How does l-glutamate transport relate to selection of mixed nitrogen sources in Rhizobium leguminosarum biovar trifolii MNF1000 and cowpea Rhizobium MNF2030?

When growing on a mixture of ammonia and l-glutamate as nitrogen sources, Rhizobium leguminosarum biovar trifolii MNF1000 utilizes ammonia exclusively, while cowpea Rhizobium MNF2030 utilizes both compounds at similar rates. l-Glutamate transport in both strain MNF1000 and MNF2030 is active, giving rise to a 60-fold concentration gradient across the membrane of cells of strain MNF2030. Both strains produce two kinetically distinguishable glutamate transport systems under all conditions of growth — a high affinity system with an apparent K _m of 0.06–0.17 M but of relatively low V _max, and a low affinity system with a K _m of 1.2–6.7\ M, but of higher overall capacity. l-Glutamate transport activity in cells of MNF2030 was relatively insensitive to the presence of ammonia in the growth medium. By contrast, ammonia in the growth medium resulted in low activities of glutamate transport in cells of MNF1000 which were provided with a carbon source, offering one explanation for the failure of this strain to use glutamate in the presence of ammonia. However, in cells of MNF1000 growing on glutamate as sole source of carbon and nitrogen, the glutamate transport system is synthesized, even in the presence of accumulated or added ammonia. This suggests that the regulation of the glutamate permease also depends on availability of carbon source.Abbreviations CCCP carbonyl cyanide m-chlorophenyl hydrazone - HEPES N-hydroxyethylpiperazine-N-2-ethanesulphonic acid     

New motile anaerobic bacteria growing by succinate decarboxylation to propionate

Three strains of new anaerobic, gram-negative bacteria which grew with succinate as sole source of carbon and energy were isolated from anoxic marine and freshwater mud samples. Cells of the three strains were small, non-spore-forming, motile rods or spirilla. The guanine-plus-cytosine content of the DNA of strain US2 was 52.6±1.0 mol%, of strain Ft2 63.5±1.4 mol%, and of strain Ft1 62.6±1.0 mol%. Succinate was fermented stoichiometrically to propionate and carbon dioxide. The growth yields were 1.2–2.6 g dry cell mass per mol succinate degraded. Strains US2 and Ft2 required 0.05% w/v yeast extract in addition to succinate for reproducible growth. Optimal growth occurred at 30°–37°C and pH 6.8–8.0. Addition of acetate as cosubstrate did not stimulate growth with any strain. Strain Ft2 grew only under strictly anaerobic conditions, whereas strains US2 and Ft1 tolerated oxygen up to 20% in the headspace. Strains US2 and Ft2 grew only with succinate. Strain Ft1 also converted fumarate, aspartate, and sugars to propionate and acetate. This strain also oxidized propionate with nitrate to acetate. Very low amounts of a c-type cytochrome were detected in propionate plus nitrate- or glucose-grown cells of this strain (0.4 g x g protein^-1). Moderate activities of avidin-sensitive methylmalonyl-CoA decarboxylase were found in cell-free extracts of all strains.     

Growth,acetylene reduction activity and localization of nitrogenase in relation to vesicle formation in Frankia strains Cc1.17 and Cp1.2

A comparative study was conducted on the effect of NH₄Cl on growth, vesicle formation and formation of nitrogenase of Frankia strains Cc1.17 and Cp1.2, derived from root nodules of Colletia cruciata and Comptonia peregrina, respectively. On a medium without combined nitrogen (P-N), both strains formed spherical cells, called vesicles, like many other Frankia strains. Data are presented on the number of vesicles per mg protein, after cultivation in media with sodium propionate as C-source without combined nitrogen (P-N) or with 0.2 g NH₄Cl/l (P+N). Strain Cp1.2 as may other Frankia strains, showed on P+N medium a very strong reduction of vesicle formation of 99% relative to the number of vesicles formed on P-N medium, after 11 days growth. However, in strain Cc11.17 this reduction was only 70%. The occurence of relatively large numbers of vesicles in P+N media has not yet been reported for other Frankia strains. No acetylene reduction activity was found in NH ₄ ⁺ -grown cells. The regulation of induction of nitrogenase in Frankia by NH₄Cl was tested by immuno-gelectrophoresis using antisera against nitrogenase of Rhizobium leguminosarum PRE. The component I of the enzyme showed crossreactivity while the component II had only a weak crossreaction. The experiments indicated that no nitrogenase was detectable in the NH ₄ ⁺ -grown cells. For the localization of nitrogenase, relative amounts of the enzyme were compared in whole cells and vesicle-enriched fractions. Western blots showed a significant enrichment of nitrogenase in the vesicle fractions, which indicated that most of the nitrogenase was localized in the vesicle.     

Kinetics of growth and lactic acid production in continuous and batch culture

Summary In a lactic acid fermentation by Streptococcus faecalis, the specific consumption rate of glucose (v) and the specific production rate of lactic acid () were represented by the following simple equations as functions of the specific growth rate (): 1/=(1/) + 1/ = (1/) + By use of data from a batch culture, these two equations were derived from enzyme kinetics of the product inhibition. These equations were successfully applied to the results of batch culture and chemostat culture. In addition, calculation of ATP yield by these equations agreed with the experimental results better than the conventional Leudeking-Piret type equation, which includes two terms associated with growth and not with growth. Correspondence to: H. Ohara     

Bioremediation of selenite in oil refinery wastewater

Selenium-oxyanion-containing wastewater, with levels of selenite as high as 3690 g Se/l and very low levels of selenate, was treated in a laboratory-scale biological reactor system inoculated with the selenate-respiring bacterium Thauera selenatis. The wastewater contained selenite that had been removed from refinery effluent wastewater using iron-coprecipitation followed by selenite release to yield a more concentrated selenium-containing wastewater. The reactor system consisted of recycling sludge-blanket (500 ml; 200 g sand) and fluidized-bed reactors (500 ml; 150 g sand). The flow rate through the reactor system was 3.5 ml/min. The carbon source fed into the reactor was acetate (3 mM); nitrate was also present (3 mM). The selenium oxyanion levels in the wastewater were reduced by 95%. T. selenatis was the only selenate-reducing bacterium detected in the reactor system and it presumably reduced a portion of the selenate present in the water to selenite. The selenite present in the water, and that formed by selenate reduction, was reduced both by the Thauera and by a population of denitrifying bacteria also present in high numbers in the reactor system.     

A Paecilomyces fumosoroseus mutant over-producing chitinase displays enhanced virulence against Bemisia tabaci

A Paecilomyces fumosoroseus strain was mutagenized by u.v. Among 200 colonies, one mutant (M84), showed a large and stable chitin hydrolysis-halo. Glucose consumption and biomass production were similar for M84 and the parental strain. Chitinase was inducible by chitin and repressed by glucose in both strains but, when they were grown on minimal medium plus colloidal chitin as sole carbon source, the parental and M84 strains yielded 198 and 690 mol N-acetylglucosamine, respectively. This results indicate that the mutant strain synthesized a chitinase with a higher activity. Bioassays against Bemisia tabaci nymph, showed that M84 incited a 2-fold higher incidence of disease compared to the parental strain.     

An artificial bifunctional enzyme, γ-glutamyl kinase/γ-glutamyl phosphate reductase, improves NaCl tolerance when expressed in Escherichia coli

Summary An artificial bifunctional enzyme, -glutamyl kinase/-glutamyl phosphate reductase, was obtained by fusing the Escherichia coli genes proA and proB. The proB gene was fused to the 5-end of the proA gene with a linker encoding five amino acids. When expressed in E. coli enhanced intracellular concentrations of proline were observed. At 0.6 M NaCl the growth rates for the strain carrying the fusion enzyme and a control harbouring a plasmid encoding the wild-type enzymes were 320 and 530 min, respectively.     

Chemolithotrophic metabolism of the newly-isolated moderately thermophilic,obligately autotrophic Thiobacillus tepidarius

Thiobacillus tepidarius, isolated from the hot springs at Bath, Avon, UK, grew optimally at 43–45°C and pH 6.0–7.5 on thiosulphate or tetrathionate. In batch culture, thiosulphate was oxidized stoichiometrically to tetrathionate, with a rise in pH. The tetrathionate was then oxidized to sulphate, supporting growth and producing a fall in pH to a minimum of ph 4.8. The organism contained high levels of thiosulphate-oxidizing enzyme, rhodanese and ribulose bisphosphate carboxylase. It was obligately chemolithotrophic and autotrophic. In chemostat culture, T. tepidarius grew autotrophically with the following sole energy-substrates: sulphide, thiosulphate, trithionate, tetrathionate, hexathionate or heptathionate. Thiocyanate, dithionate and sulphite were not used as sole substrates, although sulphite enhanced growth yields in the presence of thiosulphate. Maximum specific growth rate on tetrathionate was 0.44 h^-1. True growth yields (Y _max) and maintenance coefficients (m) were calculated for sulphide, thiosulphate, trithionate and tetrathionate and observed yields at a single fixed dilution rate compared with those on hexathionate and heptathionate. Mean values for Y _max, determined from measurements of absorbance, dry wt, total organic carbon and cell protein, were similar for sulphide, thiosulphate and trithionate (10.9 g dry wt/mol substrate) as expected from their equivalent oxygen consumption for oxidation. Y _max for tetrathionate (20.5) and the relative Y _o values (as g dry wt/g atom oxygen consumed) for thiosulphate and all four polythionates indicated that substrate level phosphorylation did not contribute significantly to energy conservation. These Y _max values were 40–70% higher than any of those previously reported for obligately aerobic thiobacilli. Mean values for m were 6.7 mmol substrate oxidized/g dry wt·h for sulphide, thiosulphate and trithionate, and 2.6 for tetrathionate.Abbreviation PIPES Piperazine-N,N-bis(ethane sulphonic acid)     

Influence of the nitrogen source on the production and rheological properties of scleroglucan produced by Sclerotium rolfsii ATCC 201126

Scleroglucan production by Sclerotium rolfsii ATCC 201126 has been studied using nitrate or ammonium as nitrogen sources at several concentrations. In all the experiments carried out, both growth and production were modelled by an unstructured kinetic model using logistic and Luedeking–Piret equations for describing growth and production, respectively. The kinetic parameters for growth ( and Y_XN) and for production ( and ) were obtained by fitting the data to the model using the single-response non-linear regression technique by means of the algorithm of Marquardt coupled to a fourth-order Runge–Kutta algorithm. Biomass and scleroglucan production were higher when nitrate was the nitrogen source. Rheological properties of scleroglucan produced using nitrate as nitrogen source were studied and rheological parameters calculated, revealing similarity between this biopolymer and commercial scleroglucan.     

Cell yield (YM) of Thauera selenatis grown anaerobically with acetate plus selenate or nitrate

Thauera selenatis was grown anaerobically in minimal medium with either selenate or nitrate as the terminal electron acceptor and acetate as the carbon source and electron donor. The molar cell protein yields, Y_M-protein (selenate) and Y_M-protein (nitrate), were found to be 7.8 g cell protein/mol selenite formed and 7.5 g cell protein/mol nitrite formed, respectively. These values represent Y_M values of 57 and 55 g (dry weight)/mol acetate when selenate or nitrate was the electron acceptor, respectively. Based upon a calculated Y_ATP value of 10.0 g (dry weight) cells/mol ATP, for growth on acetate in inorganic salts, growth with selenate as the terminal electron acceptor theoretically yielded 5.7 ATP/acetate oxidized, and 5.5 ATP when nitrate was the terminal electron acceptor. The results support the conclusion that energy is conserved via electron transport phosphorylation when selenate or nitrate reduction are the terminal electron acceptors during anaerobic growth with acetate.     

Extension growth and cold hardening of young ‘Valencia’ orange trees sprayed with AMO-1618

Rate of extension growth, as measured by height, of 2-month-old Valencia orange trees (Citrus sinensis (L.) Osbeck) on rough lemon rootstock (C. limon Burm. f.) was reduced to 0.5 mm from 5.0 mm day^–1 with 0.1% (w/v) sprays of the growth retardant AMO-1618 (4 hydroxy-5-isopropyl-2-methyl phenyl trimethyl-ammonium chloride, 1 piperdine carboxylate) every 2 weeks during 11 weeks under natural daylight in a glasshouse. Trees sprayed with AMO-1618 were 10-fold shorter, more compact in appearance, and leaves were greener and more oval shaped than those on untreated trees. There was no chemical burn. AMO-1618-sprayed trees were more cold hardy than untreated trees during controlled-temperature, cold-hardening regimes. Alone, AMO-1618 had no effect on freeze tolerance at -5.5° C. AMO-1618 also was associated with greater tree tolerance to freeze injury determined by O₂ uptake in Valencia leaves to as low as -6.7° C.This paper reports the results of research only. Mention of a trademark of a proprietary product does not constitute a guarantee or warranty of the product by the U.S. Department of Agriculture, and does not imply its approval to the exclusion of other products that may also be suitable.     

Degradation of polyaromatic hydrocarbons by Burkholderia cepacia 2A-12

A new strain of bacterium degrading polyaromatic hydrocarbons (PAHs), Burkholderia cepacia 2A-12, was isolated from oil-contaminated soil. Of three PAHs, the isolated strain could utilize naphthalene (Nap) and phenanthrene (Phe) as a sole carbon source but not pyrene (Pyr). However, the strain could degrade Pyr when a cosubstrate such as yeast extract (YE) was supplemented. The PAH degradation rate of the strain was enhanced by the addition of other organic materials such as YE, peptone, glucose, and sucrose. YE was a particularly effective additive in stimulating cell growth as well as PAH degradation. When 1 g YE l^–1, an optimum concentration, was supplemented into the basal salt medium (BSM) with 215 mg Phe l^–1, the specific growth rate (0.30 h^–1) and Phe-degrading rate (29.6 mol l^–1 h^–1) were enhanced approximately ten and three times more than those obtained in the BSM with 215 mg Phe l^–1, respectively. Both cell growth and PAH degradation rates were increased with increasing Phe and Pyr concentrations, and B. cepacia 2A-12 had a tolerance against Phe and Pyr toxicity at the high concentration of 730–760 mg l^–1. Through kinetic analysis, the maximum specific growth rate ( _max) and PAH degrading rate ( _max) for Phe were obtained as 0.39 h^–1 and 300 mol l^–1 h^–1, respectively. Also, _max and _max for Pyr were 0.27 h^–1 and 52 mol l^–1 h^–1, respectively. B. cepacia 2A-12 could simultaneously degrade crude oil as well as PAHs, indicating that this bacterium is very useful for the removal of oils and PAHs contaminants.     

Effect of different carbon and nitrogen sources on the growth and sporulation of Claviceps microcephal (Wallr) TUL.

The effect of different carbon and nitrogen compounds on growth and sporulation ofC. microcephala (Wallr.)Tul. causing ergot disease of Bajra has been studied. Nine different sources of carbon were used but cane sugar was found to be the best source for both, growth and sportulation of the fungus. Glucose, sucrose and maltose gave good growth but fair sporulation. Lactose and sorbitaol proved to be the poor sources. However, fungus failed to utilize starch, dextrin and mannitol.Nineteen nitrogen compounds were tried for the growth and sporulation of the fungus. Best growth and sporulation were supported by peptone and glycine. L-asparagine, DL-valine, Urea, magnesium nitrate and L-proline supported good growth and fair sporulation except DL-valine where it was excellent. Poor growth was obtained on L-isoleucin, ammonium sulphate, potassium nitrate,-alanine, ammonium chloride, DL-aspartic acid and DL-methionine. Fungus failed to utilize thio-urea.     

Ammonia rhythm in Microcystis firma studied by in vivo 15N and 31P NMR spectroscopy

Cultures of the cyanobacterium Microcystis firma show rhythmic uptake and release of ammonia under conditions of carbon limitation. The massive removal of ammonia from the medium during the first light phase has little impact on the intracellular pH: a pH shift of less than 0.2 U towards the alkaline can be measured by in vivo ³¹P NMR. Furthermore, the energy status of the cells remains regulated. In vivo ¹⁵N NMR of M. firma, cultivated either with labelled nitrate or ammonia as the sole nitrogen source, reveals only gradual differences in the pool of free amino acids. Additionally both cultivation types show -aminobutyric acid, acid amides and yet unassigned secondary metabolites as nitrogen storing compounds. Investigating the incorporation of nitrogen under carbon limitation, however, only the amide nitrogen of glutamine is found permanently labelled in situ. While transamination reactions are blocked, nitrate reduction to ammonia can still proceed. Cation exchange processes in the cell wall are considered regarding the ammonia disappearance in the first phase, and the control of ammonia uptake is discussed with respect to the avoidance of intracellular toxification.Abbreviations GABA -aminobutyric acid - GOGAT glutamate synthase - GS glutamine synthetase - MDP methylene diphosphonate - MOPSO 3-(N-morpholino)-2-hydroxy-propanesulfonic acid - NDPS nucieoside diphosphosugars - NOE nuclear Overhauser effect - NMR nuclear magnetic resonance For convenience, the term ammonia is used throughout to denote ammonia or ammonium ion when there is no good evidence as to which chemical species is involved     

Comparative Genomic Analysis of Sulfurospirillum cavolei MES Reconstructed from the Metagenome of an Electrosynthetic Microbiome

Sulfurospirillum spp. play an important role in sulfur and nitrogen cycling, and contain metabolic versatility that enables reduction of a wide range of electron acceptors, including thiosulfate, tetrathionate, polysulfide, nitrate, and nitrite. Here we describe the assembly of a Sulfurospirillum genome obtained from the metagenome of an electrosynthetic microbiome. The ubiquity and persistence of this organism in microbial electrosynthesis systems suggest it plays an important role in reactor stability and performance. Understanding why this organism is present and elucidating its genetic repertoire provide a genomic and ecological foundation for future studies where Sulfurospirillum are found, especially in electrode-associated communities. Metabolic comparisons and in-depth analysis of unique genes revealed potential ecological niche-specific capabilities within the Sulfurospirillum genus. The functional similarities common to all genomes, i.e., core genome, and unique gene clusters found only in a single genome were identified. Based upon 16S rRNA gene phylogenetic analysis and average nucleotide identity, the Sulfurospirillum draft genome was found to be most closely related to Sulfurospirillum cavolei. Characterization of the draft genome described herein provides pathway-specific details of the metabolic significance of the newly described Sulfurospirillum cavolei MES and, importantly, yields insight to the ecology of the genus as a whole. Comparison of eleven sequenced Sulfurospirillum genomes revealed a total of 6246 gene clusters in the pan-genome. Of the total gene clusters, 18.5% were shared among all eleven genomes and 50% were unique to a single genome. While most Sulfurospirillum spp. reduce nitrate to ammonium, five of the eleven Sulfurospirillum strains encode for a nitrous oxide reductase (nos) cluster with an atypical nitrous-oxide reductase, suggesting a utility for this genus in reduction of the nitrous oxide, and as a potential sink for this potent greenhouse gas.     

Production of β-glucosidase by Aspergillus terreus

The production of -glucosidase by Aspergillus terreus was investigated in liquid shake cultures. Enzyme production was maximum on the 7th day of growth (2.18 U/ml) with the initial pH of the medium in the range of 4.0–5.5. Cellulose (Sigmacell Type 100) at 1.0% (wt/vol) gave maximum -glucosidase activity among the various soluble and insoluble carbon sources tested. Potassium nitrate was a suitable nitrogen source for enzyme production. Triton X-100 at 0.15% (vol/vol) increased the enzyme levels of A. terreus. The test fungal strain showed an ability to ferment glucose to ethanol.     

The role of tungstate and/or molybdate in the formation of aldehyde oxidoreductase in Clostridium thermoaceticum and other acetogens; immunological distances of such enzymes

Besides Clostridium thermoaceticum and C. formicoaceticum other resting acetogenic clostridia such as C. aceticum and C. thermoautotrophicum and to a lesser extent non-clostridial acetogens such as Butyribacterium methylotrophicum and Eubacterium limosum were able to reduce propionate to propanol at the expense of carbon monoxide or formate. Methylviologen usually increased the reduction rate. Ten M molybdate in the growth medium decreased this capability for C. thermoaceticum but increased it or had no effect for the other organisms. Ten M tungstate in the growth medium increased the aldehyde oxidoreductase activity in all organisms. Crude extracts of C. thermoaceticum cells grown in the presence of 10 M or 1 mM molybdate showed by ELISA the same or even a 4 fold concentration of aldehyde oxidoreductase in the latter case. However, the enzymic activity was very low in both cases. Omission of dithionite in the growth medium diminished the antigen by a factor of about 8. The immunological distance between the enzyme from C. thermoaceticum and C. thermoautotrophicum was rather low but very large to C. formicoaceticum and undeterminably large to the other organisms.Abbreviations Ald-DH aldehyde dehydrogenase - AOR aldehyde oxidoreductase - CO-DH carbon-monoxide dehydrogenase - ELI-SA enzyme-linked immunosorbent assay - FDH formate dehydrogenase - MV methylviologen - V⁺⁺ oxidised - V^+. reduced viologen     

Influence of cultivation and induction conditions on β-lactamase production in Acinetobacter calcoaceticus

Summary The formation and localization of the -lactamase of Acinetobacter calcoaceticus CCM 5593 is strongly affected by cultivation and induction conditions. Optimal parameters for enzyme yield are cultivation on minimal salts medium with acetate (10 g·1^–1) as carbon source and addition of yeast extract (5–10 g·l^–1), induction by cefotaxime (50g·ml^–1) immediately after inoculation and growth for 24 h at 25° C. The strain forms a basal level of -lactamase constitutively [70 units (U)·g^–1]. Nearly all of this was found to be cell-bound. However, -lactamase activity additionally produced after induction (up to 500 U·g^–1 wet bacteria) was located in the culture medium (up to 96%). This unusual localization is a special feature of A. calcoaceticus and is not attributed to cell lysis. Offprint requests to: P. Borneleit     

Interaction of free fatty acids with the erythrocyte membrane as affected by hyperthermia and ionizing radiation

The interference of hyperthermia and ionizing radiation, respectively, with the effects of capric (100), lauric (120), myristic (140), oleic (cis-181) and elaidic (trans-181) acids on the osmotic resistance of human erythrocytes was investigated. The results are summarized as follows: (A) not only at 37°, but also at 42° and 47°C lauric acid (120) represents the minimum chain length for the biphasic behaviour of protecting against hypotonic hemolysis at a certain lower concentration range and hemolysis promotion at subsequent higher concentrations; (B) with increasing temperatures the protecting as well as the hemolytic effects occur at lower concentrations of the fatty acids; (C) the increase of temperature promotes the extent of hemolysis and reduces the extent of protection against hypotonic hemolysis; (D) Gamma-irradiation of erythrocytes selectively affects the concentration of oleic acid at which maximum protection against hypotonic hemolysis occurs, without altering the minimum concentration for 100% hemolysis.     

A mutant of Saccharomyces cerevisiae lacking catabolic NAD-specific glutamate dehydrogenase Growth characteristics of the mutant and regulation of enzyme synthesis in the wild-type strain

NAD-specific glutamate dehydrogenase (GDH-B)¹ was induced in a wild-type strain derived of - 1278b by -amino acids, the nitrogen of which according to known degradative pathways is transferred to 2-oxoglutarate. A recessive mutant (gdhB) devoid of GDH-B activity grew more slowly than the wild type if one of these amino acids was the sole source of nitrogen. Addition of ammonium chloride, glutamine, asparagine or serine to growth media with inducing -amino acids as the main nitrogen source increased the growth rate of the gdhB mutant to the wild-type level and repressed GDH-B synthesis in the wild type. Arginine, urea and allantoin similarly increased the growth rate of the gdhB mutant and repressed GDH-B synthesis in the presence of glutamate, but not in the presence of aspartate, alanine or proline as the main nitrogen source. These observations are consistent with the view that GDH-B in vivo deaminates glutamate. Ammonium ions are required for the biosynthesis of glutamine, asparagine, arginine, histidine and purine and pyrimidine bases. Aspartate and alanine apparently are more potent inducers of GDH-B than glutamate.Anabolic NADP-specific glutamate dehydrogenase (GDH-A) can not fulfil the function of GDH-B in the gdhB mutant. This is concluded from the equal growth rates in glutamate, aspartate and proline media as observed with a gdhB mutant and with a gdhA, gdhB double mutant in which both glutamate dehydrogenases are lacking. The double mutant showed an anomalous growth behaviour, growth rates on several nitrogen sources being unexpectedly low.The following abbreviations and symbols are used GDH-A NADP-specific glutamate dehydrogenase [l-glutamate - NADP⁺ oxido-reductase (deaminating), EC 1.4.1.4] - gdhA genotype associated with GDH-A deficiency - GDH-B NAD-specific glutamate dehydrogenase, [L-glutamate NAD⁺ oxido-reductase (deaminating), EC 1.4.1.2] - gdhB genotype associated with GDH-B deficiency - gdhCR genotype associated with derepressed GDH-B synthesis - specific growth rate (h^-1) - x cell density - t time (h)