Glucose repression of xylitol production in Candida tropicalis mixed-sugar fermentations

Glucose repressed xylose utilization inCandida tropicalis pre-grown on xylose until glucose reached approximately 0–5 g l^–1. In fermentations consisting of xylose (93 g l^–1) and glucose (47 g l^–1), xylitol was produced with a yield of 0.65 g g^–1 and a specific rate of 0.09 g g^–1 h^–1, and high concentrations of ethanol were also produced (25 g l^–1). If the initial glucose was decreased to 8 g l^–1, the xylitol yield (0.79 g g^–1) and specific rate (0.24 g g^–1 h^–1) increased with little ethanol formation (<5 g l^–1). To minimize glucose repression, batch fermentations were performed using an aerobic, glucose growth phase followed by xylitol production. Xylitol was produced under O₂ limited and anaerobic conditions, but the specific production rate was higher under O₂ limited conditions (0.1–0.4 vs. 0.03 g g^–1 h^–1). On-line analysis of the respiratory quotient defined the time of xylose reductase induction.     

Anaerobic fermentation of Salmonella typhimurium with and without pyruvate carboxylase

A plasmid that expressed pyruvate carboxylase (PYC) from Rhizobium etli was introduced into Salmonella typhimurium LT2. Anaerobic fermentations of S. typhimurium with and without PYC were compared with glucose as a carbon source. The presence of PYC increased the succinate yield from glucose from 0.044 g g^–1 to 0.22 g g^–1, while the lactate yield decreased from 0.31 g g^–1 to 0.16 g g^–1. Metabolic flux calculations during the early growth phase indicate that under these growth conditions in the presence of PYC more carbon flows to oxaloacetate via pyruvate carboxylase than via phosphoenolpyruvate carboxylase. Also, under these growth and induction conditions, the presence of PYC diminished the cell growth rate from 0.34 h^–1 to 0.28 h^–1, the specific rate of ATP formation from 45 mmol l^–1 h^–1 to 27 mmol l^–1 h^–1, and the specific rate of glucose consumption from 17 mmol l^–1 h^–1 to 10 mmol l^–1 h^–1.     

An adaptive on-line control feed rate system in a laboratory scale bakers yeast process

Summary A new control policy for the on-line optimization of the nutrient supply in bakers yeast process is proposed. A feed rate corresponding to minimal substrate uptake time was shown to be optimal for cell yield and specific growth rate. Cultivation results of baker's yeast are presented.Nomenclature c glucose concentration in wort (mol.l^–1) - C total glucose used (mol) - c_e ethanol concentration in wort (mg.l^–1) - c_p glucose concentration in fresh medium (mol.l^–1) - dt/dc glucose consumption time (sec.mol^–1) - F substrate feed rate (litre.hr^–1) - q_c glucose uptake rate (mol.hr^–1) - Q_c specific glucose uptake rate (moll.g^–1.hr^–1) - qO₂ oxygen uptake rate (mol.hr^–1) - QO₂ specific oxygen uptake rate (mol.g^–1.hr^–1) - r_x productivity (g.l^–1.hr^–1) - t time (hr) - x biomass concentration (g.l^–1) - X total biomass (g) - Y_x/c cell yield (g.g^–1): (g.mol^–1) - Y_o/c consumed oxygen to glucose ratio (mol.mol^–1)     

Biological conversion of wood hydrolysate to succinic acid by Anaerobiospirillum succiniciproducens

Anaerobiospirillum succiniciproducens grew on a minimal salts medium containing wood hydrolysate (equivalent to 27 g glucose l^–1) and, when supplemented with 10 g corn steep liquor l^–1 as a complex nitrogen source, succinic acid at 24 g l^–1 was obtained (yield = 88% w/w glucose). This may therefore be an economical method to produce succinic acid.     

Poly(3-hydroxybutyrate) synthesis in fed-batch culture of Ralstonia eutropha with phosphate limitation under different glucose concentrations

Poly(3-hydroxybutyrate) (PHB) was produced by fed-batch cultures of Ralstonia eutropha with phosphate limitation under different glucose concentrations. When glucose was kept at 2.5 g l^–1, cell growth and PHB synthesis were limited due to the shortage of carbon source but a higher PHB content occurred in the cell-growth stage. This shows that a low glucose concentration is favorable for PHB accumulation in R. eutropha. PHB obtained with glucose at 9 g l^–1 is 1.6 times that obtained with 40 g l^–1. When glucose was in the range of 9 to 40 g l^–1, PHB concentration and productivity decreased significantly with the increase of glucose concentration. The highest PHB productivity was obtained with glucose at 9 g l^–1.     

Preparation and testing of Sardinella protein hydrolysates as nitrogen source for extracellular lipase production by Rhizopus oryzae

Various fish protein hydrolysates (FPH) from sardinella (Sardinella aurita) were used as nitrogen sources for the production of extracellular lipase by the filamentous fungus Rhizopus oryzae. The best results were obtained with defatted meat–fish protein hydrolysates (DMFPH), indicating the presence in the lipid fraction of some constituents which may repress lipase synthesis. Furthermore, it was found that the extensive hydrolysis of fish proteins resulted in a higher lipase production. The use of 40 g DMFPH l^–1 for the growth of Rhizopus oryzae in medium R1 resulted in a lipase production of 394 U ml^–1, higher than the yield obtained with standard soy peptone as nitrogen source (373 U ml^–1). The most appropriate medium for the growth and the production of lipase is composed only of 24 g DMFPH l^–1 and 10 g glucose l^–1, indicating that the strain can obtain its nitrogen and salts requirements directly from fish substrate.     

Conversion of xylose to ethanol by a novel phenol-tolerant strain of Enterobacteriaceae isolated from olive mill wastewater

A xylose-fermenting bacterium of the family Enterobacteriaceae was isolated from olive mill wastewater. It converted xylose to ethanol with a yield of 0.19 g ethanol g^–1 xylose. Although phenolic compounds normally inhibit pentose-utilizing microorganisms, this isolate was tolerant to phenol. Both the yield and the productivity of xylose fermentation decreased by 30% when phenol was added at a final concentration of 0.8 g phenol l^–1. Xylose (23 g l^–1) was totally fermented to ethanol (4.3 g l^–1) within 48 h in the absence of phenol; however, in the presence of 0.8 g phenol l^–1, only 3.3 g ethanol l^–1 was obtained from the same starting concentration of xylose after 70 h.     

Kinetic analysis of ethanol production by an acetate-resistant strain of recombinant Zymomonas mobilis

Zymomonas mobilis ZM4/Ac^R (pZB5), a mutant recombinant strain with increased acetate resistance, has been isolated following electroporation of Z. mobilis ZM4/Ac^R. This mutant strain showed enhanced kinetic characteristics in the presence of 12 g sodium acetate l^–1 at pH 5 in batch culture on 40 g glucose, 40 g xylose l^–1 medium when compared to ZM4 (pZB5). In continuous culture, there was evidence of increased maintenance energy requirements/uncoupling of metabolism for ZM4/Ac^R (pZB5) in the presence of sodium acetate; a result confirmed by analysis of the effect of acetate on other strains of Z. mobilis. Nomenclature m Cell maintenance energy coefficient (g g^–1 h^–1)Maximum overall specific growth rate (1 h^–1)Maximum specific ethanol production rate (g g^–1 h^–1)Maximum specific total sugar utilization rate (g g^–1 h^–1)Biomass yield per mole of ATP (g mole^–1 Ethanol yield on total sugars (g g^–1)Biomass yield on total sugars (g g^–1)True biomass yield on total sugars (g g^–1)     

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     

Energetics and product formation by Saccharomyces cerevisiae grown in anaerobic chemostats under nitrogen limitation

Anaerobic fermentation of glucose (20 g/l) by Saccharomyces cerevisiae CBS 8066 was studied in a chemostat (dilution rate = 0.05–0.25 h^–1) at different concentrations of the nitrogen source (5.00 g/l or 0.36 g/l ammonium sulphate). The ethanol yield (g ethanol produced/g glucose consumed) was found to be higher and the glycerol yield (g glycerol formed/g glucose consumed) lower during nitrogen limitation than under carbon limitation. The biomass yield on ATP (g dry weight biomass produced/mol ATP consumed) was consequently found to be lower during nitrogen-limited conditions.     

Acetone butanol ethanol (ABE) production from concentrated substrate: reduction in substrate inhibition by fed-batch technique and product inhibition by gas stripping

Acetone butanol ethanol (ABE) was produced in an integrated fed-batch fermentation-gas stripping product-recovery system using Clostridium beijerinckii BA101, with H₂ and CO₂ as the carrier gases. This technique was applied in order to eliminate the substrate and product inhibition that normally restricts ABE production and sugar utilization to less than 20 g l^–1 and 60 g l^–1, respectively. In the integrated fed-batch fermentation and product recovery system, solvent productivities were improved to 400% of the control batch fermentation productivities. In a control batch reactor, the culture used 45.4 g glucose l^–1 and produced 17.6 g total solvents l^–1 (yield 0.39 g g^–1, productivity 0.29 g l^–1 h^–1). Using the integrated fermentation-gas stripping product-recovery system with CO₂ and H₂ as carrier gases, we carried out fed-batch fermentation experiments and measured various characteristics of the fermentation, including ABE production, selectivity, yield and productivity. The fed-batch reactor was operated for 201 h. At the end of the fermentation, an unusually high concentration of total acids (8.5 g l^–1) was observed. A total of 500 g glucose was used to produce 232.8 g solvents (77.7 g acetone, 151.7 g butanol, 3.4 g ethanol) in 1 l culture broth. The average solvent yield and productivity were 0.47 g g^–1 and 1.16 g l^–1 h^–1, respectively.     

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     

Observer design for differential-algebraic model of an aerobic culture of a recombinant yeast

The mathematical model of an aerobic culture of recombinant yeast presented in work by Zhang et al. (1997) is given by a differential-algebraic system. The classical nonlinear observer algorithms are generally based on ordinary differential equations. In this paper, first we extend the nonlinear observer synthesis to differential-algebraic dynamical systems. Next, we apply this observer theory to the mathematical model proposed in Zhang et al. (1997). More precisely, based on the total cell concentration and the recombinant protein concentration, the observer gives the online estimation of the glucose, the ethanol, the plasmid-bearing cell concentration and a parameter that represents the probability of plasmid loss of plasmid-bearing cells. Numerical simulations are given to show the good performances of the designed observer.Symbols C ₁ activity of pacing enzyme pool for glucose fermentation (dimensionless) - C ₂ activity of pacing enzyme pool for glucose oxidation (dimensionless) - C ₃ activity of pacing enzyme pool for ethanol oxidation (dimensionless) - E ethanol concentration (g/l) - G glucose concentration (g/l) - k _a regulation constant for (g glucose/g cell h^–1) - k _b regulation constant for (dimensionless) - k _c regulation constant for (g glucose/g cell h^–1) - k _d regulation constant for (dimensionless) - K _m1 saturation constant for glucose fermentation (g/l) - K _m2 saturation constant for glucose oxidation (g/l) - K _m3 saturation constant for ethanol oxidation (g/l) - L ( t) time lag function (dimensionless) - p probability of plasmid loss of plasmid-bearing cells (dimensionless) - P recombinant protein concentration (mg/g cell) - q _G total glucose flux culture time (g glucose/g cell h) - t culture time (h) - t _lag lag time (h) - X total cell concentration (g/l) - X ⁺ plasmid-bearing cell concentration (g/l) - Y ^F _{X / G} cell yield for glucose fermentation pathway (g cell/g glucose) - Y ^O _{X / G} cell yield for glucose oxidation pathway (g cell/g glucose) - Y _{X / E} cell yield for ethanol oxidation pathway (g cell/g ethanol) - Y _{E / X} ethanol yield for fermentation pathway based on cell mass (g ethanol·g cell) - ₂ glucoamylase yield for glucose oxidation (units/g cell) - ₃ glucoamylase yield for ethanol oxidation (units/g cell) - µ₁ specific growth rate for glucose fermentation (h^–1) - µ₂ specific growth rate for glucose oxidation (h^–1) - µ₃ specific growth rate for ethanol oxidation (h^–1) - µ_1max maximum specific growth rate for glucose fermentation (h^–1) - µ_2max maximum specific growth rate for glucose oxidation (h^–1) - µ_3max maximum specific growth rate for ethanol oxidation (h^–1)     

Evaluation of xylitol production from corn cob hemicellulose hydrolysate by Candida parapsilosis

Candida parapsilosis was grown for 59 h in a medium containing corn cob hydrolysate consisting of 50 g xylose l^–1, 3.0 g glucose l^–1, 2.0 g arabinose l^–1, and 0.9 g acetic acid l^–1. A biomass of 9.1 g l^–1 was produced with 36 g xylitol l^–1 and 2.5 g ethanol l^–1. In a medium containing 50 g xylose l^–1 instead of corn cob hydrolysate, the concentrations of cells, xylitol, and ethanol were 8.6 g l^–1, 33 g l^–1, and 0.2 g l^–1, respectively. The differences between two cultures were due to the glucose and arabinose in the corn cob hydrolysate stimulating growth and the low concentration of acetic acid stimulating xylitol production.     

Multiple growth inhibition of <Emphasis Type="Italic">Klebsiella pneumoniae</Emphasis> in 1,3-propanediol fermentation

The inhibition of substrate and product on the growth of Klebsiella pneumoniae in anaerobic and aerobic batch fermentation for the production of 1,3-propanediol was studied. The cells under anaerobic conditions had a higher maximum specific growth rate of 0.19 h^–1 and lower tolerance to 110 g glycerol l^–1, compared to the maximum specific growth rate of 0.17 h^–1 and tolerance to 133 g glycerol l^–1 under aerobic conditions. Acetate was the main inhibitory metabolite during the fermentation under anaerobic conditions, with lactate and ethanol the next most inhibitory. The critical concentrations of acetate, lactate and ethanol were assessed to be 15, 19, 26 g l^–1, respectively. However, cells grown under aerobic conditions were more resistant to acetate and lactate but less resistant to ethanol. The critical concentrations of acetate, lactate and ethanol were assessed to be 24, 26, and 17 g l^–1, respectivelyRevisions requested 8 september; Revisions received 2 November 2004     

Optimized production of L-β-hydroxybutyric acid by a mutant of Yarrowia lipolytica

A mutant strain of Yarrowia lipolytica was developed which produced 8.0 g l--hydroxybutyric acid l^–1 from butyric acid in a batch culture. The optimum culture conditions in the fermenter for maintenance of a high cell activity, determined by chemostat analyses, were a specific growth rate of 0.06 h^–1, a glucose concentration of 2.0 g l^–1, and a butyric acid concentration of 8.1 g l^–1. A fed-batch fermentation was performed under these conditions resulting in an l--hydroxybutyric acid yield of 31 g l^–1.     

Glycerol production by Candida krusei employing NaCl as an osmoregulator in batch and continuous fermentations

Addition of 40 g NaCl l^–1 to a chemically defined medium containing 140 g glucose l^–1 in shake-flask culture improved glycerol production by Candida krusei from 16.5 g l^–1 to 47.7 g l^–1. With 40 g NaCl l^–1 at a dilution rate of 0.065 h^–1, glycerol concentration, glycerol yield (based on glucose consumed), and productivity in a four-stage cascade bioreactor were higher by 240%, 27% and 28%, respectively, than in a single-stage continuous culture system.     

Growth inhibition by ammonia and use of a pH-controlled feeding strategy for the effective cultivation of Mycobacterium chlorophenolicum

The inhibitory effect of ammonia on the growth of the polychlorinated xenobiotic-degrading bacterium Mycobacterium chlorophenolicum was examined. The strain is inhibited by both the ionized and nonionized forms of ammonia. At pH 6.9 50% reduction of the growth rate was observed at 6.8 g l^–1 total ammonium. For 23 experiments performed in shake-flask culture at different pH values and ammonium concentrations a growth model based on the extended Monod kinetic fits the data with a deviation of 5.3%. To overcome growth inhibition in bioreactors a pH-controlled feeding strategy was developed for effective cultivation of M. chlorophenolicum at an ammonium level below 0.3 g l^–1. The ammonium addition was controlled on-line by the stoichiometric interdependence of ammonium consumption and pH decline. With this on-line control strategy a biomass concentration as high as 26.2 g l^–1 can be achieved within less than 1 week of cultivation, compared to a biomass concentration of 15.5 g l^–1 in normal batch culture after 2 weeks of cultivation. The yield is also increased from 0.32 g to 0.43 g biomass (g glucose)^–1. The strategy developed provides an effective method for the production of biomass of M. chlorophenolicum serving as the inoculum in remediation technologies.     

Effect of the dilution rate on the biomass yield ofBacillus thuringiensis and determination of its rate coefficients under steady-state conditions

Depending on the biomass yield on glucose and the cell morphology ofBacillus thuringiensis, three different metabolic states were observed in continuous culture. At dilution rates between 0.18 h^–1 and 0.31 h^–1 vegetative cells, sporulating bacteria and spores coexisted, while glucose and amino acids were consumed. Only vegetative cells were observed at dilution rates between 0.42 h^–1 and 0.47 h^–1 and glucose was used as the main carbon and energy source. AtD = 0.50 h^–1 the biomass yield on glucose decreases sharply. To define better the specific growth rate range in which the microorganism uses mainly glucose, a dilution rate of 0.25–0.45 h^–1 was studied. The experimental data could be adjusted to a Monod model and the following rate coefficients and growth yields were determined: maximum specific growth rate 0.54 h^–1, saturation constant 0.56 mg glucose ml^–1, biomass growth yields 0.43 g cells (g glucose)^–1, and 0.76 g cells (g oxygen)^–1, and maintenance coefficients 0.065 g glucose (g cells)^–1 h^–1 and 0.039 g oxygen (g cells)^–1 h^–1.     

The effect of micro-aerobic conditions on continuous ethanol production by Saccharomyces cerevisiae

Summary The effect of trace amounts of oxygen on the degree of ethanol inhibition in a continuous anaerobic culture of Saccharomyces cerevisiae was studied at the 100 gl ^–1 feed glucose concentration level. Results showed that the use of micro-aerobic conditions (0,5% of saturation) enhanced the utilisation of substrate by increasing the ethanol tolerance of the yeast without any significant decrease in the ethanol yield per unit substrate consumed. When the results were fitted to an equation of the form % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbyacaqG8o% GaaeypaiqabY7agaqcaiaab6cadaWcaaGcbaqcLbyacaqGdbWaaSba% aSqaaKqzagGaae4CaaWcbeaaaOqaaKqzagGaae4qamaaBaaaleaaju% gGbiaabohaaSqabaqcLbyacqGHRaWkcaqGlbWaaSbaaSqaaKqzagGa% ae4CaaWcbeaaaaqcLbyacaGGUaWaaSaaaOqaaKqzagGaae4samaaBa% aaleaajugGbiaabchaaSqabaaakeaajugGbiaabUeadaWgaaWcbaqc% LbyacaqGWbaaleqaaKqzagGaey4kaSIaaeywamaaBaaaleaajugGbi% aabchacaqGZbaaleqaaKqzagGaaiOlaiaacIcacaqGdbWaaSbaaSqa% aKqzagGaae4CaiaabAgaaSqabaqcLbyacqGHsislcaqGdbWaaSbaaS% qaaKqzagGaae4CaaWcbeaajugGbiaacMcaaaaaaa!6301!\[{\text{\mu = \hat \mu }}{\text{.}}\frac{{{\text{C}}_{\text{s}} }}{{{\text{C}}_{\text{s}} + {\text{K}}_{\text{s}} }}.\frac{{{\text{K}}_{\text{p}} }}{{{\text{K}}_{\text{p}} + {\text{Y}}_{{\text{ps}}} .({\text{C}}_{{\text{sf}}} - {\text{C}}_{\text{s}} )}}\]it was found that the values for % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiVdyaaja% aaaa!373F!\[{\text{\hat \mu }}\], K_s and Y_ps were the same as for the non-aerobic case while the ethanol inhibition constant, K_p , had increased from 5,2 to 14,0 gl ^–1.Notation C_sf feed substrate concentration - gl ^–1 - C_s substrate concentration gl ^–1 - C_p product concentration - gl ^–1 - C_x cell concentration - gl ^–1 - D dilution rate - h^-1 - K_s substrate saturation constant - gl ^–1 - K_p product inhibition constant - gl ^–1 - m maintenance coefficient - h^–1 - Y_ps product yield coefficient - g EtOH/g glucose - Y_xs cell yield coefficient - g cells/g glucose - specific growth rate - h^–1 - % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiVdyaaja% aaaa!373F!\[{\text{\hat \mu }}\] maximum specific growth rate - h^–1