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
|
Muzika F, Jurašek R, Schreiberová L, Radojković V, Schreiber I. Identifying the Oscillatory Mechanism of the Glucose Oxidase–Catalase Coupled Enzyme System. J Phys Chem A 2017; 121:7518-7523. [DOI: 10.1021/acs.jpca.7b08564] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- František Muzika
- Department of Chemical Engineering, University of Chemistry and Technology, Prague, Technická 5, 166 28 Praha 6, Czech Republic
| | - Radovan Jurašek
- Department of Chemical Engineering, University of Chemistry and Technology, Prague, Technická 5, 166 28 Praha 6, Czech Republic
| | - Lenka Schreiberová
- Department of Chemical Engineering, University of Chemistry and Technology, Prague, Technická 5, 166 28 Praha 6, Czech Republic
| | - Vuk Radojković
- Department of Chemical Engineering, University of Chemistry and Technology, Prague, Technická 5, 166 28 Praha 6, Czech Republic
| | - Igor Schreiber
- Department of Chemical Engineering, University of Chemistry and Technology, Prague, Technická 5, 166 28 Praha 6, Czech Republic
| |
Collapse
|
4
|
Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems. Chem Eng Sci 2010. [DOI: 10.1016/j.ces.2010.03.008] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
5
|
Schmitz G, Kolar-Anić LZ, Anić SR, Čupić ŽD. Stoichiometric Network Analysis and Associated Dimensionless Kinetic Equations. Application to a Model of the Bray−Liebhafsky Reaction. J Phys Chem A 2008; 112:13452-7. [DOI: 10.1021/jp8056674] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Guy Schmitz
- Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium, Faculty of Physical Chemistry, University of Belgrade, P.O.Box 47, 11000 Belgrade, Serbia, and Department of Catalysis and Chemical Engineering, IChTM, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
| | - Ljiljana Z. Kolar-Anić
- Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium, Faculty of Physical Chemistry, University of Belgrade, P.O.Box 47, 11000 Belgrade, Serbia, and Department of Catalysis and Chemical Engineering, IChTM, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
| | - Slobodan R. Anić
- Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium, Faculty of Physical Chemistry, University of Belgrade, P.O.Box 47, 11000 Belgrade, Serbia, and Department of Catalysis and Chemical Engineering, IChTM, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
| | - Željko D. Čupić
- Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium, Faculty of Physical Chemistry, University of Belgrade, P.O.Box 47, 11000 Belgrade, Serbia, and Department of Catalysis and Chemical Engineering, IChTM, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
| |
Collapse
|
6
|
Stemwedel JD, Ross J, Schreiber I. Formulation of Oscillatory Reaction Mechanisms by Deduction from Experiments. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141489.ch5] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/07/2023]
|
7
|
Danø S, Madsen MF, Schmidt H, Cedersund G. Reduction of a biochemical model with preservation of its basic dynamic properties. FEBS J 2006; 273:4862-77. [PMID: 17010168 DOI: 10.1111/j.1742-4658.2006.05485.x] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
The complexity of full-scale metabolic models is a major obstacle for their effective use in computational systems biology. The aim of model reduction is to circumvent this problem by eliminating parts of a model that are unimportant for the properties of interest. The choice of reduction method is influenced both by the type of model complexity and by the objective of the reduction; therefore, no single method is superior in all cases. In this study we present a comparative study of two different methods applied to a 20D model of yeast glycolytic oscillations. Our objective is to obtain biochemically meaningful reduced models, which reproduce the dynamic properties of the 20D model. The first method uses lumping and subsequent constrained parameter optimization. The second method is a novel approach that eliminates variables not essential for the dynamics. The applications of the two methods result in models of eight (lumping), six (elimination) and three (lumping followed by elimination) dimensions. All models have similar dynamic properties and pin-point the same interactions as being crucial for generation of the oscillations. The advantage of the novel method is that it is algorithmic, and does not require input in the form of biochemical knowledge. The lumping approach, however, is better at preserving biochemical properties, as we show through extensive analyses of the models.
Collapse
Affiliation(s)
- Sune Danø
- Department of Medical Biochemistry and Genetics, University of Copenhagen, Denmark
| | | | | | | |
Collapse
|
8
|
Abstract
This paper reviews recent developments in the field of nonlinear chemical kinetics. Five topics are dealt with: (a) new approaches to complex reaction mechanisms, stoichiometric network analysis, classification of chemical oscillators and formulation of their mechanisms by deduction from experiments, and correlation metric construction of reaction pathways from measurements; (b) thermodynamic and stochastic theory of nonequilibrium processes, the eikonal approximation, the evaluation of stochastic potentials, experimental tests of the thermodynamic and stochastic theory of relative stability, and fluctuation-dissipation relations in nonequilibrium chemical systems; (c) chemical kinetics and cellular automata and lattice gas automata; (d) theoretical approaches and experimental studies of stochastic resonance in chemical kinetics; and (e) rate processes in disordered systems, stochastic Liouville equations, stretched exponential relaxation in disordered systems, and universality classes for rate processes in systems with static or dynamic disorder.
Collapse
Affiliation(s)
- J Ross
- Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA.
| | | |
Collapse
|
9
|
Abstract
We present a powerful, general method of fitting a model of a biochemical pathway to experimental substrate concentrations and dynamical properties measured at a stationary state, when the mechanism is largely known but kinetic parameters are lacking. Rate constants and maximum velocities are calculated from the experimental data by simple algebra without integration of kinetic equations. Using this direct approach, we fit a comprehensive model of glycolysis and glycolytic oscillations in intact yeast cells to data measured on a suspension of living cells of Saccharomyces cerevisiae near a Hopf bifurcation, and to a large set of stationary concentrations and other data estimated from comparable batch experiments. The resulting model agrees with almost all experimentally known stationary concentrations and metabolic fluxes, with the frequency of oscillation and with the majority of other experimentally known kinetic and dynamical variables. The functional forms of the rate equations have not been optimized.
Collapse
Affiliation(s)
- F Hynne
- Department of Chemistry and CATS, H.C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark.
| | | | | |
Collapse
|
10
|
Samoilov M, Arkin A, Ross J. On the deduction of chemical reaction pathways from measurements of time series of concentrations. CHAOS (WOODBURY, N.Y.) 2001; 11:108-114. [PMID: 12779446 DOI: 10.1063/1.1336499] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We discuss the deduction of reaction pathways in complex chemical systems from measurements of time series of chemical concentrations of reacting species. First we review a technique called correlation metric construction (CMC) and show the construction of a reaction pathway from measurements on a part of glycolysis. Then we present two new improved methods for the analysis of time series of concentrations, entropy metric construction (EMC), and entropy reduction method (ERM), and illustrate (EMC) with calculations on a model reaction system. (c) 2001 American Institute of Physics.
Collapse
Affiliation(s)
- Michael Samoilov
- Department of Chemistry, Stanford University, Stanford, California 94305
| | | | | |
Collapse
|
11
|
Nielsen K, Sørensen PG, Hynne F, Busse HG. Sustained oscillations in glycolysis: an experimental and theoretical study of chaotic and complex periodic behavior and of quenching of simple oscillations. Biophys Chem 1998; 72:49-62. [PMID: 17029704 DOI: 10.1016/s0301-4622(98)00122-7] [Citation(s) in RCA: 50] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Revised: 01/16/1998] [Accepted: 02/13/1998] [Indexed: 11/24/2022]
Abstract
We report sustained oscillations in glycolysis conducted in an open system (a continuous-flow, stirred tank reactor; CSTR) with inflow of yeast extract as well as glucose. Depending on the operating conditions, we observe simple or complex periodic oscillations or chaos. We report the response of the system to instantaneous additions of small amounts of several substrates as functions of the amount added and the phase of the addition. We simulate oscillations and perturbations by a kinetic model based on the mechanism of glycolysis in a CSTR. We find that the response to particular perturbations forms an efficient tool for elucidating the mechanism of biochemical oscillations.
Collapse
Affiliation(s)
- K Nielsen
- Department of Chemistry and CATS, H.C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | | | | | | |
Collapse
|
12
|
Nagy A, Sørensen PG, Hynne F. Quenching Analysis of the Permanganate−Hydroxylamine Oscillator. J Phys Chem A 1997. [DOI: 10.1021/jp962559k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Arpád Nagy
- Department of Chemistry and CATS, H. C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | - Preben Graae Sørensen
- Department of Chemistry and CATS, H. C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | - Finn Hynne
- Department of Chemistry and CATS, H. C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| |
Collapse
|
13
|
Vukojević V, Sørensen PG, Hynne F. Predictive Value of a Model of the Briggs−Rauscher Reaction Fitted to Quenching Experiments. ACTA ACUST UNITED AC 1996. [DOI: 10.1021/jp960785o] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- V. Vukojević
- Department of Chemistry and CATS, H. C. Ørsted Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - P. Graae Sørensen
- Department of Chemistry and CATS, H. C. Ørsted Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - F. Hynne
- Department of Chemistry and CATS, H. C. Ørsted Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| |
Collapse
|
14
|
|
15
|
Hynne F. Experimental determination of Ginzburg-Landau parameters for reaction-diffusion systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:4106-4109. [PMID: 9961072 DOI: 10.1103/physreve.48.4106] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
16
|
Clarke BL, Jiang W. Method for deriving Hopf and saddle‐node bifurcation hypersurfaces and application to a model of the Belousov–Zhabotinskii system. J Chem Phys 1993. [DOI: 10.1063/1.466073] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
17
|
Hynne F, So/rensen PG, Mo/ller T. Complete optimization of models of the Belousov–Zhabotinsky reaction at a Hopf bifurcation. J Chem Phys 1993. [DOI: 10.1063/1.464667] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|