Research areas

 Our research interests may be roughly divided into following areas:
Mechanistic and design studies of chemical oscillators
Pattern formation;
        autonomous homogeneous chemical systems
        reaction-diffusion systems under external forcing
        nonhomogeneous reaction-diffusion media
Systems of biological interest
Within each of these areas, there may be several sub-areas as well as projects that are more experimentally or more theoretically oriented.  For each area we give below a brief description, a list of sub-areas, and a few recent relevant projects/publications.

Mechanistic and Design Studies of Chemical Oscillators

 Our group pioneered the systematic design and mechanistic study of oscillating chemical reactions.We continue to be interested in developing new reactions that have particularly desirable features, e.g., producing specific types of patterns or being photosensitive.We also carry out studies to elucidate the mechanisms of reactions that display complex dynamical behavior.

Recent projects:
Kinetic and Mechanistic Studies

· A.P. Muñuzuri, M. Dolnik, A.M. Zhabotinsky, I.R.Epstein, "Control of the chlorine dioxide-iodine-malonic acid oscillating reaction by illumination"; J.Am.Chem.Soc. 121, , 8065-8069 (1999). (abstract)
· M. Orbán, K. Kurin-Csörgei, G.Rábai, I.R. Epstein, "Mechanistic studies of oscillatory copper(II) catalyzed oxcidation reactions of sulfur compounds", Chem. Eng. Sci. 55, 2000, 267-273. (abstract)
· A.K. Horváth, M. Dolnik, A.M. Zhabotinsky, I.R. Epstein, "Kinetics of photoresponse of the chlorine dioxide-iodine-malonic acid reaction", J.Phys. Chem A 104, 5766-5769 (2000). (abstract)
· V.K. Vanag, A.M. Zhabotinsky, I.R. Epstein,"Role of dibromomalonic acid in the photosensitivity of the Ru(bpy)(3)(2+)-catalyzed Belousov-Zhabotinsky reaction" J Phys Chem A 104, 8207-8215 (2000). (abstract)
Design of New Reactions

  Pattern formation in uncatalyzed bromate oscillatory system visualized by various indicators
· M. Orbán, K. Kurin-Csörgei, A.M. Zhabotinsky and I.R. Epstein, "New Indicators for Visualizing Pattern Formation in Uncatalyzed Bromate Oscillatory Systems," J. Am. Chem. Soc. 120, 1146-1150 (1998).(abstract)
· K. Kurin-Csörgei, M. Orbán, A.M. Zhabotinsky, and I.R. Epstein, "A New Chemical System for Studying Pattern Formation: Bromate - Hypophosphite - Acetone - Dual Catalyst", Disc. Faraday Soc., in press (2001).
Pattern Formation - autonomous homogeneous chemical systems
 One of the most visually striking occurrences in chemical systems is the formation of spatial patterns and waves.These phenomena are thought to be of importance in a variety of pattern formation phenomena in living systems.We are studying the dynamical origin of pattern formation, attempting to design new kinds of patterns, and investigating how introducing feedback can induce or alter pattern formation.

Recent projects:
Pattern Formation Associated with the Wave Instability


Standing wave patterns on a disc -  pattern with C6 symmetry (top), pattern with C9 symmetry (bottom)
· M. Dolnik, A.B. Rovinsky, A.M. Zhabotinsky and I.R. Epstein, "Standing Waves in a Two-Dimensional Reaction-Diffusion Model with the Short-Wave Instability," J. Phys. Chem. A 103, 38-45 (1999). (abstract)
·M.Dolnik M., A.M.Zhabotinsky, A.B. Rovinsky, I.R. Epstein, "Spatio-temporal patterns in a reaction-diffusion system with wave instability", Chem. Eng. Sci. 55, 223-231 (2000). (abstract)
Effects of Global Feedback on Pattern Formation
· L.Yang, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein,"Oscillatory clusters in a model of the photosensitive Belousov-Zhabotinsky reaction system with global feedback", Phys. Rev. E 62, 6414-6420 (2000).  (abstract)
· 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 104A,  11566-11577 (2000). (abstract)

Pattern Formation - reaction-diffusion systems under external forcing
When an oscillator is driven by an external force, a variety of phenomena, including resonance, may arise. When two or more chemical oscillators are coupled to one another, they can exhibit a much richer range of behavior than the individual component oscillators. We are seeking to understand what happens when systems that oscillate not only in time but also in space (pattern formation) are forced and/or coupled. Biological examples include organisms under the periodic forcing resulting from circadian oscillations in light intensity.

Recent projects:
Temporally Periodic Forcing

· 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). (abstract)
Spatiotemporal Forcing of Turing Structures

      Modulation of Turing structures in CDIMA reaction with spatial periodic forcing  (PRL 87,238301,2001)
· Horváth A.K., Dolnik M., Muñuzuri A.P., Zhabotinsky A.M.,Epstein I.R., "Control of the Turing structures by periodic illumination"; Phys. Rev. Lett. 83,  2950-2952 (1999). (abstract)
· M. Dolnik, A.M. Zhabotinsky and I.R. Epstein,"Resonant Suppression of Turing Patterns by Periodic Illumination", Phys. Rev. E 63, 026101-1-10 (2001).(abstract)
· A. Sanz-Anchelergues, A.M. Zhabotinsky, I. R. Epstein and A. P. Muñuzuri, "Turing Pattern Formation Induced by Spatially Correlated Noise", Phys. Rev. E 63, 056124-1-4 (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).

Pattern Formation - nonhomogeneous reaction-diffusion media
 Most studies of patterns and waves in chemical systems assume or attempt to create uniform, homogeneous media.  Real reaction-diffusion systems, particularly those of biological or industrial importance, involve media that are not homogeneous.We are seeking to understand how the structure of the medium affects the behavior of such systems. Recent work has focused on a microemulsion, a mixture of oil, water and a surfactant, where we are able to “tune” the structure of the medium, and hence the behavior of the system, by varying the composition.

Recent projects:


Fully developed inwardly moving spirals and target patterns
in BZ-AOT microemulsion
· 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).

Systems of Biological Interest
 We are always interested in applying insights and techniques from our studies of chemical systems to systems of significance in other areas, particularly biology. Two areas in which we have recently been active are the development of a model for synaptic memory and the understanding and design of synthetic gene expression networks. Although these projects primarily involve mathematical modeling, we also collaborate with experimentalists working on the relevant biological systems.

Recent projects:
Synaptic Memory


Schematic of the first two steps of autophosporylation of CaMKII holoenzyme and hysteresis loop in the system with the Ca2+
independent protein phosphatase in vitro
· A. M. Zhabotinsky, "Bistability in the Ca2+/calmodulin-dependent protein kinase-phosphatase system", Biophys. J. 79, 2211-2221 (2000). (abstract)
·J.E. Lisman and A.M. Zhabotinsky,"A Model of Synaptic Memory: A CaMKII/PP1 Switch that Potentiates Transmission by Organizing an AMPA Receptor Anchoring Assembly", Neuron 31, 191-201 (2001). (abstract)