Oscillating chemical reactions and pattern formation in reaction-diffusion systems. Mathematical modeling of biochemical kinetics and neural systems

Research in our group covers oscillatory chemical reactions, spatial pattern formation, dynamical systems and neurobiology.

Many phenomena in living systems involve periodic changes. In the past decade, oscillating chemical reactions have blossomed from a curiosity studied by an obscure group of Russians to a major area of scientific research. We study these systems both experimentally and theoretically, from several points of view. We have achieved the first successful design of a new chemical oscillator. We have used our systematic design algorithm to expand the family of chemical oscillators from two accidentally discovered reactions to some two dozen deliberately constructed systems. While we continue the search for new types of oscillators, we probe by a variety of techniques, including spectrophotometry, potentiometry, rapid mixing and computer simulation, the mechanisms of those that have already been discovered.

Chemical oscillators can be "tweaked" to give a variety of related phenomena, some with suggestive connections to biological systems. We study spatial pattern formation, in which an initially homogeneous medium spontaneously gives rise to concentric rings, or spiral color patterns resembling those seen in embryonic development or the aggregation of slime molds, and chemical chaos, in which concentrations oscillate deterministically, but in an aperiodic and apparently irreproducible fashion that depends very sensitively on the initial conditions. We investigate, both experimentally and theoretically, Turing structures, patterns that arise from the interaction of reaction and diffusion, which have been suggested as the mechanism of spatial pattern formation in phenomena ranging from biological morphogenesis to geological stratification.

We are interested in the phenomena that can occur when two or more oscillators are coupled together, either physically, i.e., by diffusion or an electrical connection, or chemically, by having two oscillators share a common chemical species. Such systems can give rise to surprising phenomena, such as "oscillator death," the cessation of oscillation in two coupled oscillating systems, or the converse, "rhythmogenesis," in which coupling two systems at steady state causes them to start oscillating. Coupled chemical oscillators provide simple models for networks of oscillatory neurons. We have begun to apply some of the insights gained in our studies of coupled chemical oscillators to the modeling of small neural networks in conjunction with the Marder laboratory, to develop chemical analogs of neural oscillators and to coupling chemical and neural oscillators.

T. Bánsági, Jr., S. Ansari, I. R. Epstein and M. Dolnik, “Rearrangement Dynamics of Fishbonelike Turing Patterns Generated by Spatial Periodic Forcing,” Phys. Rev. E 81, 066207-1-7 (2010). F. Rossi, V. K. Vanag, E. Tiezzi, and I. R. Epstein, “Quaternary Cross-Diffusion in Water-in-oil Microemulsion Loaded with a component of the Belousov-Zhabotinsky reaction. Taylor Dispersion Method,” J. Phys. Chem. B, 114, 8140-8146 (2010). Y. Lu, Q, Gao, L Xu, Y. Zhao and I. R Epstein, “Oxygen-sulfur species distribution and kinetic analysis in the hydrogen peroxide – thiosulfate system,” Inorg. Chem. 49, 6026–6034 (2010). L. Yuan, Q. Gao, Y. Zhao, X. Tang and I. R Epstein, “Temperature-induced bifurcations in the Cu(II)-catalyzed and catalyst-free hydrogen peroxide-thiosulfate oscillating reaction,” J. Phys. Chem. A 114, 7014-7020 (2010). E.P. Zemskov and I.R. Epstein, “Wave propagation in a FitzHugh-Nagumo-type model with modified excitability,” Phys. Rev. E 82, 026207-1-6 (2010) M. Sajewicz, M. Gontarska, D. Kronenbach, M. Leda, T. Kowalska and I.R. Epstein, “Condensation oscillations in the peptidization of phenylglycine,” J. Syst. Chem. 1, 7-1-16 (2010). V.K. Vanag and I.R. Epstein, “Periodic perturbation of one of two identical chemical oscillators coupled via inhibition,” Phys. Rev. E 81, 066213-1-10 (2010). I. R. Epstein, J. A. Pojman and Q. Tran-Cong-Miyata, “What is Nonlinear Dynamics and How Does It Relate to Polymers?,” in J. A. Pojman and Q. Tran-Cong-Miyata, Eds., “Nonlinear Dynamics with Polymers,” Wiley-VCH, Weinheim, 2010, pp. 5-20. M. Sajewicz, M. Matlengiewicz, M. Leda, M. Gontarska, D. Kronenbach, T. Kowalska, and I. R. Epstein, “Spontaneous Oscillatory in vitro Chiral Conversion of Simple Carboxylic Acids and Its Possible Mechanism,” J. Phys. Org. Chem. 23, 1066-1073 (2010). Anderson, W.A., Drennan, C.L., Banerjee, U., Elgin, S.C.R., Epstein, I.R., Handelsman, J., Hatfull, G.F., Losick, R., O’Dowd, D.K., Olivera, B.M., Strobel, S.A., Walker, G.C., Warner, I.M., “Changing the Culture of Science Education at Research Universities,” Science, 331, 152-153 (2011). F. Rossi, V.K. Vanag, and I. R. Epstein, “Pentanary Cross-Diffusion in Water-in-Oil Microemulsions Loaded with Two Components of the Belousov-Zhabotinsky Reaction,” Chem. Eur. J. 17, 2138-2145 (2011). T. Bánsági, Jr., V.K. Vanag and I.R. Epstein, “Three-dimensional Turing Patterns in a Reaction Diffusion System,” Science 331, 1309-1312 (2011). J. Delgado, N. Li, M. Leda, H.O. González-Ochoa, S. Fraden and I.R. Epstein, “Coupled Oscillators in a 1D Emulsion of Belousov-Zhabotinsky Droplets,” Soft Matter 7, 3155-3167 (2011). E.P. Zemskov, K. Kassner, M.A. Tsyganov and I.R. Epstein, “Speed of traveling fronts in a sigmoidal reaction-diffusion system,” Chaos 21, 013115-1-5 (2011).

J. Delgado, Y. Zhang, B. Xu and I. R. Epstein, “Terpyridine- and bipyridine-based ruthenium complexes as catalysts for the Belousov-Zhabotinsky reaction,” J. Phys. Chem. A 115, 2208-2215 (2011).