Abstract

Excitation and oscillation are central to living systems. For excitable systems, which can be brought into oscillation by an external stimulus, the excitation threshold is a crucial parameter. This is evident for neurons, which only generate an action potential when exposed to a sufficiently high concentration of excitatory neurotransmitters, which may only be achieved when multiple presynaptic axons deliver their action potential simultaneously to the synaptic cleft. Dynamic systems composed of relatively simple chemicals are of interest because they can serve as a model for physiological processes or can be exploited to implement chemical computing. With these applications in mind, we have studied the properties of the oscillatory Belousov-Zhabotinsky (BZ) reaction in 3D-printed reaction vessels with open channels of different dimensions. It is demonstrated that the channel geometry can be used to modulate the excitability of the BZ medium, switching a continuously oscillating medium to an excitable medium. Because large networks of channel-connected reaction wells of different depth can easily be fabricated by 3D printing, local excitability modulation could be built into the structure of the reaction vessel itself, opening the way to more extensive experimentation with networks of chemical oscillators.

1 Introduction

Coupling between oscillating systems underpins a large variety of physiological processes, including the circadian pacemaker and the electrical synchronization of beating heart cells [9, 36]. Excitable systems are inherently dynamic and can be brought into a pulselike oscillation by an external stimulus. The prototypical excitable cell is the neuron, which will initiate the ion-flux-mediated membrane depolarization cycle known as the action potential when its dendrites are exposed to excitatory neurotransmitters, released by presynaptic axons into the synaptic cleft. Information-processing properties of biological neural networks arise from connectivity patterns because an individual neuron will only generate an action potential when the neurotransmitter concentration in the synaptic cleft exceeds a threshold value, and this may only be achieved when multiple presynaptic neurons, representing for example different external stimuli, deliver their action potential to the synaptic cleft within a short time window [3, 20].

Nonlinear chemical reactions such as the Belousov-Zhabotinsky (BZ) reaction are of interest because their excitable properties are suitable for mimicking physiological processes and for constructing and connecting chemical logic gates in the context of chemical information processing [4, 19]. The BZ reaction can either oscillate continuously between an oxidized and a reduced state (visible as a blue or a red color) or exhibit a single oscillation cycle, manifested as a blue wavefront, upon a chemical or physical trigger. The reaction cycle involves the oxidation of an organic molecule by the bromate ion at very low pH and is usually catalyzed by a metal ion [7]. The properties of the BZ medium—for example, the frequency of oscillations, or (when excitable but not self-oscillating) the threshold input to trigger an oscillation—are usually determined by the choice of the initial ratio of the reaction molecules. Alternatively, the excitability of the BZ reaction can also be modulated by external factors, for example by inserting a biased electrode that depletes one of the reaction components [23], typically affecting the entire BZ solution.

A considerable effort has been spent on the implementation of chemical oscillators for information processing [10, 11, 19], using a variety of experimental strategies to impart spatial organization to the BZ medium. Logic gates with BZ medium were first realized by Tóth et al., who used thin glass capillaries for axon-like chemical wave propagation and an intercapillary reservoir as an equivalent of a synaptic junction [33, 34]. The features of these gates depended on the geometrical configuration of the capillaries, the synchronization of the input waves, and the capillary diameter, with the last two parameters relating to the threshold for wave induction in the intercapillary reservoir [34]. More recently, Steinbock and coworkers studied BZ wave propagation inside glass capillaries, reporting specific wave transmission phenomena, including backfiring pulses, in addition to linear pulse propagation [15, 21]. A closely related experimental approach is to exploit wave propagation properties through BZ compartments that are separated by a solid wall with a small opening for BZ pulse transmission [26].

The latter method can also be implemented by compartmentalization of the BZ solution as a droplet in oil, with droplet-droplet contact areas, or a thin oil layer between adjacent droplets, serving as a physicochemical barrier that requires a transfer of excitatory species for cross-droplet signal propagation [30, 32]. However, in many studies on pulse propagation through networks of compartmentalized BZ solution, boundaries only existed for the (light-sensitive) catalyst material, which was immobilized on a gel in a continuous-reagent-flow reactor, with regions of BZ activity being defined by light exposure through a photomask with a specific geometrical pattern. Unidirectional wave propagation in narrow channels of activated catalyst has been achieved [17, 18, 22], while wave propagation properties in small networks of channel-connected chambers [28, 29] and in gap-connected spheres [1, 2, 12], mimicking BZ droplets in oil, have been shown to represent various logic operations, including or, and, not, xnor, and nor.

In the present study, we explore an alternative strategy for exploiting the properties of a chemical oscillator for artificial signal transduction: three-dimensional printing of a solid plastic matrix as a substrate that defines channels and wells that are open to the air. In contrast to the spatial patterning of reaction medium discussed above, this approach enables rapid manufacturing of high-density channel-well networks, enabling more complex connection patterns, and does not require catalyst patterning or reagent flow. We systematically investigated the excitability of BZ reaction mixtures in channels of different width and depth, connected to a central well with a self-oscillating BZ solution, and identified dimensions where channel-confined BZ medium does not self-oscillate but is able to accept and propagate input waves. This ability to modulate chemical excitability by changing the depth of the channels and wells in the reaction substrate is extremely convenient in that it enables BZ networks with expanded functionality without the need for different BZ compositions at specific points in the network.

2 Materials and Methods

The reaction vessels were designed using SolidWorks 2011 (Dassault Systems, France), and the geometry was subsequently exported as an STL coordinate file to a 3D printer (Objet350 Connex™ from Stratasys Ltd, USA) that deposits UV-curable material layer by layer in the desired pattern with an ink-jet-like printer head, building up the structure from bottom to top [13]. The reaction substrate was printed using Objet Fullcure720, a transparent material that gives a hard plastic matrix after curing, upon a bed of Fullcure705 support material. This support material formed a temporary scaffold to aid the detachment of the substrate from the printer bed. After the support layer was removed entirely using a high-pressure water jet, the substrate was baked overnight at 80°C to fully cure the Fullcure720 plastic. An example of a reaction substrate 3D-printed with this material is shown in Figure 1. The elastomer polydimethylsiloxane that is commonly used for microfluidic devices was not used in this study, because it interferes with the BZ reaction cycle [8, 16].

Figure 1. 

Fabrication of the reaction substrates. The central well and the side channels of various widths and depths are designed in a 3D software package (left) and exported as a coordinate file to a 3D printer that deposits the desired geometry layer by layer, resulting in a hard plastic reaction substrate (right).

Figure 1. 

Fabrication of the reaction substrates. The central well and the side channels of various widths and depths are designed in a 3D software package (left) and exported as a coordinate file to a 3D printer that deposits the desired geometry layer by layer, resulting in a hard plastic reaction substrate (right).

The Belousov-Zhabotinsky reaction mixture was prepared by addition of reaction components in the following order: 150 μL of 2.5 M H2SO4, 405 μL of H2O, 750 μL of 1.5 M NaBrO3, 870 μL of 1.0 M malonic acid, 150 μL of 1.0 M KBr, and 170 μL of 25 mM ferroin. This gives a BZ composition of 150 mM H2SO4, 450 mM NaBrO3, 350 mM malonic acid, 60 mM KBr, and 1.7 mM ferroin, which gives rise to self-oscillation in bulk solution. The catalyst ferroin was only added after the yellow color of the BZ mixture had dissipated. For BZ compositions with a higher H2SO4 concentration, the amount of H2SO4 stock solution was increased and the H2O volume was proportionally decreased. All BZ mixtures were degassed in a vacuum desiccator. The degassed reaction mixture was loaded in a syringe and was dispensed in the reaction substrate in a single step with the aid of a syringe pump (Harvard Apparatus, USA). If the BZ solution did not fully fill a channel, it was manually guided into the channel with a pipette tip.

The evolution of the BZ patterns in the entire reaction substrate (central well and all side channels) was recorded at a rate of 32 frames/s with a Prosilica GX2300C high-resolution CCD camera with a sensor chip of 2336 × 1752 pixels (Allied Vision Technologies, Germany). The raw files produced were debayered and converted into PNG format using custom software. These images were then processed with ImageMagick® software (ImageMagick Studio LLC), using sequential crop, red channel separation, negate, and brightness-contrast functions to obtain enhanced images where the BZ excitations are visible as bright waves on a dark background. The images were finally processed into videos, using the avconv function, for visual analysis of the BZ excitation patterns. Specific BZ characteristics were only assigned to specific channel dimensions when observed in duplicate channels.

3 Results and Discussion

3.1 Reaction Substrate Fabrication

Initially, the vessel substrates were designed with a circular central well with fixed-length side channels of various depths and widths protruding from it in a radial pattern. However, it was found that the walls of the channels, as built by the 3D printer, were stepped rather than straight, causing small variations in the channel width. Moreover, these discrete width transitions were found to act as nucleation sites for gas bubble formation. It was subsequently established that stepped channel walls could be avoided by only building channels in a direction parallel with or perpendicular to the movement of the printer head, implying that the stepped channels are a consequence of voxel mesh aliasing.

To avoid this fabrication artifact, we designed reaction substrates with a square central well, from which channels protrude exclusively at straight angles, as depicted in Figure 1. It was found that the 3D printer could indeed build this geometry with straight channel walls, facilitating interpretation of the BZ excitability inside the channels. Various reaction substrates were fabricated, all with a 40 × 40-mm square central well of 8.0-mm depth and with 20 side channels that are each 10 mm long. The different designs offered different ranges of width and depth of the channels, with two identical channels per substrate, giving ten different channel dimensions for each reaction substrate. Channels with different dimensions were positioned randomly around the central well (Figure 1) as an internal control for a directional bias in BZ excitability, as potentially caused by a slight tilt of the printed substrate or by an illumination-induced temperature gradient.

3.2 BZ Excitability in the Reaction Substrate

The central well of the chamber should serve as a source of BZ excitation waves that act as input wavefronts for the side channels. We established that BZ mixtures with a sulfuric acid concentration between 150 and 210 mM consistently enabled self-oscillations in the central well. A sulfuric acid concentration below 150 mM did not reproducibly give rise to self-oscillation of the BZ medium, whereas concentrations higher than 210 mM were not used, because under these conditions the H2SO4-enabled increase in BZ activity (i.e., a higher frequency of self-oscillation) resulted in an excessive amount of gaseous reaction products, most likely CO2 and Br2 [5]. This could be observed as a large number of gas bubbles, and it was undesirable because these frequently blocked the entrance to the channels, preventing well-to-channel wave propagation.

The central well was filled to the top with BZ medium, ensuring that the channels were also filled completely with the same BZ reaction mixture. Over several reaction chambers, the width of the channels ranged from 0.8 to 3.0 mm, while the depth ranged from 0.3 to 5.0 mm. Channels with a width below ≈0.7 mm were difficult to fill with BZ solution, while features <0.2 mm approach the resolution limit of the 3D printer. The volume of the channels was kept between 10 and 100 mm3, because smaller channels cannot easily be filled without active fluid pumping and larger channels would occupy too much space for future reaction vessel applications with networked channels. Examples of observed wave patterns in a reaction substrate are shown in Figure 2, for the BZ mixture with an intermediate H2SO4 concentration of 180 mM.

Figure 2. 

Reaction substrate with the central well and all the channels filled with a BZ mixture containing 180 mM H2SO4. These snapshots from the same experiment show that most channels are able to accept waves that arrive from the central well but that waves can also be generated inside the channels by self-oscillation of channel-confined BZ medium.

Figure 2. 

Reaction substrate with the central well and all the channels filled with a BZ mixture containing 180 mM H2SO4. These snapshots from the same experiment show that most channels are able to accept waves that arrive from the central well but that waves can also be generated inside the channels by self-oscillation of channel-confined BZ medium.

For BZ mixtures with a sulfuric acid concentration of 150 mM, it was observed that the BZ mixture in channels with a depth of 0.3–1.2 mm (width ranging from 3.0 to 1.6 mm) did not self-oscillate and could not propagate a BZ wave from the well when the wavefront reached the entrance of the channel. Hence confinement of the BZ medium in channels of shallow depth rendered the reaction mixture non-excitable. In contrast, BZ medium in channels with a depth of 3.5–5.0 mm (width ranging from 2.4 to 1.0 mm) did self-oscillate. Although channels with self-oscillating BZ medium could also propagate waves that arrived from the central well, these waves were frequently annihilated after collision with waves that had emerged in the channel itself. Examples of wave propagation inside channels, with and without self-oscillations of channel-confined BZ medium, are given in Figure 3.

Figure 3. 

Different scenarios for BZ wave propagation and wave emergence in channels for a BZ mixture with 180 mM H2SO4. The top row shows that the BZ solution inside the channel accepts an incoming wave from the central well and propagates this wave through the channel, which is the desired behavior for logic gate implementations. The middle row shows that a wavefront emerges inside the channel as a result of BZ self-oscillation and collides with a wavefront that has been accepted from the central well, annihilating this incoming wave and preventing its propagation through the channel. The bottom row depicts how a wave emerges inside the channel, propagates through the channel in both directions, and exits the channel at the side of the central well, inducing a wavefront inside the well. BZ wave induction in wells by channel-propagated BZ waves is a desired property for logic gate operation in more complex reaction substrates with networks of connected channels and wells.

Figure 3. 

Different scenarios for BZ wave propagation and wave emergence in channels for a BZ mixture with 180 mM H2SO4. The top row shows that the BZ solution inside the channel accepts an incoming wave from the central well and propagates this wave through the channel, which is the desired behavior for logic gate implementations. The middle row shows that a wavefront emerges inside the channel as a result of BZ self-oscillation and collides with a wavefront that has been accepted from the central well, annihilating this incoming wave and preventing its propagation through the channel. The bottom row depicts how a wave emerges inside the channel, propagates through the channel in both directions, and exits the channel at the side of the central well, inducing a wavefront inside the well. BZ wave induction in wells by channel-propagated BZ waves is a desired property for logic gate operation in more complex reaction substrates with networks of connected channels and wells.

Interestingly, for channels with an intermediate depth of 2.0–3.2 mm (1.9 to 3.0 mm wide), the BZ medium with 150 mM H2SO4 did not self-oscillate, but was able to propagate waves that arrived from the central well at the entrance of the channel. This interesting consequence of channel confinement of the BZ solution is illustrated in Figure 4. For BZ solutions with a H2SO4 concentration of 180 or 210 mM, this behavior was also observed, although typically in the somewhat more restricted depth range of 2.0–2.6 mm (see Figure 3, top row). Thus, these more active BZ reaction mixtures typically displayed self-oscillations in channels with a depth of 2.6–3.2 mm (Figure 3, middle and bottom row), whereas the less active BZ solution with a H2SO4 concentration of 150 mM did not. This observation again illustrates that the suppression of BZ excitability becomes weaker at greater channel depth, suggesting an effect that originates from the top surface of the BZ solution.

Figure 4. 

Excitability of channel-confined BZ solution with 150 mM H2SO4. (a) The 8.0-mm-deep central well shows self-oscillation of the BZ medium, generating numerous wavefronts. (b) In channels with a depth of 2.0–3.2 mm (1.9 to 3.0 mm wide), the BZ solution does not self-oscillate but is still excitable and can accept and propagate waves that arrive from the central well. (c) In channels that are 1.2 mm deep or shallower (3.0 to 1.6 mm wide), the BZ medium does not self-oscillate and does not propagate waves that are delivered by the central well. (d) In channels that are 3.5 mm deep or deeper (2.4 to 1.0 mm wide), the BZ medium is able to self-oscillate and generate waves independent from the central well. Note that the channels are present in duplicate and that inhibition of BZ excitability was only assigned to a specific channel geometry if it occurred in both channels.

Figure 4. 

Excitability of channel-confined BZ solution with 150 mM H2SO4. (a) The 8.0-mm-deep central well shows self-oscillation of the BZ medium, generating numerous wavefronts. (b) In channels with a depth of 2.0–3.2 mm (1.9 to 3.0 mm wide), the BZ solution does not self-oscillate but is still excitable and can accept and propagate waves that arrive from the central well. (c) In channels that are 1.2 mm deep or shallower (3.0 to 1.6 mm wide), the BZ medium does not self-oscillate and does not propagate waves that are delivered by the central well. (d) In channels that are 3.5 mm deep or deeper (2.4 to 1.0 mm wide), the BZ medium is able to self-oscillate and generate waves independent from the central well. Note that the channels are present in duplicate and that inhibition of BZ excitability was only assigned to a specific channel geometry if it occurred in both channels.

3.3 Effectors of Excitability of Confined BZ Medium

Depth-dependent modulation of the excitability of channel-confined BZ medium was also observed for channels of different volume, namely, for channels with the same depth range of 2.0–5.0 mm, but with a different width range. For example, in a reaction substrate with channel widths from 1.0 to 1.5 mm (channel volumes from 48 to 30 mm3, respectively) as well as in a substrate with channel widths from 1.9 to 3.0 mm (channel volume from 95 to 60 mm3), the BZ excitation behavior in the channels was similar when channels had identical depths. This observation suggests that the volume-to-area ratio, that is, the relative area of the side walls and bottom surface of the channels (solution exposure to the plastic matrix), does not have a prominent effect on BZ excitability. Although the substrate material could influence the BZ reaction by absorption or release of specific molecules [16], it is therefore unlikely that the excitability modulation results to a significant extent from inhibitory interactions with the plastic channel boundaries.

In a final experiment, the BZ solution with 150 mM H2SO4 was prepared using the standard procedure described above, but with an additional nitrogen-purging step. Immediately before filling the substrate, the BZ reaction mixture was saturated with nitrogen gas by placing the gas outlet at the bottom of the glass vial with the BZ medium. When placed in the reaction substrate, this nitrogen-purged BZ medium exhibited a very different behavior in the channels than the non-purged medium: All channels supported BZ self-oscillations, irrespective of channel depth. Moreover, the frequency of the self-oscillations of nitrogen-purged BZ medium was higher than for non-purged reaction mixtures. Because N2 molecules are not thought to participate in the BZ reaction cycle [5], the effect of the nitrogen purging is most probably that all gaseous molecules are removed from the BZ mixture. We hypothesize that the purging procedure increased the excitability of the reaction mixture because it removed oxygen. However, the gases CO2 and Br2, which are generated by oscillating BZ medium [5], will also have been expelled, changing the properties of the BZ mixture to an extent that depends on the relative amounts of all the solubilized gases, which cannot be determined.

Because the BZ excitability depends on the depth of the channels rather than on their width (excluding prominent channel-wall effects) and the depth-dependent BZ inhibition is not observed after nitrogen purging, we postulate that the behavior of channel-confined BZ solution is influenced by the absorption of molecular oxygen from the air. Oxygen inhibition of BZ reactions is a well-known phenomenon, also specifically for the ferroin-catalyzed malonic acid system employed here (e.g., [24, 25, 27, 35]). Dissolved molecular oxygen can oxidize malonic acid and its intermediate species and may also interact directly with the radical (e.g., [14, 31]), thereby initiating additional chemical reactions, not captured in the original Field-Körös-Noyes and Oregonator models [5,7], that increase the concentration of bromide ions, and these inhibit the BZ reaction cycle. Oxygen effects can be avoided or minimized by using closed reaction chambers, without or with continuous nitrogen or argon purging (e.g., [24, 35]), preventing the BZ solution from coming into contact with air.

For non-stirred reaction mixtures exposed to air, absorption of molecular oxygen is expected to play a larger role near the top surface of the solution, while diffusion of oxygen into deeper regions of the solution may become apparent on longer time scales. Taylor et al. investigated the effect of oxygen absorption as a function of solution depth by using an optically transparent square reaction vessel and by imaging BZ oscillations from the side of this vessel, thus obtaining a BZ activity profile as a function of distance from the solution-air surface [31] rather than the conventional top-view lateral oscillation profile. For their ferroin-catalyzed malonic acid BZ reaction with 250 mM H2SO4, the authors observed that there is a layer of approximately 0.4-mm depth immediately below the solution-air interface, into which oxidation waves that were generated deeper in the solution could not penetrate, and attributed this effect to the absorption of oxygen from the air because wave inhibition was not observed under a nitrogen atmosphere [31].

In our study, top-view imaging is possible because our reaction substrates contain channels of different depth. As outlined above, we do not observe self-oscillations or triggered oscillations in channels that are shallower than ≈1.2–2.0 mm for our BZ mixtures that range in H2SO4 concentration from 150 to 210 mM. Although this represents a somewhat wider inhibition depth range than the 0.4 mm observed by Taylor et al. [31], these values are nevertheless comparable. The shallower inhibition depth measured by Taylor et al. could be explained by the different composition of their BZ medium [31]. For more active BZ reaction mixtures it can be expected that inhibition of wave formation requires a higher concentration of dissolved oxygen than less active mixtures, implying that complete inhibition can only be achieved at a closer distance from the solution-air interface, where the oxygen concentration is highest.

4 Conclusions

We have used 3D-printed reaction vessels with an open central well containing a self-oscillating BZ medium as a wave generator, and with open side channels of various width and depth as wave transmitters, to demonstrate that the BZ excitability is modulated by the channel geometry. This effect is attributed to a concentration gradient of dissolved molecular oxygen, with the highest concentration of oxygen at close distance to the air-solution interface. Hence, the same BZ solution can be self-oscillating in the central well but non-oscillating in the connected channels when these channels are relatively shallow. We have identified a depth range (2.0–3.2 or 2.0–2.6 mm, depending on the H2SO4 concentration) where the BZ medium in the channels ceases to self-oscillate but can still accept and propagate waves that are delivered by the central well.

These properties are favorable for networks of reaction wells that have multiple input channels and one or more output channels, as previously implemented, on a limited scale, by a variety of methods by several groups (e.g., [2, 28, 29, 34]). The approach presented here implies that the size and depth of physical wells can be designed such that a higher or lower concentration of excitatory BZ species is required to transmit a BZ wave over the well, from an input channel to an output channel. A stronger input signal (i.e., more chemical excitations arriving simultaneously) would be required when the inter-channel wells have a larger area or when they are less deep—respectively, because of more lateral diffusion or because of a stronger effect of oxygen inhibition. It is thus an enticing prospect to print reaction vessels with large numbers of closely spaced channels and wells, and to establish whether these networks are able to support more complex signal propagation properties than reported to date.

For example, Steinbock et al. implemented various and, or, and xnor gates by defining up to three wells with multiple input, inter-well, and output channels as light-exposed areas of immobilized catalyst in a continuous BZ phase, and envisioned that connecting such elementary logic elements would give a reaction substrate capable of a wide range of logic functions, especially when threshold-switch elements could be included [28]. In a related study, Stevens et al. also highlighted the functionality of areas of subexcitable BZ within a network, but did not implement these, because the required light intensity range is narrow and also varies for different locations in the substrate [29]. Notably, with the methodology described in this article, basic logic units of structured BZ medium can readily be interconnected by 3D printing of large numbers of reaction vessels, with threshold and subexcitability nodes defined by localized depth variations. Our approach thus enables a new direction in chemical information processing by imparting both structure and function to chemical oscillators in physical reaction substrates.

Acknowledgments

The authors gratefully acknowledge funding from the European Union through the “NEUNEU” FP7 Future and Emerging Technologies grant 248992.

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Author notes

Contact author.

∗∗

Computational Engineering and Design Group, Engineering Centre of Excellence, University of Southampton. Southampton SO16 7QF, United Kingdom. E-mail: p.h.king@soton.ac.uk

Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom. E-mail: cma1g09@ecs.soton.ac.uk (C.H.A.); kpz@ecs.soton.ac.uk (K.-P.Z.)

Electronics and Computer Science and Institute for Life Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom. E-mail: mdp@ecs.soton.ac.uk