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In silico analysis of lactate producing metabolic network in Lactococcus lactis
Enzyme and Microbial Technology 35 (2004) 654–662
In silico analysis of lactate producing metabolic network in Lactococcus lactis Jae Wook Nama , Kyoung Hoon Hana , En Sup Yoona , Dong Il Shinb , Jong Hwa Jinc , Do Heon Leed , Sang Yup Leee , Jinwon Leec,∗ a
Department of Chemical Engineering, Seoul National University, Seoul 151-744, South Korea Department of Chemical Engineering, Myongji University, Kyunggido 449-728, South Korea c Department of Chemical Engineering, Kwangwoon University, Wolgye-dong, Nowon-gu, Seoul 139-701, South Korea d Bio-Information System Laboratory, Department of BioSystems, Korea Advanced Institute of Science and Technology, South Korea e Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea b
Abstract Today the importance of in silico experiment grows bigger than before by the advance of computing power. More detailed mathematical modeling handled by simulation can produce more reasonable and meaningful results. In this research, we suggest the metabolic network of Lactococcus lactis for aerobic condition. Using a mathematical model, we observed the effect of enzymes on lactate production using flux distribution analysis, metabolic control analysis, and in silico experiment by biochemical simulation software. Each analysis showed some different results because of their characteristics but some key enzymes for lactate production were found from them. © 2004 Elsevier Inc. All rights reserved. Keywords: Lactococcus lactis; Metabolic engineering; Metabolic control analysis; Pyruvate branch
1. Introduction The lactic acid bacterium Lactococcus lactis is commonly used in the dairy industry for the manufacture of fermented milk and cheese. This is mainly due to the ability of this organism to rapidly convert the sugars present in milk to lactic acid, whereby a preservative effect is obtained. However, this organism has been focused again as a producer of biodegradable polymer, poly lactate [1]. Use of this organism can substitute for existing chemical methods for an important part of environmentally friendly processes. Previously most experiments have focused on anaerobic condition, but yield of lactate production to total fermentation is already over 90%. Thus the interest in experiments on the aerobic condition, in which organisms can be considered as a heterofermentative, is growing. An intuitive approach to the optimization of fluxes towards the desired end products can not always attain proper ∗
Corresponding author. Tel.: +82 2 940 5172; fax: +82 2 909 0701. E-mail address: [email protected] (J. Lee).
0141-0229/$ – see front matter © 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.enzmictec.2004.08.032
results from complex metabolism such as a highly branched system including redox [NAD(P)H] and Gibbs free energy (ATP) carriers. In this respect, a more systematic approach such as biological system theory, metabolic control analysis metabolic control analyses, and metabolic design, have an important role in analyzing complex multi-enzyme systems [2,3]. Also the trends of increasing computer power deliver us with the ability to handle more complex mathematical models than the past. The accuracy of in silico experiments has increased greatly than the past, and in many fields of biology in silico experiments have significant impact on analyzing complex metabolic networks predicatively and quantitatively. In this study, the metabolic network on subject organism, L. lactis, was expressed in a stoichiometric metabolic network model and its mathematical model was constructed and analyzed by the bio-chemical simulator, GEPASI. The importance of flux in model was quantified by metabolic control analysis and the effects of modulation in key enzyme activity to pyruvate branch, which are directly related to fermentation, were examined.
J.W. Nam et al. / Enzyme and Microbial Technology 35 (2004) 654–662
Nomenclature AC acetate ACAL acetaldehyde ACALDH acetaldehyde dehydrogenase ACCOA acetyl coenzyme A ACET acetoin ACETDH acetoin dehydrogenase ACETEFF acetoin efflux ACK acetate kinase ACLAC acetolactate ACP acetyl phosphate ADH alcohol dehydrogenase ALD acetolactate decarboxylase ALS acetolactate synthase ATP adenosine triphosphate ATPase adenosine triphosphatease BPG 1,3-bisphosphoglycerate BUT 2,3-butanediol COA coenzyme A DHAP dihydroxyacetone phosphate ENO enolase ETOH ethanol F16P fructose-1,6-biphosphate F6P fructose-6-phosphate G6P glucose-6-phosphate GAP glyceraldehyde-3-phosphate GAPDH glyceraldehyde 3-phosphate dehydrogenase GLC glucose GLCT non-enzymic glucose transfer GLK glucokinase k rate constant K Michaelis–Menten constant Keq equilibrium constant Ki inhibition constant Km affinity constant LAC lactate N Hill coefficient NADH nicotinamide adenine dinucleotide NEALC non-enzymic acetolactate decarboxylation NOX NADH oxidase O oxygen P inorganic phosphate P2G 2-phosphoglycerate P3G 3-phosphoglycerate PTA phosphotransacetylase PDH pyruvate dehydrogenase PEP phospho-enol-pyruvate PFK phosphofructokinase PGI phosphoglucoisomerase PGK 3-phosphoglycerate kinase PGM phosphoglycerate mutase PPT phosphotransferase TIM triosephosphate isomerase V maximum reaction rate
655
In metabolic control analysis, flux control coefficients quantify the importance of an enzyme for the magnitude of a flux caused by a 1% modulation of the enzyme activity [4]. By the result from comparing flux control coefficients of enzymes in lactate production network, key steps, which can have significant effects on lactate production could be determined. However, flux control coefficient points at the effect of enzyme on flux with a very small change in any enzyme activity. In this point, it cannot deal with the more relevant larger changes, which have a practical matter of concern and interest in bioengineering. To supplement this disadvantage, we used in silico experiments, which use modulation of enzyme activity in an integrated mathematical model by varying kinetic parameters of enzyme reactions, and we illustrated the expected effects of enzymes on the pyruvate branch from this method.
2. Methods We gathered information about kinetic modeling from databases and literature [5,6]. 2.1. Assumption To construct a stoichiometric network model, we assumed that L. lactis live in an aerobic condition. Therefore, we excluded formate secretion from the network. Almost all gathered kinetic models and data were assumed to be at ambient temperature. pH also has significant effects on the whole metabolic system, but we considered the effect of pH only on NADH + NAD moiety conservation [7]. TCA cycle (tricarboxylic acid cycle) was not considered in this model because the exponential growth was assumed for more secretion of byproducts. AMP was not considered because gathered information did not include this metabolite. Thus, moiety conservation about Gibbs free energy was ATP + ADP = 10 mM [7]. 2.2. Simulation environment We used the biochemical simulator, GEPASI. It has been built and maintained by Pedro M. since 1993 and cited by many researchers [8,9]. GEPASI uses the damped Newton method in derivative calculation. In order to obtain results, Newton limit, which expresses the number of iterations that the Newton method executes, sets to 50. In order to solve ordinary differential equation (ODE), it uses Livermore Solver of Ordinary Differential Equation (LSODE), which solves systems dy/dt = f with a full or banded Jacobian when the problem is stiff, but it automatically selects between non-stiff (Adams) and stiff (BDF, backward differentiation formula) methods. LSODE adopts the non-stiff method initially, and dynamically monitors data in order to decide which method to use. For adjustable parameter for LSODE, Adams order, this determines the maximum order that the Adams method
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is allowed to take, sets to 12. And BDF order, which determine the maximum order that the BDF method is allowed to take, sets to 12. In this experiment, we adopted Newton and integration simultaneously in a strategy for steady-state solution [10].
this method, we have observed their effects on the pyruvate branch indirectly.
2.3. Analysis method
We have constructed a kinetic model in L. lactis describing glycolysis and fermentation part as shown in Figs. 1 and 2, Tables 1 and 2 [5,11–13]. The model prediction of the flux distribution in the wild type strain was shown Fig. 2. The model described an essentially heterofermentation. Most products from fermentation were lactate and acetate, and other metabolites production such as ethanol, acetoin, and butanol production had a
We have examined flux control coefficients in a lactate producing network. Through this comparison, we chose some enzymes, which make possibly significant effects on the lactate production rate. Because GEPASI does not use enzyme activity term, we used varying kinetic parameter, Vmax which belong to reaction related to these enzymes, instead. Using
3. Results and discussion
Fig. 1. Constructed metabolic network of Lactococcus lactis: 22 enzymes and 26 metabolites, flux are expressed by arrows and big sized bold words mean metabolites and small sized word means enzymes.
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Table 1 Collection of rate equation from proposed metabolic network of Lactoco-ccuslactis Reaction name
Enzyme kinetics
GLCT
V (S − (P/Keq )) S + Kms (1 + (p/KmP ))
GLK
V · GLCi · PEP KGLC KPEP (1 + (GLCi /KGLC ) + (G6P/KG6P ))(1 + (PEP/KPEP ) + (PYR/KPYR ))
PGI
V (G6P − F6P/Keq ) KG6P + G6P + (KG6P F6P/KF6P ) N
PFK
PEP V (F6P/KF6P )N ATP(1 − (PEPNPEP /(KPEP + PEPNPEP )))
KATP (1 + (ATP/KATP ) + (ADP/KADP ))(1 + (F6P/KF6P )N + (F16P/K16P ))
ALD
V · F16P(1 − (GAP · DHAP/Keq FBP)) KF16P (1 + (DHAP/KDHAP ) + (F16P/KF16P ) + (GAP/KGAP ) + ((DHAP · GAP)/(KDHAP KGAP )) + ((F16P · GAP)/(KF16P KiGAP ))
GAPDH
V (GAP · NAD − (BPG · NADH/Keq )) KGAP KNAD (1 + (GAP/KGAP ) + (BPG/KBPG ))(1 + (NAD/KNAD ) + (NADH/KNADH ))
PGK
V · BPG · ADP(1 − (P3G · ATP)/(Keq ADP · BPG)) KADP KDPG (1 + (ATP/KATP ) + (ADP/KADP ))(1 + (BPG/KBPG ) + (P3G/KP3G ))
PGM
V · P3G(1 − (P2G/Keq P3G)) KP3G (1 + (P2G/KP2G ) + (P3G/KP3G ))
ENO
V · P2G(1 − (PEP/Keq P2G)) KP2Gs (1 + (P2G/KP2G ) + (PEP/KPEP ))
PYK
ATPase
V (PEP/K · PEP)N ADP(1 − (PYR · ATP/Keq ADP · PEP)) KADP (1 + (ATP/KATP ) + (ADP/KADP ))(1 + (PEP/KPEP )N + (PYR/KPYR )) V (ATP/ADP)N + (ATP/ADP)N
N KATP
TIM
V · DHAP(1 − (GAP/Keq DHAP)) KDHAP (1 + (DHAP/KDHAP ) + (GAP/KGAP ))
LDH
V (1/KPYR KNADH )(PYR · NADH − (LAC · NAD/Keq )) (1 + (PYR/KPYR ) + (LAC/KLAC ))(1 + (NADH/KNADH ) + (NAD/KNAD ))
PDH
V (PYR/KPYR )(NAD/KNAD )(1/(1 + (Ki NADH/NAD)))(COA/KCOA ) (1 + (PYR/KPYR ))(1 + (NAD/KNAD ) + (NADH/KNADH ))(1 + (COA/KCOA ) + (ACCOA/KACCOA ))
PTA
V (1/Ki Km )(ACCOA · P − ACP · COA/Keq ) 1 + (ACCOA/Ki ) + (P/Ki ) + (ACP/Ki ) + (COA/Ki ) + ((ACCOA · P/Ki Km ) + (ACP · COA/Km Ki ))
ACK
V (1/(KADP KACP ))(ACP · ADP − AC(ATP/Keq )) (1 + (ACP/KACP ) + (AC/KAC ))(1 + (ADP/KADP ) + (ATP/KATP ))
ACALDH
V (1/KACCOA KNADH )(ACCOA · NADH − COA · NAD · ACAL/Keq ) (1 + (NAD/KNAD ) + (NADH/KNADH ))(1 + (ACCOA/KACCOA ) + (COA/KCOA ) + (ACAL/KACAL ) + (ACAL · COA/KACAL KCOA ))
ADH
V (1/KADP kACP )(ACAL · NADH − (ETOH · NAD/Keq )) (1 + (NAD/KNAD ) + (NADH/KNADH ))(1 + (ACAL/KACAL ) + (ETOH/KETOH ))
ALS
V (PYR/KPYR )(1 − ACLAC/PYR · Keq )((PYR/KPYR + ACLAC/KACLAC )N−1 ) (1 + PYR/KPYR + ACLAC/KACLAC )N
ALDC
V (ACLAC/KACLAC ) (1 + (ACLAC/KACLAC ) + (ACET/KACET ))
ACETDH
V · (1/(KACET KNADH ))(ACET · NADH − (BUT · NAD/Keq )) (1 + (ACET/KACET ) + (BUT/KBUT )(1 + (NADH/KNADH ) + (NAD/KNAD ))
NOX
V (NADH · O/KNADH Ko ) (1 + NAD/KNADH + NAD/KNAD )(1 + O/Ko )
NEALC
k · ACLAC
ACETEFF
V (ACET/KACET ) 1 + ACET/KACET
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J.W. Nam et al. / Enzyme and Microbial Technology 35 (2004) 654–662
negligible flux rate. Relatively large flux in ATP and NADH consumptions (which involve ATPase and NOX) was due to a large flux around the pyruvate branch. For ATP from glycolysis and fermentation network, generation of ATP was mostly done in PGK, PYK, ACK, and consumption of ATP was almost done in PFK. It means that J(ATPase) = 2.81 × 10−3 mM/min was nearly as the same as the sum of J(PGK) = 1.97 × 10−3 mM/min, J(PYK) = 0.846 × 10−3 mM/min, J(ACK) = 0.938 × 10−3 mM/min and J(PFK) = −9.38 × 10−3 mM/min. And for NADH from the network, generation of NADH was done in GADPH, LDH and PDH. It means that J(NOX) = 3.93 × 10−3 mM/min was nearly as the same as the sum of J(GAPDH) = 1.97 × 10−3 mM/min, J(LDH) = 1.12 × 10−3 mM/min and J(PDH) = 0.846 × 10−3 mM/min. From this result, we could intuitively infer that ATPase and NOX
seem to have a significant effect on lactate production. From network topology, we can also assume that LDH and PDH might control the pyruvate branch. From the information above, we can intuitively determine that the pyruvate branch is controlled by major four enzymes, LDH, PDH, ATPase, and NOX. A more systematic approach can be done by metabolic control analysis and the results are shown in Table 3. As mentioned above, flux control coefficients of LDH can be used for determining the effect of other enzymes. From this analysis, we noticed that GLK, PYK, PDH, LDH, ATPase, and NOX are candidates for key enzymes. Compared with the intuitive method, GLK and PYK seem to be new important enzymes, which have significant effects on lactate production. This means that total carbon influx to the pyruvate branch could be an important factor and could be
Fig. 2. Calculated flux in proposed metabolic network by GEPASI software through flux distribution analysis: the flux here is net flux which is vector sum of forward and backward flux and only 3 digit significant figure are considered.
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Fig. 3. Graphical representation of pyruvate branch between wild-type (Vmax (PDH) = 60 mM/min) and PDH knock-out (Vmax (PDH) = 0 mM/min): as the activity of PDH decrease, flux of lactate production increase.
Fig. 4. The plot of branch split ratio of pyruvate branch1 by changing Vmax of each enzyme: the target enzymes are (a) PDH, (b) PYK, (c) GLK, (d) LDH, (e) APTase, (f) NOX. Because of stability problem, which did not reach steady state, all range of Vmax are not plotted.
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Table 2 Collection of enzyme kinetic parameter from literature and BRENDA database: each parameter is used by rate equation which are composing proposed metabolic network of Lactococcus lactis in Table 1 Reaction name GLCT
Kinetic parameter Kms Kmp Vf Keq
Value
Reference/derivation
1.1918 1.1918 70 0.51079
http://www.bio.vu.nl/ www.bio.vu.nl www.bio.vu.nl www.bio.vu.nl
GLK
V KGLC KPEP KG6P KPYR
126 0.015 0.3 500 0.3
Obtained by fitting
V Keq KG6P KF6P
160 0.13 0.8 0.15
V KF6P N NPEP KF16P KATP KADP
227 0.25 2.9 2 5.8 0.18 0.3
§
V Keq KF116P KDHAP KGAP Ki,GAP
1100 0.056 0.17 0.13 0.03 0.23
§
V Keq KGAP KNAD KBPG KNADH
4984 0.00007 0.25 0.2 0.05 0.067
§
V Keq KADP KBPG KATP KP3G
1306.5 3200 0.53 0.3 0.003 0.2
Obtained by fitting
V Keq KP3G , KP2G
1340 1.2 0.1
§
V Keq KP2G KPEP
1600 4.6 0.04 0.5
§
V KPEP N Keq KADP KATP KPYR
2030 0.17 1.3 6500 1 10 21
§
V KATP N
30 6.196 2.58
V Keq KDHAP KG3P
17500 0.045 2.8 0.3
PGI
PFK
ALD
GAPDH
PGK
PGM
ENO
PYK
ATPase
TIM
Table 2 (Continued ) Reaction name
Kinetic parameter
Value
Reference/derivation
LDH
V KPYR KNADH Keq KLAC KNAD
5118 1.5 0.08 21120.7 100 2.4
Hogenholtz and Starrenburg (1992)
V KPYR KNAD Ki KCOA KNADH KACCOA
259 1 0.4 46.4 0.014 0.1 0.008
V Ki,ACCOA KmP Keq Ki,p Ki,ACP
42 0.2 2.6 0.0281 2.6 0.2
Abbe et al. (1982)
V KACP KADP Keq KAC KATP
2700 0.16 0.5 174.2 7 0.08
S. mutans; Abbe et al. (1982)
V KACCOA KNADH Keq KNAD KCOA
97 0.007 0.025 1 0.08 0.008
S. mutans; Abbe et al. (1982)
V KACAL KNADH Keq KNAD KETOH
162 0.03 0.05 12354.9 0.08 1
Cachon and Divies (1993)
ALS
V Keq PPYR KACLAC N
600 900,000 50 100 2.4
Snoep et al. (1992a)
ALDC
V KACLAC KACET
106 10 100
Swindell et al. (1996) Monnet et al. (1994a)
ACETDH
V KACET KNADH Ki KBUT KNAD
105 0.06 0.041 1400 2.6 0.16
V KNADH Ko KNAD
118 0.041 0.01 1
PDH
§ § § § §
Obtained by fitting §
PTA
§
§ § § §
ACK
§ §
§ § §
ACALDH
§ §
§ § §
ADH
§ §
§ § § § §
§ §
§ § §
§
Obtained by fitting § § §
NOX
§ § §
Obtained by fitting § § § §
NEALC ACETEFF
K V KACET § mark indicated that that ac.za.
Thauer et al. (1977) Crow and Pritchard (1977)
Snoep et al. (1992a) Snoep et al. (1992b) Estimated from Snoep et al. (1993)
Azotobacter; Bresters et al. (1975)
Thauer et al. (1997)
E.coli; Fox and Roseman (1986)
Thauer et al. (1997)
Thauer et al. (1977) Zymomonas; Wills et al. (1981)
Snoep et al. (1992a)
Gibson et al. (1991) Strecker and Haray (1954) Enterobacter; Carballo et al. (1991) S. faecalis; Schmidt et al. (1986)
0.0003 Monnet et al. (1994b) 200 5 parameter is excerpted from www.jjj.biochem.
J.W. Nam et al. / Enzyme and Microbial Technology 35 (2004) 654–662
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Table 3 Calculated flux control coefficient value of flux of LDH for each enzyme which is composing proposed metabolic network of Lactococcus lactis by metabolic control analysis. Flux control coefficient is defined as C(J(fluxi ), enzymek ), and fluxi is ith flux, enzymek is kth enzyme, respectively at steady state condition Flux control coefficient
Value
Flux control coefficient
Value
C(J(LDH), GLCT) C(J(LDH), GLK) C(J(LDH), PGI) C(J(LDH), PFK) C(J(LDH), ALD) C(J(LDH), GAPDH) C(J(LDH), PGK) C(J(LDH), PGM) C(J(LDH), ENO) C(J(LDH), PYK) C(J(LDH), ATPase) C(J(LDH), TIM)
3.90E−06 4.86E+00 4.12E−10 6.90E−07 −3.44E−10 1.02E−10 5.38E−11 1.38E−13 8.50E−14 −3.74E+00 −1.22E−01 1.44E−11
C(J(LDH),LDH) C(J(LDH),PDH) C(J(LDH),PTA) C(J(LDH),ACK) C(J(LDH),ACALDH) C(J(LDH),ADH) C(J(LDH),ALS) C(J(LDH),ALDC) C(J(LDH),ACETDH) C(J(LDH),NOX) C(J(LDH),NEALC) C(J(LDH),ACETEFF)
4.10E−01 −4.11E−01 −1.14E−06 −2.80E−06 1.33E−08 1.59E−04 −9.11E−07 3.35E−12 3.33E−13 −6.94E−05 9.49E−17 −3.42E−13
used to determine pyruvate branch split ratio. Even though coefficients of GLK and PYK were relatively greater than other coefficients, the results could be different with other simulation conditions, for example, due to different parameter values. To prove this situation, we have examined the effects of these enzymes on lactate production through in silico simulation. In GEPASI simulation, there were some parameters directly related to enzyme activity, as mentioned above. So varying the value of the parameter Vmax was used instead of varying enzyme activity. Variation of Vmax,PDH , which has the same effect of variation of PDH activity, has an important meaning because it can directly modify the branch split ratio. Fig. 3 shows its effect on the pyruvate branch point. For simulation Vmax,PDH in wild type L. lactis was 60 and the one in PDH knock out mutant was 0. Although metabolic control analysis coefficient of PDH was relatively smaller than other enzymes, its effect on the pyruvate branch for GLK and PYK was greater in the longer range. We have examined the spilt ratio of branch point, J(LDH)/J(Branch input), in various conditions as shown in Fig. 4. First, varying Vmax,PDH showed a non-linear curve, which means that the effect of enzyme PDH was not always as the same as in the wild type and its effect was more significant at lower activity (Fig. 4a). Also we examined the effect of PYK and GLK, which have large flux control coefficient values, in the same way (Fig. 4b and c). But there were some stability problems in metabolic network, which did not reach a steady state, when Vmax,PYK was lower than 900 mM/min and Vmax,GLK was lower than 80 mM/min. So we considered these values as lower bounds and examined the effect on the pyruvate branch. Varying conditions of the activity of LDH, ATPase, and NOX were also examined. In the LDH case, we have obtained reasonable results of larger Vmax,LDH , which means higher spilt ratio. In case of ATPase and NOX, we fixed the range of spilt ratio of branch point from 0.4 to 1, and compared the result of the effect. These two enzymes had only small effects on spilt ratio of branch point when the activities were relatively large.
However, NOX showed an interesting result when NOX had lower activity. The split ratio of branch point was abruptly increased when the activity of NOX decreased toward 0 as shown in Fig. 4f. In this situation, the value of J(Branch input) and J(PDH) decreased, J(ALS) and J(LDH) increased. It seems that the states of lower NAD concentration favor lactate production but this assumption could not be solved by simulation only, and it must be supported by in vitro or in vivo experiments. Even though flux control coefficients shows that PYK and GLK seemed to be most significant enzymes in lactate production, Fig. 4 shows that PDH, LDH, and NOX were the key enzymes, which had an influence on lactate production.
4. Conclusion In this research, we have suggested the mathematical model of L. lactis based on the analysis of metabolism and network. From the flux distribution analysis, ATPase, NOX, LDH, and PDH seem to have significant effects on the lactate pyruvate branch. But this was only an intuitive approach, so in order to verify the key enzymes systematically, we performed the metabolic control analysis. The flux control coefficients of LDH showed that input into the pyruvate branch could be another important factor because flux control coefficient values of GLK and PYK were higher than others. But metabolic control analysis was effective in a narrow range of enzyme activity so we performed in silico experiments by GEPASI software to examine the effect of enzyme activity to the pyruvate branch and lactate production. In this experiment, we have found that PDH, LDH, and NOX seemed to be the primary key enzymes of lactate production. In summary, many enzymes consist of metabolic network of L. lactis but their effects on lactate production were different from each other. So by performing various in silico analyses, we could narrow down our concern to key enzymes before doing wet experiments. We also found that the branch input flux could affect the lactate production from the metabolic control analysis results of the proposed network.
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This observation needs to be studied deeply by following wet experiments or in silico experiments. To get more detailed results, we are trying to prepare wet experiments. Acknowledgements This work was supported by the Korean Systems Biology Research Grant (M10309020000-03B5002-00000) from the Ministry of Science and Technology. References [1] Rafel AA. Poly(lactic acid) flims as food packaging materials. School of packaging, MSU, East lansing, USA; 2002. p. 3–4. [2] Acerenza L, Sauro HM, Kacser H. Control analysis of timedependent metabolic systems. J Theoret Biol 1989;137:423–44. [3] Gregory NS. Metabolic engineering. A principles and methodologies. Academic Press; 1998. [4] Cornish-Bowden A. Metabolic control analysis in theory and practice. Adv Mol Cell Biol 1995;11:21–64.
[5] http://jjj.biochem.ac.za/. [6] Hoefnagel MHN, Starrenburg MJC, Martens DE, Hugenholtz J, Kleerebezem M, Van Swam II, Bongers R, Westerhoff HV, Snoep JL. Metabolic engineering of lactic acid bacteria the combined approach: kinetic modeling metabolic control and experimental analysis. Microbiology 2002;148:1003–13. [7] Hofmeyr J-HS, Kacser H, van der Merwe KJ. Metabolic control analysis of moiety-conserved cycles. Eur J Biochem 1986;155:631– 41. [8] Mendes P. GEPASI: a software package for modelling the dynamics, steady states and control of biochemical and other systems. Comput Appl Biosci 1993;9:563–71. [9] http://www.gepasi.org/. [10] Hindmarsh AC. ODEPACK, a systematised collection of ODE solvers. In: Stepleman RS et al., editors. Scientific computing. Amsterdam: North-Holland; 1983. p. 55–64. [11] http://brenda.uni-koeln.de/. [12] Hoefnagel MHN, van der Burgt A, Martens DE. Time dependent response of glycolytic intermediates in a detailed glycolytic model of Lactococcus lactis during glucose run-out experiments. Kluwer Academic Publishers; 2002. [13] Mendes P, Kell DB, Welch GR. Metabolic channeling in organized enzyme systems: experiments and models. Adv Mol Cell Biol 1995;11:1–19.
In silico analysis of lactate producing metabolic network in Lactococcus lactis Jae Wook Nama , Kyoung Hoon Hana , En Sup Yoona , Dong Il Shinb , Jong Hwa Jinc , Do Heon Leed , Sang Yup Leee , Jinwon Leec,∗ a
Department of Chemical Engineering, Seoul National University, Seoul 151-744, South Korea Department of Chemical Engineering, Myongji University, Kyunggido 449-728, South Korea c Department of Chemical Engineering, Kwangwoon University, Wolgye-dong, Nowon-gu, Seoul 139-701, South Korea d Bio-Information System Laboratory, Department of BioSystems, Korea Advanced Institute of Science and Technology, South Korea e Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea b
Abstract Today the importance of in silico experiment grows bigger than before by the advance of computing power. More detailed mathematical modeling handled by simulation can produce more reasonable and meaningful results. In this research, we suggest the metabolic network of Lactococcus lactis for aerobic condition. Using a mathematical model, we observed the effect of enzymes on lactate production using flux distribution analysis, metabolic control analysis, and in silico experiment by biochemical simulation software. Each analysis showed some different results because of their characteristics but some key enzymes for lactate production were found from them. © 2004 Elsevier Inc. All rights reserved. Keywords: Lactococcus lactis; Metabolic engineering; Metabolic control analysis; Pyruvate branch
1. Introduction The lactic acid bacterium Lactococcus lactis is commonly used in the dairy industry for the manufacture of fermented milk and cheese. This is mainly due to the ability of this organism to rapidly convert the sugars present in milk to lactic acid, whereby a preservative effect is obtained. However, this organism has been focused again as a producer of biodegradable polymer, poly lactate [1]. Use of this organism can substitute for existing chemical methods for an important part of environmentally friendly processes. Previously most experiments have focused on anaerobic condition, but yield of lactate production to total fermentation is already over 90%. Thus the interest in experiments on the aerobic condition, in which organisms can be considered as a heterofermentative, is growing. An intuitive approach to the optimization of fluxes towards the desired end products can not always attain proper ∗
Corresponding author. Tel.: +82 2 940 5172; fax: +82 2 909 0701. E-mail address: [email protected] (J. Lee).
0141-0229/$ – see front matter © 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.enzmictec.2004.08.032
results from complex metabolism such as a highly branched system including redox [NAD(P)H] and Gibbs free energy (ATP) carriers. In this respect, a more systematic approach such as biological system theory, metabolic control analysis metabolic control analyses, and metabolic design, have an important role in analyzing complex multi-enzyme systems [2,3]. Also the trends of increasing computer power deliver us with the ability to handle more complex mathematical models than the past. The accuracy of in silico experiments has increased greatly than the past, and in many fields of biology in silico experiments have significant impact on analyzing complex metabolic networks predicatively and quantitatively. In this study, the metabolic network on subject organism, L. lactis, was expressed in a stoichiometric metabolic network model and its mathematical model was constructed and analyzed by the bio-chemical simulator, GEPASI. The importance of flux in model was quantified by metabolic control analysis and the effects of modulation in key enzyme activity to pyruvate branch, which are directly related to fermentation, were examined.
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Nomenclature AC acetate ACAL acetaldehyde ACALDH acetaldehyde dehydrogenase ACCOA acetyl coenzyme A ACET acetoin ACETDH acetoin dehydrogenase ACETEFF acetoin efflux ACK acetate kinase ACLAC acetolactate ACP acetyl phosphate ADH alcohol dehydrogenase ALD acetolactate decarboxylase ALS acetolactate synthase ATP adenosine triphosphate ATPase adenosine triphosphatease BPG 1,3-bisphosphoglycerate BUT 2,3-butanediol COA coenzyme A DHAP dihydroxyacetone phosphate ENO enolase ETOH ethanol F16P fructose-1,6-biphosphate F6P fructose-6-phosphate G6P glucose-6-phosphate GAP glyceraldehyde-3-phosphate GAPDH glyceraldehyde 3-phosphate dehydrogenase GLC glucose GLCT non-enzymic glucose transfer GLK glucokinase k rate constant K Michaelis–Menten constant Keq equilibrium constant Ki inhibition constant Km affinity constant LAC lactate N Hill coefficient NADH nicotinamide adenine dinucleotide NEALC non-enzymic acetolactate decarboxylation NOX NADH oxidase O oxygen P inorganic phosphate P2G 2-phosphoglycerate P3G 3-phosphoglycerate PTA phosphotransacetylase PDH pyruvate dehydrogenase PEP phospho-enol-pyruvate PFK phosphofructokinase PGI phosphoglucoisomerase PGK 3-phosphoglycerate kinase PGM phosphoglycerate mutase PPT phosphotransferase TIM triosephosphate isomerase V maximum reaction rate
655
In metabolic control analysis, flux control coefficients quantify the importance of an enzyme for the magnitude of a flux caused by a 1% modulation of the enzyme activity [4]. By the result from comparing flux control coefficients of enzymes in lactate production network, key steps, which can have significant effects on lactate production could be determined. However, flux control coefficient points at the effect of enzyme on flux with a very small change in any enzyme activity. In this point, it cannot deal with the more relevant larger changes, which have a practical matter of concern and interest in bioengineering. To supplement this disadvantage, we used in silico experiments, which use modulation of enzyme activity in an integrated mathematical model by varying kinetic parameters of enzyme reactions, and we illustrated the expected effects of enzymes on the pyruvate branch from this method.
2. Methods We gathered information about kinetic modeling from databases and literature [5,6]. 2.1. Assumption To construct a stoichiometric network model, we assumed that L. lactis live in an aerobic condition. Therefore, we excluded formate secretion from the network. Almost all gathered kinetic models and data were assumed to be at ambient temperature. pH also has significant effects on the whole metabolic system, but we considered the effect of pH only on NADH + NAD moiety conservation [7]. TCA cycle (tricarboxylic acid cycle) was not considered in this model because the exponential growth was assumed for more secretion of byproducts. AMP was not considered because gathered information did not include this metabolite. Thus, moiety conservation about Gibbs free energy was ATP + ADP = 10 mM [7]. 2.2. Simulation environment We used the biochemical simulator, GEPASI. It has been built and maintained by Pedro M. since 1993 and cited by many researchers [8,9]. GEPASI uses the damped Newton method in derivative calculation. In order to obtain results, Newton limit, which expresses the number of iterations that the Newton method executes, sets to 50. In order to solve ordinary differential equation (ODE), it uses Livermore Solver of Ordinary Differential Equation (LSODE), which solves systems dy/dt = f with a full or banded Jacobian when the problem is stiff, but it automatically selects between non-stiff (Adams) and stiff (BDF, backward differentiation formula) methods. LSODE adopts the non-stiff method initially, and dynamically monitors data in order to decide which method to use. For adjustable parameter for LSODE, Adams order, this determines the maximum order that the Adams method
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is allowed to take, sets to 12. And BDF order, which determine the maximum order that the BDF method is allowed to take, sets to 12. In this experiment, we adopted Newton and integration simultaneously in a strategy for steady-state solution [10].
this method, we have observed their effects on the pyruvate branch indirectly.
2.3. Analysis method
We have constructed a kinetic model in L. lactis describing glycolysis and fermentation part as shown in Figs. 1 and 2, Tables 1 and 2 [5,11–13]. The model prediction of the flux distribution in the wild type strain was shown Fig. 2. The model described an essentially heterofermentation. Most products from fermentation were lactate and acetate, and other metabolites production such as ethanol, acetoin, and butanol production had a
We have examined flux control coefficients in a lactate producing network. Through this comparison, we chose some enzymes, which make possibly significant effects on the lactate production rate. Because GEPASI does not use enzyme activity term, we used varying kinetic parameter, Vmax which belong to reaction related to these enzymes, instead. Using
3. Results and discussion
Fig. 1. Constructed metabolic network of Lactococcus lactis: 22 enzymes and 26 metabolites, flux are expressed by arrows and big sized bold words mean metabolites and small sized word means enzymes.
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Table 1 Collection of rate equation from proposed metabolic network of Lactoco-ccuslactis Reaction name
Enzyme kinetics
GLCT
V (S − (P/Keq )) S + Kms (1 + (p/KmP ))
GLK
V · GLCi · PEP KGLC KPEP (1 + (GLCi /KGLC ) + (G6P/KG6P ))(1 + (PEP/KPEP ) + (PYR/KPYR ))
PGI
V (G6P − F6P/Keq ) KG6P + G6P + (KG6P F6P/KF6P ) N
PFK
PEP V (F6P/KF6P )N ATP(1 − (PEPNPEP /(KPEP + PEPNPEP )))
KATP (1 + (ATP/KATP ) + (ADP/KADP ))(1 + (F6P/KF6P )N + (F16P/K16P ))
ALD
V · F16P(1 − (GAP · DHAP/Keq FBP)) KF16P (1 + (DHAP/KDHAP ) + (F16P/KF16P ) + (GAP/KGAP ) + ((DHAP · GAP)/(KDHAP KGAP )) + ((F16P · GAP)/(KF16P KiGAP ))
GAPDH
V (GAP · NAD − (BPG · NADH/Keq )) KGAP KNAD (1 + (GAP/KGAP ) + (BPG/KBPG ))(1 + (NAD/KNAD ) + (NADH/KNADH ))
PGK
V · BPG · ADP(1 − (P3G · ATP)/(Keq ADP · BPG)) KADP KDPG (1 + (ATP/KATP ) + (ADP/KADP ))(1 + (BPG/KBPG ) + (P3G/KP3G ))
PGM
V · P3G(1 − (P2G/Keq P3G)) KP3G (1 + (P2G/KP2G ) + (P3G/KP3G ))
ENO
V · P2G(1 − (PEP/Keq P2G)) KP2Gs (1 + (P2G/KP2G ) + (PEP/KPEP ))
PYK
ATPase
V (PEP/K · PEP)N ADP(1 − (PYR · ATP/Keq ADP · PEP)) KADP (1 + (ATP/KATP ) + (ADP/KADP ))(1 + (PEP/KPEP )N + (PYR/KPYR )) V (ATP/ADP)N + (ATP/ADP)N
N KATP
TIM
V · DHAP(1 − (GAP/Keq DHAP)) KDHAP (1 + (DHAP/KDHAP ) + (GAP/KGAP ))
LDH
V (1/KPYR KNADH )(PYR · NADH − (LAC · NAD/Keq )) (1 + (PYR/KPYR ) + (LAC/KLAC ))(1 + (NADH/KNADH ) + (NAD/KNAD ))
PDH
V (PYR/KPYR )(NAD/KNAD )(1/(1 + (Ki NADH/NAD)))(COA/KCOA ) (1 + (PYR/KPYR ))(1 + (NAD/KNAD ) + (NADH/KNADH ))(1 + (COA/KCOA ) + (ACCOA/KACCOA ))
PTA
V (1/Ki Km )(ACCOA · P − ACP · COA/Keq ) 1 + (ACCOA/Ki ) + (P/Ki ) + (ACP/Ki ) + (COA/Ki ) + ((ACCOA · P/Ki Km ) + (ACP · COA/Km Ki ))
ACK
V (1/(KADP KACP ))(ACP · ADP − AC(ATP/Keq )) (1 + (ACP/KACP ) + (AC/KAC ))(1 + (ADP/KADP ) + (ATP/KATP ))
ACALDH
V (1/KACCOA KNADH )(ACCOA · NADH − COA · NAD · ACAL/Keq ) (1 + (NAD/KNAD ) + (NADH/KNADH ))(1 + (ACCOA/KACCOA ) + (COA/KCOA ) + (ACAL/KACAL ) + (ACAL · COA/KACAL KCOA ))
ADH
V (1/KADP kACP )(ACAL · NADH − (ETOH · NAD/Keq )) (1 + (NAD/KNAD ) + (NADH/KNADH ))(1 + (ACAL/KACAL ) + (ETOH/KETOH ))
ALS
V (PYR/KPYR )(1 − ACLAC/PYR · Keq )((PYR/KPYR + ACLAC/KACLAC )N−1 ) (1 + PYR/KPYR + ACLAC/KACLAC )N
ALDC
V (ACLAC/KACLAC ) (1 + (ACLAC/KACLAC ) + (ACET/KACET ))
ACETDH
V · (1/(KACET KNADH ))(ACET · NADH − (BUT · NAD/Keq )) (1 + (ACET/KACET ) + (BUT/KBUT )(1 + (NADH/KNADH ) + (NAD/KNAD ))
NOX
V (NADH · O/KNADH Ko ) (1 + NAD/KNADH + NAD/KNAD )(1 + O/Ko )
NEALC
k · ACLAC
ACETEFF
V (ACET/KACET ) 1 + ACET/KACET
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negligible flux rate. Relatively large flux in ATP and NADH consumptions (which involve ATPase and NOX) was due to a large flux around the pyruvate branch. For ATP from glycolysis and fermentation network, generation of ATP was mostly done in PGK, PYK, ACK, and consumption of ATP was almost done in PFK. It means that J(ATPase) = 2.81 × 10−3 mM/min was nearly as the same as the sum of J(PGK) = 1.97 × 10−3 mM/min, J(PYK) = 0.846 × 10−3 mM/min, J(ACK) = 0.938 × 10−3 mM/min and J(PFK) = −9.38 × 10−3 mM/min. And for NADH from the network, generation of NADH was done in GADPH, LDH and PDH. It means that J(NOX) = 3.93 × 10−3 mM/min was nearly as the same as the sum of J(GAPDH) = 1.97 × 10−3 mM/min, J(LDH) = 1.12 × 10−3 mM/min and J(PDH) = 0.846 × 10−3 mM/min. From this result, we could intuitively infer that ATPase and NOX
seem to have a significant effect on lactate production. From network topology, we can also assume that LDH and PDH might control the pyruvate branch. From the information above, we can intuitively determine that the pyruvate branch is controlled by major four enzymes, LDH, PDH, ATPase, and NOX. A more systematic approach can be done by metabolic control analysis and the results are shown in Table 3. As mentioned above, flux control coefficients of LDH can be used for determining the effect of other enzymes. From this analysis, we noticed that GLK, PYK, PDH, LDH, ATPase, and NOX are candidates for key enzymes. Compared with the intuitive method, GLK and PYK seem to be new important enzymes, which have significant effects on lactate production. This means that total carbon influx to the pyruvate branch could be an important factor and could be
Fig. 2. Calculated flux in proposed metabolic network by GEPASI software through flux distribution analysis: the flux here is net flux which is vector sum of forward and backward flux and only 3 digit significant figure are considered.
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Fig. 3. Graphical representation of pyruvate branch between wild-type (Vmax (PDH) = 60 mM/min) and PDH knock-out (Vmax (PDH) = 0 mM/min): as the activity of PDH decrease, flux of lactate production increase.
Fig. 4. The plot of branch split ratio of pyruvate branch1 by changing Vmax of each enzyme: the target enzymes are (a) PDH, (b) PYK, (c) GLK, (d) LDH, (e) APTase, (f) NOX. Because of stability problem, which did not reach steady state, all range of Vmax are not plotted.
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Table 2 Collection of enzyme kinetic parameter from literature and BRENDA database: each parameter is used by rate equation which are composing proposed metabolic network of Lactococcus lactis in Table 1 Reaction name GLCT
Kinetic parameter Kms Kmp Vf Keq
Value
Reference/derivation
1.1918 1.1918 70 0.51079
http://www.bio.vu.nl/ www.bio.vu.nl www.bio.vu.nl www.bio.vu.nl
GLK
V KGLC KPEP KG6P KPYR
126 0.015 0.3 500 0.3
Obtained by fitting
V Keq KG6P KF6P
160 0.13 0.8 0.15
V KF6P N NPEP KF16P KATP KADP
227 0.25 2.9 2 5.8 0.18 0.3
§
V Keq KF116P KDHAP KGAP Ki,GAP
1100 0.056 0.17 0.13 0.03 0.23
§
V Keq KGAP KNAD KBPG KNADH
4984 0.00007 0.25 0.2 0.05 0.067
§
V Keq KADP KBPG KATP KP3G
1306.5 3200 0.53 0.3 0.003 0.2
Obtained by fitting
V Keq KP3G , KP2G
1340 1.2 0.1
§
V Keq KP2G KPEP
1600 4.6 0.04 0.5
§
V KPEP N Keq KADP KATP KPYR
2030 0.17 1.3 6500 1 10 21
§
V KATP N
30 6.196 2.58
V Keq KDHAP KG3P
17500 0.045 2.8 0.3
PGI
PFK
ALD
GAPDH
PGK
PGM
ENO
PYK
ATPase
TIM
Table 2 (Continued ) Reaction name
Kinetic parameter
Value
Reference/derivation
LDH
V KPYR KNADH Keq KLAC KNAD
5118 1.5 0.08 21120.7 100 2.4
Hogenholtz and Starrenburg (1992)
V KPYR KNAD Ki KCOA KNADH KACCOA
259 1 0.4 46.4 0.014 0.1 0.008
V Ki,ACCOA KmP Keq Ki,p Ki,ACP
42 0.2 2.6 0.0281 2.6 0.2
Abbe et al. (1982)
V KACP KADP Keq KAC KATP
2700 0.16 0.5 174.2 7 0.08
S. mutans; Abbe et al. (1982)
V KACCOA KNADH Keq KNAD KCOA
97 0.007 0.025 1 0.08 0.008
S. mutans; Abbe et al. (1982)
V KACAL KNADH Keq KNAD KETOH
162 0.03 0.05 12354.9 0.08 1
Cachon and Divies (1993)
ALS
V Keq PPYR KACLAC N
600 900,000 50 100 2.4
Snoep et al. (1992a)
ALDC
V KACLAC KACET
106 10 100
Swindell et al. (1996) Monnet et al. (1994a)
ACETDH
V KACET KNADH Ki KBUT KNAD
105 0.06 0.041 1400 2.6 0.16
V KNADH Ko KNAD
118 0.041 0.01 1
PDH
§ § § § §
Obtained by fitting §
PTA
§
§ § § §
ACK
§ §
§ § §
ACALDH
§ §
§ § §
ADH
§ §
§ § § § §
§ §
§ § §
§
Obtained by fitting § § §
NOX
§ § §
Obtained by fitting § § § §
NEALC ACETEFF
K V KACET § mark indicated that that ac.za.
Thauer et al. (1977) Crow and Pritchard (1977)
Snoep et al. (1992a) Snoep et al. (1992b) Estimated from Snoep et al. (1993)
Azotobacter; Bresters et al. (1975)
Thauer et al. (1997)
E.coli; Fox and Roseman (1986)
Thauer et al. (1997)
Thauer et al. (1977) Zymomonas; Wills et al. (1981)
Snoep et al. (1992a)
Gibson et al. (1991) Strecker and Haray (1954) Enterobacter; Carballo et al. (1991) S. faecalis; Schmidt et al. (1986)
0.0003 Monnet et al. (1994b) 200 5 parameter is excerpted from www.jjj.biochem.
J.W. Nam et al. / Enzyme and Microbial Technology 35 (2004) 654–662
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Table 3 Calculated flux control coefficient value of flux of LDH for each enzyme which is composing proposed metabolic network of Lactococcus lactis by metabolic control analysis. Flux control coefficient is defined as C(J(fluxi ), enzymek ), and fluxi is ith flux, enzymek is kth enzyme, respectively at steady state condition Flux control coefficient
Value
Flux control coefficient
Value
C(J(LDH), GLCT) C(J(LDH), GLK) C(J(LDH), PGI) C(J(LDH), PFK) C(J(LDH), ALD) C(J(LDH), GAPDH) C(J(LDH), PGK) C(J(LDH), PGM) C(J(LDH), ENO) C(J(LDH), PYK) C(J(LDH), ATPase) C(J(LDH), TIM)
3.90E−06 4.86E+00 4.12E−10 6.90E−07 −3.44E−10 1.02E−10 5.38E−11 1.38E−13 8.50E−14 −3.74E+00 −1.22E−01 1.44E−11
C(J(LDH),LDH) C(J(LDH),PDH) C(J(LDH),PTA) C(J(LDH),ACK) C(J(LDH),ACALDH) C(J(LDH),ADH) C(J(LDH),ALS) C(J(LDH),ALDC) C(J(LDH),ACETDH) C(J(LDH),NOX) C(J(LDH),NEALC) C(J(LDH),ACETEFF)
4.10E−01 −4.11E−01 −1.14E−06 −2.80E−06 1.33E−08 1.59E−04 −9.11E−07 3.35E−12 3.33E−13 −6.94E−05 9.49E−17 −3.42E−13
used to determine pyruvate branch split ratio. Even though coefficients of GLK and PYK were relatively greater than other coefficients, the results could be different with other simulation conditions, for example, due to different parameter values. To prove this situation, we have examined the effects of these enzymes on lactate production through in silico simulation. In GEPASI simulation, there were some parameters directly related to enzyme activity, as mentioned above. So varying the value of the parameter Vmax was used instead of varying enzyme activity. Variation of Vmax,PDH , which has the same effect of variation of PDH activity, has an important meaning because it can directly modify the branch split ratio. Fig. 3 shows its effect on the pyruvate branch point. For simulation Vmax,PDH in wild type L. lactis was 60 and the one in PDH knock out mutant was 0. Although metabolic control analysis coefficient of PDH was relatively smaller than other enzymes, its effect on the pyruvate branch for GLK and PYK was greater in the longer range. We have examined the spilt ratio of branch point, J(LDH)/J(Branch input), in various conditions as shown in Fig. 4. First, varying Vmax,PDH showed a non-linear curve, which means that the effect of enzyme PDH was not always as the same as in the wild type and its effect was more significant at lower activity (Fig. 4a). Also we examined the effect of PYK and GLK, which have large flux control coefficient values, in the same way (Fig. 4b and c). But there were some stability problems in metabolic network, which did not reach a steady state, when Vmax,PYK was lower than 900 mM/min and Vmax,GLK was lower than 80 mM/min. So we considered these values as lower bounds and examined the effect on the pyruvate branch. Varying conditions of the activity of LDH, ATPase, and NOX were also examined. In the LDH case, we have obtained reasonable results of larger Vmax,LDH , which means higher spilt ratio. In case of ATPase and NOX, we fixed the range of spilt ratio of branch point from 0.4 to 1, and compared the result of the effect. These two enzymes had only small effects on spilt ratio of branch point when the activities were relatively large.
However, NOX showed an interesting result when NOX had lower activity. The split ratio of branch point was abruptly increased when the activity of NOX decreased toward 0 as shown in Fig. 4f. In this situation, the value of J(Branch input) and J(PDH) decreased, J(ALS) and J(LDH) increased. It seems that the states of lower NAD concentration favor lactate production but this assumption could not be solved by simulation only, and it must be supported by in vitro or in vivo experiments. Even though flux control coefficients shows that PYK and GLK seemed to be most significant enzymes in lactate production, Fig. 4 shows that PDH, LDH, and NOX were the key enzymes, which had an influence on lactate production.
4. Conclusion In this research, we have suggested the mathematical model of L. lactis based on the analysis of metabolism and network. From the flux distribution analysis, ATPase, NOX, LDH, and PDH seem to have significant effects on the lactate pyruvate branch. But this was only an intuitive approach, so in order to verify the key enzymes systematically, we performed the metabolic control analysis. The flux control coefficients of LDH showed that input into the pyruvate branch could be another important factor because flux control coefficient values of GLK and PYK were higher than others. But metabolic control analysis was effective in a narrow range of enzyme activity so we performed in silico experiments by GEPASI software to examine the effect of enzyme activity to the pyruvate branch and lactate production. In this experiment, we have found that PDH, LDH, and NOX seemed to be the primary key enzymes of lactate production. In summary, many enzymes consist of metabolic network of L. lactis but their effects on lactate production were different from each other. So by performing various in silico analyses, we could narrow down our concern to key enzymes before doing wet experiments. We also found that the branch input flux could affect the lactate production from the metabolic control analysis results of the proposed network.
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This observation needs to be studied deeply by following wet experiments or in silico experiments. To get more detailed results, we are trying to prepare wet experiments. Acknowledgements This work was supported by the Korean Systems Biology Research Grant (M10309020000-03B5002-00000) from the Ministry of Science and Technology. References [1] Rafel AA. Poly(lactic acid) flims as food packaging materials. School of packaging, MSU, East lansing, USA; 2002. p. 3–4. [2] Acerenza L, Sauro HM, Kacser H. Control analysis of timedependent metabolic systems. J Theoret Biol 1989;137:423–44. [3] Gregory NS. Metabolic engineering. A principles and methodologies. Academic Press; 1998. [4] Cornish-Bowden A. Metabolic control analysis in theory and practice. Adv Mol Cell Biol 1995;11:21–64.
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