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.
Selected
Publications
- I.R. Epstein and J.A. Pojman, Introduction to Nonlinear Chemical Dynamics. Oscillations, Waves, Patterns and Chaos, Oxford University Press, New York, 1998, 392 pp.
- V.K. Vanag, L. Yang, M. Dolnik, A.M. Zhabotinsky and I.R. Epstein, "Oscillatory Cluster Patterns in a Homogeneous Chemical System with Global Feedback," Nature 406, 389-391 (2000). [abstract]
- V.K. Vanag, A.M. Zhabotinsky and I.R. Epstein, "Pattern Formation in the Belousov-Zhabotinsky Reaction with Photochemical Global Feedback," J. Phys. Chem. A 104, 11566-11577 (2000).
- V. K. Vanag, A. M. Zhabotinsky and I.R. Epstein, "Oscillatory Clusters in the Periodically Illuminated, Spatially Extended Belousov-Zhabotinsky Reaction," Phys. Rev. Lett. 86, 552-555 (2001).
- V.K. Vanag and I.R. Epstein, "Inwardly Rotating Spiral Waves in a Reaction-Diffusion System," Science 294, 835-837 (2001). [abstract]
- V.K. Vanag and I.R. Epstein, "Pattern Formation in a Tunable Reaction-Diffusion Medium: The BZ Reaction in an Aerosol OT Microemulsion," Phys. Rev. Lett. 87, 228301-1-4 (2001). [abstract]
- M. Dolnik, I. Berenstein, A.M. Zhabotinsky and I.R. Epstein, "Spatial Periodic Forcing of Turing Structures," Phys. Rev. Lett. 87, 238301-1-4 (2001). [abstract]
- V.K. Vanag and I.R. Epstein, "Packet Waves in a Reaction-Diffusion System," Phys. Rev. Lett. 88, 088303-1-4 (2002). [abstract]
- G. Peintler, I. Nagypál, I.R. Epstein and K. Kustin, "Extracting Experimental Information from Large Matrices. Part II. Model-Free Resolution of Absorbance Matrices: M3," J. Phys. Chem. A 106, 3899-3904 (2002).
- A.K. Horváth, I. Nagypál and I.R. Epstein, "Oscillatory Photochemical Decomposition of Tetrathionate Ion," J. Am. Chem. Soc. 124, 10956-10957 (2002).
- I.R. Epstein, "Oscillations, Waves and Patterns in Chemistry and Biology," in Structures and Mechanisms: From Ashes to Enzymes, G.R. Eaton, D.C. Wiley and O. Jardetzky, eds., ACS Symp. Ser. Vol. 827, Oxford University Press, 2002, pp. 103-116.
- L. Yang, M. Dolnik, A.M. Zhabotinsky and I.R. Epstein, "Pattern Formation Arising from Interactions between Turing and Wave Instabilities," J. Chem. Phys. 117, 7259-7265 (2002).
- B. Shargel, H. Sayama, I. R. Epstein and Y. Bar-Yam, "Optimization of Robustness and Connectivity in Complex Networks," Phys. Rev. Lett. 90, 068701-1-4 (2003).
- V.K. Vanag and I.R. Epstein, "Dash-waves in a Reaction Diffusion System," Phys. Rev. Lett. 90, 098301-1-4 (2003). [abstract]
- F. Sagués and I. R. Epstein, "Nonlinear Chemical Dynamics," Dalton Trans. 1201-1217 (2003) (cover article).
- L. Yang and I.R. Epstein, "Oscillatory Turing Patterns in Reaction-Diffusion Systems with Two Coupled Layers," Phys. Rev. Lett. 90, 178303-1-4 (2003). [abstract]
- I. Berenstein, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein, "Spatial Periodic Perturbation of Turing Pattern Development Using a Striped Mask," J. Phys. Chem. A 107, 4428-4435 (2003).
- I. Berenstein, L. Yang, M. Dolnik, A.M. Zhabotinsky and I.R. Epstein, "Superlattice Turing Structures in a Photosensitive Reaction-Diffusion System," Phys. Rev. Lett. 91, 058302-1-4 (2003). [abstract]
- H.G. Rotstein, N. Kopell, A. Zhabotinsky and I.R. Epstein, "A Canard Mechanism for Localization in Systems of Globally Coupled Oscillators" SIAM J. Appl. Math. 63, 1998-2019 (2003).
- V.K. Vanag and I.R. Epstein, "Segmented Spiral Waves in a Reaction-Diffusion System," Proc. Nat. Acad. Sci. USA 100, 14635-14638 (2003) (cover article). [abstract]
- Y. Bar-Yam and I.R. Epstein, "Response of Complex Networks to Stimuli," Proc. Natl. Acad. Sci. 101, 4341-4345 (2004). [abstract]
- A.K. Horváth, I. Nagypál, G. Peintler and I.R. Epstein, "Autocatalysis and Selfinhibition: Coupled Kinetic Phenomena in the Chlorite Tetrathionate Reaction," J. Am. Chem. Soc. 126, 6246-6247 (2004).
- I. Berenstein, M. Dolnik, L. Yang, A.M. Zhabotinsky and I.R. Epstein, "Turing Pattern Formation in a Two-Layer System: Superposition and Superlattice Patterns," Phys. Rev. E 70, 046219-1-5 (2004).
- K. Kurin-Csörgei, M. Orbán and I.R. Epstein, "Systematic Design of Chemical Oscillators Using Complexation and Precipitation Equilibria," Nature 433, 139-142 (2005).
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Epstein
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