is an effort to manipulate the metabolism of an organism worthy and reasonable , 	 knowing 
 that this cellular process has been continuously modified and refined through 
 evolution and natural selection for adapting , in the most convenient manner , to 
 the ongoing environmental conditions ?
the 
 answer to this question seems obvious when three broad areas of research and 
 development are identified in which manipulation of metabolic pathways is 
 relevant : ( a ) drug design to treat diseases , ( b ) genetic engineering of 
 organisms of biotechnological interest , and ( c ) genetic syndromes therapy .
historically , drug design was 
 the first area in which modification of metabolism was tried : the primary goal 
 of drug administration is the inhibition of essential metabolic pathways , for 
 example , in a parasite or a tumor cell .
thus , any metabolic pathway can be a potential 
 therapeutic target . in the absence of a solid 
 theoretical background that may build a strategy for the rational design of 
 drugs ,
the pharmaceutical industry has applied the knowledge of inorganic and 
 organic chemistry for the arbitrary and rather randomized modification of 
 metabolic intermediaries by replacing hydrogen atoms in a model molecule with 
 any other element or compound .
the era of rational drug 
 design probably started in the 50s when hans krebs proposed that , after having 
 an exact description of a metabolic pathway , the  pacemaker  enzyme or 
  rate - limiting step  had to be identified .
this approach certainly decreased the amount 
 of intermediaries to be chemically modified , focusing only on the substrates , 
 products , and allosteric effectors of the  rate - limiting step ,  instead of dispersing 
 efforts on all the metabolic pathway intermediates .
the experimental approaches used in the 
 identification of the pacemaker , key enzymes ,  bottlenecks .
 limiting steps , or 
 regulatory enzymes [ 1 , 2 ] were 
 inspection of the metabolic pathway architecture : due to cell 
  economy and for reaching the highest efficiency , pathway control must 
  reside in the enzymes localized at the beginning of a pathway or after a 
  branch ( teleological approach);determination of nonequilibrium reactions : those reactions in which 
  the quotient between the mass action ratio (  ) and its equilibrium constant ( keq ) is low , /keq 1 ( thermodynamic 
  approach);identification of the steps with the lowest maximal rates ( vmax ) in cellular extracts : the key 
  enzyme of the pathway is the one that has the lowest rate ( kinetic 
  approach);enzymes with sigmoidal kinetics : steps that are susceptible to 
  alteration in their kinetic properties by compounds different from 
  substrates and products and which may coordinate the entire metabolism 
  ( nadh / nad ; nadph / nadp , atp / adp ; acetyl coa / coa ; ca / mg ; 
  high ph / low ph ) or at least two metabolic pathways ( citrate , pi , amp , 
  malonyl - coa);crossover theorem . comparing the intermediary concentrations 
  between a basal and an active steady - state pathway flux , the rate - limiting 
  step in the basal condition will be that for which its substrate 
  concentration diminishes and its product concentration increases when the 
  system changes from the basal to the active state or vice versa ( crossover 
  point on a histogram of each intermediary versus its normalized variation in concentration);the shape of the metabolic flux inhibition curve : a sigmoidal curve 
  on a plot of inhibitor concentration versus flux shows that the sensitive 
  step to the inhibitor exerts no control , that is , there is not proportionality between enzyme 
  activity inhibition and pathway flux inhibition because there is an 
   excess  of enzyme .
on the other 
  hand , a hyperbolic curve indicates that the enzyme susceptible to the 
  inhibitor controls the flux . 
 
inspection of the metabolic pathway architecture : due to cell 
  economy and for reaching the highest efficiency , pathway control must 
  reside in the enzymes localized at the beginning of a pathway or after a 
  branch ( teleological approach ) ; determination of nonequilibrium reactions : those reactions in which 
  the quotient between the mass action ratio (  ) and its equilibrium constant ( keq ) is low , /keq 1 ( thermodynamic 
  approach ) ; identification of the steps with the lowest maximal rates ( vmax ) in cellular extracts : the key 
  enzyme of the pathway is the one that has the lowest rate ( kinetic 
  approach ) ; enzymes with sigmoidal kinetics : steps that are susceptible to 
  alteration in their kinetic properties by compounds different from 
  substrates and products and which may coordinate the entire metabolism 
  ( nadh / nad ; nadph / nadp , atp / adp ; acetyl coa / coa ; ca / mg ; 
  high ph / low ph ) or at least two metabolic pathways ( citrate , pi , amp , 
  malonyl - coa ) ; crossover theorem . comparing the intermediary concentrations 
  between a basal and an active steady - state pathway flux
, the rate - limiting 
  step in the basal condition will be that for which its substrate 
  concentration diminishes and its product concentration increases when the 
  system changes from the basal to the active state or vice versa ( crossover 
  point on a histogram of each intermediary versus its normalized variation in concentration ) ; the shape of the metabolic flux inhibition curve : a sigmoidal curve 
  on a plot of inhibitor concentration versus flux shows that the sensitive 
  step to the inhibitor exerts no control , that is , there is not proportionality between enzyme 
  activity inhibition and pathway flux inhibition because there is an 
   excess  of enzyme . on the other 
  hand ,
a hyperbolic curve indicates that the enzyme susceptible to the 
  inhibitor controls the flux .
once a site in a metabolic 
 pathway has been identified with at least one of the criteria described above 
 as  the rate - limiting step , 
researchers have frequently concluded that such 
 enzyme or transporter is the only limiting step of the metabolic flux and 
 extend this conclusion to all cell types and to all conditions .
for example , inspection of the glycolytic pathway ( teleological approach ) suggests that 
 hexokinase ( hk ) and phosphofructokinase-1 ( pfk-1 ) ( which are at the beginning 
 and after a branch of the pathway ) are the key steps of glycolysis .
however , all studies on glycolysis in the 60s , 
 70s , and 80s were performed by taking into account only the intracellular 
 reactions from hk to ldh ( i.e. , without including the glucose transport 
 reaction through the plasma membrane ) and by considering glycolysis as a linear 
 pathway without branches . to this
regard , 
 it is recalled that the glucose transporter ( glut ) includes a family of 
 proteins and genes that are susceptible of regulation .
thus , if the extracellular glucose is 
 considered as the initial glycolytic substrate , then another potential key step 
 would be glut .
hence , if all the 
 branches of the pathway are considered ( figure 1 ) , then according to the 
 teleological approach there will be additional potential rate - limiting sites .
application of the thermodynamic and kinetic approaches to glycolysis reveals that hk , 
 pfk-1 , and pyruvate kinase ( pyk ) are the rate - limiting steps because in the 
 living cell they catalyze reactions that are far away from equilibrium ( /keq = 1010 ) , and they are also the slowest 
 enzymes in the pathway by at least one order of magnitude ( they have the lowest vmax values ) .
the use of the enzyme cooperativity approach has established that the regulatory 
 steps of glycolysis are ( i ) pfk-1 and pyk because they are allosteric enzymes 
 and ( ii ) hk because it is inhibited by its products ( g6p and adp , or amp as an adp - analogue ) . 
  the application of the crossover theorem 
 ( approach no .
v ) to glycolysis has shown a consistent variation in the pfk-1 substrate 
 ( f6p ) and product ( f1,6bp ) .
up to now , 
 there are few studies on control of glycolysis using the shape of the inhibitor 
 titrating curve ( approach no .
vi ) , due to the lack of specific inhibitors for 
 any of the three presumed key steps .
an exception is iodoacetate which is indeed 
 a potent inhibitor of gapdh , but also of other highly reactive 
 cysteine - containing enzymes [ 35 ] . by 
 using iodoacetate as specific inhibitor ,
both gapdh activity and flux showed 
 identical titration curves , leading to the conclusion that gapdh was the 
 rate - limiting step of glycolysis in streptococcus lactis and s. cremoris   ( see , 
 however , section 3.2 ; glycolysis in lactobacteria below ) . all together , these results constitute 
 the main reason why many intermediary metabolism researchers , including the 
 authors of biochemistry text books , have proposed hk , pfk-1 , and pyk as the 
 rate - limiting steps of glycolysis . in 
 consequence , to vary the glycolytic flux , one of these enzymes has to be 
 modified .
although the above - described experimental approaches are qualitative , full control has 
 been automatically assigned to the  key  steps because the concept of the rate - limiting 
 step assumes that there is only one single enzyme controlling the metabolic 
 pathway flux ( and the concentration of the final product of the pathway ) and , 
 in consequence , assigns values of zero to the control exerted by the other 
 enzymes and transporters .
however , as analyzed for glycolysis , researchers have commonly  identified  more than one 
 limiting step . in the case of oxidative 
 phosphorylation ( oxphos ) , in the 70s and 80s some researchers considered 
 cytochrome c oxidase as the rate - limiting step , whereas others preferred the 
 atp / adp translocator or the krebs cycle
ca - sensitive 
 dehydrogenases ( for a review , see ) . rephrasing the initial question , which could be the aim of manipulating a metabolic 
 pathway such as glycolysis , knowing its universal distribution in the living 
 organisms ? from a clinical standpoint , the inhibition of glycolysis is relevant for the treatment of human parasitic 
 or pathological diseases such as cancer .
the glycolytic reactions are almost identical in all organisms ; in 
 addition , the enzymes catalyzing these reactions are highly conserved throughout 
 the evolutionary scale ( their amino acid sequences are highly similar ) . in mammals ,
the genes of the 12 glycolytic 
 enzymes are scattered throughout the genome , generally in different chromosomes , 
 whereas in bacteria many of the glycolytic enzymes are clustered in operons . 
  however , there are organisms ( like some 
 human parasites ) that contain enzymes with remarkable differences in their 
 biochemical properties ( substrate selectivity , catalytic capacity , stability , 
 and oligomeric structure ) , or in genetic expression regulation in comparison to 
 the human enzymes , which could be considered as drug targets . furthermore , some glycolytic products are of commercial interest such as ethanol for wine , 
 beer , and other alcoholic beverages ; co2 for bread manufacturing ; and 
 lactic acid and other organic acids for cheese production .
thus , from a biotechnological standpoint , it 
 is convenient to accelerate the pathway flux to diminish the processing time and 
 it is also desirable to increase the concentration of the metabolite to obtain 
 robust commercial products . here
, it is important to emphasize that the metabolic pathways are designed to attain 
 changes in flux with minimal disturbances in the intermediary concentrations . for example
, the glycolytic flux in skeletal 
 muscle can increase from rest to an active state by 100 fold , without large 
 changes in metabolites .
then , it is physiologically more common to change a metabolic flux and the production of 
 the final metabolite in the pathway than varying the intermediary concentrations 
 .
however , we will see that , by 
 using a suitable approach of metabolic control analysis , it is possible to 
 design strategies to manipulate not only fluxes but also metabolic intermediary 
 concentrations .
when the yeast saccharomyces 
 cerevisiae is exposed to high glucose ( > 2% ; 0.11 m ) , the genes of all 
 glycolytic enzymes are induced ( pdc and eno increase their expression by 20 fold ; 
 pgk , pyk , and adh , 310 times ; and the 
 others , 2 fold in average ) [ 811 ]
. however , 
 when the methodological development of genetic engineering allowed modulating the 
 expression of enzymes within cells , researchers turned to the rate - limiting 
 step concept to manipulate a metabolic pathway to increase flux and/or its 
 intermediates , hypothesizing that the overexpression of only one , or of a few 
 key glycolytic genes , should increase the flux .
historically , heinisch   in germany was the first author to 
 obtain a 3.5 fold overexpression of pfk-1 in   s. cerevisiae , but 
 surprisingly he observed that the rate of ethanol production was not modified .
subsequent experiments for increasing the 
 ethanol production rate by overexpressing either each of the presumed limiting 
 steps , or in combination with other glycolytic enzymes ( table 1 ) , have been 
 unsuccessful and , even in some cases , a slight decrease in flux has been 
 attained .
for instance , the simultaneous 
 overexpression of seven enzymes of the final section of glycolysis induced only 
 a 21% increase in ethanol production after 2 hours of culture ( table 1 ) .
this was accompanied by a 1020% decrease in pfk-1 
 expression , which might have attenuated the flux increase . in yeasts , hk is not product inhibited 
 by g6p or adp ; instead , it is strongly feedback inhibited by trehalose-6-phosphate 
 ( tre6p ) .
deletion 
 of the tre6p synthase gene does not 
 bring about an increased ethanol production , but it rather induces a defective cellular 
 growth on glucose and fructose and a lowered ethanol production , as a result of 
 a highly active hk that leads to hyperaccumulation of hexose phosphate 
 metabolites ( particularly f1,6bp ) and fast depletion of atp , pi , and downstream 
 metabolites .
the explanation for this event is that , in the tre6p synthase 
 mutants , the rate of glucose phosphorylation exceeds the rate of glycolytic atp 
 synthesis ( named  turbo effect  ) .
heterologous expression of a tre6p - insensitive hk does not recover 
 completely the wild - type phenotype .
furthermore , deletion of the tre6p synthase gene in the 
 tre6p - insensitive hk strain did affect growth , suggesting other interactions 
 and functions of tre6p synthase in the control of sugar metabolism , at 
 least in schizosaccharomyces pombe .
davies and brindle   obtained a 5-fold overexpression of 
 pfk-1 in s. cerevisiae , but the increase in ethanol production was not attained 
 under anaerobic conditions .
there was a slight 
 increase in ethanol production in resting cells in aerobic conditions , under 
 which the mitochondrial metabolism contributes to the atp supply .
in all these works , it may be noted that 
 enzyme overexpression indeed affects the concentration of several intermediaries , 
 but this effect has not been further examined .
it is worth noting that the 
 experiments described in table 1 do not rigorously reproduce the physiological 
 situation , in which overexpression of all the enzymes should be carried out in 
 the proportions found in the organisms .
the 
 rationale behind this observation is that overexpression of only one  limiting  

step leads to a flux control redistribution , a condition at which other steps 
 now become rate limiting .
thus , the 
 concept of  rate - limiting step  offers no simple answer to the question of 
 increasing the yeast glycolytic flux , and it rather makes this problem to 
 appear as a difficult task to solve .
in contrast , it seems that all relevant controlling steps 
 have to be overexpressed , thus reproducing what natural 
 selection has already successfully accomplished .
in addition to s. cerevisiae , overexpression of glycolytic enzymes in other 
 organisms such as e. coli [ 15 , 16 ] , 
 lactobacteria , tomato , potato , and 
 hamster ovary cells   has been accomplished , although without increasing 
 flux ( table 1 ) .
it is somewhat surprising to note that in the glycolytic enzyme 
 overexpression experiments , the strong inhibitory effect of g6p ( or tre6p in s. cerevisiae ) , and citrate on hk and pfk-1 , respectively , have been neglected .
this 
 regulatory mechanism does not disappear in the cells overexpressing the enzymes 
 but , on the contrary , it is exacerbated .
then , what would be the aim of overexpressing hk , pfk-1 or any other 
 allosteric , or strongly product - inhibited enzyme if they will be more 
 inhibited ?
a successful experiment of increasing 
 the glycolytic flux was performed in primary cultures of rat hepatocytes .
the transformed 
 hepatocytes showed higher activity of 18.7- and 7.1-times for hk and gk , 
 respectively , at 3 mm glucose , and of 6.3- and 7.1-times at 20 mm glucose .
however , at 20 mm glucose , the flux to 
 lactate was not modified in hk - transformed cells , just like the experiments 
 described above ( table 1 ) .
in contrast , 
 with gk overexpression , a 3-fold increase in flux was achieved .
the mechanistic difference is the hk 
 inhibition by g6p ( 10 mm g6p inhibits hk activity by 90% ) , whereas gk is not product inhibited . 

the end products , lactate and h , are 
 expelled and acidify the external medium which contributes to cheese flavor and 
 texture and inhibits the growth of other bacteria .
similarly to yeast , the lack of carbon source 
 in lactobacteria promotes a metabolic change that leads to the production of 
 formic and acetic acids , ethanol , and , in a lower proportion , l - lactic acid , 
 altering the product quality .
thus , from a commercial point of view , it does 
 not seem important to know what controls the flux to lactate ( because its rate 
 of production is adequate ) , but what controls the branching flux . to understand the process , and to eventually inhibit the production of secondary acids , andersen et al .  
constructed ldh mutants , 
 using a synthetic promoter library for tuning the gene expression . in mutants 
 lacking this enzyme ,
most of the pyruvate was transformed into acetic and 
 formic acids ( figure 1 ) . in turn
, flux 
 to lactate was affected in mutants expressing only 10% or less of wild - type ldh 
 levels , which indicated that ldh exerts no control of the glycolytic flux in 
 wild - type bacteria . only with a normal content of this enzyme ( 100% ) ,
therefore , the flux to formic and acetic 
 acids is negatively controlled by ldh , and positively by pyk [ 17 , 25 ] . as in s. cerevisiae , overexpression of 
 pfk-1 , pyk , or gapdh in lactobacteria
did not increase the flux to l - lactic 
 acid [ 17 , 25 ] . similarly to e. coli glycolysis , glycolysis in l. lactis was controlled by the atp 
 demand when working below its maximum capacity [ 27 , 28 ] , whereas , under high - rate 
 conditions , the glucose and lactate transporters exerted the main flux control .
furthermore , this kind of observations indicates 
 that the flux control may reside outside the pathway [ 2729 ] , and it also supports the proposal 
 by hofmeyr and cornish - bowden   that the end - product demand ( which is 
 usually overlooked in studies of metabolism because these metabolites are 
 frequently not considered as part of the pathway ) might be essential in flux 
 control .
glutathione ( -glu - cys - gly ; gsh ) is the most abundant nonproteinaceous 
 thiol compound ( 110 mm ) 
 in almost all living cells .
gsh is 
 involved in the oxidative stress processing , xenobiotic detoxification , and , in 
 some plants and yeasts , in the inactivation of toxic heavy metals ( for a recent 
 revision see ) .
gsh is synthesized by two enzymes : -glutamylcysteine synthetase 
 ( -ecs ) and glutathione synthetase ( gs ) ( figure 2 ) , 
 which catalyze reactions with high - equilibrium constants ( keq > 1000 ) . under a low gsh demand ( unstressed 
 conditions )
, the producing block of enzymes has to receive information from the 
 last part of the pathway to ( i ) avoid the excessive and toxic accumulation of 
 the intermediary -ec and ( ii ) reach a stable steady state .
this information transfer is mediated by gsh , 
 which exerts strong competitive inhibition of -ecs   ( figure 2 ) .
gsh and cys also exert inhibition on the 
 atp - sulfurylase ( atps ) and on sulfate transporters ( figure 2 ) ( for a review , 
 see ) .
the feedback inhibition of -ecs has led several researchers to propose 
 that this enzyme is the rate - limiting step of gsh synthesis [ 3335 ] .
although there are no studies about the 
 pathway 's behavior under stressed conditions , which means under a high gsh 
 demand , the proposal that -ecs is the key enzyme has been automatically 
 extended to any environmental condition such as heavy metal exposure . by assuming that -ecs is the rate - limiting step , many research groups 
 have tried to increase , in plants and yeasts , the rate of synthesis and the 
 concentration of gsh and phytochelatins ( pcs ) with the aim of fortifying their 
 heavy metal resistance and storage capacity , mainly toward cd .
the development of organisms able to grow in 
 soils and water systems contaminated with heavy metals , which may have the 
 ability of accumulating toxic metal ions , is of biotechnological interest for 
 bioremediation strategies . with this goal in mind
, 
 researchers have then overexpressed -ecs and other pathway enzymes , including 
 phytochelatin synthase ( pcs ) ( table 2 ) .
some of these experiments have been 
 partially successful in increasing gsh levels , although this has been rather 
 marginal with no correlation between enzyme levels and gsh concentration .
unfortunately , these overexpression experiments 
 have not been accompanied by determinations of fluxes or other relevant metabolite 
 concentrations such as pcs or cys .
on 
 the other hand , the overexpression of pcs has surprisingly induced oxidative stress 
 and necrosis instead of increasing cd accumulation and resistance 
 .
this result suggests that , under high 
 gsh demand ( i.e. , for pcs synthesis and for direct heavy metal 
 sequestration by gsh ) , the gsh concentration does not suffice for maintaining 
 the other essential gsh functions such as oxidative stress management and 
 xenobiotic detoxification .
another problem in the study 
 of gsh biosynthesis for its eventual manipulation is that the pathway has been 
 analyzed considering only the gsh - synthetic reactions without taking into 
 account the gsh - consuming reactions ( figure 2 ) , .
the analysis of an incomplete pathway leads to 
 misleading conclusions about the control of flux .
metabolic modeling has shown that only with 
 the incorporation of the consuming reactions of the pathway end products , a true 
 steady state can be established . in 
 conclusion , without a solid theoretical framework , the overexpression of only 
 one enzyme ( the  rate - limiting step  ) , or of many arbitrarily selected enzymes 
 ( tables 1 and 2 ) , the problem of increasing the flux or metabolite 
 concentrations can not be solved .
there are some successful examples of the genetic engineering approach to manipulate 
 metabolism : overexpression 
 ( approx .
23 fold ) of the five genes of the tryptophan synthesis pathway in s. 
 cerevisiae , to increase ( 9-fold ) flux ; increase 
 in amino acids ( trp , ile , lys , val , thr ) and 
 trehalose production in corynebacterium glutamicum , in which some proteins of 
 each metabolic pathway are simultaneously overexpressed , but some of them with 
 mutations that confer insensitivity to feedback inhibition [ 4853 ] . in these transformed bacteria ,
the end products 
 are indeed overproduced and their excretion is accelerated;overexpression 
 of pfk and pyk to increase ethanol production by 35% in e. coli , although lactic acid formation was not modified ; mannitol 
 1-phosphate dehydrogenase and mannitol 1-phosphatase overexpression to increase 
 mannitol production by 2750% in ldh - deficient lactococcus lactis ; increase 
 in sorbitol production ( 5 fold ) in ldh - deficient lactobacillus plantarum through the overexpression of sorbitol 
 6-phosphate dehydrogenase ( activity up to 250 fold in mutants versus wild type ) ; overexpression 
 of pfk ( 14 fold ) or ldh ( 3.5 times ) to increase 2 - 3 times the homolactic 
 fermentation flux in lactococcus lactis growing on maltose , and in parallel decrease fluxes toward secondary acids and 
 ethanol . 
  overexpression 
 ( approx
. 23 fold ) of the five genes of the tryptophan synthesis pathway in s. 
 cerevisiae , to increase ( 9-fold ) flux ; increase 
 in amino acids ( trp , ile , lys , val , thr ) and 
 trehalose production in corynebacterium glutamicum , in which some proteins of 
 each metabolic pathway are simultaneously overexpressed , but some of them with 
 mutations that confer insensitivity to feedback inhibition [ 4853 ] .
in these transformed bacteria , the end products 
 are indeed overproduced and their excretion is accelerated ; overexpression 
 of pfk and pyk to increase ethanol production by 35% in e. coli , although lactic acid formation was not modified ; mannitol 
 1-phosphate dehydrogenase and mannitol 1-phosphatase overexpression to increase 
 mannitol production by 2750% in ldh - deficient lactococcus lactis ; increase 
 in sorbitol production ( 5 fold ) in ldh - deficient lactobacillus plantarum through the overexpression of sorbitol 
 6-phosphate dehydrogenase ( activity up to 250 fold in mutants versus wild type ) ; overexpression 
 of pfk ( 14 fold ) or ldh ( 3.5 times ) to increase 2 - 3 times the homolactic 
 fermentation flux in lactococcus lactis growing on maltose , and in parallel decrease fluxes toward secondary acids and 
 ethanol .
several glycolytic enzymes are overexpressed in 
 at least 70% of human cancers . except 
 for glucose transporter 1 ( glut-1 ) , the other 11 glycolytic enzymes ( hk to ldh ) 
 are overexpressed in brain and nervous system cancers .
prostate and lymphatic nodule cancers ( hodgkin 
 and non - hodgkin lymphomas ; myelomas ) overexpress 10 glycolytic enzymes ( except 
 for hk ; in prostate cancer glut1 is also overexpressed ) .
there is a second group of cancers that overexpresses 68 glycolytic 
 genes ( skin , kidney , stomach , testicles , lung , liver , placenta , pancreas , 
 uterus , ovary , eye , head and neck , and mammary gland ) .
a third group includes those cancers overexpressing 
 1 or 2 glycolytic genes ( bone , bone marrow , cervix , and cartilage ) . in animals ,
gene expression of glycolytic enzymes is regulated ( both coordinately 
 and individually ) under hypoxic conditions by hypoxia - responsive transcription 
 factors such as hif-1 ( hypoxia - inducible factor 1 ) , sp family factors , ap-1 , and possibly mre 
 ( metal response elements ) [ 8 , 5961 ] .
. there are binding sites ( consensus sequence acgt ) for hif-1 in the promoters of genes for hk , pfk-1 , 
 aldo , gapdh , pgk , eno , pyk , and ldh ( reviewed in ) .
tpi and perhaps hpi and pgam are also induced 
 by hypoxia , but it is not clear whether hif-1 mediates this induction , and whether this 
 factor regulates other metabolic pathways associated with glucose 
 catabolism .
for example , although 
 glycogen phosphorylase is overexpressed under hypoxia in human tissues , 
 the role of hif-1 has not been demonstrated .
if direct manipulation of 
 pathway genes becomes difficult , then the overexpression or repression of 
 transcription factors such as hif-1 , ap1 , and mres might solve the problem of changing 
 flux , although overexpression of transcription factors may also be difficult 
 due to the numerous upstream and downstream factors involved .
the kinetoplastid parasites trypanosoma 
 cruzi , trypanosoma brucei , and leishmania are the causative agents of 
 chagas disease , african trypanosomiasis , and leishmaniasis , respectively . the 
 available drugs to treat these diseases are highly toxic for humans .
moreover , the 
 parasites may become resistant , and hence the search for new drugs and drug 
 targets is relevant for solving these public health problems . in these parasites ,
the 
 metabolism is organized in a peculiar way ; they have a subcellular structure 
 called glycosome in which several metabolic pathways take place : 
 gluconeogenesis , reactions of the pentose phosphate pathway , purine salvage and 
 pyrimidine biosynthesis , -oxidation 
 of fatty acids , fatty acid elongation , biosynthesis of ether lipids , and the 
 first seven steps of glycolysis .
glycosomal glycolytic enzymes have unique structural , kinetic , and 
 regulatory features not found in their human counterparts , and therefore have 
 been the subject of extensive biochemical studies to use them as drug targets .
the rationale behind this is to synthesize 
 inhibitors that affect mainly the parasitic enzymes with relatively low effect 
 on the human enzymes since the infective parasite stages rely mostly on 
 glycolysis for atp supply .
there are reports on the 
 design of presumed specific inhibitors for some of the t. brucei glycolytic 
 enzymes : glut ( bromoacetyl-2-glucose ) , hk , hpi , pfk , aldo , tpi , gapdh , 
 pgk , pyk , and glycerol-3-phosphate dehydrogenase .
although the purified enzymes display 
 very low ki values for these 
 inhibitors and some of them inhibit 
 parasite growth or infective capabilities , their effect on inhibiting the 
 glycolytic flux has not been explored .
therefore , it is not yet possible to 
 directly ascribe the effects seen in parasite culture with the in vitro effects 
 on the isolated enzymes . to identify the 
 best drug targets ,
determination of the flux control steps of glycolysis 
 in t. brucei has been recently initiated .
trypanothione ( tsh2 ) 
 is a reducing agent present in trypanosomatids that is synthesized from one 
 spermidine and two gsh molecules by tsh2 synthetase ( trys ) 
 ( figure 3 ) .
this metabolite and its reducing enzyme , 
 tsh2 reductase ( tryr ) , replace the antioxidant and metabolic 
 functions of the more common gsh / gsh reductase system present in mammals .
in 
 fact , most of the antioxidant metabolism of these parasites depend on tsh2 ( figure 3 ) [ 69 , 70 ] . thus , the enzymes of this metabolic pathway have been 
 proposed as drug targets for killing the parasites .
diminution in its gene transcription yields a 
 loss of activity between 5690% , depending on 
 the genetic technique [ 7275 ] . in 
 knockdown t. brucei cells
( i.e. , when tryr activity has diminished 
 to less than 10% of the wild - type level ) , the parasites show growth diminution 
 and higher sensitivity to h2o2 in culture and loss of 
 infectiveness in mice . however , tsh2 and thiol compound contents 
 were not affected .
tryr 
 downregulation by > 85% in leishmania species causes inability to survive under 
 oxidative stress inside macrophages [ 7274 ] .
in contrast , when tryr is 14- and 10 fold 
 overexpressed in leishmania and t. cruzi , respectively , there are no 
 significant differences in h2o2 susceptibility between 
 control and transfected cells ; both types of cells are also equally resistant 
 to the oxidative stress - inducers gentian violet , and nitrofurans .
intriguingly , the cellular levels of tsh2 , 
 gsh , and glutathionyl - spermidine , determined in both types of experiments ( tryr 
 suppression and overexpression ) were similar in control and transformed cells .  
knockdown 
 of trys by sirna in procyclic t. brucei causes ( i ) viability impairment and arrest of proliferation when tsh2 levels decrease to 15% of the wild - type level , ( ii ) increased sensitivity to h2o2 and alkyl hydroperoxides , ( iii ) damage to the plasma membrane , and ( iv ) 
 diminution of the tsh2 content and accumulation of gsh and 
 glutathionyl - spermidine .
a similar metabolite variation ( lower tsh2 ; 
 higher gsh ) was attained with a trys knockdown induced by sirna in the 
 bloodstream form of t. brucei .
this 
 trys knockdown also induced an increased sensitivity to different compounds 
 that affect tsh2 metabolism such as arsenicals , melarsen oxide , 
 trivalent antimonials , and nifurtimox .
indeed , western blot analysis showed , 
 in addition to the expected ( 10-fold ) decrease in trys protein , a 2 - 3-folds increase in -ecs and tryr .
the changes in expression of 
 other enzymes suggest unveiled compensatory or pleiotropic effects on tsh2 metabolism .  
other researchers have selected -glutamylcysteine synthetase ( -ecs ) , the presumed rate - limiting step of gsh 
 synthesis , as an alternative drug target of tsh2 synthesis in t. brucei ( figure 3 ) .
knockdown of -ecs gene in the parasite induces cell death 
 and depletion of gsh and tsh2 only after 80% decrease in the enzyme 
 content .
the -ecs knockdown cells are rescued from death by 
 adding external gsh , which elevates the cellular gsh and tsh2 levels 
 .
glutathione synthetase ( gs ) has not been manipulated in trypanosomatids , or in any other organism , perhaps 
 because it has been considered as a nonrate - limiting step of gsh and tsh2 biosynthesis . however , dna microarray 
 analysis of antimonite - resistant leishmania tarentolae shows increased 
 transcription of -ecs , gs , and p - glycoprotein a rnas . 
 although it was not evaluated whether increase in gene transcription correlated 
 with an increase in enzyme activity , it may be possible that under high gsh 
 demand ( i.e. , under oxidative stress conditions ) gs might exert control of tsh2 synthesis . on the other hand , ornithine 
 decarboxylase
( odc ) overexpression in t. brucei ( the presumed limiting 
 step of spermidine synthesis ) causes no change in tsh2 levels 
 .
therefore , odc does not seem to be 
 a controlling step of tsh2 synthesis .
although almost full inhibition ( > 80% ) of gene transcription or activity of any of 
 these enzymes results in parasite death , the question remains of how tsh2 metabolism is affected when the enzymes are less inhibited .
for example , in the therapeutic treatment of 
 patients it is certain that drugs have to be administered for long periods of 
 time .
if the parasites are not 
 completely cleared from the patient , disease recurrence and generation of drug - resistant 
 parasites are possible .
the results described 
 above indicate that each enzyme by itself has low control on tsh2 synthesis and concentration ; therefore , highly specific and very potent 
 inhibitors have to be designed in order to attain the required full activity blockade 
 to affect tsh2 metabolism in these parasites .
the metabolic 
 control analysis ( mca ) was initially developed by kacser and burns in scotland [ 82 , 83 ] and by heinrich and rapoport 
 in east germany 
  [ 84 , 85 ] .
this analysis establishes a 
 theoretical framework that explains the results observed with the enzyme 
 overexpression and downregulation experiments . in addition , it helps to identify and design 
 experimental strategies for the manipulation of a given process in an organism 
 ( heavy metal hyperaccumulation ; increased production of ethanol , co2 , 
 lactate or acetate ; or inhibition of a metabolic pathway flux with therapeutic 
 purposes ) .
mca rationalizes the quantitative 
 determination of the degree of control that a given enzyme exerts on flux and 
 on the concentration of metabolites .
different 
 experimental approaches have been developed to detect and direct what has to be 
 done and measured , in order to identify and understand why an enzyme exerts a 
 significant or a negligible control on flux and metabolite concentration in a 
 metabolic pathway .
experiments for identifying and manipulating the conceptually wrong  rate - limiting 
 step . 
to 
 understand how a metabolic pathway is controlled and could be manipulated , its 
 control structure has to be evaluated . the 
 control structure of a pathway is constituted by the flux control coefficient ( cvi ) , which is the degree of control that the rate ( v ) of a given enzyme i exerts 
 on flux j ; the concentration control coefficient ( cvi ) , which is the degree of control that a given enzyme i exerts on the concentration of a metabolite 
 ( x ) ; and the elasticity coefficients .
the control coefficients are systemic 
 properties of the pathway that are mechanistically determined by the elasticity 
 coefficients ( x ) , which are defined as the degree of sensitivity 
 of a given enzyme vi 
  ( i.e. , the enzyme 's ability to change 
 its rate ) when any of its ligands ( x : substrate , products or allosteric 
 modulators ) is varied .
viojo , in which the expression dj / dvi describes 
 the variation in flux ( j ) when an infinitesimal change is done in the enzyme i concentration or activity . in practice , 

the infinitesimal changes in vi 
  are undetectable , and hence measurable noninfinitesimal changes are undertaken . 
 
if a small change in vi 
  promotes a significant 
 variation in j , then this enzyme exerts an elevated flux control ( figure 4 , 
 position 1 ) .
in contrast , if a rather small 
 or negligible change in flux is observed when vi 
  is greatly varied , then the enzyme does not exert 
 significant flux control ( figure 4 , position 2 ) . to obtain dimensionless and normalized values 
 of cvi the scaling factor
vio / jo is applied , which represents the ratio between the initial values from which 
 the slope dj / dvi 
  is 
 calculated .
if all cvi of the pathway enzymes and transporters are added up , the sum comes to 
 one ( summation theorem ) .
the mca clearly distinguishes 
 between the control exerted by a given enzyme on flux ( flux control 
 coefficient ) and on the metabolite concentration ( concentration control 
 coefficient ) .
thus , an enzyme can have significant control on a metabolite 
 concentration but not on the pathway flux .
on one hand , the use of the rate - limiting step concept 
 for manipulating metabolic pathways does not make such differentiation , which 
 probably has contributed to the many unsuccessful experiments reported in the 
 literature ; on the other hand , it should be clearly defined whether the aim of the 
 project is to increase flux and/or a metabolite concentration since mca 
 establishes for each aim a different experimental design . to determine the flux control 
 coefficient of a given enzyme , small variations in the enzyme content , or 
 preferentially , in activity are required , without altering the rest of the 
 pathway , and then the changes in flux are determined .
the experimental points are plotted as shown 
 in figure 4 to calculate the slope at the reference point vio / jo .
this experiment , apparently easy to perform , 
 has demanded great intellectual and experimental effort .
several experimental strategies have been 
 developed to determine cvi : 
 formation of heterokarionts and heterocygots ( classical genetics),titration of flux with specific inhibitors , elasticity analysis , mathematical modeling ( in 
  silico biology),in vitro reconstitution of metabolic pathways , genetic engineering to manipulate in vivo protein levels . 
 
formation of heterokarionts and heterocygots ( classical genetics ) , titration of flux with specific inhibitors , mathematical modeling ( in 
  silico biology ) , in vitro reconstitution of metabolic pathways , genetic engineering to manipulate in vivo protein levels .
the arginine biosynthesis in neurospora crassa was the first metabolic 
 pathway in which flux control coefficients were experimentally determined by 
 kacser 's laboratory .
this fungus 
 forms multinucleated mycelia that facilitate the generation of polyploid cells . 
  by mixing different ratios of spores containing 
 genes encoding wild ( active ) and mutant ( inactive ) enzymes of this pathway , it 
 was possible to generate heterokaryont mycelia with different content , and 
 activity , of four pathway enzymes .
the authors built plots of enzyme activity versus 
 flux ( see figure 4 ) for acetyl - ornithine aminotransferase , ornithine 
 transcarbamoylase , arginine - succinate synthetase , and arginine - succinate lyase . 
 
all the experimental points of these 
 heterokaryonts localized near to position 2 of figure 4 with cvi =   0.020.2 ( flux control by these enzymes was 
 only 220% ) , which indicated that none of these enzymes exerted significant 
 control on arginine synthesis .
the authors did not determine the remaining flux 
 control ( 75% ) , which might reside in carbamoyl - phosphate synthetase i ( this mitochondrial 
 ammonium - dependent isoform can be bound to the mitochondrial inner membrane or 
 form complexes with ornithine transcarbamoylase [ 87 , 88 ] ) and in mitochondrial citruline / ornithine 
 transporter , both of which have been proposed as limiting steps , or might be in 
 the arginine demand for protein synthesis .
organisms 
 with many alleles of one enzyme may form homo - and heterozygotes expressing 
 different activity levels .
drosophila 
 melanogaster has three adh alleles encoding for isoforms with different vmax . when three natural homozygotes , a null mutant , and 
 some heterozygotes were generated , different adh activities were attained but 
 the ethanol consuming rate did not change ( figure 4 , position 2 ) .
oxidative phosphorylation ( oxphos ) is 
 the only pathway for which specific and potent inhibitors for many enzymes and 
 transporters are available .
oxphos is divided in two segments ( figure 5 ) : the 
 oxidative system ( os ) formed by substrate transporters ( pyruvate , 
 2-oxoglutarate , glutamate , glutamate / aspartate , dicarboxylates ) , krebs cycle 
 enzymes , and the respiratory chain complexes ; and the phosphorylating system 
 ( ps ) constituted by the atp / adp ( ant ) and pi ( pit ) transporters , and atp 
 synthase .
when the flux ( atp synthesis ) 
 is titrated by adding increasing concentrations of each specific inhibitor , 
 plots are generated in which the enzyme activity is progressively diminished by 
 increasing inhibitor concentration .
hence , the cvi value depends on the type of 
 inhibitor usedfor irreversible inhibition,(2)cvij  =  ( imaxjo)(djdi)[i]0 , 
 for simple noncompetitive inhibition,(3)cvij  =  ( kijo)(djdi)[i]0 , 
 for simple competitive inhibition,(4)cvij  =  ( -ki[(1+s)/km]jo)(djdi)[i]0 , 
  where jo is the pathway flux in the absence 
 of inhibitor ; imax , minimal 
 inhibitor concentration to reach maximal flux inhibition ; k 
 i , inhibition constant ; s , 
 substrate concentration ; km , 
 michaelis - menten constant ; and d 
 j / d 
 i , 
 initial slope ( [ i ] = 0 ) of inhibition titration curve . for irreversible inhibition,(2)cvij 
=  ( imaxjo)(djdi)[i]0 , 
  for simple noncompetitive inhibition,(3)cvij  =  ( kijo)(djdi)[i]0 , 
  for simple competitive inhibition,(4)cvij  =  ( -ki[(1+s)/km]jo)(djdi)[i]0 , 
  to estimate flux control 
 coefficients from inhibitor titration of adp - stimulated ( state 3 ) respiratory 
 rates ( i.e. , mitochondrial o2 consumption coupled to atp synthesis ) , ( 2 ) for irreversible inhibitors was used 
 because researchers assumed that mitochondrial inhibitors such as rotenone , 
 antimycin , carboxyatractyloside , and oligomycin were 
however , under this assumption flux control coefficients were usually 
 overestimated [ 90 , 91 ] . to solve this 
 problem , gellerich et al .  
developed ( 5 ) for noncompetitive 
 tightly - bound inhibitors and , by using nonlinear regression analysis , it was 
 possible to include all experimental points from the titration curve thus 
 increasing accuracy in calculating cvi:(5)j  =  [ n(joji)2encojoeon[(n    co)jo    ( nji)en ] ]  +  ji  e2+(kd+ieo)ekdeo=0 , in which jo and ji are the 
 respiration fluxes in the noninhibited ( e = eo ) and inhibited ( e = 0 ) states ; k 
 d is the dissociation constant of 
 the enzyme - inhibitor complex , and n is an empirical component that expresses the relationship between substrate 
 concentration and the reaction catalyzed by the enzyme e. the analysis of data in table 3 shows that oxphos is not controlled by only one 
 limiting step , but the flux control is rather distributed among several enzymes 
 and transporters .
it is worth noting 
 that the value of the flux control coefficient depends on the content of enzyme 
 or transporter , which varies from tissue to tissue .
perhaps the atp / adp translocase in as-30d hepatoma mitochondria 
 might reach the status of being the  oxphos limiting step  with a ca nt = 0.70 , or the pi transporter in kidney mitochondria , or the 
 atp / adp translocase and the respiratory chain complex 3 in liver mitochondria , but 

it should be noted that other steps also exert significant control ( table 3 ) .
although the distribution of control varies 
 between tissues , the flux control mainly resides in the ps of organs with high atp 
  demand such as the heart   ( cpt+ant+atpsynthase = cps = 0.73 ) , kidney ( cps = 0.75 ; cos = 0.31 ) , and   fast - growing tumors ( cps = 0.98 ) .
in contrast , in the 
 liver   ( cos = 0.80 ; cps = 0.65 ) and brain ( cos = 0.35 ; cps = 0.41 ) , the control is shared by both systems .
determined that the oxphos 
 control was shared by the ps ( cps = 0.62 ) and the atp demand ( purified atpase ) . in turn ,
rossignol et al .   concluded that 
 the os exerted the main control ( cos = 0.68 ) , but these authors apparently used low - quality mitochondria 
 ( low respiratory control values that lead to low rates of atp synthesis 
 associated with high rates of respiration ) that were not incubated under near physiological 
 conditions ( 10 mm pyruvate , 10 mm malate , 10 mm pi , ph 7.4 in tris buffer ) , and the authors incorrectly assumed that rotenone and antimycin 
 were irreversible inhibitors .
it is notorious 
 that in all works shown in table 3 at least one of these mistakes is evident .
there are some inhibitors for enzymes and transporters from other pathways , but they 
 are not quite specific and may affect other sites . due to the fact that there are no inhibitors 
 for every step in these pathways ,
examples 
 of these inhibitors are 6-chloro-6-deoxyglucose for glucose transporters in 
 bacteria , 2-deoxyglucose for hpi , iodoacetate for gapdh , 1,4-dideoxy-1,4-imino - d - arabinitol 
 for glycogen phosphorylase , oxalate and oxamate for ldh , 6-amino 
 nicotinamide for the phosphate pentose pathway , amino - oxyacetate for 
 aminotransferases and kirureninase ( tryptophan synthesis ) , norvaline for 
 ornithine transcarbamylase , mercaptopycolinate for pep carboxykinase , acetazolamide 
 for carbonic anhydrase , and isobutyramide for adh ( compiled by 
 fell ) .
potential uses of the experimental approachmitochondrial 
 pathologies are a heterogeneous group of metabolic perturbations characterized 
 by morphological abnormalities and/or oxphos dysfunction .
mitochondrial dna analysis has revealed specific 
 mutations for some mitochondriopathies . although the specific oxphos mutations causing 
 the disease may appear in all tissues , the functioning of only some of them is 
 altered .
the organ 's sensitivity might be related to the different flux control 
 coefficients of the mutated enzyme in the different tissues ( table 3 ) and to 
 their atp supply dependence from oxphos versus 
 glycolysis.mca allows for the analysis of a metabolic flux or intermediate concentration by focusing 
 either on one step or by grouping enzymes in blocks or in pathways .
thus , a comparative analysis of oxphos control 
 distribution reveals that heart , kidney , some fast growing tumors ( rat as-30d 
 hepatoma , mouse fibrosarcoma , human breast , lung , thyroid carcinoma , melanoma ) 
 , and perhaps skeletal muscle are more susceptible to mitochondrial mutations 
 in atp synthase , which is the only ps site with subunits encoded in the mitochondrial 
 genome . on the other side , liver and 
 brain
might be more susceptible to mitochondrial mutations of the respiratory 
 chain enzymes ( see table 3 ) .
considering that the brain is a fully aerobic 
 organ , whereas the liver depends on both oxphos ( 7080% ) and glycolysis 
 ( 2030% ) for atp supply , then it can be postulated that the brain is more 
 sensitive to mutations in the mitochondrial genome than the liver because subunits 
 of complexes i , iii , and iv are encoded by the mitochondrial genome.titration of flux with 
 specific inhibitors to determine the flux control coefficients of oxphos has been 
 applied to intact tumor cells .
the results showed that the flux control 
 resided mainly in site 1 of the respiratory chain ( csitel = 0.30 ) , whereas the other evaluated sites exerted a marginal 
 control .
this observation could 
 have therapeutic application if site 1 does not exert control in healthy cells , 
 leading to less severe side effects.the use of inhibitors in 
 intact cells to determine control coefficients might pose two problems : hydrophilic 
 inhibitors such as carboxyatractyloside ( for ant ) and -cyano-4-hydroxy - cinammate ( for pyruvate transporter ) 
 can not readily enter the cell due to the presence of the plasma membrane 
 barrier ; the other problem is that hydrophobic but slow inhibitors , such as 
 oligomycin , require long incubation times to ensure the interaction with the 
 specific sites .
these problems can be 
 solved by incubating the cells for long periods of time and taking care of cell 
 viability , for instance , as-30d hepatoma cells are fairly resistant to this 
 mechanical manipulation as they maintain high viability after a lengthy 
 incubation under smooth orbital agitation of 1 h at 37c 
 .
mitochondrial 
 pathologies are a heterogeneous group of metabolic perturbations characterized 
 by morphological abnormalities and/or oxphos dysfunction .
mitochondrial dna analysis has revealed specific 
 mutations for some mitochondriopathies . although the specific oxphos mutations causing 
 the disease may appear in all tissues , the functioning of only some of them is 
 altered .
the organ 's sensitivity might be related to the different flux control 
 coefficients of the mutated enzyme in the different tissues ( table 3 ) and to 
 their atp supply dependence from oxphos versus 
 glycolysis .
mca allows for the analysis of a metabolic flux or intermediate concentration by focusing 
 either on one step or by grouping enzymes in blocks or in pathways .
thus , a comparative analysis of oxphos control 
 distribution reveals that heart , kidney , some fast growing tumors ( rat as-30d 
 hepatoma , mouse fibrosarcoma , human breast , lung , thyroid carcinoma , melanoma ) 
 , and perhaps skeletal muscle are more susceptible to mitochondrial mutations 
 in atp synthase , which is the only ps site with subunits encoded in the mitochondrial 
 genome . on the other side , liver and 
 brain might be more susceptible to mitochondrial mutations of the respiratory 
 chain enzymes ( see table 3 ) . considering that the brain is a fully aerobic 
 organ ,
whereas the liver depends on both oxphos ( 7080% ) and glycolysis 
 ( 2030% ) for atp supply , then it can be postulated that the brain is more 
 sensitive to mutations in the mitochondrial genome than the liver because subunits 
 of complexes i , iii , and iv are encoded by the mitochondrial genome .
titration of flux with 
 specific inhibitors to determine the flux control coefficients of oxphos has been 
 applied to intact tumor cells .
the results showed that the flux control 
 resided mainly in site 1 of the respiratory chain ( csitel = 0.30 ) , whereas the other evaluated sites exerted a marginal 
 control .
this observation could 
 have therapeutic application if site 1 does not exert control in healthy cells , 
 leading to less severe side effects .
the use of inhibitors in 
 intact cells to determine control coefficients might pose two problems : hydrophilic 
 inhibitors such as carboxyatractyloside ( for ant ) and -cyano-4-hydroxy - cinammate ( for pyruvate transporter ) 
 can not readily enter the cell due to the presence of the plasma membrane 
 barrier ; the other problem is that hydrophobic but slow inhibitors , such as 
 oligomycin , require long incubation times to ensure the interaction with the 
 specific sites .
these problems can be 
 solved by incubating the cells for long periods of time and taking care of cell 
 viability , for instance , as-30d hepatoma cells are fairly resistant to this 
 mechanical manipulation as they maintain high viability after a lengthy 
 incubation under smooth orbital agitation of 1 h at 37c 
 .
xovio , which is a dimensionless number that show the rate variation v of a given enzyme or transporter i when the concentration of a ligand x ( substrate s , product p or allosteric modulator ) is varied in infinitesimal 
 proportions .
the elasticity coefficients are positive for those metabolites 
 that increase the enzyme or transporter rate ( substrate or activator ) , and they 
 are negative for the metabolites that decrease the enzyme or transporter rates 
 ( product or inhibitor ) .
an enzyme working , under a steady - state metabolic flux , at saturating conditions of s or p , 
 is no longer sensitive to changes in these metabolites .
thus , its elasticity is close to zero ( figure 6 , x = 0 ) . 
  in turn
, an enzyme working at s or p 
 concentrations well below the michaelis constant ( kms or kmp ) 
 is expected to be highly sensitive to small variations in these metabolites ( figure 
 6 , x = 1 ) .
if the kinetic parameters of an enzyme are 
 known ( vmf , vmr ,   kms , and kmp ) , then the enzyme elasticity for any given metabolite 
 concentration may be calculated as shown in the following equations . for substrate,(7)svi  =  s / kms1  +  s / kms  +  p / kmp  +  11    /keq , and 
 for product,(8)pvi  =  p / kmp1  +  s / kms  +  p / kmp    /keq1    /keq , in which  is
the mass 
 action ratio , and keq is the equilibrium constant preferentially determined 
 under physiological conditions .
an enzyme with low elasticity can not increase ( or decrease ) its rate despite large 
 variations in s ( or p ) concentration ; in consequence , such enzyme exerts a high 
 flux control . in turn
, an enzyme with a 
 high elasticity can adjust its rate to the variation in s or p concentrations , 
 and thus it does not interfere with the metabolic flux , exerting a low flux control .
this inverse relationship between the 
 elasticity and the flux control coefficients is expressed in a formal equation 
 denominated connectivity theorem .
a 
 metabolic pathway can be divided in two blocks around an intermediary x : the 
 producing ( synthetic , supply ) and the consuming ( demand ) enzyme blocks of x are i1 and i2 , respectively .
thus , the connectivity theorem for this two - block system is(9)cv1jcv2j  =  xv2xv1 .
the negative sign of the right part of the equation 
 cancels with x , which is negative because x 
 is a product of enzyme block i1 ( figure 6 ) . to obtain the flux control coefficients
many strategies have been designed [ 90 , 103108 ] , but the most 
 used and probably more trustworthy is that in which the initial pathway metabolite 
 ( so ) concentration is varied to increase the x concentration ( any intermediary 
 in the pathway ) , and measuring in parallel the variation in flux . under steady - state conditions , the flux rate 
 is equal to the rate of end - product formation ( i.e. , lactate or alcohol for 
 glycolysis ; oxygen consumption for oxphos ) and to the rate of any partial 
 reaction .
the slope , calculated at the reference 
 coordinate ( xo , jo ) that is 
 equivalent to ( so , vio ) , yields 
 the elasticity coefficient of the consuming block of x. in another set of experiments , an inhibitor is 
 added to block one or more enzymes after x. the x concentration and flux are determined and 
 plotted as shown in figure 7 , from which the elasticity coefficient of the 
 producing block is calculated .
the flux 
 control coefficients are determined by using the connectivity theorem and 
 considering that the sum of the control coefficients comes to 1 , c1 + c2 = 1 ( summation theorem):(10)cv1j  =  xv2xv2    xv1,cv2j  =    xv1xv2    xv1 . 
 
this method for determining cvi using the elasticities of the two blocks was called double 
 modulation by kacser and burns .
years 
 later , brand and his group [ 103 , 104 ] renamed this method as top - down approach . by applying the procedure shown in figure 7 
 and using ( 10 ) for different metabolites along the metabolic pathway , it 
 is possible to identify those sites that exert a higher control ( which may be 
 the sites for therapeutic use or biotechnological manipulation ) and those that 
 exert a negligible control under a given physiological or pathological 
 situation .
elasticity analysis has been used to evaluate the oxphos control distribution 
 in tumor cells .
almost all studies on 
 this subject have been carried out with isolated mitochondria incubated in 
 sucrose - based medium at 25 or 30c or with the more physiological kcl - based medium but 
 still at 30c ( table 3 ) .
furthermore , 
 these studies did not consider that the product , atp , never accumulates in the 
 living cells , which does occur in experiments with isolated mitochondria .
under such a condition , a steady state in atp production can 
 never be reached as in living cells . in 
 other words , the distribution of control in mitochondria ( table 3 ) has been 
 determined in the absence of an atp - consuming system . a remarkable exception to
this incomplete 
 experimental design was the work done by wanders et al . , in which isolated liver mitochondria were incubated 
 with two different atp - consuming systems ( or adp - regenerating systems ) : hk + 
 glucose and creatine kinase ( ck ) + creatine . under this
more physiological setting , the oxphos 
 flux control distributed between ant and the atp - consuming system ; however , flux 
 control by the other pathway components was not examined .
therefore , to accurately evaluate oxphos control 
 distribution , mitochondria should be incubated in the presence of an 
 atp - consuming system or in their natural environment ( i.e. , inside the cell ) .
the rate of oxphos in intact 
 cells is determined from the rate of oligomycin - sensitive respiration : in the 
 steady state , the enzyme rates are the same and constant ; in branched pathways 
 the sum of the branched fluxes equals the flux that supplies the branches .
the global elasticity of the atp - consuming processes 
 ( e.g. , synthesis of protein , 
 nucleic acid , and other biomolecules , as well as ion atpases to maintain the 
 ionic gradients , mechanical activity such as muscular contraction or flagellum 
 and cilium movement , and secretion of hormones , digestive enzymes and 
 neurotransmitters ) is estimated by inhibiting flux with low concentrations of 
 oligomycin or a respiratory chain inhibitor . to determine the elasticity of the 
 atp - producing block , flux , and [ atp ]
are varied with streptomycin , an inhibitor 
 of protein synthesis ( figure 7 ) .
the 
 elasticity coefficients are calculated from the initial coordinate slopes 
 ( without inhibitors ) of each titration . with 
 this procedure
, it has been determined that the atp - consuming block exerts a 
 significant flux control of 34% .
remarkably , 
 this flux control value obtained in cells is quite similar to the flux control 
 coefficients of the atp - consuming system ( hk or ck ) reported by wanders 
 et al .   with isolated 
 mitochondria .
elasticity analysis by enzyme 
 blocks allows the inclusion of the end - product demand as another pathway block . 
 
the conclusions obtained from this 
 analysis have formulated the supply - demand theory , which proposes that when 
 flux is controlled by one block ( demand ) , the concentration of the end - product 
 is determined by the other block ( supply ) . the ratio of elasticities determines the distribution of flux control 
 between supply and demand blocks . for 
 instance , if x > x ( i.e. , demand becomes saturated by the end - product x , 
 and hence its elasticity is near zero ) , then the demand block exerts the main 
  flux control . for concentration control , 
 at larger x  x ,   smaller absolute values of both csupply and cdemand are attained ; hence , under demand saturation , 
 the supply elasticity fully governs the magnitude of the variation in the 
 end - product concentration . on the other 
 hand ,
when demand increases , it loses flux control and induces a diminution in 
 the end - product concentration . in turn , supply gains flux control and loses 
 concentration control . in the presence of feed - back inhibition ,
the system can 
 maintain the end - product concentration orders of magnitude away from 
 equilibrium ( at a concentration around the k0.5 of the allosteric enzyme ) . as mentioned before ,
the 
 demand is not usually included in the pathway because it is erroneously thought 
 that it is not part of it .
but then , is 
 it valid to analyze the control of a metabolite synthesis if its demand is not 
 considered ?
when the demand block is not 
 included , it is assumed that the metabolic pathway produces a metabolite at the 
 same rate regardless whether the metabolite demand is high or low .
this reasoning is incorrect because a 
 metabolic pathway indeed responds to changes in the metabolite demand and , more 
 importantly , a pathway without end - products consumption reactions is unable to 
 reach a steady state .
the intermediary x linking the two blocks is one 
 of the end - products of the producing block ( e.g. , 
 pyruvate or lactate or ethanol , and atp for glycolysis ) .
the variation in rate of the two blocks in 
 response to a variation in x can be theoretical or experimentally determined ( figure 8(a ) ) .
it is worth noting that , for this 
 supply - demand approach , it is not necessary to know the kinetics of each 
 pathway enzyme because the rate response of each block reflects the global kinetics 
 of all participating enzymes
. when the x 
 concentration is increased , the rate of the supply block decreases ( i ) because x 
 is its product and ( ii ) because usually an enzyme within this block receives 
 information from the final part of the pathway , decreasing its rate through 
 feedback inhibition . in turn
to better 
 visualize the effect of large rate changes , the kinetics of both blocks are 
 plotted in a logarithmic scale .
figure 8(b ) shows the kinetics described in figure 8(a ) converted to natural 
 logarithm . the intersection point 
 between kinetic curves , at which the supply and demand rates are identical , 
 represents the pathway steady - state flux ( in the y axis ) and end - product 
 concentration ( in the x axis ) .
since the 
 elasticity is also defined as x = dlnvi / dlnx , the slope at the intersection point represents the elasticity of each 
 block towards the intermediary x. here , 
 the use of the scalar factor is not necessary because it is included in the 
 logarithmic equation . with the elasticity 
 coefficients calculated from plots like those shown in figure 8 , and the 
 connectivity theorem ,
the example in figure 8(b ) shows that 
 the demand exerts a high flux control ( and has low elasticity ) and the supply 
 block exerts low control ( and has high elasticity ) . the 
 fact that the demand may exert a high flux control in metabolite pathways has 
 at least three important implications : ( a ) the supply block responds to variations 
 in the demand ( high elasticity ) ; ( b ) the demand block has information transfer 
 mechanisms towards the supply block that avoid the unrestricted intermediary accumulation under a low demand , 
 particularly when the supply block has reactions with large keq ( > 100 ; g > 3 kcal mol at 37c ) ; and ( c ) 
 if the main flux control resides in the demand block , then the supply block may 
 only exert control on the intermediary concentration but not on the flux [ 30 , 32 ] .
this last conclusion explains why it 
 is incorrect to consider that an enzyme that controls flux must also control 
 the intermediary concentration
. regulatory mechanisms of 
 enzyme activity are modulation of protein concentration by synthesis and 
 degradation , as well as covalent modification and variation in the substrate or 
 product concentrations ( which are components of the pathway ) .
in addition , another regulatory mechanism is the 
 modulation by molecules that are not part of the pathway , that is , through allosteric interaction with cooperative ( sigmoidal 
 kinetics ) or noncooperative enzymes ( hyperbolic kinetics ) ( e.g. , ca activates some krebs cycle dehydrogenases ; citrate inhibits pfk-1 ; malonyl - coa inhibits 
 the mitochondrial transporter of acyl - carnitine / carnitine ; or the initial 
 substrate of a pathway that has not entered the system ) . for these last cases , kacser and burns 

proposed the use of the response coefficient r which is defined by the 
 following expression:(11)rm  j  =  cvijmvi , where m is the external modulator of the i enzyme .
the response coefficient is dj / dmmo / jo . 
  if the elasticity of the sensitive 
 enzyme toward the external effector is also determined , then it is possible to 
 calculate cvi by using ( 11 ) .
unfortunately , due to the experimental complexity for determining the 
 elasticity coefficient , this coefficient is often calculated in a theoretical 
 way by using the respective rate equation ( michaelis - menten or hill equations ) 
 and the kinetic parameters km and vmax determined by someone else under optimal 
 assay conditions , which are commonly far away from the physiological ones .
therefore , for this theoretical determination 
 of elasticity only the value of the external modulator concentration is required .
it is convenient to emphasize that the determination 
 of the flux control coefficients becomes more reliable when they are calculated 
 from several experimental points ( figure 7 ) , instead of only one , as occurs 
 with the theoretical elasticity analysis .
determined the flux control distribution of gluconeogenesis 
 from lactate in hepatocytes by using both theoretical and experimental elasticity 
 analysis and the response coefficient .
these authors concluded that gluconeogenesis 
 stimulated by glucagon was controlled by the pyruvate carboxylase ( cpc = 0.83 ) ; in the absence of this hormone , the 
 control was shared by pc , pyk , eno - pgk segment , and tpi - fructose-1,6-biphosphatase 
 segment .
elasticity 
 analysis has been applied to elucidate the flux control of atp - producing 
 pathways in fast - growing tumor cells . for oxphos
, this approach showed that respiratory chain complex i and 
 the atp - consuming pathways were the enzymes with higher control ( cvi = 0.7 ) .
for glycolysis , the main flux control ( cvi = 0.71 ) resided in glut + hk reactions because 
 hk is strongly inhibited by its product g6p despite extensive enzyme overexpression 
 .
examples of elasticity analysis on 
 other pathways are photosynthesis , ketogenesis , serine   and 
 threonine synthesis in e. coli , glycolysis in yeast , glucose 
 transport in yeast , dna supercoiling , glycogen synthesis in muscle , 
 and galactose synthesis in yeast . in conclusion
, the elasticity 
 analysis is the most frequently used method for determining flux control 
 coefficients because it does not need a group of specific inhibitors for all 
 the enzymes and transporters of the pathway , neither does it require knowledge 
 of the inhibitory mechanisms or kinetic constants .
it is only necessary to produce a variation in 
 the intermediary concentration x by using an inhibitor of either block or by 
 directly varying the x concentration . in agreement with fell
, it seems impossible for a researcher to analyze one by 
 one the rate equation of each enzyme in a metabolic pathway to predict and 
 explain the system behavior as a whole . to deal with this problem , in the last three 
 decades
some scientists have constructed mathematical models for some metabolic 
 pathways using several software programs .
thus , the specific variation of a single enzyme 
 activity without altering the rest of the pathway ( figure 4 ) , which has been an 
 experimentally difficult task for applying mca , becomes easier to achieve with 
 reliable computing models .
there are two basic types of modeling : ( a ) structural modeling and ( b ) kinetic 
 modeling .
the former is related to the pathway chemical reaction structure and 
 does not involve kinetic information .
the information obtained with structural modeling is the 
 description of the following : the exact determination of which reactions and 
 metabolites interact among them;the conservation reactions .
there are metabolites for 
 which their sum is always constant or conserved ( e.g. , nadh + nad ; nadph + nadp ; 
 ubiquinol + ubiquinone ; atp + adp + amp ; coa + acetyl - coa ) .
the identification of 
 conserved metabolites might not be obvious;enzyme groups catalyzing reactions in a given relationship 
 with another group of enzymes;elemental modules , which are defined as the minimal 
 number of enzymes required to reach a steady state , which can be isolated from the 
 system ( for a review about structural modeling ; see ) . 
 
the exact determination of which reactions and 
 metabolites interact among them ; the conservation reactions .
there are metabolites for 
 which their sum is always constant or conserved ( e.g. , nadh + nad ; nadph + nadp ; 
 ubiquinol + ubiquinone ; atp + adp + amp ; coa + acetyl - coa ) .
the identification of 
 conserved metabolites might not be obvious ; enzyme groups catalyzing reactions in a given relationship 
 with another group of enzymes ; elemental modules , which are defined as the minimal 
 number of enzymes required to reach a steady state , which can be isolated from the 
 system ( for a review about structural modeling ; see ) .
in addition to an appropriate computing 
 program , this approach requires the knowledge of the stoichiometries , rate 
 equations , and keq values of each reaction in the pathway ( or the vmax in the forward and reverse 
 reactions ) , as well as the intermediary concentrations reached under a given 
 steady state .
some currently used 
 softwares are copasi ( http://www.copasi.org/tiki-index.php ) 
 based on gepasi ( http://www.gepasi.org/ ; ) ; metamodel ; winscamp 
 and jarnac   ( both available at http://www.sys-bio.org/ ) ; and pysces 
 ( http://pysces.sourcesforge.net/ ; ) . for
other programs and links , go to http://sbml.org/index.psp . to reach a steady - state flux ,
it is necessary 
 to fix the initial metabolite concentration to a constant value and the 
 irreversible and constant removal of the end products . except for the final reactions in which their 
 products have to be removed from the system ,
all pathway reactions have to be 
 considered as reversible , notwithstanding whether they have large keq ( if there 
 is an irreversible reaction under physiological conditions , then a reversible rate 
 equation that includes the keq suffices to maintain the reaction as practically 
 irreversible ) .
care should be taken to include the enzyme 's sensitivity toward 
 its products because this property is related with the enzyme elasticity and hence 
 with its flux control ; omission of this parameter may very likely lead to 
 erroneous conclusions .
it 
 should be pointed out that the purpose of kinetic modeling is not merely to 
 replicate experimental data but also to explain them .
thus , pathway modeling is a powerful tool 
 that allows for ( i ) the detection of those properties of the pathway that are 
 not so obvious to visualize when the individual kinetic characteristics of the 
 participating enzymes are examined ; and ( ii ) the understanding of the biochemical 
 mechanisms involved in flux and intermediary concentration control .
modeling requires the consideration of all 
 reported experimental data and interactions that have been described for the 
 components of a specific pathway , thus allowing for the integration of disperse 
 data , discarding irrelevant facts . although all models are oversimplifications of complex cellular 
 processes , they are useful for the deduction of essential relationships , for 
 the design of experimental strategies that evaluate the control of a metabolic 
 pathway , and for the detection of incompatibilities in the kinetic parameters 
 of the participating enzymes and transporters , which may prompt the 
 experimental revision of the most critical uncertainties . with 

the model initially constructed , the simulation results do not usually concur 
 with the experimental results ; in consequence , the model normally requires 
 refinement , a point at which the researcher 's thinking and knowledge of biology 
 plays a fundamental role in modifying the structure and parameters of the model . 
 
the discrepancies observed between modeling 
 and experimentation unequivocally pinpoint what elements or factors have to be re - evaluated 
 or incorporated so that the model approximates more closely reality ( i.e. , experimental data ) .
the comparison of the experimentally obtained 
 intermediary concentrations and fluxes with those obtained by simulation is an 
 appropriate validating index of the model ; this index indicates whether the 
 model approximation to the physiological situation is acceptable or whether 
 re - evaluation of the kinetic properties of some enzymes and transporters and/or 
 incorporation of other reactions or factors is required .
a reason to why the results obtained by modeling may substantially differ from the 
 experimental results is that the kinetic parameters of the pathway enzyme and 
 transporters and the keq values used 
 were determined by different research groups , under different experimental 
 conditions and in different cell types .
moreover , 
 enzyme kinetic assays are carried out at low , diluted enzyme 
 concentrations ( thus discarding or ignoring relevant protein - protein 
 interactions ) , and at optimal ( but not physiological ) ph and  room temperature  
 ( which may be far away from the physiological values ) . in addition , no experimental information is 
 usually available regarding the reactions reversibility and the product 
 inhibition of the enzymes and transporters ( particularly for physiological 
 irreversible reactions , i.e. , reactions with large keq ) . with worrisome 
 frequency ,
the researcher has to adjust the experimentally determined vm and km values to achieve a model behavior that acceptably resembles 
 that observed in the biological system .
apparently , 
 this type of limitations as well as the sometimes overwhelming amount of 
 kinetic data necessary for the construction of a kinetic model has restricted 
 the number of reliable models that can be used for the prediction of the 
 pathway control structure . once the kinetic model stability , robustness ,
structural and dynamic properties have 
 been evaluated , and experimentally validated , the model may become a virtual 
 laboratory in which any parameter or component can be modified or replaced and 
 any aspect of the pathway behavior can be explored within a wide diversity of 
 circumstances or limits . at this 
 stage ,
glycolysis 
 in s. bayanus , s. cerevisiae [ 113 , 123 , 124 ] , and trypanosoma brucei [ 125 , 126 ] is the 
 metabolic pathway that has been more extensively modeled .
both cell types 
 have a very active glycolysis and are fully dependent on this metabolic pathway 
 for atp supply , under anaerobiosis and aerobiosis , respectively .
one advantage 
 of modeling glycolysis in these cell types is that most of the kinetic 
 parameters used have been experimentally determined by the same groups under 
 the same experimental conditions .
however , 
 the kinetics of the reverse reactions has not been determined and thus these 
 authors used kmp and keq 
 values reported by others and obtained in other cell types under rather different 
 experimental conditions , or they were adjusted to improve model fitting .
nevertheless , the simulation 
 results yielded relevant information on the control of the glycolytic flux . in both cases , the enzymes traditionally considered 
 the rate - limiting steps , hk , atp - pfk-1 , and pyk did not contribute to the flux 
 control , whereas the main control resided in glut ( 54% in the parasite and 85100% in yeast ) . under some conditions
, hk may exert some 
 control ( 15% ) in s. cerevisiae and some nonallosteric enzymes such as 
 aldo , gapdh , and pgk may also exert some flux control in t. brucei .
mca 
 through kinetic modeling has been applied to several pathways : glycolysis in 
 erythrocytes   in which flux control distributes between hk ( 71% ) and pfk-1 
 ( 29%);carbohydrate 
 metabolism during differentiation in dictyostelium discoideum   with 
 cellulose synthase ( 86% ) as the main controlling step;sucrose accumulation 
 in sugar cane with hk , invertase , fructose uptake , glucose uptake , and vacuolar 
 sucrose transporter having the most significant flux control ; glycerol 
 synthesis in s. cerevisiae with gapdh 
 ( 85% ) as the main control step ; penicillin 
 synthesis in penicillium chrysogenum controlled 
 ( 7598% ) either by d-(a - aminoadipyl ) cysteinylvaline synthetase ( short 
 incubation times < 30 hour ) or isopenicillin n. synthetase ( long incubation 
 times > 100 h ) ; calvin cycle 
  controlled by gapdh ( 50% ) and sedoheptulose-1,7-bisphosphatase ( 50%);threonine 
 synthesis in e. coli controlled by homoserine dehydrogenase ( 46% ) , 
 aspartate kinase ( 28% ) , and aspartate semialdehyde dehydrogenase ( 25% ) ; lysine 
 production in corynebacterium glutamicum mainly 
 controlled by aspartate kinase and permease ; nonoxidative 
 pentose pathway in erythrocytes mainly controlled by transketolase ( 74% ) ; egf - induced mapk 
 signaling in tumor cells controlled by ras - activation by egf ( 21% ) , ras 
 dephosphorylation ( 43% ) , erk phosphorylation by mek ( 44% ) , and mek 
 phosphorylation by ras ( 143% ) ; 
 aspergillus niger  
  arabinose utilization with 
 flux control shared by arabinose reductase ( 68% ) , arabitol dehydrogenase ( 17% ) , 
 and xylulose reductase ( 14% ) ; glycolysis in l. lactis in which several end products are generated ( lactate , 
 organic acids , ethanol , acetoin ) .
model predictions indicated that flux toward diacetyl and acetoin 
 ( important flavor compounds ) was mainly controlled by ldh but not by 
 acetolactate synthetase , the first enzyme of this branch . 
 
glycolysis in 
 erythrocytes   in which flux control distributes between hk ( 71% ) and pfk-1 
 ( 29% ) ; carbohydrate 
 metabolism during differentiation in dictyostelium discoideum   with 
 cellulose synthase ( 86% ) as the main controlling step ; sucrose accumulation 
 in sugar cane with hk , invertase , fructose uptake , glucose uptake , and vacuolar 
 sucrose transporter having the most significant flux control ; glycerol 
 synthesis in s. cerevisiae with gapdh 
 ( 85% ) as the main control step ; penicillin 
 synthesis in penicillium chrysogenum controlled 
 ( 7598% ) either by d-(a - aminoadipyl ) cysteinylvaline synthetase ( short 
 incubation times < 30 hour ) or isopenicillin n. synthetase ( long incubation 
 times > 100 h ) ; calvin cycle 
  controlled by gapdh ( 50% ) and sedoheptulose-1,7-bisphosphatase ( 50% ) ; threonine 
 synthesis in e. coli controlled by homoserine dehydrogenase ( 46% ) , 
 aspartate kinase ( 28% ) , and aspartate semialdehyde dehydrogenase ( 25% ) ; lysine 
 production in corynebacterium glutamicum mainly 
 controlled by aspartate kinase and permease ; nonoxidative 
 pentose pathway in erythrocytes mainly controlled by transketolase ( 74% ) ; egf - induced mapk 
 signaling in tumor cells controlled by ras - activation by egf ( 21% ) , ras 
 dephosphorylation ( 43% ) , erk phosphorylation by mek ( 44% ) , and mek 
 phosphorylation by ras ( 143% ) ; 
 aspergillus niger  
  arabinose utilization with 
 flux control shared by arabinose reductase ( 68% ) , arabitol dehydrogenase ( 17% ) , 
 and xylulose reductase ( 14% ) ; glycolysis in l. lactis in which several end products are generated ( lactate , 
 organic acids , ethanol , acetoin ) .
model predictions indicated that flux toward diacetyl and acetoin 
 ( important flavor compounds ) was mainly controlled by ldh but not by 
 acetolactate synthetase , the first enzyme of this branch .
we modeled 
 the gsh and pcs biosynthesis ( figure 2 ) to determine and understand the control 
 structure of the pathway and thus be able to identify potential sites for genetic 
 engineering manipulation that might lead to the generation of improved species 
 in heavy metal resistance and accumulation .
two models were constructed , one 
 for higher plants and the other for yeast , both exposed to high concentrations 
 of cd . due to the 
 similarity in the results , only the plant results are analyzed below .
an interesting conclusion from the gsh - pcs synthesis modeling is that control of flux 
 ( and gsh concentration ) is shared between the gsh supply and demand under both unstressed 
 and cd exposure 
 conditions ( table 4 ) .
this observation strongly differs from the 
 idea that -ecs is the rate - limiting step [ 3335 ] . for many researchers , the concept of -ecs being the key controlling step has seemed to be 
 correct because ( a ) -ecs receives information from the final part 
 of the pathway , as it is potently inhibited by gsh , the pathway end - product ; 
 and ( b ) -ecs is localized in the first part of the 
 pathway ( figure 2 ) . in addition
however , in most of the 
 studies on the control of gsh synthesis , the gsh demand has not been 
 considered .
the gsh synthesis modeling shows that under a physiological feedback 
 inhibition of -ecs by gsh a small increase in demand increases 
 flux because the gsh concentration decreases and the -ecs inhibition attenuates .
in contrast , if the demand remains constant , then 
 an increase in -ecs activity or content ( by overexpression ) does 
 not increase flux because the gsh inhibition is still there and operates on 
 both new and old enzymes .
the same pattern is also observed when hk is 
 overexpressed to increase 
 glycolytic flux since it is still inhibited by g6p ( see section 3 ) . on the other hand ,
-ecs indeed exerts significant concentration control 
 on gsh , which means that a -ecs increase results in higher gsh 
 concentration ( table 4 ) .
this last 
 observation demonstrates that an enzyme controlling a metabolite concentration does 
 not necessarily control the flux .
cd exposure promotes a high gsh demand because significant oxidative stress surges , 
 thus causing oxidation of gsh through gsh peroxidases , and because gsh and pcs 
 are used for sequestering the toxic metal ion ; hence , a higher gsh consuming 
 rate sets up . under this condition , 
 modeling predicted that control was almost equally shared between the supply 
 and demand blocks , but particularly between -ecs and pcs ( see figure 2 ) .
modeling was also able to explain why pcs overexpression 
 can have toxic effects on the cell .
an increase in the gsh demand ( pcs 
 overexpression ) under high - demand conditions ( cd stress ) leads to 
 gsh depletion that severely compromises other processes such as the oxidative 
 stress control and xenobiotic detoxification .
the 
 conclusions drawn by this model led us to propose that , to significantly increase 
 the cd resistance and accumulation , -ecs and pcs should be simultaneously overexpressed 
 ( table 4 ; figure 9 ) .
this particular 
 manipulation promotes an increase in the rate of gsh and pcs synthesis 
 ( determined by the high - to - low transition of their flux control coefficients ) 
 and in the gsh and pcs concentrations 
 ( determined by their high concentration control coefficients ) .
the model predicts that a 2-fold increase in 
 the simultaneous overexpression of -ecs and pcs brings about a 1.92.4-fold 
 increase in flux to gsh ( jgs ) 
 and pcs ( jpcs ) and in pcs 
 concentration ( figure 9 ) ; a 5-fold overexpression further increases by 4.58.1 
 times the fluxes and pcs concentration .
this proposed enzyme overexpression 
 should not exceed the gs and the complex pc - cd ( or gs - cd - gs ) vacuolar 
 transporters ' maximal activities , in order to keep the cell away from a severe 
 oxidative stress caused by gsh depletion or -ec accumulation .
indeed , the concentration of gsh was maintained high and constant although 
 -ec accumulated with the simultaneous overexpression 
 ( figure 9 ) .
furthermore , this enzyme 
 manipulation should avoid the increase of the pc - cd and gs - cd - gs complexes in 
 cytosol to toxic levels .
in other words , 
 excessive enzyme overexpression should be avoided , unless this is accompanied 
 by compensating overexpression of consuming enzymes ( gs for -ecs overexpression and pcs vacuolar transporters for 
 that of pcs ) . in yeasts and plants ,
cd is ultimately inactivated by the additional interaction with s and 
 the subsequent formation of stable high molecular weight complexes with pcs , cd , 
 s , and gsh [ 138 , 139 ] . in 

parallel to the -ecs and pcs overexpression , moderate repression 
 of gsh - s - transferases , which compete for the available gsh ( figure 2 ) , may also 
 promote an increase in gsh concentration and pcs formation flux .
in contrast , gene overexpression induces large 
 changes in activity ; hence , further theoretical background has been developed for 
 predicting the effect on flux and metabolite concentrations induced by large 
 enzyme changes .
such a theoretical background was initially developed by small 
 and kacser , who depicted ( 12 ) based on the flux control coefficients to 
 predict the effect promoted by large changes in enzyme activity:(12)fejmrj  =  11    i = jm(cvi0jo    ( ri    1)/ri ) , in which f is the amplification factor ( the flux increase ) , and r represents how many times the enzyme is overexpressed .
to predict the flux changes , promoted by identical 
 overexpression of two enzymes ( same r value ) with different cvi , 
 the equation is 
 ( 13)fejmrj  =  11    ( cij  +  cjj )    ( ( r    1)/r ) . 
 

figure 10 shows the effect on flux when one or more enzymes with different cvi are changed by the same r factor .
if the sum of cvi 
 of one or more enzymes is less than 0.25 , the 
 impact on flux is discrete when the expression increases 5 folds ( which is the 
 most common variation in the overexpression experiments analyzed in section 
 2 ) .
but for a 3-fold overexpression of 
 a group of enzymes , for which their sum of cvi is more than 0.5 , then a significant flux 
 change is achieved .
if the sum of cvi is 1 , the flux varies in a linear proportion 
 with the degree of overexpression .
it 
 has to be remarked , however , that the predicted change in flux ( figure 10 ) will 
 be valid until certain degree , the limits of which being determined by the 
 other pathway enzymes that should stay as noncontrolling steps . 

figure 10 also shows the effect on flux of decreasing an enzyme activity ( third 
 quadrant ) .
this segment plot is useful when inhibition of pathway flux is being 
 pursued for therapeutic purposes or for understanding the molecular basis of the 
 genetic dominance and recessivity . like 
 in the enzyme overexpression experiment , only a significant effect on flux is 
 achieved when the enzymes with high cvi values are inhibited . for an enzyme or group of enzymes with cvi 
 of 0.25 , greater than 80%
inhibition has to be 
 attained to decrease 50% the pathway flux . in this context
, it seems feasible 
 to explain why knockdown of enzymes involved in tsh2 synthesis has 
 to be almost total to detect an effect on tsh2 content or to alter 
 functional or pathogenic properties of the parasites ( section 4.3 ) .
the knockdown or knockout experiments in 
 trypanosomatids suggest that -ecs , trys , and tryr most probably have low flux control 
 and concentration - control coefficients since their contents or activities have 
 to be reduced > 80% of the normal levels to reach changes in intermediary 
 levels or in oxidative stress handling .
contrary 
 to the several unsuccessful overexpression experiments carried out to increase 
 the flux or metabolites of a metabolic pathway , modeling may allow for a more 
 focused and appropriate design of experimental strategies of genetic 
 engineering to increase flux or a given metabolite , and for selecting drug 
 targets to decrease flux or metabolite concentration . for these predictions , modeling considers 
 that overexpression of a controlling enzyme or transporter may promote flux or 
 metabolite control redistributions . 
 
thus , a low - control step may become a 
 controlling point when overexpressing another step and , in consequence , the 
 prediction shown in figure 10 based on ( 11 ) and ( 12 ) may be inaccurate . by considering the whole pathway components , 

modeling is also a powerful tool for predicting the effects on flux and 
 metabolite concentration of varying an enzyme activity ( by overexpression or 
 drug inhibition ) .
model predictions to inhibit a pathway fluxkinetic modeling has been used to identify the flux controlling steps in trypanosoma 
 brucei glycolysis for drug targeting purposes .
interestingly , modeling has predicted 
 controlling steps for the parasite pathway different from those described for 
 glycolysis in human host cells [ 125 , 126 ] . 

the parasite lacks functional 
 mitochondria and has neither krebs cycle nor oxphos enzyme activities .
therefore , 
 substrate level phosphorylation by glycolysis is the only way to generate atp 
 for cellular work .
an important 
 difference in amebal glycolysis in comparison to glycolysis in human cells is 
 that it contains the pyrophosphate ( ppi)-dependent enzymes phosphofructokinase 
 ( ppi - pfk ) and pyruvate phosphate dikinase ( ppdk ) , which replace the highly 
 modulated atp - pfk and pyk present in human cells .
moreover , both have been 
 proposed as drug targets by using ppi analogues ( bisphosphonates ) .we recently described the 
 construction of a kinetic model of e. histolytica glycolysis to 
 determine the control distribution of this energetically important pathway in 
 the parasite .
the model was 
 constructed using the gepasi software and was based on the kinetic parameters 
 determined in the purified recombinant enzymes , as well as the enzyme 
 activities , fluxes , and metabolite concentrations found in the parasite .
the results of the 
 metabolic control analysis 
 indicated that hk and pgam are the main flux control steps of the pathway ( 73 
 and 65% , resp . ) and perhaps glut . in 
 contrast
, the ppi - pfk and ppdk displayed low flux control ( 13 and 0.1% , resp . ) 
 because they have overcapacity over the glycolytic flux .
the amebal model allowed evaluating the 
 effect on flux of  inhibiting  the pathway enzymes .
the model predicted that in order to diminish 
 by 50% the glycolytic flux ( and the atp concentration ; data not shown ) , hk and 
 pgam should be inhibited by 24 and 55% , respectively , or both enzymes by 18% 
 ( figure 11 ) .
in contrast , to attain the 
 same reduction in flux by inhibiting ppi - pfk and ppdk , they should be decreased 
 > 70% ( figure 11 ) .
therefore , the 
 kinetic model results indicate that hk can be an appropriate drug target 
 because its specific inhibition can compromise the energy levels in the 
 parasite .
they also indicate that although 
 ppi - pfk and ppdk remain as promising drug targets because of their divergence 
 from the human glycolytic enzymes , highly potent and very specific inhibitors 
 should be designed for these enzymes in order to affect the parasite 's energy 
 metabolism .
kinetic modeling has been used to identify the flux controlling steps in trypanosoma 
 brucei glycolysis for drug targeting purposes .
interestingly , modeling has predicted 
 controlling steps for the parasite pathway different from those described for 
 glycolysis in human host cells [ 125 , 126 ] . 

the parasite lacks functional 
 mitochondria and has neither krebs cycle nor oxphos enzyme activities .
therefore , 
 substrate level phosphorylation by glycolysis is the only way to generate atp 
 for cellular work .
an important 
 difference in amebal glycolysis in comparison to glycolysis in human cells is 
 that it contains the pyrophosphate ( ppi)-dependent enzymes phosphofructokinase 
 ( ppi - pfk ) and pyruvate phosphate dikinase ( ppdk ) , which replace the highly 
 modulated atp - pfk and pyk present in human cells .
moreover , both have been 
 proposed as drug targets by using ppi analogues ( bisphosphonates ) .
we recently described the 
 construction of a kinetic model of e. histolytica glycolysis to 
 determine the control distribution of this energetically important pathway in 
 the parasite .
the model was 
 constructed using the gepasi software and was based on the kinetic parameters 
 determined in the purified recombinant enzymes , as well as the enzyme 
 activities , fluxes , and metabolite concentrations found in the parasite .
the results of the 
 metabolic control analysis 
 indicated that hk and pgam are the main flux control steps of the pathway ( 73 
 and 65% , resp . ) and perhaps glut . in 
 contrast
, the ppi - pfk and ppdk displayed low flux control ( 13 and 0.1% , resp . ) 
 because they have overcapacity over the glycolytic flux .
the amebal model allowed evaluating the 
 effect on flux of  inhibiting  the pathway enzymes .
the model predicted that in order to diminish 
 by 50% the glycolytic flux ( and the atp concentration ; data not shown ) , hk and 
 pgam should be inhibited by 24 and 55% , respectively , or both enzymes by 18% 
 ( figure 11 ) .
in contrast , to attain the 
 same reduction in flux by inhibiting ppi - pfk and ppdk , they should be decreased 
 > 70% ( figure 11 ) .
therefore , the 
 kinetic model results indicate that hk can be an appropriate drug target 
 because its specific inhibition can compromise the energy levels in the 
 parasite .
they also indicate that although 
 ppi - pfk and ppdk remain as promising drug targets because of their divergence 
 from the human glycolytic enzymes , highly potent and very specific inhibitors 
 should be designed for these enzymes in order to affect the parasite 's energy 
 metabolism .
another experimental approach 
 for determining the enzyme control coefficients is the in vitro reconstitution 
 of segments of metabolic pathways .
it is 
 recalled that for determining the flux control coefficient exerted by a given 
 step on a metabolic pathway the enzyme activity has to be varied , without 
 altering the other components in the system , and the flux variations are to be 
 measured ( figure 4 ) .
such an experiment can be readily made if a pathway is 
 reconstituted with purified enzymes .
some advantages of this approach are that the 
 pathway structure is known , in which the components concentration may be 
 manipulated and analyzed separately , and the enzyme effectors can be assayed .
as 
 the system composition is strictly controlled , the results may be highly 
 reproducible .
the main disadvantage is 
 that the enzyme concentrations in the assays are diluted and thus the enzyme 
 interactions are not favored . if this interaction 
 is important for activity , the in vitro reconstitution may limit the 
 extrapolation to the metabolic pathway inside the cell .
there are not many studies 
 describing this type of experiments , most probably due to the fact that for 
 applying mca the pathway must be working under steady - state conditions . in a reconstituted system
, only a quasi steady 
 state may be reached because there is net substrate , and cofactors consumption , 
 as well as product accumulation , since it is difficult to attain a constant 
 substrate supply and release of products .
one of the first experimental 
 reports on control coefficient determination in a reconstituted system was 
 carried out for the upper glycolytic segment with the commercially available 
 rabbit muscle hk , hpi , pfk-1 , aldo , and tpi .
each enzyme was separately titrated and the 
 flux variation to glycerol-3-phosphate ( by coupling the reconstituted system to 
 an excess of -gpdh ) was measured in the presence of ck to maintain 
 the atp concentration constant .
the results showed that pfk-1 and hk exerted the 
 main flux control ( 65% and 20% , resp . ) , whereas the remaining 15% resided in 
 the other enzymes .
these authors observed that the addition of f1,6bp , a pfk-1 
 activator slightly diminished the flux control exerted by pfk-1 and increases 
 that of hk .
the lower glycolytic segment 
 has also been reconstituted with commercial enzymes for determining the flux 
 control coefficients .
the results 
 showed that flux was mainly controlled by pyk ( 60100% ) , although under some 
 conditions control was shared with pgam ; eno did not contribute to the flux 
 control .
another important limitation 
 of the reconstitution experiments is that the commercial availability of the 
 purified enzymes from the same organism is restricted or inexistent .
however , by using the information from the 
 genome sequence projects and the recombinant dna technology , it is now possible 
 to access all the enzyme genes from a metabolic pathway in the same organism , thus 
 facilitating their cloning , overexpression , and purification . with this strategy ,
we cloned , overexpressed , 
 and purified the 10 glycolytic enzymes of entamoeba histolytica   for 
 studying the flux control distribution in this organism by using kinetic 
 modeling   and pathway reconstitution .
the reconstitution 
 experiments of the lower amebal glycolytic segment , under near physiological 
 conditions of ph , temperature , and enzyme activity ( figure 12 ) showed that pgam 
 and , to a lesser extent , ppdk exert the main flux control ( these amebal enzymes 
 are genetically and kinetically different from their human counterparts ) with 
 eno exhibiting negligible control . in turn , reconstitution of the upper amebal 
 glycolytic segment has revealed that hk and , to a much lesser extent hpi , 
 ppi - pfk , and ald , exerted the main flux control , with tpi having negligible 
 control .
these results strongly 
 correlate with the enzyme catalytic efficiencies previously reported , in 
 which hk is highly sensitive to amp inhibition , ald , and pgam have the lowest 
 catalytic efficiencies among the glycolytic enzymes , leading to high flux control 
 coefficients and thus becoming suitable candidates for therapeutic 
 intervention .
the reconstitution results 
 also agree with the pathway modeling predictions previously analyzed ( section 
 5.4 ) , in which hk and pgam are two of the main controlling steps .
the in vitro reconstitution 
 experiments are also useful for studying the effect on control redistribution of 
 an enzyme modulation that is particularly difficult to manage in vivo ; the main controlling steps 
 identified with the reconstitution experiments should be further analyzed with 
 other experimental strategies such as elasticity analysis in the in vivo 
 systems .
this experimental approach for determining the control coefficients could be part of 
 the genetic approach analyzed in section 5.1 , but it was separated due to its 
 recent methodological development and because it actually belongs to the 
 molecular genetics rather than to the mendelian genetics .
this approach is based on the in vivo modulation of the enzyme levels using the rna 
 antisense technology .
there are at least 
 three strategies to 
 inhibit gene expression : ( a ) the use of single stranded antisense 
 oligonucleotides , which form a double stranded rna that might be degraded by rnase 
 h ; ( b ) target rna degradation with catalytically active oligonucleotides , known 
 as ribozymes that bind to their specific rna ; and ( c ) rna degradation using sirnas 
 ( 2123 nucleotides ) .
the rna antisense technology was applied for control coefficient determination of the 
 ribulose - bisphosphate - carboxylase ( rubisco ) that fixes co2 in the 
 plant calvin cycle .
this enzyme considered 
 the rate - limiting step of the calvin cycle and of the whole photosynthetic 
 process , despite its high concentration ( 4 mm ) in the chloroplasts stroma that compensates 
 its low catalytic efficiency .
attempts to make rubisco a nonlimiting step , either by modifying its catalytic efficiency 
 or by overexpressing it , have been unsuccessful .
the plants were transformed with dna antisense against the 
 mrna of the enzyme 's small subunit , thus promoting its degradation . for calvin cycle enzymes , the pleiotropic 
 effects were minimal .
the results showed 
 that rubisco may indeed be the photosynthesis limiting step with a crubisco = 0.690.83 when plants are exposed to high 
 illumination ( 1050 mol quanta ms ) , high 
 humidity ( 85% ) , and low co2 concentrations ( 25 pa ) .
however , this flux control decreases to 
 0.050.12 under moderate illumination or high co2 levels .
unfortunately , the authors did not determine 
 the control coefficients of the other pathway enzymes or the branches fluxes which 
 may be significant .
as described in section 5.4 , the results of the t. brucei glycolysis 
 modeling indicated that glut was the main flux control step ( cglut  50% ) , [ 125 , 126 ] .
this model predicted a large overcapacity for 
 hk , pfk-1 , aldo , gapdh , pgam , eno , and pyk over the glycolytic flux leading to 
 low flux control coefficients [ 125 , 126 ] . to validate the modeling results , the concentrations of hk , pfk-1 , pgam , 
 eno , and pyk
these knockdown expression experiments showed 
 overcapacity of hk and pyk over the flux , although at lower levels than predicted 
 by the model . a good correlation for 
 pgam and eno
was obtained between model predictions and experimental results . however , a large difference ( 9 folds ) was 
 obtained for pfk-1 .
this discrepancy is 
 perhaps related to pleiotropic effects of pfk-1 downregulation , as these mutants 
 also displayed diminution in the activities of other enzymes ( hk , eno , and pyk ) . 
 
the combination of these two approaches , 
 in silico modeling and in vivo experimentation , is complementary : on one 
 hand , modeling identifies the enzymes ( out of 19 that contain the model ) that 
 display the highest flux control coefficients , whereas in vivo experimentation validates the 
 accuracy of the model to establish predictions about the pathway 's behavior .
the knockdown experiments described above usually yield only two experimental points 
 of the plot shown in figure 4 : the 
 wild - type and the knockdown strain protein levels or enzyme activities .
thus , with 
 such an approach high levels of inhibition ( > 80% ) are mostly analyzed , 
 whereas intermediate levels of downregulation ( if obtained ) are generally 
 overlooked .
therefore , knockdown 
 experiments are not very useful to obtain the complete set of experimental data 
 ( above and below the wild - type levels of enzyme activity with the corresponding 
 flux ) for determining reliable control coefficients . a strategy to determine flux 
 control coefficients from several protein levels
has been developed by using 
 adenovirus - mediated glucose-6-phosphatase ( g6pase ) overexpression under the 
 control of the cytomegalovirus promoter in rat hepatocytes .
a 2-fold g6pase overexpression did not alter cg6pase or cgk ( gk , glucokinase ) .
however , if g6pase is overexpressed by 4 folds , then cgk 
 diminished from 2.8 to 1.8 and there was a 35% lowering in glycogen synthesis .
however , this approach allows titration of flux only above the basal 
 enzyme activities found in the cell , but not below .
these experimental inconveniences have been circumvented by using inducible gene 
 expression systems based in the lac , 
 lambda , nisin , gal , tetracycline , and other inducible promoters , in bacteria 
 and yeast [ 151 , 152 ] . however , a problem 
 frequently encountered with inducible promoters is that a steady - state of 
 protein expression is difficult to attain [ 151 , 152 ] .  
recently , 
 jensen and hammer described the design of synthetic promoter libraries ( spl ) , in 
 particular for l. lactis metabolic 
 optimization .
these promoters 
 maintain constant the array of the known consensus sequences for l. lactis gene transcription ( 10 and 
 35 boxes ) , while the nucleotide sequence between these boxes ( a spacer 
 sequence of 17  1 bp ) is randomized , thus producing a set of promoters with 
 different transcriptional strength .
these promoter libraries allow the transcription and protein expression 
 several folds above and below the wild - type levels of enzyme activity , 
 thus enhancing the usefulness of this approach for mca studies .
the 
 control distribution of glycolysis in e. 
 coli and l. lactis , as discussed 
 in section 3.2 [ 17 , 24 , 27 , 151 ] , has been determined by using the spl 
 technology . spl for yeast , mammalian and 
 plant cells are also under development [ 151 , 152 ] .
certainly , the advances in genetic 
 engineering in combination with mca allow better experimental designs for 
 metabolic optimization of micro - organisms of biotechnological interest .
concluding remarks 
 the frequently recurred idea of manipulating the key 
 enzyme or rate - limiting step ( a concept based on a qualitative and rather 
 intuitive background ) to change metabolism is incorrect .
as mca has demonstrated , flux control is shared 
 by multiple steps and it is not usually localized in only one step .
mca determines quantitatively the control that 
 a given enzyme exerts on the flux and on intermediary concentration and helps 
 to explain why an enzyme does or does not exert control .
a metabolic pathway is manipulated to change the rate 
 of the end - product formation ( i.e. , 
 the flux ) or the concentration of a relevant intermediary . as it is demonstrated in many unsuccessful 
 experiments ,
it is not enough to overexpress one enzyme ( the rate - limiting step ) 
 or many arbitrarily selected sites of the pathway .
mca proposes an initial experimental analysis 
 that determines the structural control of the pathway and identifies the sites 
 ( enzymes and transporters ) with higher control coefficients values ( i.e. , targets to be manipulated ) .
for example , if there is a system composed of 
 six enzymes and three of them have flux control coefficients with values of 0.2 
 or higher and the other three with values of 0.1 or lower , the three enzymes 
 with high control coefficients must be overexpressed ( if a flux increase is 
 desired ) or repressed ( if flux inhibition is the objective ) and not only one of 
 them .
if one of the selected enzymes is 
 strongly inhibited by its product or has allosteric inhibition , the overexpression 
 of this enzyme might not be enough to increase the flux , as it may also be 
 necessary to moderately vary the product and allosteric modulator consuming 
 enzymes.if the aim of the researcher is a metabolite 
 concentration increase , which is not the end product of the pathway , mca 
 suggests the overexpression of those enzymes or transporters in the supply 
 block with the highest control coefficients and/or the repression of those 
 enzymes in the demand block with the highest control coefficients .
these manipulations may become complicated if 
 the metabolite of interest has allosteric interactions with enzymes and 
 transporters ( inhibition and activation ) of both the supply and demand blocks .
it is recalled that ethanol production in 
 yeast and lactate and acetate production in lactobacteria do not increase by 
 overexpressing pfk-1 , an allosteric enzyme and the presumed rate - limiting step 
 of glycolysis .
however , the analysis of these results reveals 
 that the f1,6bp concentration is indeed increased many times over the control 
 level . another strategy for eliminating 
 the feedback inhibition might be the introduction of mutations on the enzymes 
 that are closer to the metabolite of interest . 
 

the frequently recurred idea of manipulating the key 
 enzyme or rate - limiting step ( a concept based on a qualitative and rather 
 intuitive background ) to change metabolism is incorrect . as mca has demonstrated , flux control is shared 
 by multiple steps and it is not usually localized in only one step .
mca determines quantitatively the control that 
 a given enzyme exerts on the flux and on intermediary concentration and helps 
 to explain why an enzyme does or does not exert control .
a metabolic pathway is manipulated to change the rate 
 of the end - product formation ( i.e. , 
 the flux ) or the concentration of a relevant intermediary . as it is demonstrated in many unsuccessful 
 experiments ,
it is not enough to overexpress one enzyme ( the rate - limiting step ) 
 or many arbitrarily selected sites of the pathway .
mca proposes an initial experimental analysis 
 that determines the structural control of the pathway and identifies the sites 
 ( enzymes and transporters ) with higher control coefficients values ( i.e. , targets to be manipulated ) .
for example , if there is a system composed of 
 six enzymes and three of them have flux control coefficients with values of 0.2 
 or higher and the other three with values of 0.1 or lower , the three enzymes 
 with high control coefficients must be overexpressed ( if a flux increase is 
 desired ) or repressed ( if flux inhibition is the objective ) and not only one of 
 them .
if one of the selected enzymes is 
 strongly inhibited by its product or has allosteric inhibition , the overexpression 
 of this enzyme might not be enough to increase the flux , as it may also be 
 necessary to moderately vary the product and allosteric modulator consuming 
 enzymes.if the aim of the researcher is a metabolite 
 concentration increase , which is not the end product of the pathway , mca 
 suggests the overexpression of those enzymes or transporters in the supply 
 block with the highest control coefficients and/or the repression of those 
 enzymes in the demand block with the highest control coefficients .
these manipulations may become complicated if 
 the metabolite of interest has allosteric interactions with enzymes and 
 transporters ( inhibition and activation ) of both the supply and demand blocks .
it is recalled that ethanol production in 
 yeast and lactate and acetate production in lactobacteria do not increase by 
 overexpressing pfk-1 , an allosteric enzyme and the presumed rate - limiting step 
 of glycolysis .
however , the analysis of these results reveals 
 that the f1,6bp concentration is indeed increased many times over the control 
 level . another strategy for eliminating 
 the feedback inhibition might be the introduction of mutations on the enzymes 
 that are closer to the metabolite of interest . 
 
the frequently recurred idea of manipulating the key 
 enzyme or rate - limiting step ( a concept based on a qualitative and rather 
 intuitive background ) to change metabolism is incorrect . as mca has demonstrated , flux control is shared 
 by multiple steps and it is not usually localized in only one step .
mca determines quantitatively the control that 
 a given enzyme exerts on the flux and on intermediary concentration and helps 
 to explain why an enzyme does or does not exert control .  
a metabolic pathway is manipulated to change the rate 
 of the end - product formation ( i.e. , 
 the flux ) or the concentration of a relevant intermediary . as it is demonstrated in many unsuccessful 
 experiments ,
it is not enough to overexpress one enzyme ( the rate - limiting step ) 
 or many arbitrarily selected sites of the pathway .
mca proposes an initial experimental analysis 
 that determines the structural control of the pathway and identifies the sites 
 ( enzymes and transporters ) with higher control coefficients values ( i.e. , targets to be manipulated ) .
for example , if there is a system composed of 
 six enzymes and three of them have flux control coefficients with values of 0.2 
 or higher and the other three with values of 0.1 or lower , the three enzymes 
 with high control coefficients must be overexpressed ( if a flux increase is 
 desired ) or repressed ( if flux inhibition is the objective ) and not only one of 
 them .
if one of the selected enzymes is 
 strongly inhibited by its product or has allosteric inhibition , the overexpression 
 of this enzyme might not be enough to increase the flux , as it may also be 
 necessary to moderately vary the product and allosteric modulator consuming 
 enzymes .
if the aim of the researcher is a metabolite 
 concentration increase , which is not the end product of the pathway , mca 
 suggests the overexpression of those enzymes or transporters in the supply 
 block with the highest control coefficients and/or the repression of those 
 enzymes in the demand block with the highest control coefficients .
these manipulations may become complicated if 
 the metabolite of interest has allosteric interactions with enzymes and 
 transporters ( inhibition and activation ) of both the supply and demand blocks .
it is recalled that ethanol production in 
 yeast and lactate and acetate production in lactobacteria do not increase by 
 overexpressing pfk-1 , an allosteric enzyme and the presumed rate - limiting step 
 of glycolysis .
however , the analysis of these results reveals 
 that the f1,6bp concentration is indeed increased many times over the control 
 level . another strategy for eliminating 
 the feedback inhibition might be the introduction of mutations on the enzymes 
 that are closer to the metabolite of interest .
   the traditional experimental approaches used for changing the flux or the concentration of a particular metabolite of a metabolic pathway have been mostly based on the inhibition or over - expression of the presumed rate - limiting step .   
 however , the attempts to manipulate a metabolic pathway by following such approach have proved to be unsuccessful .   
 metabolic control analysis ( mca ) establishes how to determine , quantitatively , the degree of control that a given enzyme exerts on flux and on the concentration of metabolites , thus substituting the intuitive , qualitative concept of rate limiting step .   
 moreover , mca helps to understand ( i ) the underlying mechanisms by which a given enzyme exerts high or low control and ( ii ) why the control of the pathway is shared by several pathway enzymes and transporters .   by applying mca 
 it is possible to identify the steps that should be modified to achieve a successful alteration of flux or metabolite concentration in pathways of biotechnological ( e.g. , large scale metabolite production ) or clinical relevance ( e.g. , drug therapy ) .   
 the different mca experimental approaches developed for the determination of the flux - control distribution in several pathways are described .   
 full understanding of the pathway properties when is working under a variety of conditions can help to attain a successful manipulation of flux and metabolite concentration . 
1. INTRODUCTION
2. CONTROLLING SITES IN A METABOLIC PATHWAY
3. IN VIVO OVEREXPRESSION EXPERIMENTS  OF ENZYMES
4. DOWNREGULATION OF ENZYMES TO  MANIPULATE METABOLISM
5. THEORY OF METABOLIC CONTROL ANALYSIS