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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]
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BMC Systems Biology

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