Spatial bistability: a source of complex dynamics. From spatiotemporal reaction-diffusion patterns to chemomechanical structures

Spatiotemporal dynamics of minimal bromate oscillators in an open one-side-fed reactor

Minimal bromate oscillators represent the simplest version of the oscillatory reactions based on the chemistry of the oxybromine species. Here, we present numerical and experimental evidence of the existence of reaction-diffusion waves in the ferroin catalyzed minimal bromate oscillator. The wave dynamics depend not only on the characteristic chemical timescales but also on those of the diffusive matter exchange which occurs between the reaction-diffusion medium and its environment. We show that the extended reactivity of the ferroin catalyst towards the oxybromine species plays an essential role in the observed phenomena. For the cerium catalyzed minimal bromate oscillator the simulations support only the formation of spatial bistability.

Design of localized spatiotemporal pH patterns by means of antagonistic chemical gradients

Spatially localized moving and stationary pH patterns are generated in two-side-fed reaction-diffusion systems. The patterns are sandwiched between two quiescent zones and positioned by the antagonistic gradients of the reactants of the self-activatory process. Spatial bistability, spatiotemporal oscillations, and formation of stationary Turing patterns have been predicted by numerical simulations and observed in experiments performed by using different hydrogen ion autocatalytic chemical systems. The formation of stationary patterns due to long-range inhibition is promoted by a large molecular weight hydrogen ion binding polymer.

Spatially localized moving and stationary pH patterns are generated in two-side-fed reaction-diffusion systems.

Experimental Evidence of Large Amplitude pH Mediated Autonomous Chemomechanical Oscillation

Large amplitude autonomous chemomechanical oscillations were observed in a coupled system consisting of a porous pH-responsive hydrogel and a bromate-sulfite-manganese (II) pH oscillatory reaction. The porous structure effectively improves the chemomechanical response speed, and the negative feedback species of the bulk oscillation Mn2+ takes part in the coupling by forming complex and physical crosslinks with the responsive group in the gel. It strengthens the porous gel by forming additional networks, which may contribute to sustaining the long-lasting chemomechanical oscillation. Additionally, the interaction between Mn2+ and the hydrogel alters the period of the oscillatory reaction due to its binding competition with H⁺, the positive feedback species.

Pattern Formation in the Bromate-Sulfite-Ferrocyanide Reaction

Mixed Landolt-type pH oscillators are versatile systems that allow the experimental study of a wide range of nonlinear phenomena including multistability, oscillations, and spatiotemporal patterns. We report on the dynamics of the bromate-sulfite-ferrocyanide reaction operated in a open one-side-fed reactor, where spatial bistability, spatiotemporal oscillations, front and Turing-type patterns have been observed. The role of different experimental parameters, like the input flow concentrations of the hydrogen and the ferrocyanide ions, the temperature and the thickness of the gel medium (which affects the rate of the diffusive feed) have been investigated. We point out that all these parameters can be efficiently used to control the spatiotemporal dynamics. We show that the increase of ionic strength stabilizes the uniform states at the expense of the patterned one. Some general aspects of the spatiotemporal dynamics of mixed Landolt type systems, which are based on the oxidation of sulfite ions by strong oxidants, are emphasized.

Sustained large-amplitude chemomechanical oscillations induced by the Landolt clock reaction

Synergetic chemomechanical oscillators represent a fundamentally new class of oscillators, where a clock reaction, owning no oscillatory chemical kinetics, generates shrinking-swelling cycles in a chemoresponsive gel under appropriate fixed nonequilibrium boundary conditions. Sufficiently large size-changes are a condition for continually switching between a reacted and an unreacted chemical state in the gel through sufficiently large differences in the diffusion time between the environment and the core of the gel. Two former experimental demonstrations with acid autocatalytic reactions were frustrated either by complex behaviors (chlorite-tetrathionate system) or by side reactions with the gel matrix (bromate-sulfite system). With the Landolt (iodate-sulfite) reaction, regular large-amplitude chemomechanical oscillations can be sustained for more than a week. This enabled a fine study of the temperature and stoichiometry range of operation. I have identified several key steps that are experimentally essential to the systematic design of further synergetic oscillators. The robust realization of this type of self-organization in artificial systems is currently unique.

Formation of localized structures in bistable systems through nonlocal spatial coupling. II. The nonlocal Ginzburg-Landau equation

We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts. We show this for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.

Interaction of multiarmed spirals in bistable media

We study the interaction of both dense and sparse multiarmed spirals in bistable media modeled by equations of the FitzHugh-Nagumo type. A dense one-armed spiral is characterized by its fixed tip. For dense multiarmed spirals, when the initial distance between tips is less than a critical value, the arms collide, connect, and disconnect continuously as the spirals rotate. The continuous reconstruction between the front and the back drives the tips to corotate along a rough circle and to meander zigzaggedly. The rotation frequency of tip, the frequency of zigzagged displacement, the frequency of spiral, the oscillation frequency of media, and the number of arms satisfy certain relations as long as the control parameters of the model are fixed. When the initial distance between tips is larger than the critical value, the behaviors of individual arms within either dense or sparse multiarmed spirals are identical to that of corresponding one-armed spirals.

Mechano-chemical oscillations and waves in reactive gels

We review advances in a new area of interdisciplinary research that concerns phenomena arising from inherent coupling between non-linear chemical dynamics and mechanics. This coupling provides a route for chemical-to-mechanical energy transduction, which enables materials to exhibit self-sustained oscillations and/or waves in both concentration and deformation fields. We focus on synthetic polymer gels, where the chemo-mechanical behavior can be engineered into the material. We provide a brief review of experimental observations on several types of chemo-mechanical oscillations in gels. Then, we discuss methods used to theoretically and computationally model self-oscillating polymer gels. The rest of the paper is devoted to describing results of theoretical and computational modeling of gels that undergo the oscillatory Belousov-Zhabotinsky (BZ) reaction. We discuss a remarkable form of mechano-chemical transduction in these materials, where the application of an applied force or mechanical contact can drive the system to switch between different dynamical behavior, or alter the mechanical properties of the material. Finally, we discuss ways in which photosensitive BZ gels could be used to fabricate biomimetic self-propelled objects. In particular, we describe how non-uniform illumination can be used to direct the movement of BZ gel 'worms' along complex paths, guiding them to bend, reorient and turn.

Spatiotemporal dynamics of mixed Landolt systems in open gel reactors: effect of diffusive feed

In this report we present an experimental study on the spatiotemporal dynamics of the iodate-sulfite-ferrocyanide and the iodate-sulfite-thiourea systems. Both systems are capable of producing nontrivial reaction-diffusion patterns when they are operated in a one-side-fed open spatial reactor. An important parameter of these types of reactors is the time scale of the diffusive feed, which is determined by the "thickness" of the gel and diffusion coefficients of the chemicals. A conical shape gel is used to study the effect of the thickness gradient on the dynamics. We show that spatiotemporal oscillations stop below a critical thickness. It is demonstrated that the period of the oscillations is determined by the time scale of the inhibitory kinetics and the time scale of the diffusive feed together. In the case of the iodate-sulfite-thiourea system we observed the appearance of a stationary iodine front in the presence of the oscillating pH front. An experimentally supported kinetic explanation is given to account this phenomena.

Propagating waves separate two states of actin organization in living cells

Propagating actin waves are dynamic supramolecular structures formed by the self-assembly of proteins within living cells. They are built from actin filaments together with single-headed myosin, the Arp23 complex, and coronin in a defined three-dimensional order. The function of these waves in structuring the cell cortex is studied on the substrate-attached surface of Dictyostelium cells by the use of total internal reflection fluorescence (TIRF) microscopy. Actin waves separate two areas of the cell cortex from each other, which are distinguished by the arrangement of actin filaments. The Arp23 complex dominates in the area enclosed by a wave, where it has the capacity of building dendritic structures, while the proteins prevailing in the external area, cortexillin I and myosin-II, bundle actin filaments and arrange them in antiparallel direction. Wave propagation is accompanied by transitions in the state of actin with a preferential period of 5 min. Wave generation is preceded by local fluctuations in actin assembly, some of the nuclei of polymerized actin emanating from clathrin-coated structures, others emerging independently. The dynamics of phase transitions has been analyzed to provide a basis for modeling the nonlinear interactions that produce spatio-temporal patterns in the actin system of living cells.

Oscillatory dynamics induced in polyelectrolyte gels by a non-oscillatory reaction: a model

We develop a general model and the associated numerical algorithm to compute the swelling dynamics of chemo-responsive polyelectrolyte gels immersed in a reactive ionic solution kept at a non equilibrium stationary state by a permanent feed of fresh reactants. Using an autocatalytic bistable but nonoscillatory reaction, namely, the bromate-sulfite reaction, we predict that a piece of hydrogel that swells/shrinks as a function of pH can exhibit spontaneous mechanical and chemical oscillations. This constitutes the extension to realistic and experimentally feasible conditions of results previously obtained on a toy model with artificial swelling conditions.

The transition from pH waves to iodine waves in the iodate/sulfite/thiosulfate reaction-diffusion system

Nonlinear spatial temporal behavior of the iodate/thiosulfate/sulfite reaction is investigated both in a stirred and spatially extended media. In accord with the temporal dynamics in the homogeneous media, both propagating fronts and target patterns are achieved in the spatially extended medium. On increasing the iodate concentration the system evolves from exhibiting propagating fronts to circular waves and then shows target patterns and finally the iodine waves. Influences of concentrations of sulfite, thiosulfate and acid on the reaction kinetics and pattern formation are also investigated systematically, and transitions from pH waves to iodine waves can be achieved via adjusting the concentration of the three species. The propagation velocities of pH and iodine waves are understood with the quadratic and cubic autocatalysis of proton and iodide respectively.

Pattern formation in the ferrocyanide-iodate-sulfite reaction: the control of space scale separation

We revisit the conditions for the development of reaction-diffusion patterns in the ferrocyanide-iodate-sulfite bistable and oscillatory reaction. This hydrogen ion autoactivated reaction is the only example known to produce sustained stationary lamellar patterns and a wealth of other spatio-temporal phenomena including self-replication and localized oscillatory domain of spots, due to repulsive front interactions and to a parity-breaking front bifurcation (nonequilibrium Ising-Bloch bifurcation). We show experimentally that the space scale separation necessary for the observation of stationary patterns is mediated by the presence of low mobility weak acid functional groups. The presence of such groups was overlooked in the original observations made with hydrolyzable polyacrylamide gels. This missing information made the original observations difficult to reproduce and frustrated further experimental exploitation of the fantastic potentialities of this system. Using one-side-fed spatial reactors filled with agarose gel, we can reproduce all the previous pattern observations, in particular the stationary labyrinthine patterns, by introducing, above a critical concentration, well controlled amounts of polyacrylate chains in the gel network. We use two different geometries of spatial reactors (annular and disk shapes) to provide complementary information on the actual three-dimensional character of spatial patterns. We also reinvestigate the role of other feed parameters and show that the system exhibits both a domain of spatial bistability and of large-amplitude pH oscillations associated in a typical cross-shape diagram. The experimental method presented here can be adapted to produce patterns in the large number of oscillatory and bistable reactions, since the iodate-sulfite-ferrocynide reaction is a prototype of these systems.

Sustained Spatiotemporal Patterns in the Bromate−Sulfite Reaction

The acid autoactivated bromate-sulfite reaction exhibits spatial bistability, travelling acid-base fronts, and spatiotemporal oscillations when operated in an unstirred one-side-fed spatial reactor. We show that a skeleton kinetic model, recently proposed by Szántó and Rábai, in which we take into account the charge and the actual diffusivity of solvated ions, provides theoretical results in good agreement with experimental observations. The differences with previous observations made with the homologous iodate-sulfite reaction are discussed. Despite the analogies in the phase diagram of these two systems, it is concluded that the relevant kinetic mechanism of the iodate-sulfite system cannot be just a homologous transcription of that presently working well for the bromate-sulfite system, even in excess sulfite conditions.

Spatio-temporal behaviors of a clock reaction in an open gel reactor

The concentration profiles along the feeding direction of a one side fed gel reactor are analyzed for the iodate-arsenous acid reaction. Multiplicity of inhomogeneous stationary solutions is derived. It is also shown that such profiles may undergo oscillatory bifurcations under long range activation conditions. The bifurcation diagram is analyzed using a Galerkin approximation, the asymptotic validity of which is discussed.