Kinetics of nitrate uptake by freshwater algae

The kinetics of nitrate (NO₃ ^–) uptake, the maximum uptake velocity (V_m) and the half-saturation constant (K_s), were determined for 18 species of batch-cultured freshwater algae grown without nitrogen limitation. Values of K_s ranged from 0.25 to 6.94 µM l^–1 Chlorella pyrenoidosa Chick, and Navicula pelliculosa (Breb.) Hilse, respectively. Values of V_m ranged from 0.51 to 5.07 µM l^–1 h^–1 for Anabaena A7214 and Nitzschia W-32 O'Kelley, respectively. The mean positive values of K_s for Chlorophyta, Cyanophyta and Chrysophyta were 1.89, 3.67 and 4.07 µM l^–1, respectively. The mean values of V_m for the same phyla were 1.61, 1.02 and 2.97 µM l^–1 h^–1 10⁵ cells^–1, respectively. The ranges of these kinetic parameters encompass values of kinetic parameters for marine and freshwater species in batch culture, for freshwater algae grown in N-limited chemostats and for natural populations of freshwater phytoplankton. Thus, in spite of variability between species, uptake parameters for both marine and freshwater algae are identical.     

Effect of dilution rate on eicosapentaenoic acid productivity ofPhaeodactylum tricornutum utex 640 in outdoor chemostat culture

Summary Eicosapentaenoic acid (EPA) volumetric productivity from an outdoor chemostat culture ofPhaeodactylum tricornutum UTEX 640 in a 50-l tubular photobioreactor varies with dilution rate, reaching a maximum of 47.8 mg l^–1 d^–1 at D=0.36 d^–1. Continuous culture at high dilution rates' is proposed as the most adequate operating mode to maximize polyunsaturated fatty acid production.     

The isolation and characterisation of a salicylate-hydroxylase-producing strain of Pseudomonas putida

Summary A salicylate-hydroxylase-producing strain of Pseudomonas putida with an unusual capability to grow at toxic levels of salicylate up to 10 g l^–1 has been isolated. It grew well under continuous culture conditions, with optimum growth at pH 6.5 and a temperature of 25° C. The use of an ammonium salt as a nitrogen source, instead of nitrate, resulted in a 30–40% increase in its biomass yield coefficient. Optimum growth under continuous culture conditions was achieved using 4 g l^–1 salicylate at 25° C, pH 6.5 and 0.2 h^–1 dilution rate. High salicylate hydroxylase enzyme activity [236 units (U) l^–1] and productivity (424.8 U h^–1) were obtained at a dilution rate of 0.45 h^–1 using a mineral medium containing 4 g l^–1 of salicylate. Operating under continuous culture conditions with oxygen limitation and a slight accumulation of residual salicylate (0.2 g l^–1) resulted in a decrease in culture performance and enzyme productivity. Correspondence to: R. Marchant     

Integration of consumer-targeted microalgal production with marine fish effluent biofiltration – a strategy for mariculture sustainability

EU regulations recommend effluent treatment and nutrient recycling for aquaculture sustainability, so a study was undertaken to provide base-line data for the integration of commercial fish-farm effluents with the production of microalgae. The project relates to a specific bivalve consumer (Tapes decussatus) and biofiltration. Effluent inorganic nutrient composition was assessed and evaluated as culture media for Phaeodactylum tricornutum, Tetraselmis suecica and Tetraselmis sp. Optimization of the microalgal compartment included studies on preparation of a simple medium, nutrient or dilution rate manipulation and nutrient removal. Cell harvest was increased chiefly by N correction (6-fold for Tetraselmis sp.) and semi-continuous or continuous operation (by a factor of 3 to 11). Nutrient removal efficiency was high for ammonium and nitrite-nitrogen (80–100%), depending on species, nutrient ratio (Si correction for P. tricornutum) and culture regime for nitrate (41–100%) or phosphorus (21–99%). Data obtained under cyclostat cultivation (yields of 1.38 and 0.50×10⁶ P. tricornutum or Tetraselmis sp. cells mL⁻¹ d⁻¹ and nutrient uptake rates of 2.32 mg N L⁻¹ d⁻¹ and 0.96 mg P L⁻¹ d⁻¹) were used to show clam production and simultaneous wastewater treatment possibilities through the proposed fish-microalgae-clam integrated aquaculture system.     

On the annual variation of phytoplankton biomass in Finnish inland waters

Annual variations in phytoplankton biomass in 63 lakes in Southern and Central Finland are discussed. Biomass is rather small during winter (January–April), usually <0.05 mg l^–1 (fresh weight) and there are no differences between oligotrophic and eutrophic lakes. In early spring and in autumn biomass varies widely, depending mainly on water temperature. Phytoplankton biomass is smaller in July than in June and August in oligotrophic lakes (biomass <0.20 mg l^–1 fresh weight) and mesotrophic (biomass 1.0–2.5 mg l^–1) lakes, but greater in eutrophic (biomass 2.5–10.0 mg l^–1) and hypereutrophic (biomass >10.0 mg l^–1) lakes. The standard deviation of phytoplankton biomass in Finnish inland waters is usually smallest in July, which facilitates the comparison of phytoplankton between different kinds of lakes.     

Limitations in substrate utilization efficiency by Zymomonas mobilis

Summary Optimal growth conditions for Zymomonas mobilis have been established using continuous cultivation methods. Optimal substrate utilization efficiency occurs with 2.5 g l^–1 yeast extract, 2.0 g l^–1 ammonium sulfate and 6.0 g l^–1 magnesium sulfate in the media. Catabolic activity is at its maximum with glucose uptake rates of 16–18 g l^–1 h^–1 and ethanol production rates of 8–9 g l^–1 h^–1, Q_g values of 22–26 and Q_p values between 11 and 13, which results in 40 g l^–1 h^–1 ethanol yields using a 100 g l^–1 substrate feed. Any increase in these parameters goes on cost of substrate utilization efficiency. Calcium pantothenate can not substitute yeast extract.Abbreviations G Glucose (%) - Pant Calcium pantothenate (mg l^–1) - D Dilution rate (h^–1) - NH₄ Ammonium sulfate (%) - M_g Magnesium sulfate (%) - S₁ Residual glucose in the fermenter (g l^–1) - S₀ Glucose feed (g l^–1) - Eth Ethanol concentration (g l^–1) - GUR Glucose uptake rate (g l^–1 h^–1) - Q_g Specific glucose uptake rate (g g^–1 h^–1) - Q_p Specific ethanol production rate (g g^–1 h^–1) - EPR Ethanol production rate (g l^–1 h^–1) - Y_g Yield coefficient for glucose (g g^–1) - Y_p Conversion efficiency (%) - C Biomass concentration (g l^–1) Present address: (Until June 1982) Institut für Mikrobiologie, TH Darmstadt, 6100 Darmstdt, Federal Republic of Germany     

Production of medium chain length polyhydroxyalkanoates by fed-batch culture of Pseudomonas oleovorans

Pseudomonas oleovorans was cultivated to produce medium chain length polyhydroxyalkanoates (MCL-PHAs) from octanoic acid and ammonium nitrate as carbon and nitrogen source, respectively, by a pH-stat fed-batch culture technique. The octanoate in the culture broth was maintained below 4 g l^–1 by feeding the mixture of octanoic acid and ammonium nitrate when the culture pH rose above 7.1. The final cell concentrations of 63, 55 and 9.5 g l^–1, PHA contents of 62, 75 and 67% of dry cell wt, and productivities of 1, 0.63 and 0.16 g l^–1 h^–1 were obtained when the C/N ratios in the feed were 10, 20 and 100 g octanoic acid g^–1 ammonium nitrate, respectively.     

Selective ingestion of phytoplankton by the bivalvesMytilus edulis L. andCerastoderma edule (L.)

Blue mussles (Mytilus edulis) and cockles (Cerastoderma edule) were collected in the Oosterschelde estuary (SW Netherlands) and exposed to diets consisting of the diatomPhaeodactylum tricornutum and silt. Algal concentrations were kept constant (20.10³ cells.ml^–1), and silt concentrations were varied between 3–80 mg.l^–1 (mussel experiments) and 20–120 mg.l^–1 (cockle experiments). Chlorophyll-a concentrations in the pseudofaeces were reduced compared to the diets, indicating selective ingestion of the algae. It was estimated that the mussels increase the ingestion of chlorophyll-a 2.0 times, and the cockles increase the chlorophyll-a ingestion 2.8 times, compared to the ingestion rate without selection. The selection coefficients were not affected by the SPM concentrations used. Phaeophytin-a concentrations in the faeces showed an increase as a consequence of the digestion of the ingested algae. Digestive efficiencies of chlorophyll-a varied between 36–92% The digestive efficiencies decreased with increasing SPM concentrations.Communication no. 541 of the Delta Institute for Hydrobiological Research.     

Protein production from whey usingPenicillium cyclopium; growth parameters and cellular composition

Summary The growth parameters ofPenicillium cyclopium have been evaluated in a continuous culture system for the production of fungal protein from whey. Dilution rates varied from 0.05 to 0.20 h^–1 under constant conditions of temperature (28°C) and pH (3.5). The saturation coefficients in the Monod equation were 0.74 g l^–1 for lactose and 0.14 mg l^–1 for oxygen, respectively. For a wide range of dilution rates, the yield was 0.68 g g^–1 biomass per lactose and the maintenance coefficient 0.005 g g^–1 h^–1 lactose per biomass, respectively. The maximum biomass productivity achieved was 2 g l^–1 h^–1 biomass at dilution rates of 0.16–0.17 h^–1 with a lactose concentration of 20 g l^–1 in the feed. The crude protein and total nucleic acid contents increased with a dilution rate, crude protein content varied from 43% to 54% and total nucleic acids from 6 to 9% in the range of dilution rates from 0.05 to 0.2 h^–1, while the Lowry protein content was almost constant at approximately 37.5% of dry matter.Nomenclature (mg l^–1) C_o initial concentration of dissolved oxygen - (h^–1) D dilution rate - (mg l^–1) K₀₂ saturation coefficient for oxygen - (g l^–1) K_s saturation coefficient for substrate - (g g^–1 h^–1) lactose per biomass) m maintenance energy coefficient - (mM g^–1 h^–1O₂ per biomass) Q₀₂ specific oxygen uptake rate - (g l^–1) S residual substrate concentration at steady state - (g l^–1) S_o initial substrate concentration in feed - (min) t_1/2 time when C_o is equal to C_o/2 - (g l^–1) X biomass concentration - (g l^–1) X biomass concentration at steady state - (g g^–1 biomass per lactose) Y_G yield coefficient for cell growth - (g g^–1 biomass per lactose) Y_x/s overall yield coefficient - (h^–1) specific growth rate     

Production potential of eicosapentaenoic acid by the diatom Nitzschia laevis

To investigate the production potential of eicosapentaenoic acid (EPA) by the diatom Nitzschia laevis, the growth characteristics and fatty acid composition of the cells were studied under photoautotrophic, mixotrophic and heterotrophic conditions of growth. The specific growth rate and maximum biomass concentration were respectively 0.466 d^–1 and 2.27 g l^–1 for mixotrophic culture, 0.344 d^–1 and 2.04 g l^–1 for heterotrophic culture, and 0.167 d^–1 and 0.5 g l^–1 for photoautotrophic culture, respectively. As for EPA production, the yield and productivity were respectively 52.32 mg l^–1 and 10.46 mg l^–1 d for mixotrophic culture, 35.08 mg l^–1 and 6.37 mg l^–1 d for heterotrophic culture, and 6.78 mg l^–1 and 3.39 mg l^–1 d for photoautotrophic culture, respectively. Results suggest that mixotrophic culture is the most suitable growth mode for the production of EPA by the diatom Nitzschia laevis. The results are useful for the development of a cost-effective fermentation process for EPA production by Nitzschia laevis.     

Biomass and icosapentaenoic acid productivities from an outdoor batch culture of Phaeodactylum tricornutum UTEX 640 in an airlift tubular photobioreactor

An outdoor tubular photobioreactor, based on an external-loop airlift, has been used to cultivate the diatom Phaeodactylum tricornutum UTEX 640, rich in icosapentaenoic acid (EPA). The system was operated in batch mode. The specific growth rate in the exponential phase, averaged over the whole day, was 0.254 day^–1 · A 25 gl^–1 maximum biomass concentration was obtained by the end of the culture period. The dissolved oxygen generated never rose over 210% of air saturation nor was there impediment to biomass generation or inhibition of photosynthesis. Furthermore, around 2 × 10¹⁷ quanta cm^–2 s^–1 light intensity seemed to saturate the photosynthetic activity. Biomass losses during the night could be reduced to less than 5% by maintaining the culture at 16°C at night. The maximum concentration and productivity of EPA were 423 mgl^–1 and 13 mgl^–1 day^–1, respectively, at the end of the culture, although a 21-mgl^–1 day^–1 net EPA generation rate was obtained at the linear growth phase.     

Interactive Effects of Ocean Acidification and Nitrogen-Limitation on the Diatom Phaeodactylum tricornutum

Climate change is expected to bring about alterations in the marine physical and chemical environment that will induce changes in the concentration of dissolved CO₂ and in nutrient availability. These in turn are expected to affect the physiological performance of phytoplankton. In order to learn how phytoplankton respond to the predicted scenario of increased CO₂ and decreased nitrogen in the surface mixed layer, we investigated the diatom Phaeodactylum tricornutum as a model organism. The cells were cultured in both low CO₂ (390 μatm) and high CO₂ (1000 μatm) conditions at limiting (10 μmol L⁻¹) or enriched (110 μmol L⁻¹) nitrate concentrations. Our study shows that nitrogen limitation resulted in significant decreases in cell size, pigmentation, growth rate and effective quantum yield of Phaeodactylum tricornutum, but these parameters were not affected by enhanced dissolved CO₂ and lowered pH. However, increased CO₂ concentration induced higher rETR_max and higher dark respiration rates and decreased the CO₂ or dissolved inorganic carbon (DIC) affinity for electron transfer (shown by higher values for K_{1/2 DIC} or K_{1/2 CO2}). Furthermore, the elemental stoichiometry (carbon to nitrogen ratio) was raised under high CO₂ conditions in both nitrogen limited and nitrogen replete conditions, with the ratio in the high CO₂ and low nitrate grown cells being higher by 45% compared to that in the low CO₂ and nitrate replete grown ones. Our results suggest that while nitrogen limitation had a greater effect than ocean acidification, the combined effects of both factors could act synergistically to affect marine diatoms and related biogeochemical cycles in future oceans.     

Denitrification kinetics of simulated fish processing wastewater at different ratios of nitrate to biomass

Denitrification was studied in anoxic batch cultures of a simulated fish processing wastewater at 37 r C and pH 7.5, using a denitrifying enrichment culture from fishery wastewater. Different initial nitrate to biomass ratios (So/Xo) were used: nitrate and biomass varied from 7.5 to 94.7 mg NO₃-N l^–1, and from 20 to 4300 mg volatile suspended solids l^–1, respectively. The specific maximum denitrification rate (r _m) and the cell yield (Y _{X / S}) depended on the So/Xo ratio under anoxic conditions: r _m increased from 1.2 to 1584 mg NO₃-N g^–1 VSS h^–1 and Y _{X / S} decreased from 42 to 0.03 mg VSS mg^–1 NO₃-N when So/Xo varied from 5.5 10^{– 3} to 9.3 mg NO₃-N/mg VSS. Nomenclature C_{NO3 – N} nitrate concentration, mg NO₃-N l^–1 K _S saturation constant, mg NO₃-N l^–1 r _m specific maximum denitrification rate, mg NO₃-N g^–1 VSS h^–1 So initial substrate concentration, mg l^–1 t time, h TOC total organic carbon VSS volatile suspended solids x biomass concentration, g VSS l^–1 Xo initial biomass concentration, g VSS l^–1 Y _X/S substrate to biomass cell yield, mg VSS/mg N Greek symbols: _m maximum specific growth rate of the anoxic microbial population, 1 h^–1     

Aerobic nitrate and nitrite reduction in continuous cultures of Escherichia coli E4

Nitrate and nitrite was reduced by Escherichia coli E4 in a l-lactate (5 mM) limited culture in a chemostat operated at dissolved oxygen concentrations corresponding to 90–100% air saturation. Nitrate reductase and nitrite reductase activity was regulated by the growth rate, and oxygen and nitrate concentrations. At a low growth rate (0.11 h^–1) nitrate and nitrite reductase activities of 200 nmol · mg^–1 protein · min^–1 and 250 nmol · mg^–1 protein · min^–1 were measured, respectively. At a high growth rate (0.55 h^–1) both enzyme activities were considerably lower (25 and 12 nmol mg^–1 · protein · min^–1). The steady state nitrite concentration in the chemostat was controlled by the combined action of the nitrate and nitrite reductase. Both nitrate and nitrite reductase activity were inversely proportional to the growth rate. The nitrite reductase activity decreased faster with growth rate than the nitrate reductase. The chemostat biomass concentration of E. coli E4, with ammonium either solely or combined with nitrate as a source of nitrogen, remained constant throughout all growth rates and was not affected by nitrite concentrations. Contrary to batch, E. coli E4 was able to grow in continuous cultures on nitrate as the sole source of nitrogen. When cultivated with nitrate as the sole source of nitrogen the chemostat biomass concentration is related to the activity of nitrate and nitrite reductase and hence, inversely proportional to growth rate.     

Seasonal change in the proportion of bacterial and phytoplankton production along a salinity gradient in a shallow estuary

We intended to evaluate the relative contribution of primary production versus allochthonous carbon in the production of bacterial biomass in a mesotrophic estuary. Different spatial and temporal ranges were observed in the values of bacterioplankton biomass (31–273 g C l^–1) and production (0.1–16.0 g C l^–1 h^–1, 1.5–36.8 mg C m^–2 h^–1) as well as in phytoplankton abundance (50–1700 g C l^–1) and primary production (0.1–512.9 g C l^–1 h^–1, 1.5–512.9 mg C m^–2 h^–1). Bacterial specific growth rate (0.10–1.68 d^–1) during the year did not fluctuate as much as phytoplankton specific growth rate (0.02–0.74 d^–1). Along the salinity gradient and towards the inner estuary, bacterio- and phytoplankton biomass and production increased steadily both in the warm and cold seasons. The maximum geographical increase observed in these variables was 12 times more for the bacterial community and 8 times more for the phytoplankton community. The warm to cold season ratios of the biological variables varied geographically and according to these variables. The increase at the warm season achieved its maximum in the biomass production, particularly in the marine zone and at high tide (20 and 112 times higher in bacterial and phytoplankton production, respectively). The seasonal variation in specific growth rate was most noticeable in phytoplankton, with seasonal ratios of 3–26. The bacterial community of the marine zone responded positively – generating seasonal ratios of 1–13 in bacterial specific growth rate – to the strong warm season increment in phytoplankton growth rate in this zone. In the brackish water zone where even during the warm season allochthonous carbon accounted for 41% (on average) of the bacterial carbon demand, the seasonal ratio of bacterial specific growth rate varied from about 1 to 2. During the warm season, an average of 21% of the primary production was potentially sufficient to support the whole bacterial production. During the cold months, however, the total primary production would be either required or even insufficient to support bacterial production. The estuary turned then into a mostly heterotrophic system. However, the calculated annual production of biomass by bacterio- and phytoplankton in the whole ecosystem showed that auto- and heterotrophic production was balanced in this estuary.     

Biooxidation of ferrous iron by immobilized Acidithiobacillus ferrooxidans in poly(vinyl alcohol) cryogel carriers

PVA-cryogels entrapping about 10⁹ cells of Acidithiobacillus ferrooxidans per ml of gel were prepared by freezing-thawing procedure, and the biooxidation of Fe²⁺ by immobilized cells was investigated in a 0.365 l packed-bed bioreactor. Fe²⁺ oxidation fits a plug-flow reaction model well. A maximum oxidation rate of 3.1 g Fe²⁺ l^–1 h^–1 was achieved at the dilution rate of 0.4 h^–1 or higher, while no obvious precipitate was determined at this time. In addition, cell-immobilized PVA-cryogels packed in bioreactor maintained their oxidative ability for more than two months under non-sterile conditions. Nomenclature: C _A0 – Concentration of Fe²⁺ in feed stream (g l^–1) C _A – Concentration of Fe^{2 +} in outlet stream (g l^{– 1}) D – Dilution rate of the packed-bed bioreactor (h^–1) F – Volumetric flow rate of iron solution (l h^–1) F _A0 – Mass flow rate of Fe²⁺ in the feed stream (g h^–1) K – Kinetic constant (l l^–1 h^–1) r _A – Oxidation rate of Fe²⁺ (g l^–1 h^–1) V – Volume of packed-bed bioreactor (l) X _A – Conversion ratio of Fe²⁺ (%)     

Production of poly-γ-glutamic acid by fed-batch culture of Bacillus licheniformis

Fed-batch cultures of Bacillus licheniformis produced poly--glutamic acid (PGA), a water-soluble biodegradable polymer. PGA reached 35 g l^–1 with a productivity of 1 g l^–1 h^–1 by pulsed-feeding of citric acid (1.44 g h^–1) and l-glutamic acid (2.4 g h^–1) when citric acid was depleted from the culture medium.     

Methanol Production by a Broad Phylogenetic Array of Marine Phytoplankton

Methanol is a major volatile organic compound on Earth and serves as an important carbon and energy substrate for abundant methylotrophic microbes. Previous geochemical surveys coupled with predictive models suggest that the marine contributions are exceedingly large, rivaling terrestrial sources. Although well studied in terrestrial ecosystems, methanol sources are poorly understood in the marine environment and warrant further investigation. To this end, we adapted a Purge and Trap Gas Chromatography/Mass Spectrometry (P&T-GC/MS) method which allowed reliable measurements of methanol in seawater and marine phytoplankton cultures with a method detection limit of 120 nanomolar. All phytoplankton tested (cyanobacteria: Synechococcus spp. 8102 and 8103, Trichodesmium erythraeum, and Prochlorococcus marinus), and Eukarya (heterokont diatom: Phaeodactylum tricornutum, coccolithophore: Emiliania huxleyi, cryptophyte: Rhodomonas salina, and non-diatom heterokont: Nannochloropsis oculata) produced methanol, ranging from 0.8–13.7 micromolar in culture and methanol per total cellular carbon were measured in the ranges of 0.09–0.3%. Phytoplankton culture time-course measurements displayed a punctuated production pattern with maxima near early stationary phase. Stabile isotope labeled bicarbonate incorporation experiments confirmed that methanol was produced from phytoplankton biomass. Overall, our findings suggest that phytoplankton are a major source of methanol in the upper water column of the world’s oceans.     

Nitrogen and phosphorus uptake in seedlings of the seagrass Amphibolis antarctica in Western Australia

The uptake of nitrate, ammonium and phosphate was examined in vitro in seedlings of the seagrass Amphibolis antarctica ((Labill.) Sonder ex Aschers.). Uptake of all three nutrients was significantly correlated with external concentration up to 800 µ g l^–1. The uptake of nitrate (0–200 µ g NO₃-N g dry wt^–1 h^–1) was significantly lower than the uptake of ammonium (0–500 µ g NH₄-N g dry wt^–1 h^–1), suggesting that the seedlings have a higher affinity for this form of nitrogen in the water column.Data were in general agreement with uptake rates recorded for other seagrasses, notably Zostera marina. In comparison to the dominant macroalgae for the same region, seedlings had either similar or higher uptake rates in relation to external concentration, lending support to the hypothesis that seedlings, which do not possess roots, behave like macroalgae in terms of nutrient acquisition from the water column.A comparison with literature data on adult seagrass suggests, however, that seagrasses show lower uptake rates than macroalgae suggesting that the macroalgae, which are totally reliant on the water column for nutrients, are more efficient at uptake than seagrasses which may potentially use the sediment for a nutrient source.     

Invertase and phosphatase of yeast in a phosphate-limited continuous culture

Summary Deficiency of inorganic phosphate caused the hyper production of invertase and the derepression of acid phosphatase in a continuous culture ofSaccharomyces carlsbergensis. The specific invertase activity was 40,000 enzyme units per g dry cell weight at a dilution rate lower than 0.05 h^–1 with a synthetic glucose medium of which the molecular ratio of KH₂PO₄ to glucose was less than 0.006. This activity is eight fold higher than in a batch growth and 1.5 fold as much as the highest enzyme activity observed so far in a glucose-limited continuous culture.For the hyper production of invertase, it is necessary to culture the yeast continuously by keeping the Nyholm's conservative inorganic phosphate concentration at less than 0.2 m mole per g dry weight cell. The derepression of acid phosphatase brought about by phosphate deficiency, was similar in both batch and continuous cultures.Nomenclature D dilution rate of continuous culture (h^–1) - E_i invertase concentration in culture (enzyme unit l^–1) - E_p acid phosphatase concentration in culture (enzyme unit l^–1) - P inorganic phosphate concentration in culture (mM) - S glucose concentration in culture (mM) - X cell concentration in culture (g dry weight cell l^–1) Greek Letter specific rate of growth (h^–1) Suffix f feed - 0 initial value