Microfluidic Networks of the Compartmentalized Belousov-Zhabotinsky Reaction

Transcription

1 Microfluidic Networks of the Compartmentalized Belousov-Zhabotinsky Reaction Master s Thesis Presented to The Faculty of the Graduate School of Arts and Sciences Brandeis University Department of Biochemistry In Partial Fulfillment of the Requirements for the Degree Master of Science in Biochemistry and Biophysics by Thomas Litschel May 2016

2 Copyright by Thomas Litschel 2016

3 Acknowledgements Firstly, I would like to thank my advisor Seth Fraden for his support and guidance as a mentor. I would like to thank Matthew Cambria who introduced me to microfluidics processing, non-linear chemodynamics and was a big help during the first couple of months in lab. I would like to thank Ethan Chan, Xiaotong Geng, and Rémi Boros who contributed to most of what is shown in this thesis and with whom I had lots of fun. Finally, I'd like to thank my girlfriend Charlotte Kelley, and all my friends and family. III

4 Abstract Microfluidic Networks of the Compartmentalized Belousov-Zhabotinsky Reaction A thesis presented to the Biochemistry Department Graduate School of Arts and Sciences Brandeis University Waltham, Massachusetts By Thomas Litschel The oscillating Belousov-Zhabotinsky reaction provides an experimental system with which to study networks of coupled oscillators. We developed a method that allows for creating highly configurable coupled networks of Belousov-Zhabotinsky micro-oscillators. With novel microfluidic techniques we pattern custom planar arrays of nanoliter-scale wells into thin sheets of polydimethylsiloxane (PDMS). Once loaded into these compartments and confined by glass the oscillatory Belousov-Zhabotinsky reaction commences. The discrete oscillators are either inhibitorily coupled via diffusion through PDMS or excitatorily coupled via diffusion through thin channels connecting the wells. By varying geometrical parameters of the device s design, we are able to alter the strength and quality of the chemical coupling between these oscillatory cells and create network of heterogeneously interacting oscillators. Exploiting our ability to design network topology and the nature of the inter-cell coupling we construct chemical circuits that achieve the complexity of the autonomous nervous system of a variety of organisms. IV

5 Table of Contents Acknowledgements... III Abstract... IV Table of Contents... V List of Figures... VI Introduction... 1 Materials and Methods... 4 The Belousov-Zhabotinsky Reaction... 4 The Mechanism... 6 Fabrication of Microfluidic Chips... 9 Fabrication of Photoresist Master Fabrication of PDMS Device Loading device with BZ solution Imaging and Light Inhibition Experimental Results Spatio-temporal Patterns in Planar Networks Early Experiments without Controlling Initial Conditions Controlling In-Phase and Antiphase Initial Conditions with Light Waves in 1D Rows Nonhomogeneous Networks (Central Pattern Generator) Quantification of Inter-Cellular Coupling Conclusion Bibliography V

6 List of Figures Figure 1.0.1: Schematic of wells in PDMS loaded with BZ with interactions... 2 Figure 2.1.1: Oscillatory color changes of the BZ reaction in a beaker... 5 Figure 2.1.2: Scheme illustrating the key processes during the BZ reaction... 6 Figure 2.1.3: Vanag-Epstein Model of the Belousov-Zhabothinsky reaction... 9 Figure 2.2.1: Illustration of the intermediate products of the fabrication process Figure 2.2.2: 3D topographical false color image of a two layer microfluidic chip Figure 2.2.3: Fabricating a thin PDMS device Figure 2.3.1: Clamping device used for sealing the PDMS chip loaded with BZ solution Figure 2.4.1: The optical layout of the PIM with distances between elements Figure 3.1.1: Microfluidic PDMS chips filled with the oscillating BZ reaction Figure 3.1.2: Scheme that illustrates ideal oscillatory patterns for arrays of inhibitory coupled wells Figure 3.1.3: Square array of oscillators trained for antiphase oscillations Figure 3.2.1: Experiment with light-isolated 1D colums Figure 3.2.2: Wave speed analysis Figure 3.3.1: Example for biological central pattern generator Figure 3.3.2: BZ implementation of a central pattern generator Figure 3.4.1: Experiments for quantifying the coupling between neighboring wells Figure 3.4.2: Phase response curve to perturbation by an oxidation spike from neighboring wells VI

7 Introduction There are numerous examples of both natural and artificial networks of coupled oscillators. Systems as diverse as the heart [1], a group of fireflies [2], and a power grid [3] can all be modeled as such networks. Despite their ubiquity in nature, there are few experimental systems with which to study networks of coupled oscillators and those that do exist have numerous limitations. The oscillating Belousov-Zhabotinsky (BZ) chemical reaction provides a convenient system with which to study these networks. Existing approaches of utilizing the BZ reaction, such as with coupled reactors [4, 5], catalyst beads [6-8], in millimeter-scale polydimethylsiloxane (PDMS) arrays [9, 10], or in an surfactant stabilized water-in-oil emulsion environment [11-17], are limited in either their ability to control their network topology, boundary conditions or quality and strength of coupling. We developed an experimental method based on microfluidic chips fabricated by soft lithography that allows control over these properties. Besides limitations in the aspect ratio of the features, this method shows few restrictions in terms of two dimensional topology of the microfluidic device, which allows us to create custom planar networks of oscillators. Furthermore, we can not only control coupling strength of one type of coupling, but tune this property separately for inhibitory and excitatory coupling of oscillations. To control boundary and initial conditions we use externally applied light. This technology enables synchronization engineering [9, 10, 18-20] of networks of nonlinear chemical oscillators for applications in fields such as soft robotics [21-23]. The BZ reaction is a metal ion-catalyzed oxidation of an organic substrate in which chemical concentrations of reactants and products oscillate over time [24]. It is the prototype of nonlinear 1

8 dynamics in chemistry [13] and a preferred system for exploring the dynamics of coupled nonlinear oscillators [25]. In previous work [11-15, 17] we studied aqueous droplets containing the oscillatory Belousov Zhabotinsky (BZ) reaction, separated by narrow gaps of a fluorinated oil in 1-D and 2-D geometries. In this system interdrop coupling is governed by the non-polar communicator of inhibition, Br2, which diffuses between droplets through the polar oil that separates the droplets, resulting in anti-phase attractors. The permeation of BZ chemicals in PDMS and oil are very similar. PDMS is an organic elastomer so like in emulsion, the non-polar bromine will diffuse between reactors [26]. BZ solutions that are fully separated by PDMS are therefore inhibitory coupled. In addition to inhibitor-coupling, here we have the ability to construct channels between wells, allowing a connection of continuous BZ solution between reactors and therefore a diffusion of all BZ species. Since in continuous BZ solution the activator species dominated the coupling, wells with direct channels are activator-coupled (see Figure 1.0.1). Figure 1.0.1: Schematic of wells in PDMS loaded with BZ and the interactions between BZ compartments. Red: BZ solution. Blue: PDMS. Purple arrows: permeation flux. Yellow arrow: fluid connection. 2

9 We fabricate our microfluidic chips using standard photo- and soft lithography techniques. The chip consists of an 80 µm µm thin sheet of PDMS attached to a microscope glass slide; the wells are patterned into the sheet of PDMS. Due to the permeability of PDMS to all apolar species of the BZ reaction, it is essential for our experiments to minimize the layer of excess PDMS beneath our features. In order to maintain BZ oscillations for several hours and to observe the desired coupling, the microfluidic wells must be sealed. The BZ solution cannot come in contact with any kind of gas and the independent compartments must not be connected by excess BZ solution. To achieve these conditions, we designed a clamping device that allows us to isolate the desired volume from air by a glass lid and apply pressure in a way that all wells are evenly sealed (see Chapter 2.3). To control boundary and initial conditions we use a Programmable Illumination Microscope (PIM) consisting of a computer projector reconfigured to couple 450 nm light into the microscope to inhibit individual oscillators of the photosensitive BZ reaction (see Chapter 2.4). 3

10 Materials and Methods The Belousov-Zhabotinsky Reaction The BZ reaction is an oscillating chemical reaction discovered in the 1950s by the Russian biochemist Boris Belousov. He was attempting to make a chemical system imitating the Krebs cycle by mixing citric acid and bromate ions in a sulfuric acid solution, along with a cerium catalyst. He observed that the color of the solution he created spontaneously oscillated between two colors. This reaction was investigated further by Anatol Zhabotinsky, who investigated wave propagation in thin, unstirred layers of BZ solution [27, 28]. The BZ reaction soon became a standard chemical system used to study nonlinear dynamics quantitatively in a controlled, experimental system [29]. Boris Belousov was not accredited until several years after his death for his discovery since it was considered impossible to exist [30]. Chemical reactions generally proceed directly towards equilibrium and an oscillating chemical reactions seem to violate the 2nd Law of Thermodynamics. However, the 2nd Law of Thermodynamics does not necessarily forbid reactions from oscillating toward equilibrium, which is what happens in the BZ reaction. Therefore, such chemical oscillators can exist far from equilibrium, from which the system's entropy gradually increases with each oscillatory cycle. 4

11 Figure 2.1.1: Oscillatory color changes of the BZ reaction in a beaker. Here with different reagents and faster cycles than the reactions studied in this project. [Source: Wikipedia entry for Belousov Zhabotinsky reaction] The BZ reaction follows two pathways: one involving an auto-catalytic process and a second that inhibits the autocatalysis (compare Figure 2.1.3). Figure shows a sequence of a continuously stirred beaker. The blue color change is due to the autocatalytic oxidation of the catalyst, corresponding to the oxidized state, while the red color corresponds to the reduced state, where the oxidized catalyst is being reduced. Since the beaker is continuously stirred, the color change occurs almost simultaneously throughout the entire beaker. In an unstirred solution, i.e. in a petri dish filled with BZ solution, the BZ reaction exhibits spatial oscillations observable as concentric and spiral waves [31]. In this thesis however, we will focus on BZ reactions confined in micron-scale compartments that we assume to behave like a distinct homogeneous oscillator. There are several versions of the BZ reaction that use different organic substrates and metallic catalysts. The reaction used here employs malonic acid as the organic substrate involved in the oxidation of the catalyst, ferroin redox indicator (which will be referred to simply as ferroin) as a metal catalyst, and tris-bipyridine-ruthenium (II) chloride (referred to as Ru(Bipy)3) as a 5

12 photosensitive co-catalyst. These reagents are mixed together in aqueous solution in the concentrations listed in Table Name Chemical Formula Concentration Malonic Acid CH 2(COOH) mm Sulfuric Acid H 2SO 4 80 mm Sodium Bromide NaBr 10 mm or 25 mm Sodium Bromate NaBrO mm Ferroin C 36H 24FeN mm Ru(bipy) 3 C 30H 24N 6Cl 2Ru 6H 2O 1.2 mm Table 2.1.1: List of the reagents used in the Belousov-Zhabotinsky reaction with the common name, the chemical formula of each reagent and the concentrations used. The Mechanism Figure 2.1.2: Scheme illustrating the key processes during the BZ reaction [32]. Lines associated with different reactions are marked in a different color. For reaction equations see below. MA = malonic acid. BrMA = bromomalonic acid. [Source: Guzowski, J., et al. (2016)] 6

13 The BZ mechanism in its entirety is extremely complicated, with models containing up to 80 elementary reactions and 26 chemical concentration variables [33]. One popular simplification to 7 variables is known as the Field-Körös-Noyes mechanism [34]. In the first process, the inhibitor is being consumed. Once the inhibitor reaches a critically low concentration, the autocatalytic process (Process 2) starts, and the metal species is oxidized at a rapid rate. At a sufficiently high concentration of the oxidized metal, Process 3 takes place where the inhibitor will be produced at a rapid rate, and oxidation will be inhibited. At the same time, the oxidized metal is being reduced by malonic acid. The reaction then repeats starting with Process 1. The equations below (also compare Figure 2.1.2) show the major chemical reactions which characterize these three general processes [11]. Process 1 2 H + + BrO3 - + Br - HBrO2 + HOBr (light green line in Figure 2.1.3) H + + HBrO2 + Br - 2 HOBr (yellow line in Figure 2.1.3) HOBr + Br - + H+ Br2 + H2O (black dashed line in Figure 2.1.3) Br2 + CH2(COOH)2 BrCh(COOH)2 + Br - + H + (dark purple line in Figure 2.1.3) Process 2 BrO3 - + HBrO2 + H + 2 BrO2 + H2O (brown line in Figure 2.1.3) H + + BrO2 + Fe(phen)3 2+ Fe(phen) HBrO2 (brown line in Figure 2.1.3) 2 HBrO2 BrO3 - + HOBr + H + (light blue line in Figure 2.1.3) 7

14 Process 3 2 H2O + BrCH2(COOH)2 + 4 Fe(phen) Fe(phen) Br - + HCOOH + 2 CO2 + 5 H + (light purple line in Figure 2.1.3) 2 H2O + CH2(COOH)2 + 6 Fe(phen) Fe(phen) HCOOH + 2 CO2 + 6 H + (dark green line in Figure 2.1.3) Another crucial chemical process in our BZ system involves the light-sensitive reagent Ru(bipy)3. When Ru(bipy)3 is exposed to light at 452 nanometers in wavelength (blue light), the ruthenium catalyst goes to an excited state and is oxidized by brominated malonic acid in the solution, releasing a bromide ion as a byproduct [25, 35]. Therefore, by exposing a sample of BZ solution to blue light, inhibitory ions can be produced in order to either elongate the period of the reaction cycle or suppress the reaction completely. Ru(bpy) hν Ru * (bipy)3 2+ BrCH2(COOH)2 + Ru * (bipy)3 2+ Ru(bpy) Br - An even more reduced model of the Belousov-Zhabotinsky reaction is the four-variable model developed by Vladimir Vanag and Irving Epstein [25]. In future work we want to compare simulations using this model with our experimental results. Figure shows the two variables of the model most crucial to understanding the oscillatory behavior of the Belousov-Zhabotinsky reaction. 8

15 Figure 2.1.3: Vanag-Epstein Model of the Belousov-Zhabothinsky reaction. Red: Concentration of the oxidized state of ferroin. Blue: Concentration of Br - ions. Fabrication of Microfluidic Chips Our microfluidic chips consist of an 80 μm 100 µm thick layer of silicone rubber (PDMS) which contains arrays of nanoliter sized wells attached to a 25 mm x 75 mm x 1 mm microscope glass slide (see Figure bottom). PDMS is a commonly used material in soft lithography and is relatively impermeable to polar species, but highly permeable to apolar gases and fluids. This makes it important to minimize the amount of PDMS beneath our features. This new approach of compartmentalizing BZ reactions using microfluidic devices, allows us to define the geometrical parameters of the compartments. For typical dimensions of the features, see Figure. The manufacturing of our chips is a 2-step process using photo- and soft lithography (Figure 2.2.1). The first step is to create an inverse master by curing UV-sensitive photoresist on a silicon wafer using a photomask. In the second step we use this master as a mold to cure PDMS with imprints of the features. 9

16 Figure 2.2.1: Illustration of the intermediate products of the fabrication process. From top to bottom: Photomask, silicon-photoresist master and final chip. Structures are not to scale. Fabrication of Photoresist Master We create a photoresist master with the desired features in inverse using standard photolithography methods with a silicon wafer as a base. Briefly, this means spin coating SU-8 negative photoresist on a silicon wafer, soft-baking the photoresist prior to the UV light exposure, placing and aligning a photomask with the desired features on the photoresist, UV-exposing the photoresist, hard baking the photoresist, and developing the master with propylene glycol methyl ether acetate. We design the photomasks using Autodesk AutoCAD and have them printed externally in high resolution. 10

17 Figure 2.2.2: 3D topographical false color image of a two layer microfluidic chip (final PDMS chip) taken with an optical profiler. The wells have a side length of 105 µm and are 100 µm deep. Channels are 60 µm long, 20 µm wide and 20 µm deep. A similar chip was used in the experiment shown in Figure (A)-(C). Certain experiments, such as those shown in Section 3.2 and 3.4, require a microfluidic device whose features are not uniform in height. The channels in the devices used for these experiments are thin in height and do not reach the bottom of the wells (see Figure 2.2.2). In order to make chips with such features, we must spin, expose and bake two layers of photoresist with two different photomasks on top of one another. This requires the alignment of the second photomask on the intermediate chip after curing the first layer of photoresist. We include alignment marks on the photomask designs for this purpose. These alignment marks are visible on the first layer of the device and therefore can be used to align the second photomask according to the first layer. To increase the visibility of these alignment marks we perform a partial development of the intermediate chip in which only the areas in which the alignment marks are located are developed [36]. 11

18 Fabrication of PDMS Device Figure 2.2.3: Fabricating a thin PDMS device. A silicon-photoresist master with the desired features in inverse is placed in a square dish on top of a sheet of aluminum foil, a sheet of mylar and a glass spacer. 10 g of PDMS are poured over the features and degassed. Two glass slides taped together by invisible tape are plasma cleaned and placed on the PDMS. Another mylar sheet is placed over the glass followed by some spacer glass slides so that a heavy weight can be put on top of the stack. The second part of the fabrication process is done as shown in Figure We place a 50 mm x 75 mm glass slide on the bottom of a square dish as a spacer and to provide an even surface. Then we line the dish with a sheet of Mylar to facilitate the disassembly after curing and a sheet of aluminum foil to keep the sheet of Mylar in place. Next we coat the silicon-photoresist master with Cytop and place it in the center of the lined dish. Cytop is an amorphous fluoropolymer which, among other applications, is used as a mold release agent. We mix 10 g of PDMS (Dow Corning SYLGARD 184 Silicone Elastomer Kit) with a centrifugal mixer (Thinky planetary nonvacuum centrifugal mixer) and pour it onto the master. The centrifugal mixer limits bubble 12

19 formation during mixing, but does not prevent air from being trapped in the small features of the master after pouring. Therefore, we vacuum pump the setup for 10 to 20 minutes in order for the bubbles to enlarge, float to the top and pop. We use invisible tape to join two Gold Seal 25 mm x 75 mm microscope slides and plasma clean them with our Diener Zepto plasma cleaner. After plasma cleaning, the two glass slides are placed immediately onto the degassed PDMS, with the taped sides facing up. Another Mylar sheet is placed over the carrier glasses followed by several more spacer glasses so that a lead weight can be put on top without touching the rim of the petri dish. We let the PDMS cure for 6-12 hours at room temperature before replacing the heavy weight with a lighter weight so that we are able to put the entire setup in an 80 C oven for another hours. After curing the setup is carefully disassembled. The PDMS sheet of these microfluidic devices is very thin and has almost the same thickness as the height of its wells. The devices we fabricate have on average a layer of only 5 µm of excess PDMS beneath the features. This has shown to be crucial for our experiments. A thick layer of excess PDMS beneath the features results in less or no noticeable inhibitor coupling between wells. We assume that this is due to the inhibitory species of the reaction (bromine) diffusing into the unsaturated PDMS. A larger volume of PDMS results in the bromine mainly diffusing into the PDMS and less diffusion of bromine as an inhibitor between wells. For this reason, we also take actions to saturate the PDMS before starting an experiment (see Section 2.3). The critical step in fabricating these devices with thin sheets of PDMS is the separating of the final chip from its photoresist master after curing. Since the surface area between master and chip is larger than the surface area between PDMS and glass slide, the probability is high that parts of the PDMS stick to the photoresist master when trying to separate the two. Therefore, it is essential to have a strong bond between PDMS and glass, as well as a weak bonding between PDMS and 13

20 master. As mentioned this is done by plasma cleaning the glass surface and by coating the master with Cytop. The development of an efficient method for fabricating the devices presented in this thesis was a major part of this project. The existing methods did not allow for highly detailed features as necessary for the experiments presented here and involved 2 additional steps for transferring the structures of the rigid silicon and photoresist master to a flexible polyurethane master before the final step [17]. The use of Cytop as a coating agent and other improvements finally led to the simplification of the process and the ability to form features as small as 20 µm wide channels. Loading device with BZ solution In order to maintain BZ oscillations for several hours and to achieve the desired coupling, the microfluidic wells have to be properly sealed. The BZ solution must not come in contact with any kind of gas and the BZ compartments should not be connected by excess BZ solution. To achieve these conditions, we designed a clamping device (Figure 2.3.1), which isolates the desired volume from air by a glass lid and applies pressure in a way that all wells are evenly sealed. The device consists of a bottom and top clamp frame that has been laser cut from of acrylic glass plates. A rubber O-ring encloses an additional reservoir of BZ solution surrounding the sealed area to diminish concentration gradients and diffusion from the inside through the PDMS. The PDMS wells are sealed by a square glass window attached to a 25 mm x 25 mm glass slide. A round PDMS window attached to another 25 mm x 25 mm glass slide allows for even and orthogonal pressure and thus prevents the sealing glass from bending when pressure is applied. 14

21 Figure 2.3.1: Clamping device used for sealing the PDMS chip loaded with BZ solution. From bottom to top: Screws, bottom plexi glass clamping frame, microfluidic device, rubber O-ring, sealing window, pressure equilizer window, top plexi glass clamping frame, washers, screw nuts. For simplification purposes the microfluidic device has only one array of wells. We use devices with 15 separate arrays. The size of the array with wells is depicted larger than it is. (A) Side view. (B) Top view. Before the BZ solution can be put onto the PDMS chip, the chip needs to be plasma cleaned in order to charge the PDMS surface and make it hydrophilic. Due to the small size of the wells and the hydrophobicity of PDMS (and the surface tension of the aqueous solution) skipping this step prevents BZ solution from properly filling the wells. We mix the 6 reagents of the BZ reaction together in aqueous solution and immediately pipette the solution onto an array of wells. We then place the setup into our clamp, and the device is tightened under a microscope so that a slight degree of compression is visible, which we assume guarantees proper sealing. Before we start recording we wait for 30 to 40 minutes. This has shown to be crucial when choosing high initial concentrations of NaBr, since a premature mounting onto the PIM and a concomitant exposure to low levels of light cause oscillations to not set in or even an already ongoing oscillating reaction to decease. 15

22 We choose a high concentration of NaBr because it has shown to provide stronger inhibitory coupling in the beginning of an experiment and therefore an overall more constant level of inhibitory coupling over the course of an experiment. We assume that this is due to time it takes for the PDMS to saturate with bromine, the inhibitor species of the reaction. We assume that if the PDMS is not saturated with bromine, less bromine diffuses between wells. At the same time this high initial concentration of bromide/bromine delays the onset of oscillations. The bromine decays over time and the reaction only starts after the concentration falls under a certain threshold. Exposure to light produces bromide (due to the light sensitive Ru(bipy)3), lets the concentration decrease slower and therefore an early exposure to light increases the initial delay by a multiple. Imaging and Light Inhibition A schematic of our microscopic setup, the programmable illumination microscope (PIM), with optical paths is displayed in Figure We illuminate our sample with a uniform Köhler illumination using a cyan LED and a green filter that filters light of a wavelength of 510 ±10 nm. Green light does not significantly excite Ru(bipy)3, but at the same time is very well suited to capture the BZ oxidation spikes. This is because green light is absorbed by the red colored ferroin, but transmitted through the blue colored ferriin [12]. When imaged by the black-and-white CCD cameras we use, the BZ solution appears bright in the oxidized state and dark in the reduced state, as seen in various figures in the result section like Figure and Figure With the PIM we furthermore have the ability to control the oscillations of the BZ reaction by light inhibition. It allows us to shine light on specific regions as small as a fraction of a single well. It consists of a commercial three-color liquid-crystal display (LCD) projector with the optics inverted so that it focuses inward instead of outward. It is coupled with MATLAB code that is able to detect, 16

23 track, and project light onto individual wells [37]. The PIM has various possible applications but was specifically developed for light inhibition in the BZ-emulsion system. It required only a few modifications to make it suitable for our system with microfluidic PDMS chips. Figure 2.4.1: The optical layout of the PIM with distances between elements [37]. The different optical paths are shown in different colors. [Source: Tompkins, N., et al. (2016)] We project blue light with a wavelength of about 452 nm such that it excites the Ru(bipy)3 and as a result can inhibit oscillations in particular wells as discussed in Section 2.1. We have control over size, shape and intensity of the projected areas and thus have control over how much and what regions of the BZ reaction are inhibited. 17

24 We use two different illumination approaches to control oscillations. One uses constant illumination to inhibit droplets, one quasi-constant illumination. The experiments described in Section 3.4 require feedback over the oxidation state of the BZ reaction to determine period time. In order to be able to process the data in real time we create 5 second cycles in which an image is taken, calculations are done and light is projected for 30% of the duty cycle (1.5 seconds). Because the frequency of oscillation is much smaller than the frequency of pulsed light, we can consider these light pulses as the equivalent to constant light at reduced intensity. 18

25 Experimental Results Spatio-temporal Patterns in Planar Networks Early Experiments without Controlling Initial Conditions In order to verify our new experimental system, we started with qualitative experiments without the intention of further analysis of the data or quantitatively comparing results. First experiments were done with wells in hexagonal arrays analogous to the BZ emulsions. Despite positive results, we soon switched to wells in square arrays, due to the simpler network topology. Figure shows snapshots and space-time plots (also known as kymographs) of four different experiments: experiments with hexagonal arrays of hexagonal wells, and experiments of square arrays of square wells. For each case there is one experiment with channels connecting the wells and one experiment with PDMS fully isolating the wells from another. 19

26 Figure 3.1.1: Microfluidic PDMS chips filled with the oscillating BZ reaction with 4 different microfluidic designs. Left side: Single frames of recorded experiments. Right side: Space-time plots along the red lines in snapshots on left side. (A) Hexagonal array of hexagonal wells connected by channels. Wells have an outer diameter of 270 µm and are 100 µm deep. Channels are 20 µm wide, 60 µm long and 100 µm deep. (B) Same dimensions as in (A) but without channels. (C) Square array of square wells. Wells are 218 µm wide and 115 µm deep. Channels are 20 µm wide, 15 µm deep and 60 µm long. (D) Square array of square wells. No channels connecting the wells. Square wells are 151 µm wide and 80 µm deep. 20

27 The results of our first experiments matched our expectations based on what we know from the emulsion system studied previously in our group, and from the BZ reaction in a continuous media. We observe waves of oxidation spikes for designs in which channels interconnect wells and oscillation patterns similar to those in BZ emulsions for the wells without BZ connections. In most experiments with excitatory coupling we saw waves that originate from a single well and then propagate in as concentric wave across the chip. This center of the wave was not stationary in most experiments but changed its location over time. In some cases, we saw several points from which the waves start propagating and in some others even lines (like the border of the array) from which waves originate. In experiments with only thin channels connecting the wells we observe the waves getting disrupted, splitting the array in 2 or more areas with separate waves. A similar behavior is noticeable in the 1D waves in Figure (D)-(F). In experiments with inhibitory coupled wells it was apparent that neighboring wells are very unlikely to oscillate in phase but with a maximal phase shift to each other. In videos these out-of phase oscillations seem rather chaotic across the whole array, but in space-time plots a pattern is more apparent (see Figure (D) and (H)). Controlling In-Phase and Antiphase Initial Conditions with Light Even though the experiments with arrays of wells that are fully separated by PDMS did clearly show local behavior that lets us assume strong inhibitory coupling, they did only show mediocre global patterns of an antiphase behavior. We assume that for a square array the preferred state for wells that are inhibitory coupled is a state in which half of the reactors oscillate together at a phase A and then half an oscillation period time later, the rest of the wells oscillate at a phase B. Wells that oscillate at time A and wells that oscillate at time B are distributed in a way that all the nearest neighbors of an A-well are B-wells and vice versa (Figure (A)). For a hexagonal array we 21

28 assume the ideal state to not be an A and B scenario with 180 phase shifts, but an A, B and C scenario with 120 phase shifts (Figure (B)). Figure 3.1.2: Scheme that illustrates ideal oscillatory patterns for on array of inhibitory coupled wells. (A) Square array of wells, oscillators illustrated in blue and oscillaors illustrated in green are phase shifted by 180 to each other. (B) Hexagonal array of wells. Oscillators of one color are 120 phase shifted to oscillators in a different color. In certain experiments we initially force the BZ reactors into these out-of-phase patterns of oscillations. To do this we apply initial conditions with light. As mentioned in Section 2.4, we can inhibit specific reactors from oscillating with our PIM by shining light on individual well. We assume that for the time of inhibition the wells are approximately fixed in a chemical state and by releasing the light they start their oscillation at a certain state in their limit cycle. Therefore, by having two reactors inhibited but then releasing them with a phase difference of half an oscillation period from each other, we expect them to begin to oscillate with this phase shift. We can apply these initial conditions not only on pairs of wells, but also for the pattern described above (and illustrated in Figure 3.1.2). Figure shows an experiment in which we used this approach for an array of square wells. 22

29 Time in sec Figure 3.1.3: Square array of oscillators trained for antiphase oscillations. (A) Frame of an experiment. Trained wells are marked in blue and green. Wells of one color are supposed to oscillate together and be phase shifted to wells of the other color by 180. Outer row of wells is light inhibited througout the entire experiment to provide better boundary conditions. Red line indicates line for space-time plot in (B). (B) Space-time plots referring to the red line marked in (A). The light inhibition can be seen. First all wells are light inhibited, then every other well gets lightreleased (and oscillates) and in the third stage only the outer wells are illuminated. (C) Histogramm of oscillations of the two groups of wells. The number of oscillation spikes for each group seperately is counted in 10 second wide histogram bins. The colors of the two histogram curves refer to the groups of wells marked in that color in (A). The space-time plot in Figure (B) shows that we were able to train the oscillators so that they begin oscillating in the desired pattern. In contrast to our expectations the oscillations did not happen exactly in phase but with a small phase difference resulting in a spatial time delay gradient, which was observable as waves. These waves are present from the beginning but become more distinctive over time as the wave speed decreases. Figure (C) shows a histogram of oscillation 23

30 spikes over time. The two groups of wells (referred to as A and B above) ore separated in two histogram curves (green and blue). The slowing down of the wave results in a flattening of the peaks over time and a broader distribution of the counts within one oscillation wave. The initial conditions in the experiment shown in Figure are set in a way that the initial phase shift is not 180 but about 260 (in Figure (C) it appears as since the very first oscillation wave is not shown). But the histogram and the space-time plot show that over time the oscillations shift toward the preferred 180 phase difference. Waves in 1D Rows To gain a better understanding of a system with excitatory coupling we wanted to take a closer look at the traveling waves in a design with channels connecting wells. Specifically, we want to determine if and how the speed of a propagating wave through an array of wells depends on certain geometrical parameters. First attempts to look at wave speed in 2D square arrays of wells taught us to rather restrain the oscillations to one dimensional rows. We create these one-dimensional rows by using our PIM to inhibit certain regions of the square array in a way that only chains of wells are uninhibited. 24

31 Figure 3.2.1: Experiment with 1D colums. BZ in square wells in a square array connected by channels. 1D colums of wells are light isolated. (A) Wells are 105 µm wide and 115 µm deep. Channels are 20 µm wide, 60 µm long and 20 µm deep. All wells except for 4 colums of wells were light inhibited. The light inhibition is barely visible, but in each uninhibited column one reactor can be found that is undergoing a color change. (B) Space time plot that shows one out of the four uninhibited columns (marked in red in (A)). (C) Magnified region of the space-time plot in (B). (D) Array of wells with a side length of 218 µm and 115 µm deep. Channels are 20 µm wide, 60 µm long and 20 µm deep. In this experiment all wells except for 3 colums of wells were light inhibited. (E) and (F) show two out of the three colums in this experiment. Since the two experiments were recorded with different frame rates, the space-time plots have different time resolutions. In first experiments we compared designs with different sizes of square wells while keeping channel size and distance between wells constant. Figure shows two such experiments. Our observations when changing the size of the wells showed us that changing this parameter not only affects one but several properties of the row that have an effect on wave behavior: by altering the 25

32 size of the wells, not only the volume of BZ solution inside one well is being varied, but also the number of channels per distance and the area through which inhibitory coupling takes place. We observed that with large wells a propagating wave often gets disrupted. An interesting observation is that the location where the wave gets disrupted propagates, visible as diagonal gaps in the spacetime plots in Figure (E) and (F). We think the increased likelihood of a wave being blocked, is due to the larger area of the PDMS wall separating the wells and therefore increased inhibitory coupling. At the same time, a wave traveling through such a row of large wells is faster than a wave through a row of small wells (compare Figure (A) with Figure (B)). This might be due to the fact that there are more (narrow) channels per distance. This does in theory not agree with a simple model of waves in excitable media, in which a more narrow passage shouldn t slow down a wave, but could be explained by a suppression of the chemical wave due to the very thin channels and a purely diffusive intracellular communication [38-40]. In future experiments we want to investigate the effects of each of the mentioned parameters independently. We would test inhibitory coupling by altering the width of the wells but not the volume; and we would investigate the implications of the amount of channels by varying number of channels but not width of the row. In another series of experiments, we varied the height of the channel, while keeping all other geometrical parameters constant. We did this by altering the ratio of channel height to height of the total well with our 2-layer fabrication method (Figure and following text). In these experiments we had several experimental problems and were not able yet to quantitatively compare our results to a satisfying extent. 26

33 Figure 3.2.2: Wave speed analysis. (A) Graph that shows the change of the wave speed in one column over the course of an experiment with the chip with 105 µm-wells shown in Figure (A)-(C). Each point represents one complete traveling wave. The wave speed is calculated with the time difference in oxidation spikes of two distant wells in the column. (B) Graph that show sthe change of the wave speed over the course of the experiment with 218 µmwells shown in in Figure (D)-(F). Since the experiment was recorded with 20 times less frames per second and the waves don t travel across the entire width of the array this graph is less precise than the one in (A). (C) Period time over time of the two distant wells that were used to calculate the wave speed in (A). (D) Graph that shows the spatial change in wave speed. The wave speed slows down as the wave propagates. We think this behavior in combination with a moving wave origin causes the curve in (A) to increase after reaching a minimum and also causes the wide distribution in (B). One consistent observation throughout all experiments is the decreasing speed of traveling waves over the course of the experiments (Figure (A) with Figure (B)). This decrease takes place during the first few oscillations, most likely because during that initial phase the PDMS is not saturated with the inhibitory BZ species. Due to the fact that in the large wells most waves don t travel across the entire width of an array, it was more difficult to measure wave speed in these experiments. We generated Figure (A) by using the times of oscillation spikes of two wells in one column of the recording, while in Figure (B) we included measurements over several columns and positions from one recording. Figure (C) shows the period time of two wells 27

34 over the course of a recording. It was surprising to us that even though the wave speed changes, the period time of the oscillation stays approximately constant, from which follows that the wavelength of the wave decreases over time. Another unexpected observation is the spatial decrease in wave speed. We observed that the wave speed is the highest at the origin of the wave and then slows down over distance. Figure (D) shows this behavior. It is also visible in Figure (C) as the diagonals have a certain curvature. This last mentioned behavior makes it more difficult for us to quantify the wave speed, especially because we lack control over where waves originate. (We think this causes the wave speed in Figure (A) to increase again after reaching a minimum and also causes the wide distribution in wave speed in Figure (B).) We want to address these problems in future experiments with the following changes: To gain control over the origin of waves we want to create a pacemaker well through low levels of light inhibition (below the threshold of complete inhibition) or light gradients. To have more spatially consistent wave speed we want to do experiments with the Belousov- Zhabotinsky reaction in its excitable state instead of the self-oscillatory state. In this state the reaction does not oscillate, but waves can be triggered. Here the reaction is an excitable media for which the behavior of waves is well studied and easier to understand [31, 41]. We think we can achieve this state through light inhibition; in this case one oscillating well would also serve as a pacemaker and at the same time as a trigger. Non-homogeneous light inhibition and diffusion of too much bromine from surrounding, inhibited wells is another problem in these experiments. The projector we use does not project spatially homogeneous light, which is an experimental issue for several reasons. One effect is that some non-illuminated wells or entire columns get inhibited through production of too much bromine in 28

35 surrounding wells. We want to address this problem on two levels: by improving the PIM to provide more constant illumination; and by fabricating designs specifically for these 1D experiments with 1D columns that are isolated from surrounding BZ reservoirs. Nonhomogeneous Networks (Central Pattern Generator) We think that we created a unique system in which we can create custom networks of controllable interacting oscillators. With the microfluidic design we can not only determine network topology, but also chose between inhibitory and excitatory coupling. This means we are not restricted to homogeneous arrays in terms of coupling quality, but are able combine the two forms of coupling in non-trivial ways. We think with the system presented in this thesis we provide a foundation for soft robotics. As a first step, we want to create central pattern generators (CPGs), a basic component found in animal nervous systems. Figure 3.3.1: Example for biological central pattern generator. Neurons running down the spinal column are excited in sequence causing the musculature to contract, thereby propelling the lamprey1. (a) Waves of muscle contraction in swimming fish. (b) Spinal cord with left and right paired neurons. (c) Time trace of neural firings for two pairs of neurons. [Figure based on: Murray, J.D. (2002)] CPGs produce rhythmic signals controlling periodic behavior, e.g. walking of a human and swimming of a lamprey. The swimming motion of primitive vertebrates, like lampreys, is caused by neural signals propagating along their spinal cord (Figure 3.3.1). The bursts in neural activity 29

36 travel down the spinal cord as a wave, while two laterally opposed neurons within a segment of the spinal cord are phase locked 180 out of phase (Figure (B)) [42]. Given that coupled Belousov-Zhabotinsky (BZ) reactors in a polydimethylsiloxane (PDMS) system can interact in both, an excitatory and an inhibitory fashion, a BZ-based system allows us to construct an artificial CPG. Figure 3.3.2: BZ implementation of a central pattern generator. (A) Reduced schematic of a central pattern generator. Wells are horizontally connected by channels, causing activator coupling, but vertically sperated by PDMS. (B) Snapchot of micropfluidic central pattern generator loaded with BZ solution. Light inhibited BZ wells surround the CPG. (C) space time plots along blue and purple line showing inhibitor coupling resulting in antiphase oscillations over time. (D) space time plot along green line showing traviling waves along the row of interconnected wells. Figure (B) shows the microfluidic device that we consider a central pattern generator consisting of two inhibitory coupled rows. Figure (A) shows a schematic of the interactions between wells. We create excitatory coupling between cells within one row, by implementing direct channels. The presence of an intact PDMS layer between parallel cell rows will by itself create inhibitory coupling. The excitatory coupling along the row as opposed to the inhibitory coupling laterally will imitate the neural signaling system of a lamprey CPG as in Figure Initial experiments with our microfluidic CPG devices where successful as the space time plots in Figure (C) and (D) show. The waves fire in a pattern analogous to that observed in the living models. In future experiments we will vary the strength of excitatory vs. inhibitory coupling, 30

37 the amount and pattern of inhibitory light exposure and size and network topology of BZ cells in order to optimize oscillation behavior and lifetime. The CPG is only the first component towards creating bioinspired soft robotics. With this BZ in PDMS-model we try to imitate the neural part of biological swimmers. In future work we will optimize the second component, which is the imitation of muscular tissue with hydrogels. Biological systems have developed ways of converting chemical energy to motion that are more efficient and environmentally benign than in man-made machines. With volume changing hydrogels we want to create bioinspired materials with these properties. The working principle of poly N-isopropyl-acrylamide (pnipam) gels is based on an intrinsic BZ reaction: the redox wave of the reaction serves as the energy source of contractions [43]. Thus, the BZ CPG can eventually be coupled to a contractile gel to serve as the initiator and regulator of those contractions. Quantification of Inter-Cellular Coupling We attempt to quantify the coupling between wells by looking at pairs of wells. We examine the influence on a reactor s oscillatory cycle when a neighboring reactor is released from photoinhibition to allow it to undergo one oxidation spike. This releases chemicals into the oscillating cell through diffusion. Depending on whether the pair of cells is connected by BZ or fully isolated by PDMS, this causes either elongation or shortening of the first reactor s oscillatory cycle. We plot the response to stimulations at different points in its cycle is modeled in a phase response curve. Each point on the curve is determined experimentally by stimulating an oscillator at a specific point in its cycle and measuring the resulting phase shift. 31

38 Figure 3.4.1: Experiments for quantifying the coupling between neighboring wells. (A) Microfluidic device for investigating coupling between pairs of by channels connected wells. Well marked in blue and well marked in red correspond to curves in (C). (B) Microfluidic device with square array of square wells not connected by channels. Experiment to test the effect of reactors perturbing one oscillating reactor. Wells marked in red and blue correspond to curves in (D). (C) Grayscale intensity over time of two wells in experiment shown in (A). Continously oscillating reactor in blue, at a specific point in time light released perturbing reactor in red, and light that is being shone on perturbing reactor in green. (D) Same as in (C) but for experiment in (B). Figure (A) shows a microfluidic chip with an array of pairs of wells connected by a thin channel. The chip contains a total of nine pairs of wells which we use to measure the coupling. A high number of experiments in parallel grants approximately identical conditions for each experiment. The top part of the chip contains two control features. Surrounding each pair of wells is an additional volume of BZ solution which is light suppressed during the entire experiment. We learned from experiments that maximizing the ratio of volume of BZ solution to volume of PDMS gives us the anticipated results. As mentioned in Chapter 2.2 and Chapter 2.3 we assume that for achieving constant inhibitory coupling it is crucial to saturate the PDMS with bromine. Therefore, we want to minimize the volume of PDMS and at the same time saturate the indispensable PDMS 32