1
|
Radojković V, Schreiber I. Constrained stoichiometric network analysis. Phys Chem Chem Phys 2018; 20:9910-9921. [PMID: 29619463 DOI: 10.1039/c8cp00528a] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Stoichiometric network analysis (SNA) is a method for studying the 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 a network's stability via interplay of positive and negative feedback. Experimentally studied complex (bio)chemical reactions often display dynamical instabilities leading to oscillations or bistable switches. When modelling such systems, a frequently met case is that an assumed detailed mechanism in terms of power law kinetics is available, but some of the rate coefficients are unknown and obtaining them by traditional kinetic methods based on a least-square fit is cumbersome or unfeasible. We propose a method combining the SNA and experimental data at the point of instability, which provides an estimate of the unknown rate coefficients along with unknown steady state concentrations. The core of the method rests in using constrained linear optimization to find a combination of the elementary subnetworks such that the dominant instability-causing subnetwork is just counter-balanced by stabilizing effects of all other subnetworks to obtain the instability threshold, and at the same time, the experimentally available data (inflow constraints, measured steady state concentrations of some species, frequency of emerging oscillations, etc.) are exactly matched. We illustrate this approach by examining two classical chemical oscillators: the Brusselator chosen as the simplest model for illustration of our methods and the Belousov-Zhabotinsky reaction and its mechanism represented by the Oregonator model as a more advanced example.
Collapse
Affiliation(s)
- Vuk Radojković
- Department of Chemical Engineering, University of Chemistry and Technology, Technická 5, 166 28 Prague 6, Czech Republic.
| | | |
Collapse
|
2
|
Anić SR, Čupić ŽD. Dynamics and kinetics of complex reaction systems. Contributions of the Professor emeritus Ljiljana Kolar-Anić. REACTION KINETICS MECHANISMS AND CATALYSIS 2018. [DOI: 10.1007/s11144-017-1290-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
3
|
Veber T, Schreiberová L, Schreiber I. Classification of the pH-oscillatory hydrogen peroxide-thiosulfate-sulfite reaction. J Phys Chem A 2013; 117:12196-207. [PMID: 24182198 DOI: 10.1021/jp407621j] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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 multiple steady states coexisting over a range of operating conditions. The aim of the presented experimental study is a classification of the role of species and the underlying mechanism in the periodic oscillatory mode by applying single pulse additions of chosen reaction species. The external perturbations at various phases of the periodically oscillating system may cause phase advance or phase delay of the oscillations. The resulting phase transition curves are obtained for hydrogen ions, hydroxide ions, thiosulfate ions, sulfite ions, and hydrogen sulfite ions. These curves are compared with the phase transition curves calculated using the prototype mechanisms representing categories of chemical oscillators established in previous work. We found our system to be compatible with the mechanism of the category 1CX.
Collapse
Affiliation(s)
- Tomáš Veber
- Department of Chemical Engineering, Institute of Chemical Technology, Prague , Technická 5, 166 28 Prague 6, Czech Republic
| | | | | |
Collapse
|
4
|
Otero-Muras I, Banga JR, Alonso AA. Characterizing multistationarity regimes in biochemical reaction networks. PLoS One 2012; 7:e39194. [PMID: 22802936 PMCID: PMC3389020 DOI: 10.1371/journal.pone.0039194] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2011] [Accepted: 05/20/2012] [Indexed: 11/18/2022] Open
Abstract
Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.
Collapse
Affiliation(s)
- Irene Otero-Muras
- Department of Biosystems Science and Engineering, The Swiss Federal Institute of Technology Zurich, Zurich, Switzerland
| | - Julio R. Banga
- BioProcess Engineering Group, Instituto Investigaciones Marinas- Consejo Superior de Investigaciones Científicas, Spanish National Research Council, Vigo, Spain
| | - Antonio A. Alonso
- BioProcess Engineering Group, Instituto Investigaciones Marinas- Consejo Superior de Investigaciones Científicas, Spanish National Research Council, Vigo, Spain
| |
Collapse
|
5
|
Abstract
This review presents several methods of determining complex chemical reaction mechanisms and their functions. One method is based on correlation functions of measured time series of concentrations of chemical species, another is on measurements of temporal responses of concentrations to various perturbations of arbitrary magnitude, the third deals with the analysis of oscillatory systems, and the fourth describes the use of genetic algorithms. All methods are applicable to chemical, biochemical, and biological reaction systems and to genetic networks. The methods depend on the design of appropriate experiments for the whole system and corresponding theories for interpretation that lead to information on the causal chemical connectivity of species, reaction pathways, reaction mechanisms, control centers in the system, and functions of the system. The first three methods require no assumption of a model or hypothesis, nor extensive calculations, unlike the interpretation of measurements made on a gene network at only one time. The methods offer advantageous approaches to systems biology.
Collapse
Affiliation(s)
- John Ross
- Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA.
| |
Collapse
|
6
|
Ross J. Determination of complex reaction mechanisms. Analysis of chemical, biological and genetic networks. J Phys Chem A 2008; 112:2134-43. [PMID: 18275175 DOI: 10.1021/jp711313e] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present several methods of determining, not guessing, complex chemical reaction mechanisms and their functions. One method is based on the theory of correlation functions of measured time series of concentrations of chemical species; another is on measurements of temporal responses of concentrations to various perturbations of arbitrary magnitude; a third deals with the analysis of oscillatory systems; a fourth is on the use of genetic algorithms to determine functions of chemical reaction networks. All methods are applicable to chemical, biochemical, and biological reaction systems and to genetic networks and systems biology. The methods depend on the design of appropriate experiments on the whole system and corresponding theories for interpretation that lead to information on the causal chemical connectivity of species, on reaction pathways, on reaction mechanisms, on control centers in the system, and on functions of the system. The first three methods require no assumption of a model or hypothesis, nor extensive calculations, unlike the interpretation of measurements made on a gene network at only one time.
Collapse
|
7
|
Shen J, Pullela S, Marquez M, Cheng Z. Ternary Phase Diagram for the Belousov−Zhabotinsky Reaction-Induced Mechanical Oscillation of Intelligent PNIPAM Colloids. J Phys Chem A 2007; 111:12081-5. [DOI: 10.1021/jp072574x] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jingyi Shen
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, Interdisciplinary Network of Emerging Science and Technologies (INEST) Group Postgraduate Program, Philip Morris USA, Richmond, Virginia 23234, NIST Center for Theoretical and Computational Nanosciences, Gaithersburg, Maryland 20899, Harrington Department of Bioengineering, Arizona State University, Tempe, Arizona 85287, and Research Center, Philip Morris USA, Richmond, Virginia 23234
| | - Srinivasa Pullela
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, Interdisciplinary Network of Emerging Science and Technologies (INEST) Group Postgraduate Program, Philip Morris USA, Richmond, Virginia 23234, NIST Center for Theoretical and Computational Nanosciences, Gaithersburg, Maryland 20899, Harrington Department of Bioengineering, Arizona State University, Tempe, Arizona 85287, and Research Center, Philip Morris USA, Richmond, Virginia 23234
| | - Manuel Marquez
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, Interdisciplinary Network of Emerging Science and Technologies (INEST) Group Postgraduate Program, Philip Morris USA, Richmond, Virginia 23234, NIST Center for Theoretical and Computational Nanosciences, Gaithersburg, Maryland 20899, Harrington Department of Bioengineering, Arizona State University, Tempe, Arizona 85287, and Research Center, Philip Morris USA, Richmond, Virginia 23234
| | - Zhengdong Cheng
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, Interdisciplinary Network of Emerging Science and Technologies (INEST) Group Postgraduate Program, Philip Morris USA, Richmond, Virginia 23234, NIST Center for Theoretical and Computational Nanosciences, Gaithersburg, Maryland 20899, Harrington Department of Bioengineering, Arizona State University, Tempe, Arizona 85287, and Research Center, Philip Morris USA, Richmond, Virginia 23234
| |
Collapse
|
8
|
Goldstein B. Switching mechanism for branched biochemical fluxes: Graph-theoretical analysis. Biophys Chem 2007; 125:314-9. [PMID: 17011698 DOI: 10.1016/j.bpc.2006.09.005] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2006] [Revised: 09/08/2006] [Accepted: 09/08/2006] [Indexed: 11/22/2022]
Abstract
A graph-theoretical method is applied to characterize the structure of a simplest switching mechanism of common biochemical importance. This mechanism is based on competition of two coupled substrate-binding pathways for a single substrate. No other regulatory interactions are shown to be needed for the switching phenomenon to be observed. It is shown that switch in branch effluxes is observed as bistability or reciprocal oscillations, depending on the value of steady influx. Frequency of reciprocal efflux oscillations in branches is regulated by steady influx. Therefore, the switching mechanism can function as the coding mechanism in the manner of "influx steady level-efflux frequency". The calculated kinetic equations for the switching mechanism demonstrate very steep transitions in the branch fluxes without using high non-linearity of these equations.
Collapse
Affiliation(s)
- Boris Goldstein
- Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, 142290 Russia.
| |
Collapse
|
9
|
Kiss IZ, Kazsu Z, Gáspár V. Tracking unstable steady states and periodic orbits of oscillatory and chaotic electrochemical systems using delayed feedback control. CHAOS (WOODBURY, N.Y.) 2006; 16:033109. [PMID: 17014214 DOI: 10.1063/1.2219702] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Experimental results are presented on successful application of delayed-feedback control algorithms for tracking unstable steady states and periodic orbits of electrochemical dissolution systems. Time-delay autosynchronization and delay optimization with a descent gradient method were applied for stationary states and periodic orbits, respectively. These tracking algorithms are utilized in constructing experimental bifurcation diagrams of the studied electrochemical systems in which Hopf, saddle-node, saddle-loop, and period-doubling bifurcations take place.
Collapse
Affiliation(s)
- István Z Kiss
- Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
| | | | | |
Collapse
|
10
|
Marek M, Schejbal M, Kocí P, Nevoral V, Kubícek M, Hadac O, Schreiber I. Oscillations, period doublings, and chaos in CO oxidation and catalytic mufflers. CHAOS (WOODBURY, N.Y.) 2006; 16:037107. [PMID: 17014241 DOI: 10.1063/1.2354429] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
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) reduction, and hydrocarbon oxidation taking place in a three-way catalyst (TWC) converter, the most common reactor for detoxification of automobile exhaust gases. This reactor is typically operated with periodic variation of inlet oxygen concentration. For an unforced lumped model, we report results of the stoichiometric network analysis of a CO reaction subnetwork determining feedback loops, which cause the oscillations within certain regions of parameters in bifurcation diagrams constructed by numerical continuation techniques. For a forced system, numerical simulations of the CO oxidation reveal the existence of a period-doubling route to chaos. The dependence of the rotation number on the amplitude and period of forcing shows a typical bifurcation structure of Arnold tongues ordered according to Farey sequences, and positive Lyapunov exponents for sufficiently large forcing amplitudes indicate the presence of chaotic dynamics. Multiple periodic and aperiodic time courses of outlet concentrations were also found in simulations using the lumped model with the full TWC kinetics. Numerical solutions of the distributed model in two geometric coordinates with the CO oxidation subnetwork consisting of several tens of nonlinear partial differential equations show oscillations of the outlet reactor concentrations and, in the presence of forcing, multiple periodic and aperiodic oscillations. Spatiotemporal concentration patterns illustrate the complexity of processes within the reactor.
Collapse
Affiliation(s)
- Milos Marek
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Institute of Chemical Technology, Prague, Technická 5, 166 28 Prague 6, Czech Republic.
| | | | | | | | | | | | | |
Collapse
|
11
|
Kiss IZ, Kazsu Z, Gaspar V. Experimental Strategy for Characterization of Essential Dynamical Variables in Oscillatory Systems: Effect of Double-Layer Capacitance on the Stability of Electrochemical Oscillators. J Phys Chem A 2005; 109:9521-7. [PMID: 16866403 DOI: 10.1021/jp053656t] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An experimentally accessible algorithm for changing the time scale associated with a dynamical variable is proposed. In general, a differential controller can be applied to (a) identify the essential species in oscillatory systems and (b) explore their role in the feedback loops. Here, we report on classifying electrochemical oscillators by changing the time scale over which the electrode potential varies; the type of different electrochemical oscillators is identified based on whether the controlled modification of pseudo-capacitance induces or suppresses current oscillations.
Collapse
Affiliation(s)
- Istvan Z Kiss
- Department of Chemical Engineering, University of Virginia, 102 Engineers' Way, Charlottesville, Virginia 22904, USA
| | | | | |
Collapse
|
12
|
Nonlinear dynamics of automobile exhaust gas converters: the role of nonstationary kinetics. Chem Eng Sci 2004. [DOI: 10.1016/j.ces.2004.07.115] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|