A new paradigm for producing astaxanthin from the unicellular green alga Haematococcus pluvialis

The unicellular green alga Haematococcus pluvialis has been exploited as a cell factory to produce the high‐value antioxidant astaxanthin for over two decades, due to its superior ability to synthesize astaxanthin under adverse culture conditions. However, slow vegetative growth under favorable culture conditions and cell deterioration or death under stress conditions (e.g., high light, nitrogen starvation) has limited the astaxanthin production. In this study, a new paradigm that integrated heterotrophic cultivation, acclimation of heterotrophically grown cells to specific light/nutrient regimes, followed by induction of astaxanthin accumulation under photoautotrophic conditions was developed. First, the environmental conditions such as pH, carbon source, nitrogen regime, and light intensity, were optimized to induce astaxanthin accumulation in the dark‐grown cells. Although moderate astaxanthin content (e.g., 1% of dry weight) and astaxanthin productivity (2.5 mg L^?1 day^?1) were obtained under the optimized conditions, a considerable number of cells died off when subjected to stress for astaxanthin induction. To minimize the susceptibility of dark‐grown cells to light stress, the algal cells were acclimated, prior to light induction of astaxanthin biosynthesis, under moderate illumination in the presence of nitrogen. Introduction of this strategy significantly reduced the cell mortality rate under high‐light and resulted in increased cellular astaxanthin content and astaxanthin productivity. The productivity of astaxanthin was further improved to 10.5 mg L^?1 day^?1 by implementation of such a strategy in a bubbling column photobioreactor. Biochemical and physiological analyses suggested that rebuilding of photosynthetic apparatus including D1 protein and PsbO, and recovery of PSII activities, are essential for acclimation of dark‐grown cells under photo‐induction conditions. Biotechnol. Bioeng. 2016;113: 2088–2099. © 2016 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc.

     

Kinetic models for astaxanthin production by high cell density mixotrophic culture of the microalga Haematococcus pluvialis

High cell density cultivation of Haematococcus pluvialis for astaxanthin production was carried out in batch and fed-batch modes in 3.7-L bioreactors with stepwise increased light intensity control mode. A high cell density of 2.65 g L⁻¹ (batch culture) or 2.74 g L⁻¹ (fed-batch culture) was obtained, and total astaxanthin production in the fed-batch culture (64.36 mg L⁻¹) was about 20.5% higher than in the batch culture (53.43 mg L⁻¹). An unstructured kinetic model to describe the microalga culture system including cell growth, astaxanthin formation, as well as sodium acetate consumption was proposed. Good agreement was found between the model predictions and experimental data. The models demonstrated that the optimal light intensity for mixotrophic growth of H. pluvialis in batch or fed-batch cultures in a 3.7-L bioreactor was 90–360 μmol m⁻² s⁻¹, and that the stepwise increased light intensity mode could be replaced by a constant light intensity mode. Received 24 December 1998/ Accepted in revised form 23 April 1999     

Heterotrophic cultivation of Euglena gracilis Z for efficient production of α-tocopherol

Effects of hydrodynamic stress, dissolved oxygen (DO) concentration and carbon sources on heterotrophic α-tocopherol production by Euglena gracilis were investigated. In a jar fermentor without baffle plates, increasing the agitation speed up to 500 rpm had no significant effect on cell growth and α-tocopherol production. However, in a jar fermentor equipped with baffle plates, both the cell growth and α-tocopherol production were highly suppressed at 500 rpm. At high hydrodynamic stress, the cells secreted nucleic acid-related substances to the culture broth and the shape of the cells shifted from elongated toward spherical. High DO concentration had adverse effects on both cell growth and α-tocopherol production, the optimum DO concentration being below 0.8 ppm. In comparison with glucose, the growth rate was lower but the α-tocopherol content of the cells was almost four times higher when ethanol was used as the organic carbon source. In a fed-batch culture with ethanol, a very high cell concentration of 39.5 g L^-1 was obtained with α-tocopherol content of 1200 μg g-cell^-1. This α-tocopherol content is very close to the values reported for photoautotrophic and photoheterotrophic cultures. A very high α-tocopherol productivity of 102 μg L^-1 h^-1 was obtained, indicating that heterotrophic cultivation of E. gracilis has a very high potential as a substitute for the current method of extraction from vegetable oils. This revised version was published online in June 2006 with corrections to the Cover Date.     

Growth-associated biosynthesis of astaxanthin in heterotrophic Chlorella zofingiensis (Chlorophyta)

The green microalga Chlorella zofingiensis can produce the ketocarotenoid astaxanthin under heterotrophic culture conditions. Here we report the growth-associated biosynthesis of astaxanthin in this biotechnologically important alga. With glucose as sole carbon and energy source, C. zofinginesis grew fast in the dark with rapid exhaustion of nitrogen and carbon sources from media, leading to a high specific growth rate (0.034 h⁻¹). Cultures started at a cell concentration of about 3.4 × 10⁹ cells l⁻¹ reached, after 6 days, standing biomass values of 1.6 × 10¹¹ cells or 8.5 g dry weight l⁻¹. Surprisingly, the biosynthesis of astaxanthin was found to start at early exponential phase, independent of cessation of cell division. A general trend was observed that the culture conditions benefiting cell growth also benefited astaxanthin accumulation, indicating that astaxanthin was a growth-associated product in this alga. The maximum cell dry biomass and astaxanthin yield were 11.75 g l⁻¹ and 11.14 mg l⁻¹ (about 1 mg g⁻¹), simultaneously obtained in the fed-batch culture with a combined glucose–nitrate mixture addition, which were the highest ever reported in dark-heterotrophic algal cultures. The possible reasons why dark-heterotrophic C. zofingiensis could produce astaxanthin during the course of cell growth were discussed.     

Utilization of cane molasses towards cost-saving astaxanthin production by a Chlorella zofingiensis mutant

The aim of the present study was to survey the growth and astaxanthin production of E17, an astaxanthin-rich mutant of Chlorella zofingiensis, through feeding the low-cost carbon source cane molasses. In heterotrophic batch cultivation, E17 fed with pretreated molasses achieved biomass (1.79 g L^?1 day^?1) and astaxanthin (1.99 mg L^?1 day^?1) productivities comparable to those with glucose, which were about 2- and 2.8-fold of those fed with untreated molasses, respectively. Molasses-induced astaxanthin accumulation may be attributed to the elicited expression of carotenogenic genes, in particular the genes specifically responsible for the ketolation and hydroxylation of β-carotene to form astaxanthin. A two-stage fed-batch strategy was employed to grow E17 and induce astaxathin accumulation, resulting in 45.6 g L^?1 biomass and 56.1 mg L^?1 astaxanthin, the highest volumetric astaxanthin yield ever reported for this alga. In addition, the astaxanthin production by E17 was tested with a semi-continuous culture method, where the directly diluted raw molasses (giving 5 g L^?1 sugar) was used as the carbon source. Little growth inhibition of E17 was observed in the semi-continuous culture with a biomass productivity of 1.33 g L^?1 day^?1 and an astaxanthin productivity of 0.83 mg L^?1 day^?1. The mixotrophic semi-continuous cultures enhanced the biomass and astaxanthin productivities by 29.3 % and 42.2 %, respectively. This study highlights the potential of using the industrially cheap cane molasses towards large-scale cost-saving production of the high-value ketocarotenoid astaxanthin.     

Effect of culture conditions on growth of green alga — <Emphasis Type="Italic">Haematococcus pluvialis</Emphasis> and astaxanthin production

Influence of culture conditions such as light, temperature and C/N ratio was studied on growth of Haematococcus pluvialis and astaxanthin production. Light had significant effect on astaxanthin production and it varied with its intensity and direction of illumination and effective culture ratio (ECR, volume of culture medium/volume of flask). A 6-fold increase in astaxanthin production (37 mg/L) was achieved with 5.1468·10⁷ erg·m⁻²·s⁻¹ light intensity (high light, HL) at effective culture ratio of 0.13 compared to that at 0.52 ECR, while the difference in the astaxanthin production was less than 2 — fold between the effective culture ratios at 1.6175·10⁷ erg·m⁻²·s⁻¹ light intensity (low light, LL). Multidirectional (three-directional) light illumination considerably enhanced the astaxanthin production (4-fold) compared to unidirectional illumination. Cell count was high at low temperature (25 °C) while astaxanthin content was high at 35 °C in both autotrophic and heterotrophic media. In a heterotrophic medium at low C/N ratio H. pluvialis growth was higher with prolonged vegetative phase, while high C/N ratio favoured early encystment and higher astaxanthin formation.     

Fed-batch culture of astaxanthin-rich Haematococcus pluvialis by exponential nutrient feeding and stepwise light supplementation

A fed-batch culture process followed by subsequent photoautotrophic induction was established for the high density culture of astaxanthin-rich Haematococcus pluvialis using a CO₂-fed flat type photobioreactor under unsynchronized illumination. Fed-batch culture was performed with an exponential feeding strategy of the growth-limiting nutrients, nitrate and phosphate, concurrently with the stepwise supplementation of light depending on the cell concentration. During the growth phase, a biomass of 1.47 g/L was obtained at a biomass productivity of 0.33 g/L/day. Photoautotrophic induction of the well-grown vegetative cells was performed consecutively by increasing the light intensity to 400 μmol photon/m²/s, while keeping the other conditions in the CO₂-fed flat type photobioreactor fixed, yielding an astaxanthin production of 190 mg/L at an astaxanthin productivity of 14 mg/L/day. The proposed sequential photoautotrophic process has high potential as simple and productive process for the production of valuable Haematococcus astaxanthin.     

Comparison of heterotrophic and photoautotrophic induction on astaxanthin production by Haematococcus pluvialis

During light induction for astaxanthin formation in Haematococcus pluvialis, we substituted photoautotrophic induction for heterotrophic induction using acetate, both to prevent contamination by heterotrophs due to addition of organic carbon and to enhance carbon assimilation in the induced cells. Strong photoautotrophic induction was performed by N-deprivation of photoautotrophically grown Haematococcus cells followed by supplementation with bicarbonate (HCO₃^–) or CO₂. Bicarbonate-induced cells contained more astaxanthin than acetate-induced cells, and even further enhancement of astaxanthin accumulation was achieved by continuous CO₂ supply. The maximum astaxanthin content (77.2 mg g^–1 biomass, 3.4-fold higher than with heterotrophic induction) was obtained under conditions of 5% CO₂, yielding astaxanthin concentration and productivity of 175.7 mg l^–1 and 6.25 mg l^–1 day^–1, respectively. The results indicate that photoautotrophic induction is more effective than heterotrophic induction for astaxanthin synthesis in H. pluvialis.     

High efficiency production of astaxanthin by autotrophic cultivation of Haematococcus pluvialis in a bubble column photobioreactor

Haematococcus pluvialis was cultivated under photoautotrophic conditions in a bubble column with fed-batch addition of nutrients, especially nitrate, and a cell number above 5 × 10⁶ cells mL⁻¹ was attained after 300 h.The reduction of nutrient concentrations accompanied by dilution of the fermentation broth and an increase in the light intensity enhanced accumulation of astaxanthin. The final astaxanthin concentration of 390 mg L⁻¹ was several times higher than ever reported. This combination of fed-batch addition of nutrients and dilution of broth for nutrient deficiency is a promising method for attainment of high cell and astaxanthin concentrations in a bubble column photobioreactor.     

Growth kinetics ofSaccharomyces cerevisiae in batch and fedbatch cultivation using sugarcane molasses and glucose syrup from cassava starch

Growth kinetics ofSaccharomyces cerevisiae in glucose syrup from cassava starch and sugarcane molasses were studied using batch and fed-batch cultivation. The optimum temperature and pH required for growth were 30°C and pH 5.5, respectively. In batch culture the productivity and overall cell yield were 0.31 g L^–1 h^–1 and 0.23 g cells g^–1 sugar, respectively, on glucose syrup and 0.22 g L^–1 h^–1 and 0.18 g cells g^–1 sugar, respectively, on molasses. In fed-batch cultivation, a productivity of 3.12 g L^–1 h^–1 and an overall cell yield of 0.52 g cells g^–1 sugar in glucose syrup cultivation and a productivity of 2.33 g L^–1 h^–1 and an overall cell yield of 0.46 g cells g^–1 sugar were achieved in molasses cultivation by controlling the reducing sugar concentration at its optimum level obtained from the fermentation model. By using an on-line ethanol sensor combined with a porous Teflon^® tubing method in automating the feeding of substrate in the fed-batch culture, a productivity of 2.15 g L^–1 h^–1 with a yield of 0.47 g cells g^–1 sugar was achieved using glucose syrup as substrate when ethanol concentration was kept at a constant level by automatic control.     

Enhanced astaxanthin production from microalga,Haematococcus pluvialis by two-stage perfusion culture with stepwise light irradiation

For efficient astaxanthin production from the culture of green microalga, Haematococcus pluvialis, a two-stage mixotrophic culture system was established with stepwise increased light irradiance. By perfusion process, high density biomass (2.47 g/L) was achieved during the vegetative stage due to no detrimental effect of inhibitory metabolites, which was 3.09 and 1.67 times higher than batch and fed-batch processes, respectively. During the induction stage, biomass and astaxanthin were subsequently produced to the very high level 12.3 g/L and 602 mg/L, under stepwise increased light irradiance (150–450 μE/m²/s), respectively. These results indicate that the combinatorial approach of perfusion culture during the vegetative stage and stepwise light irradiation during the induction stage is a promising strategy for the simultaneous production of high concentration of biomass and astaxanthin in microalgae including H. pluvialis.     

Acetate production byClostridium thermoaceticum in corn steep liquor media

A low-cost nutrient medium based on corn steep liquor (CSL) was developed for the production of acetates byClostridium thermoaceticum. Pre-treatment of CSL with dolime and vitamin supplementation increased the rate of acetate production. Adding excess nutrients in a fed-batch mode minimized by-product formation and increased final acetate concentration from 19 g L^–1 to 40 g L^–1 acetic acid. High yields of acetic acid (0.95 g g^–1 glucose in fed-batch mode) was probably due to the conversion of the lactic acid in CSL into acetic acid by the organism.     

Glucose and acetate influences on the behavior of the recombinant strainEscherichia coli HB 101 (GAPDH)

Summary This study highlights data about the production of a recombinant protein (glyceraldehyde-3-phosphate dehydrogenase) byE. coli HB 101 (GAPDH) during batch and fed-batch fermentations in a complex medium. From a small number of experiments, this strain has been characterized in terms of protein production performance and glucose and acetate influences on growth and recombinant protein production. The present results show that this strain is suitable for recombinant protein production, in fed-batch culture 55 g L^–1 of biomass and 6 g L^–1 of GAPDH are obtained. However this strain, and especially GAPDH overproduction is sensitive to glucose availability. During fermentations, maximum yields of GAPDH production have been obtained in batch experiments for glucose concentration of 10 g L^–1, and in fed-batch experiments for glucose availability of 10 g h^–1 (initial volume 1.5 L). The growth of the strain and GAPDH overproduction are also inhibited by acetate. Moreover acetate has been noted as an activator of its own formation.     

Induction of astaxanthin formation by reactive oxygen species in mixotrophic culture of Chlorococcum sp.

The induction of astaxanthin formation by reactive oxygen species in mixotrophic culture of Chlorococcum sp. was investigated. H₂O₂ (0.1 mM) enhanced the total astaxanthin formation from 5.8 to 6.5 mg g^–1 cell dry wt. Fe²⁺ (0.5 mM) added to the medium with H₂O₂ (0.1 mM) further promoted astaxanthin formation to 7.1 mg g^–1 cell dry wt. Similarly, Fe²⁺ (0.5 mM) together with methyl viologen (0.01 mM) promoted astaxanthin formation to 6.3 mg g^–1 cell dry wt. In contrast, an addition of KI (1 mM), a specific scavenger for hydroxyl radicals (OH), together with H₂O₂ (0.1 mM) and Fe²⁺ (0.5 mM), to the medium decreased astaxanthin formation to 1.8 mg g^–1 cell dry wt. KI (1 mM) also inhibited the enhancement of carotenogenesis by superoxide anion radicals (O₂ ^–), with a decrease of astaxanthin formation to 1.7 mg g^–1 cell dry wt. This suggested that O₂ ^– might be transformed to OH before promoting carotenogenesis in Chlorococcum sp.     

Heterotrophic high-cell-density fed-batch and continuous-flow cultures of <Emphasis Type="Italic">Galdieria sulphuraria</Emphasis> and production of phycocyanin

Production of biomass and phycocyanin (PC) were investigated in highly pigmented variants of the unicellular rhodophyte Galdieria sulphuraria, which maintained high specific pigment concentrations when grown heterotrophically in darkness. The parental culture, G. sulphuraria 074G was grown on solidified growth media, and intensely coloured colonies were isolated and grown in high-cell-density fed-batch and continuous-flow cultures. These cultures contained 80–110 g L⁻¹ biomass and 1.4–2.9 g L⁻¹ PC. The volumetric PC production rates were 0.5–0.9 g L⁻¹ day⁻¹. The PC production rates were 11–21 times higher than previously reported for heterotrophic G. sulphuraria 074G grown on glucose and 20–287 times higher than found in phototrophic cultures of Spirulina platensis, the organism presently used for commercial production of PC.     

Evaluation of different cell disruption processes on encysted cells of Haematococcus pluvialis: effects on astaxanthin recovery and implications for bio-availability

Although Haematococcus pluvialis is one of the most importantnatural sources of the carotenoid astaxanthin as a pigmentor for theaquaculture industry, the thick sporopollenin cell wall in the cysts hindersastaxanthin extraction and its subsequent bio-availability to fish. A rangeof physical and chemical processes were tested to promote the disruptionof the encysted cells. The efficacy of these processes was evaluated interms of astaxanthin recovery, which was assessed by determining theextent of leaching of astaxanthin into an organic solvent. The processestested were: autoclave 30 min, 121 ^°C, 1 atm; HCl 0.1 M, 15min and 30 min; NaOH 0.1 M, 15 min and 30 min; enzymatictreatment with a mixture of 0.1% protease K and 0.5% driselase in aphosphate buffer, pH 5.8, 30 ^°C, for one hour; spray drying, inlet180 ^°C, outlet 115 ^°C; and mechanical disruption, with acell homogeniser developed for this purpose. The mechanical(homogenisation) and autoclave treatments were the most effective in termsof extraction and availability.     

Evaluation of factors promoting astaxanthin production by a unicellular green alga,Haematococcus pluvialis,with fractional factorial design

Factors affecting the astaxanthin production by a unicellular green alga, Haematococcus pluvialis UTEX 16, were evaluated with sequential fractional factorial design. To simulate an actual production mode, a two-stage process was adapted for astaxanthin production: the alga was first cultivated under vegetative growth conditions, and then astaxanthin production was induced by applying various induction methods. A high dose of irradiation was most effective for the production of astaxanthin both in weight (mg/g) and in cellular (pg/cell) contents. A combination of nitrogen deficiency and acetate addition also significantly increased the astaxanthin content of cells on a dry weight basis. Meanwhile, the acetate addition alone increased only the cellular content of astaxanthin. Although the addition of ferrous ion alone had a negative effect on the weight content of astaxanthin, simultaneous addition of ferrous ion and acetate was effective for increasing the cellular content of astaxanthin.     

Screening for a low-cost Haematococcus pluvialis medium reveals an unexpected impact of a low N/P ratio on vegetative growth

The green alga Haematococcus pluvialis is the current best source of natural astaxanthin, a high-value carotenoid. Traditionally, the production process of astaxanthin by this algae is achieved by a two-stage system: during the first stage, vegetative “green” cells are produced and then converted, in the second stage, into cysts that accumulate astaxanthin. In this work, a medium screening strategy based on the mixing of a three-component hydroponic fertilizer was applied to identify a new formulation optimized for the vegetative stage. A maximal and high cell density of 2?×?10⁶ cells mL^?1 was obtained in a medium containing a high level of phosphate relative to nitrate, resulting in a N/P ratio much lower than commonly used media for H. pluvialis. In this medium, cells remained at the vegetative and motile stage during a prolonged period of time. Both high cell density culture and motile stage persistence was proved to be related to the N/P feature of this medium. We conclude that the macrozoid stage of H. pluvialis is favored under high-P and low-N supply and that low-cost hydroponic fertilizers can be successfully used for achieving high density cultures of vegetative cells of H. pluvialis.     

Nannochloropsis (Eustigmatophyceae) as source of commercially valuable pigments

Pigment composition and its variation with culture agewere analyzed in six strains of Nannochloropsis(Eustigmatophyceae). The capacity for accumulationof the ketocarotenoids astaxanthin and canthaxanthinwas higher in N. salina and N. gaditanathan in the other strains studied here. Theinfluence of salinity (15 to 100 practical units) onpigment production was studied in N. gaditana,where a defined pattern of variation could not befound apart from a notable increase in zeaxanthin at100. In cultures grown in a photobioreactor and athigh cell densities of about 10⁹ cells mL^-1,pigment production reached: 350 mg L^-1 forchlorophyll a, 50 mg L^-1 for violaxanthin,5 mg L^-1 for canthaxanthin, 3 mg L^-1 forastaxanthin. The highest contents of canthaxanthin andastaxanthin obtained in experiments with N.gaditana were 19.4 and 14.6 ng pigment (10⁶cells)^-1, respectively, which accounts for 0.7%dry weight. By means of xanthophyll cycle inductionthrough exposure of cells to high irradiance and at40 ^°C, conversion of violaxanthin intozeaxanthin may attain up to 70% of the violaxanthincontent, which corresponds to 0.6% dry weight. Theresults indicate that interest in Nannochloropsis as a source of valuable pigments isnot related to its capacity for single pigmentaccumulation, but the availability of a range ofpigments such as chlorophyll a, zeaxanthin,canthaxanthin and astaxanthin, each with highproduction levels.     

Modeling of the pyruvate production with<Emphasis Type="Italic"> Escherichia coli</Emphasis> in a fed-batch bioreactor

A family of 10 competing, unstructured models has been developed to model cell growth, substrate consumption, and product formation of the pyruvate producing strain Escherichia coli YYC202 ldhA::Kan strain used in fed-batch processes. The strain is completely blocked in its ability to convert pyruvate into acetyl-CoA or acetate (using glucose as the carbon source) resulting in an acetate auxotrophy during growth in glucose minimal medium. Parameter estimation was carried out using data from fed-batch fermentation performed at constant glucose feed rates of q_VG=10 mL h^–1. Acetate was fed according to the previously developed feeding strategy. While the model identification was realized by least-square fit, the model discrimination was based on the model selection criterion (MSC). The validation of model parameters was performed applying data from two different fed-batch experiments with glucose feed rate q_VG=20 and 30 mL h^–1, respectively. Consequently, the most suitable model was identified that reflected the pyruvate and biomass curves adequately by considering a pyruvate inhibited growth (Jerusalimsky approach) and pyruvate inhibited product formation (described by modified Luedeking–Piret/Levenspiel term).List of symbols c_A acetate concentration (g L^–1) - c_A,0 acetate concentration in the feed (g L^–1) - c_G glucose concentration (g L^–1) - c_G,0 glucose concentration in the feed (g L^–1) - c_P pyruvate concentration (g L^–1) - c_P,max critical pyruvate concentration above which reaction cannot proceed (g L^–1) - c_X biomass concentration (g L^–1) - K_I inhibition constant for pyruvate production (g L^–1) - K_I^A inhibition constant for biomass growth on acetate (g L^–1) - K_P saturation constant for pyruvate production (g L^–1) - K_P inhibition constant of Jerusalimsky (g L^–1) - K_S^A Monod growth constant for acetate (g L^–1) - K_S^G Monod growth constant for glucose (g L^–1) - m_A maintenance coefficient for growth on acetate (g g^–1 h^–1) - m_G maintenance coefficient for growth on glucose (g g^–1 h^–1) - n constant of extended Monod kinetics (Levenspiel) (–) - q_V volumetric flow rate (L h^–1) - q_VA volumetric flow rate of acetate (L h^–1) - q_VG volumetric flow rate of glucose (L h^–1) - r_A specific rate of acetate consumption (g g^–1 h^–1) - r_G specific rate of glucose consumption (g g^–1 h^–1) - r_P specific rate of pyruvate production (g g^–1 h^–1) - r_P,max maximum specific rate of pyruvate production (g g^–1 h^–1) - t time (h) - V reaction (broth) volume (L) - Y_P/G yield coefficient pyruvate from glucose (g g^–1) - Y_X/A yield coefficient biomass from acetate (g g^–1) - Y_X/A,max maximum yield coefficient biomass from acetate (g g^–1) - Y_X/G yield coefficient biomass from glucose (g g^–1) - Y_X/G,max maximum yield coefficient biomass from glucose (g g^–1) - growth associated product formation coefficient (g g^–1) - non-growth associated product formation coefficient (g g^–1 h^–1) - specific growth rate (h^–1) - _max maximum specific growth rate (h^–1)