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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
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.
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.
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.
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 :
Ra 
A
  X 1 (t )
t
Rb 
B
 X 1 (t )  X 2 (t )  X 3 (t )
t
Rc 
C
 X 2 (t )
t
Rd 
D
 X 3 (t )
t
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.
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) = R
Where 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.
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.
Principle Of metabolic flux analysis :
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.
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.
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
Ax  r  A Ax  A r  x  ( A A) 1 A r
For the stoichiometry and measured metabolic rates given in the fig. ,
this equation reads
 1  1
 rA 
 3
 1 0 . X 1    rB    X 1   1  5  1. 1 1 0. 1   1
 X  9   1 2    1 0 2    2

 X   


 4   
 2
 0 2   2  rC 
 
This shows that intracellular fluxes can be quantified by
measuring only the uptake and secretion rates of the relevant
metabolites.
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.
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.
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
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
Metabolic networks at different conditions :
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.
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.
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.