Kenneth Showalter of West Virginia University is supported by an award from the Theoretical and Computational Chemistry program for research into the spatiotemporal dynamics and collective behavior of chemical systems. Partial co-funding for this award was provided by the Applied Mathematics program in the Division of Mathematical Sciences. Three main lines of investigation are being pursued in this work: (i) the collective behavior of particle-like reaction-diffusion waves; (ii) the synchronization and dynamical quorum sensing behavior of large populations of oscillatory beads; and (iii) the behavior of collections of self-propelled catalytic particles. In the first project, populations of stabilized waves in a distributed photosensitive Belousov-Zhabotinsky (BZ) medium are being studied to characterize collective behavior in a controlled laboratory setting. Waves interact via a Lennard Jones type potential and the origin of different types of collective behavior, such as processional and rotational modes, is being characterized. In the second project, large populations of catalyst-loaded beads are studied in catalyst-free BZ reaction mixtures. The focus of these studies is to examine synchronization and dynamical quorum sensing behavior in stirred suspensions and spatiotemporal distributed systems. The third project involves studies of the interactions of self-propelled catalytic particles in reactant solutions. Silica spheres are prepared with various metal or enzyme coatings, such as Pt or horseradish peroxidase, that catalyze the decomposition of a reactant, such as hydrogen peroxide. The propagation behavior of these particles is then studied as a function of particle density to determine correlations in velocity leading to collective behavior.
All three lines of research are expected to yield new and important information about spatiotemporal dynamics and collective behavior in chemical systems and offer insights into such behavior in biological systems. The studies of interacting particle-like waves will advance control of spatiotemporal systems and will offer insights into collective behavior from laboratory experiments. A better understanding of synchronization and dynamical quorum sensing mechanisms will be gained in the studies of large populations of discrete oscillators, offering insights into related dynamics of microorganisms. The studies of interacting self-propelled catalytic particles will provide new examples of collective behavior and new chemical model systems for developing an understanding of complex interactions. The impact of the work is further broadened through Showalter's participation in outreach activites involving the International Center for Theoretical Physics that are bringing hands-on research experiences to scientists in developing countries such as India, Brazil and Cameroon.
Chemical systems continue to play an important role in studies of nonlinear dynamics and complexity, as relatively simple chemical systems can exhibit remarkably complex behavior, much like behavior found in living systems, yet they are readily investigated because they are both experimentally and theoretically accessible. This grant has supported research aimed at developing insights into the complex dynamics of living systems from studies of dynamical behavior of chemical model systems. Our studies of chemical model systems over the award period have yielded significant advances in understanding synchronization behavior in large populations of oscillators, providing insights into the dynamics of interacting microorganisms such as yeast cells. Over 30 years ago, biologists discovered that suspensions of whole yeast cells are oscillatory above a certain cell number density but exhibit quiescent behavior at lower number densities. This discovery led to yeast becoming a paradigmatic model system for cell signaling, since cells must communicate for synchronous oscillations to occur. However, the transition from the oscillatory to the quiescent state was not characterized until recent studies of suspensions of yeast cells in open, flow reactors, which showed the transition to be much like quorum sensing transitions in populations of bacteria. Our studies of large populations of chemical oscillators (~100,000) revealed two different types of transitions from the oscillatory state to the quiescent state, which depend on the number density (number of oscillators per unit volume) and the rate of exchange of signaling molecules between the oscillators and the surrounding solution. As shown in the Figure, increasing number density at low exchange rates (e.g., kex = 0.3 s-1) results in a gradual synchronization of the oscillators, known as a Kuramoto transition. At high exchange rate (e.g., kex = 3.0 s-1), an increasing number density results in the sudden "switching on" of synchronized oscillatory behavior, similar to a quorum sensing transition. We find regimes where a gradual synchronization transition is exhibited and regimes where a quorum-sensing-like transition is exhibited, thus showing how these different density-dependent transitions are related. The quorum sensing transition is unusual in that thousands of oscillators, each having a different inherent oscillatory frequency, undergo a transition at a critical number density (or exchange rate of signaling molecules) from a steady state to a completely synchronized oscillatory population. The gradual Kuramoto synchronization transition occurs smoothly above a critical coupling strength, with the frequency and phase of the oscillators becoming increasingly aligned with increasing coupling strength. However, rather than smoothly synchronizing, clusters of oscillators may form that are frequency synchronized but are out of phase with other clusters of oscillators. We studied the formation of phase clusters in large populations of chemical oscillators by changing the catalyst of the oscillatory reaction to give the more complex synchronization transition. This phenomenon, at any moment, gives rise to groups of oscillators with different chemical environments within the population of oscillators. Many types of unicellular organisms switch from individual to collective behavior in response to increasing cell numbers when they are spatially distributed in colonies. In this process, cells communicate via the diffusive exchange of chemical signaling species through the extracellular solution. We studied collective behavior in groups of spatially distributed catalyst particles that were immersed in unstirred catalyst-free reaction mixtures. The particles diffusively exchange activator and inhibitor species with the surrounding solution. All particles were nonoscillatory when separated from the other particles; however, target and spiral waves were exhibited in groups larger than a critical group size, demonstrating a collective switching from quiescent to oscillatory behavior analogous to quorum sensing transitions in colonies of bacteria. Other studies supported by this grant include motion analysis of self-propelled particles, in which 1.0 micrometer Pt-silica beads undergo diffusiophoresis in hydrogen peroxide solutions, and a theoretical study of extreme multistability in chemical model systems. Developing a better understanding of self-motion of very small objects in liquids is important in characterizing microorganism movement, and novel examples of multiple states further the development of nonlinear dynamics and complexity. The research supported by this grant has played an important role in the educational infrastructure of West Virginia University. Three students have graduated during the award period with Ph.D. degrees. Six Ph.D. chemistry graduate students and one Ph.D. mathematics graduate student have received advanced research training during the award period. Our main outreach activities during the award period have focused on promoting science education and research in the developing world. With colleagues from the University of Maryland and the University of Texas, we have developed a series of schools that promote science in the developing world with a U.S. base. We are officially affiliated with the International Center for Theoretical Physics (ICTP, Trieste), and we have developed a series of four ICTP satellite schools, which are called "Hands-On Research in Complex Systems Schools."
