A procedure for the estimation over time of metabolic fluxes in scenarios where measurements are uncertain and/or insufficient

Llaneras, Francisco; Picó, Jesús

doi:10.1186/1471-2105-8-421

Table 2 Comparison of different estimations of the non-measured fluxes

From: A procedure for the estimation over time of metabolic fluxes in scenarios where measurements are uncertain and/or insufficient

Ref (v₁, v₆, v₇, v₁₉, v₂₀, v₂₂)		G (no v₂₂)		F (no v₂₀)		E (no v₁₉)		B (no v₆)		A (no v₁)		C (no v₇)		I (no v₂₀v₂₂)		H (no v₁₉v₂₂)
Reactions ^d	MI^a [^b]	MI [^a]	[%^c]	MI [^b]	[%]	MI [^b]	[%]	MI [^b]	[%]	MI [^b]	[%]	MI [^b]	[%]	MI [^b]	[%]	MI [^b]	[%]
1: G→G6P	0.267^e	0.267	-	0.267	-	0.267	-	0.267	-	x	-	0.267	-	0.267	-	0.267	-
2: G6P→G3P+DAP	0.367	0.387	5%	0.628	71%	0.541	47%	0.398	8%	x	-	0.627	71%	0.628	71%	0.572	56%
3: G6P→R5P+CO2	0.131	0.199	53%	0.526	303%	0.340	160%	0.131	0%	0.131	0%	0.401	207%	0.526	303%	0.383	193%
4: DAP→G3P	0.367	0.387	5%	0.628	71%	0.541	47%	0.398	8%	x	-	0.627	71%	0.628	71%	0.572	56%
5: G3P→Pyr	0.735	0.774	5%	1.256	71%	1.082	47%	0.795	8%	x	-	1.253	71%	1.256	71%	1.144	56%
6: Pyr→L	0.475	0.475	-	0.475	-	0.475	-	x	-	0.475	-	0.475	-	0.475	-	0.475	-
7: Pyr+Glu→A+aKG	0.100	0.100	-	0.100	-	0.100	-	0.100	-	0.100	-	1.488	inf	0.100	-	0.100	-
8: Pyr→ACA+CO2	1.031	1.031	0%	1.562	51%	1.901	84%	x	-	x	-	0.957	-7%	1.562	51%	1.906	85%
9: Oxa+ACA→Cit	1.031	1.031	0%	1.562	51%	1.901	84%	x	-	x	-	0.957	-7%	1.562	51%	1.906	85%
10: Cit→aKG+CO2	1.031	1.031	0%	1.562	51%	1.901	84%	x	-	x	-	0.957	-7%	1.562	51%	1.906	85%
11: aKG→Mal+CO2	1.156	1.156	0%	1.604	39%	2.532	119%	x	-	x	-	1.443	25%	1.604	39%	2.530	119%
12: Mal→Oxa	0.994	0.994	0%	1.398	41%	1.769	78%	x	-	x	-	1.093	10%	1.398	41%	1.769	78%
13: Mal→Pyr+CO2	0.209	0.240	15%	0.352	68%	0.920	341%	0.209	0%	0.209	0%	0.903	332%	0.352	68%	0.918	340%
14: Oxa+Glu→Asp+aKG	0.131	0.199	53%	0.526	303%	0.340	160%	0.131	0%	0.131	0%	0.401	207%	0.526	303%	0.383	193%
15: Glu→aKG+NH4	0.150	0.182	21%	0.298	98%	0.870	479%	0.150	0%	0.150	0%	0.586	289%	0.298	98%	0.870	479%
16: Q→Glu+NH4	0.117	0.145	23%	0.325	177%	0.553	372%	0.117	0%	0.117	0%	0.569	386%	0.325	177%	0.548	367%
17: R5P+Asp+Q→Pu	0.104	0.277	165%	0.293	181%	0.200	91%	0.104	0%	0.104	0%	0.225	116%	0.526	404%	0.383	267%
18: R5P+Asp+2Q→Py	0.078	0.132	69%	0.283	262%	0.177	126%	0.078	0%	0.078	0%	0.209	168%	0.263	237%	0.163	108%
19:→NH4	0.141	0.141	-	0.141	-	1.419	904%	0.141	-	0.141	-	0.141	-	0.141	-	1.412	899%
20:→Q	0.132	0.132	-	1.127	752%	0.132	-	0.132	-	0.132	-	0.132	-	1.107	737%	0.132	-
21:→CO2	3.338	3.338	0%	4.770	43%	6.966	109%	x	-	x	-	3.843	15%	4.770	43%	6.966	109%
22: Pu-Py (constraint)	0.100	0.354	254%	0.100	-	0.100	-	0.100	-	0.100	-	0.100	-	0.526	426%	0.383	283%
Mean	0.554	0.587	39%	0.899	155%	1.138	196%	0.217	2%	0.156	0%	0.802	122%	0.927	180%	1.168	214%
Measured fluxes [number]	6	5		5		5		5		5		5		4		4
Estimated fluxes [number]	16/16	17/17		17/17		17/17		7/17		10/17		17/17		18/18		18/18
<25% (·Ref)			12		0		0		10		7		5		0		0
25–100% (<2·Ref)			3		11		8		0		0		4		11		7
100–300% (2–4·Ref)			2		3		5		0		0		5		2		7
>300% (>4·Ref)			0		3		4		0		0		3		5		4

Column Ref: FSA is applied by using the six available measurements (Determined case). Columns F, G, E B, A and C: FSA is applied by using a different set of 5 measurements in each case (underdetermined, 1 degree of freedom). Columns I and H: FSA is applied by using two different sets of 4 measurements (underdetermined, 2 degrees of freedom). In all cases the band of uncertainty described in the text has been used. ^a Mean interval size along time evolution; ^b in [mM/(d * 10^9 cells)]; ^c Intervals enlargement w.r.t. case Ref. (in percentage); ^d The nomenclature is given in the additional file 1; ^e Measured values are in bold.

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