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
Vanag VK, Epstein IR. (2008) Design and control of patterns in reaction-diffusion systems. Chaos. 2008 Jun;18(2):026107.
Horvath V, Kurin-Csörgei K, Epstein IR, Orban M. (2008) Oscillations in the concentration of fluoride ions induced by a pH oscillator. J Phys Chem A. 2008 May 8;112(18):4271-6.
Epstein IR, Berenstein IB, Dolnik M, Vanag VK, Yang L, Zhabotinsky AM. (2008) Coupled and forced patterns in reaction-diffusion systems. Philos Transact A Math Phys Eng Sci. 2008 Feb 13;366(1864):397-408.
Vanag VK, Epstein IR. (2007) Localized patterns in reaction-diffusion systems. Chaos. 2007 Sep;17(3):037110.
Míguez DG, Vanag VK, Epstein IR. (2007) Fronts and pulses in an enzymatic reaction catalyzed by glucose oxidase. Proc Natl Acad Sci U S A. 2007 Apr 24;104(17):6992-7.
Epstein IR. Chemistry. (2007) Can droplets and bubbles think? Science. 2007 Feb 9;315(5813):775-6.
Vanag VK, Míguez DG, Epstein IR. (2006) Designing an enzymatic oscillator: bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor. 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. Epub 2006 Sep 11.
Epstein IR. (2006) Predicting complex biology with simple chemistry. Proc Natl Acad Sci U S A. 2006 Oct 24;103(43):15727-8. Epub 2006 Oct 16.
Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. (2006) Turing patterns beyond hexagons and stripes. Chaos. 2006 Sep;16(3):037114.
Zhabotinsky AM, Camp RN, Epstein IR, Lisman JE. (2006)
Role of the neurogranin concentrated in spines in the induction
of long-term potentiation. J Neurosci. 2006 Jul 12;26(28):7337-47.
[abstract]
Kurin-Csorgei K, Epstein IR, Orban M. (2006) Periodic pulses
of calcium ions in a chemical system. J Phys Chem A Mol
Spectrosc Kinet Environ Gen Theory. 2006 Jun 22;110(24):7588-92.
[abstract]
Kaminaga A, Vanag VK, Epstein IR. (2006) A reaction-diffusion
memory device. Angew Chem Int Ed Engl. 2006 May 5;45(19):3087-9.
Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. (2006) Turing
patterns beyond hexagons and stripes. Chaos. 2006
Sep;16(3):037114. [abstract]
Epstein IR. (2006) Predicting complex biology with simple
chemistry. Proc Natl Acad Sci U S A. 2006 Oct 24;103(43):15727-8.
Epub 2006 Oct 16.
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.
Epub 2006 Sep 11.[abstract]
Vanag VK, Miguez DG, Epstein IR. (2006) Designing an enzymatic
oscillator: bistability and feedback controlled oscillations
with glucose oxidase in a continuous flow stirred tank reactor.
J Chem Phys. 2006 Nov 21;125(19):194515. [abstract]
Epstein IR, Vanag VK. (2005) Complex patterns in reactive
microemulsions: self-organized nanostructures? Chaos.
2005 Dec;15(4):047510. [abstract]
Vanag VK, Epstein IR. (2005) Out-of-phase oscillatory Turing
patterns in a bistable reaction-diffusion system. Phys
Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt
2):066212. Epub 2005 Jun 23. [abstract]
Kaminaga A, Vanag VK, Epstein IR. (2005) "Black spots"
in a surfactant-rich Belousov-Zhabotinsky reaction dispersed
in a water-in-oil microemulsion system. J Chem Phys.
2005 May 1;122(17):174706. [abstract]
Berenstein I, Yang L, Dolnik M, Zhabotinsky AM, Epstein
IR. (2005) Dynamic mechanism of photochemical induction
of turing superlattices in the chlorine dioxide-iodine-malonic
acid reaction-diffusion system. J Phys Chem A Mol Spectrosc
Kinet Environ Gen Theory. 2005 Jun 23;109(24):5382-7.
[abstract]
K. Kurin-Csörgei, M. Orbán and I. R. Epstein, "Systematic
Design of Chemical Oscillators Using Complexation and Precipitation
Equilibria," Nature 433, 139-142 (2005). [abstract]
Y. Bar-Yam and I.R. Epstein, "Response of Complex Networks
to Stimuli," Proc. Natl. Acad. Sci. 101, 4341-4345
(2004). [abstract]
Vanag VK, Epstein IR. (2003) Translational and nontranslational
motion of perturbed Turing patterns. Phys Rev E Stat
Nonlin Soft Matter Phys. 2003 Jun;67(6 Pt 2):066219.
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]
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]
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]
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).
F. Sagués and I. R. Epstein, "Nonlinear Chemical Dynamics,"
Dalton Trans. 1201-1217 (2003) (cover article).
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).
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.
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, 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]
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.
Search PubMed for Publications: Irving
Epstein
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