPE,” J. Crystal Growth, vol. 272, no. 1–4, pp. 211–220, Dec. 10, 2004. [41] B. A. Wacaser, K. A. Dick, J. Johansson, M. T. Borgstrom, K. Deppert, and L. Samuelson, “Preferential interface nucleation: An expansion of the VLS growth mechanism for nanowires,” Adv. Mat., vol. 21, no. 2, pp. 153–165, Jan. 12, 2009. [42] M. Lard, L. T. Siethoff, A. Mansson, and H. Linke, “Tracking actomyosin at fluorescence check points,” Sci. Rep., vol. 3, p. 1092, Jan. 2013. [43] A. Månsson, M. Sundberg, R. Bunk, M. Balaz, I. A. Nicholls, P. Omling, J. O. Tegenfeldt, S. Tågerud, and L. Montelius, “Actin-based molecular motors for cargo transportation in nanotechnology—Potentials and challenges,” IEEE Trans. Adv. Packag., vol. 28, no. 4, pp. 547–555, Nov. 2005. [44] M. Persson, N. Albet-Torres, M. Sundberg, L. Ionov, S. Diez, F. Höök, A. Månsson, and M. Balaz, “Heavy meromyosin molecules extend more than 50 nm above adsorbing electronegative surfaces,” Langmuir, vol. 26, no. 12, pp. 9927–9936, 2010. [45] M. Kaya and H. Higuchi, “Nonlinear elasticity and an 8-nm working stroke of single myosin molecules in myofilaments,” Science, vol. 329, no. 5992, pp. 686–689, Aug. 6, 2010. [46] T. Q. Uyeda, H. M. Warrick, S. J. Kron, and J. A. Spudich, “Quantized velocities at low myosin densities in an in vitro motility assay,” Nature, vol. 352, no. 6333, pp. 307–311, 1991. [47] M. Balaz, M. Sundberg, M. Persson, J. Kvassman, and A. Månsson, “Effects of surface adsorption on catalytic activity of heavy meromyosin studied using fluorescent ATP analogue,” Biochemistry, vol. 46, no. 24, pp. 7233–7251, 2007. [48] K. Tokuraku, R. Kurogi, R. Toya, and T. Q. Uyeda, “Novel mode of cooperative binding between myosin and Mg2 -actin filaments in the presence of low concentrations of ATP,” J. Mol. Biol., vol. 386, no. 1, pp. 149–162, Feb. 2009. [49] E. Prochniewicz, T. F. Walseth, and D. D. Thomas, “Structural dynamics of actin during active interaction with myosin: Different effects of weakly and strongly bound myosin heads,” Biochemistry, vol. 43, no. 33, pp. 10642–10652, Aug. 24, 2004. [50] M. J. Greenberg, K. Kazmierczak, D. Szczesna-Cordary, and J. R. Moore, “Cardiomyopathy-linked myosin regulatory light chain mutations disrupt myosin strain-dependent biochemistry,” Proc. Natl. Acad. Sci. USA, vol. 107, no. 40, pp. 17403–17408, Oct. 2010.

297

[51] P. VanBuren, K. A. Palmiter, and D. M. Warshaw, “Tropomyosin directly modulates actomyosin mechanical performance at the level of a single actin filament,” Proc. Natl. Acad. Sci. USA, vol. 96, no. 22, pp. 12488–12493, Oct. 1999. [52] J. A. Spudich, “Hypertrophic and dilated cardiomyopathy: Four decades of basic research on muscle lead to potential therapeutic approaches to these devastating genetic diseases,” Biophys. J., vol. 106, no. 6, pp. 1236–1249, Mar. 2014. [53] Y. Takagi, E. E. Homsher, Y. E. Goldman, and H. Shuman, “Force generation in single conventional actomyosin complexes under high dynamic load,” Biophys. J., vol. 90, no. 4, pp. 1295–1307, Feb. 2006. [54] P. G. Vikhorev, N. N. Vikhoreva, and A. Mansson, “Bending flexibility of actin filaments during motor-induced sliding,” Biophys. J., vol. 95, no. 12, pp. 5809–5819, Dec. 15, 2008. [55] S. Walcott, D. M. Warshaw, and E. P. Debold, “Mechanical coupling between myosin molecules causes differences between ensemble and single-molecule measurements,” Biophys. J., vol. 103, pp. 501–510, 2012. [56] A. Månsson, D. E. Rassier, and G. Tsiavaliaris, “Poorly understood aspects of striated muscle contraction,” Bio. Med. Res. Int., 2015, to be published. [57] A. F. Huxley, “Muscle structure and theories of contraction,” Prog. Biophys. Biophys. Chem., vol. 7, pp. 255–318, 1957. [58] A. Mansson, “Actomyosin-ADP states, inter-head cooperativity and the force-velocity relation of skeletal muscle,” Biophys. J., vol. 98, pp. 1237–1246, 2010. [59] E. Pate and R. Cooke, “Simulation of stochastic processes in motile crossbridge systems,” J. Muscle. Res. Cell. Motil., vol. 12, no. 4, pp. 376–393, 1991. [60] M. Regnier, A. J. Rivera, C. K. Wang, M. A. Bates, P. B. Chase, and A. M. Gordon, “Thin filament near-neighbour regulatory unit interactions affect rabbit skeletal muscle steady-state force-Ca(2 ) relations,” J. Physiol., vol. 540, pt. 2, pp. 485–97, Apr. 15, 2002. [61] R. Knöll, “Myosin binding protein C: Implications for signal-transduction,” J. Muscle Res. Cell Motil., vol. 33, no. 1, pp. 31–42, May 2012. [62] B. M. Millman, “The filament lattice of striated muscle,” Physiol. Rev., vol. 78, no. 2, pp. 359–391, Apr. 1998. [63] G. Piazzesi, M. Reconditi, M. Linari, L. Lucii, P. Bianco, E. Brunello, V. Decostre, A. Stewart, D. B. Gore, T. C. Irving, M. Irving, and V. Lombardi, “Skeletal muscle performance determined by modulation of number of Myosin motors rather than motor force or stroke size,” Cell, vol. 131, no. 4, pp. 784–795, Nov. 16, 2007. [64] M. Persson, E. Bengtsson, L. ten Siethoff, and A. Mansson, “Nonlinear cross-bridge elasticity and post-power-stroke events in fast skeletal muscle actomyosin,” Biophys. J., vol. 105, no. 8, pp. 1871–1881, Oct. 2013. [65] J. Howard, Mechanics of Motor Proteins and the Cytoskeleton. Sunderland, MA, USA: Sinauer Assoc., 2001.