Irving R. Epstein

Modeling of Turing Structures in the Chlorite—Iodide—Malonic Acid—Starch Reaction System

Recent experiments on the chlorite-iodide-malonic acid-starch reaction in a gel reactor give the first evidence of the existence of the symmetry breaking, reaction-diffusion structures predicted by Turing in 1952. A five-variable model that describes the temporal behavior of the system is reduced to a two-variable model, and its spatial behavior is analyzed. Structures have been found with wavelengths that are in good agreement with those observed experimentally. The gel plays a key role by binding key iodine species, thereby creating the necessary difference in the effective diffusion coefficients of the activator and inhibitor species, iodide and chlorite ions, respectively.

Cooperative and non-cooperative binding of large ligands to a finite one-dimensional lattice: A model for ligand-ougonucleotide interactions

A combinatorial approach is employed to calculate exact expressions for the extent of binding to a finite one dimensional lattice of ligands which cover more than one lattice site. The binding may be either cooperative or non-cooperative. It is found that the assumption of an effectively infinite lattice is generally a good one, except with relatively low concentrations of strongly cooperative ligands. An approach to analyzing experimental data is suggested which makes explicit use of the lattice length dependence of binding to extract more information about the binding parameters than can be obtained using the infinite lattice approximation. It is shown that irreversible binding cannot be viewed as a limiting case of reversible binding. The reasons for this difference are discussed, and expressions for the extent of irreversible binding are derived.

Changing the Culture of Science Education at Research Universities

Universities must better recognize, reward, and support the efforts of researchers who are also excellent and dedicated teachers. Professors have two primary charges: generate new knowledge and educate students. The reward systems at research universities heavily weight efforts of many professors toward research at the expense of teaching, particularly in disciplines supported extensively by extramural funding (1). Although education and lifelong learning skills are of utmost importance in our rapidly changing, technologically dependent world (2), teaching responsibilities in many STEM (science, technology, engineering, and math) disciplines have long had the derogatory label “teaching load” (3, 4). Some institutions even award professors “teaching release” as an acknowledgment of their research accomplishments and success at raising outside research funds.

Diffusively Coupled Chemical Oscillators in a Microfluidic Assembly

From fireflies that synchronize their flashes with each other to heart muscles contracting and relaxing in unison, synchronized behavior of living cells or organisms is ubiquitous in nature. Chemical reaction–diffusion systems can help us understand the mechanisms that underlie such synchronization. Coupled chemical oscillators have previously been studied in the laboratory with large reactors connected directly by small channels for controlled mass exchange of bulk solution. In this case, coupling occurs via all species. In living systems, however, coupling often occurs through special signaling molecules, as in synaptic communication or chemotaxis. Collections of neural oscillators can access a vast repertoire of coordinated behavior by utilizing a variety of topologies and modes of coupling, including gap junctions and synaptic links, which may be either excitatory or inhibitory, depending on the neurotransmitter involved. To mimic such a fine level of communication in a chemical system, we need to do two things: a) reduce the size of each oscillator in order to bring the characteristic time of communication between diffusively coupled oscillators to or below the period of oscillation; and b) introduce a semipermeable membrane or other medium between the microoscillators to permit communication only via selected species. These goals can be achieved with the use of microfluidic devices. Our experimental system (Figure 1a) is a linear array of tens of droplets of nanoliter volume containing aqueous ferroin-catalyzed Belousov–Zhabotinsky (BZ) solution separated by octane drops in a glass capillary. The BZ reaction, in which the oxidation of malonic acid (MA) by bromate is catalyzed by a metal complex in acidic aqueous solution, is a well known chemical oscillator. Owing to the small spatial extent (lw= 100–400 mm) of the BZ droplets, the characteristic time of diffusive mixing within a single droplet, lw /D (5–80 s, D=diffusion constant of aqueous species), is smaller than the period of oscillation (180–300 s), and individual BZ droplets can be considered homogeneous. Bromine, an inhibitory intermediate of the BZ reaction, is quite hydrophobic and diffuses readily into hydrocarbons such as octane, thus mediating inhibitory interdroplet coupling. We have shown theoretically that in such heterogeneous systems patterns analogous to the Turing patterns found in homogeneous systems can emerge. Without compartmentalization, the homogeneous BZ solution in a similar capillary exhibits trigger waves of excitation. Partitioning the medium into droplets dramatically changes this behavior. For BZ droplets (Figure 1b) with lw> 400 mm or oil droplets with length lO> 400 mm, no discernible coherent patterns are seen. However if lw= 100– 400 mm and lO= 50–400 mm, we observe stable anti-phase oscillations (Figure 2a) at larger [MA] (greater than 100 mm) and Turing patterns (Figure 2b) at smaller [MA] (less than 40 mm). At higher levels of [MA], initially in-phase arrays of droplets evolve to an anti-phase configuration within a few periods of oscillation (Movie in Supporting Information). For [MA]= 40 mm, the transition to the Turing regime goes through intermediate anti-phase oscillations. For slightly smaller [MA] (35 mm), initially in-phase droplets transform into Turing patterns almost immediately, without intermediate anti-phase oscillations. At small [MA], the behavior is rather sensitive to the size of droplets, with small drops reaching stationary state more rapidly than larger ones. To establish whether bromine is responsible for communication between the BZ droplets, surfactant Span80 (sorbitan mono-oleate) at concentrations of 5% was added to the octane. In separate experiments, it was found that Span80, which possesses an unsaturated double bond in its hydrocarbon tail, reacts with bromine in octane in less than 1 s. The water-insoluble Span80 thus acts as a trap for bromine, removing it from the octane. When Span80 is added to the droplet system, inhibiting the communication between BZ droplets, individual droplets oscillate independently. If we initiate the system (see Experimental Section) with all droplets in the same phase, in-phase oscillations persist. Figure 1. a) Schematic representation of the microfluidic device. Red droplets correspond to the reduced form of the catalyst (ferroin), blue droplets to the oxidized form (ferriin). A new method for fabricating such junctions is outlined in the Supporting Information. b) Snapshot of two capillaries with droplets. BZ droplets with convex surfaces are dark due to ferroin. Horizontal length of the frame and inner diameter (ID) of the capillary are 4.8 mm and 150 mm, respectively. BZ droplets were recorded by a CCD camera through a microscope with illumination by light passed through a 510 nm interference filter.

Testing Turing’s theory of morphogenesis in chemical cells

Significance Turing proposed that intercellular reaction-diffusion of molecules is responsible for morphogenesis. The impact of this paradigm has been profound. We exploit an abiological experimental system of emulsion drops containing the Belousov–Zhabotinsky reactants ideally suited to test Turing’s theory. Our experiments verify Turing’s thesis of the chemical basis of morphogenesis and reveal a pattern, not previously predicted by theory, which we explain by extending Turing’s model to include heterogeneity. Quantitative experimental results obtained using this artificial cellular system establish the strengths and weaknesses of the Turing model, applicable to biology and materials science alike, and pinpoint which directions are required for improvement. Alan Turing, in “The Chemical Basis of Morphogenesis” [Turing AM (1952) Philos Trans R Soc Lond 237(641):37–72], described how, in circular arrays of identical biological cells, diffusion can interact with chemical reactions to generate up to six periodic spatiotemporal chemical structures. Turing proposed that one of these structures, a stationary pattern with a chemically determined wavelength, is responsible for differentiation. We quantitatively test Turing’s ideas in a cellular chemical system consisting of an emulsion of aqueous droplets containing the Belousov–Zhabotinsky oscillatory chemical reactants, dispersed in oil, and demonstrate that reaction-diffusion processes lead to chemical differentiation, which drives physical morphogenesis in chemical cells. We observe five of the six structures predicted by Turing. In 2D hexagonal arrays, a seventh structure emerges, incompatible with Turing’s original model, which we explain by modifying the theory to include heterogeneity.

Tomography of reaction-diffusion microemulsions reveals three-dimensional turing patterns

Tomography reveals three-dimensional Turing patterns created by the Belousov-Zhabotinsky reaction running in a microemulsion. Spatially periodic, temporally stationary patterns that emerge from instability of a homogeneous steady state were proposed by Alan Turing in 1952 as a mechanism for morphogenesis in living systems and have attracted increasing attention in biology, chemistry, and physics. Patterns found to date have been confined to one or two spatial dimensions. We used tomography to study the Belousov-Zhabotinsky reaction in a microemulsion in which the polar reactants are confined to aqueous nanodroplets much smaller than the scale of the stationary patterns. We demonstrate the existence of Turing patterns that can exist only in three dimensions, including curved surfaces, hexagonally packed cylinders, spots, and labyrinthine and lamellar patterns.

A systematically designed homogeneous oscillating reaction: the arsenite-iodate-chlorite system

Journal of the American Chemical Society is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 A systematically designed homogeneous oscillating reaction: the arsenite-iodate-chlorite system Patrick De Kepper, Irving R. Epstein, and Kenneth Kustin J. Am. Chem. Soc., 1981, 103 (8), 2133-2134• DOI: 10.1021/ja00398a061 • Publication Date (Web): 01 May 2002 Downloaded from http://pubs.acs.org on April 10, 2009

Segmented spiral waves in a reaction-diffusion system

Pattern formation in reaction-diffusion systems is often invoked as a mechanism for biological morphogenesis. Patterns in chemical systems typically occur either as propagating waves or as stationary, spatially periodic, Turing structures. The spiral and concentric (target) waves found to date in spatially extended chemical or physical systems are smooth and continuous; only living systems, such as seashells, lichens, pine cones, or flowers, have been shown to demonstrate segmentation of these patterns. Here, we report observations of segmented spiral and target waves in the Belousov–Zhabotinsky reaction dispersed in water nanodroplets of a water-in-oil microemulsion. These highly ordered chemical patterns, consisting of short wave segments regularly separated by gaps, form a link between Turing and trigger wave patterns and narrow the disparity between chemistry and biology. They exhibit aspects of such fundamental biological behavior as self-replication of structural elements and preservation of morphology during evolutionary development from a simpler precursor to a more complex structure.

Pattern formation arising from interactions between Turing and wave instabilities

We study pattern formation arising from the interaction of the stationary Turing and wave (oscillatory Turing) instabilities. Interaction and competition between these symmetry-breaking modes lead to the emergence of a large variety of spatiotemporal patterns, including modulated Turing structures, modulated standing waves, and combinations of Turing structures and spiral waves. Spatial resonances are obtained near codimension-two Turing-wave bifurcations. Far from bifurcation lines, we obtain inwardly propagating spiral waves with Turing spots at their tips. We demonstrate that the coexistence of Turing spots and traveling waves is a result of interaction between Turing and oscillatory modes, while the inwardly propagating waves (antispirals) do not require this interaction; they can arise from the wave instability combined with a negative group velocity.

Role of the Neurogranin Concentrated in Spines in the Induction of Long-Term Potentiation

Synaptic plasticity in CA1 hippocampal neurons depends on Ca2+ elevation and the resulting activation of calmodulin-dependent enzymes. Induction of long-term depression (LTD) depends on calcineurin, whereas long-term potentiation (LTP) depends on Ca2+/calmodulin-dependent protein kinase II (CaMKII). The concentration of calmodulin in neurons is considerably less than the total concentration of the apocalmodulin-binding proteins neurogranin and GAP-43, resulting in a low level of free calmodulin in the resting state. Neurogranin is highly concentrated in dendritic spines. To elucidate the role of neurogranin in synaptic plasticity, we constructed a computational model with emphasis on the interaction of calmodulin with neurogranin, calcineurin, and CaMKII. The model shows how the Ca2+ transients that occur during LTD or LTP induction affect calmodulin and how the resulting activation of calcineurin and CaMKII affects AMPA receptor-mediated transmission. In the model, knockout of neurogranin strongly diminishes the LTP induced by a single 100 Hz, 1 s tetanus and slightly enhances LTD, in accord with experimental data. Our simulations show that exchange of calmodulin between a spine and its parent dendrite is limited. Therefore, inducing LTP with a short tetanus requires calmodulin stored in spines in the form of rapidly dissociating calmodulin–neurogranin complexes.