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Table 2 Summary statistics about rate constants estimated from the proposed hybrid method a,b

From: Extraction of elementary rate constants from global network analysis of E. coli central metabolism

Enzyme Ordinary differential equations K-values c (Mean ± SD) CV (%) CI (95%) fval-values (Mean ± SD)
Phosphogluco -isomerase (pgi) K1f,PGI*[G6P]*[EPGI] (1.27 ± 0.00) × 105 0.0 (1.27, 1.27) × 105 (9.2 ± 2.4) × 10-3
  K1r,PGI*[EPGI-G6P] (1.28 ± 0.00) × 105 0.0 (1.28, 1.28) × 105  
  K2f,PGI*[EPGI-G6P] (2.41 ± 0.00) × 105 0.0 (2.41, 2.41) × 105  
  K2r,PGI*[F6P]*[EPGI] (1.39 ± 0.01) × 106 0.0 (1.39, 1.39) × 106  
Phosphofructo -kinase (pfkA)d K1f,PFKA*f*[EPFKATR]*[ATP]m (4.21 ± 0.63) × 101 15.0 (3.83, 4.59) × 101 (5.4 ± 1.2) × 10-2
  K1r,PFKA*[EPFKAR-ATP] (1.73 ± 1.94) × 100 112.7 (0.55, 2.90) × 100  
  K2f,PFKA*[EPFKAR-ATP]*[F6P]n (4.70 ± 0.50) × 103 10.7 (4.39, 5.00) × 103  
  K2r,PFKA*[EPFKAR-ATP-F6P] (6.52 ± 7.93) × 101 121.6 (1.73, 11.31)×101  
  K3f,PFKA*[EPFKAR-ATP-F6P] (3.50 ± 0.76) × 102 21.8 (3.05, 3.96) × 102  
  K4f,PFKA*[EPFKAR-ADP] (3.67 ± 3.01) × 105 82.2 (1.85, 5.49) × 105  
Fructose- bisphosphate aldolase (fba) K1f,FBA*[FDP]*[EFBA] (4.98 ± 0.01) × 103 0.2 (4.98, 4.98) × 103 (4.8 ± 0.1) × 10-3
  K1r,FBA*[EFBA-FDP] (9.14 ± 0.02) × 102 0.2 (9.13, 9.14) × 102  
  K2f,FBA*[EFBA-FDP] (4.33 ± 0.00) × 102 0.0 (4.33, 4.33) × 102  
  K2r,FBA*[GAP]*[EFBA-DHAP] (9.98 ± 0.02) × 104 0.2 (9.98, 9.99) × 104  
  K3f,FBA*[EFBA-DHAP] (5.95 ± 0.01) × 104 0.2 (5.94, 5.95) × 104  
  K3r,FBA*[DHAP]*[EFBA] (1.04 ± 0.00) × 104 0.0 (1.04, 1.04) × 104  
Triosephosphate isomerase (tpiA) K1f,TPIA*[DHAP]*[ETPIA] (1.17 ± 0.00) × 103 0.0 (1.17, 1.17) × 103 (1.5 ± 0.6) × 10-4
  K1r,TPIA*[ETPIA-DHAP] (2.34 ± 0.00) × 102 0.0 (2.34, 2.34) × 102  
  K2f,TPIA*[ETPIA-DHAP] (3.04 ± 0.00) × 103 0.0 (3.04, 3.04) × 103  
  K2r,TPIA*[GAP]*[ETPIA] (1.09 ± 0.00) × 104 0.0 (1.09, 1.09) × 104  
Glyceraldehyde 3- phosphate dehydrogenase (gapA) K1f,GAP*[NAD]*[EGAP] (3.01 ± 0.00) × 104 0.0 (3.01, 3.01) × 104 (7.8 ± 0.4) × 10-2
  K1r,GAP*[EGAP-NAD] (7.57 ± 0.00) × 103 0.0 (7.57, 7.57) × 103  
  K2f,GAP*[GAP]*[EGAP-NAD] (1.85 ± 0.25) × 104 13.5 (1.75, 1.95) × 104  
  K2r,GAP*[EGAP-NAD-GAP] (9.61 ± 0.90) × 105 9.4 (9.25, 9.96) × 105  
  K3f,GAP*[EGAP-NAD-GAP] (1.67 ± 0.83) × 106 50.0 (1.34, 2.00) × 106  
  K3r,GAP*[PGP]*[EGAP-NADH] (1.99 ± 0.64) × 109 32.3 (1.74, 2.24) × 109  
  K4f,GAP*[EGAP-NADH] (7.61 ± 0.01) × 103 0.2 (7.61, 7.62) × 103  
  K4r,GAP*[NADH]*[EGAP] (7.36 ± 0.13) × 10-1 0.2 (7.35, 7.37) × 10-1  
Phosphoglycerate kinase (pgk) K1f,PGK*[PGP]*[EPGK] (1.77 ± 0.00) × 106 0.0 (1.77, 1.77) × 106 (3.4 ± 1.4) × 10-3
  K1r,PGK*[EPGK-PGP] (8.30 ± 0.00) × 104 0.0 (8.30, 8.30) × 104  
  K2f,PGK*[ADP]*[EPGK-PGP] (4.58 ± 0.05) × 105 0.0 (4.57, 4.60) × 105  
  K2r,PGK*[EPGK-PGP-ADP] (4.52 ± 0.35) × 103 7.8 (4.41, 4.63) × 103  
  K3f,PGK*[EPGK-PGP-ADP] (3.47 ± 3.45) × 105 99.5 (2.36, 4.57) × 105  
  K3r,PGK*[ATP]*[EPGK-PG3] (5.10 ± 4.99) × 105 97.9 (3.50, 6.69) × 105  
  K4f,PGK*[EPGK-PG3] (1.64 ± 0.88) × 105 53.6 (1.36, 1.92) × 105  
  K4r,PGK*[PG3]*[EPGK] (1.24 ± 0.68) × 105 54.7 (1.03, 1.46) × 105  
Phosphoglycerate Mutase (pgm) K1f,PGM*[PG3]*[EPGM] (2.01 ± 0.00) × 106 0.0 (2.01, 2.01) × 106 (2.8 ± 1.3) × 10-2
  K1r,PGM*[EPGM-PG3] (3.64 ± 0.00) × 105 0.0 (3.64, 3.64) × 105  
  K2f,PGM*[EPGM-PG3] (3.71 ± 0.00) × 104 0.0 (3.71, 3.71) × 104  
  K2r,PGM*[PG2]*[EPGM] (1.08 ± 0.01) × 106 1.3 (1.07, 1.09) × 106  
Enolase (eno) K1f,ENO*[PG2]*[EENO] (1.42 ± 0.00) × 105 0.0 (1.42, 1.42) × 105 (2.6 ± 1.2) × 10-2
  K1r,ENO*[EENO-PG2] (2.37 ± 0.00) × 103 0.0 (2.37, 2.37) × 103  
  K2f,ENO*[EENO-PG2] (1.18 ± 0.00) × 104 0.0 (1.18, 1.18) × 104  
  K2r,ENO*[PEP]*EENO] (1.05 ± 0.02) × 105 1.9 (1.05, 1.06) × 105  
Pyruvate kinase (pykF) e K1f,PYKF*f*[EPYKFTR]*[PEP] (1.59 ± 0.00) × 102 0.0 (1.59, 1.59) × 102 (6.0 ± 2.0) × 10-4
  K1r,PYKF*[EPYKFR-PEP] (4.96 ± 0.17) × 101 3.4 (4.89, 5.03) × 101  
  K2f,PYKF*[EPYKFR-PEP]*[ADP] (4.58 ± 2.92) × 102 63.9 (3.37, 5.78) × 102  
  K2r,PYKF*[EPYKFR-PEP-ADP] (2.43 ± 1.85) × 102 76.2 (1.67, 3.19) × 102  
  K3f,PYKF*[EPYKFR-PEP-ADP] (2.71 ± 1.71) × 102 63.2 (2.00, 3.41) × 102  
  K4f,PYKF*[EPYKFR-ATP] (7.89 ± 3.09) × 101 39.2 (6.61, 9.16) × 101  
  1. a Rate constants are the statistical solutions from 25 optimization runs which were performed with different random initial guesses for parameters of an individual enzyme. Through hybrid MRL/ARL model, MRL parameters for each enzyme are estimated in separate steps. Units are mM-1 s-1 and s-1 for second and first-order rate constants, respectively.
  2. b SD: Standard deviation; CV: Coefficient of variation; CI: Confidence interval; fval: cost function value.
  3. c Due to uncertainty in the source data [21], we have truncated to three digits, regarding of SD.
  4. d Reaction orders for allosteric enzyme pfkA are non-integer with respect to ATP and F6P, allowing for fractal properties [43] due to enzyme conformational changes. Values of m and n are 5.19 ± 0.28 and 9.80 ± 0.41, respectively, after optimization.
  5. e Reaction for allosteric enzyme pyruvate kinase is first order with respect to PEP and ADP, according to Tormonia's paper [39]