Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX
pubs.acs.org/JPCA
Distinguishing the Dynamic Fingerprints of Two- and ThreeDimensional Chemical Waves in Microbeads Masakazu Kuze,† Hiroyuki Kitahata,‡ Oliver Steinbock,§ and Satoshi Nakata*,† †
Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan Department of Physics, Chiba University, Chiba 263-8522, Japan § Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States ‡
S Supporting Information *
ABSTRACT: Spatiotemporal oscillations confined to quasi-2D surface layers or 3D volumes play an important role for wave-based information relay and global oscillations in living systems. Here, we describe experiments with the Belousov−Zhabotinsky reaction confined to microbeads, in which the catalyst is selectively loaded either onto the surface or into the body of the spherical beads. We find that the dynamics of global oscillations, traveling reaction fronts, and rotating spiral waves under surface confinement are strikingly different from those in the bead volume. Our results establish a useful model system for the study of geometrical effects on nonlinear chemical processes and provide diagnostic features that allow the distinction of membrane-mediated 2D and cytosolic 3D processes in biological cells.
1. INTRODUCTION
at system boundaries or the alternative formation of vortex rings.14 Chemical wave patterns exist not only in spatially extended solutions and gels15,16 but can also be confined to small droplets17−20 and ion-exchange resin beads.21−29 For example, BZ beads have been used to experimentally investigate the synchronization of two or more nonlinear oscillators, since their coupling strengths can be adjusted by varying the spatial arrangements of the beads in catalyst-free solutions.22−24,28,29 BZ droplets form cell-like units that can begin to move, change shapes, and even undergo chemotaxis.18−20 These features hold potential for the construction of nonbiological cell systems for specific tasks such as active cargo transport. The motion of these units typically depends on the redox changes of the system’s catalyst and hence the internal wave pattern. Understanding the wave dynamics in small drop- or bead-like systems is hence of additional interest for engineering applications. We also emphasize that several recent studies analyze nonlinear phenomena, such as echo behavior11 (relevant to AI research) and chimera states,30 in chemical networks of coupled beads. With these technological and biological motivations in mind, we here investigate chemical waves in stationary polymer microbeads and demonstrate a transition from 2D to 3D vortex patterns.
Propagating reaction-diffusion waves exist in a great variety of chemical and biological systems ranging from CO oxidation on Pt surfaces1,2 and corroding metals3 to actin waves in single cells4 and messenger waves in cell colonies.5 In living organisms, they typically allow the transport of signals over large distances or perform other functions such as the central positioning of the division plane during cell division. These subcellular wave phenomena can occur either in the entire cell volume or in close vicinity of the inner cytoplasmic membrane.6 The latter case is well established for Min protein waves in E. coli and other biochemical processes in certain cyanobacteria.7 The differences between these pseudo-two and three-dimensional processes are poorly understood but dynamically interesting and important issues that we address here for the example of the Belousov−Zhabotinsky (BZ) reaction.8,9 The BZ reaction is one of the most widely studied chemical reactions, in which concentrations of key compounds, specifically the system’s activator (HBrO2) and inhibitor (Br−), oscillate periodically far from the thermodynamic equilibrium. The redox states of the catalyst self-organize patterns and excitation waves that are readily detected by optical methods.8−11 These dissipative structures include expanding target patterns, rotating spiral waves,12 andin three dimensionscontinuous stacks of spirals known as scroll waves.13 Spiral and scroll waves rotate around zero- and onedimensional phase singularities, respectively. The latter have curvature-dependent dynamics and must obey topological constraints that include the necessary termination of the curves © XXXX American Chemical Society
Received: December 12, 2017 Revised: February 7, 2018 Published: February 8, 2018 A
DOI: 10.1021/acs.jpca.7b12210 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A
Figure 1. (a) Schematic illustration of the preparation of 2D and 3D BZ bead systems. (b) Snapshots of sliced BZ beads (thickness: ∼0.1 mm) at t = (1) 1 h, (2) 12 h, and (3) 48 h after the start of ferroin loading. (c) Distribution of ferroin as a function of l (distance from the surface toward the center of the bead) for different t for the sliced beads based on the experimental results (solid curves) together with the fitted curves considering diffusion in a spherical body (dotted curves) (see Sections A and B in the SI).
2. EXPERIMENTS 1,10-Phenanthroline (phen) and FeSO4·7H2O (Fe(II)) (Wako Pure Chemical Industries, Ltd., Japan) were used to prepare a Fe(phen)32+ (ferroin) solution. H2SO4 (10.25 M) and NaBrO3 were purchased from Nacalai Tesque, Japan, and malonic acid (MA) was obtained from Wako Pure Chemical Industries, Ltd. These reagents were used without further purification. Figure 1a shows a schematic representation of the bead preparation with ferroin either loaded to a thin surface layer or the entire volume. For this, 1 g of cation-exchange resin beads (Dowex 50W-X4, U.S.A., average diameter: 0.86 mm) were loaded with a 1.1 × 10−3 M aqueous ferroin solution (10 mL) under gentle stirring at room temperature. One hour after the start of this process, the solution became colorless, and accordingly, 4.9 × 10−9 mol of ferroin had been transferred to each individual bead. Figure 1b shows micrographs of the center section of the bead for different loading times. To obtain these images, we cut the ferroin-loaded bead using two razor blades separated with a spacer (blade distance: ∼0.1 mm). One hour after the loading, the BZ catalyst was localized on and near the surface of the bead (see Figure 1b-1). We refer to this situation as a “2Dloaded bead”. The 2D-loaded beads were used immediately after preparation to examine spatiotemporal oscillations on the surface of the bead. For these experiments, we placed the beads into a BZ solution without catalyst. Alternatively, we increased the time (t) elapsed after loading to 48 h. During this long period, ferroin became homogeneously distributed throughout the bead volume (see Figure 1b-3). This second system will be referred to as a “3D-loaded bead” and was used to examine spatiotemporal oscillations within the whole body of the bead. Figure 1c shows the distributions of ferroin across the sliced bead for different loading times and as a function of the distance from the surface toward the center of the bead (l). From these data and an analytically obtained equation for diffusion in a spherical body (see Sections A and B in the Supporting Information (SI)), we estimated the diffusion coefficient of ferroin in the cation-exchange region as ∼3.5 × 10−8 mm2 s−1 by fitting. The initial reactant concentrations in the BZ solution without catalyst were 0.2 M NaBrO3, 0.4 M MA, and 1.0 M H2SO4. The observation was started 2 h after soaking of the
loaded beads into the BZ solution to obtain periodic oscillations (see Section C in SI). All experiments were performed at 298 ± 1 K. The BZ solution was always poured into a rectangular vessel (depth of BZ solution: 5 mm) and monitored with two digital video cameras (SONY, HDR-CX590V and HDR-CX485, Japan) from top and side simultaneously. The loaded beads were irradiated from the bottom by a light source (Trytec, Treviewer B4−400, Japan) at a low light intensity of 580 lx. Under these conditions, the photosensitivity of the ferroin catalyzed BZ reaction is negligibly low.31 Oscillatory phenomena between reduced and oxidized states of ferroin were spatiotemporally analyzed with ImageJ software (National Institutes of Health, Bethesda, MD, U.S.A.). To enhance spatiotemporal patterns within or on the bead, the following steps were performed: (i) the brightness of every image was evaluated as the brightness of the green color channel and (ii) difference images were computed from video frames taken at a time interval of 2/3 s.
3. RESULTS AND DISCUSSION 3.1. Classification of Patterns. We investigated the wave dynamics of both single 2D- and single 3D-loaded beads in the BZ solution. Global oscillations (GO), traveling waves (TW), or spiral/scroll waves (SW) were observed for a 2D- or 3Dloaded bead of which diameter was 0.4−1.2 mm. GO spontaneously occurred for both single 2D- and 3D-loaded beads. TW spontaneously appeared for a single 3D-loaded bead but not for a single 2D-loaded bead. However, TW were observed for the single 2D-loaded bead when another 2Dloaded bead was placed near the 2D-loaded bead. SW spontaneously appeared for a single 2D-loaded bead but not for a single 3D-loaded bead. However, SW were observed for the single 3D-loaded bead when an iron needle was placed at the single 3D-loaded bead. Dependences of period on the diameter for 2D- and 3D-loaded beads are shown in Figure S2 (see Section D in SI). 3.2. Global Oscillations in 2D- and 3D-Loaded Beads. Figure 2 shows (a) snapshots and (b) space−time plots along a center straight line for (i) 2D- and (ii) 3D-loaded beads. Under the given experimental conditions, global oscillations occurred for both 2D- and 3D-loaded beads. These oscillations occurred without spatial phase differences for the 2D-loaded bead. For B
DOI: 10.1021/acs.jpca.7b12210 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A
Figure 2. (a) Snapshots of (i) 2D- and (ii) 3D-loaded beads when global oscillation occurred (time interval: (i) 3 s, (ii) 4 s). Dotted lines correspond to the edge of the bead. (b) Space−time plots illustrating the propagation of chemical waves for (i) 2D- and (ii) 3D-loaded beads. The spatiotemporal plot was generated along the x-axis, as shown in the right side in (b), and x = 0 corresponds to the center of the bead. Diameter of the bead: (i) 0.66 mm, (ii) 0.50 mm (see Movies S1 and S2). Figure 3. (a) Snapshots of (i) 2D- and (ii) 3D-loaded beads with chemical waves propagating from the left to the right (time between frames: 5 s), and Wn (n = 1, 2, 3, or 4) denoting the number of the chemical wave. Another loaded bead (not shown) was placed at the left side of the observed bead (the distance between two beads: ∼50 μm). Diameter of the bead: (i,ii) 1.08 mm (see Movies S3 and S4). (b) Snapshots of rotating chemical waves on (i) single 2D- and in (ii) 3Dloaded beads. Time between frames: 3 s. Diameter of the bead: (i) 1.16 mm, (ii) 1.04 mm (see Movies S5 and S6).
the 3D-loaded bead, however, we observed rapid phase waves spreading periodically from the inside outward. The reaction dynamics changed profoundly, if a second catalyst-loaded bead was placed close to the original bead. This procedure breaks the spherically symmetric distributions of chemical species around the primary bead and allowed us to observe spatiotemporal pattern formation other than global oscillations. 3.3. Traveling and Spiral Waves in 2D- and 3D-Loaded Beads. For example, traveling waves occurred at the point closest to the other bead (left side of the bead) and propagated to the opposite point (right side of the bead), as shown in Figure 3a. So far, we discussed global oscillations and traveling waves, but additional patterns were found for bead diameters that exceeded about 0.8 mm. Representative examples are shown in Figure 3b. The topological constraints ruling chemical rotors require pairwise existence of spirals on finite-size domains such as our bead surface, and our 2D systems indeed exhibited two spiral tips located at approximately the 10 and 4 o’clock positions, as shown in Figure 3b-i. These wave patterns must be clearly distinguished from single scroll waves that would occupy the entire bead volume and rotate around a onedimensional curve that begins and ends on the bead surface, which was observed in the 3D systems, as shown in Figure 3bii. Figures 4b and c show space−time plots and graphs of the wave velocity along (I) the x-axis or (II) the periphery of (i) 2D- and (ii) 3D-loaded beads. In the case of the 2D-loaded bead, the wave velocity along the x-axis reached its maximum at the center of the bead (x = 0) and its minimum around the edge of the bead (x ≈ ± 0.5 mm) (Figure 4I(c-i)). In the 3Dloaded bead, however, the wave velocity along the x-axis was almost constant for every location on the x-axis (Figure 4I(cii)). If the chemical wave propagates on the surface of the bead at a constant velocity (v{2D}), the velocity along the x-axis, vx, is expressed as
vx =
1−
x2 v{2D} R2
(1)
where R is the radius of the bead (see Section F in SI). Leastsquare fitting of eq 1 to the experimental results yielded excellent agreement as exemplified by the continuous curve in Figure 4I(c-i). As for the 2D-loaded bead, the velocity along the periphery on the wave propagation was almost constant for every measured location, as seen in Figure 4II(c-i). In contrast, the velocity along the periphery in 3D-loaded beads increased markedly for large |θ|, as seen in Figure 4II(c-ii). If the chemical wave propagates across the bead volume at a constant velocity (v{3D}), the velocity along the periphery of the bead, vs, is given by v{3D} vs = cos(θ /2) (2) (see Section F in SI). The fitted curve based on eq 2 is in very good agreement with the experimental results, as shown in Figure 4II(c-ii).
4. CONCLUSIONS In conclusion, we have described an experimental protocol for the preparation of microbeads with chemical self-organization occurring either on the bead surface or in its entire volume. We also showed that the spherical symmetry that gives rise to global oscillations can be broken by the creation of bead pairs. These 2D and 3D cases give rise to distinct velocity profiles and even spiral waves. We believe that our results will be useful for C
DOI: 10.1021/acs.jpca.7b12210 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A
Figure 4. (a) Schematics illustrating the variables involved in the construction of space−time plots that extend along the x-axis (Analysis I, left half) or the periphery of the beads (Analysis II, right half). (b) Space−time plots of propagating chemical waves for (i) 2D- and (ii) 3D-loaded beads based on Analyses I and II. The data for (i) and (ii) correspond to those for (i) and (ii) in Figure 3a, respectively. (c) The velocity of the chemical wave propagating (i) on 2D (empty circles) and (ii) in 3D (filled circles)-loaded beads based on Analyses I and II. The solid curve in (c-i, left half) for the 2D-loaded bead was obtained by fitting with eq 1 for R = 0.52 mm, and v{2D} was set as a fitting parameter. As a result, we obtained v{2D} = 0.0330 ± 0.0008 mm s−1. The solid line in (c-ii, right half) for the 3D-loaded bead was obtained by fitting with eq 2, in which R = 0.52 mm, and v{3D} was set as a fitting parameter. As a result, we obtained v{3D} = 0.0429 ± 0.0008 mm s−1. The fitting parameters v{2D} and v{3D} were obtained from the four trials individually.
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the identification of wave localization mechanisms in biological cells that can either be constrained to the vicinity of the cell membrane or be free to evolve in the cytosol. Future studies should also investigate the network behaviors of coupled 2Dand 3D-loaded beads and related effects in self-moving reaction units.
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AUTHOR INFORMATION
Corresponding Author
*Tel. & Fax: +81-824-24-7409; E-mail: nakatas@hiroshima-u. ac.jp. ORCID
Hiroyuki Kitahata: 0000-0003-3453-9883 Oliver Steinbock: 0000-0002-7525-6399 Satoshi Nakata: 0000-0002-7290-1508
ASSOCIATED CONTENT
S Supporting Information *
Notes
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b12210. Relationship between the experimentally observed images and the concentration of ferroin; fitting of the concentration profile considering the diffusion dynamics inside a spherical body; time-variation of redox behaviors for 3D-loaded beads with different sizes; size-dependencies of the spatiotemporal pattern for the single 2D or 3D-loaded beads; derivation of the velocity dependence in eqs 1 and 2 in the main text (PDF) Movie S1: GO for the 2D-loaded bead in Fig. 2a-I (×10 speed) (AVI) Movie S2: GO for the 3D-loaded bead in Fig. 2a-ii (×10 speed) (AVI) Movie S3: TW for the 2D-loaded bead in Fig. 3a-I (×10 speed) (AVI) Movie S4: TW for the 3D-loaded bead in Fig. 3a-ii (×10 speed) (AVI) Movie S5: SW for the 2D-loaded bead in Fig. 3b-I (×10 speed) (AVI) Movie S6: SW for the 3D-loaded bead in Fig. 3b-ii (×10 speed) (AVI)
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This study was supported by the JSPS Program on Invitational Fellowships for Research in Japan to S.N. and O.S. (No. S17038), JSPS KAKENHI (No. 17K05835, No. 17KT0123), the Cooperative Research Program of “Network Joint Research Center for Materials and Devices” (No. 20173006), the Electric Technology Research Foundation of Chugoku, Satake Technical Promotion Foundation, and the Sasakawa Scientific Research Grant from The Japan Science Society to S.N. O.S. was also supported by the US National Science Foundation under Grant No. 1565734.
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DOI: 10.1021/acs.jpca.7b12210 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jpca.7b12210 J. Phys. Chem. A XXXX, XXX, XXX−XXX
