Chemical Wave Propagation in the Belousov–Zhabotinsky Reaction

Article Cite This: J. Phys. Chem. A 2019, 123, 4853−4857

pubs.acs.org/JPCA

Chemical Wave Propagation in the Belousov−Zhabotinsky Reaction Controlled by Electrical Potential Masakazu Kuze,† Mari Horisaka,† Nobuhiko J. Suematsu,‡,§ Takashi Amemiya,∥ Oliver Steinbock,⊥ and Satoshi Nakata*,† †

Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan Meiji Institute for Advanced Study of Mathematical Sciences (MIMS) and §Graduate School of Advanced Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan ∥ Graduate School of Environment and Information Sciences, Yokohama National University (YNU), 79-7 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa 240-8501, Japan ⊥ Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA

Downloaded via BUFFALO STATE on July 26, 2019 at 09:08:17 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: The Belousov−Zhabotinsky (BZ) reaction is an important experimental model for the study of chemical oscillations and waves far from the thermodynamic equilibrium. Earlier studies had observed that individual BZ microbeads can show both global oscillations and traveling waves, but failed to select these different dynamic states. Here, we report experiments, in which this control was achieved by an externally applied electrical potential. The spherical microbeads were first loaded with the catalyst, then immersed into a catalyst-free BZ solution, and finally placed onto a planar platinum electrode. For positive electrical potentials, we observed global oscillations, whereas negative potentials resulted in traveling waves. The spatio-temporal characteristics of these phenomena are discussed in relation to the activator, HBrO2, which is produced by an electrochemical reaction.

1. INTRODUCTION

oscillations in microbead and droplet systems decreases with an increase of their size.18,19 Aihara and Yoshikawa was the first to observe two distinct types of spatio-temporal dynamics in microbeads, namely global oscillations (GO) and TW. The existence of these dynamic states also depends on the diameter of the bead,13 but surprisingly there is an intermediate size range in which GO and TW coexist. This coexistence indicates dynamic bistability, which is not observed between stationary states,20,21 but rather two distinct oscillatory states, that is, GO (homogeneous oscillations) and TW (inhomogeneous oscillations). Bistability between oscillatory states is interesting because in a biomedical context, such as coupled neuronal,22 cardiac,4 and pancreatic cells,23 it could correspond to the difference between a healthy condition and a health problem. To clarify the mode change between the two oscillatory states and their bistability, we performed experiments in which ferroin-loaded beads were submerged in catalyst-free BZ solution and then placed on a platinum electrode. In these experiments, the electrical potential serves as a convenient and powerful control

Reaction-diffusion systems generate a multitude of nonlinear phenomena, such as oscillations and traveling waves (TW).1,2 The systematic investigation of these spatio-temporal patterns is not only of fundamental interest but also necessary for understanding rhythmic processes and long-range communication in living systems.3−6 In this context, the Belousov− Zhabotinsky (BZ) reaction continues to serve as an important chemical model system because it exhibits many of the nonlinear phenomena that one encounters in biology.1,2,7 In addition, it allows for the external control of oscillations and waves through powerful means such as light irradiation8,9 and external electric fields.10,11 Cell-like, chemical examples that have attracted considerable research interest are oscillating reactions in spherical microbeads. For BZ studies, the latter are typically made of cationexchange resin and loaded with the reaction’s redox catalyst (here, ferroin). Earlier studies employed populations of these microreactors for experiments on synchronization processes among coupled oscillators, but also individual beads show intriguing spatio-temporal dynamics. These dynamics can be constrained to a thin surface layer of the beads or occur within their entire volume.12−18 It was also reported that the period of © 2019 American Chemical Society

Received: March 20, 2019 Revised: May 15, 2019 Published: May 16, 2019 4853

DOI: 10.1021/acs.jpca.9b02636 J. Phys. Chem. A 2019, 123, 4853−4857

Article

The Journal of Physical Chemistry A

3. RESULTS Figure 2a shows two image sequences for TW and GO on ferroin-loaded beads (diameter: ∼0.6 mm) at an electrical

parameter. Specifically, we found that GO and TW could be reversibly selected by the electrical potential. This mode selection of GO and TW is discussed from a viewpoint of triggering oscillations based on electrochemical reactions and also the distribution of the inhibitor, Br−, around the bead.

2. EXPERIMENTS The used reagents and beads (Sigma-Aldrich, Dowex 50W-X4, U.S.A.), the preparation of a Fe(phen)32+ (ferroin) solution as a catalyst, and the preparation of a bead with ferroin loaded to its entire volume (loading time: 48 h) were reported in the previous paper.14 Figure 1 shows a schematic illustration of the

Figure 2. (a) Snapshots of loaded beads (diameter: ∼0.6 mm) with (i) TW and (ii) GO [side view, time interval: (a-i) 2, (a-ii) 1 s] at E = 0 V (see Movies S1 and S2). Broken lines correspond to the edge of the beads. (b) Oscillation periods depending on the diameter of the ferroin-loaded beads at E = 0 V (filled circles: GO, open circles: TW). Figure 1. Schematic illustration of the experimental setup for the study of the BZ-bead system under constant applied electrical potential. In these experiments, a single BZ bead was placed on a Pt plate electrode. WE, CE, and RE refer to the working, counter, and reference electrodes, respectively.

potential (E) of E = 0 V. Here, the oxidation was started from the center of the bead in GO. These beads were loaded homogeneously with the catalyst ferroin and revealed either TW or GO. Figure 2b shows the period of oscillations depending on the diameter of the beads (d) at E = 0 V. GO and TW were observed at d ≤ 0.75 mm and d ≥ 0.57 mm, respectively. Accordingly, we can observe either GO or TW at 0.57 mm ≤ d ≤ 0.75 mm. In these experiments, TW and GO were stably observed for at least 2 h without switching each other. In the following, we investigated the effect of applied electrical potentials on the oscillations and waves. Here, the diameter of the bead was fixed at d ∼ 0.6 mm, in which either GO or TW were observed. Figure 3 summarizes the occurrence rate of different dynamic states within the beads as a function of the electrical potential. These data were

experimental system. The initial reactant concentrations in the catalyst-free BZ solution were 0.2 M NaBrO3, 0.4 M malonic acid, and 1.0 M H2SO4. The observation of the bead was started 2 h after soaking of the loaded beads into the BZ solution (t = 120 min) to obtain periodic oscillations (see the Section A in the Supporting Information). The increase in the period of oscillations was within 20% from 2 to 4 h after the soaking. All experiments were performed at 298 ± 1 K. The catalystfree BZ solution was always poured into a rectangular vessel (length: 70 mm, width: 45 mm, depth of BZ solution: 5 mm) and monitored with a digital video camera (SONY, HDRCX590V, Japan) from side. A single BZ bead was placed on a Pt plate electrode. Electrical potential was applied to the experimental system using a potentiostat (NIKKO KEISOKU, NPGS-2501-10nA, Japan). A platinum plate (45 mm × 5 mm; thickness, 0.1 mm) was used as the working electrode, and a platinum disk electrode (diameter, 1 mm) was used as the counter electrode with the reference electrode. The minimum distance between the platinum plate and the disk electrode was 2 mm. The chemical oscillations and wave phenomena involve striking color changes due to the different absorption spectra of the oxidized (blue color) and reduced (red color) forms of the ferroin/ferriin redox couple. The resulting videos are spatiotemporally analyzed with ImageJ software (National Institutes of Health, Bethesda, MD). The procedure to enhance spatiotemporal patterns in and on the bead follows the steps described in the previous paper.14

Figure 3. Occurrence rate of different states in BZ microbeads as a function of electrical potential (E). White, black, and gray bars correspond to TW, GO, and no oscillations, respectively. The bead diameter was d ∼ 0.6 mm. The results for each E value were obtained from 10 experiments. 4854

DOI: 10.1021/acs.jpca.9b02636 J. Phys. Chem. A 2019, 123, 4853−4857

Article

The Journal of Physical Chemistry A

positive and negative values of E, respectively. Accordingly, GO and TW could be reversibly selected by the electrical potential. Figure 5b shows the time series of (5b-1) E and (5b-2) the oscillation periods when TW were observed at t = 120 min. In this experiment, E was changed from 0 to +0.75 V at t = 140 min to induce GO and then periodically changed between −0.75 and +0.75 V with the same holding times of 20 min. As indicated in Figure 5b-2, GO and TW were alternately observed in synchronization with the periodic change in positive and negative values of E, respectively. Thus, GO and TW could be reversibly generated depending on the positive and negative values of the electrical potential regardless of whether the initial condition was GO or TW.

obtained from a total of 100 experiments (10 for each E value) and the constant electrical potential was applied during the time interval t = 120−240 min, where t = 0 min is the time when the beads were first exposed to the catalyst-free BZ solution. Notice that only TW were observed for E ≤ −0.75 V. Furthermore, these waves propagated from the contact point between the electrode and the bead to the opposite side of the bead. Either TW or GO were observed for −0.50 V ≤ E ≤ 0.25 V. When TW or GO were observed at t = 120 min, the feature of oscillations was maintained for 2 h. Only GO were observed at 0.50 V ≤ E ≤ 0.75 V and the oxidation started from the inside of the bead indicating the presence of a rapid phase wave. No oscillations were observed at E ≥ 1.00 V and the system remained in its reduced state. Figure 4 shows the oscillation periods for different electrical potentials. The periods of GO were independent of E, but the

4. DISCUSSION Based on related papers,1,7,13,14 we can discuss the electrochemical selection of GO and TW within the ferroin-loaded BZ beads. Figure 2 shows the existence of bistability between TW and GO for 0.57 mm ≤ d ≤ 0.75 mm and E = 0 V. The existence of the bistability for a single bead size was reported in the previous paper.13 Figures 3 and 4 suggest that the bistability between TW and GO exists for −0.50 V ≤ E ≤ 0.25 V. In the present condition, we cannot discuss on detail of electrical potential, but the negative potential applied to the bead on the platinum plate is enough to induce the electrochemical reaction in eq 1 according to the related paper.7 Propagation of TW from the contact point between the bead and the platinum plate to the opposite side suggests that TW are easily induced at the contact point. In addition, the potential sensitivity of the period of TW (see Figure 4) suggests that the electrochemical reaction in eq 1 mainly occurs on the platinum plate electrode at sufficiently negative values of E based on the previous paper.7

Figure 4. Period of oscillations as a function of the electrical potential (E). The data correspond to those in Figure 3.

periods of TW increased with an increase in E. Within the potential range where TW and GO coexist, the periods of GO were longer than those of TW. The electrical potential (E) was periodically changed to clarify the bistability and reversibility between TW and GO in the same BZ bead. In this experiment, the initial value of E at t = 120−140 min was zero. As GO were observed at t = 120 min, E was changed from 0 to −0.75 V at t = 140 min to induce TW and then periodically changed between −0.75 and +0.75 V with holding times of 20 min. Figure 5a shows the time series of (5a-1) E and (5a-2) the period of chemical oscillations within a representative microbead. In Figure 5a-2, the features of oscillations were distinguished as either TW or GO by visual inspection. GO and TW were alternately observed in synchronization with the periodic change between

3H+ + BrO3− + 2e− → HBrO2 + H 2O

(1)

Because the product HBrO2 is the autocatalytic species in the BZ reaction, a chemical wave should be easy to generate from the contact point between the bead and the platinum plate electrode. Figure 5 documents that the rapid change from GO to TW is generated by an electrochemical reaction in eq 1. On the other hand, homogeneous oscillations, GO, were observed with applying the positive electrical potential. This result indicates that the positive electrical potential cannot break the symmetry of chemical conditions around the beads. The period of GO independent of the electrical potential (see

Figure 5. Time series of (1) E and (2) period of oscillations and distinction between TW (open circles) and GO (filled circles) when (a) GO or (b) TW were observed at t = 120 min at E = 0 V [see Movies S3 and S4 for (a,b), respectively]. 4855

DOI: 10.1021/acs.jpca.9b02636 J. Phys. Chem. A 2019, 123, 4853−4857

Article

The Journal of Physical Chemistry A

Program of “Network Joint Research Center for Materials and Devices” (no. 20183003), and Electric Technology Research Foundation of Chugoku to S.N. O.S. was also supported by the US National Science Foundation under grant no. 1565734. T.A. was supported from JSPS KAKENHI (no. 19H04205).

Figure 4) also suggests that the positive electrical potential induces neither the reaction in eq 1 nor any other electrochemical reactions that affect the BZ reaction. Snapshots of GO in Figure 2a, that is, the generation of the oxidation in the bead center, suggest that the concentration of the inhibitor, Br−,10,11 at the inside of the bead may be lower than that at the surface of the bead. A repulsive force between Br− and the sulfonate group in the BZ bead prevents the penetration of Br− into the bead (see the Section C in the Supporting Information). Reversible switching between GO and TW synchronized with the periodic change in the positive and negative potential agrees with the suggested mechanism.

■

5. CONCLUSIONS In this study, we examined ferroin-loaded BZ beads in the dynamic bistable state between GO and TW at zero electrical potential. GO and TW could be selectively and reversibly generated by positive and negative values of electrical potential, respectively. The negative potential induces the production of the activator (HBrO2) on the electrode, and therefore chemical waves are easily triggered at the contact point between the electrode and the ferroin-loaded bead. That is, the activated surface of the bead induces TW. On the other hand, the positive potential maintains the homogeneous distributions of the activator and the inhibitor around the bead. In addition, the activated inside rather than the surface of the bead induces GO due to the chemical component of the bead. We suggest that the control of spatio-temporal oscillations in chemical systems like the BZ reaction helps to understand the spatially homogeneous and inhomogeneous development of oscillatory phenomena in living organisms.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.9b02636. Size- and elapsed time dependences of spatio-temporal transition in the 3D-loaded beads and distribution of the inhibitor (Br−) around the BZ beads (PDF) TW for the BZ bead (AVI) GO for the BZ bead (AVI) Oscillations for the BZ bead where the initial condition was GO at t = 120 min (AVI) Oscillations for the BZ bead where the initial condition was TW at t = 120 min (AVI)

■

REFERENCES

(1) Field, R. J.; Burger, M. Oscillations and Traveling Waves in Chemical Systems; Wiley: New York, USA, 1985. (2) Kapral, R.; Showalter, K. Chemical Waves and Patterns; Kluwer Academic: Dordrecht, Netherlands, 1995. (3) Boitano, S.; Dirksen, E.; Sanderson, M. Intercellular Propagation of Calcium Waves Mediated by Inositol Trisphosphate. Science 1992, 258, 292−295. (4) Luther, S.; Fenton, F. H.; Kornreich, B. G.; Squires, A.; Bittihn, P.; Hornung, D.; Zabel, M.; Flanders, J.; Gladuli, A.; Campoy, L.; et al. Low-Energy Control of Electrical Turbulence in the Heart. Nature 2011, 475, 235−239. (5) Allard, J.; Mogilner, A. Traveling Waves in Actin Dynamics and Cell Motility. Curr. Opin. Cell Biol. 2013, 25, 107−115. (6) Goldbeter, A. Oscillations and Waves of Cyclic AMP in Dicyostelium: A Prototype for Spatio-Temporal Organization and Pulsatile Intercellular Communication. Bull. Math. Biol. 2006, 68, 1095−1109. (7) Field, R. J.; Koros, E.; Noyes, R. M. Oscillations in Chemical Systems. II. Thorough Analysis of Temporal Oscillation in the Bromate-Cerium-Malonic Acid System. J. Am. Chem. Soc. 1972, 94, 8649−8664. (8) Kuhnert, L.; Agladze, K. I.; Krinsky, V. I. Image Processing Using Light-sensitive Chemical Waves. Nature 1989, 337, 244−247. (9) Sakurai, T.; Mihaliuk, E.; Chirila, F.; Showalter, K. Design and Control of Wave Propagation Patterns in Excitable Media. Science 2002, 296, 2009−2012. (10) Š evčíková, H.; Marek, M.; Müller, S. C. The Reversal and Splitting of Waves in an Excitable Medium Caused by an Electrical Field. Science 1992, 257, 951−954. (11) Taboada, J. J.; Muñuzuri, A. P.; Pérez-Muñuzuri, V.; GómezGesteira, M.; Pérez-Villar, V. Spiral breakup induced by an electric current in a Belousov-Zhabotinsky medium. Chaos 1994, 4, 519−524. (12) Nishiyama, N.; Eto, K. Experimental Study on Three Chemical Oscillators Coupled with Time Delay. J. Chem. Phys. 1994, 100, 6977−6978. (13) Aihara, R.; Yoshikawa, K. Size-Dependent Switching of the Spatiotemporal Structure between a Traveling Wave and Global Rhythm. J. Phys. Chem. A 2001, 105, 8445−8448. (14) Kuze, M.; Kitahata, H.; Steinbock, O.; Nakata, S. Distinguishing the Dynamic Fingerprints of Two- and Three-Dimensional Chemical Waves in Microbeads. J. Phys. Chem. A 2018, 122, 1967−1971. (15) Tinsley, M. R.; Taylor, A. F.; Huang, Z.; Showalter, K. Complex Organizing Centers in Groups of Oscillatory Particles. Phys. Chem. Chem. Phys. 2011, 13, 17802−17808. (16) Fukuda, H.; Tamari, N.; Morimura, H.; Kai, S. Entrainment in a Chemical Oscillator Chain with a Pacemaker. J. Phys. Chem. A 2005, 109, 11250−11254. (17) Miyakawa, K.; Okabe, T.; Mizoguchi, M.; Sakamoto, F. Synchronization in the Discrete Chemical Oscillation System. J. Chem. Phys. 1995, 103, 9621−9625. (18) Yoshikawa, K.; Aihara, R.; Agladze, K. Size-Dependent Belousov-Zhabotinsky Oscillation in Small Beads. J. Phys. Chem. A 1998, 102, 7649−7652. (19) Steinbock, O.; Müller, S. C. Radius-Dependent Inhibition and Activation of Chemical Oscillations in Small Droplets. J. Phys. Chem. A 1998, 102, 6485−6490. (20) Mulukutla, B. C.; Yongky, A.; Daoutidis, P.; Hu, W.-S. Bistability in Glycolysis Pathway as a Physiological Switch in Energy Metabolism. PLoS One 2014, 9, No. e98756.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone/Fax: +81-82-4247409. ORCID

Nobuhiko J. Suematsu: 0000-0001-5860-4147 Oliver Steinbock: 0000-0002-7525-6399 Satoshi Nakata: 0000-0002-7290-1508 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This study was supported from JSPS KAKENHI (no. 17K05835 and 17KT0123), the Cooperative Research 4856

DOI: 10.1021/acs.jpca.9b02636 J. Phys. Chem. A 2019, 123, 4853−4857

Article

The Journal of Physical Chemistry A (21) Kovacs, K.; McIlwaine, R. E.; Scott, S. K.; Taylor, A. F. pH Oscillations and Bistability in the Methylene Glycol−Sulfite− Gluconolactone Reaction. Phys. Chem. Chem. Phys. 2007, 9, 3711− 3716. (22) Belluscio, M. A.; Mizuseki, K.; Schmidt, R.; Kempter, R.; Buzsaki, G. Cross-Frequency Phase-Phase Coupling between Theta and Gamma Oscillations in the Hippocampus. J. Neurosci. 2012, 32, 423−435. (23) Lebreton, F.; Pirog, A.; Belouah, I.; Bosco, D.; Berney, T.; Meda, P.; Bornat, Y.; Catargi, B.; Renaud, S.; Raoux, M.; Lang, J. Slow Potentials Encode Intercellular Coupling and Insulin Demand in Pancreatic Beta Cells. Diabetologia 2015, 58, 1291−1299.

4857

DOI: 10.1021/acs.jpca.9b02636 J. Phys. Chem. A 2019, 123, 4853−4857