Philosophical Transactions of the Royal Society A, Nov 8, 2021
In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two mo... more In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two morphogen reaction–diffusion system [Turing, A. M. (1952) Phil. Trans. R. Soc. Lond. A 237 , 37–72. (doi:10.1098/rstb.1952.0012)]. While the model is simple, it has found diverse applications in fields such as biology, ecology, behavioural science, mathematics and chemistry. Chemistry in particular has made significant contributions to the study of Turing-type morphogenesis, providing multiple reproducible experimental methods to both predict and study new behaviours and dynamics generated in reaction–diffusion systems. In this review, we highlight the historical role chemistry has played in the study of the Turing mechanism, summarize the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and suggest future directions for chemical studies into Turing-type morphogenesis. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.
We demonstrate a novel mechanism for controlling the frequency, amplitude, and existence of chemi... more We demonstrate a novel mechanism for controlling the frequency, amplitude, and existence of chemical oscillations. Using a ferrocyanide-iodate-sulfite reaction, we show that a chemical buffer can increase or decrease the frequency of oscillations. Furthermore, the same buffer can completely suppress or, conversely, induce oscillations when added to the appropriate composition. This simple buffering scheme can provide a practical method for controlling the oscillations of a variety of chemical and biological systems. [S0031-9007(99)08396-9]
A model of the chlorine dioxide-iodide reaction in a single well-stirred flow-through reactor is ... more A model of the chlorine dioxide-iodide reaction in a single well-stirred flow-through reactor is analyzed. The model includes a flow regulation mechanism that allows the concentration of iodide in the system to control the flow rate. The control is accomplished through a computer-mediated sigmoidal dependence of the dynamic flow rate on the iodide concentration. The dynamical behavior of this system with slow regulation is investigated by the numerical continuation technique. Oscillatory behavior is obtained for parameter values that produce only steady state behavior in the unregulated system. Chaos and bursting also arise as a result of the control mechanism. Responses of the model to changes in input iodide concentration show the ability of the system to adjust to new conditions. Two different transient pattems of adjustment are observed depending on the direction of the change in iodide input concentration. The control mechanism mimics a similar system thought to control activity in biological neurons and may be of practical value. ' Department of Chemistry.
Various patterns of standing waves are found beyond the onset of the shortwave instability in a m... more Various patterns of standing waves are found beyond the onset of the shortwave instability in a model reactiondiffusion system. These include plain and modulated stripes, squares, and rhombi in systems with square and rectangular geometry and patterns with rotational symmetry in systems with circular geometry. We also find standing waves consisting of periodic time sequences of stripes and rhombi, stripes and squares, and stripes, rhombi, and hexagons. The shortwave instability can lead to a much greater variety of spatio-temporal patterns than the aperiodic Turing and the long-wave oscillatory instabilities. For instance, a single oscillatory cycle can display all the basic patterns related to the aperiodic Turing instabilitysstripes, hexagons, and inverted hexagons (honeycomb)sas well as rhombi and modulated stripes.
We have performed one-dimensional and two-dimensional experiments and simulations to study the fo... more We have performed one-dimensional and two-dimensional experiments and simulations to study the formation of patterns in a system that grows continuously in one direction. Depending on the growth velocity, three basic spatial configurations can be obtained: stripes that are parallel, oblique, or perpendicular to the growth direction. The dependence of the wavelength on the growth velocity has also been observed. Our results illustrate the importance of these growth mechanisms in determining the final configuration of chemical and biological pattern-forming processes.
We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to... more We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to a periodic process that is intrinsic to the cell. We investigate the synchronization properties of the coupled system, and show how the oscillator can be constructed to yield a significant amplification of cellular oscillations. We reduce the driven oscillator equations to a normal form, and analytically determine the amplification as a function of the strength of the cellular oscillations. The ability to couple naturally occurring genetic oscillations to a synthetically designed network could lead to possible strategies for entraining and/or amplifying oscillations in cellular protein levels.
Journal of the Chemical Society, Faraday Transactions, 1996
ABSTRACT Various patterns of modulated waves are found beyond the onset of the wave instability i... more ABSTRACT Various patterns of modulated waves are found beyond the onset of the wave instability in a model reaction-diffusion system with length between 1 and 3 times the basic wavelength. With periodic boundary conditions, we observe low-frequency modulation of the speed of the travelling waves. A fascinating pattern of waves that periodically change their direction of propagation along the ring is found when the ring length is between 1.05 and 1.35 times the basic wavelength. With zero-flux boundary conditions, a related pattern of modulated standing waves is found between the domains of the half-wavelength and the one-wavelength standing waves; the period of modulation contains two phases of non-stationary travelling waves, moving alternately left and right, separated by phases of short-lived asymmetric standing waves.
We utilize a simple three-variable reaction}di!usion model to study patterns that emerge beyond t... more We utilize a simple three-variable reaction}di!usion model to study patterns that emerge beyond the onset of the (short-)wave instability. We have found various wave patterns including standing waves, traveling waves, asymmetric standing}traveling waves and target patterns. We employ both periodic and zero #ux boundary conditions in the simulations, and we analyze the patterns using space}time two-dimensional Fourier spectra. A fascinating pattern of waves which periodically change their direction of propagation along a ring is found for very short systems. A related pattern of modulated standing waves is found for systems with zero #ux boundary conditions. In a two-dimensional system with small overcriticality we observe a wide variety of standing wave patterns. These include plain and modulated stripes, squares and rhombi. We also "nd standing waves consisting of periodic time sequences of stripes, rhombi and hexagons. The shortwave instability can lead to a much greater variety of spatio-temporal patterns than the aperiodic Turing and the long-wave oscillatory instabilities. For example, a single oscillatory cycle may display all the basic patterns related to the aperiodic Turing instability * stripes, hexagons and inverted hexagons (honeycomb) * as well as rhombi and modulated stripes. A rich plethora of patterns is seen in a system with cylindrical geometry * examples include rotating patterns of standing waves and counter-propagating waves.
Proceedings of the National Academy of Sciences of the United States of America, Nov 24, 1998
We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential... more We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.
Turing patterns in the chlorine dioxide-iodine-malonic acid reaction were modified through additi... more Turing patterns in the chlorine dioxide-iodine-malonic acid reaction were modified through additions of sodium halide salt solutions. The range of wavelengths obtained is several times larger than in the previously reported literature. Pattern wavelength was observed to significantly increase with sodium bromide or sodium chloride. A transition to a uniform state was found at high halide concentrations. The observed experimental results are qualitatively well reproduced in numerical simulations with the Lengyel-Epstein model with an additional chemically realistic kinetic term to account for the added halide and an adjustment of the activator diffusion rate to allow for interhalogen formation.
The unique possibility of encoding information into symbol dynamics corresponding to a chaotic tr... more The unique possibility of encoding information into symbol dynamics corresponding to a chaotic transmitter has been demonstrated by Hayes and Grebogi (1993, 1994) and the authors (1997). To take advantage of sensitive dependence by using only small deliberate parameter perturbations requires that we respect the grammar of the symbol dynamics which represents the physical dynamical system. We present a new algorithm to learn the observed grammar of a symbol dynamics in terms of observed transitions between bins defined by the symbol generating partition.
In this paper we describe a technique of encoding and then decoding symbol sequences containing i... more In this paper we describe a technique of encoding and then decoding symbol sequences containing information into chaotic oscillations of the Belousov-Zhabotinsky reaction. The encoding technique is based on controlling the chaotic oscillations by applying small parameter perturbations and on learning the grammar of corresponding symbol dynamics produced by the free-running chaotic system. The use of small parameter perturbations requires that we respect the grammar of the symbol dynamics which represents the physical dynamical system. We present a method for learning the grammar of a symbol dynamics in terms of allowed transitions between the bins defined by the symbol generating partition. The encoding technique can be easily utilized for targeting and stabilization of any unstable periodic orbit. ͓S1063-651X͑97͒10904-7͔
We use control of chaos to encode information into the oscillations of the Belousov-Zhabotinsky r... more We use control of chaos to encode information into the oscillations of the Belousov-Zhabotinsky reaction. An arbitrary binary message is encoded by forcing the chaotic oscillations to follow a specified trajectory. The information manipulating control requires only small perturbations to vary the binary message. In this paper we extend our recent theoretical work ͓Bollt and Dolnik, Phys. Rev. E 64, 1196 ͑1990͔͒ by introducing a new and simplified encoding technique which can be utilized in the presence of experimental noise. We numerically and theoretically study several practical aspects of controlling symbol dynamics including: modeling noisy time-series, learning underlying symbol dynamics, and evaluation of derivatives for control by observing system responses to an intelligent and deliberate sequence of input parameter variations. All of the modeling techniques incorporated here are ultimately designed to learn and control symbol dynamics of experimental data known only as an observed time-series; the simulation assumes no global model. We find that noise affects reliability of encoding information and may cause coding errors. But, if the level of noise is confined to relatively small values, which are achievable in experiments, the control mechanism is robust to the noise. Thus we can still produce a desired symbolic code. However, scarce errors in encoding may occur due to rare but large fluctuations. These errors may be corrected during the decoding process by a variation of the filtering technique suggested by Rosa et al. ͓Phys.
We present a model study of two mass-coupled reactors containing the Belousov-Zhabotinsky reactio... more We present a model study of two mass-coupled reactors containing the Belousov-Zhabotinsky reaction under chaotic conditions. The critical coupling strength is estimated for symmetry breaking when two identical low flow rate chaotic modes are coupled. Our results confirm that the critical coupling strength is directly proportional to the maximum Lyapunov exponent of the uncoupled system. The constant of proportionality is found to be somewhat larger than the theoretical value. Direct integration reveals a rich structure of dynamical behavior when the coupling strength and the flow rate in one cell are varied. Our simulations reveal domains of oscillator death, in which a stable steady state coexists with limit cycle oscillations. We introduce a simple model for predicting the dynamics of the coupled system from the dynamical behavior of the uncoupled subsystems and the dependence on the coupling strength of the Hopf bifurcation of the coupled system. The model gives good estimates of the dynamical behavior of two coupled oscillators with a small difference in one parameter at intermediate and high coupling strengths. ͓S1063-651X͑96͒01210-X͔
We present an experimental and numerical study of the chlorine dioxide-iodide (CDI) reaction in a... more We present an experimental and numerical study of the chlorine dioxide-iodide (CDI) reaction in a single, well-stirred, flow-through reactor with feedback regulation of flow rate in three different arrangements. The control is accomplished through a computer-mediated sigmoidal dependence of the dynamic flow rate(s) on the iodide concentration. Numerical simulations predict interesting dynamics in the CDI reaction system, which, without control, displays only steady-state and/or simple periodic oscillations. Our experiments confirm that bursting emerges as a result of the feedback control. We attribute bursting to the coexistence of the stable steady state and oscillations in the uncontrolled system. A period doubling sequence leading to chaos results from the nonlinear dependence of the oscillatory period on the flow rate in the vicinity of a Hopf bifurcation point.
Reaction Kinetics, Mechanisms and Catalysis, May 5, 2020
This is our fifth consecutive study carried out in an order to collect experimental evidence on t... more This is our fifth consecutive study carried out in an order to collect experimental evidence on the impact of heavy water (D 2 O) on the spontaneous peptidization of proteinogenic α-amino acids and this time its subject matter is L-alanine (L-Ala). Our four earlier studies have been focused on the two sulfur-containing α-amino acids (i.e., L-cysteine (L-Cys) and L-methionine (L-Met)), and on two structurally related α-amino acids (i.e., L-proline (L-Pro) and L-hydroxyproline (L-Hyp)). It seemed interesting to assess the effect exerted by D 2 O on L-Ala, the simplest chiral (endogenous and proteinogenic) α-amino acid with as low molar weight, as 89.09 g mol −1 only. As analytical techniques, we used high-performance liquid chromatography with the diode array detection (HPLC-DAD), mass spectrometry (MS), and scanning electron microscopy (SEM). The obtained results make it clear that the impact of heavy water on the dynamics of the spontaneous peptidization of L-Ala is even stronger than with the four other α-amino acids discussed earlier (although in all five cases, heavy water significantly hampers spontaneous oscillatory peptidization). Unlike in the four previous cases, though, the solubility of L-Ala in pure D 2 O is quite low and it takes twice as much time to dissolve it in D 2 O than in MeOH + X, 70:30 (v/v). Consequently, the peptidization of L-Ala in heavy water is even more obstructed than it was the case with the other investigated α-amino acids and it results in considerable yields of the L-Ala crystals (most probably at least partially deuterated) at the expense of the L-Ala-derived peptides. Perhaps it might be interesting to add that out of five α-amino acids investigated so far, which can be divided into two groups of endogenous and exogenous species, two endogenous species (L-Cys and L-Pro) undergo spontaneous oscillatory peptidization in an aqueousorganic solvent (i.e., in the absence of D 2 O) following the circadian rhythm, whereas two exogenous ones (i.e., L-Met and L-Hyp) do not. The third endogenous species (L-Ala) first undergoes two initials oscillations which are damped (not periodic) and the oscillatory changes are on a scale of ca. 10 h (as estimated with use of the Fourier transform approach) and after that, the system reaches a steady state.
We employ high-performance liquid chromatography with diode array, evaporative light scattering, ... more We employ high-performance liquid chromatography with diode array, evaporative light scattering, and mass spectrometric detection to monitor the oligomerization of L-lactic acid in pure acetonitrile and in 70% aqueous ethanol. The production of higher oligomers appears to proceed in an oscillatory fashion. A model is presented that involves the formation of aggregates (micelles), which catalyze the oligomerization.
Well defined and thoroughly studied chemical reaction systems such as the Belousov-Zhabotinskii (... more Well defined and thoroughly studied chemical reaction systems such as the Belousov-Zhabotinskii (BZ) reaction [4] often enable a comparison of experimental results with the results of modelling both in oscillatory and excitable systems [2, 5, 8]. In this paper we make an attempt to demonstrate that properties of distributed forced excitable BZ systems can be understood on the basis of the response of the corresponding lumped parameter system (CSTR) to a single or periodic pulse forcing. We introduce an experimental technique for the construction of the phase excitation curve (PEC), based on double pulse experiments and demonstrate its use for the modelling and interpretation of the dynamical response of excitable systems to external forcing.
We report our experimental observation of modulated standing waves that invade bulk oscillations ... more We report our experimental observation of modulated standing waves that invade bulk oscillations exhibited by the Belousov-Zhabotinsky-Aerosol OT reverse microemulsion system. The modulated standing waves form within domains bounded by a traveling wave. We also observe that the modulated standing waves give way to traveling waves, which we connect to numerical simulations in a simple chemical model.
Philosophical Transactions of the Royal Society A, Nov 8, 2021
In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two mo... more In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two morphogen reaction–diffusion system [Turing, A. M. (1952) Phil. Trans. R. Soc. Lond. A 237 , 37–72. (doi:10.1098/rstb.1952.0012)]. While the model is simple, it has found diverse applications in fields such as biology, ecology, behavioural science, mathematics and chemistry. Chemistry in particular has made significant contributions to the study of Turing-type morphogenesis, providing multiple reproducible experimental methods to both predict and study new behaviours and dynamics generated in reaction–diffusion systems. In this review, we highlight the historical role chemistry has played in the study of the Turing mechanism, summarize the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and suggest future directions for chemical studies into Turing-type morphogenesis. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.
We demonstrate a novel mechanism for controlling the frequency, amplitude, and existence of chemi... more We demonstrate a novel mechanism for controlling the frequency, amplitude, and existence of chemical oscillations. Using a ferrocyanide-iodate-sulfite reaction, we show that a chemical buffer can increase or decrease the frequency of oscillations. Furthermore, the same buffer can completely suppress or, conversely, induce oscillations when added to the appropriate composition. This simple buffering scheme can provide a practical method for controlling the oscillations of a variety of chemical and biological systems. [S0031-9007(99)08396-9]
A model of the chlorine dioxide-iodide reaction in a single well-stirred flow-through reactor is ... more A model of the chlorine dioxide-iodide reaction in a single well-stirred flow-through reactor is analyzed. The model includes a flow regulation mechanism that allows the concentration of iodide in the system to control the flow rate. The control is accomplished through a computer-mediated sigmoidal dependence of the dynamic flow rate on the iodide concentration. The dynamical behavior of this system with slow regulation is investigated by the numerical continuation technique. Oscillatory behavior is obtained for parameter values that produce only steady state behavior in the unregulated system. Chaos and bursting also arise as a result of the control mechanism. Responses of the model to changes in input iodide concentration show the ability of the system to adjust to new conditions. Two different transient pattems of adjustment are observed depending on the direction of the change in iodide input concentration. The control mechanism mimics a similar system thought to control activity in biological neurons and may be of practical value. ' Department of Chemistry.
Various patterns of standing waves are found beyond the onset of the shortwave instability in a m... more Various patterns of standing waves are found beyond the onset of the shortwave instability in a model reactiondiffusion system. These include plain and modulated stripes, squares, and rhombi in systems with square and rectangular geometry and patterns with rotational symmetry in systems with circular geometry. We also find standing waves consisting of periodic time sequences of stripes and rhombi, stripes and squares, and stripes, rhombi, and hexagons. The shortwave instability can lead to a much greater variety of spatio-temporal patterns than the aperiodic Turing and the long-wave oscillatory instabilities. For instance, a single oscillatory cycle can display all the basic patterns related to the aperiodic Turing instabilitysstripes, hexagons, and inverted hexagons (honeycomb)sas well as rhombi and modulated stripes.
We have performed one-dimensional and two-dimensional experiments and simulations to study the fo... more We have performed one-dimensional and two-dimensional experiments and simulations to study the formation of patterns in a system that grows continuously in one direction. Depending on the growth velocity, three basic spatial configurations can be obtained: stripes that are parallel, oblique, or perpendicular to the growth direction. The dependence of the wavelength on the growth velocity has also been observed. Our results illustrate the importance of these growth mechanisms in determining the final configuration of chemical and biological pattern-forming processes.
We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to... more We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to a periodic process that is intrinsic to the cell. We investigate the synchronization properties of the coupled system, and show how the oscillator can be constructed to yield a significant amplification of cellular oscillations. We reduce the driven oscillator equations to a normal form, and analytically determine the amplification as a function of the strength of the cellular oscillations. The ability to couple naturally occurring genetic oscillations to a synthetically designed network could lead to possible strategies for entraining and/or amplifying oscillations in cellular protein levels.
Journal of the Chemical Society, Faraday Transactions, 1996
ABSTRACT Various patterns of modulated waves are found beyond the onset of the wave instability i... more ABSTRACT Various patterns of modulated waves are found beyond the onset of the wave instability in a model reaction-diffusion system with length between 1 and 3 times the basic wavelength. With periodic boundary conditions, we observe low-frequency modulation of the speed of the travelling waves. A fascinating pattern of waves that periodically change their direction of propagation along the ring is found when the ring length is between 1.05 and 1.35 times the basic wavelength. With zero-flux boundary conditions, a related pattern of modulated standing waves is found between the domains of the half-wavelength and the one-wavelength standing waves; the period of modulation contains two phases of non-stationary travelling waves, moving alternately left and right, separated by phases of short-lived asymmetric standing waves.
We utilize a simple three-variable reaction}di!usion model to study patterns that emerge beyond t... more We utilize a simple three-variable reaction}di!usion model to study patterns that emerge beyond the onset of the (short-)wave instability. We have found various wave patterns including standing waves, traveling waves, asymmetric standing}traveling waves and target patterns. We employ both periodic and zero #ux boundary conditions in the simulations, and we analyze the patterns using space}time two-dimensional Fourier spectra. A fascinating pattern of waves which periodically change their direction of propagation along a ring is found for very short systems. A related pattern of modulated standing waves is found for systems with zero #ux boundary conditions. In a two-dimensional system with small overcriticality we observe a wide variety of standing wave patterns. These include plain and modulated stripes, squares and rhombi. We also "nd standing waves consisting of periodic time sequences of stripes, rhombi and hexagons. The shortwave instability can lead to a much greater variety of spatio-temporal patterns than the aperiodic Turing and the long-wave oscillatory instabilities. For example, a single oscillatory cycle may display all the basic patterns related to the aperiodic Turing instability * stripes, hexagons and inverted hexagons (honeycomb) * as well as rhombi and modulated stripes. A rich plethora of patterns is seen in a system with cylindrical geometry * examples include rotating patterns of standing waves and counter-propagating waves.
Proceedings of the National Academy of Sciences of the United States of America, Nov 24, 1998
We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential... more We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.
Turing patterns in the chlorine dioxide-iodine-malonic acid reaction were modified through additi... more Turing patterns in the chlorine dioxide-iodine-malonic acid reaction were modified through additions of sodium halide salt solutions. The range of wavelengths obtained is several times larger than in the previously reported literature. Pattern wavelength was observed to significantly increase with sodium bromide or sodium chloride. A transition to a uniform state was found at high halide concentrations. The observed experimental results are qualitatively well reproduced in numerical simulations with the Lengyel-Epstein model with an additional chemically realistic kinetic term to account for the added halide and an adjustment of the activator diffusion rate to allow for interhalogen formation.
The unique possibility of encoding information into symbol dynamics corresponding to a chaotic tr... more The unique possibility of encoding information into symbol dynamics corresponding to a chaotic transmitter has been demonstrated by Hayes and Grebogi (1993, 1994) and the authors (1997). To take advantage of sensitive dependence by using only small deliberate parameter perturbations requires that we respect the grammar of the symbol dynamics which represents the physical dynamical system. We present a new algorithm to learn the observed grammar of a symbol dynamics in terms of observed transitions between bins defined by the symbol generating partition.
In this paper we describe a technique of encoding and then decoding symbol sequences containing i... more In this paper we describe a technique of encoding and then decoding symbol sequences containing information into chaotic oscillations of the Belousov-Zhabotinsky reaction. The encoding technique is based on controlling the chaotic oscillations by applying small parameter perturbations and on learning the grammar of corresponding symbol dynamics produced by the free-running chaotic system. The use of small parameter perturbations requires that we respect the grammar of the symbol dynamics which represents the physical dynamical system. We present a method for learning the grammar of a symbol dynamics in terms of allowed transitions between the bins defined by the symbol generating partition. The encoding technique can be easily utilized for targeting and stabilization of any unstable periodic orbit. ͓S1063-651X͑97͒10904-7͔
We use control of chaos to encode information into the oscillations of the Belousov-Zhabotinsky r... more We use control of chaos to encode information into the oscillations of the Belousov-Zhabotinsky reaction. An arbitrary binary message is encoded by forcing the chaotic oscillations to follow a specified trajectory. The information manipulating control requires only small perturbations to vary the binary message. In this paper we extend our recent theoretical work ͓Bollt and Dolnik, Phys. Rev. E 64, 1196 ͑1990͔͒ by introducing a new and simplified encoding technique which can be utilized in the presence of experimental noise. We numerically and theoretically study several practical aspects of controlling symbol dynamics including: modeling noisy time-series, learning underlying symbol dynamics, and evaluation of derivatives for control by observing system responses to an intelligent and deliberate sequence of input parameter variations. All of the modeling techniques incorporated here are ultimately designed to learn and control symbol dynamics of experimental data known only as an observed time-series; the simulation assumes no global model. We find that noise affects reliability of encoding information and may cause coding errors. But, if the level of noise is confined to relatively small values, which are achievable in experiments, the control mechanism is robust to the noise. Thus we can still produce a desired symbolic code. However, scarce errors in encoding may occur due to rare but large fluctuations. These errors may be corrected during the decoding process by a variation of the filtering technique suggested by Rosa et al. ͓Phys.
We present a model study of two mass-coupled reactors containing the Belousov-Zhabotinsky reactio... more We present a model study of two mass-coupled reactors containing the Belousov-Zhabotinsky reaction under chaotic conditions. The critical coupling strength is estimated for symmetry breaking when two identical low flow rate chaotic modes are coupled. Our results confirm that the critical coupling strength is directly proportional to the maximum Lyapunov exponent of the uncoupled system. The constant of proportionality is found to be somewhat larger than the theoretical value. Direct integration reveals a rich structure of dynamical behavior when the coupling strength and the flow rate in one cell are varied. Our simulations reveal domains of oscillator death, in which a stable steady state coexists with limit cycle oscillations. We introduce a simple model for predicting the dynamics of the coupled system from the dynamical behavior of the uncoupled subsystems and the dependence on the coupling strength of the Hopf bifurcation of the coupled system. The model gives good estimates of the dynamical behavior of two coupled oscillators with a small difference in one parameter at intermediate and high coupling strengths. ͓S1063-651X͑96͒01210-X͔
We present an experimental and numerical study of the chlorine dioxide-iodide (CDI) reaction in a... more We present an experimental and numerical study of the chlorine dioxide-iodide (CDI) reaction in a single, well-stirred, flow-through reactor with feedback regulation of flow rate in three different arrangements. The control is accomplished through a computer-mediated sigmoidal dependence of the dynamic flow rate(s) on the iodide concentration. Numerical simulations predict interesting dynamics in the CDI reaction system, which, without control, displays only steady-state and/or simple periodic oscillations. Our experiments confirm that bursting emerges as a result of the feedback control. We attribute bursting to the coexistence of the stable steady state and oscillations in the uncontrolled system. A period doubling sequence leading to chaos results from the nonlinear dependence of the oscillatory period on the flow rate in the vicinity of a Hopf bifurcation point.
Reaction Kinetics, Mechanisms and Catalysis, May 5, 2020
This is our fifth consecutive study carried out in an order to collect experimental evidence on t... more This is our fifth consecutive study carried out in an order to collect experimental evidence on the impact of heavy water (D 2 O) on the spontaneous peptidization of proteinogenic α-amino acids and this time its subject matter is L-alanine (L-Ala). Our four earlier studies have been focused on the two sulfur-containing α-amino acids (i.e., L-cysteine (L-Cys) and L-methionine (L-Met)), and on two structurally related α-amino acids (i.e., L-proline (L-Pro) and L-hydroxyproline (L-Hyp)). It seemed interesting to assess the effect exerted by D 2 O on L-Ala, the simplest chiral (endogenous and proteinogenic) α-amino acid with as low molar weight, as 89.09 g mol −1 only. As analytical techniques, we used high-performance liquid chromatography with the diode array detection (HPLC-DAD), mass spectrometry (MS), and scanning electron microscopy (SEM). The obtained results make it clear that the impact of heavy water on the dynamics of the spontaneous peptidization of L-Ala is even stronger than with the four other α-amino acids discussed earlier (although in all five cases, heavy water significantly hampers spontaneous oscillatory peptidization). Unlike in the four previous cases, though, the solubility of L-Ala in pure D 2 O is quite low and it takes twice as much time to dissolve it in D 2 O than in MeOH + X, 70:30 (v/v). Consequently, the peptidization of L-Ala in heavy water is even more obstructed than it was the case with the other investigated α-amino acids and it results in considerable yields of the L-Ala crystals (most probably at least partially deuterated) at the expense of the L-Ala-derived peptides. Perhaps it might be interesting to add that out of five α-amino acids investigated so far, which can be divided into two groups of endogenous and exogenous species, two endogenous species (L-Cys and L-Pro) undergo spontaneous oscillatory peptidization in an aqueousorganic solvent (i.e., in the absence of D 2 O) following the circadian rhythm, whereas two exogenous ones (i.e., L-Met and L-Hyp) do not. The third endogenous species (L-Ala) first undergoes two initials oscillations which are damped (not periodic) and the oscillatory changes are on a scale of ca. 10 h (as estimated with use of the Fourier transform approach) and after that, the system reaches a steady state.
We employ high-performance liquid chromatography with diode array, evaporative light scattering, ... more We employ high-performance liquid chromatography with diode array, evaporative light scattering, and mass spectrometric detection to monitor the oligomerization of L-lactic acid in pure acetonitrile and in 70% aqueous ethanol. The production of higher oligomers appears to proceed in an oscillatory fashion. A model is presented that involves the formation of aggregates (micelles), which catalyze the oligomerization.
Well defined and thoroughly studied chemical reaction systems such as the Belousov-Zhabotinskii (... more Well defined and thoroughly studied chemical reaction systems such as the Belousov-Zhabotinskii (BZ) reaction [4] often enable a comparison of experimental results with the results of modelling both in oscillatory and excitable systems [2, 5, 8]. In this paper we make an attempt to demonstrate that properties of distributed forced excitable BZ systems can be understood on the basis of the response of the corresponding lumped parameter system (CSTR) to a single or periodic pulse forcing. We introduce an experimental technique for the construction of the phase excitation curve (PEC), based on double pulse experiments and demonstrate its use for the modelling and interpretation of the dynamical response of excitable systems to external forcing.
We report our experimental observation of modulated standing waves that invade bulk oscillations ... more We report our experimental observation of modulated standing waves that invade bulk oscillations exhibited by the Belousov-Zhabotinsky-Aerosol OT reverse microemulsion system. The modulated standing waves form within domains bounded by a traveling wave. We also observe that the modulated standing waves give way to traveling waves, which we connect to numerical simulations in a simple chemical model.
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Papers by Milos Dolnik