Here we present a versatile strategy for creating self-regulating, self-powered, homeostatic materials capable of precisely tailored chemo-mechano-chemical feedback loops on the nano- or microscale. We apply this design to trigger organic, inorganic and biochemical reactions that undergo reversible, repeatable cycles synchronized with the motion of the microstructures and the driving external chemical stimulus.
By exploiting a continuous feedback loop between various exothermic catalytic reactions in the nutrient layer and the mechanical action of the temperature-responsive gel, we then create exemplary autonomous, self-sustained homeostatic systems that maintain a user-defined parameter—temperature—in a narrow range. The experimental results are validated using computational modelling that qualitatively captures the essential features of the self-regulating behaviour and provides additional criteria for the optimization of the homeostatic function, subsequently confirmed experimentally.
This design is highly customizable owing to the broad choice of chemistries, tunable mechanics and its physical simplicity, and may lead to a variety of applications in autonomous systems with chemo-mechano-chemical transduction at their core. Bao, G. Molecular biomechanics: the molecular basis of how forces regulate cellular function.
Fratzl, P. Biomaterial systems for mechanosensing and actuation. Nature , — Guyton, A. Human Physiology and Mechanisms of Disease 6th edn 3—8 Saunders, Prosser, B. X-ROS signaling: rapid mechano-chemo transduction in heart. Science , — Sambongi, Y. Spaet, T. Analytical review: hemostatic homeostasis. Blood 28 , — Hess, H. Engineering applications of biomolecular motors.
Translating biomolecular recognition into nanomechanics. Lahann, J. Smart materials with dynamically controllable surfaces. MRS Bull. Li, D. Molecular, supramolecular, and macromolecular motors and artificial muscles. Paxton, W. Chemical locomotion. Sidorenko, A. Reversible switching of hydrogel-actuated nanostructures into complex micropatterns. Ariga, K. Todres, Z. Harris, T. A review of performance monitoring and assessment techniques for univariate and multivariate control systems. Process Contr. Stuart, M. Emerging applications of stimuli-responsive polymer materials. Nature Mater.
Yerushalmi, R. Stimuli responsive materials: new avenues toward smart organic devices. Such a non-monotonous dispersion relation has been observed in a recent variant of BZ reaction . The existence of such stationary structures was first analytically demonstrated by Turing . In the proposed mechanism, patterns develop spontaneously in an initially uniform system. It is presented as a possible model for the spontaneous development of shapes and patterns observed during biological morphogenesis.
We shall present them in an heuristic way. More rigorous developments can be found in Chapter 3 and in references there in. Let us consider, as Meinhardt , an activator-inhibitor system where the activator produces its own inhibitor. Suppose a stable uniform state where the activatory and inhibitory processes balance each other and operate on the same time scale so that the system would not undergo an oscillatory instability.
Consider a local excess of the activator, due to a perturbation or a concentration fluctuation Figure 10a. This increased concentration of the activator induces, over the same time scale, an associated increase of inhibitor, as schematized on Figure 10b. The levels of the activator and inhibitor turn back to their initial stable uniform state composition. As a result there will be shortage in the inhibitor at the center and the concentration of the activator will grow Figure 10c. A stable activatory peak forms and settles for as long as the reagents are supplied.
In this heuristic description, it is understandable that an other activatory peak can only develop at a finite minimal distance from an existing one Figure 10d. In the special case of the Turing bifurcation the initial homogeneous state is unstable to spatial perturbations in a finite range of wavelength. Fluctuations are random.
The peaks of activator compete for space. From this competition a well ordered pattern ruled by the nonlinear interactions emerges Figure 10e. In uniform two-dimensional systems, near to onset, the pattern selection process leads to two ordered 20 P. Schematic growth mechanism of a Turing pattern in an activator full black curves inhibitor dashed gray curves system: a fluctuation in the concentration of the activator; b followed by the associated increase of the inhibitor; c the inhibitor spreads faster than the activator and stabilizes the peak of activator; d another fluctuation of the activator can grow only beyond a critical distance from a well developped peak; e the competition between growing activator peaks settles into a periodic pattern.
In uniformly fed three-dimensional systems the spatial concentration modulations organize in body-centered-cubic, hexagonal arrays of columns, and lamellea structures . However, none of these more exotic patterns have been experimentally identified, so far. There is an important property toTuring structures that distinguish them from other nonlinear patterns found in other field of physics.
Geometric parameters only play a minor role in the selection or orientation of patterns. As seen above, the major routes to the development of stationary patterns require appropriate space and time scale separation between activatory and inhibitory processes. The complex is in rapid equilibrium with X, so that one can eliminate Eq. This derivation can be made more rigorous but the result remains valid in the frame of our approximations. Appropriate conditions for the development of stationary patterns are shown to be reached this way.
This approach was further generalized by Pearson and Bruno  and by Strier and Ponce-Dawson  who show that, whatever the number of variables and the number of complexing agents, or if the inertness of the complex is partly relaxed, a Turing bifurcation can be obtained. Furthermore, the Turing bifurcation is obtained for parameter values where, in the absence of the complex, the steady uniform system is temporally unstable going from an unstable focus to an unstable node.
The quenching of the oscillations is associated to the absence of reactivity of the hypothetic complex, a requirement that is very commonly fulfilled by macromolecular complexes. Other route to stationary patterns, e.
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Experimental observations The most remarkable fall out from the early development of open spatial reactors is the first observation of sustained stationary chemical patterns resulting from a Turing instability . The reaction is one of the very few that is able to exhibit transient oscillations in batch conditions. It was shown that during the oscillatory behavior, the actual main reagents are chlorine dioxide, iodine and malonic acid , while the activatory and inhibitory processes were essentially driven by the iodide and chlorite ions, respectively.
These two type of patterns, observed in a twoside-fed strip reactor a reactor geometry similar to the one in Figure 7a are illustrated in Figure 11a and b where the dark and clear regions correspond to high and low concentrations of the colored polyiodide complex C. At low concentration of starch, localized trains of traveling wave are observed, while, at higher starch concentration, a row of equally spaced standing clear spots is obtained.
This latter property is used in the experiment presented in Figure 12 where patterns are made to develop in a beveled disc reactor. One witnesses, 24 P. Potassium iodide: a and b 1. All other parameters are fixed.
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Figure Turing pattern planforms developed in disc reactor in the TSFR mode with a ramp of thickness and opposedly fed by a chlorite and an iodide solution as in Figure The distance between the circular faces varies from 1. The first two pattern planforms are the two standard stable spatial pattern symmetries predicted for two-dimensional Turing patterns see Chapter 3. However, the onset of patterns and their relative stability can be significantly modified . Note that these monolayer patterns are actually three-dimensional structures: spots are spheroids and stripes are, here, clear cylindrical structures laying parallel to the feed surface.
The re-entrant hexagonal pattern observed past half way in the figure would correspond to arrays of short cylinders with their axis now orthogonal to the feed surface. Hexagonal arrays of columnar structures are expected in three-dimensional systems  see Chapter 3. Modeling, the observations in this geometry is a great challenge which would require advanced kinetic models to properly handle the large range of reactant concentrations scanned through the ramps.
Computational attractive, reduced kinetic models of reactions with nonlinear kinetic mechanisms are usually suited only over relatively restricted ranges of concentrations. However, tentative tries have been made in this direction to estimate the width and position of the patterning stratum in the CIMA reaction . Modeling experimental results in one-side-fed reactors To avoid the above problems, most recent studies are performed in thin OSFRs.
In such spatial reactor feed mode, one can distinguish two cases: First, the few reactions that can exhibit transient batch oscillations where the main reagents are only partly consumed during one oscillatory period. According to the work of Lengyel and Epstein on this reaction, if no external gradients are imposed, the variations of the major reactant concentrations are small on the distance of a wavelength or over a period of oscillation . If all the input reactants are fed onto one side of a thin enough film of gels, i. Accordingly, the thin disc reactor should approximate a uniformly constrained two-dimensional system.
Experiments were performed in a 0. More details in the text. For an appropriate feed of the CSTR, the standard sequence of twodimensional hexagonal and striped patterns arrays are observed, as in the case of monolayers in the TSFR, but the dimensionality of the patterns is now directly controlled by the geometric parameters of the reactor. From left to right Figure 13 , one can distinguish three regions: i a region of uniform stationary state, ii a region of stationary hexagonal and striped Turing patterns, iii a region where the CSTR contents oscillate and for which the dynamics in the gel was disregarded.
In doing this, the kinetic model can be reduced to only two variables. In spite of this agreement, one can be astonished that this approximation works so well and even that patterns are experimentally observed in such a thin gel. In Section 2. Here the wavelength and the thickness of the gel are similar i. The homogeneity onto the feed face should force uniformity across the whole thin gel. The patterns are thus free to develop in planes parallel to the faces . In this case, a well defined chemical boundary layer develops. It gives rise to a new property of autoactivated systems: spatial bistability .
Obviously, for non-equilibrium instabilities and patterns to develop in the gel, the 28 P. In a fictitious experiments where one would continuously change w, a hysteresis phenomenon would be observed as a function of w Figure This is spatial bistability. As for temporal bistability, the range of spatial bistability can be controlled by the chemical feed parameters or the temperature of the system. A typical example of F and FT state profiles, obtained by numerical simulations of a detailed kinetic model of the CDI reaction is shown in Figure At the phase diagram level, these numerical calculations semi-quantitatively account for the experimental observations Figure 16 .
Schematic spatial bistability. Representations with increasing w, top row, and decreasing w, bottom row. Switching from one type of profile to the other occurs with hysteresis at wmin and wmax. In systems extended in directions parallel to the feed boundary, in the spatial bistability domain, one can create interfaces between the two spatial states.
Depending on the relative stability of the two states, one or the other states would expand at the expense of the other . The control of the direction of propagation and the interaction of these interfaces on head-on collision can plays an important role in the development of stationary pulse patterns. However, such stationary structures require an expanded version of the CDI reaction , as explained in the next section. The method was initially tested on the ferrocyanide-iodate-sulfite FIS reaction .
However, until recently  no other group could reproduce these observations for unidentified reasons. The reaction is a two-substrate pH bistable and oscillatory reaction . In this range of pH, the protons can be reversibly binded by carboxilate functions. In the absence of macromolecular proton-binding species, the reaction develops spatial bistability when operated in an agarose gel OSFR.
Note that a cross-shape diagram is also recovered in the OSFR. The success of the original experiments probably resulted from an unintentional and uncontrolled slight hydrolysis of the amide functions of the polyacrylamide gel network used at that time. Supercritical concentrations of low mobility carboxilate functions could be reached by the hydrolysis of only a few tenths of percent of the amide functions of the gel network .
In the recent experiments the concentrations of these low mobility functions are directly controlled by the feed composition. As a test for the method, it was shown that a sister chemical system, the thiourea-iodate-sulfite TuIS , also a double substrate pH oscillatory reaction, could lead to stationary patterns. In this case, the patterns emerge through a Turing bifurcation when supercritical amounts of polyacrylic functions are fed in the agarose gel OSFR .
If not compensated, this accumulation would oppose to the stabilization of a pattern. Ferrocyanide and thiourea play this role in the above two systems and malonic acid plays a similar role in the stabilization of stationary pulses in the spatial bistable domain of an extended version of the CIMA reaction . It is noteworthy that, beside appropriate space scale separation, the development of stationary patterns also requires appropriate time scales separation, specially when they develop through front interaction mechanisms.
The activatory process should evolve on a longer time scale than the inhibitory process.
Chemomechanical Instabilities in Responsive Materials
In oscillatory systems, this is just the opposite. Yet, experience show that stationary patterns are more easily obtained in the domain or in the close vicinity of the domain of parameters for which the system oscillates in the absence of low mobility complexing agent for the activator. As seen in paragraph 2. In fact, as stated above, conditions for reaching a Turing bifurcation by adding a complexing agent always correspond to an initially oscillatory domain of the phase diagram .
However, this prerequisite is, a priori, not necessary in the case of stationary patterns resulting from front pairing interactions. In the case of the FIS reaction, labyrinthine patterns can be observed for compositions corresponding to the spatial bistability domain just below the cross-point in Figure 17, but never in the absence of ferrocyanide.
SZALAI forcing [95, 96] or in more complex microemulsion systems  have not been addressed here to keep things simple. Only examples of the most basic temporal and spatial phenomena are reported with emphasis on the method and hints. A good understanding of the basic features of oscillatory reactions is necessary since they are widely used as the driving chemical engines for chemomechanical devices described in this collection lectures. Furthermore, many of the ideas which made successful the development chemical oscillations and patterns can be and are already used to produce emerging chemomechanical structures.
The change in size of a gel supporting a bistable chemical reaction can act as a negative feedback to generate oscillatory size pulsations even when the reaction has no oscillatory property in itself. Similarly using the hysteretic gate properties of a responsive gel membrane in a compartmentalized reactor a chemical feedback reaction can induce concentration oscillation in one compartment. Detailed descriptions of those systems are found in this book.
The recent gain of control and development of those chemical patterns make such studies possible now. References 1. Ostwald, Z. Bredig, J. Weinmayer, Z. Lippman, Ann. Hedges, J. Bray, J. Belousov, Sbornik Referatov po Radiatsionni Medditsine p. Fechner, Schweigger, J. Field, E. Noyes, J. Field, R. Gray, S. Scott, Chem. Shen, R. Larter, Biophys. Kern, C. Kim, J. Tyson, J. Luo, I. Epstein, Adv. Roux, P. Boissonade, Phys. A 97, ; M. Boukalouch, J. Boissonade, P. Paris 84, ; Y. Epstein, J. Dutt, M. Menzinger, J. Menzinger, A. Giraudi, J. Franck, Angew. Pacault, Compt. C, Dateo, P. De Kepper, I.
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