# Igor Schreiber's research while affiliated with University of Chemistry and Technology, Prague and other places

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## Publications (117)

We studied the kinetics of the reaction of N-acetyl-l-cysteine (NAC or RSH) with cupric ions at an equimolar ratio of the reactants in aqueous acid solution (pH 1.4–2) using UV/Vis absorption and circular dichroism (CD) spectroscopies. Cu2+ showed a strong catalytic effect on the 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonate) radical (ABTSr) co...

Chemical turbulence was observed experimentally in the 1,4-cyclohexanedione Belousov–Zhabotinsky (CHD-BZ) reaction in a double layer consisting of a catalyst-loaded gel and uncatalyzed liquid on a Petri dish. The chemical patterns in the CHD-BZ reaction occur spontaneously in various forms as follows: the initial, regular, transient, and turbulent...

We examine dynamical switching among discrete Turing patterns that enable chemical computing performed by mass-coupled reaction cells arranged as arrays with various topological configurations: three coupled cells in a cyclic array, four coupled cells in a linear array, four coupled cells in a cyclic array, and four coupled cells in a branched arra...

Stoichiometric network analysis (SNA) is a method of studying stability of steady states of reaction systems obeying mass action kinetics. Reaction rates are expressed as a linear combination of elementary subnetworks with nonnegative coefficients (convex parameters) as opposed to standard formulation using rate coefficients and input parameters (k...

We outline an approach to analysis of dynamics of biosystems formulated as reaction networks. In particular, we discuss stability analysis provided that stoichiometric equations are given for each reaction step together with power law rate expressions. Based on stoichiometry alone, the network at stationary state can be decomposed into elementary s...

We present direct experimental evidence of pH-oscillatory dynamics in the urea-urease enzymatic reaction in a continuous reactor-membrane-reservoir system. Our results are consistent with earlier model predictions requiring differential transport of...

Stoichiometric network analysis (SNA) is a method for studying stability of steady states of stoichiometric systems by decomposing the corresponding network into elementary subnetworks (also known as extreme currents) and identifying those that may cause loss of network's stability via interplay of positive and negative feedback. Experimentally stu...

Recently we have revealed a minimal reaction subnetwork in the MAPK (mitogen-activated protein kinase) cascade that is responsible for the emergence of bistable and oscillatory behavior. Here we examine a possible mechanism that provides for the propagation of increased MAPK activity in cell populations by interconnecting the intracellular MAPK sub...

We provide experimental evidence of periodic and aperiodic oscillations in an enzymatic system of glucose oxidase – catalase in a continuous-flow stirred reactor coupled by membrane with a continuous-flow reservoir supplied with hydrogen peroxide. To describe such dynamics we formulate a detailed mechanism based on partial results in the literature...

Prompted by the recent growing evidence of oscillatory behavior involving MAPK cascades we present a systematic approach of analyzing models and elucidating the nature of biochemical oscillations based on reaction network theory. In particular, we formulate a minimal biochemically consistent mass action subnetwork of the Huang-Ferrell model of the...

Our work is focused on the experimental observation of non-uniform stationary states (discrete Turing patterns) in a cyclic coupled cell array with glycolytic oscillatory reaction. Mutual mass exchange between two stirred reaction cells is realized by using a peristaltic pump delivering reciprocally the reaction mixture in both directions. The cell...

The reaction system hydrogen peroxide-thiosulfate-sulfite in diluted sulfuric acid (HPTS) displays strongly nonlinear dynamics when operated in a continuous-flow stirred tank reactor. Due to a crucial role of hydrogen ion during the reaction this system is a prime example of an inorganic pH-oscillator. Under specific external conditions the system...

A model describing simultaneous catalytic oxidation of CO and C2H2 and reduction of NOx in a cross-flow tubular reactor is explored with the aim of relating spatiotemporal patterns to specific pathways in the mechanism. For that purpose, a detailed mechanism proposed for three-way catalytic converters is split into two subsystems, (i) simultaneous...

We study instabilities leading to inhomogeneous stationary states (discrete Turing patterns) using a simple model of glycolytic oscillatory reaction in two mass-coupled stirred open reactors with equal coupling coefficients of the activator and inhibitor and explore their ability to serve as logical devices. The system represents the simplest coupl...

A bistable switch from a low pH (unreacted "off") state to a high pH (reacted "on") state was obtained in enzyme-loaded gel beads in response to supra-threshold substrate concentrations.

Successive phosphorylation cascades mediated by mitogen-activated protein kinases (MAPKs) are known to act as switches initiating various cellular processes. In addition, models of the MAPK reaction network are displaying other nonlinear phenomena including bistability and periodic oscillations. Recently bistability has been explained as a conseque...

The reaction of hydrogen peroxide with thiosulfate and sulfite in acidic solution is characterized by marked temporal pH variations suggesting autocatalytic nature of hydrogen ions. When carried out in a continuous-flow stirred tank reactor this reaction provides nonlinear dynamical regimes including periodic oscillations, chaotic behavior and mult...

We employ numerical techniques for solving time-dependent full Poisson-Nernst-Planck (PNP) equations in 2D to analyze transient behavior of a simple ion channel subject to a sudden electric potential jump across the membrane (voltage clamp). Calculated spatiotemporal profiles of the ionic concentrations and electric potential show that two principa...

We study a model system of three diffusively coupled reaction cells arranged in a linear array that display Turing patterns with special focus on the case of equal coupling strength for all components. As a suitable model reaction we consider a two-variable core model of glycolysis. Using numerical continuation and bifurcation techniques we analyze...

We study effects of oscillatory convective flow in extracellular space on the velocity of chemical signal propagation having a form of a front wave above a cellular layer. We found that the time-averaged propagation velocity under oscillatory flow for a particular Péclet number amplitude is slower than the velocity under steady laminar flow regime...

Mitogen-activated protein kinases (MAPKs) are important signal transducing enzymes, unique to eukaryotes, that are involved in many pathways of cellular regulation. Successive phosphorylation cascades mediated by MAPKs serve as sensitive switches initiating various cellular processes. Apart from this basic feature, the underlying reaction network i...

The concept of electrodiffusion based on the Nernst-Planck equations for ionic fluxes coupled with the Poisson equation expressing relation between gradient of the electric field and the charge density is widely used in many areas of natural sciences and engineering. In contrast to the steady-state solutions of the Nernst-Planck-Poisson (abbreviate...

Effects of an external electric field on dynamical patterns in a model of two coupled reaction units, each comprising a reservoir–reactor system are studied using numerical bifurcation analysis. A pH-sensitive enzyme reaction involving ionic species is assumed to take place in the stirred reactors mutually coupled by a permeable passively conductin...

Mitogen Activated Protein Kinases (MAPKs) belong to serine/threonine-specific protein kinases that respond to extracellular stimuli and modulate cellular activities. The MAPK cascade is one of the most studied signalling biochemical pathways in the eucaryotic cell where proteins transmit a signal from a receptor on the surface of the cell to the DN...

We study effects of convective transport on a chemical front wave representing a signal propagation at a simple (single layer) epithelium by means of mathematical modeling. Plug flow and laminar flow regimes were considered. We observed a nonmonotonous dependence of the propagation velocity on the ligand receptor binding constant under influence of...

The range of patterns occurring due to interaction of transport and reactions characteristic of the three-way catalytic converter (TWC) were studied. The system showed a wide variety of chaotic spatiotemporal patterns, which were examined in detail. The stoichiometric network analysis (SNA) provided a natural way on how to decompose the entire chem...

This work is focused on dynamics of the glucose-glucose oxidase-ferricyanide enzymatic reaction with or without sodium hydroxide in a continuous-flow stirred tank reactor (CSTR) and in a batch reactor. This reaction exhibits pH-variations having autocatalytic character and is reported to provide nonlinear dynamic behavior (bistability, excitability...

Glucose-catalase-glucose oxidase-hydrogen peroxide reaction is one of the few known enzymatic systems studied in vitro in the field of nonlinear chemical dynamics. This reaction belongs to the family of oscillatory enzymatic reactions, which form a natural basis of oscillations in biological systems. A parametric study of dependence on mixing, temp...

We present results of experiments focused on emergent and cooperative dynamics in a system of two coupled flow-through stirred reaction cells with diffusion-like mass exchange and a strongly nonlinear chemical reaction between hydrogen peroxide and thiosulphate catalysed by cupric ions in diluted solution of sulphuric acid. Due to complex mechanism...

The mechanism of photochemistry in the mesopause region entails a chemical oscillator forced by solar short-wave radiation. A model with periodic forcing between day and night conditions produces nonlinear dynamics including period-doubling bifurcations and chaos. The photochemical mechanism represents a network involving positive and negative feed...

We analyze dynamics of stationary nonuniform patterns, traveling waves, and spatiotemporal chaos in a simple model of a tubular cross-flow reactor. The reactant is supplied continuously via convective flow and/or by diffusion through permeable walls of the reactor. First order exothermic reaction kinetics is assumed and the system is described by m...

Dynamical behavior of reaction-transport processes in a detailed model of three-way catalytic converter, where catalytic oxidation of carbon monoxide and hydrocarbons occurs simultaneously with reduction of nitrogen oxides possesses several sources of kinetic rather than thermokinetic autocatalysis and can support sustained oscillations and pattern...

Oscillating reactions with an autocatalytic effect involving protons (pH-oscillators) are of general interest in with possible implications in functional dynamics of biological systems. We examine two inorganic pH-oscillators, the hydrogen peroxidethiosulfateCu2+H2SO4 (HPTCu) reaction and bromate-sulfite-ferrocyanide (BSF) reaction. We focus on exp...

Dynamical behavior of reaction-transport processes in a three-way catalytic converter, where catalytic oxidation of carbon monoxide and hydrocarbons occurs simultaneously with reduction of nitrogen oxides, can be in the simplest approximation described by a model of an isothermal stirred flow-through reactor where transport phenomena are largely ne...

We examine experimentally a chemical system in a flow-through stirred reactor, which is known to provide large-amplitude oscillations of the pH value. By systematic variation of the flow rate, we find that the system displays hysteresis between a steady state and oscillations, and more interestingly, a transition to chaos involving mixed-mode oscil...

The hydrogen peroxide-thiosulfate-Cu2+ reaction operated in a continuous flow stirred tank reactor is a pH-oscillator known to provide three different steady states, hysteresis, and oscillations. In addition to the various dynamical regimes established earlier, a question arises whether the reaction can be also excitable, whereby the system strongl...

Experimental observations of oscillations and chaotic dynamics in the CO catalytic combustion on supported catalysts were reported more than fifteen years ago. Recently, a detailed reaction mechanism including over 20 reaction steps has been proposed for the catalytic CO oxidation, NOx reduction and hydrocarbons oxidation taking place in a three-wa...

IntroductionConcepts and Theoretical Constructs for Oscillatory ReactionsExperimentsExample of Deduction of Reaction Mechanism from Experiments

Reaction systems that display pronounced periodic and aperiodic variations in the pH value of the reaction medium are known
as pH oscillators. A member of this family of reactions studied here, the Cu(II)-catalyzed oxidation of thiosulfate by hydrogen
peroxide in acidic solution, is known to display a rich variety of oscillatory dynamics. We focus...

Early experimental observations of chaotic behavior arising via the period-doubling route for the CO catalytic oxidation both on Pt(110) and Ptgamma-Al(2)O(3) porous catalyst were reported more than 15 years ago. Recently, a detailed kinetic reaction scheme including over 20 reaction steps was proposed for the catalytic CO oxidation, NO(x) reductio...

The reaction between tetrathionate and hydrogen peroxide forms an important part of several pH oscillators based on the oxidation of thiosulfate. The kinetics of this reaction were examined in a batch reactor by measurement of the initial pH values in the range from 8 to 10.5. Experimental data were evaluated by the method of initial reaction rates...

In this chapter we present an experimental test case of the deduction of a reaction pathway and mechanism by means of correlation metric construction from time-series measurements of the concentrations of chemical species. We choose as the system an enzymatic reaction network, the initial steps of glycolysis. Glycolysis is central in intermediary m...

We discussed some aspects of the responses of chemical systems, linear or nonlinear, to perturbations on several earlier occasions. The first was the responses of the chemical species in a reaction mechanism (a network) in a nonequilibrium stable stationary state to a pulse in concentration of one species. We referred to this approach as the “pulse...

All cellular activities and responses to environmental stimuli are determined by a complex interplay of genes, RNA, proteins, and metabolites. As the observed phenotype is the result of all reactions occurring in the cell and with the environment, a comprehensive analytical representation of the biological system is required. The ideal analytical p...

There is enormous interest in the biology of complex reaction systems, be it in metabolism, signal transduction, gene regulatory networks, protein synthesis, and many others. The field of the interpretation of experiments on such systems by application of the methods of information science, computer science, and biostatistics is called bioinformati...

It is useful to have a brief discussion of some kinetic processes that we shall treat in later chapters. Some, but not all, of the material in this chapter is presented in [1] in more detail. A macroscopic, deterministic chemical reacting system consists of a number of different species, each with a given concentration (molecules or moles per unit...

In a chemical system with many chemical species several questions can be asked: what species react with other species: in what temporal order: and with what results? These questions have been asked for over one hundred years about simple and complex chemical systems, and the answers constitute the macroscopic reaction mechanism. In Determination of...

Oscillating chemical reactions have the distinct property of a periodic or aperiodic oscillatory course of concentrations of reacting chemical species as well as temperature. This behavior is due to an interplay of positive and negative feedback with alternating dominance of these two dynamic effects. For example, an exothermic reaction produces he...

The topic of this chapter may seem like a digression from methods and approaches to reaction mechanisms, but it is not; it is an introduction to it. We worked on both topics for some time and there is a basic connection. Think of an electronic device and ask: how are the logic functions of this device determined? Electronic inputs (voltages and cur...

For an experimental test of the pulse perturbation method we choose a part of glycolysis shown in fig. 6.1. There are similarities and some differences between the model in fig. 5.12 and the reaction system in fig. 6.1. The reaction system has reactants, enzymes, and some effectors. One point of interest in choosing this system is the test of detec...

In chapter 5, we studied the responses of chemical species in a reaction system to pulse perturbations and showed the deduction of direct, causal connectivities by chemical reactions—the reaction pathway—and the reaction mechanism from such measurements. The causal connectivites give the information on how the chemical species are connected by chem...

Consider a chemical reaction system with many chemical species; it may be in a transient state but it is easier to think of it in a stable stationary state, not necessarily but usually away from equilibrium. We wish to probe the responses of the concentrations of the chemical species to a pulse perturbation of one of the chemical species. The pulse...

The mathematical computational method of genetic algorithms is frequently useful in solving optimization problems in systems with many parameters, for example, a search for suitable parameters of a given problem that achieves a stated purpose. The method searches for these parameters in an efficient parallel way, and has some analogies with evoluti...

In this chapter we develop further the theory of the correlation method introduced in chapter 7. Consider the expression of the pair correlation function where an ensemble average replaces the average over a time series of experiments on a single system. The pair correlation function defined in eq. (7.1) is the second moment of the pair distributio...

Dynamical behavior of catalytic oxidation of carbon monoxide and hydrocarbons in a catalytic converter can be in the simplest approximation described by a model of isothermal stirred flow-through reactor. Under these conditions, the model exibits multiple steady states as well as oscillatory behavior. These nonlinear phenomena cannot be explained b...

Dynamics of the reaction between hydrogen peroxide and thiosulfate catalyzed by Cu2+ in the solution of H2S04 (HPTCu) in two coupled reaction cells are studied. The coupling is mediated by a membrane allowing for mass transfer. We studied effects of varying flow rate and the coupling strength on the system. Dynamical behavior includes nonhomogeneou...

We examine wave patterns occurring in a simple reaction-diffusion-convection model describing a tubular cross-flow reactor with exothermic first order reaction. First, only reaction-diffusion equations are solved by numerical integration to find characteristic spatiotemporal patterns. Then the effects of convection on these patterns are examined. I...

A two-dimensional threshold surface of an excitable system is found as a set of threshold trajectories calculated step by step in cross sections of the phase space. The method leads to a highly nonlinear boundary value problem that can be solved numerically with the use of adaptive multiple shooting and continuation methods. We demonstrate this tec...

Bromate-sulfite-ferrocyanide reaction operated in the CSTR is sensitive to small but supercritical additions of either acid or base. When operated at two different kinds of steady states, this dynamical feature gives rise to activatory or inhibitory excitability. Spontaneous periodic oscillations are also sensitive to such perturbations. Periodical...

Following our previous work [J. Zagora et al., Faraday Discuss. 120, 313 (2001)], we present a quantitative definition of a threshold that separates large-amplitude excitatory responses and small-amplitude nonexcitatory responses to a perturbation of an excitable system with a single globally attracting steady state. For systems with two variables,...

In this study, we report the experimental and numerical investigation of the behaviour of a spontaneously oscillatory reaction in a fed-batch reactor (FBR). We use a cerium catalysed BZ model with a modified Oregonator mechanism. In fed-batch mode, we observe phase-locked, quasiperiodic and period-doubling responses, depending on the amplitude and...

We employ a method of numerical continuation which has been earlier developed into a software tool for analysis of spatiotemporal patterns emerging in systems with simultaneous reaction, diffusion and convection. As an example, we take a catalytic cross-flow tubular reactor with first order exothermic reaction kinetics. The analysis begins with det...

The classification/categorization of oscillatory chemical reactions and the determination of the connectivity of species in a reaction mechanism can be deduced from several experiments. In this article we show the same for bifurcation diagrams. We construct such diagrams for skeletal models of each of the known categories; these are distinct and ca...

We present a program package cont for modelling and analysis of nonlinear problems and use it to solve chemical engineering problems including chemical reactors and adsorption columns. Model should be in the form of ordinary differential equations (ODEs), spatially distributed systems described by partial differential equations may also be treated...

Using the bromate–sulfite–ferrocyanide (BSF) reaction in a continuously stirred tank reactor (CSTR) we study the relations between excitability, oscillations and bistability. Two kinds of excitability associated with either direct or indirect initiation of the autocatalytic production of the H+ ions are found by using pulsed addition of H+ or OH+ i...

A simple two compartment model system composed of a reservoir and a reactor is studied by means of numerical bifurcation analysis. An enzyme reaction involving ionic species is assumed to take place in the reactor connected to the reservoir via a semi-permeable electrically inert membrane. An external electric voltage is applied to this system via...

Using two different kinds of pH systems—the papain catalyzed hydrolysis of N-benzoyl-L-arginine ethyl ester in a membrane reactor and the bromate–sulfite–ferrocyanide (BSF) reaction in the CSTR—we study the relation among excitability, oscillations and bistability, and the ability of the system to respond to external periodic perturbations. Excitab...

We formulate a boundary value problem to locate homoclinic or heteroclinic orbits approaching a stationary point in an oscillatory manner so that velocity vectors on the orbit close to the stationary point are used rather than eigenvectors. A Newton method combined with multiple shooting can be used to numerically find the orbit truncated to a fini...

In this paper, we numerically investigate local properties of dynamical systems close to a Hopf bifurcation instability. We focus on chemical systems and present an approach based on the theory of normal forms for determining numerical estimates of the limit cycle that branches off at the Hopf bifurcation point. For several numerically ill-conditio...

The kinetics and mechanism of the reaction between nitrous acid and bromine are studied in dilute sulfuric acid medium, using both the stopped-flow method and conventional spectrophotometry. The partial reaction order with respect to Br2 moderately differs from 1, showing a saturation at a higher concentration of bromine. The second order of the re...

Excitable properties of selected biochemical reactions in one compartment subject to external periodic stimuli, the spreading of signals elicited by periodic stimulation in a linear array of compartments and the spreading of pulse wave trains in a continuous medium are studied. A method of calculating a threshold set and a criterion for its disappe...

In this paper we examine dynamical modes resulting from diffusion-like interaction of two model biochemical cells. Kinetics in each of the cells is given by the ICC model of calcium ions in the cytosol. Constraints for one of the cells are set so that it is excitable. One of the constraints in the other cell — a fraction of activated cell
surface r...

Non-chaotic strange attractor of a non-autonomous dissipative dynamical system with a 2-frequency-quasiperiodic forcing is studied. Following results from [1] numerical observations are refined and the route from torus to strange non-chaotic attractor is described in detail. Possible misinterpretations of experimental observations are discussed. 1...

The stability of periodic two-dimensional waves on a liquid film falling down a vertical oscillating plate was studied experimentally using the aqueous solutions of carboxy-methylcellulose. A set of capacitance probes was used to measure the instantaneous film thickness. Artificial flow fluctuations induced by the plate oscillations caused distinct...

In this paper we describe a software package for dynamic and bifurcation analysis of dynamical systems defined by a system of ordinary differential equations. The use will be demonstrated on an example of continuation of homoclinic orbits.

Experiments with oxidation circular waves in a quasi-two-dimensional Belousov−Zhabotinsky reaction medium subject to an external dc electric field reveal a variety of wave dynamics scenarios involving wave splitting, reversal, annihilation, and complex pattern formation. We also investigate effects of initial concentration of reactants on the wave...

We investigate the categorization of two or more proposed reaction mechanisms for each of the following oscillatory enzymatic reactions: (1) the peroxidase-oxidase reaction; (2) glycolytic oscillations; (3) oscillations of cyclic AMP in smile mold cells; (4) enzymatic pH oscillations; (5) calcium spiking in cytosol. We use prior work in stoichiomet...

Non-chaotic strange attractor of a non-autonomous dissipative dynamical system with a 2-frequency-quasiperiodic forcing is studied. Following results from [1] numerical observations are refined and the route from torus to strange non-chaotic attractor is described in detail. Possible misinterpretations of experimental observations are discussed. 1...