### Citations

2263 |
KEGG: Kyoto Encyclopedia of Genes and Genomes
- Kanehisa, Goto
(Show Context)
Citation Context ... model simulations with experimental data. Arabiodopsis callus model Information for metabolic pathways including their inhibition and activation was assembled from KEGG (http:// www.genome.jp/kegg/) =-=[37,38]-=- and AraCyc (http://arabidopsis.org/tools/aracyc/) [39] databases. A mathematical model was constructed based on the metabolic reaction network including 351 metabolites and 441 fluxes, which cover a ... |

220 |
a systematized collection of ODE solvers
- ODEPACK
- 1983
(Show Context)
Citation Context ...s and kinetic orders were between 0.5 and 20, and ±0.2 and ±0.8, respectively. Calculation method Differential equations were solved using automatic switching for stiff and non-stiff problems (LSODA) =-=[31]-=- using the ODE integration package from SciPy (Scientific Tools for Python) [32]. All visualizations were created using Matplotlib [33]. Details of the Arabidopsis system Arabidopsis callus culture Ar... |

156 |
Biochemistry and Molecular Biology of Plants. 1 st Edition.
- Buchanan, Gruissem, et al.
- 2000
(Show Context)
Citation Context ... is well known that the accumulation of methionine, a member of the aspartate-family amino acids together with lysine and threonine, is tightly controlled by negative feedback by lysine and threonine =-=[10]-=-. Another cause is an ambiguity in the characteristics of the metabolic flow pattern, which affects productivity and metabolic balance [11]. To elucidate their correlations among metabolites, there ar... |

130 |
Furumichi M, Tanabe M: KEGG for integration and interpretation of large-scale molecular data sets. Nuc Acids Res 2012, 40(Database issue):109–114. doi:10.1093/nar/gkr988
- Kanehisa, Goto, et al.
(Show Context)
Citation Context ... model simulations with experimental data. Arabiodopsis callus model Information for metabolic pathways including their inhibition and activation was assembled from KEGG (http:// www.genome.jp/kegg/) =-=[37,38]-=- and AraCyc (http://arabidopsis.org/tools/aracyc/) [39] databases. A mathematical model was constructed based on the metabolic reaction network including 351 metabolites and 441 fluxes, which cover a ... |

125 |
Computational analysis of biochemical systems: a practical guide for biochemists and molecular biologists,
- Voit
- 2000
(Show Context)
Citation Context ...s of the system. This result is not surprising, because multiplying the entire system with a positive constant corresponds to changing the unit of time and thereby the scale of the x-axis (see, e.g., =-=[9]-=-). Additional results are presented in Supplementary Figures S3 and S4 (additional file 1). Effect of kinetic orders on metabolic behaviors Figure 2c and 2d show patterns of normalized concentrations ... |

57 |
Metabolomics in systems biology
- Weckwerth
- 2003
(Show Context)
Citation Context ...Biology 2014, 8(Suppl 5):S4 http://www.biomedcentral.com/1752-0509/8/S5/S4 Page 3 of 16 dX2 dt = α2X g21 1 − β2Xh222 = 8X0.51 − 3X0.752 (2) dX3 dt = α3X g32 2 − β3Xh333 Xh344 = 3X0.752 − 5X0.53 X0.24 =-=(3)-=- dX4 dt = α4X g41 1 − β4Xh444 = 2X0.51 − 6X0.84 (4) Effect of rate constants on metabolic behaviors Figure 2a and 2b show patterns of normalized concentrations for each metabolite over time resulting ... |

36 |
Matplotlib: A 2D Graphics Environment
- JD
(Show Context)
Citation Context ...ing automatic switching for stiff and non-stiff problems (LSODA) [31] using the ODE integration package from SciPy (Scientific Tools for Python) [32]. All visualizations were created using Matplotlib =-=[33]-=-. Details of the Arabidopsis system Arabidopsis callus culture Arabidopsis thaliana liquid callus culture derived from accession Col-0 was prepared as described in Murota et al. [34] with slight modif... |

34 |
Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions
- MA
- 1969
(Show Context)
Citation Context ...acy. Instead, these models should be easy to construct, robust, and merely able to identify how data within a large dataset could probably be. Power-law models within Biochemical Systems Theory (BST; =-=[4]-=-) possess two great advantages that can be leveraged toward predicting the unmeasurable data as well as testing the consistency between the measured data and an alleged pathway structure and its regul... |

27 | Almeida J: Decoupling dynamical systems for pathway identification from metabolic profiles - EO |

24 |
Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation
- MA
- 1969
(Show Context)
Citation Context ...rdinary differential equation systems of a specific format: Each process is represented with a product of power-law functions. This format is the result of Taylor approximation in a logarithmic space =-=[4,9,19,20]-=-. The change in each variable of a system is thus represented as a so-called Generalized Mass Action (GMA)- system as follows: dXi dt − p∑ k=1 αik n∏ j=1 Xjgijk m∏ j=1 YjGijk− q∑ k=1 βik n∏ j=1 Xjhijk... |

20 |
Zhang P, Rhee SY: AraCyc: A Biochemical Pathway Database for Arabidopsis
- LA
(Show Context)
Citation Context ...llus model Information for metabolic pathways including their inhibition and activation was assembled from KEGG (http:// www.genome.jp/kegg/) [37,38] and AraCyc (http://arabidopsis.org/tools/aracyc/) =-=[39]-=- databases. A mathematical model was constructed based on the metabolic reaction network including 351 metabolites and 441 fluxes, which cover a wide variety of metabolic pathways related to amino aci... |

18 |
The tricarboxylic acid cycle in Dictyostelium discoideum II. Evaluation of model consistency and robustness.
- Shiraishi, Savageau
- 1992
(Show Context)
Citation Context ...uracy of BST models over quite large ranges in variation of the involved variables [22-25]. Applications of BST models were also demonstrated with various large-scale systems, including the TCA cycle =-=[26]-=-, ethanol fermentation [27], purine metabolism [28], and sphingolipid metabolism [29]. Meaning of parameters and U-system approach Model parameters of pathway systems are usually estimated from kineti... |

15 |
S-system parameter estimation for noisy metabolic profiles using Newton flow analysis
- Kutalik, Tucker, et al.
- 2007
(Show Context)
Citation Context ...dent and independent variables, respectively, p and q are the maximum numbers of influxes and effluxes, respectively, and t is time. Details have been documented in the literature many times, e.g. in =-=[6,7,9,21]-=-. 2. Validity and accuracy of BST for modeling biological systems Since the power-law format in BST appears to be quite restrictive, the accuracy of different model variants within BST has been assess... |

12 |
Sorribas A: Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: Steady-state analysis
- Cascante, Curto
- 1995
(Show Context)
Citation Context ...ite large ranges in variation of the involved variables [22-25]. Applications of BST models were also demonstrated with various large-scale systems, including the TCA cycle [26], ethanol fermentation =-=[27]-=-, purine metabolism [28], and sphingolipid metabolism [29]. Meaning of parameters and U-system approach Model parameters of pathway systems are usually estimated from kinetic information or from metab... |

10 |
Voit EO, Hannun YA: Simulation and validation of modelled sphingolipic metabolism in Saccharomyces cerevisiae
- Alvarez-Vasquez, KJ, et al.
(Show Context)
Citation Context ...2-25]. Applications of BST models were also demonstrated with various large-scale systems, including the TCA cycle [26], ethanol fermentation [27], purine metabolism [28], and sphingolipid metabolism =-=[29]-=-. Meaning of parameters and U-system approach Model parameters of pathway systems are usually estimated from kinetic information or from metabolic time series data. In Eq. (5), the familiar kinetic pa... |

10 |
Widely targeted metabolomics based on large-scale MS/MS data for elucidating metabolite accumulation patterns in plants. Plant Cell Physiol
- Sawada, Akiyama, et al.
- 2009
(Show Context)
Citation Context ...96 well plate and the residue was dissolved in 120 uL ultrapure water (no. 210-01303, Wako Pure Chemical Industries, Ltd.). One uL of the solution was subjected to widely targeted metabolome analysis =-=[36]-=- by LC-MS using UPLC-TQD system (Waters, Milford, MA, USA). The peak intensities were normalized by those of internal standards (10-campher sulfonate and lidocaine). For mathematical modeling, the nor... |

9 |
Robert-Genthon M, Cornish-Bowden A, Cardenas ML, Dumas R (2009). Understanding the regulation of aspartate metabolism using a model based on measured kinetic parameters
- Curien, Bastien
(Show Context)
Citation Context ...ity and metabolic balance [11]. To elucidate their correlations among metabolites, there are various researches focusing on the integrations of in vitro data into kinetic models for specific pathways =-=[12,13]-=- and the reconstructions of metabolic fluxes at the genome scale [14,15]. However, no large-scale kinetic models including regulatory mechanisms are known for the Arabidopsis metabolic system. In this... |

7 | A comparison of variant theories of intact biochemical systems. I: Enzyme-enzyme interactions and biochemical systems theory - Sorribas, Savageau - 1989 |

6 |
Miguet L, Sweetlove LJ, Fell DA: A genome-scale metabolic model of Arabidopsis thaliana and some of its properties
- MG
(Show Context)
Citation Context ...tabolites, there are various researches focusing on the integrations of in vitro data into kinetic models for specific pathways [12,13] and the reconstructions of metabolic fluxes at the genome scale =-=[14,15]-=-. However, no large-scale kinetic models including regulatory mechanisms are known for the Arabidopsis metabolic system. In this study, therefore, we exploited the U-system approach to construct a lar... |

6 |
Biochemical Systems Theory: A Review.
- Voit
- 2013
(Show Context)
Citation Context ...dent and independent variables, respectively, p and q are the maximum numbers of influxes and effluxes, respectively, and t is time. Details have been documented in the literature many times, e.g. in =-=[6,7,9,21]-=-. 2. Validity and accuracy of BST for modeling biological systems Since the power-law format in BST appears to be quite restrictive, the accuracy of different model variants within BST has been assess... |

5 |
Fernie AR: Plant metabolomics: towards biological function and mechanism
- Schauer
(Show Context)
Citation Context ...= 12X−0.83 − 8X0.51 − 2X0.51 (1) Sriyudthsak et al. BMC Systems Biology 2014, 8(Suppl 5):S4 http://www.biomedcentral.com/1752-0509/8/S5/S4 Page 3 of 16 dX2 dt = α2X g21 1 − β2Xh222 = 8X0.51 − 3X0.752 =-=(2)-=- dX3 dt = α3X g32 2 − β3Xh333 Xh344 = 3X0.752 − 5X0.53 X0.24 (3) dX4 dt = α4X g41 1 − β4Xh444 = 2X0.51 − 6X0.84 (4) Effect of rate constants on metabolic behaviors Figure 2a and 2b show patterns of no... |

5 |
Itaya A, Uda Y, Kijima F, Tamaki Y, Nambara E, Naito S. 2000. Mutation in the threonine synthase gene results in an over-accumulation of soluble methionine in Arabidopsis. Plant Physiology 123
- Bartlem, Lambein, et al.
(Show Context)
Citation Context ...ethionine concentration was predicted to increase. In overall, the 6 out of 7 amino acids or 85% prediction agreed with the original result from biological experiment using an Arabidopsis mto2 mutant =-=[17]-=-. The prediction was further compared to the result from metabolome analysis [18]. Figure 8 showed that 73% correctness from 11 metabolites showing the significant changes comparing with the widetype ... |

5 |
Biochemical systems analysis III: Dynamic solutions using a power-law approximation
- MA
- 1970
(Show Context)
Citation Context ...rdinary differential equation systems of a specific format: Each process is represented with a product of power-law functions. This format is the result of Taylor approximation in a logarithmic space =-=[4,9,19,20]-=-. The change in each variable of a system is thus represented as a so-called Generalized Mass Action (GMA)- system as follows: dXi dt − p∑ k=1 αik n∏ j=1 Xjgijk m∏ j=1 YjGijk− q∑ k=1 βik n∏ j=1 Xjhijk... |

5 |
Voit EO, Sorribas A, Cascante M: Mathematical models of purine metabolisms in man
- Curto
- 1998
(Show Context)
Citation Context ...ation of the involved variables [22-25]. Applications of BST models were also demonstrated with various large-scale systems, including the TCA cycle [26], ethanol fermentation [27], purine metabolism =-=[28]-=-, and sphingolipid metabolism [29]. Meaning of parameters and U-system approach Model parameters of pathway systems are usually estimated from kinetic information or from metabolic time series data. I... |

3 |
Stephanopoulos GN, Gunawan R: Parameter estimation of kinetic models from metabolic profiles: Two-phase dynamic decoupling method
- Jia
(Show Context)
Citation Context ...dent and independent variables, respectively, p and q are the maximum numbers of influxes and effluxes, respectively, and t is time. Details have been documented in the literature many times, e.g. in =-=[6,7,9,21]-=-. 2. Validity and accuracy of BST for modeling biological systems Since the power-law format in BST appears to be quite restrictive, the accuracy of different model variants within BST has been assess... |

3 |
K: Comparative metabolomics charts the impact of genotype-dependent methionine accumulation in Arabidopsis thaliana
- Kusano, Fukushima, et al.
(Show Context)
Citation Context ...no acids or 85% prediction agreed with the original result from biological experiment using an Arabidopsis mto2 mutant [17]. The prediction was further compared to the result from metabolome analysis =-=[18]-=-. Figure 8 showed that 73% correctness from 11 metabolites showing the significant changes comparing with the widetype whereas the metabolome and amino acid data showed Figure 8 Qualitative prediction... |

2 |
Ruppin E, Aharoni A, Shlomi T: Reconstruction of Arabidopsis metabolic network models accounting for subcellular compartmentalization and tissue-specificity
- Mintz-Oron, Meir, et al.
(Show Context)
Citation Context ...tabolites, there are various researches focusing on the integrations of in vitro data into kinetic models for specific pathways [12,13] and the reconstructions of metabolic fluxes at the genome scale =-=[14,15]-=-. However, no large-scale kinetic models including regulatory mechanisms are known for the Arabidopsis metabolic system. In this study, therefore, we exploited the U-system approach to construct a lar... |

2 | Savageau MA: Accuracy of alternative representations for integrated biochemical systems. Biochem - EO - 1987 |

2 | Savageau MA: Strategies for representing metabolic pathways within biochemical systems theory: Reversible pathways - Sorribas - 1989 |

1 |
EO: What if the fit is unfit? Criteria for biological systems estimation beyond residual errors
- Voit
(Show Context)
Citation Context ...l’s potential repertoire of responses, rather than addressing specific data fits. Second, the estimation of optimal parameter values for large systems is generally fraught with technical difficulties =-=[5]-=-. This issue is greatly ameliorated for BST models, because even relatively coarse numerical settings of their parameters are often sufficient to capture the behavior of a metabolic pathway system in ... |

1 |
Datko AH: Regulatory structure of the biosynthetic pathway for the aspartate family of amino acids in Lemna paucicostata Hegelm. 6746, with special reference to the role of aspartokinase. Plant Physiol
- Giovanelli, SH
- 1989
(Show Context)
Citation Context ...htly controlled by negative feedback by lysine and threonine [10]. Another cause is an ambiguity in the characteristics of the metabolic flow pattern, which affects productivity and metabolic balance =-=[11]-=-. To elucidate their correlations among metabolites, there are various researches focusing on the integrations of in vitro data into kinetic models for specific pathways [12,13] and the reconstruction... |

1 |
Sawodny O, Ederer M, Heyer AG: Mathematical modeling of the central carbohydrate metabolism in Arabidopsis reveals a substantial regulatory influence of vacuolar invertase on whole plant carbon metabolism
- Nagele, Henkel, et al.
(Show Context)
Citation Context ...ity and metabolic balance [11]. To elucidate their correlations among metabolites, there are various researches focusing on the integrations of in vitro data into kinetic models for specific pathways =-=[12,13]-=- and the reconstructions of metabolic fluxes at the genome scale [14,15]. However, no large-scale kinetic models including regulatory mechanisms are known for the Arabidopsis metabolic system. In this... |

1 |
Voit EO: Coarse but efficient identification of metabolic pathway system
- Iwata, Shiraishi
(Show Context)
Citation Context ...ax, can be converted into BST parameters, but this is seldom possible on the basis of metabolome data, which are often presented as relative rather than absolute concentrations. It was recently shown =-=[30]-=- that a coarse grid of kinetic orders is sufficient to fit time developments in pathway systems with surprisingly high accuracy. Expanding on this idea, we here fix all kinetic orders to 1, 0.5 or -0.... |

1 |
Hagiwara-Komoda Y, Komoda K, Onouchi H, Ishikawa M, Naito S: Arabidopsis cell-free extract, ACE, a new in vitro translation system derived from Arabidopsis callus cultures. Plant Cell Physiol 2011
- Murota
(Show Context)
Citation Context ... using Matplotlib [33]. Details of the Arabidopsis system Arabidopsis callus culture Arabidopsis thaliana liquid callus culture derived from accession Col-0 was prepared as described in Murota et al. =-=[34]-=- with slight modifications. For callus induction, minced seedlings were incubated in RM28 medium under constant light. The medium was changed every 6 days. For a metabolic perturbation experiment, RM2... |

1 |
SH: Methionine biosynthesis in Lemma: inhibitor studies. Plant Physiol
- AH, Mudd
- 1982
(Show Context)
Citation Context ...ngs were incubated in RM28 medium under constant light. The medium was changed every 6 days. For a metabolic perturbation experiment, RM28 medium supplemented with 10 mM L-lysine and 1 mM L-threonine =-=[35]-=- was used at the third medium change. For a control experiment, RM28 without supplementation was used. Sucrose in RM28 medium was a sole carbon source for callus culture. The experiments were carried ... |

1 |
S: Dynamics of methionine biosynthesis. Plant Biotechnol 2005, 22:379-388. doi:10.1186/1752-0509-8-S5-S4 Cite this article as: Sriyudthsak et al.: A U-system approach for predicting metabolic behaviors and responses based on an alleged metabolic reaction
- DB, Onouchi, et al.
(Show Context)
Citation Context ..., namely, aspartate, lysine, threonine, and methionine. The effects of feedback inhibition and activation were also included based on information available from the literature and pertinent databases =-=[12,40]-=-. Kinetic orders of metabolites were set to 1, while kinetic orders for inhibition and activation signals were set to -0.5 and 0.5, respectively. In the experiments to obtain relative metabolite conce... |