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Diffusion Dynamics of Motor-Driven Transport: Gradient Production and Self-Organization of Surfaces Petr G. Vikhorev,† Natalia N. Vikhoreva,† Mark Sundberg,† Martina Balaz,† Nuria Albet-Torres,† Richard Bunk,‡ Anders Kvennefors,‡ Kenneth Liljesson,† Ian A. Nicholls,† Leif Nilsson,§ Pa¨r Omling,‡ Sven Tågerud,† Lars Montelius,‡ and Alf Månsson*,† School of Pure and Applied Natural Sciences, UniVersity of Kalmar, SE-391 82 Kalmar, Sweden, DiVision of Solid State Physics and The Nanometer Consortium, UniVersity of Lund, Box 118, SE-221 00 Lund, Sweden, and Ma¨tfakta AB, Kalmar, Sweden ReceiVed May 26, 2008. ReVised Manuscript ReceiVed September 19, 2008 The interaction between cytoskeletal filaments (e.g., actin filaments) and molecular motors (e.g., myosin) is the basis for many aspects of cell motility and organization of the cell interior. In the in vitro motility assay (IVMA), cytoskeletal filaments are observed while being propelled by molecular motors adsorbed to artificial surfaces (e.g., in studies of motor function). Here we integrate ideas that cytoskeletal filaments may be used as nanoscale templates in nanopatterning with a novel approach for the production of surface gradients of biomolecules and nanoscale topographical features. The production of such gradients is challenging but of increasing interest (e.g., in cell biology). First, we show that myosin-induced actin filament sliding in the IVMA can be approximately described as persistent random motion with a diffusion coefficient (D) given by a relationship analogous to the Einstein equation (D ) kT/γ). In this relationship, the thermal energy (kT) and the drag coefficient (γ) are substituted by a parameter related to the free-energy transduction by actomyosin and the actomyosin dissociation rate constant, respectively. We then demonstrate how the persistent random motion of actin filaments can be exploited in conceptually novel methods for the production of actin filament density gradients of predictable shapes. Because of regularly spaced binding sites (e.g., lysines and cysteines) the actin filaments act as suitable nanoscale scaffolds for other biomolecules (tested for fibronectin) or nanoparticles. This forms the basis for secondary chemical and topographical gradients with implications for cell biological studies and biosensing.
Introduction The basis for cell motility and organization of the cell interior is the interaction of molecular motors (e.g., myosin, kinesin, and dynein) with cytoskeletal filaments (actin filaments and microtubules).1 One highly specialized form of cell motility is muscle contraction that is caused by force-producing interactions between myosin II motors (henceforth referred to as myosin) and actin filaments.2,3 A method that has been widely used4-11 in the study of this interaction is the in vitro motility assay (IVMA)12,13 where * Corresponding author. Phone: +46-480-446243. Fax: +46-480-446262. E-mail:
[email protected]. † University of Kalmar. ‡ University of Lund. § Ma¨tfakta AB. (1) Howard, J. Mechanics of Motor Proteins and the Cytoskeleton; Sinauer Associates: Sunderland, MA, 2001. (2) Geeves, M. A.; Holmes, K. C. AdV. Protein Chem. 2005, 71, 161–193. (3) Huxley, A. F. Prog. Biophys. Biophys. Chem. 1957, 7, 255–318. (4) Toyoshima, Y. Y.; Kron, S. J.; McNally, E. M.; Niebling, K. R.; Toyoshima, C.; Spudich, J. A. Nature 1987, 328, 536–539. (5) Harada, Y.; Noguchi, A.; Kishino, A.; Yanagida, T. Nature 1987, 326, 805–808. (6) Harada, Y.; Sakurada, K.; Aoki, T.; Thomas, D. D.; Yanagida, T. J. Mol. Biol. 1990, 216, 49–68. (7) Fraser, I. D.; Marston, S. B. J. Biol. Chem. 1995, 270, 7836–7841. (8) Tsiavaliaris, G.; Fujita-Becker, S.; Manstein, D. J. Nature 2004, 427, 558– 561. (9) Suzuki, H.; Yamada, A.; Oiwa, K.; Nakayama, H.; Mashiko, S. Biophys. J. 1997, 72, 1997–2001. (10) Bunk, R.; Klinth, J.; Montelius, L.; Nicholls, I. A.; Omling, P.; Tagerud, S.; Månsson, A. Biochem. Biophys. Res. Commun. 2003, 301, 783–788. (11) Homsher, E.; Wang, F.; Sellers, J. R. Am. J. Physiol. 1992, 262, C714– C723. (12) Kron, S. J.; Toyoshima, Y. Y.; Uyeda, T. Q.; Spudich, J. A. Methods Enzymol. 1991, 196, 399–416. (13) Kron, S. J.; Spudich, J. A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 6272– 6276.
myosin motors or rather myosin motor fragments (e.g., heavy meromyosin (HMM)) are adsorbed to artificial surface substrates. Fluorescence-labeled actin filaments are then observed while being propelled by HMM (e.g., in studies of motor function). In most in vitro motility assay experiments, the sliding actin filaments appear to change direction randomly as they are propelled by HMM molecules on the surface. Modeling has been applied for detailed analysis of the sliding paths under these conditions both at standard (low)14,15 and at very high16 filament densities. Such analysis provides information that may be of fundamental relevance to the understanding of motor function.14 However, such studies are also of relevance for the optimization of nanobiotechnological applications of the motors, involving spatial control on micro- and nanopatterned surfaces17-20 and surface self-organization.21 Earlier modeling work14-16 has assumed ideal isotropic surfaces without (accidental) chemical or topographical microor nanopatterns (known to guide the sliding directions18,22,23). Importantly, however, such patterns may not be completely absent (14) Duke, T.; Holy, T. E.; Leibler, S. Phys. ReV. Lett. 1995, 74, 330–333. (15) Nicolau, D. V.; Nicolau, D. V. Curr. Appl. Phys. 2004, 4, 316–319. (16) Kraikivski, P.; Lipowsky, R.; Kierfeld, J. Phys. ReV. Lett. 2006, 96, 258103. (17) Clemmens, J.; Hess, H.; Howard, J.; Vogel, V. Langmuir 2003, 19, 1738– 1744. (18) Sundberg, M.; Bunk, R.; Albet-Torres, N.; Kvennefors, A.; Persson, F.; Montelius, L.; Nicholls, I. A.; Ghatnekar-Nilsson, S.; Omling, P.; Tagerud, S.; Mansson, A. Langmuir 2006, 22, 7286–7295. (19) Hiratsuka, Y.; Tada, T.; Oiwa, K.; Kanayama, T.; Uyeda, T. Q. Biophys. J. 2001, 81, 1555–1561. (20) Clemmens, J.; Hess, H.; Lipscomb, R.; Hanein, Y.; Bohringer, K. F.; Matzke, C. M.; Bachand, G. D.; Bunker, B. C.; Vogel, V. Langmuir 2003, 19, 10967–10974. (21) Hess, H.; Clemmens, J.; Brunner, C.; Doot, R.; Luna, S.; Ernst, K. H.; Vogel, V. Nano Lett 2005, 5, 629–633.
10.1021/la8016112 CCC: $40.75 2008 American Chemical Society Published on Web 11/07/2008
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in a real experimental situation using standard surface substrates.24 Moreover, in real experiments, sliding directions may be modified by the presence of defect25 and clustered or oriented motors.26,27 Additionally, at very high motor and filament densities, collective ordering effects16 may emerge even in the absence of surface patterns or defect motors. Considering these complexities, it would be of interest to elucidate whether it is possible to achieve approximately isotropic conditions for HMM-propelled sliding of actin filaments resulting in persistent random motion14 of the filaments. Under such conditions, information about motor and filament properties14 should be deducible from the collective behavior of the sliding filaments. It should also be possible to determine a unique diffusion coefficient and to achieve selforganization of surfaces, such as surface gradients of biomolecules of predictable shape with the potential for interactive control. Surface gradients of biomolecules are of interest in various applications28 (e.g., in tissue engineering,29 cell biological studies,30,31 and biosensing32). However, the production of surface gradients of complex shapes is challenging, particularly on the micrometer length scale, normally requiring advanced techniques and expensive equipment.33 One interesting possibility would therefore be to create surface gradient patterns consisting of biological-motor-propelled “nanowires” (e.g., microtubules or actin filaments). The latter may act as scaffolds for the subsequent binding of other biomolecules,34,35 quantum dots,36 or gold nanoparticles.37 Because of their assembly from nanoscale monomers, actin filaments and microtubules are naturally prefunctionalized with regularly spaced binding sites (cysteines, lysines, etc.; 0.1 mm).39,54,55 For the production of practically useful gradients, it is also important with high actin filament densities (i.e., conditions with appreciable risk for the appearance of ordering effects (this article and ref 16). The production of such gradients thus imposes more severe restrictions than in the studies in Figure 3 with low filament densities. To meet these requirements, we took a number of steps: 1. TMCS-derivatized surfaces were used because they have low surface roughness and a high degree of homogeneity42 and support high-quality motility more reproducibly23,42,56 than do nitrocellulose surfaces. 2. Creatine-kinase/creatine phosphate was used in the assay solution to avoid some heads being locked to the surface by a local increase in the ADP/ATP ratio. 3. Blocking actin was added at concentrations e1 µM to minimize ordering effects due to actin filament crowding. 4. The surfaces were shaken during incubation with blocking actin to reduce the effects of flow-induced ordering during binding of the filaments to HMM. In addition to suitable conditions for isotropic filament sliding, another precondition for successful gradient production is a welldefined initial distribution of actin filaments. As illustrated below, this may be achieved using suitably micropatterned surfaces. However, symmetrical actin filament distributions of a width of less than 100 µm could also be obtained through local deposition using a microcapillary. Initial deposition by a similar method (54) Nitta, T.; Hess, H. Nano Lett 2005, 5, 1337–1342. (55) van den Heuvel, M. G.; Bolhuis, S.; Dekker, C. Nano Lett 2007, 7, 3138– 3144. (56) Albet-Torres, N.; O’Mahony, J.; Charlton, C.; Balaz, M.; Lisboa, P.; Aastrup, T.; Månsson, A.; Nicholls, I. A. Langmuir 2007, 23, 11147–11156.
should be possible for the production of a range of gradient shapes. If a short incubation time was employed, then the filaments diffused only a very short distance (∝(6Dt)) before they were retracted into the capillary or captured by high-affinity binding to HMM. Prerequisites for this approach to produce a welldefined, highly localized intial actin filament distribution are the small diffusion coefficient of the actin filaments in solution (D ≈ 1 µm2) and the high actin affinity of HMM. In addition to providing a useful basis for gradient production, as described further below, the micropipette-based local addition of actin filaments may also serve other purposes. For instance, it would allow the highly localized deposition of actin filaments loaded with particular recognition molecules such as antibodies. This could be used to add such motile actin-antibody detection conjugates to actin filament loading zones (refs 18 and 43) on appropriately nanopatterned surfaces. Such local deposition of actin filaments on loading zones is a major component of a recently patented57 miniaturized separation device based on the combination of molecular motors and topographically nanostructured43 surfaces. The production of gradients by motor-driven diffusion is illustrated in Figure 4. Here the initial distribution of actin filaments was produced by local addition via a capillary micropipette as described above (Figures 1 and 2). It can be seen that motor-driven diffusion from such an initial distribution resulted in a radial actin filament gradient of approximately Gaussian shape. Importantly, neither the rinsing step associated with addition nor that associated with the removal of ATP destroyed the developed distribution of actin filaments (data not shown). Because of the regular clustering of biomolecular binding sites along the actin filaments, the gradient in Figure 4 is not continuous on the micrometer level. Rather, what is formed is a unique type of density gradient of biological nanowires (the (57) Månsson, A.; Tågerud, S.; Sundberg, M.; Rosengren, J. P.; Montelius, L.; Omling, P.; Bunk, R.; Nicholls, I. A.; Balaz, M. Swedish Patent SE 528 700 C2 (priority, 04 September, 2004), 2007.
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Figure 5. Binding of fibronectin to actin filaments. (a) Alexa-488 Ph-labeled actin filaments added by a micropipette, followed by the addition of assay solution. The initial actin density profile had roughly ciruclar symmetry. Images were obtained after the removal of ATP, 3 min after first addition of ATP. (b) Fibronectin linked to the actin filaments in part a via streptavidin. Fibronectin visualized through labeling with rhodamine B isothiocyanate (RhB). Sum of three subsequent images obtained within 2 s. (c) Intensity profiles (average of five line profiles) along horizontal lines in a and b. Black symbols represent Alexa-488 Ph-labeled actin filaments (a), and gray symbols represent RhB-labeled fibronectin (b). The lines represent fittings of Gaussian functions to the intensity profiles that have been background subtracted and normalized. (d, e) Immobilization of RhB-labeled fibronectin molecules on individual Alexa-488 Ph-labeled actin filaments observed at high magnification. Note the selective binding of fibronectin (e) to the biotinylated and Alexa-488 Ph-labeled actin filaments (d). Actin and fibronectin fluorescence observed using FITC and TRITC filter sets, respectively.
actin filaments) of well-defined topography and regularly spaced biomolecular binding sites. The density gradient of actin filament nanowires may form the basis for the subsequent production of similar nanopatterns of any biomolecule of interest if the actin filaments are provided with appropriate “molecular handles”. A similar procedure may be used for the creation of topographical nanopatterns of larger height and roughness, (e.g., by binding appropriate nanoparticles along the actin filaments36,37). The production of nanopatterns of biomolecules with the actin filaments as templates is exemplified in Figure 5a-c. Here, a fibronectin distribution of similar shape to the actin filament distribution was produced after stopping the actin filament sliding by removing ATP and incubating the entire surface with streptavidin and then fibronectin. The final outcome was the binding of biotinylated fibronectin molecules via streptavidin to the biotinylated filaments (Figure 5d,e) with negligible nonspecific adsorption outside the actin filament scaffolds. Separate experiments showed that the biotinylation did not alter the sliding velocity (4.13 ( 0.10 µm s-1; n ) 60 filament paths) compared to that (4.13 ( 0.06 µm s-1; n ) 128) for nonbiotinylated filaments. Whereas we did not test the functionality of the fibronectin molecules, previous studies58 have shown that the attachment of fibronectin to artificial surface substrates via streptavidin-biotin links preserves the biological function. Control of the evolution of the actin filament distribution (Figures 4 and 5) is facilitated by the fact that biotinylated actin filaments can be simultaneously fluorescence-labeled, allowing monitoring in real time. Furthermore, if desired, the motor-driven diffusion can be repeatedly switched off and on by removal and addition of ATP, respectively. The diffusion coefficients from Gaussian fits in Figure 4 were 5-8 µm2 s-1 compared to 15 µm2 s-1 expected from the relationship D ) Vf LP (for actin filaments at low density). Different factors may contribute to this discrepancy (Supporting Information). However, a lower fraction of motile filaments, a lower average sliding velocity (associated with a locally increased
[ADP]/[ATP] ratio) at high actin filament densities and phototoxicity seems to be important. Furthermore, a tendency toward local ordering of filament sliding16 may also contribute and could also account for a slightly different diffusion coefficient in different directions. Importantly, however, Figure 4 suggests that an approximate prediction of the gradient shape is possible using a diffusion equation with an isotropic diffusion coefficient calculated from D ) VfLP. In particular, the maximum possible width is readily foreseen. To limit the effects of complicating factors, it may be advantageous to eliminate the use of unlabeled blocking actin to minimize the depletion of ATP and the collective ordering effects seen at high filament densities. Similarly, lower HMM densities may be preferable. For improved reproducibility, it may also be important with further standardization of the surfacederivatization procedure. Thus, in spite of exhibiting more reproducible behavior than nitrocellulose, the contact angle of the TMCS surfaces that are cleaned, derivatized, and stored under our present standard conditions can exhibit variability in the range of 65-85°. This variability may be related to the use of glass surface substrates of slightly varying properties, combined with cleaning, short-term storage, and silanization without a controlled atmosphere (e.g., by using a glovebox, Supporting Information). The variability in contact angle would be expected to correspond directly to the variability in motor density and function23,56 and therefore in the tendency for collective ordering effects (as exemplified in Figure 6). However, the latter effect, observed under some conditions, may also be of interest to exploit in the production of very dense and highly localized gradients of actin filament binding sites. This would require that similar shapes are readily reproduced in each experiment, possibly through initial ordering of the filaments by flow (as in Figure 6) to initiate the collective sliding behavior. The production of gradients in the extracellular matrix protein fibronectin was used here mainly for demonstration purposes. However, the application of the method to fibronectin is of relevance in itself (e.g., for studies of cell adhesion and migration31,59).
(58) Anamelechi, C. C.; Clermont, E. E.; Brown, M. A.; Truskey, G. A.; Reichert, W. M. Langmuir 2007, 23, 12583–12588.
(59) Smith, J. T.; Tomfohr, J. K.; Wells, M. C.; Beebe, T. P.; Kepler, T. B.; Reichert, W. M. Langmuir 2004, 20, 8279–8286.
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Figure 6. Collective ordering effects in the in vitro motility assay at high actin filament density. A large fraction of the fluorescent actin filaments were organized by HMM-induced sliding along stripes as indicated by high fluorescence intensity. The direction of these stripes is consistent with the direction of flow of the incubation solutions, including blocking actin and fluorescent actin filaments. This particular flow cell was not shaken during incubation.
Naturally, fibronectin gradients could also be produced by first adding streptavidin via a microcapillary (without the actin gradient) in the same way that the actin filaments were added. After streptavidin immobilization to produce a streptavidin gradient, this would then be followed by the addition of fibronectin to the entire surface. Importantly, however, such a procedure is conceptually entirely different from the procedure incorporating motor-driven diffusion, and several additional complications can be foreseen, particularly for the production of micrometer-scale gradients. First, it would be difficult to obtain an appreciable gradient steepness because of the high diffusion coefficient of streptavidin (see above). Second, there is minimal potential for interactive control of the gradient production. Third, because the approach involves diffusion in solution it may be readily perturbed by convective flow. Finally, it is clear (cf. Figure 5d,e) that the gradient in Figure 5, in reality, consists of irregular and discontinuous fibronectin nanopatterns with progressively lowered density toward the periphery. That this discontinuous pattern is also sustained in the center of the gradients is inferred from the actin filament structure with 0.5 mm below the illustrated part of the micropattern. (b) Nine minutes after the addition of 1 mM MgATP. (c) Intensity profiles along the area between the two white dashed lines in a (black line) and b (gray line). Measurements from gray-scale images using Image J software. The vertical dashed line in c indicates the border between TMCS and SiO2. The increased intensity over the SiO2 area after 9 min represents filaments in solution. The exposure time in a was 0.5 s compared to 0.2 s in b. The gray-scale intensities in b were therefore enhanced (by histogram stretching) to increase all pixel intensities (including those in the background) 2.5 times. The temperature is 18 °C. Effects of photobleaching were expected to be negligible because of only brief periods of illumination of low light levels (20×, 0.45 NA objective) and the presence of oxygen scavengers in the assay solution.
fibronectin molecules were transported by HMM-propelled actin filaments. The versatility of the described method to produce surface gradients would be increased by the use of micropatterned surfaces, allowing actin filament attachment only to predetermined areas (e.g., trimethylchlorosilane (TMCS)).23 Figure 7 illustrates a TMCS-SiO2 micropatterned surface and its use in the formation of a gradient pattern by motor-driven diffusion. In this case, the entire surface was incubated with HMM and subsequently with fluorescently labeled actin filaments without blocking actin. As illustrated in Figure 7a, the actin filaments were attached only to HMM molecules on the TMCS area, after a brief rinse with ATP-containing solution.23 This simple procedure for initial positioning of the filaments is advantageous compared to the deposition by a microcapillary (Figures 4 and 5). Even though there are several challenges that need to be addressed in detail before routine use, the feasibility of the approach is illustrated in Figure 7. Thus, after 9 min of incubation with 1 mM MgATP an actin filament density gradient had developed on the TMCSderivatized part of the surface (Figure 7b) starting with the initial distribution in Figure 7a. Simultaneously, a high concentration of actin filaments accumulated in solution close to the TMCS/ SiO2 border. This accumulation in solution is due to the finite probability of actin filament detachment at the TMCS/SiO2 border in the presence of MgATP18 and a small diffusion coefficient for the filaments in solution. However, importantly, upon rinsing with MgATP-free solution to remove filaments in the bulk, the surface gradient is locked in place (cf. above) by the strong actomyosin bonds (rigor bonds) in the absence of MgATP. Without any effort to produce exact quantitative agreement (as a result of remaining experimental difficulties), we show that the gradient production in Figure 7 is reasonably well reproduced by a model (Supporting Information; Figure 8) with two coupled
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Figure 8. Simulation of the data in Figure 7c using two coupled diffusion equations as described in the text. The solid noisy lines represent experimental data replotted from Figure 7c (9 min after the addition of ATP). Zero at the horizontal axis represents the TMCS/SiO2 border. The smooth solid lines represent simulated sums of filament concentrations (proportional to fluorescence intensity in Figure 7) both on the surface and in solution. The curved dashed lines in each panel represent the simulated filament density on the surface. All simulated traces have been shifted to the background level for the micrographs in Figure 7. This background, measured >100 µm away from the large TMCS pattern, exhibited higher intensity by 20 gray-scale levels after the addition of ATP (probably as a result of the uniform density of fluorescent filaments in the bulk solution). The diffusion coefficient for motor-driven diffusion was 15 µm2 s-1 when predicted from the equation D ) VfLP with LP ) 7.5 µm and Vf ) 2 µm s-1 as measured from individual actin filaments. The different panels represent (a) simulation with Ds ) 15 µm2 s-1 and (b) simulation with Ds ) 7.5 µm s-1. The equations as well as the other parameter values used in these simulations are given in the Supporting Information.
diffusion equations. The key points of this model are that the filaments attach with very high probability to the TMCS part of the surface where they execute motor-driven diffusion with the diffusion coefficient D ) VfLP. At the TMCS/SiO2 border, the filaments detach into solution with finite probability (in the presence of MgATP),18 and in solution, they diffuse by Brownian motion, with a diffusion coefficient of 2 µm2 s-1. The simulations in Figure 8 suggest that the diffusion coefficient for motor-driven diffusion on the TMCS surface was slightly lower than the value (15 µm2 s-1) predicted from the measurement of smoothly sliding individual filaments. Thus the experimental actin density gradient on the surface was in between the data simulated using diffusion coefficients of 7.5 and 15 µm2 s-1. The concentration of actin filaments in solution 9 min after the addition of ATP was not exactly reproduced by the simulations. However, this is not unexpected because of the presence of uncontrolled fluid flow in the bulk (Supporting Information). Similar challenges were involved in the gradient production on micropatterned surfaces as discussed for nonpatterned surfaces (see above). In addition, the free filaments in solution (Figures 7 and 8) may, in response to convective flow, be brought back toward the TMCS surface with the risk of reattachment and unpredictable effects on the actin filament distribution. A possible way of counteracting such effects would be to use a continuous slow flow to remove all actin filaments that detach into solution.
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Figure 9. Self-organization of actin filament nanowires on a chemically and topographically nanopatterned surface. (a) Schematic illustration showing the design of a nanopatterned surface. The nanopatterns were created in a bilayer resist system using electron beam lithography.43 The black areas and lines were derivatized with TMCS and surrounded by topographical barriers (walls with overhangs43). The top layer of the walls and the overhang consisted of oxygen-plasma-treated polymethylmetacrylate (PMMA). This hydrophilic, negatively charged polymer also covered areas (white) surrounding the TMCS tracks and open loading zones. (b) Self-organization of actin filaments on the patterned surface, illustrated by overlaying several subsequent images in a sequence (5 frames s-1) illustrating the sliding paths followed by a limited number of filaments. This would correspond to the average position of a large number of filaments at each given point in time. Brighter color corresponds to brighter fluorescence intensity. The actin filaments were initially bound with similar probability to HMM molecules on each of the micrometersized TMCS loading zones. One minute after the addition of ATP, the HMM-induced sliding of the filaments organized them into the illustrated pattern.
More details about complicating factors in the production of gradients by motor-driven diffusion are considered in the Supporting Information. Combined Stochastic and Deterministic Approach to the Motor-Driven Self-Organization of Surfaces. The above studies are largely exploiting the random sliding of the actin filaments. In contrast, several previous investigations,18,43 utilized nanoscale (∼100 nm wide) topographically and chemically defined tracks to guide actin filament sliding and make it unidirectional. By combining the latter deterministic control with the above stochastic approach, complex patterns of actin filament binding sites (involving both gradients and extended lines) can be obtained. This is shown in Figure 9. Here, HMM and actin filaments have been added to the entire surface, but actin filaments attach only to the hydrophobic areas (black in Figure 9a). Actin filament sliding and the presence of nanostructured rectifiers19 cause the surface to self-organize into the steady-state distribution of actin filaments in Figure 9b. Here, the density is illustrated by integrating the sliding of only a few filaments over time. A smoother distribution would be obtained by longer time integration or the addition of a larger number of filaments. In the pattern in Figure 9b, there are topographically defined walls and an overhanging roof at the edge of the open areas. In this case, the filaments tend to accumulate and slide preferentially along the borders43 creating different gradient shapes than on the chemically defined pattern without topographically defined borders (Figure 7). The accumulation at the borders is, most likely, attributed to a combination of two factors: (1) higher local motor density at the corner between a wall and the TMCS-derivatized floor (ref 18) and (2) a reduced probability that the filament leaves its current path along the wall-floor junction because the thermal fluctuations of the free leading end of the filament are limited to one (rather than two, as on an open surface area) direction in the surface plane (ref 14). This will reduce the probability for a change in path direction because the instantaneous change in sliding direction is governed by the thermal fluctuation of the free leading end of the filament.14,50
Diffusion Dynamics of Motor-DriVen Transport
Indeed, the structure in Figure 9 may be regarded as nanopatterned on two levels. The first is the artificial nanopattern that defines the area where motor-based transportation is possible. The second is that nanopatterning, on another level, occurs through the distribution of the discrete actin filament nanowires over the surface to provide binding sites for other biomolecules. Applications of Motor-Based Surface Organization. The most important applications would probably be the production of surface gradients of different shapes for fundamental cellbiological studies. (See above and further references elsewhere.28) In addition to gradients of different cell adhesion molecules (e.g., fibronectin), it would also be straightforward to achieve gradients in surface roughness. The variation in height on the nanometer length scale is already provided by the actin filaments themselves but could be modified by using actin filaments of different lengths (see above). Moreover, quantum dots36 or gold nanoparticles37 are readily attached to the actin filaments to increase their height further. One could also readily foresee the potential to obtain features of micrometer height by adding suitable microparticles to the actin nanowire scaffolds. In addition to cell biology studies, it would be of interest to produce micrometer-sized areas (e.g., Figures 7 and 9) with varying densities of recognition molecules (antibodies and oligonucleotides) over the active area. Such micrometer-sized surface gradients may be produced within microfluidics circuits and may be associated with CCD detectors. Finally, one may consider applications outside cell biology and biosensing. Thus, the potential to produce gold nanowires with actin nanowires as templates37 paves the way for production of highly complex self-organized electric circuits.
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Einstein equation. We have also demonstrated the potential of motor-driven diffusion in the interactive production of surface gradients of biomolecules. In these unique gradients, the biomolecules are clustered along nanoscale lines, which are topographically and chemically defined by the actin filaments. Finally, if motor-driven diffusion is combined with chemical and topographical surface patterning, then this approach has enormous potential to produce a range of highly varying biomolecular micro- and nanopatterns. The potential may increase even further by combination with other approaches for control, such as ATP gradients,68 motor density gradients69 (see also ref 70), and switchable surfaces that allow motility to be switched on and off in predetermined regions71 (see also the discussion in ref 56). Acknowledgment. The work was supported by grants from The Swedish Research Council (project nos. 621-2004-3449 and 621-2007-3449), The Carl Trygger Foundation, The Knowledge Foundation (KK-Stiftelsen), The Crafoord Foundation, The Swedish Foundation for Strategic Research, The Faculty of Natural Sciences and Engineering, University of Kalmar, and The Nanometer Structure Consortium at Lund University. Valuable discussion with Professors Carlo Canali, Heiner Linke, and Henrik Flyvbjerg are acknowledged. Supporting Information Available: Simulation of motor-driven diffusion by the finite element approach. Calculations of diffusion coefficients. Relationship between the diffusion coefficient for motordriven diffusion and actomyosin mechanics and kinetics. Methodological details. This material is available free of charge via the Internet at http://pubs.acs.org. LA8016112
Conclusions Our results show that the sliding of actin filaments in the in vitro motility assay can be approximated by persistent random motion with a diffusion coefficient given by an analogy to the
(68) Tucker, R.; Katira, P.; Hess, H. Nano Lett 2008, 8, 221–226. (69) Ionov, L.; Stamm, M.; Diez, S. Nano Lett 2005, 5, 1910–1914. (70) Kierfeld, J.; Gutjahr, P.; Kuhne, T.; Kraikivski, P.; Lipowsky, R. J. Comput. Theor. Nanosci. 2006, 3, 898–911. (71) Ionov, L.; Stamm, M.; Diez, S. Nano Lett. 2006, 6, 1982–1987.
