Department of Chemistry

Irving R. Epstein

Irving Epstein

University Professor
Henry F. Fischbach Professor of Chemistry
HHMI Professor

Group website

Curriculum Vitae (PDF)


Harvard University, PhD
Harvard University, MA
Oxford University, Diploma
Harvard College, AB


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

Many phenomena in living systems involve periodic changes. In recent years, 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 dozens of deliberately constructed systems. We continue to search for new types of oscillators while probing, both experimentally and computationally, the mechanisms of those that have already been discovered.

Epstein BZ SequenceChemical oscillators can be "tweaked" to give a variety of related phenomena, many 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 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 sensitively on the initial conditions. We investigate Turing structures, patterns that arise from the interaction of reaction and diffusion, which have been suggested as a 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.  More recently, we have begun to study chemomechanical transduction, a phenomenon in which changes in chemical composition are converted into motion, e.g., in the periodic shrinking and swelling of a gel composed of a polymer that contains the catalyst for an oscillatory reaction immersed in a solution containing the reactants of the chemical oscillator.

Selected Publications

  • V. Horvath, D. J. Kutner, J. T. Chavis III and I. R. Epstein, “Pulse-coupled BZ oscillators with unequal coupling strengths,” Phys. Chem. Chem. Phys., 17, 4664-4677 (2015).
  • J. Shi, X. W. Du, Y. Huang, J. Zhou, D. Yuan, D. Wu, Y. Zhang, R. Haburcak, I. R. Epstein and B. Xu, “Ligand-Receptor Interaction Catalyzes the Aggregation of Small Molecules To Induce Cell Necroptosis,” J. Am. Chem. Soc., 137, 26-29 (2015).
  • M. Orbán, K. Kurin-Csörgei and I. R. Epstein, “pH-Regulated Chemical Oscillators,” Acc. Chem. Res., 48, 593–601 (2015).
  • K. Showalter and I. R. Epstein, “From Chemical Systems to Systems Chemistry: Patterns in Space and Time,” Chaos 25, 097613 (2015)
  • Gaskins DK, Pruc EE, Epstein IR, Dolnik M, "Multifold Increases in Turing Pattern Wavelength in the Chlorine Dioxide-Iodine-Malonic Acid Reaction-Diffusion System." Phys Rev Lett. 117:056001 (2016).
  • Maciejowska A, Godziek A, Talik E, Sajewicz M, Kowalska T, Epstein IR. "Spontaneous Pulsation of Peptide Microstructures in an Abiotic Liquid System." J Chromatogr Sci. 54:1301-9 (2016).
  • Luo H, Wang C, Ren L, Gao Q, Pan C, Epstein IR. "Light-Modulated Intermittent Wave Groups in a Diffusively Fed Reactive Gel." Angew Chem Int Ed Engl. 55:4988-91 (2016).
  • Epstein IR, Xu B. "Reaction-diffusion processes at the nano- and microscales." Nat Nanotechnol. 11:312-9 (2016).
  • Horváth V, Epstein IR, Kustin K. "Mechanism of the Ferrocyanide-Iodate-Sulfite Oscillatory Chemical Reaction." J Phys Chem A. 120:1951-60 (2016).
  • Ren L, She W, Gao Q, Pan C, Ji C, Epstein IR. "Retrograde and Direct Wave Locomotion in a Photosensitive Self-Oscillating Gel." Angew Chem Int Ed Engl. (2016).
  • Epstein IR, Gao Q. "Photo-Controlled Waves and Active Locomotion." Chemistry. 2017 Aug 22;23(47):11181-11188
  • Saxena A, Bhattacharya A, Kumar S, Epstein IR, Sahney R. "Biopolymer matrix for nano-encapsulation of urease - A model protein and its application in urea detection." J Colloid Interface Sci. 2017 Mar 15;490:452-461.
  • Li J, Bullara D, Du X, He H, Sofou S, Kevrekidis IG, Epstein IR, Xu B. "Kinetic Analysis of Nanostructures Formed by Enzyme-Instructed Intracellular Assemblies against Cancer Cells." ACS Nano. 2018 Apr 24;12(4):3804-3815
  • Horvath V, Epstein IR. "Pulse-coupled Belousov-Zhabotinsky oscillators with frequency modulation." Chaos. 2018 Apr;28(4):045108
  • Teng R, Ren L, Yuan L, Wang L, Gao Q, Epstein IR. "Effect of Reaction Parameters on the Wavelength of Pulse Waves in the Belousov-Zhabotinsky Reaction-Diffusion System." J Phys Chem A. 2019 Oct 31;123(43):9292-9297. 
  • Horváth V, Kutner DJ, Zeng MD, Epstein IR. "Phase-frequency model of strongly pulse-coupled Belousov-Zhabotinsky oscillators." Chaos. 2019 Feb;29(2):023128
  • Konow C, Somberg NH, Chavez J, Epstein IR, Dolnik M. "Turing patterns on radially growing domains: experiments and simulations." Phys Chem Chem Phys. 2019 Mar 28;21(12):6718-6724
  • Nagao R, de Miranda RCC, Epstein IR, Dolnik M. "Modulation of Turing Patterns in the CDIMA Reaction by Ultraviolet and Visible Light." J Phys Chem A. 2019 Feb 7;123(5):992-998
  • Ren L, Yuan L, Gao Q, Teng R, Wang J, Epstein IR. "Chemomechanical origin of directed locomotion driven by internal chemical signals." Sci Adv. 2020 May 1;6(18):eaaz9125.
  • Wang L, Yu Z, Gao Q, Wang H, Ren L, Ji C, Epstein IR. "Capillarity-Induced Propagation Reversal of Chemical Waves in a Self-oscillating Gel." J Phys Chem A. 2020 May 7;124(18):3530-3534
  • Ren L, Wang L, Gao Q, Teng R, Xu Z, Wang J, Pan C, Epstein IR. "Programmed Locomotion of an Active Gel Driven by Spiral Waves. " Angew Chem Int Ed Engl. 2020 Apr 27;59(18):7106-7112
  • Awal NM, Epstein IR. "Post-canard symmetry breaking and other exotic dynamic behaviors in identical coupled chemical oscillators." Phys Rev E. 2020 Apr;101(4-1):042222
  • Konow C, Li Z, Shepherd S, Bullara D, Epstein IR. "Influence of survival, promotion, and growth on pattern formation in zebrafish skin." Sci Rep. 2021 May 10;11(1):9864.