Metabolic Flux Analysis of Lactic AcidFermentation : Effects of pH and Lactate ion Concentration

1. Metabolic Flux Analysis of Lactic AcidFermentation : Effects of pH and Lactate ion Concentration By K.V.Venkatesh Department Of Chemical Engineering, Indian Institute Of Technology, Bombay Paper Reviewed For Understanding the Metabolic Networks Analysis is “ Flux Analysis Of Underdetermined Metabolic Networks : The Quest For The Missing Constraints.” By Hendrik Bonarius, George Schmid And Johannes Tramper

2. Abstarct : A detailed metabolic flux analysis for lactic acid production by Streptococcus lactis has been carried out. A metabolic reaction set was constructed for the metabolism of S.lactis. Fluxes through these reactions were estimated by using accumulation rates of biomass, product and consumption rates of the substrate, which were obtained through experiments. The changes in the flux movement are shown for different pHs and initial lactate concentrations of the medium. The analysis indicated that pH only affected the uptake rates of lactose, whereas lactate ion concentration influenced the movement of the flux through the network.

3. Abbreviations FRUDP : Fructose diphosphate G3P : Glyceraldehyde 3 – Phosphate GAL6P : Galactose 6 – Phosphate GLC : Glucose GLC6P : Glucose 6 – Phosphate LAI : Lactic Acid LAC : Lactose LAC6P : Lactose 6 – Phosphate PEP : Phosphoenolpyruvate PGP : Diphosphoglycerate PG : Phosphoglycerate PK : Pyruvate Kinase PYR : Pyruvate.

4. Introduction Metabolites in microorganisms are produced by a series of reactions called as the metabolic pathways. Biotechnologists employ various methods to enhance the yields of metabolites that have practical significance. The main aim of the metabolic engineering is to optimize the metabolic network for maximizing the yields of necessary metabolites. It is important to know the control architecture of the metabolic reactions i.e. by observing fluxes in various branches of network at different conditions. Nodal analysis identifies various control points that need to be broken to channel the fluxes in a desired branch. In this paper flux analysis is carried out for the metabolic network of streptococcus lactis . S.Lactis is a homolactic organism and can convert lactose to lactic acid through glycolysis. It is known fact that lactic acid inhibits fermentation. Undissociated lactic acid alters the pH of the broth and inhibits the growth of the cells. The dissociated lactic acid ions ( lactate ) also inhibit fermentation and growth ceases beyond a lactate concentration of 80 – 100 g/lit. The flux analysis is carried out to give insight into these effects on the fermentation.

5. Theory : The main of this work is to calculate fluxes in various branches of the reaction system. These fluxes are estimated by measuring only the accumulation rates of extracellular metabolites. The methodology relies solely on metabolite balances, biochemical constraints and pseudo steady state approximation for intracellular metabolites. Simple mass balances are set up for the extracellular metabolites. E.g. in a simple reaction set up such as A  B B  C B D The metabolite Balance gives :

6. Where the R is accumulation rate of the various metabolites and X(t) is the flux associated with the different reactions. Once the values of the accumulation rates are determined experimentally, the X(t) values can be generated by solving the above set of example equations. When there are more equations than unknown, then final equation is utilized to verify the flux estimates. If the unknowns are more than the equations , than for some metabolites pseudo steady state approximations have to be made to eliminate some fluxes. In such case some prior metabolic information about the network would be helpful in making choice. Here for every mole of lactose taken into the cell as lactose 6-phosphate, a mole of phosphoenolpyruvate ( PEP ) is converted to pyruvate. PEP is also converted to pyruvate by PK. The remainder are normal reactions from the glycolytic pathway. To account for the carbon balance to produce nitrogen related compounds (e.g. amino acid ), the amount of pyruvate accumulation inside the cell is an equivalent amount. Since the definition of the cell changes during active steady state glycolysis and during starvation, two cell states have been defined. Since lactic acid fermentation is anaerobic in nature, reactions other than that from glycolysis are not required.

7. The preliminary biochemistry set ( set of equations in algebraic form ) is now expressed mathematically by constructing a metabolite balance for each metabolite that occurs in the set. The resulting set of equations can be expressed in a matrix form : A.X(t) = RWhere A & R are the matrices denoting , the biochemistry and accumulation rates respectively. X( t) is the matrix containing the flux value for each branch. The matrix is solved using linear algebra for X ( t ). Constraints are imposed on the flux estimates such that te directionality of the irreversible reactions is not violated.

8. This can be done if the minimization of error is subject to the constraints, C. X (t) > b, Where C is a matrix that specifies those reactions whose fluxes must equal or exceed b, which is usually taken as the null vector for the irreversible reactions. The equations are solved by minimizing the sum of squared residuals. In the case of S.lactis, only lactose, lactic and biomass are measured and the rest of the metabolite concentrations are set to zero. As it is clear from the table , that there are 14 fluxes to be estimated for the metabolic network. And the balance of the ATP is used to minimize the error for the flux estimate.

9. Principle Of metabolic flux analysis :

10. Glossary : Metabolite or mass balance : An equation that describes the accumulation and all relevant incoming and outgoing fluxes of a metabolic pool. Stoichiometric Matrix : A matrix that contain information on the reaction stoichiometry of cellular metabolism. The rows and columns of the stoichiometric matrix are associated with the metabolite balances and the metabolic fluxes respectively. Linear Dependency : Metabolite balances are linear dependent if ( a linear combination of ) the solution planes are determined by the metabolite balances are parallel. Rank : The maximum no. of linear independent metabolite balances in a metabolic network is called the rank of the stoichiometric matrix. Rank Deficient : If the rank is smaller then the no. of metabolic fluxes ( the no. of rows of SM ) then the metabolic network is rank deficient.

11. Condition number : The condition no. of a stoichiometric matrix A (the ratio of the largest to smallest eigenvalue of A ) is a measure of the sensitivity of the equation AX = r Underdetermined Networks : Metabolic networks that are rank deficient are designated “ Underdetermined “ to indicate that there are insufficient linear independent metabolite balances to determine the intracellular metabolic fluxes. Observability : In this context, the extent to which intracellular metabolic fluxes can be determined by the measurement of the extracellular metabolic rates and the biomass composition. Directionality Constraint : The demand that a ( no. of ) fluxes is non-negative. Balanceable metabolite : A metabolite whose mass balance can be closed.

12. Consider one example to have clear idea of the flux balance technique : Metabolic flux balance tech. are based on relatively simple linear algebra. If the stoichiometry of the relevant intracellular reactions and the cellular compositions are known, and the uptake and secretion rates of the relevant metabolites ( ra, rb, rc ) in fig. ) have been measured, the reaction rates ( X1 & X2 ) can be determined using the appropriate mass balance equations. A reaction network is shown for which one unique solution for the variables X1 & X2 can be estimated by least square analysis of mass balances A, B & C. The least squares method , which is used here because there are more mass balances than unknowns ( fluxes ), is calculated by inverting stoichiometric matrix A

13. For the stoichiometry and measured metabolic rates given in the fig. , this equation reads This shows that intracellular fluxes can be quantified by measuring only the uptake and secretion rates of the relevant metabolites.

14. Problems in flux balance are : The estimated flux vector, which is calculated by least square method , may be sensitive to slight changes in the measured extracellular rates of relevant metabolites ( rA, rB, rC ) . This sensitivity to error propagation can be checked by the condition number of the system, which depend on the stoichiometry of the reactions of metabolites network. A large condition no. ( > 100 ) indicates that the estimated flux distribution is sensitive to the measurement error.

15. Mass Balances of the cofactors or co-metabolites : When a co-metabolite is produced or consumed in cyclic pathway, the addition of its mass balance may yield a unique solution. It is seen that by addition of the ATP balance to a metabolite network , the rank of the stoichiometric matrix increases by one unit, because ATP balance is linear independent of the other mass balances. Moreover, relatively small changes in such estimates will have large effect on the calculated flux distribution. The mass balance of reducing equivalents, e.g. NADH and NADPH are often used to determine the split ratio of metabolic fluxes at branch points. Here also very small changes in NADH or NADPH balance can affect the mass balance estimates very highly. Irreversibility Of Reactions : Some reactions in the metabolic networks are considered irreversible. This additional information allows one to set lower boundaries to particular reactions. Fluxes determined from mass balance supplemented with data from isotropic – tracer methods, combined with fluxes estimated from mass balances supplemented with diff. Theoretical constraints, may lead to fundamental understanding of the validity of the assumptions made previously.

16. Fermentation condition Lactose Lactic acid Biomass PH 5.6 L =0 3.7 x 10-3 1.39 x 10-2 9.94 x 10-4 PH 4.5 , L = 0 5.9 x 10-4 2.1 x 10-3 2.4 x 10-4 PH 5.6 , L = 75 2.3 x 10-4 3.25 x 10-4 4.5 x 10-5 Results & Discussions : The flux distribution for lactic acid fermentation by S.lactis was determined by metabolic flux analysis. The accumulation rates obtained from experiment for lactose uptake, lactic acid formation are listed in table below Table : Accumulation rates ( in gmol / lit. Hr )used for metabolite balance

17. Metabolic networks at different conditions :

18. Fig. 2 Metabolic flux distribution for pH 4.5 at the end of 15hrs of fermentation. Dashed line indicates the positive effect of FRUDP on PK. The flux distribution is normalized with respect to the first reaction.

19. Fig. 3 Metabolic flux distribution for pH 5.6 at the end of 15hrs. Of fermentation in the presence of 75 g/lit. of lactate ions. Dotted lines indicates the negative effect of Pi on PK. The flux distribution is normalized with respect to the reaction.

20. Conclusion : The metabolic balance technique is a useful method to obtain information about flux movement inside the cell. This technique was successfully applied to lactic acid fermentation to study the effect of pH and lactate ions. The metabolic balance technique demonstrated that the pH just decreases the uptake rate of lactose, while lactate ion effect the flux movement inside the cells. The analysis predicted accumulation of inorganic Pi and PEP in the presence of lactate ions. It has been reported in the literature that Pi inhibit the formation of pyruvate and that the positive effector FRUDP was also absent in the presence of lactate, which has been shown by flux analysis. Thus the cells were in a starved state in the presence of lactate ions. It is demonstrated that such techniques can give useful information regarding the state of the cells in different extracellular conditions.