Controlling Enzymatic Reactions by Geometry in a Biomimetic

NANO LETTERS

Controlling Enzymatic Reactions by Geometry in a Biomimetic Nanoscale Network

2006 Vol. 6, No. 2 209-214

Kristin Sott,† Tatsiana Lobovkina,† Ludvig Lizana,‡ Michal Tokarz,† Brigitte Bauer,† Zoran Konkoli,‡ and Owe Orwar*,† Department of Chemistry and Bioscience, and Microtechnology Centre at Chalmers, SE-412 96 Go¨teborg, Sweden, and Department of Applied Physics, Chalmers UniVersity of Technology, SE-412 96 Go¨teborg, Sweden Received October 20, 2005; Revised Manuscript Received January 3, 2006

ABSTRACT We demonstrate that a transition from a compact geometry (sphere) to a structured geometry (several spheres connected by nanoconduits) in nanotube−vesicle networks (NVNs) induces an ordinary enzyme-catalyzed reaction to display wavelike properties. The reaction dynamics can be controlled directly by the geometry of the network, and such networks can be used to generate wavelike patterns in product formation. The results have bearing for understanding catalytic reactions in biological systems as well as for designing emerging wet chemical nanotechnological devices.

Introduction. It is well established that the rates of chemical reactions are dependent on dimensionality. For example, the rate of the reaction 2A f P is given by d[A]/dt ∝ [A]2in 3D and by d[A]/dt ∝ [A]2.46 and d[A]/dt ∝ [A]3in 2D and 1D, respectively.1 Likewise, if the size of the system is changed from macroscopic to strongly restricted (reaction range ∼ system size), then peculiar kinetics can be observed.2 For certain enzyme-catalyzed reactions, strong confinement leads to interesting behaviors such as oscillatory product formation.3 Thus, both the size and the dimensionality of a chemical reactor are important properties that can shape the dynamic properties of a chemical reaction. Here we explored how changes in the geometrical properties of a small-scale reaction container can alter the dynamics of a reaction-diffusion system with a diffusing catalyst (enzyme). By using soft-matter nanofluidic devices, we induced a change from a compact geometry (a sphere) to different linear and branched structured geometries (several spheres conjugated by conduits) (Figure 1A), where the diameters of the conduits are much smaller (nanometer-scale) than the diameters of the spheres (micrometer-scale) and just about one hundred times larger than the enzyme itself. It is demonstrated that the dynamics in a reaction-diffusion system can be controlled directly by the geometry and that nanofluidic devices can generate spatio-temporal patterns in product formation. * Corresponding author. E-mail: [email protected]. † Department of Chemistry and Bioscience, and Microtechnology Centre at Chalmers. ‡ Chalmers University of Technology. 10.1021/nl052078p CCC: $33.50 Published on Web 01/25/2006

© 2006 American Chemical Society

Figure 1. Schematic drawings showing various geometries of nanotube-vesicle networks and how they were fabricated. Panel A shows a sphere undergoing a transition from a compact to a structured geometry without changing the topology or volume. Panels B-J show the construction of a network in which each of the nanotube-conjugated vesicles has a different chemical composition, that is, enzyme or substrate, obtained using a microelectroinjection technique. The numbering of the vesicles reflects the order in which they were made. Figure 1I shows a network where vesicle nr 4 (red) contains an enzyme and vesicles 1-3 contain substrates (blue). The enzyme will diffuse down its concentration gradient into vesicles 1-3 and convert the substrate to product sequentially (green vesicles) as shown in Figure 1J (back-diffusion of substrate into vesicle nr 4 is neglected).

Lipid vesicles were prepared from soybean lecithin (SBL) as stock solution. To make unilamellar lipid vesicles, a dehydration/rehydration technique described previously4 was used with modifications.5 Briefly, 5 µL of a lipid suspension

(1 mg/mL) containing 1% v/v glycerol was placed on a cover slip glass and the solution was then dehydrated in a vacuum desiccator. When the lipid film was completely dry, it was carefully rehydrated with buffer (Trizma base 10 mM, KCl 100 mM, pH 8.9) to swell the lipid film. After a few minutes, giant unilamellar lipid vesicles were formed. Nanotube-vesicle networks (NVN) were constructed using a microelectroinjection technique described elsewhere.6,7 The electroinjections were controlled by a microinjection system (Eppendorf Femtojet, Hamburg, Germany) and a pulse generator (Digitimer Stimulator DS9A, Welwyn Garden City, U.K.). The injection tips used for formation of the networks were prepared from borosilicate capillaries (GC100TF-10, Clark Electromedical Instruments, Reading, U.K.). A CO2-laser-puller (model P-2000, Sutter Instrument Co. Novato, CA) was used to create the injection tips. A silver wire was used as the counter electrode. Rectangular cover slip glasses (no. 1) covered with photoresist polymer SU-88 with lipid vesicle suspension were placed directly on the microscope stage of an inverted confocal microscope (Leica DM IRB, Wetzlar, Germany) equipped with a Leica PL APO 63x objective. A confocal laser scanning microscopy system (Leica TCS SP2 RS, Wetzlar, Germany), with a PL APO CS 63x/1.2 W CORR objective, was used for acquisition of confocal fluorescence images. The 488-nm line of an Ar+ laser was used for excitation of fluorescein, and emission was collected by a photomultiplier tube (500-600 nm). The 543-nm line of a He/Ne laser was used for excitation of Alexa-568-marked alkaline-phosphatase, and the emission was collected by a photomultiplier tube (600-700 nm). During acquisition, images were line-averaged (2 lines) and stacked (2 frames) every 30 s and the data was collected sequentially for two detectors to avoid bleed through. Simultaneously, DIC images from the reflected light of the scanning lasers were collected. The collected data was evaluated using the Leica Lite program. The fluorescence intensities in each vesicle of the networks were estimated by the program, in so-called regions of interest (ROI), including a background ROI. For each network, the ROIs had the same size, independent of the vesicle size, but could always fit into the smallest vesicle. Trizma base, magnesium chloride, zinc chloride, fluorescein (GC grade), and alkaline phosphatase (P6772, Type VIIS) were from Sigma-Aldrich Sweden AB. Soybean lecithin (polar lipid extract) was from Avanti Polar Lipids, Inc. (700 Industrial Park Drive, Alabaster, AL 35007). Potassium chloride was from VWR International (Go¨teborg, Sweden). Fluorescein 3,6-diphosphate was from Molecular Probes (Leiden, The Netherlands). Deionized water from a Milli-Q system (Millipore Corporation, Bedford, MA) was used for preparing the solutions. The substrate (fluorescein diphosphate, FDP) and enzyme (alkaline phosphatase, AP) were divided into single use/single day aliquots in buffer (10 mM Trizma base, 100 mM KCl, 1 mM MgCl2, and 0.1 mM ZnCl2 pH 8.9) and stored at -20 °C. Stock solutions of 100 µM FDP and 4.5 µM AP were used throughout this work. The use of FDP as a substrate for AP has been described and characterized earlier.9-11 210

Alkaline phosphatase was first extensively dialyzed against carbonate-buffer (NaHCO3 0.1 M, pH 8.9) using Spectra/ Por Membrane CA-tubing with a cut off at 3500 Da. This was done in order to remove any residues of tris-buffer that can decrease the labeling efficiency. The enzyme (2.6 mg in 1 mL carbonate buffer) was then mixed with Alexa-568 succinimidyl (1 mg in 100 µL DMSO) and stirred at room temperature for 3 h. To remove any unattached dye molecules, we first dialyzed the reaction mixture extensively against enzyme buffer (5 mM Trizma base, 1 mM MgCl2, 0.1 mM ZnCl2, and 100 mM KCl, pH 8.9), using the same tubing as above, for 3 days at 4 °C. The labeled protein was then purified by running a Sephadex 10 DG column, BioRad, with a cut off at 6000 Da. The fractions containing the labeled protein were pooled, and the labeling ratio was determined by measuring the absorbance ratio between 280 (protein) and 578 nm (Alexa-568). The labeling ratio was found to be 5.5 Alexa-568 per protein. The labeled protein (AP-Alexa) solution was distributed in aliquots of 50 µL and stored at -20 °C. The conversion of the substrate FDP into product by the Alexa-labeled enzyme alkaline phosphatase was monitored by fluorescence spectroscopy using a Spex fluorometer (λexc ) 490 nm, λemm ) 512 nm). Alkaline phosphatase and FDP were mixed in a 1 × 1 cm2 quartz cuvette, using the same conditions as for the vesicle reactions (solution composition, pH, and temperature). The Michaelis-Menten constants, KM ) 3.7 µM and kcat ) 61 s-1, were obtained using a Hanes plot (not shown). Reactions in the networks were monitored using a confocal laser scanning microscopy system. We used alkaline phosphatase labeled with Alexa-568 (APA), to convert fluorescein diphosphate (FDP) to fluorescein. First a network, where all vesicles contained the same concentration (100 µM) of substrate, was made. Second, one or occasionally two enzyme-filled vesicles (4.5 µM) were connected to designated vesicles in such networks by nanotubes to initiate the diffusion of the enzyme within the network. Schematic drawings of how the networks were built and how the reaction cascades were initiated are shown in Figure 1B-J. The content of a newly formed vesicle was defined by the content of the micropipet. The first daughter vesicle was made with a substrate-filled pipet and transferred to a coverslip surface (Figure 1C). The second daughter vesicle was initially formed in the same way (Figure 1D). To connect it in series with the first formed daughter vesicle, its nanotube was translated across the first formed nanotube and then across the surface of the first formed daughter vesicle as shown in Figure 1E.7,10,12,13 Following this operation, which is possible because of the fluid character of bilayer membranes, the vesicle was immobilized on the surface (Figure 1F). By repeating the process, several substrate-filled vesicles could be translated and immobilized in a consecutive manner. Finally, by changing the pipet solution, the enzyme-filled vesicle was formed (Figure 1G) and placed between the first substrate-filled vesicle and the mother liposome (Figure 1HI). Immediately after the enzyme vesicle was introduced into the network, the reaction started (Figure 1J). The radii of Nano Lett., Vol. 6, No. 2, 2006

Figure 2. Diffusive transport of fluorescein through a nanotube-vesicle network (NVN). (A) Fluorescence microscopy image of a NVN containing fluorescein only in the first vesicle (vesicle 1). (B-C) With time, fluorescein diffuses down its concentration gradient, and eventually, the concentration is distributed evenly in the whole network. The boundaries of the vesicles and the connecting nanotubes are marked with dashed lines. (D) Graph showing normalized fluorescence intensity plotted versus time. The color of each curve corresponds to the color of the dashed line around the vesicles in Figure A-C. The dash-dotted lines show the theoretical fit to experimental data. Fluorescence images were digitally edited to improve image quality. The scale bar represents 10 µm.

the vesicles were usually 5-10 µm, the tube diameters were 100-300 nm, and the tube lengths were some tens of micrometers. In contrast to microfluidic systems, diffusion is an efficient means of transport and mixing at such short length scales.14,15 A model based on rate equations that describes the dynamics of the reaction-diffusion system in NVNs was developed. For simplicity, reactions in the tubes are neglected. The rate equations allow us to map the concentration of enzyme (E), substrate (S), and product (P), respectively, in the different network nodes as a function of time and read ∂t cPj(t) )

∑i k(P) ij [cPi(t) - cPj(t)] + kcat/KM cEj(t) cSj(t) (P) cPi(t) (1a) kdissipj

∂t cSj(t) )

∑i k(S) ij [cSi(t) - cSj(t)] - kcat/KM cEj(t) cSj(t) (S) cSi(t) (1b) kdissipj

∂t cEj(t) )

∑i k(E) ij [cEi(t) - cEj(t)]

(1c)

The three terms on the right-hand side represent transport (diffusion), reaction, and dissipation, respectively. A theory for diffusive transport in a network of containers coupled by thin tubes was developed recently in ref 15 where it was demonstrated that the rate for particle transport from 2 container i to j is given by k(q) ij ) Dqπa /Vjlij where Dq is the diffusion coefficient of substance q, a is the tube radius, lij ) lji is the length of the tube connecting containers i and j, and Vj is the volume of vesicle j. A Michaelis-Menten enzymatic reaction k1

kcat

} ES 98 E + P E + S {\ k -1

is assumed. A steady-state approximation on the intermediate enzyme-substrate complex (ES) leads to terms containing cEi(t) cSi(t) with KM ) (kcat + k-1)/k1. In addition to reaction Nano Lett., Vol. 6, No. 2, 2006

and diffusion, there is a continuous loss of particles from the system because of leakage of product through the vesicle wall. The substrate, however, has a low tendency to translocate across bilayer membranes. Also, the product is susceptible to photodestruction by laser illumination. Here, these leakage and bleaching effects are described by a (q) phenomenological loss term, kdissipj . The theoretical predictions for diffusing enzyme-catalyzed reactions in the NVNs employed in this study were based on solving eq 1, which tracks product formation as indicated by the dash-dotted lines in the graphs in Figures 2 and 3. Equation 1 was solved numerically using the methods developed in ref 15. Even though the theory was developed to describe only diffusive transport, it is straightforward to modify the original methods to solve eq 1. The curves produced from the theoretical calculations were fitted to the (q) as fitting parameters. The experimental data using kdissipi network geometry was read off from microscopy images, and the values used for KM and kcat were taken from bulk measurements. We believe that the reaction volumes (defined by the size of the containers) are sufficiently large in order for these values of KM and kcat to be correct. An alternative way of matching the theory and the experiment could be to use KM and kcat instead of the dissipation factors as fitting parameters. This approach should give the same result, but it has not been tested in this work mainly because of the fact that the dissipation factors are more difficult to determine experimentally. The numerical parameters used in order to produce the theoretical curves are given as Supporting Information. We first characterized diffusion of fluorescein (100 µM) through a network and compared the results with theoretical predictions. Figure 2A shows a three-vesicle network filled with fluorescein, where two of the vesicles (2 and 3) were photobleached by laser illumination (488 nm). The diffusion of fluorescein from vesicle 1 into the rest of the network was then monitored over time (Figure 2B and C). The fluorescence intensity in the nonbleached vesicle decayed rapidly, and the fluorescence signal in all vesicles eventually converged to the same value, indicating an even distribution of fluorescein throughout the network (Figure 2D). The poor 211

Figure 3. Fluorescence microscopy images (A-C, E-G, I-K, M, and N) showing product (fluorescein) formation in networks with different geometries. Graphs D, H, L, and O show the normalized fluorescence intensities of the corresponding measurements plotted versus time. Initially, the enzyme-filled vesicles are vesicle 1 in Figures A-C, E-G, and I-K, and vesicles 1 and 5 in M-N. The rest of the vesicles are filled with substrate. The dash-dotted lines in graphs 3D, H, L, and O show the theoretical fit to the experimentally measured product formation. Fluorescence images were digitally edited to improve image quality. The scale bar represents 10 µm.

recovery of the fluorescence in vesicle 2 and 3 is caused by bleaching and leakage of fluorescein. When we couple one enzyme-filled vesicle to several substrate-filled vesicles, a completely different pattern consisting of waves of product formation develops (Figure 3). Figure 3A-C shows a linear network where vesicle 1 is filled with enzyme and vesicles 2-4 are filled with substrate. The enzyme molecules diffuse throughout the network and sequentially initiate reactions in vesicles 2-4. Graph D shows the corresponding intensity graph. Qualitatively, the shape of the curves can be understood as follows. As enzymes enter the substrate-filled vesicles, the substrate molecules are converted into product. This process results in an initial increase of the product concentration. However, the product molecules will leave the network through the walls, and the product molecules will also be photobleached; thus, the product concentration will reach a maximum value and then start to decrease. The slope of the intensity curves (i.e., the rate of the reaction) is a function of enzyme concentration (large slope indicates a high enzyme 212

concentration). The height of the curve is proportional to the product concentration and thus the number of available substrate particles in combination with dissipation effects (i.e., leakage and bleaching). The decrease in fluorescence intensity, after the maximum is reached, is caused by dissipation and substrate depletion. The transport properties of the reactants vary with network geometry, and therefore the directional, temporal, and spatial coordinates of a reaction wave can be controlled by system configuration parameters. Figure 3E-G shows a bifurcating network where the substrate vesicles are placed in a V-shaped manner. Initially, vesicle 1 contains enzyme, and vesicles 2-4 contain substrate. Figure 3H displays the fluorescence intensity measurements for each of the nodes. By diffusion from vesicle 1, enzymes first reach vesicle 2 and start to catalyze the conversion of substrate into product. From this bifurcation node, the enzyme molecules can diffuse to vesicle 3 and 4 (or return to vesicle 1). Because nanotube II is shorter (12 µm) than nanotube III (68 µm) they reach vesicle 3 before vesicle 4. Figure 3I-K shows another bifurcating Nano Lett., Vol. 6, No. 2, 2006

network similar to the previous, except that another vesicle was added to the left branch. Vesicle 1 is filled with enzyme, and vesicles 2-5 are filled with substrate. The graphs in Figure 3L show the fluorescence intensity measurements of product formation in each node. Even though the traveling distance between vesicles 2-5 is longer than that between vesicles 2-4 (115 compared to 79 µm), the enzyme first reaches vesicle 5 before vesicle 4. This is because the intermediate container, 3, locally dilutes the enzyme concentration and thus presents a barrier for efficient diffusion of enzyme to vesicle 4. Thus, the rate-limiting step is not the transport through the nanotubes (which is fast, once the enzymes have entered), but rather the low probability of finding the entrance orifice to the nanotube from the container space.14,15 It is evident from the results above that the pattern of the product formation depends on the connectivity to enzymefilled vesicles. In the examples presented so far, we used a single source of enzyme that diffuses down its concentration gradient in the networks. Now we demonstrate that two discrete sources of enzyme can be injected to the system to create a pattern of counter-propagating product waves. Figure 3M-O show product formation in a network consisting of three connected substrate vesicles (vesicles 2-4) positioned between two enzyme-filled containers conjugated to terminal vesicles 1 and 5. In this system, where we have two sources of counter-propagating enzymes, we initially observed product formation simultaneously in vesicles 2 and 4, respectively, which are situated close to the enzyme containers. Second, product formation in the middle vesicle was observed. Graphs of fluorescence intensity as function of length (linear network length) map the concentration of product in each node (Figure 4). In a linear network, with a single terminal enzyme source, the vesicle closest to the enzyme vesicle display the highest fluorescence intensity that gradually falls off in the consecutive vesicles (Figure 4A). In contrast, a network with two terminal enzyme sources produces a product pattern-wave that is mirror-symmetrically distributed around the center line (Figure 4B). Note that in both of these graphs, the back-propagation of substrate into the enzyme vesicles is readily observed. These graphs further show that the location of injection points of enzyme and network connectivity in general will affect the distribution of product waves. In summary, we have shown that an ordinary enzymatic reaction following Michaelis-Menten kinetics can display wavelike behavior where reactions occur as a cascade through a series of reaction nodes tied together by nanoscale conduits. The key to this behavior lies in the small tube entrances that act as transport barriers for the enzyme. Essentially, these systems can be used to generate various wavelike patterns in product formation by controlling network geometry. Although we have focused on monitoring product fluorescence, the secondary and higher order waves of other reactants can be mapped onto the system as timeor space-dependent coordinates using the presented equations or modifications thereof. These systems are continuous with Nano Lett., Vol. 6, No. 2, 2006

Figure 4. Graphs showing the fluorescence intensity of the productwave as a function of distance from an enzyme source. The origin (x ) 0) is located on the edge of vesicle 1 (shown in red in the insets) that is farthest away from the tube inlet. Graphs 4A and B correspond to the experiments shown in Figure 3A-D and 3M-O, respectively. The graphs were generated by measuring the intensity profile across the vesicles when they had reached their maximum values. In graph 4B, vesicle 2 was slightly overexposed, resulting in a saturated response.

respect to network architecture but initially discontinuous with respect to their interior chemical network connectivity. The networks can, however, be controlled dynamically and the flexibility of the lipid material makes it possible to change, for example, network connectivity, tube lengths, or vesicle volumes during the course of a chemical reaction.6,7,10,16 In this way, the network structure can be altered dynamically to amplify and optimize certain properties of the dynamical process that it sustains. The results suggest strongly that network structures in both biology and nanofluidic reaction devices can directly influence and modulate a catalytic reaction. Thus, many reactions that appear to be “oscillatory” or time-varying, or otherwise have anomalous behavior, can sometimes be rationalized by the particular geometrical organization of the space in which they occur, that is, they do not need to be, for example, inherently autocatalytic or feedback modulated. Acknowledgment. Professor Lars-Erik Andreasson is acknowledged for valuable discussions. This work was supported by the Royal Swedish Academy of Sciences, the Swedish Research council (VR), the Swedish Foundation for Strategic Research (SSF) through a donation from the Wallenberg Foundation, and the Go¨ran Gustafsson Foundation. 213

Supporting Information Available: Numerical parameters used in order to produce the theoretical curves. This material is available free of charge via the Internet at http:// pubs.acs.org. References (1) Savageau, M. A. J. Theor. Biol. 1995, 176, 115-24. (2) Khairutdinov, R. F.; Serpone, N. Prog. React. Kinet. 1996, 21, 1-68. (3) Stange, P.; Zanette, D.; Mikhailov, A.; Hess, B. Biophys. Chem. 1999, 79, 233-47. (4) Criado, M.; Keller, B. U. FEBS Lett. 1987, 224, 172-6. (5) Karlsson, M.; Nolkrantz, K.; Davidson, M. J.; Stromberg, A.; Ryttsen, F.; Akerman, B.; Orwar, O. Anal. Chem. 2000, 72, 5857-62. (6) Karlsson, M.; Sott, K.; Cans, A.; Karlsson, A.; Karlsson, R.; Orwar, O. Langmuir 2001, 17, 6754-6758. (7) Karlsson, M.; Sott, K.; Davidson, M.; Cans, A. S.; Linderholm, P.; Chiu, D.; Orwar, O. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 11573-8.

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(8) Hurtig, J.; Karlsson, M.; Orwar, O. Langmuir 2004, 20, 56375641. (9) Huang, Z.; Olson, N. A.; You, W.; Haugland, R. P. J. Immunol. Methods 1992, 149, 261-6. (10) Karlsson, A.; Sott, K.; Markstrom, M.; Davidson, M.; Konkoli, Z.; Orwar, O. J. Phys. Chem. B 2005, 109, 1609-1617. (11) Bruckbauer, A.; Zhou, D. J.; Ying, L. M.; Abell, C.; Klenerman, D. Nano Lett. 2004, 4, 1859-1862. (12) Derenyi, I.; Julicher, F.; Prost, J. Phys. ReV. Lett. 2002, 88, 238101. (13) Evans, E.; Bowman, H.; Leung, A.; Needham, D.; Tirrell, D. Science 1996, 273, 933-5. (14) Dagdug, L.; Berezhkovskii, A. M.; Shvartsman, S. Y.; Weiss, G. H. J. Chem. Phys. 2003, 119, 12473-12478. (15) Lizana, L.; Konkoli, Z. Phys. ReV. E 2005, 72, 026305. (16) Karlsson, A.; Karlsson, R.; Karlsson, M.; Cans, A. S.; Stromberg, A.; Ryttsen, F.; Orwar, O. Nature 2001, 409, 150-2.

NL052078P

Nano Lett., Vol. 6, No. 2, 2006