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.

 

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Selected Publications

Pattern formation mechanisms in reaction-diffusion systems. Vanag VK, Epstein IR. Int J Dev Biol. 2009;53(5-6):673-81.

High-frequency oscillations in the Belousov-Zhabotinsky reaction. Bánsági T Jr, Leda M, Toiya M, Zhabotinsky AM, Epstein IR. J Phys Chem A. 2009 May 14;113(19):5644-8.

Temperature control of pattern formation in the Ru(bpy)(3)(2+)-catalyzed BZ-AOT system. McIlwaine R, Vanag VK, Epstein IR. Phys Chem Chem Phys. 2009 Mar 14;11(10):1581-7.

Cross-diffusion and pattern formation in reaction-diffusion systems. Vanag VK, Epstein IR. Phys Chem Chem Phys. 2009 Feb 14;11(6):897-912.

Oscillations and mechanistic analysis of the chlorite-sulfide reaction in a continuous-flow stirred tank reactor. Mao S, Gao Q, Wang H, Zheng J, Epstein IR. J Phys Chem A. 2009 Feb 19;113(7):1231-4.

Small-amplitude and mixed-mode pH oscillations in the bromate-sulfite-ferrocyanide-aluminum(III) system. Kovacs K, Leda M, Vanag VK, Epstein IR. J Phys Chem A. 2009 Jan 8;113(1):146-56.

Breathing spiral waves in the chlorine dioxide-iodine-malonic acid reaction-diffusion system. Berenstein I, Muñuzuri AP, Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 2):025101.

Diffusively coupled chemical oscillators in a microfluidic assembly. Toiya M, Vanag VK, Epstein IR. Angew Chem Int Ed Engl. 2008;47(40):7753-5.

Cross-diffusion in a water-in-oil microemulsion loaded with malonic acid or ferroin. Taylor dispersion method for four-component systems. Vanag VK, Rossi F, Cherkashin A, Epstein IR. J Phys Chem B. 2008 Jul 31;112(30):9058-70. Epub 2008 Jul 9.

Design and control of patterns in reaction-diffusion systems.Vanag VK, Epstein IR. Chaos. 2008 Jun;18(2):026107.

Oscillations in the concentration of fluoride ions induced by a pH oscillator. Horvath V, Kurin-Csörgei K, Epstein IR, Orban M. J Phys Chem A. 2008 May 8;112(18):4271-6.

Coupled and forced patterns in reaction-diffusion systems. Epstein IR, Berenstein IB, Dolnik M, Vanag VK, Yang L, Zhabotinsky AM. Philos Transact A Math Phys Eng Sci. 2008 Feb 13;366(1864):397-408.

Localized patterns in reaction-diffusion systems. Vanag VK, Epstein IR. Chaos. 2007 Sep;17(3):037110.

Fronts and pulses in an enzymatic reaction catalyzed by glucose oxidase. Míguez DG, Vanag VK, Epstein IR. Proc Natl Acad Sci U S A. 2007 Apr 24;104(17):6992-7.

Designing an enzymatic oscillator: bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor.Vanag VK, Míguez DG, Epstein IR. J Chem Phys. 2006 Nov 21;125(19):194515.

Yang L, Zhabotinsky AM, Epstein IR. (2006) Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability. Phys Chem Chem Phys. 2006 Oct 28;8(40):4647-51.

Predicting complex biology with simple chemistry.Epstein IR. Proc Natl Acad Sci U S A. 2006 Oct 24;103(43):15727-8. Epub 2006 Oct 16.

Turing patterns beyond hexagons and stripes.Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. Chaos. 2006 Sep;16(3):037114.

Role of the neurogranin concentrated in spines in the induction of long-term potentiation.Zhabotinsky AM, Camp RN, Epstein IR, Lisman JE. J Neurosci. 2006 Jul 12;26(28):7337-47. [abstract]

Periodic pulses of calcium ions in a chemical system.Kurin-Csorgei K, Epstein IR, Orban M. J Phys Chem A Mol Spectrosc Kinet Environ Gen Theory. 2006 Jun 22;110(24):7588-92. [abstract]

A reaction-diffusion memory device. Kaminaga A, Vanag VK, Epstein IR. Angew Chem Int Ed Engl. 2006 May 5;45(19):3087-9.

Turing patterns beyond hexagons and stripes.Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. Chaos. 2006 Sep;16(3):037114. [abstract]

Predicting complex biology with simple chemistry.Epstein IR. Proc Natl Acad Sci U S A. 2006 Oct 24;103(43):15727-8.

Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability.Yang L, Zhabotinsky AM, Epstein IR. Phys Chem Chem Phys. 2006 Oct 28;8(40):4647-51. Epub 2006 Sep 11.[abstract]

Designing an enzymatic oscillator: bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor. Vanag VK, Miguez DG, Epstein IR. J Chem Phys. 2006 Nov 21;125(19):194515. [abstract]

Complex patterns in reactive microemulsions: self-organized nanostructures? Epstein IR, Vanag VK. Chaos. 2005 Dec;15(4):047510. [abstract]

Out-of-phase oscillatory Turing patterns in a bistable reaction-diffusion system.Vanag VK, Epstein IR. Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):066212. Epub 2005 Jun 23. [abstract]

"Black spots" in a surfactant-rich Belousov-Zhabotinsky reaction dispersed in a water-in-oil microemulsion system. Kaminaga A, Vanag VK, Epstein IR. J Chem Phys. 2005 May 1;122(17):174706. [abstract]

Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system. Berenstein I, Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. J Phys Chem A Mol Spectrosc Kinet Environ Gen Theory. 2005 Jun 23;109(24):5382-7. [abstract]

Systematic Design of Chemical Oscillators Using Complexation and Precipitation Equilibria. K. Kurin-Csörgei, M. Orbán and I. R. Epstein. Nature 433, 139-142 (2005). [abstract]

Response of Complex Networks to Stimuli. Y. Bar-Yam and I.R. Epstein. Proc. Natl. Acad. Sci. 101, 4341-4345 (2004). [abstract]

Translational and nontranslational motion of perturbed Turing patterns.Vanag VK, Epstein IR. Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jun;67(6 Pt 2):066219.

Segmented Spiral Waves in a Reaction-Diffusion System. V.K. Vanag and I.R. Epstein. Proc. Nat. Acad. Sci. USA 100, 14635-14638 (2003) (cover article). [abstract]

Superlattice Turing Structures in a Photosensitive Reaction-Diffusion System. I. Berenstein, L. Yang, M. Dolnik, A.M. Zhabotinsky and I.R. Epstein. Phys. Rev. Lett. 91, 058302-1-4 (2003). [abstract]

Oscillatory Turing Patterns in Reaction-Diffusion Systems with Two Coupled Layers. L. Yang and I.R. Epstein. Phys. Rev. Lett. 90, 178303-1-4 (2003). [abstract]

Optimization of Robustness and Connectivity in Complex Networks. B. Shargel, H. Sayama, I. R. Epstein and Y. Bar-Yam. Phys. Rev. Lett. 90, 068701-1-4 (2003).

 

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Last review: July 14, 2009