Effect of iron concentration on hydrogen fermentation

The effect of the iron concentration in the external environment on hydrogen production was studied using sucrose solution and the mixed microorganisms from a soybean-meal silo. The iron concentration ranged from 0 to 4000 mgFeCl₂ l⁻¹. The temperature was maintained at 37°C. The maximum specific hydrogen production rate was found to be 24.0 mlg⁻¹ VSSh⁻¹ at 4000 mgFeCl₂ l⁻¹. The specific production rate of butyrate increased with increasing iron concentration from 0 to 20 mgFeCl₂ l⁻¹, and decreased with increasing iron concentration from 20 to 4000 mgFeCl₂ l⁻¹. The maximum specific production rates of ethanol (682 mgg⁻¹ VSSh⁻¹) and butanol (47.0 mgg⁻¹ VSSh⁻¹) were obtained at iron concentrations of 5 and 3 mgFeCl₂ l⁻¹, respectively. The maximum hydrogen production yield of 131.9 mlg⁻¹ sucrose was obtained at the iron concentration of 800 mgFeCl₂ l⁻¹. The maximum yields of acetate (389.3 mgg⁻¹ sucrose), propionate (37.8 mgg⁻¹ sucrose), and butyrate (196.5 mg g⁻¹ sucros) were obtained at iron concentrations of 3, 200 and 200 mgFeCl₂ l⁻¹, respectively. The sucrose degradation efficiencies were close to 1.0 when iron concentrations were between 200 and 800 mgFeCl₂ l⁻¹. The maximum biomass production yield was 0.283 gVSSg⁻¹ sucrose at an iron concentration of 3000 mgFeCl₂ l⁻¹.     

Effects of medium glucose concentration and pH on docosahexaenoic acid content of heterotrophic Crypthecodinium cohnii

The effects of medium glucose concentration and pH on growth and docosahexaenoic acid (DHA, C22:6 ω-3) content of Crypthecodinium cohnii were investigated. Over a range of glucose concentrations (5–40 g l⁻¹) investigated, the highest specific growth rate (0.12 h⁻¹), highest cell dry weight concentration (3.13 g l⁻¹) and highest growth yield on glucose (0.6 g g⁻¹) were obtained at 20 g l⁻¹ glucose. However, the highest degree of fatty acid unsaturation (3.2) and highest DHA proportion (53.4% of total fatty acids) were achieved at 5 g l⁻¹ glucose. Low glucose concentrations enhanced the degree of fatty acid unsaturation and DHA formation. Medium pH also affected cell growth, fatty acid unsaturation and DHA proportion. When medium pH was 7.2, the highest specific growth rate (0.089 h⁻¹), highest cell dry weight concentration (2.73 g l⁻¹), highest growth yield on glucose (0.564 g g⁻¹), highest degree of fatty acid unsaturation (3.4) and highest DHA proportion (56.8% of total fatty acids) were obtained. Results suggest that glucose concentration and pH value could be effectively manipulated to achieve maximum DHA production by C. cohnii.     

In vitro culture of the seagrass Halophila decipiens

The seagrass Halophila decipiens Ostenfeld was grown axenically in a culture medium consisting of 20% artificial seawater, f/4 nutrients (except that glutamic acid was the nitrogen source), and 1% sucrose (w:v). The culture medium was adjusted to pH 5.0. A root–rhizome layer was created by solidifying a portion of the medium with 0.9% agar (w:v) and 1% activated charcoal (w:v). The rhizome layer also contained the following vitamins: 0.5 mg l⁻¹ nicotinic acid, 0.5 mg l⁻¹ pyridoxine, 0.5 mg l⁻¹ biotin, 0.5 mg l⁻¹ cyanocobalamin and 0.1 mg l⁻¹ of thiamine HCl. The liquid overlay (without vitamins or charcoal) was poured onto the agar-solidified root–rhizome layer. Growth of H. decipiens was not improved by the addition of the auxins indoleacetic acid (IAA), indolebutyric acid (IBA) or naphthaleneacetic acid (NAA) at either of the tested concentrations (10 and 50 μM). At a concentration of 10 μM, the cytokinins 6-(γ,γ-dimethylallylamino) purine (2iP) and benzylaminopurine (BA) stimulated shoot and branch production compared to controls with no cytokinins. Among the tested nitrogen sources, growth was best on 1.7 mM glutamic acid. Cultures grown on 1.7 mM NH₄Cl showed the same growth rates as those grown on glutamic acid, but the leaves were smaller and curled, suggesting incipient ammonium toxicity. Use of nitrate or urea led to mortality of the cultures. Long term axenic culture of H. decipiens appears to require the added vitamins. Hence, H. decipiens is the first seagrass known to need exogenous vitamins. Cultures of H. decipiens died when grown suspended in liquid cultures or in a biphasic medium system without activated charcoal in the root–rhizome layer. The use of more highly charged κ-carrageenan could not replace the use of activated charcoal and agar in the root–rhizome layer.     

High-density cultivation of Perilla frutescens cell suspensions for anthocyanin production: Effects of sucrose concentration and inoculum size

High-density cultivation of Perilla frutescens cells for anthocyanin production was carried out in both batch and fed-batch modes in a 500-ml shake flask. In fed-batch cultures, a high cell density of 27.7 g dry cells l⁻¹ and a total anthocyanin production of 3.87 g l⁻¹ by intermittent feeding of all medium components except hormones were obtained. In batch cultures, both initial sucrose concentration and inoculum size showed a conspicuous effect on the kinetics of cell growth, sugar consumption, and secondary metabolite (anthocyanins) production by suspended P. frutescens cells. At an inoculum size of 50 g wet cells l⁻¹, the maximum cell density of 38.3 g dry cells l⁻¹ was obtained after 11 days of cultivation at an initial sucrose concentration of 60 g l⁻¹, the highest pigment production of>5.8 g l⁻¹ was attained after 10 days of cultivation at an initial sucrose concentration of 45 g l⁻¹. These amounts of cell mass and anthocyanin pigments were 3.3 and 24 times higher than those at an initial sucrose concentration of 15 g l⁻¹ and inoculum size of 15 g wet cells l⁻¹, respectively.     

Aerobic chromate reduction by chromium-resistant bacteria isolated from serpentine soil

A group of 34 chromium-resistant bacteria were isolated from naturally occurring chromium percolated serpentine soil of Andaman (India). These isolates displayed different degrees of chromate reduction under aerobic conditions. One of the 34 isolates identified as Bacillus sphaericus was tolerant to 800 mg l⁻¹ Cr(VI) and reduced >80% Cr(VI) during growth. In Vogel Bonner broth, B. sphaericus cells (10¹⁰ cells ml⁻¹) reduced 62% of 20 mg l⁻¹ of Cr(VI) in 48 h with concomitant discoloring of yellow medium to white one. Reduction of chromate was pronounced by the addition of glucose and yeast extract as electron donors. In the presence of 4.0 g l⁻¹ of glucose, 20 mg l⁻¹ of Cr(VI) was reduced to 2.45 mg l⁻¹ after 96 h of incubation. Optimum pH and temperature for reduction were 6.0 and 25 °C, respectively. Increase in cell density and initial Cr(VI) concentration increased chromate reduction but was inhibited by metal ions like, Ni²⁺, Co²⁺, Cd²⁺ and Pb²⁺. Experiments with cell-free extracts indicated that the soluble fraction of the cell was responsible for aerobic reduction of Cr(VI) by this organism.     

Studies on composition and stability of a large membered bacterial consortium degrading phenol

A ten member microbial consortium (AS) consisting of eight phenol-degrading and two non-phenol-degrading strains of bacteria was developed and maintained in a fed-batch reactor by feeding 500 mg l⁻¹ phenol for four years at 28 ± 3 °C. The consortium could degrade 99% of 500 mg l⁻¹ phenol after 24 hours incubation with a biomass increase of 2.6 × 10⁷ to 4 × 10¹² CFU ml⁻¹. Characterization of the members revealed that it consisted of 4 principal genera, Bacillus, Pseudomonas, Rhodococcus, Streptomyces and an unidentified bacterium. Phenol degradation by the mixed culture and Bacillus subtilis, an isolate from the consortium was compared using a range of phenol concentrations (400 to 700 mg l⁻¹) and by mixing with either 160 mg l⁻¹ glucose or 50 mg l⁻¹ of 2,4-dichlorophenol in the medium. Simultaneous utilization of unrelated mixed substrates (glucose/2,4-dichlorophenol) by the consortium and Bacillus subtilis, indicated the diauxic growth pattern of the organisms. A unique characteristic of the members of the consortia was their ability to oxidize chloro aromatic compounds via meta pathway and methyl aromatic compounds via ortho cleavage pathway. The ability of a large membered microbial consortia to maintain its stability with respect to its composition and effectiveness in phenol degradation indicated its suitability for bioremediation applications.     

Efficient plant regeneration from seedling explants of two commercially important temperate eucalypt species–Eucalyptus nitens and E. globulus

A reliable and reproducible method for plant regeneration in vitro of two important temperate eucalypts, Eucalyptus nitens and E. globulus, has been developed which utilises seedling explants. Highly regenerative callus was obtained from individual cotyledon and hypocotyledon explants of both species following cultivation on Murashige and Skoog’s (MS) basal nutrient medium supplemented with 30 g l⁻¹ sucrose, 5–10% (v/v) coconut water, 0.8% agar, 1 mg l⁻¹ -naphthalene-acetic acid (NAA) and 0.5 mg l⁻¹ N⁶ benzylaminopurine (BAP). Shoot differentiation was observed 7–8 weeks after transfer of callus onto regeneration medium containing 0.5 mg l⁻¹ NAA and 1 mg l⁻¹ BAP. In a few instances, direct shoot regeneration occurred without an intervening callus phase in both species. The frequency of plant regeneration was higher for callus derived from hypocotyl segments (30–35%) compared to cotyledonary explants (20–25%) though the average number of shoots per cotyledonary explant was generally higher than for hypocotyl explants. Somatic embryos were observed occasionally in E. nitens, arising from the surface of organogenic callus. Organised structures closely resembling somatic embryos were also observed in E. globulus. Regenerated shoots (30–40%) of both species could be rooted in modified MS media containing indole-3-butyric acid (IBA) and plantlets were successfully transferred to soil.     

The growth and nutrient utilization of the insect cell line Spodoptera frugiperda Sf9 in batch and continuous culture

The growth of the Spodoptera frugiperda cell line Sf9 was studied in batch and continuous culture. The results of batch cultivations showed that glucose was the preferred energy and carbon source limiting the cell density in both TNM-FH and IPL-41 media. Continuous culture using IPL-41-based feeding medium with different glucose (2.5, 5 and 10 g l⁻¹) and yeast extract concentrations (4, 8 and 16 g l⁻¹) showed that in serum-supplemented medium the maximum cell density was limited by glucose and yeast extract concentration. The transition to glucose limitation caused a decrease in growth rate and viability. A high cell density culture (18 × 10⁶ ml⁻¹) was obtained using a glucose concentration of 10 g l⁻¹ and a yeast extract concentration of 8 g l⁻¹ in the feeding medium. A yeast extract concentration of 16 g l⁻¹ inhibited growth. Unlike mammalian cell cultures, lactate, alanine and ammonia were not involved in growth inhibition. Lactate did not accumulate under aerobic conditions. Ammonia accumulation, if observed, was insignificant. The level of alanine synthesized and excreted into the culture medium never reached an inhibitory level. During glucose limitation alanine did not accumulate and ammonia was released. However, even in the presence of glucose significant amounts of Asp, Glu, Gln, Asn, Ser, Arg and Met were utilized for energy production. The amino groups of these amino acids were transferred to pyruvate or used for nucleic acid synthesis and excreted in the form of alanine into the culture medium. The consumption of His, Lys, Thr, Gly, Val, Leu, Phe, Tyr, Trp and Ile by growing Sf-9 cells was almost equal to their concentration in the biomass.     

A medium optimization strategy for improvement of growth and methane production by Methanobacterium thermoautotrophicum

Methanobacterium thermoautotrophicum, strain Hveragerdi, has been cultivated in a completely defined mineral salts medium, under strictly anaerobic conditions with CO₂ and H₂ as sole carbon and energy source, respectively. During optimization of the medium an iron limitation was identified that could not be overcome by the simple addition of iron—or iron complexed with nitrilotriacetate (NTA)—to the medium, due to the formation of insoluble FeS complexes. In order to define a medium optimization strategy, and to avoid laborious empirical optimization procedures, a theoretical model has been developed in order to describe the solubility of iron and other mineral species in the medium as a function of the concentration of sulfur and NTA. This model may be applied for the optimization of any medium component. With this information sulfide has been replaced by a combination of cysteine and thiosulphate in conjunction with a non-toxic reducing agent (titanium (III) citrate). Using this defined medium precipitation was avoided and an iron limitation was overcome resulting in a 5-fold improvement of the final biomass concentration from 2–3 g l⁻¹ to 11.2 g l⁻¹ together with a 2-fold increase (from 45 to almost 100%) in the conversion of CO₂ and H₂ to CH₄, even at gas flow rates as high as 6 l min⁻¹.     

Batch and continuous fermentation of succinic acid from wood hydrolysate by Mannheimia succiniciproducens MBEL55E

Batch and continuous cultures of Mannheimia succiniciproducens MBEL55E were carried out in a complex medium containing a NaOH-treated wood hydrolysate for the production of succinic acid. The wood hydrolysate based medium was treated with NaOH before sterilization to reduce the formation of inhibitory compounds. M. succiniciproducens MBEL55E utilized xylose as well as glucose in the wood hydrolysate based medium as a carbon source for the succinic acid production. In batch cultures, the final succinic acid concentration of 11.73 g l⁻¹ was obtained from the pre-treated wood hydrolysate based medium, resulting in a succinic acid yield of 56% and a succinic acid productivity of 1.17 g l⁻¹ h⁻¹, while the corresponding continuous cultures gave the succinic acid yield and productivity of 55% and 3.19 g l⁻¹ h⁻¹, respectively. These results suggest that succinic acid can be produced economically and efficiently by the fermentation of M. succiniciproducens MBEL55E from an inexpensive biomass-based wood hydrolysate.     

High cell density culture of the diatom Nitzschia laevis for eicosapentaenoic acid production: fed-batch development

A fed-batch process was developed for high cell density culture of the diatom Nitzschia laevis for enhanced production of eicosapentaenoic acid (EPA). Firstly, among the various medium components, glucose (Glu) was identified as the limiting substrate while nitrate (NO₃⁻), tryptone (Tr) and yeast extract (Ye) were found to promote cell growth by enhancing specific growth rate. Therefore, these components were considered essential and were included in the feed medium for subsequent fed-batch cultivation. With the optimized ratio of NO₃⁻:Tr:Ye being 1:2.6:1.3 (by weight), the relative proportions of glucose to the nitrogen sources in the feed were investigated. The optimal ratios of Glu:NO₃⁻ for specific growth rate and EPA productivity were both determined to be 32:1 (by weight). Finally, based on the residual glucose concentration in the culture, a continuous medium feeding strategy for fed-batch fermenter cultivation was developed, with which, the maximal cell dry weight and EPA yield obtained were 22.1 g l⁻¹ and 695 mg l⁻¹, respectively, which were great improvements over those of batch cultures.     

Optimization of bio-indigo production by recombinant E. coli harboring fmo gene

A bacterial flavin-containing monooxygenase (FMO) gene was cloned from Methylophaga aminisulfidivorans MP^T, and a plasmid pBlue 2.0 was constructed to express the bacterial fmo gene in E. coli. To increase the production of bio-indigo, upstream sequence size of fmo gene was optimized and response surface methodology was used. The pBlue 1.7 plasmid (1686 bp) was prepared by the deletion of upstream sequence of pBlue 2.0. The recombinant E. coli harboring the pBlue 1.7 plasmid produced 662 mg l⁻¹ of bio-indigo in tryptophan medium after 24 h of cultivation in flask. The production of bio-indigo was optimized using a response surface methodology with a 2ⁿ central composite design. The optimal combination of media constituents for the maximum production of bio-indigo was determined as tryptophan 2.4 g l⁻¹, yeast extract 4.5 g l⁻¹ and sodium chloride 11.4 g l⁻¹. In addition, the optimum culture temperature and pH were 30 °C and pH 7.0, respectively. Under the optimized conditions mentioned above, the recombinant E. coli harboring pBlue 1.7 plasmid produced 920 mg of bio-indigo per liter in optimum tryptophan medium after 24 h of cultivation in fermentor. The combination of truncated insert sizes and culture optimization resulted in a 575% increase in the production of bio-indigo.     

Cadmium biosorption on Spirulina platensis biomass

Dry biomass of Spirulina platensis re-hydrated for 48 h was employed as a biosorbent in tests of cadmium(II) removal from water. Various concentrations of biomass (from 1 to 4 g l⁻¹) and metal (from 100 to 800 mg l⁻¹) were tested. Low biomass levels (X_o  2 g l⁻¹) ensured metal removal up to 98% only at Cd₀= 100 and 200 mg l⁻¹, while X_o  2.0 g l⁻¹ were needed at Cd₀ = 400 mg l⁻¹ to achieve satisfactory results. Whereas X_o = 4.0 g l⁻¹ was effective to remove up to Cd₀ = 500 mg l⁻¹, a further increase in metal concentration (Cd₀ = 600 and 800 mg l⁻¹) led to progressive worsening of the system performance. At a given biomass levels, the kinetics of the process was better at low Cd²⁺ concentrations, while, raising the adsorbent level from 1.0 to 2.0 g l⁻¹ and then to 4.0 g l⁻¹, the rate constant of biosorption increased by about one order of magnitude in both cases and the adsorption capacity of the system progressively decreased from 357 to 149 mg g⁻¹.     

Continuous production of lactic acid from whey permeate by Lactobacillus helveticus in two chemostats in series

The effect of dilution rate on the production of lactic acid from whey permeate by Lactobacillus helveticus has been investigated. In the first chemostat of a two-stage system, total conversion (98.1%) and maximum lactic acid concentration (43.7 g l⁻¹) were obtained at a dilution rate (D_Itot) of 0.06 h⁻¹. Maximum volumetric productivities of lactic acid (8.27 g l⁻¹ h⁻¹) and biomass (1.90 g l⁻¹ h⁻¹) occurred at D_Itot of 0.40 h⁻¹. The fraction of -lactate in the product was found to increase with dilution rate and reached a maximum of 66% at the same dilution rate. The maximum specific growth rate (μ_max) on this medium was 0.7 h⁻¹. A Y_ATP (max) value of 22.4 g dry weight (mol ATP)⁻¹ and a maintenance coefficient of 8.0 mmol ATP (g dry weight h)⁻¹ were determined. The second stage, in series with the first, confirmed these results and further showed that the total residence time could be reduced by 50%, compared with a single chemostat for the same nearly complete level of substrate conversion.     

Rapid production of thermostable cellulase-free xylanase by a strain of Bacillus subtilis and its properties

A Bacillus subtilis strain isolated from a hot-spring was shown to produce xylanolytic enzymes. Their associative/synergistic effect was studied using a culture medium with oat spelts xylan as xylanase inducer. Optimal xylanase production of about 12 U ml⁻¹ was achieved at pH 6.0 and 50°C, within 18 h fermentation. At 50°C, xylanase productivity obtained after 11 h in shake-flasks, 96,000 U l⁻¹ h⁻¹, and in reactor, 104,000 U l⁻¹ h⁻¹ was similar. Increasing temperature to 55°C a higher productivity was obtained in the batch reactor 45,000 U l⁻¹ h⁻¹, compared to shake-flask fermentations, 12,000 U l⁻¹ h⁻¹. Optimal xylanolytic activity was reached at 60°C on phosphate buffer, at pH 6.0. The xylanase is thermostable, presenting full stability at 60°C during 3 h. Further increase in the temperature caused a correspondent decrease in the residual activity. At 90°C, 20% relative activity remains after 14 min. Under optimised fermentation conditions, no cellulolytic activity was detected on the extract. Protein disulphide reducing agents, such as DTT, enhanced xylanolytic activity about 2.5-fold. When is used xylan as substrate, xylanase production decreased as function of time in contrast, with trehalose as carbon source, xylanase production in maintained constant for at least 80 h fermentation.     

Simultaneous production of anthocyanin and triterpenoids in suspension cultures of Perilla frutescens

When cultivated in Murashige & Skoog medium supplemented with 0.2 mg l⁻¹ 2,4-dichlorophenoxy acetic acid and 0.5 mg l⁻¹ 6-benzyladenine, Perilla frutescens cells in suspension culture grew rapidly reaching about 13.6 g dry wt l⁻¹ after 12 days. The cell line produced both anthocyanin 0.9 g l⁻¹ and triterpenoids: 16 mg l⁻¹ oleanolic acid (OA), 25 mg l⁻¹ ursolic acid (UA) and 14 mg l⁻¹ tormentic acid (TA). When P. frutescens cells of 7-day-old cultures were exposed to a yeast elicitor at 0.5–5% (v/v) for 7 days, it was found that anthocyanin content peaked at 10.2% of dry weight with yeast elicitor at 1% (v/v) whereas the maximum production of oleanolic acid and ursolic acid in cultures treated with 2% (v/v) yeast elicitor was 19 and 27 mg l⁻¹, a 46 and 24% increase over the control, respectively. This is the first report of simultaneous production of both anthocyanin and triterpenoids in a single culture system.     

Effects of feed sugar concentration on continuous ethanol fermentation of cheese whey powder solution (CWP)

Cheese whey powder (CWP) solution with different CWP or sugar concentrations was fermented to ethanol in a continuous fermenter using pure culture of Kluyveromyces marxianus (DSMZ 7239). Sugar concentration of the feed CWP solution varied between 55 and 200 g l⁻¹ while the hydraulic residence time (HRT) was kept constant at 54 h. Ethanol formation, sugar utilization and biomass formation were investigated as functions of the feed sugar concentration. Percent sugar utilization and biomass concentrations decreased and the effluent sugar concentration increased with increasing feed sugar concentrations especially for the feed sugar contents above 100 g l⁻¹. Ethanol concentration and productivity (DP) increased with increasing feed sugar up to 100 g l⁻¹ and then decreased with further increases in the feed sugar content. The highest ethanol concentration (3.7%, v v⁻¹) and productivity (0.54 gE l⁻¹ h⁻¹) were obtained with the feed sugar content of 100 g l⁻¹ or 125 g l⁻¹. The ethanol yield coefficient (Y_P/S) was also maximum (0.49 gE gS⁻¹) when the feed sugar was between 100 and 125 g l⁻¹. The growth yield coefficient (Y_X/S) decreased steadily from 0.123 to 0.063 gX gS⁻¹ when the feed sugar increased from 55 to 200 g l⁻¹ due to adverse effects of high sugar contents on yeast growth. The optimal feed sugar concentration maximizing the ethanol productivity and sugar utilization was between 100 and 125 g l⁻¹ under the specified experimental conditions.     

Arachidonic acid production by Mortierella alpina with growth-coupled lipid synthesis

The fungus Mortierella alpina LPM 301, a producer of arachidonic acid (ARA), was found to possess a unique property of a growth-coupled lipid synthesis. An increase in specific growth rate (μ) from 0.03 to 0.05 h⁻¹ resulted in a two-fold increase in the specific rate of lipid synthesis (milligram lipid (gram per lipid-free biomass) per hour). Under batch cultivation in glucose-containing media with urea or potassium nitrate as nitrogen sources, the ARA content was 46.0 and 60.4% of lipid; 16.4 and 18.8% of dry biomass; and 4.2 and 4.5 g l⁻¹, respectively. Under continuous cultivation of the strain, the productivity of ARA synthesis was 16.2 and 19.2 mg l⁻¹ h⁻¹ at μ=0.05 and 0.03 h⁻¹, respectively.     

Degradation of ferrous(II) cyanide complex ions by Pseudomonas fluorescens

Degradation of ferrous(II) cyanide complex (ferrocyanide) ions by free cells of P. fluorescens in the presence of glucose and dissolved oxygen was investigated as a function of initial pH, initial ferrocyanide and glucose concentrations and aeration rate in a batch fermenter. The microorganism used the ferrocyanide ions as the sole source of nitrogen. The ferrocyanide biodegradation rate was 30.7 mg g⁻¹ h⁻¹ under the conditions of initial pH: 5, stirring rate: 150 rpm, aeration rate: 0.15 vvm, initial ferrous(II) cyanide complex ion and glucose concentrations: 100 mg l⁻¹ and 0.465 g l⁻¹, respectively. The culture utilized glucose as the main substrate following the non-competitive toxic component inhibition model in the presence of 100 mg l⁻¹ initial ferrous(II) cyanide complex ion concentration. The inhibition of ferrous(II) cyanide complex ions as a secondary substrate began at very low concentrations. A mathematical model, based on non-competitive substrate inhibition was used to describe the inhibitory effect of ferrous(II) cyanide complex ions on the growth of microorganism and the best fitted model parameters were determined by non-linear regression techniques.