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
|
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
|
3
|
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]
|
4
|
Hald B, Madsen MF, Danø S, Quistorff B, Sørensen PG. Quantitative evaluation of respiration induced metabolic oscillations in erythrocytes. Biophys Chem 2008; 141:41-8. [PMID: 19162390 DOI: 10.1016/j.bpc.2008.12.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2008] [Revised: 12/15/2008] [Accepted: 12/20/2008] [Indexed: 11/19/2022]
Abstract
The changes in the partial pressures of oxygen and carbon dioxide (P(O(2)) and P(CO(2))) during blood circulation alter erythrocyte metabolism, hereby causing flux changes between oxygenated and deoxygenated blood. In the study we have modeled this effect by extending the comprehensive kinetic model by Mulquiney and Kuchel [P.J. Mulquiney, and P.W. Kuchel. Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: equations and parameter refinement, Biochem. J. 1999, 342, 581-596.] with a kinetic model of hemoglobin oxy-/deoxygenation transition based on an oxygen dissociation model developed by Dash and Bassingthwaighte [R. Dash, and J. Bassingthwaighte. Blood HbO(2) and HbCO(2) dissociation curves at varied O(2), CO(2), pH, 2,3-DPG and temperature levels, Ann. Biomed. Eng., 2004, 32(12), 1676-1693.]. The system has been studied during transitions from the arterial to the venous phases by simply forcing P(O(2)) and P(CO(2)) to follow the physiological values of venous and arterial blood. The investigations show that the system passively follows a limit cycle driven by the forced oscillations of P(O(2)) and is thus inadequately described solely by steady state consideration. The metabolic system exhibits a broad distribution of time scales. Relaxations of modes with hemoglobin and Mg(2+) binding reactions are very fast, while modes involving glycolytic, membrane transport and 2,3-BPG shunt reactions are much slower. Incomplete slow mode relaxations during the 60 s period of the forced transitions cause significant overshoots of important fluxes and metabolite concentrations - notably ATP, 2,3-BPG, and Mg(2+). The overshoot phenomenon arises in consequence of a periodical forcing and is likely to be widespread in nature - warranting a special consideration for relevant systems.
Collapse
Affiliation(s)
- Bjørn Hald
- Department of Biomedical Sciences, University of Copenhagen, Denmark.
| | | | | | | | | |
Collapse
|
5
|
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]
|
6
|
Cedersund G. Elimination of the initial value parameters when identifying a system close to a Hopf bifurcation. ACTA ACUST UNITED AC 2006; 153:448-56. [PMID: 17186706 DOI: 10.1049/ip-syb:20050068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
One of the biggest problems when performing system identification of biological systems is that it is seldom possible to measure more than a small fraction of the total number of variables. If that is the case, the initial state, from where the simulation should start, has to be estimated along with the kinetic parameters appearing in the rate expressions. This is often done by introducing extra parameters, describing the initial state, and one way to eliminate them is by starting in a steady state. We report a generalisation of this approach to all systems starting on the centre manifold, close to a Hopf bifurcation. There exist biochemical systems where such data have already been collected, for example, of glycolysis in yeast. The initial value parameters are solved for in an optimisation sub-problem, for each step in the estimation of the other parameters. For systems starting in stationary oscillations, the sub-problem is solved in a straight-forward manner, without integration of the differential equations, and without the problem of local minima. This is possible because of a combination of a centre manifold and normal form reduction, which reveals the special structure of the Hopf bifurcation. The advantage of the method is demonstrated on the Brusselator.
Collapse
Affiliation(s)
- G Cedersund
- Department of Electrical Engineering, LinköpingUniversity, SE-581, 83 Linköping, Sweden.
| |
Collapse
|
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
|
Cedersund G, Knudsen C. Improved parameter estimation for systems with an experimentally located Hopf bifurcation. ACTA ACUST UNITED AC 2006; 152:161-8. [PMID: 16986279 DOI: 10.1049/ip-syb:20050013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
When performing system identification, we have two sources of information: experimental data and prior knowledge. Many cell-biological systems are oscillating, and sometimes we know an input where the system reaches a Hopf bifurcation. This is the case, for example, for glycolysis in yeast cells and for the Belousov-Zhabotinsky reaction, and for both of these systems there exist significant numbers of quenching data, ideal for system identification. We present a method that includes prior knowledge of the location of a Hopf bifurcation in estimation based on time-series. The main contribution is a reformulation of the prior knowledge into the standard formulation of a constrained optimisation problem. This formulation allows for any of the standard methods to be applied, including all the theories regarding the method's properties. The reformulation is carried out through an over-parametrisation of the original problem. The over-parametrisation allows for extra constraints to be formed, and the net effect is a reduction of the search space. A method that can solve the new formulation of the problem is presented, and the advantage of adding the prior knowledge is demonstrated on the Brusselator.
Collapse
Affiliation(s)
- G Cedersund
- Department of Electrical Engineering, Linköping University, Sweden.
| | | |
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
|
Zhou LQ, Ouyang Q. Experimental studies on long-wavelength instability and spiral breakup in a reaction-diffusion system. PHYSICAL REVIEW LETTERS 2000; 85:1650-1653. [PMID: 10970580 DOI: 10.1103/physrevlett.85.1650] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/1999] [Indexed: 05/23/2023]
Abstract
We investigate the behavior of spiral waves in a quasi-two-dimensional spatial open reactor using Belousov-Zhabotinsky reaction. The goal of this study is to answer two questions raised recently: Can a system sustain a stable long-wavelength modulated spiral? What causes the transition from spiral to defect-mediated turbulence? Our experimental results show that in a certain range of control parameters, a sustained long-wavelength modulated spiral is stable. The amplitude and the wavelength of modulations increase with the control parameter. As the latter is increased to across a threshold, defects are generated far away from the spiral center as a result of the neighboring two wave fronts being too close.
Collapse
Affiliation(s)
- LQ Zhou
- Department of Physics, Mesoscopic Physics Laboratory, Peking University, Beijing 100871, Peoples Republic of China
| | | |
Collapse
|
11
|
Abstract
Glycolytic oscillations in yeast have been studied for many years simply by adding a glucose pulse to a suspension of cells and measuring the resulting transient oscillations of NADH. Here we show, using a suspension of yeast cells, that living cells can be kept in a well defined oscillating state indefinitely when starved cells, glucose and cyanide are pumped into a cuvette with outflow of surplus liquid. Our results show that the transitions between stationary and oscillatory behaviour are uniquely described mathematically by the Hopf bifurcation. This result characterizes the dynamical properties close to the transition point. Our perturbation experiments show that the cells remain strongly coupled very close to the transition. Therefore, the transition takes place in each of the cells and is not a desynchronization phenomenon. With these two observations, a study of the kinetic details of glycolysis, as it actually takes place in a living cell, is possible using experiments designed in the framework of nonlinear dynamics. Acetaldehyde is known to synchronize the oscillations. Our results show that glucose is another messenger substance, as long as the glucose transporter is not saturated.
Collapse
Affiliation(s)
- S Danø
- Department of Chemistry and CATS, H.C. Orsted Institute, University of Copenhagen, Denmark.
| | | | | |
Collapse
|
12
|
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
|
13
|
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
|
14
|
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
|
15
|
Vance W, Ross J. Entrainment, phase resetting, and quenching of chemical oscillations. J Chem Phys 1995. [DOI: 10.1063/1.469669] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
16
|
|
17
|
Kramer L, Hynne F, Graae Sorenson P, Walgraef D. The Ginzburg-Landau approach to oscillatory media. CHAOS (WOODBURY, N.Y.) 1994; 4:443-452. [PMID: 12780119 DOI: 10.1063/1.166022] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Close to a supercritical Hopf bifurcation, oscillatory media may be described, by the complex Ginzburg-Landau equation. The most important spatiotemporal behaviors associated with this dynamics are reviewed here. It is shown, on a few concrete examples, how real chemical oscillators may be described by this equation, and how its coefficients may be obtained from the experimental data. Furthermore, the effect of natural forcings, induced by the experimental realization of chemical oscillators in batch reactors, may also be studied in the framework of complex Ginzburg-Landau equations and its associated phase dynamics. We show, in particular, how such forcings may locally transform oscillatory media into excitable ones and trigger the formation of complex spatiotemporal patterns.
Collapse
Affiliation(s)
- L. Kramer
- Physikalisches Institut der Universitat Bayreuth, D-95440 Bayreuth, GermanyDepartment of Chemistry. H. C. Orsted Institute, University of Copenhagen, DK-2100 Copenhagen, DenmarkCenter for Nonlinear Phenomena and Complex Systems of the Free University of Brussels, B-1050 Brussels, Belgium
| | | | | | | |
Collapse
|
18
|
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]
|
19
|
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
|
20
|
Hynne F, Graae So/rensen P, Mo/ller T. Current and eigenvector analyses of chemical reaction networks at Hopf bifurcations. J Chem Phys 1993. [DOI: 10.1063/1.464657] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|