Diffusively coupled chemical oscillators in a microfluidic assembly.

From fireflies that synchronize their flashes with each other to heart muscles contracting and relaxing in unison, synchronized behavior of living cells or organisms is ubiquitous in nature. Chemical reaction–diffusion systems can help us understand the mechanisms that underlie such synchronization. Coupled chemical oscillators have previously been studied in the laboratory with large reactors connected directly by small channels for controlled mass exchange of bulk solution. In this case, coupling occurs via all species. In living systems, however, coupling often occurs through special signaling molecules, as in synaptic communication or chemotaxis. Collections of neural oscillators can access a vast repertoire of coordinated behavior by utilizing a variety of topologies and modes of coupling, including gap junctions and synaptic links, which may be either excitatory or inhibitory, depending on the neurotransmitter involved. To mimic such a fine level of communication in a chemical system, we need to do two things: a) reduce the size of each oscillator in order to bring the characteristic time of communication between diffusively coupled oscillators to or below the period of oscillation; and b) introduce a semipermeable membrane or other medium between the microoscillators to permit communication only via selected species. These goals can be achieved with the use of microfluidic devices. Our experimental system (Figure 1a) is a linear array of tens of droplets of nanoliter volume containing aqueous ferroin-catalyzed Belousov–Zhabotinsky (BZ) solution separated by octane drops in a glass capillary. The BZ reaction, in which the oxidation of malonic acid (MA) by bromate is catalyzed by a metal complex in acidic aqueous solution, is a well known chemical oscillator. Owing to the small spatial extent (lw= 100–400 mm) of the BZ droplets, the characteristic time of diffusive mixing within a single droplet, lw /D (5–80 s, D=diffusion constant of aqueous species), is smaller than the period of oscillation (180–300 s), and individual BZ droplets can be considered homogeneous. Bromine, an inhibitory intermediate of the BZ reaction, is quite hydrophobic and diffuses readily into hydrocarbons such as octane, thus mediating inhibitory interdroplet coupling. We have shown theoretically that in such heterogeneous systems patterns analogous to the Turing patterns found in homogeneous systems can emerge. Without compartmentalization, the homogeneous BZ solution in a similar capillary exhibits trigger waves of excitation. Partitioning the medium into droplets dramatically changes this behavior. For BZ droplets (Figure 1b) with lw> 400 mm or oil droplets with length lO> 400 mm, no discernible coherent patterns are seen. However if lw= 100– 400 mm and lO= 50–400 mm, we observe stable anti-phase oscillations (Figure 2a) at larger [MA] (greater than 100 mm) and Turing patterns (Figure 2b) at smaller [MA] (less than 40 mm). At higher levels of [MA], initially in-phase arrays of droplets evolve to an anti-phase configuration within a few periods of oscillation (Movie in Supporting Information). For [MA]= 40 mm, the transition to the Turing regime goes through intermediate anti-phase oscillations. For slightly smaller [MA] (35 mm), initially in-phase droplets transform into Turing patterns almost immediately, without intermediate anti-phase oscillations. At small [MA], the behavior is rather sensitive to the size of droplets, with small drops reaching stationary state more rapidly than larger ones. To establish whether bromine is responsible for communication between the BZ droplets, surfactant Span80 (sorbitan mono-oleate) at concentrations of 5% was added to the octane. In separate experiments, it was found that Span80, which possesses an unsaturated double bond in its hydrocarbon tail, reacts with bromine in octane in less than 1 s. The water-insoluble Span80 thus acts as a trap for bromine, removing it from the octane. When Span80 is added to the droplet system, inhibiting the communication between BZ droplets, individual droplets oscillate independently. If we initiate the system (see Experimental Section) with all droplets in the same phase, in-phase oscillations persist. Figure 1. a) Schematic representation of the microfluidic device. Red droplets correspond to the reduced form of the catalyst (ferroin), blue droplets to the oxidized form (ferriin). A new method for fabricating such junctions is outlined in the Supporting Information. b) Snapshot of two capillaries with droplets. BZ droplets with convex surfaces are dark due to ferroin. Horizontal length of the frame and inner diameter (ID) of the capillary are 4.8 mm and 150 mm, respectively. BZ droplets were recorded by a CCD camera through a microscope with illumination by light passed through a 510 nm interference filter.