Bottleneck Enzyme Research Articles

Hepatocyte nuclear factor 4α mediated quinolinate phosphoribosylltransferase (QPRT) expression in the kidney facilitates resilience against acute kidney injury

Nicotinamide adenine dinucleotide (NAD+) levels decline in experimental models of acute kidney injury (AKI). Attenuated enzymatic conversion of tryptophan to NAD+ in tubular epithelium may contribute to adverse cellular and physiological outcomes. Mechanisms underlying defense of tryptophan-dependent NAD+ production are incompletely understood. Here we show that regulation of a bottleneck enzyme in this pathway, quinolinate phosphoribosyltransferase (QPRT) may contribute to kidney resilience. Expression of QPRT declined in two unrelated models of AKI. Haploinsufficient mice developed worse outcomes compared to littermate controls whereas novel, conditional gain-of-function mice were protected from injury. Applying these findings, we then identified hepatocyte nuclear factor 4 alpha (HNF4α) as a candidate transcription factor regulating QPRT expression downstream of the mitochondrial biogenesis regulator and NAD+ biosynthesis inducer PPARgamma coactivator-1-alpha (PGC1α). This was verified by chromatin immunoprecipitation. A PGC1α - HNF4α -QPRT axis controlled NAD+ levels across cellular compartments and modulated cellular ATP. These results propose that tryptophan-dependent NAD+ biosynthesis via QPRT and induced by HNF4α may be a critical determinant of kidney resilience to noxious stressors.

The cold receptor TRPM8, a new target against the aggravating effects of metabolic syndrome in heart failure with preserved ejection fraction

Heart failure with preserved ejection fraction (HFpEF) has nowadays become a major public health issue worldwide. HFpEF is usually associated with metabolic syndrome (MS) such as type II diabetes. A growing attention has been shed on Δ9-desaturase (SCD1), the bottleneck enzyme in the mono-desaturation of fatty acids. Indeed, SCD1 controls the balance between inflammation regulated by saturated lipids and weight gain regulated by unsaturated lipids. Targeting SCD1 looks an attractive strategy in limiting the deleterious effects of the MS and HFpEF. In our recent work, we found that isoforms of the cold receptor, TRPM8, control SCD1 expression in epithelial cells and we wonder if this mechanism could be used to prevent HFpEF. (1) To identify the mechanisms by which TRPM8 regulates SCD1 in cell models. (2) Study whether genetic or pharmacological inhibition of TRPM8 prevents MS and HFpEF. Epithelial cells were transfected by siRNA targeting TRPM8 then SCD1 expression was assessed by western blot. Golgi expansion was studied by immunofluorescence after transfection with SCD1-YFP. In vivo, we will finish the metabolic and cardiac phenotype of TRPM8-/- mice. Then we plan to feed wild type and TRPM8-/- mice with chow or high fat high sucrose diet for 16 weeks. Endurance test, blood chemistry, echocardiography will be done to assess development of HFpEF. Lipidomic analysis will assess changes in lipid profile between the 2 groups and inflammation will be assessed by ELISA and flow cytometry. In vitro studies: SCD1 expression has transiently increased upon TRPM8 knockdown in epithelial cells. This was associated with an increase in unsaturated lipids (MUFAs and PUFAs) that led to increase in the Golgi surface area and impairment of vesicles trafficking. Golgi expansion could be suppressed by SCD1 knockdown. In vivo studies, phenotyping the TRPM8-/- mouse line showed a lean phenotype, with modifications in lipid metabolism in liver characterized by a 50% decrease in SCD1 level and resistance to adipogenesis under a short-term high fat diet. Besides, TRPM8-/- mice were less fat and had a heavier heart. TRPM8 regulates the expression of SCD1, which is dysregulated in metabolic disorders. We aim to exploit this mechanism and study if TRPM8 inhibition can prevent MS and HFpEF.

Cell stress response impairs de novo NAD+ biosynthesis in the kidney.

The biosynthetic routes leading to de novo nicotinamide adenine dinucleotide (NAD+) production are involved in acute kidney injury (AKI), with a critical role for quinolinate phosphoribosyl transferase (QPRT), a bottleneck enzyme of de novo NAD+ biosynthesis. The molecular mechanisms determining reduced QPRT in AKI, and the role of impaired NAD+ biosynthesis in the progression to chronic kidney disease (CKD), are unknown. We demonstrate that a high urinary quinolinate-to-tryptophan ratio, an indirect indicator of impaired QPRT activity and reduced de novo NAD+ biosynthesis in the kidney, is a clinically applicable early marker of AKI after cardiac surgery and is predictive of progression to CKD in kidney transplant recipients. We also provide evidence that the endoplasmic reticulum (ER) stress response may impair de novo NAD+ biosynthesis by repressing QPRT transcription. In conclusion, NAD+ biosynthesis impairment is an early event in AKI embedded with the ER stress response, and persistent reduction of QPRT expression is associated with AKI to CKD progression. This finding may lead to identification of noninvasive metabolic biomarkers of kidney injury with prognostic and therapeutic implications.

Structure-based virtual screening, molecular dynamics simulation and in vitro evaluation to identify inhibitors against NAMPT

Nicotinamide phosphoribosyltransferase (NAMPT) is a bottleneck enzyme that plays a key role in recycling nicotinamide to maintain the adequate NAD + level inside the cell. It involves maintaining the cellular bioenergetics and providing a necessary substrate for functions essential to rapidly proliferating the cancer cells. Therefore, inhibition of NAMPT appears as a therapeutic potential for cancer treatment. Here, the vast virtual screening followed by focused docking and in-vitro analysis was carried out to identify the promising hits of NAMPT. We have identified two potential hits from the filtered molecules, which are chemically diverse and have shown comparable quantitative values with reported co-crystal ‘1QS’ as their binding pattern matched nicely. These two compounds are further explored through molecular dynamics simulations (MD) combined with pharmacokinetics profiling and thermodynamic analysis demonstrating their suitability as novel NAMPT inhibitors that can be used as starting points for a hit-to-lead campaign. Communicated by Ramaswamy H. Sarma

Recent Advances in NAMPT Inhibitors: A Novel Immunotherapic Strategy.

Nicotinamide adenine dinucleotide (NAD) is a cofactor of many enzymatic reactions as well as being a substrate for a number of NAD-consuming enzymes (e.g., PARPS, sirtuins, etc). NAD can be synthesized de novo starting from tryptophan, nicotinamide, nicotinic acid, or nicotinamide riboside from the diet. On the other hand, the nicotinamide that is liberated by NAD-consuming enzymes can be salvaged to re-form NAD. In this former instance, nicotinamide phosphoribosyltransferase (NAMPT) is the bottleneck enzyme. In the many cells in which the salvage pathway is predominant, NAMPT, therefore, represents an important controller of intracellular NAD concentrations, and as a consequence of energy metabolism. It is, therefore, not surprising that NAMPT is over expressed by tumoral cells, which take advantage from this to sustain growth rate and tumor progression. This has led to the initiation of numerous medicinal chemistry programs to develop NAMPT inhibitors in the context of oncology. More recently, however, it has been shown that NAMPT inhibitors do not solely target the tumor but also have an effect on the immune system. To add complexity, this enzyme can also be secreted by cells, and in the extracellular space it acts as a cytokine mainly through the activation of Toll like Receptor 4 (TLR4), although it has not been clarified yet if this is the only receptor responsible for its actions. While specific small molecules have been developed only against the intracellular form of NAMPT, growing evidences sustain the possibility to target the extracellular form. In this contribution, the most recent evidences on the medicinal chemistry of NAMPT will be reviewed, together with the key elements that sustain the hypothesis of NAMPT targeting and the drawbacks so far encountered.

NAMPT: A pleiotropic modulator of monocytes and macrophages

Nicotinamide phosphoribosyltransferase (NAMPT) is the bottleneck enzyme of the NAD salvage pathway and thereby is a controller of intracellular NAD concentrations. It has been long known that the same enzyme can be secreted by a number of cell types and acts as a cytokine, although its receptor is at present unknown. Investigational compounds have been developed that target the enzymatic activity as well as the extracellular action (i.e. neutralizing antibodies). The present contribution reviews the evidence that links intracellular and extracellular NAMPT to myeloid biology, for example governing monocyte/macrophage differentiation, polarization and migration. Furthermore, it reviews the evidence that links this protein to some disorders in which myeloid cells have a prominent role (acute infarct, inflammatory bowel disease, acute lung injury and rheumatoid arthritis) and the data showing that inhibition of the enzymatic activity or the neutralization of the cytokine is beneficial in preclinical animal models.

Metabolic engineering of a carbapenem antibiotic synthesis pathway in Escherichia coli.

Carbapenems, a family of β-lactam antibiotics, are among the most powerful bactericidal compounds in clinical use. However, as rational engineering of native carbapenem-producing microbes is not currently possible, the present carbapenem supply relies upon total chemical synthesis of artificial carbapenem derivatives. To enable access to the full diversity of natural carbapenems, we have engineered production of a simple carbapenem antibiotic within Escherichia coli. By increasing concentrations of precursor metabolites and identifying a reducing cofactor of a bottleneck enzyme, we improved productivity by 60-fold over the minimal pathway and surpassed reported titers obtained from carbapenem-producing Streptomyces species. We stabilized E. coli metabolism against antibacterial effects of the carbapenem product by artificially inhibiting membrane synthesis, which further increased antibiotic productivity. As all known naturally occurring carbapenems are derived from a common intermediate, our engineered strain provides a platform for biosynthesis of tailored carbapenem derivatives in a genetically tractable and fast-growing species.

Rational and combinatorial approaches to engineering styrene production by Saccharomyces cerevisiae.

BackgroundStyrene is an important building-block petrochemical and monomer used to produce numerous plastics. Whereas styrene bioproduction by Escherichia coli was previously reported, the long-term potential of this approach will ultimately rely on the use of hosts with improved industrial phenotypes, such as the yeast Saccharomyces cerevisiae.ResultsClassical metabolic evolution was first applied to isolate a mutant capable of phenylalanine over-production to 357 mg/L. Transcription analysis revealed up-regulation of several phenylalanine biosynthesis pathway genes including ARO3, encoding the bottleneck enzyme DAHP synthase. To catalyze the first pathway step, phenylalanine ammonia lyase encoded by PAL2 from A. thaliana was constitutively expressed from a high copy plasmid. The final pathway step, phenylacrylate decarboxylase, was catalyzed by the native FDC1. Expression of FDC1 was naturally induced by trans-cinnamate, the pathway intermediate and its substrate, at levels sufficient for ensuring flux through the pathway. Deletion of ARO10 to eliminate the competing Ehrlich pathway and expression of a feedback-resistant DAHP synthase encoded by ARO4K229L preserved and promoted the endogenous availability precursor phenylalanine, leading to improved pathway flux and styrene production. These systematic improvements allowed styrene titers to ultimately reach 29 mg/L at a glucose yield of 1.44 mg/g, a 60% improvement over the initial strain.ConclusionsThe potential of S. cerevisiae as a host for renewable styrene production has been demonstrated. Significant strain improvements, however, will ultimately be needed to achieve economical production levels.Electronic supplementary materialThe online version of this article (doi:10.1186/s12934-014-0123-2) contains supplementary material, which is available to authorized users.

Discovering Echinococcus granulosus thioredoxin glutathione reductase inhibitors through site-specific dynamic combinatorial chemistry

In this study, we report a strategy using dynamic combinatorial chemistry for targeting the thioredoxin (Trx)-reductase catalytic site on Trx glutathione reductase (TGR), a pyridine nucleotide thiol-disulfide oxido-reductase. We chose Echinococcus granulosus TGR since it is a bottleneck enzyme of platyhelminth parasites and a validated pharmacological target. A dynamic combinatorial library (DCL) was constructed based on thiol-disulfide reversible exchange. We demonstrate the use of 5-thio-2-nitrobenzoic acid (TNB) as a non-covalent anchor fragment in a DCL templated by E. granulosus TGR. The heterodimer of TNB and bisthiazolidine (2af) was identified, upon library analysis by HPLC (IC50 = 24 μM). Furthermore, 14 analogs were synthetically prepared and evaluated against TGR. This allowed the study of a structure-activity relationship and the identification of a disulfide TNB-tricyclic bisthiazolidine (2aj) as the best enzyme inhibitor in these series, with an IC50 = 24 μM. Thus, our results validate the use of DCL for targeting thiol-disulfide oxido-reductases.

The Crystal Structure and Mechanism of an Unusual Oxidoreductase, GilR, Involved in Gilvocarcin V Biosynthesis

GilR is a recently identified oxidoreductase that catalyzes the terminal step of gilvocarcin V biosynthesis and is a unique enzyme that establishes the lactone core of the polyketide-derived gilvocarcin chromophore. Gilvocarcin-type compounds form a small distinct family of anticancer agents that are involved in both photo-activated DNA-alkylation and histone H3 cross-linking. High resolution crystal structures of apoGilR and GilR in complex with its substrate pregilvocarcin V reveals that GilR belongs to the small group of a relatively new type of the vanillyl-alcohol oxidase flavoprotein family characterized by bicovalently tethered cofactors. GilR was found as a dimer, with the bicovalently attached FAD cofactor mediated through His-65 and Cys-125. Subsequent mutagenesis and functional assays indicate that Tyr-445 may be involved in reaction catalysis and in mediating the covalent attachment of FAD, whereas Tyr-448 serves as an essential residue initiating the catalysis by swinging away from the active site to accommodate binding of the 6R-configured substrate and consequently abstracting the proton of the hydroxyl residue of the substrate hemiacetal 6-OH group. These studies lay the groundwork for future enzyme engineering to broaden the substrate specificity of this bottleneck enzyme of the gilvocarcin biosynthetic pathway for the development of novel anti-cancer therapeutics.

DnaA-ATP acts as a molecular switch to control levels of ribonucleotide reductase expression in Escherichia coli

Ribonucleotide reductase (RNR) is the bottleneck enzyme in the synthesis of dNTPs required for DNA replication. In order to avoid the mutagenic effects of imbalances in dNTPs the amount and activity of RNR enzyme in the cell is tightly regulated. RNR expression from the nrdAB operon is thus coupled to coincide with the initiation of DNA replication. However, the mechanism for the co-ordination of gene transcription and DNA replication remains to be elucidated. The timing and synchrony of DNA replication initiation in Escherichia coli is controlled in part by the binding of the DnaA protein to the origin of replication. DnaA is also a transcription factor of the nrdAB operon and could thus be the link between these two processes. Here we show that RNA polymerase can form a stable transcription initiation complex at the nrdAB promoter by direct interaction with the far upstream sites required for the timing of expression as a function of DNA replication. In addition, we show that the binding of DnaA on the promoter can either activate or repress transcription as a function of its concentration and its nucleotide-bound state. However, transcription regulation by DnaA does not significantly affect the timing of expression of RNR from the nrdAB operon.

Identification of bottleneck enzymes with negative dynamic sensitivities: Ethanol fermentation systems as case studies

Dynamic logarithmic gains (normalised time-varying sensitivities) or their products with metabolite concentrations, called an instantaneous bottleneck ranking indicator (instantaneous BR indicator), can express the time courses of bottleneck enzyme ranking. The integrated value of the instantaneous BR indicator, called an overall BR indicator, provides a ranking of bottleneck enzymes over the entire reaction period of time. Owing to the property of the logarithmic gains, these BR indicators are allowed to include both positive and negative values and in turn raise several questions on the identification of a bottleneck enzyme. To eliminate these questions, the present work studies the identification of bottleneck enzymes in four ethanol fermentation systems using suspended and immobilised cells at pH 4.5 and 5.5 as case studies. These systems consist of both intracellular reactions without cell growth (intracellular reaction systems) and those with cell growth (cell growth systems). The analyses of the intracellular reaction systems reveal that both the suspended and immobilised cell systems at pH 5.5 are not robust. In the cell growth systems, therefore, the analyses are conducted only for the suspended and immobilised cell models at pH 4.5. The enzyme glyceraldehyde 3-phosphate dehydrogenase (gapd) initially has the largest logarithmic gains under all conditions, whereas the system becomes insensitive to it over time. Interestingly, the instantaneous BR indicator for gapd is negatively large. Also, other indicators change in positive and/or negative regions. To deal with these values of different signs, all the indicators are integrated to obtain and rank the overall BR indicators in the order of the magnitudes of their absolute values. The result shows that the ranking of enzymes are completely identical to that of the final ethanol concentrations obtained by finitely increasing or decreasing the relevant enzyme activities in accordance with the signs of overall BR indicators. This result indicates that the enzymes must be ranked in the order of the magnitudes of their absolute values to determine a bottleneck enzyme. As a result, the analyses of the intracellular reaction systems reveal that the bottleneck enzyme is switched from a membrane-bound glucose transporter enzyme to phosphofructokinase when the cell-retaining condition is changed from suspension to immobilisation. In the cell growth systems, gapd is identified as the most likely bottleneck enzyme, suggesting that the gapd activity must be decreased to increase the ethanol productivity.

Instantaneous and Overall Indicators for Determination of Bottleneck Ranking in Metabolic Reaction Networks

A dynamic logarithmic gain expresses the percentage change in a dependent variable or metabolite concentration in response to an infinitesimal percentage change in an independent variable or enzyme activity. This article discusses the usefulness of several bottleneck ranking (BR) indicators that are functions of the logarithmic gain, to determine the most likely bottleneck enzyme in a dynamic metabolic reaction system. Mathematical models for penicillin V and ethanol fermentations are considered as case studies. The calculated results reveal that the instantaneous BR indicator, which is a product of the dynamic logarithmic gain and the metabolite concentration, is an effective measure for instantaneous bottleneck enzyme ranking changed during the fermentation period, whereas the overall BR indicator, which is a time-averaged value of the instantaneous BR indicator, is an effective measure for bottleneck enzyme ranking throughout the entire fermentation period.

Method for Determination of the Main Bottleneck Enzyme in a Metabolic Reaction Network by Dynamic Sensitivity Analysis

In fermentation processes, it is important to identify the bottleneck enzyme in a given metabolic reaction network, because increasing its activity would lead to an enhancement in the productivity of a desired metabolite. To efficiently identify the bottleneck enzyme, the present work discusses a systematic approach using dynamic logarithmic gains, i.e., percentage changes in the concentration of the desired metabolite in the response to an infinitesimal percentage change in enzyme activities, as an indicator. A penicillin V fed-batch fermentation model proposed by other researchers was used as an example of application. The calculated results showed that not only the time courses of the dynamic logarithmic gains but also the ranking of the magnitudes of their values is changed with time, implying that the bottleneck enzyme is changed with time in this fermentation process. To determine the bottleneck enzyme from such time-transient behaviors, the dynamic logarithmic gains were integrated over the entire ...

Differential inhibition of photosynthesis during pre‐flowering drought stress in Sorghum bicolor genotypes with different senescence traits

Young (16‐day‐old) Sorghum bicolor plants of a late‐ and slow‐senescing Texas A&M line (B 35) and of an early‐ and fast‐senescing descendant of an Ethiopian landrace (E 36‐1) were subjected to drought stress by decreasing the soil water content to 30% field capacity over 6 days. Plant water potentials decreased from − 2 bar (controls) to − 10 to − 18 bar, and this drought stress resulted in: (1) differential phenotypic reactions and (2) differential decreases in photosynthesis rates in the two cultivars. While E 36‐1 tended to lose viable leaf area from the leaf tips downwards, B 35 showed a gradual overall drying of the leaf. At the same time, photosynthesis rates decreased from 31.5 ± 1.6 to 12.3 ± 5.0 µmol CO2 m−2 s−1 (E 36‐1) and from 30.5 ± 1.6 to 3.3 ± 2.6 µmol CO2 m−2 s−1 (B 35), respectively. In vitro enzyme activities of phosphoenolpyruvate carboxylase (PEPCase), malate dehydrogenase (MDH) and malic enzyme (ME) on a leaf area basis exceeded the photosynthesis rates. Pyruvate phosphate dikinase (PPDK) activity was close to the photosynthesis rates in control plants and higher than the photosynthesis rates in drought‐stressed plants. Thus, none of the enzymes appeared to limit photosynthesis under drought stress, and likely bottleneck enzyme activities of the C3 pathway in the bundle‐sheath cells, i.e. ribulose‐1,5‐bisphosphate carboxylase (RubisCO) and stromal fructose‐1,5‐bisphosphatase (sFBPase), also showed sufficient activities to sustain higher photosynthesis rates than those observed in the stressed plants. However, under drought stress, total leaf malate concentrations were higher in B 35 (up to 33.1 µmol g−1 FW) than in E 36‐1 (up to 22.4 µmol g−1 FW). In particular, at the presumed cytosolic pH of 7.0–7.3, S. bicolor PEPCase was strongly inhibited by malate. In contrast with the in vitro PEPCase enzyme activities, the A/Ci curves suggested a stronger decrease in the in vivo activity of the enzyme in B 35 under drought stress than in E 36‐1. It is therefore suggested that photosynthesis under drought stress may be inhibited differentially through feedback malate inhibition of PEPCase in S. bicolor.

Tryptophan decarboxylase from Catharanthus roseus cell suspension cultures: purification, molecular and kinetic data of the homogenous protein

The purification of tryptophan decarboxylase from Catharanthus roseus (TDC, E.C.:4.1.1.27), to apparent homogeneity, is described. The enzyme represents a soluble protein with a molecular weight of 115 000±3 000, consisting of 2 identical subunits of 54 000±1 000. The pI was estimated to be 5.9 and the Km for L-tryptophan was found to be 7.5×10(-5) M. Phenylalanine, tyrosine and DOPA were not decarboxylated by tryptophan decarboxylase from Catharanthus cells. Similar to the aromatic amino acid decarboxylase from hog kidney the enzyme does not appear to be obligatorily dependent on exogenously supplied pyridoxal phosphate, as it seems to contain a certain amount of this cofactor. The average percentage of TDC in the cells was found to be 0.002% in the growth medium while the level increased up to 0.03% when indole alkaloid biosynthesis was induced. The role of the protein as a bottleneck enzyme of indole alkaloid biosynthesis is discussed.

Regulation of ammonia assimilation in ammonia-limited chemostat cultures of Escherichia coli ML 30: evidence of bistability.

In a preceding paper evidence of two stationary stable states (bistability) in the specific activity of glutamine synthetase (GS) in ammonia-limited steady-state cultures of Escherichia coli ML 30 at dilution rates (D) about 0.15 h-1 was described (Müller et al. 1977). For better understanding of the regulation mechanisms leading to GS bistability chemostat experiments were performed over a wide range of dilution rates up to D = 0.8 h-1. For each steady state the specific activities of GS and glutamate dehydrogenase (GDH)--the other key enzyme of the two NH3 assimilation routes in E. coli--and in addition the remaining NH3 concentration in the culture liquid were determined. Parallel to GS bistability two states of GDH activity and NH3 concentration are found. The higher state of GS is connected with a lower GDH activity and NH3 concentration. With rising D the GS activities decrease whereas GDH activities and NH3 concentrations increase. Since no adenylation of the GS is detectable GS bistability seems to be regulated on the level of enzyme synthesis like GDH bistability. From the experimental findings a mathematical model is derived based on the bottle neck enzyme theory of growth. It describes the dependence between the specific growth rates on the one hand and the specific enzyme activities and NH3 concentration on the other. It is shown that the specific uptake rate of the limiting NH3 and the specific growth rates, respectively, depend on the simultaneous action of two bottle neck enzymes which are connected by a regulative link.

Wachstumskinetik einer thiaminbedürftigen Candida lipolytica bei Thiaminlimitation: Auftreten einer linearen Wachstumsphase

AbstractThe growth kinetics of batch cultures of the thiamine requiring Candida lipolytica 695 was investigated. It was established that a phase of logarithmic growth is followed by a linear growth phase. The time length of the linear phase and the relative increasing of the biomass during the linear phase are nearly constant and independend of the concentration of thiamine. The existence of the linear phase is discussed in connection with a constant activity of one of the two 2‐ketoacid dehydrogenases as a bottle neck enzyme which needs thiamine pyrophosphate as coenzyme. Critical intracellular thiamine concentrations were calculated necessary for transition from the logarithmic to the linear phase and from the logarithmic to the stationary growth phase. Without the existence of the second critical thiamine concentration the linear growth would continue infinitely.

Growth kinetics of thiamine requiring Candida lipolytica during thiamine limitation: the existence of a linear growth phase

The growth kinetics of batch cultures of the thiamine requiring Candida lipolytica 695 was investigated. It was established that a phase of logarithmic growth is followed by a linear growth phase. The time length of the linear phase and the relative increasing of the biomass during the linear phase are nearly constant and independend of the concentration of thiamine. The existence of the linear phase is discussed in connection with a constant activity of one of the two 2-ketoacid dehydrogenases as a bottle neck enzyme which needs thiamine pyrophosphate as coenzyme. Critical intracellular thiamine concentrations were calculated necessary for transition from the logarithmic to the linear phase and from the logarithmic to the stationary growth phase. Without the existence of the second critical thiamine concentration the linear growth would continue infinitely.