Matrix method for determining steps most rate-limiting to metabolic fluxes in biotechnological processes

The metabolic control theory developed by Kacser, Burns, Heinrich, and Rapoport is briefly outlined, extended, and transformed so as optimally to address some biotechnological questions. The extensions include (i) a new theorem that relates the control of metabolite concentrations by enzyme activities to flux ratios at branches in metabolic pathways; (ii) a new theorem that does the same for the control of the distribution of the flux over two branches; (iii) a method that expresses these controls into properties (the so-called elasticity coefficients) of the enzymes in the pathway; and (iv) a theorem that relates the effects of changes in metabolite concentrations on reaction rates to the effects of changes in enzyme properties on the same rates. Matrix equations relating the flux control and concentration control coefficients to the elasticity coefficients of enzymes in simple linear and branched pathways incorporating feedback are given, together with their general solutions and a numerical example. These equations allow one to develop rigorous criteria by which to decide the optimal strategy for the improvement of a microbial process. We show how this could be used in deciding which property of which enzyme should be changed in order to obtain the maximal concentration of a metabolite or the maximal metabolic flux.     

Inherent properties of adenylosuccinate lyase could explain S-Ado/SAICAr ratio due to homozygous R426H and R303C mutations

Adenylosuccinate lyase (ADSL) is a homotetrameric enzyme involved in the de novo purine biosynthesis pathway and purine nucleotide cycle. Missense mutations in the protein lead to ADSL deficiency, an inborn error of purine metabolism characterized by neurological and physiological symptoms. ADSL deficiency is biochemically diagnosed by elevated levels of succinylaminoimidazolecarboxamide riboside (SAICAr) and succinyladenosine (S-Ado), the dephosphorylated derivatives of the substrates. S-Ado/SAICAr ratios have been associated with three phenotypic groups. Different hypotheses to explain these ratios have been proposed. Recent studies have focused on measuring activity on the substrates independently. However, it is important to examine mixtures of the substrates to determine if mutations affect enzyme activity on both substrates similarly in these conditions. The two substrates may experience an indirect communication due to being acted upon by the same enzyme, altering their activities from the non-competitive case. In this study, we investigate this hidden coupling between the two substrates. We chose two mutations that represent extremes of the phenotype, R426H and R303C. We describe a novel electrochemical-detection method of measuring the kinetic activity of ADSL in solution with its two substrates at varying concentration ratios. Furthermore, we develop an enzyme kinetic model to predict substrate activity from a given ratio of substrate concentrations. Our findings indicate a non-linear dependence of the activities on the substrate ratios due to competitive binding, distinct differences in the behaviors of the different mutations, and S-Ado/SAICAr ratios in patients could be explained by inherent properties of the mutant enzyme.     

The mechanism of rabbit muscle phosphofructokinase at pH8.

The mechanism of rabbit muscle phosphofructokinase was investigated by measurement of fluxes, isotope trapping and steady-state velocities at pH8 in triethanolamine/HCl buffer with 4 mM free Mg2+. Most observations were made at I0.2. The ratio Flux of fructose 1,6-bisphosphate----fructose 6-phosphate/Flux of fructose 1,6-bisphosphate----ATP at zero ATP concentration increased hyperbolically from unity to about 3.2 as the concentration of fructose 6-phosphate was increased. Similarly, the ratio Flux of fructose 1,6-bisphosphate----ATP/Flux of fructose 1,6-bisphosphate----fructose 6-phosphate at zero fructose 6-phosphate concentration increased from unity to about 1.4 as the concentration of ATP was increased. The addition of substrates must therefore be random, whatever the other aspects of the reaction. Further, from the plateau values of the ratios, it follows that the substrates dissociate very infrequently from the ternary complex and that at a low substrate concentration 72% of the reaction follows the pathway in which ATP adds first to the enzyme. Isotope-trapping studies with [32P]ATP confirmed that ATP can bind first to the enzyme in rate-limiting step and that dissociation of ATP from the ternary complex is slow in relation to the forward reaction. No isotope trapping of [U-14C]-fructose 6-phosphate could be demonstrated. The ratios Flux of ATP----fructose 1,6-bisphosphate/Flux of ATP----ADP measured at zero ADP concentration and the reciprocal of the ratio measured at zero fructose 1,6-bisphosphate concentration did not differ significantly from unity. Calculated values for these ratios based on the kinetics of the reverse reaction and assuming ordered dissociations of products or a ping-pong mechanism gave values very significantly greater than unity. These findings exclude an ordered dissociation or a substantial contribution from a ping-pong mechanism, and it is concluded that the reaction is sequential and that dissociation of products is random. Rate constants were calculated for the steps in the enzyme reaction. The results indicate a considerable degree of co-operativity in the binding between the two substrates. The observations on phosphofructokinase are discussed in relation to methods of measurement and interpretation of flux ratios and in relation to the mechanism of other kinase enzymes.     

Substrate flux through methylenetetrahydrofolate dehydrogenase: predicted effects of the concentration of methylenetetrahydrofolate on its partitioning into pathways leading to nucleotide biosynthesis or methionine regeneration

Folic acid exists in mammalian cells with a poly-gamma-glutamate tail that may regulate the flux of folates through the various cellular pathways. The substrate polyglutamate specificity of methylenetetrahydrofolate dehydrogenase from pig liver has been examined by using a competitive method and measuring apparent tritium kinetic isotope effects on Vmax/Km for methylenetetrahydrofolate. This competitive method yields very accurate ratios of Km values for alternate substrates of an enzyme and may also be applied to reactions with no isotope effect. In combination with published data from our own and other laboratories, the kinetic parameters of methylenetetrahydrofolate dehydrogenase were used to calculate the initial velocities of pig liver methylenetetrahydrofolate dehydrogenase, thymidylate synthase, and methylenetetrahydrofolate reductase, at physiological concentrations of substrates and enzymes. These calculations suggest that the cellular concentration of methylenetetrahydrofolate may regulate the flux of this metabolite into the pathways leading to nucleotide biosynthesis and methionine regeneration. An increase in the cellular level of methylenetetrahydrofolate would permit more one-carbon units to be directed toward nucleotide biosynthesis.     

Effect of a pyruvate kinase (pykF-gene) knockout mutation on the control of gene expression and metabolic fluxes in Escherichia coli

The metabolic regulation of Escherichia coli lacking a functional pykF gene was investigated based on gene expressions, enzyme activities, intracellular metabolite concentrations and the metabolic flux distribution obtained based on (13)C-labeling experiments. RT-PCR revealed that the glycolytic genes such as glk, pgi, pfkA and tpiA were down regulated, that ppc, pckA, maeB and mdh genes were strongly up-regulated, and that the oxidative pentose phosphate pathway genes such as zwf and gnd were significantly up-regulated in the pykF mutant. The catabolite repressor/activator gene fruR was up-regulated in the pykF mutant, but the adenylate cyclase gene cyaA was down-regulated indicating a decreased rate of glucose uptake. This was also ascertained by the degradation of ptsG mRNA, the gene for which was down-regulated in the pykF mutant. In general, the changes in enzyme activities more or less correlated with ratios of gene expression, while the changes in metabolic fluxes did not correlate with enzyme activities. For example, high flux ratios were obtained through the oxidative pentose phosphate pathway due to an increased concentration of glucose-6-phosphate rather than to favorable enzyme activity ratios. In contrast, due to decreased availability of pyruvate (and acetyl coenzyme A) in the pykF mutant compared with the wild type, low flux ratios were found through lactate and acetate forming pathways.     

Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells

A mathematical model of glycolysis in human erythrocytes is proposed to study the influence of a pyruvate kinase deficiency on the energy metabolism. The model takes into account the main regulatory properties of the non-equilibrium enzymes and the magnesium-complex formation by the adenine nucleotides and by 2,3-bisphosphoglycerate. In the normal case (no enzyme defect) the calculated flux rates and metabolite concentrations are in a good agreement with experimental data. It is shown that a severe pyruvate kinase deficiency manifested in a tenfold diminished activity of that enzyme leads to a remarkable decrease of the glycolytic flux and the ATP concentration of about 50% of the normal values. On the other hand a lowering of the pyruvate kinase activity to half of the normal value, characteristic for the heterozygotes, gives no significant alterations of the metabolite concentrations and the flux rates compared with the normal case which is in accordance with the lack of clinical symptoms for a metabolic disease of these probands. For three patients with known alterations of their pyruvate kinase mutants the calculated metabolite concentrations and the control characteristics permit estimation of the degree of disorder of the glycolytic pathway. The resulting classification corresponds well to other independent experimental and clinical findings. In particular, the calculation demonstrates that there is no simple correlation between the lowered enzyme activity and the reduced flux rate through the affected pathway.     

Aerobic adaptation in yeast, IV. Alterations in enzyme synthesis during anaerobic-aerobic transitions in exponentially growing cultures.

As a corollary to the metabolite data obtained from yeast cultures undergoing an exponential anaerobic-aerobic phase transition, levels of various glycolytic and citric acid cycle enzyme activities have been monitored in these cells. The relation of the changes in these enzyme activities in cells grown on either glucose or galactose is discussed on light of different metabolic postures these cells demonstrate as a result of their transitions. A general discussion is presented which compares the results obtained in this series of papers from both step-down and exponential transfer experiments and relates these data to control of mitochondriogenesis in yeast.     

A simple mechanism decreasing free metabolite pool size in static spatial channelling

We propose a simple mechanism which enables decrease of the free pool of channelled metabolite in static spatial channelling, when the concentration of the enzyme consuming the channelled metabolite is greater than the concentration of the enzyme producing this metabolite. Spatial channelling occurs between two enzymes when the common metabolite is released to a small space between these enzymes and does not form a ternary covalent complex with them, as is the case in covalent (dynamic or static) channelling. The mechanism proposed is qualitatively independent of rate constants, metabolite concentrations as well as other kinetic properties and is quantitatively significant for all physiologically relevant conditions. Calculations show that the free metabolite pool must decrease, when the concentration of the enzyme consuming the channelled metabolite is greater than the enzyme producing it. This mechanism is much more effective than increase in the concentration (or rate constant) of the enzyme consuming the metabolite in the absence of spatial channelling.     

The Pharmacogenetic Footprint of ACE Inhibition: A Population-Based Metabolomics Study

Angiotensin-I-converting enzyme (ACE) inhibitors are an important class of antihypertensives whose action on the human organism is still not fully understood. Although it is known that ACE especially cleaves COOH-terminal dipeptides from active polypeptides, the whole range of substrates and products is still unknown. When analyzing the action of ACE inhibitors, effects of genetic variation on metabolism need to be considered since genetic variance in the ACE gene locus was found to be associated with ACE-concentration in blood as well as with changes in the metabolic profiles of a general population. To investigate the interactions between genetic variance at the ACE-locus and the influence of ACE-therapy on the metabolic status we analyzed 517 metabolites in 1,361 participants from the KORA F4 study. We replicated our results in 1,964 individuals from TwinsUK. We observed differences in the concentration of five dipeptides and three ratios of di- and oligopeptides between ACE inhibitor users and non-users that were genotype dependent. Such changes in the concentration affected major homozygotes, and to a lesser extent heterozygotes, while minor homozygotes showed no or only small changes in the metabolite status. Two of these resulting dipeptides, namely aspartylphenylalanine and phenylalanylserine, showed significant associations with blood pressure which qualifies them—and perhaps also the other dipeptides—as readouts of ACE-activity. Since so far ACE activity measurement is substrate specific due to the usage of only one oligopeptide, taking several dipeptides as potential products of ACE into account may provide a broader picture of the ACE activity.     

Use of flux ratio measurements for the determination of the order of addition of substrates and products in enzyme reactions.

1. Methods of determining the order of addition of substrates and dissociation of products by using flux ratios are investigated. Where an enzyme obeys hyperbolic steady-state velocity kinetics it is concluded that it may be particularly useful to compare the measured flux ratios with those calculated from the steady-state velocity parameters. 2. An expression is derived relating the relative contribution of the two pathways in a branched pathway to the flux ratios. 3. The relationship of equilibrium-reaction-rate measurements [Boyer & Silverstein (1963) Acta Chem. Scand. 17, Suppl. 1, S195] to the flux ratios is considered. Equilibrium-reaction rates are shown to be affected both by the addition of substrates and dissociation of products. Methods of analysing the data to distinguish between these events are discussed. 4. Methods of measurement of flux ratios are described, and it is concluded that the non-equilibrium steady-state method is preferable to measurements at chemical equilibrium. 5. The relative significance of flux ratio measurements and steady-state velocity inhibition data is discussed. It is concluded that flux ratios, when taken in conjunction with the inhibition data, provide the least ambiguous information about mechanism.     

Experimental and theoretical bases of specific affinity, a cytoarchitecture-based formulation of nutrient collection proposed to supercede the Michaelis-Menten paradigm of microbial kinetics

A theory for solute uptake by whole cells was derived with a focus on the ability of oligobacteria to sequester nutrients. It provided a general relationship that was used to obtain the kinetic constants for in situ marine populations in the presence of naturally occurring substrates. In situ affinities of 0.9 to 400 liters g of cells(-1) h(-1) found were up to 10(3) times smaller than those from a "Marinobacter arcticus " isolate, but springtime values were greatly increased by warming. Affinities of the isolate for usual polar substrates but not for hydrocarbons were diminished by ionophores. A kinetic curve or Monod plot was constructed from the best available data for cytoarchitectural components of the isolate by using the theory together with concepts and calculations from first principles. The order of effect of these components on specific affinity was membrane potential > cytoplasmic enzyme concentration > cytoplasmic enzyme affinity > permease concentration > area of the permease site > translation coefficient > porin concentration. Component balance was influential as well; a small increase in cytoplasmic enzyme concentration gave a large increase in the effect of permease concentration. The effect of permease concentration on specific affinity was large, while the effect on K(m) was small. These results are in contrast to the Michaelis-Menten theory as applied by Monod that has uptake kinetics dependent on the quality of the permease molecules, with K(m) as an independent measure of affinity. Calculations demonstrated that most oligobacteria in the environment must use multiple substrates simultaneously to attain sufficient energy and material for growth, a requirement consistent with communities largely comprising few species.     

The rationalization of high enzyme concentration in metabolic pathways such as glycolysis

The cellular concentration of enzymes of some major metabolic pathways, such as glycolysis, can approach millimolarity. This concentration of enzyme can catalyze in vitro rates which are 100-fold higher than maximum pathway flux. In an attempt to understand the need for such high enzyme concentration, an artificial metabolic pathway of five enzymes (apropos the central enzymes of glycolysis) has been modeled. Numerical methods were then used to determine the effect of enzyme concentration on: (1) the change in total free metabolite concentration as the pathway changes from low flux to high flux, (2) the time lag (transient time) in the rate of final product formation upon the transition from low flux to high flux. Both the changes in metabolite pool size and the transient time decreased with increased enzyme concentrations. When all enzymatic reactions were assigned Keq of unity, a concentration for each enzyme of 25 microM is sufficient to provide a transient time of 1 sec. When Keq different from unity are introduced, more enzyme is required to provide comparably short transient times. Under the latter condition, a pathway of sufficiently low transient time would require all the enzyme available in mammalian muscle. It is shown that there is little scope for further increases in either enzyme concentration or of catalytic efficiency of independent enzymes. Therefore, an alternative method of increasing efficiency is considered in which enzyme-bound metabolites can serve directly as substrates for subsequent enzymes in a metabolic pathway.     

Analysis of the compartmentation of glycolytic intermediates, nucleotides, sugars, organic acids, amino acids, and sugar alcohols in potato tubers using a nonaqueous fractionation method

The compartmentation of metabolism in heterotrophic plant tissues is poorly understood due to the lack of data on metabolite distributions and fluxes between subcellular organelles. The main reason for this is the lack of suitable experimental methods with which intracellular metabolism can be measured. Here, we describe a nonaqueous fractionation method that allows the subcellular distributions of metabolites in developing potato (Solanum tuberosum L. cv Desiree) tubers to be calculated. In addition, we have coupled this fractionation method to a recently described gas chromatography-mass spectrometry procedure that allows the measurement of a wide range of small metabolites. To calculate the subcellular metabolite concentrations, we have analyzed organelle volumes in growing potato tubers using electron microscopy. The relative volume distributions in tubers are very similar to the ones for source leaves. More than 60% of most sugars, sugar alcohols, organic acids, and amino acids were found in the vacuole, although the concentrations of these metabolites is often higher in the cytosol. Significant amounts of the substrates for starch biosynthesis, hexose phosphates, and ATP were found in the plastid. However, pyrophosphate was located almost exclusively in the cytosol. Calculation of the mass action ratios of sucrose synthase, UDP-glucose pyrophosphorylase, phosphoglucosisomerase, and phosphoglucomutase indicate that these enzymes are close to equilibrium in developing potato tubers. However, due to the low plastidic pyrophosphate concentration, the reaction catalyzed by ADP-glucose pyrophosphorylase was estimated to be far removed from equilibrium.     

Control of gluconeogenesis in rat liver cells. Flux control coefficients of the enzymes in the gluconeogenic pathway in the absence and presence of glucagon.

We have used control analysis to quantify the distribution of control in the gluconeogenic pathway in liver cells from starved rats. Lactate and pyruvate were used as gluconeogenic substrates. The flux control coefficients of the various enzymes in the gluconeogenic pathway were calculated from the elasticity coefficients of the enzymes towards their substrates and products and the fluxes through the different branches in the pathway. The elasticity coefficients were either calculated from gamma/Keq. ratios (where gamma is the mass-action ratio and Keq. is the equilibrium constant) and enzyme-kinetic data or measured experimentally. It is concluded that the gluconeogenic enzyme pyruvate carboxylase and the glycolytic enzyme pyruvate kinase play a central role in control of gluconeogenesis. If pyruvate kinase is inactive, gluconeogenic flux from lactate is largely controlled by pyruvate carboxylase. The low elasticity coefficient of pyruvate carboxylase towards its product oxaloacetate minimizes control by steps in the gluconeogenic pathway located after pyruvate carboxylase. This situation occurs when maximal gluconeogenic flux is required, i.e. in the presence of glucagon. In the absence of the hormone, when pyruvate kinase is active, control of gluconeogenesis is distributed among many steps, including pyruvate carboxylase, pyruvate kinase, fructose-1,6-bisphosphatase and also steps outside the classic gluconeogenic pathway such as the adenine-nucleotide translocator.     

Enzymatic production of linalool esters in organic and solvent-free system

This work investigated the influence of temperature, enzyme concentration, substrates molar ratio, in the absence and presence of organic solvent, at two molar ratios of the substrates on the enzymatic production of linalil esters using the immobilized lipase Novozym 435 as catalyst, different acids and linalool and Ho-Sho essential oil as substrates. The best reaction conversion was obtained at the highest temperature (70 °C), for both solvent free (3.81%) and with solvent addition (2.25%), for a solvent to substrates molar ratio of 2:1, enzyme concentration of 5 wt% and acid to alcohol molar ratio of 1:1. The reaction kinetics revealed that Ho-Sho essential oil afforded the greatest conversions when compared with pure linalool. Higher linalil esters production were achieved after 10 h reaction (5.58%) in 2:1 solvent to substrates molar ratio, with enzyme concentration of 5 wt%, at 70 °C and anhydride to alcohol molar ratio of 1:1 using Ho-Sho essential oil as substrate.     

Changes of pentose phosphate pathway flux in vivo in Corynebacterium glutamicum during leucine-limited batch cultivation as determined from intracellular metabolite concentration measurements

Corynebacterium glutamicum is an important organism for the industrial production of amino acids such as lysine. In the present study time-dependent changes in the oxidative pentose phosphate pathway activity, an important site of NADPH regeneration in C. glutamicum, are investigated, whereby intracellular metabolite concentrations and specific enzyme activities in two isogenic leucine auxotrophic strains differing only in the regulation of their aspartate kinases were compared. After leucine limitation only the strain with a feedback-resistant aspartate kinase began to excrete lysine into the culture medium. Concomitantly, the intracellular NADPH to NADP concentration ratio increased from 2 to 4 in the non-producing strain, whereas it remained constant at about 1.2 in the lysine-producing strain. From these data the in'vivo flux through the pentose phosphate pathway was calculated. These results were used to approximate the total NADPH regeneration by glucose-6-phosphate dehydrogenase, 6-phosphogluconate dehydrogenase and isocitrate dehydrogenase, which agreed fairly well with the calculated demands for biomass formation and lysine biosynthesis. The analysis allowed to conclude that NADPH regeneration in the pentose phosphate pathway is essential for lysine biosynthesis in C. glutamicum.     

Steady-state kinetics and spectral properties of Corynebacterium sarcosine oxidase

The overall reaction kinetics of Corynebacterium sarcosine oxidase were investigated and the reaction was shown to follow a ping-pong, bi-bi mechanism with two substrates, sarcosine and molecular oxygen. Sarcosine analogs, such as acetate, propionate and methoxyacetate, were competitive inhibitors of the reaction. Acetate caused characteristic alterations in optical and circular dichroic spectra, indicating that the microenvironment of the substrate-binding region of the enzyme increased in hydrophobicity on binding with the substrate analog. The dissociation constants of the analogs calculated from the spectral changes were in agreement with the kinetic inhibition constants. Inorganic metallic ions were also inhibitory. Of interest was the finding that the inhibition by Hg2+ was proportional to the square of its concentration, which suggests that at least two sulfhydryl groups are related to the catalytic activity of the enzyme.     

Stopped-flow analysis of substrate binding to neuronal nitric oxide synthase.

The kinetics of binding L-arginine and three alternative substrates (homoarginine, N-methylarginine, and N-hydroxyarginine) to neuronal nitric oxide synthase (nNOS) were characterized by conventional and stopped-flow spectroscopy. Because binding these substrates has only a small effect on the light absorbance spectrum of tetrahydrobiopterin-saturated nNOS, their binding was monitored by following displacement of imidazole, which displays a significant change in Soret absorbance from 427 to 398 nm. Rates of spectral change upon mixing Im-nNOS with increasing amounts of substrates were obtained and found to be monophasic in all cases. For each substrate, a plot of the apparent rate versus substrate concentration showed saturation at the higher concentrations. K(-)(1), k(2), k(-)(2), and the apparent dissociation constant were derived for each substrate from the kinetic data. The dissociation constants mostly agreed with those calculated from equilibrium spectral data obtained by titrating Im-nNOS with each substrate. We conclude that nNOS follows a two-step, reversible mechanism of substrate binding in which there is a rapid equilibrium between Im-nNOS and the substrate S followed by a slower isomerization process to generate nNOS'-S: Im-nNOS + S if Im-nNOS-S if nNOS'-S + Im. All four substrates followed this general mechanism, but differences in their kinetic values were significant and may contribute to their varying capacities to support NO synthesis.     

Substrate ground state binding energy concentration is realized as transition state stabilization in physiological enzyme catalysis

Previously published kinetic data on the interactions of seventeen different enzymes with their physiological substrates are re-examined in order to understand the connection between ground state binding energy and transition state stabilization of the enzyme-catalyzed reactions. When the substrate ground state binding energies are normalized by the substrate molar volumes, binding of the substrate to the enzyme active site may be thought of as an energy concentration interaction; that is, binding of the substrate ground state brings in a certain concentration of energy. When kinetic data of the enzyme/substrate interactions are analyzed from this point of view, the following relationships are discovered: 1) smaller substrates possess more binding energy concentrations than do larger substrates with the effect dropping off exponentially, 2) larger enzymes (relative to substrate size) bind both the ground and transition states more tightly than smaller enzymes, and 3) high substrate ground state binding energy concentration is associated with greater reaction transition state stabilization. It is proposed that these observations are inconsistent with the conventional (Haldane) view of enzyme catalysis and are better reconciled with the shifting specificity model for enzyme catalysis.     

Assessment of amino-acid substitutions at tryptophan 16 in alpha-galactosidase.

The tryptophan residue at position 16 of coffee bean alpha-galactosidase has previously been shown to be essential for enzyme activity. The potential role of this residue in the catalytic mechanism has been further studied by using site-directed mutagenesis to substitute every other amino acid for tryptophan at that site. Mutant enzymes were expressed in Pichia pastoris, a methylotrophic yeast strain, and their kinetic parameters were calculated. Only amino acids containing aromatic rings (phenylalanine and tyrosine) were able to support a significant amount of enzyme activity, but the kinetics and pH profiles of these mutants differed from wild-type. Substitution of arginine, lysine, methionine, or cysteine at position 16 allowed a small amount of enzyme activity with the optimal pH shifted towards more acidic. All other residues abolished enzyme activity. Our data support the hypothesis that tryptophan 16 is affecting the pKa of a carboxyl group at the active site that participates in catalysis. We also describe an assay for continuously measuring enzyme kinetics using fluorogenic 4-methylumbelliferyl substrates. This is useful in screening enzymes from colonies and determining the enzyme kinetics when the enzyme concentration is not known.