Isocitrate dehydrogenase kinase/phosphatase: aceK alleles that express kinase but not phosphatase activity

Kinases on Double Duty: A Review of UniProtKB Annotated Bifunctionality within the Kinome

Phosphorylation facilitates the regulation of all fundamental biological processes, which has triggered extensive research of protein kinases and their roles in human health and disease. In addition to their phosphotransferase activity, certain kinases have evolved to adopt additional catalytic functions, while others have completely lost all catalytic activity. We searched the Universal Protein Resource Knowledgebase (UniProtKB) database for bifunctional protein kinases and focused on kinases that are critical for bacterial and human cellular homeostasis. These kinases engage in diverse functional roles, ranging from environmental sensing and metabolic regulation to immune-host defense and cell cycle control. Herein, we describe their dual catalytic activities and how they contribute to disease pathogenesis.

The impact of cell structure, metabolism and group behavior for the survival of bacteria under stress conditions

Microbes from diverse types of habitats are continuously exposed to external challenges, which may include acidic, alkaline, and toxic metabolites stress as well as nutrient deficiencies. To promote their own survival, bacteria have to rapidly adapt to external perturbations by inducing particular stress responses that typically involve genetic and/or cellular changes. In addition, pathogenic bacteria need to sense and withstand these environmental stresses within a host to establish and maintain infection. These responses can be, in principle, induced by changes in bacterial cell structure, metabolism and group behavior. Bacterial nucleic acids may serve as the core part of the stress response, and the cell envelope and ribosomes protect genetic structures from damage. Cellular metabolism and group behavior, such as quorum sensing system, can play a more important role in resisting stress than we have now found. Since bacteria survival can be only appreciated if we better understand the mechanisms behind bacterial stress response, here we review how morphological and physiological features may lead to bacterial resistance upon exposure to particular stress-inducing factors.

Loopβ3αC plays an important role in the structure and function of isocitrate dehydrogenase kinase/phosphatase

This work aims to investigate the role of the loopβ3αC amino acids in the structure and function of isocitrate dehydrogenase kinase/phosphatase (AceK). The results demonstrate that the precise configuration of loopβ3αC is very important for AceK structure and function: structural changes alter the affinity of the enzyme for the isocitrate dehydrogenase (ICDH), which modifies enzyme activity. Intriguingly, D340 is significant for the retention of kinase and phosphatase activities, for the conformational stability of AceK and for binding ICDH. The deletion Δ341-345 increases enzyme activity by increasing the maximum velocity and affinity for ICDH. The β3αC loop is thus critical for the structure and function of AceK.

Role of Glyoxylate Shunt in Oxidative Stress Response

The glyoxylate shunt (GS) is a two-step metabolic pathway (isocitrate lyase, aceA; and malate synthase, glcB) that serves as an alternative to the tricarboxylic acid cycle. The GS bypasses the carbon dioxide-producing steps of the tricarboxylic acid cycle and is essential for acetate and fatty acid metabolism in bacteria. GS can be up-regulated under conditions of oxidative stress, antibiotic stress, and host infection, which implies that it plays important but poorly explored roles in stress defense and pathogenesis. In many bacterial species, including Pseudomonas aeruginosa, aceA and glcB are not in an operon, unlike in Escherichia coli In P. aeruginosa, we explored relationships between GS genes and growth, transcription profiles, and biofilm formation. Contrary to our expectations, deletion of aceA in P. aeruginosa improved cell growth under conditions of oxidative and antibiotic stress. Transcriptome data suggested that aceA mutants underwent a metabolic shift toward aerobic denitrification; this was supported by additional evidence, including up-regulation of denitrification-related genes, decreased oxygen consumption without lowering ATP yield, increased production of denitrification intermediates (NO and N2O), and increased cyanide resistance. The aceA mutants also produced a thicker exopolysaccharide layer; that is, a phenotype consistent with aerobic denitrification. A bioinformatic survey across known bacterial genomes showed that only microorganisms capable of aerobic metabolism possess the glyoxylate shunt. This trend is consistent with the hypothesis that the GS plays a previously unrecognized role in allowing bacteria to tolerate oxidative stress.

Tricarboxylic Acid Cycle and Glyoxylate Bypass

The tricarboxylic acid (TCA) cycle plays two essential roles in metabolism. First, under aerobic conditions the cycle is responsible for the total oxidation of acetyl-CoA that is derived mainly from the pyruvate produced by glycolysis. Second, TCA cycle intermediates are required in the biosynthesis of several amino acids. Although the TCA cycle has long been considered a "housekeeping" pathway in Escherichia coli and Salmonella enterica, the pathway is highly regulated at the transcriptional level. Much of this control is exerted in response to respiratory conditions. The TCA cycle gene-protein relationship and mutant phenotypes have been well studied, although a few loose ends remain. The realization that a "shadow" TCA cycle exists that proceeds through methylcitrate has cleared up prior ambiguities. The glyoxylate bypass has long been known to be essential for growth on carbon sources such as acetate or fatty acids because this pathway allowsnet conversion of acetyl-CoA to metabolic intermediates. Strains lacking this pathway fail to grow on these carbon sources, since acetate carbon entering the TCA cycle is quantitatively lost as CO2 resulting in the lack of a means to replenish the dicarboxylic acids consumed in amino acid biosynthesis. The TCA cycle gene-protein relationship and mutant phenotypes have been well studied, although the identity of the small molecule ligand that modulates transcriptional control of the glyoxylate cycle genes by binding to the IclR repressor remains unknown. The activity of the cycle is also exerted at the enzyme level by the reversible phosphorylation of the TCA cycle enzyme isocitrate dehydrogenase catalyzed by a specific kinase/phosphatase to allow isocitratelyase to compete for isocitrate and cleave this intermediate to glyoxylate and succinate.

Structure of the bifunctional isocitrate dehydrogenase kinase/phosphatase

The Escherichia coli isocitrate dehydrogenase kinase/phosphatase (AceK) is a unique bifunctional enzyme that phosphorylates or dephosphorylates isocitrate dehydrogenase (ICDH) in response to environmental changes, resulting in the inactivation or, respectively, activation of ICDH. ICDH inactivation short-circuits the Krebs cycle by enabling the glyoxlate bypass. It was the discovery of AceK and ICDH that established the existence of protein phosphorylation regulation in prokaryotes. As a 65-kDa protein, AceK is significantly larger than typical eukaryotic protein kinases. Apart from the ATP-binding motif, AceK does not share sequence homology with any eukaryotic protein kinase or phosphatase. Most intriguingly, AceK possesses the two opposing activities of protein kinase and phosphatase within one protein, and specifically recognizes only intact ICDH. Additionally, AceK has strong ATPase activity. It has been shown that AceK kinase, phosphatase and ATPase activities reside at the same site, although the molecular basis of such multifunctionality and its regulation remains completely unknown. Here we report the structures of AceK and its complex with ICDH. The AceK structure reveals a eukaryotic protein-kinase-like domain containing ATP and a regulatory domain with a novel fold. As an AceK phosphatase activator and kinase inhibitor, AMP is found to bind in an allosteric site between the two AceK domains. An AMP-mediated conformational change exposes and shields ATP, acting as a switch between AceK kinase and phosphatase activities, and ICDH-binding induces further conformational change for AceK activation. The substrate recognition loop of AceK binds to the ICDH dimer, allowing higher-order substrate recognition and interaction, and inducing critical conformational change at the phosphorylation site of ICDH.

Comparative in vivo gene expression of the closely related bacteria Photorhabdus temperata and Xenorhabdus koppenhoeferi upon infection of the same insect host, Rhizotrogus majalis

BACKGROUND

Photorhabdus and Xenorhabdus are Gram-negative, phylogenetically related, enterobacteria, forming mutualism with the entomopathogenic nematodes Heterorhabditis and Steinernema, respectively. The mutualistic bacteria living in the intestines of the nematode infective juveniles are pathogenic to the insect upon release by the nematodes into the insect hemolymph. Such a switch needs activation of genes that promote bacterial virulence. We studied in vivo gene expression in Photorhabdus temperata and Xenorhabdus koppenhoeferi upon infection of the white grub Rhizotrogus majalis using selective capture of transcribed sequences technique.

RESULTS

A total of 40 genes in P. temperata and 39 in X. koppenhoeferi were found to be upregulated in R. majalis hemolymph at 24 h post infection. Genomic presence or upregulation of these genes specific in either one of the bacterium was confirmed by the assay of comparative hybridization, and the changes of randomly selected genes were further validated by quantitative real-time PCR. The identified genes could be broadly divided into seven functional groups including cell surface structure, regulation, virulence and secretion, stress response, intracellular metabolism, nutrient scavenging, and unknown. The two bacteria shared more genes in stress response category than any other functional group. More than 60% of the identified genes were uniquely induced in either bacterium suggesting vastly different molecular mechanisms of pathogenicity to the same insect host. In P. temperata lysR gene encoding transcriptional activator was induced, while genes yijC and rseA encoding transcriptional repressors were induced in X. koppenhoeferi. Lipopolysaccharide synthesis gene lpsE was induced in X. koppenhoeferi but not in P. temperata. Except tcaC and hemolysin related genes, other virulence genes were different between the two bacteria. Genes involved in TCA cycle were induced in P. temperata whereas those involved in glyoxylate pathway were induced in X. koppenhoeferi, suggesting differences in metabolism between the two bacteria in the same insect host. Upregulation of genes encoding different types of nutrient uptake systems further emphasized the differences in nutritional requirements of the two bacteria in the same insect host. Photorhabdus temperata displayed upregulation of genes encoding siderophore-dependent iron uptake system, but X. koppenhoeferi upregulated genes encoding siderophore-independent ion uptake system. Photorhabdus temperata induced genes for amino acid acquisition but X. koppenhoeferi upregulated malF gene, encoding a maltose uptake system. Further analyses identified possible mechanistic associations between the identified gene products in metabolic pathways, providing an interactive model of pathogenesis for each bacterium species.

CONCLUSION

This study identifies set of genes induced in P. temperata and X. koppenhoeferi upon infection of R. majalis, and highlights differences in molecular features used by these two closely related bacteria to promote their pathogenicity in the same insect host.

Control of Isocitrate Dehydrogenase Catalytic Activity by Protein Phosphorylation in Escherichia coli

During aerobic growth of Escherichia coli on acetate as sole source of carbon and energy, the organism requires the operation of the glyoxylate bypass enzymes, namely isocitrate lyase (ICL) and the anaplerotic enzyme malate synthase (MS). Under these conditions, the glyoxylate bypass enzyme ICL is in direct competition with the Krebs cycle enzyme isocitrate dehydrogenase (ICDH) for their common substrate and although ICDH has a much higher affinity for isocitrate, flux of carbon through ICL is assured by virtue of high intracellular level of isocitrate and the reversible phosphorylation/inactivation of a large fraction of ICDH. Reversible inactivation is due to reversible phosphorylation catalysed by ICDH kinase/phosphatase, which harbours both catalytic activities on the same polypeptide. The catalytic activities of ICDH kinase/phosphatase constitute a moiety conserved cycle, require ATP and exhibit 'zero-order ultrasensitivity'. The structural gene encoding ICDH kinase/phosphatase (aceK) together with those encoding ICL (aceA) and MS (aceB) form an operon (aceBAK; otherwise known as the ace operon) the expression of which is intricately regulated at the transcriptional level by IclR, FadR, FruR and IHF. Although ICDH, an NADP(+)-dependent, non-allosteric dimer, can be phosphorylated at multiple sites, it is the phosphorylation of the Ser-113 residue that renders the enzyme catalytically inactive as it prevents isocitrate from binding to the active site, which is a consequence of the negative charge carried on phosphoserine 113 and the conformational change associated with it. The ICDH molecule readily undergo domain shifts and/or induced-fit conformational changes to accommodate the binding of ICDH kinase/phosphatase, the function of which has now been shown to be central to successful adaptation and growth of E. coli and related genera on acetate and fatty acids.

Bacillus subtilis isocitrate dehydrogenase. A substrate analogue for Escherichia coli isocitrate dehydrogenase kinase/phosphatase

In Escherichia coli, the homodimeric Krebs cycle enzyme isocitrate dehydrogenase (EcIDH) is regulated by reversible phosphorylation of a sequestered active site serine. The phosphorylation cycle is catalyzed by a bifunctional protein, IDH kinase/phosphatase (IDH-K/P). To better understand the nature of the interaction between EcIDH and IDH-K/P, we have examined the ability of an IDH homologue from Bacillus subtilis (BsIDH) to serve as a substrate for the kinase and phosphatase activities. BsIDH exhibits extensive sequence and structural similarities with EcIDH, particularly around the phosphorylated serine. Our previous crystallographic analysis revealed that the active site architecture of these two proteins is almost completely conserved. We now expand the comparison to include a number of biochemical properties. Both IDHs display nearly equivalent steady-state kinetic parameters for the dehydrogenase reaction. Both proteins are also phosphorylated by IDH-K/P in the same ratio (1 mole of phosphate per mole of monomer), and this stoichiometric phosphorylation correlates with an equivalent inhibition of IDH activity. Furthermore, tandem electrospray mass spectrometry demonstrates that BsIDH, like EcIDH, is phosphorylated on the corresponding active site serine residue (Ser-104). Despite the high degree of sequence, functional, and structural congruence between these two proteins, BsIDH is surprisingly a much poorer substrate of IDH-K/P than is EcIDH, with Michaelis constants for the kinase and phosphatase activities elevated by 60- and 3,450-fold, respectively. These drastically disparate values might result from restricted access to the active site cavity and/or from the lack of a potential docking site for IDH-K/P.

Mutations lowering the phosphatase activity of HPr kinase/phosphatase switch off carbon metabolism

The oligomeric bifunctional HPr kinase/P-Ser-HPr phosphatase (HprK/P) regulates many metabolic functions in Gram-positive bacteria by phosphorylating the phosphocarrier protein HPr at Ser46. We isolated Lactobacillus casei hprK alleles encoding mutant HprK/Ps exhibiting strongly reduced phosphatase, but almost normal kinase activity. Two mutations affected the Walker motif A of HprK/P and four a conserved C-terminal region in contact with the ATP-binding site of an adjacent subunit in the hexamer. Kinase and phosphatase activity appeared to be closely associated and linked to the Walker motif A, but dephosphorylation of seryl-phosphorylated HPr (P-Ser-HPr) is not simply a reversal of the kinase reaction. When the hprKV267F allele was expressed in Bacillus subtilis, the strongly reduced phosphatase activity of the mutant enzyme led to increased amounts of P-Ser-HPr. The hprKV267F mutant was unable to grow on carbohydrates transported by the phosphoenolpyruvate:glycose phosphotransferase system (PTS) and on most non-PTS carbohydrates. Disrupting ccpA relieved the growth defect only on non-PTS sugars, whereas replacing Ser46 in HPr with alanine also restored growth on PTS substrates.

Locations of the regulatory sites for isocitrate dehydrogenase kinase/phosphatase

Isocitrate dehydrogenase (IDH)(1) of Escherichia coli is regulated by a bifunctional protein, IDH kinase/phosphatase. In this paper, we demonstrate that the effectors controlling these activities belong to two distinct classes that differ in mechanism and in the locations of their binding sites. NADPH and isocitrate are representative members of one of these effector classes. NADPH inhibits both IDH kinase and IDH phosphatase, whereas isocitrate inhibits only IDH kinase. Isocitrate can "activate" IDH phosphatase by reversing product inhibition by dephospho-IDH. Mutations in icd, which encodes IDH, had parallel effects on the binding of these ligands to the IDH active site and on their effects on IDH kinase and phosphatase, indicating that these ligands regulate IDH kinase/phosphatase through the IDH active site. Kinetic analyses suggested that isocitrate and NADPH prevent formation of the complex between IDH kinase/phosphatase and its protein substrate. AMP, 3-phosphoglycerate, and pyruvate represent a class of regulatory ligands that is distinct from that which includes isocitrate and NADPH. These ligands bind directly to IDH kinase/phosphatase, a conclusion which is supported by the observation that they inhibit the IDH-independent ATPase activity of this enzyme. These effector classes can also be distinguished by the observation that mutant derivatives of IDH kinase/phosphatase expressed from aceK3 and aceK4 exhibited dramatic changes in their responses to AMP, 3-phosphoglycerate, and pyruvate but not to NADPH and isocitrate.

Regulation of acetate metabolism by protein phosphorylation in enteric bacteria

Growth of enteric bacteria on acetate as the sole source of carbon and energy requires operation of a particular anaplerotic pathway known as the glyoxylate bypass. In this pathway, two specific enzymes, isocitrate lyase and malate synthase, are activated to divert isocitrate from the tricarboxylic acid cycle and prevent the quantitative loss of acetate carbons as carbon dioxide. Bacteria are thus supplied with the metabolic intermediates they need for synthesizing their cellular components. The channeling of isocitrate through the glyoxylate bypass is regulated via the phosphorylation/dephosphorylation of isocitrate dehydrogenase, the enzyme of the tricarboxylic acid cycle which competes for a common substrate with isocitrate lyase. When bacteria are grown on acetate, isocitrate dehydrogenase is phosphorylated and, concomitantly, its activity declines drastically. Conversely, when cells are cultured on a preferred carbon source, such as glucose, the enzyme is dephosphorylated and recovers full activity. Such reversible phosphorylation is mediated by an unusual bifunctional enzyme, isocitrate dehydrogenase kinase/phosphatase, which contains both modifying and demodifying activities on the same polypeptide. The genes coding for malate synthase, isocitrate lyase, and isocitrate dehydrogenase kinase/phosphatase are located in the same operon. Their expression is controlled by a complex dual mechanism that involves several transcriptional repressors and activators. Recent developments have brought new insights into the nature and mode of action of these different regulators. Also, significant advances have been made lately in our understanding of the control of enzyme activity by reversible phosphorylation. In general, analyzing the physiological behavior of bacteria on acetate provides a valuable approach for deciphering at the molecular level the mechanisms of cell adaptation to the environment.

Linkage map of Escherichia coli K-12, edition 10: the traditional map

This map is an update of the edition 9 map by Berlyn et al. (M. K. B. Berlyn, K. B. Low, and K. E. Rudd, p. 1715-1902, in F. C. Neidhardt et al., ed., Escherichia coli and Salmonella: cellular and molecular biology, 2nd ed., vol. 2, 1996). It uses coordinates established by the completed sequence, expressed as 100 minutes for the entire circular map, and adds new genes discovered and established since 1996 and eliminates those shown to correspond to other known genes. The latter are included as synonyms. An alphabetical list of genes showing map location, synonyms, the protein or RNA product of the gene, phenotypes of mutants, and reference citations is provided. In addition to genes known to correspond to gene sequences, other genes, often older, that are described by phenotype and older mapping techniques and that have not been correlated with sequences are included.

Isocitrate dehydrogenase kinase/phosphatase. Kinetic characteristics of the wild-type and two mutant proteins

Isocitrate dehydrogenase (IDH) of Escherichia coli is regulated by a bifunctional protein, IDH kinase/phosphatase. In addition to the kinase and phosphatase activities, this protein catalyzes an intrinsic ATPase reaction. The initial velocity kinetics of these activities exhibited extensive similarities. IDH kinase and phosphatase both yielded intersecting double-reciprocal plots. In addition, we observed similar values for the kinetic constants describing interactions of the kinase and phosphatase with their protein substrates and the interactions of all three activities with ATP. In contrast, while the maximum velocities of IDH kinase and IDH phosphatase were nearly equal, they were 10-fold less than the maximum velocity of the ATPase. Although the IDH phosphatase reaction required either ATP or ADP, it was not supported by the nonhydrolyzable ATP analogue 5'-adenylyl imidodiphosphate. The kinetic properties of wild-type IDH kinase/phosphatase were compared with those of two mutant derivatives of this protein. The mutations in these proteins selectively inhibit IDH phosphatase activity. Inhibition of IDH phosphatase resulted from three factors: decreases in the maximum velocities, reduced affinities for phospho-IDH, and a loss of coupling between ATP and phospho-IDH. These mutations also affected the properties of IDH kinase, increasing the maximum velocities and decreasing the affinities for ATP and phospho-IDH. The intrinsic ATPase activities also exhibited reduced affinity for ATP. These results are discussed in the context of a model which proposes that all three activities occur at the same active site.

Functions of the gene products of Escherichia coli

A list of currently identified gene products of Escherichia coli is given, together with a bibliography that provides pointers to the literature on each gene product. A scheme to categorize cellular functions is used to classify the gene products of E. coli so far identified. A count shows that the numbers of genes concerned with small-molecule metabolism are on the same order as the numbers concerned with macromolecule biosynthesis and degradation. One large category is the category of tRNAs and their synthetases. Another is the category of transport elements. The categories of cell structure and cellular processes other than metabolism are smaller. Other subjects discussed are the occurrence in the E. coli genome of redundant pairs and groups of genes of identical or closely similar function, as well as variation in the degree of density of genetic information in different parts of the genome.

Relative expression of the products of glyoxylate bypass operon: contributions of transcription and translation

Although the genes of the aceBAK operon are expressed from the same promoter, the relative cellular levels of their products are approximately 0.3:1:0.003. Gene and operon fusions with lacZ were constructed to characterize this differential expression. The upshift in expression between aceB and aceA resulted from differences in translational efficiency. In contrast, inefficient translation and premature transcriptional termination contributed to the downshift in expression between aceA and aceK. Premature transcriptional termination occurred within aceK and appears to result from inefficient translation. Deletion of repetitive extragenic palindromic elements between aceA and aceK had little effect on the relative expression of these genes. Rather, the sequences responsible for inefficient expression of aceK lie within the aceK ribosome binding site.

The isocitrate dehydrogenase phosphorylation cycle: regulation and enzymology

Isocitrate dehydrogenase (IDH) of Escherichia coli is regulated by phosphorylation and dephosphorylation. This phosphorylation cycle controls the flow of isocitrate through the glyoxylate bypass, a pathway which bypasses the CO2 evolving steps of the Krebs' cycle. IDH is phosphorylated at a single serine which resides in its active site. Phosphorylation blocks isocitrate binding, thereby inactivating IDH. The IDH phosphorylation cycle is catalyzed by a bifunctional protein kinase/phosphatase. The kinase and phosphatase reactions appear to be catalyzed at the same site and may share some catalytic steps. A variety of approaches have been used to examine the IDH phosphorylation cycle in the intact organism. The picture which has emerged is one of an exquisitely sensitive and flexible system which is capable of adapting efficiently to the environment both inside and outside the cell.

Heterologous expression and secretion of a Streptomyces scabies esterase in Streptomyces lividans and Escherichia coli

The esterase gene from Streptomyces scabies FL1 was cloned and expressed in Streptomyces lividans on plasmids pIJ486 and pIJ702. In S. lividans, the esterase gene was expressed during later stages of growth and was regulated by zinc, as is seen with S. scabies. The 36-kDa secreted form of the esterase was purified from S. lividans. N-terminal amino acid sequencing indicated that the processing site utilized in S. lividans for the removal of the signal sequence was the same as that recognized for processing in S. scabies. Western blots (immunoblots) revealed the presence of a 40-kDa precursor form of the esterase in cytoplasmic extracts. A 23-amino-acid deletion was introduced into the putative signal sequence for the esterase. When this deleted form of the esterase was expressed in S. lividans, a cytoplasmic 38-kDa precursor protein was produced but no secreted esterase was detected, suggesting the importance of the deleted sequence for efficient processing and secretion. The esterase gene was also cloned into the pUC119 plasmid in Escherichia coli. By using the lac promoter sequence, the esterase gene was expressed, and the majority of the esterase was localized to the periplasmic space.

Isocitrate dehydrogenase kinase/phosphatase: identification of mutations which selectively inhibit phosphatase activity

Mutations in aceK, the gene encoding isocitrate dehydrogenase kinase/phosphatase, which selectively inhibit phosphatase activity have been isolated. These mutations yield amino acid substitutions within a 113-residue region of this 578-residue protein. These mutations may define a regulatory domain of this protein.

Growth rate of Escherichia coli

It should be possible to predict the rate of growth of Escherichia coli of a given genotype in a specified environment. The idea that the rate of synthesis of ATP determines the rate of growth and that the yield of ATP determines the yield of growth is entrenched in bacterial physiology, yet this idea is inconsistent with experimental results. In minimal media the growth rate and yield vary with the carbon source in a manner independent of the rate of formation and yield of ATP. With acetate as the carbon source, anapleurotic reactions, not ATP synthesis, limit the growth rate. For acetate and other gluconeogenic substrates the limiting step appears to be the formation of triose phosphate. I conclude that the rate of growth is controlled by the rate of formation of a precursor metabolite and, thus, of monomers such as amino acids derived from it. The protein-synthesizing system is regulated according to demand for protein synthesis. I examine the conjecture that the signal for this regulation is the ratio of uncharged tRNA to aminoacyl-tRNA, that this signal controls the concentration of guanosine tetraphosphate, and that the concentration of guanosine tetraphosphate controls transcription of rrn genes. Differential equations describing this system were solved numerically for steady states of growth; the computed values of ribosomes and guanosine tetraphosphate and the maximal growth rate agree with experimental values obtained from the literature of the past 35 years. These equations were also solved for dynamical states corresponding to nutritional shifts up and down.