Improved ethanol production from xylose with glucose isomerase and Saccharomyces cerevisiae using the respiratory inhibitor azide

Summary Ethanol was produced from xylose, using the enzyme glucose isomerase (xylose isomerase) and Saccharomyces cerevisiae. The influence of aeration, pH, enzyme concentration, cell mass and the concentration of the respiratory inhibitor sodium azide on the production of ethanol and the formation of by-products was investigated. Anaerobic conditions at pH 6.0, 10 g/l enzyme, 75 g/l dry weight cell mass and 4.6 mM sodium azide were found to be optimal. Under these conditions theoretical yields of ethanol were obtained from 42 g/l xylose within 24 hours.In a fed-batch culture, 62 g/l ethanol was produced from 127 g/l xylose with a yield of 0.49 and a productivity of 1.35 g/l·h.     

Fed-batch culture of hybridoma cells: comparison of optimal control approach and closed loop strategies

Control of fed-batch culture of hybridoma cells was investigated based on two approaches optimal control theory and feedback control. Experiments were conducted for both approaches-with a feed enriched in glutamine. The optimal feed trajectory, a decreasing one, yielded a final monoclonal antibody (MAb) concentration of 170 mg/l, a three-fold increase compared to a typical batch operation.The feedback strategy relied on the on-line estimation of the net specific growth rate of cells from the measurement of the CO₂ production rate with a mass-spectrometer. A PI controller was then used to maintain the growth rate at a desired value by adjusting the dilution rate to the reactor. For the chosen set-point (0.1 d^–1), the final MAb concentration achieved was about 100 mg/1. It was found that there was a delay in the assimilation of the glutamine that should be included in the model to explain the lower MAb production in feedback mode. A higher production can be expected also for a lower set-point in feedback operation.List of Symbols Amm mM ammonia concentration - CPR l/(ld) carbon dioxide production rate - D _t l/d dilution rate - e _t l/d control error - F L/d feed flow rate - Glc mM glucose concentration - Gln mM glutamine concentration - Lac mM lactate concentration - I mg performance index - k _d l/d specific death rate - K _damm l/(mM · d) kinetic parameter for death rate - K _dgln mM kinetic parameter for death rate - K _dlac l/(mM·d) kinetic parameter for death rate - K _c l controller gain - K _glc mM kinetic parameter for growth rate - K _gln mM kinetic parameter for growth rate - K _tr L/(cell·d) transport coefficient - K l/d kinetic parameter for Mab production - m _glc mM/(cell·d) maintenance coefficient - M _Ab mg/l monoclonal antibody concentration - P _t covariance matrix - q _glc l/(l·cell·d) specific CO₂ production rate - q _glc mM/(cell·d) specific glucose uptake rate - q _gln mM/(cell·d) specific glutamine uptake rate - q _Mab mg/(l·cell·d) specific monoclonal antibody production - t _f d final culture time - T d sampling rate - u control input - V l reactor volume - X cell/l total cells concentration - X _v cell/l viable cells concentration - Y yield coefficient Greek mg/cell variable yield coefficient - ₀ mg/(cell·d) growth-associated kinetic parameter - mg/(cell·d) non growth-associated kinetic parameter - _t+1 defined by Eq. (19) - forgetting factor - l/d specific growth rate - _max l/d specific growth rate - _i d controller integral time constant     

Physiological control and process kinetics of clavine alkaloid production byClaviceps purpurea

Summary Kinetic parameters of production of clavine alkaloids were evaluated in twoClaviceps purpurea strains. Mutagenesis brought about enhanced resistance of the biosynthetic system towards alkaloids. Addition of glucose into the fermentation medium altered the zero order kinetics of production to activation-inhibition kinetics. The glucose treatment allowed performance of both elymoclavine-inhibitionless and clavine alkaloid-decompositionless fermentations if a combination of fermentation and separation units in a closed loop was used.Nomenlacture k ₁ rate constant of agroclavine synthesis (mg Agro · mg Elymo/l·g DW·day for stage 1, mg Agro/g DW·day for stage 2) - k ₂ parameter describing inhibition of agroclavine formation rate by elymoclavine (mg Elymo/l) - k ₃ specific rate of agroclavine decay (l/g DW·day) - k ₄ maximal specific rate of elymoclavine synthesis (stage 1, 1/g DW·day, stage 2, mg Elymo/g DW·day) - k ₄ ^– maximal specific rate of elymoclavine synthesis in stage 1 (inhibition-activation mechanism) (mg Elymo/g DW·day) - k ₅ physiological constant describing the elymoclavine decay rate (l²/g DW·day·mg Elymo) - k ₅ ^– physiological constant describing the activation of elymoclavine biosynthesis by elymoclavine (mg Elymo/l) - k ₆ physiological constant describing the repression of elymoclavine biosynthesis by elymoclavine (mg Elymo/l) - k ₇ maximal specific growth rate (1/day) - k ₈ specific rate of biomass decay (l/g DW·day) - A agroclavine concentration (mg/l) - E elymoclavine concentration (mg/l) - r _A specific rate of agroclavine biosynthesis (mg Agro/g DW·day) - r _E specific rate of elymoclavine biosynthesis (mg Elymo/g DW·day) - r _i specific rate of alkaloid biosynthesis (mg alkaloid/g DW·day) - X dry biomass concentration (g/l) - specific growth rate (1/day) Abbreviations Agro agroclavine - Elymo elymoclavine - Chano chanoclavine - DW dry weight of biomass     

Production of mead by immobilized cells of Hansenula anomala

Summary Mead was produced by immobilized cells of Hansenula anomala in calcium alginate gels. The immobilized cell beads of 3 mm diameter packed in column reactors of dimensions 2.2x60, 4x40 and 8x80 cm, produced mead containing maximum concentrations of ethanol and ethyl acetate of 70 g/l and 730 mg/l, respectively at a dilution rate of 0.1 h^–1. The maximum alcohol productivity achieved was 23.1 g/l·h at a dilution rate of 0.33 h^–1. With intermittent regenerations of the cells the reactor operated continuously for 110 days. This process enables the quick production of matured mead by a single culture and the elimination of the traditionally used long aging periods.     

Comparative study of ethanol production by an immobilized yeast in a tubular reactor and in a multistage reactor

Summary The productivity of continuous ethanol fermentation has been increased using fixed bed reactors where a high density of yeast cells was maintained on a packing of wood chips. Two different systems have been used: 1. A tubular reactor which produced alcohol solutions containing up to 13.5% (V/V) ethanol. High CO₂ retention and a poor mass transfer between bulk medium and immobilized biomass prevented production rates higher than 2.2 g/l·h. 2. A multistage reactor where a better utilisation of the reactor volume led to improved performances. Solutions containing 132 g/l of ethanol (16.5% V/V) were produced with a productivity increased up to 4.8 g/l·h. A better distribution of the active biomass and a lower gradient of alcohol concentration between support and bulk medium are possible reasons for this improvement.     

NH + 4 -N recovery from ammonia-treated straw-whey ensilage and cell biomass formation by Rhodobacter capsulatus ATCC 23782 on silage filtrates

Summary Growth of Rhodobacter capsulatus ATCC 23782 on silage filtrates under both axenic and non-axenic conditions was evaluated. Under both conditions, 96% assimilation of NH ₊ ⁴ -N at rates of about 0.1 g/l·d was attained. Assimilation was complete when the C/N ratio was adjusted to ca. 5. Thus assimilation rates of 0.2 g/l·d were achieved for an acid-C and NH ₊ ⁴ -N concentration of 2.0 and 0.4 g/l respectively. The corresponding biomass production amounted about 104 mg/g silage, dry matter.     

Use of a sequencing batch reactor to study the biodegradation of 4-chlorophenol in soil

Summary A sequencing batch reactor (SBR) was used to study the biodegradation of 4-chlorophenol (4CP) in a soil slurry. The SBR system was controlled by measuring the carbon dioxide evolution rate (CER) in the gas phase. The biodegradation rate was increased from 3.2 to 67 mg 4CP/l·h after 13 cycles.     

Effects of CO2 enrichment and water stress on gas exchange of Liquidambar styraciflua and Pinus taeda seedlings grown under different irradiance levels

Summary The effects of CO₂ enrichment and water stress on gas exchange of Liquidambar styraciflua L. (sweetgum) and Pinus taeda L. (loblolly pine) seedlings were examined for individuals grown from seed under high (1000 mol·m^-2·s^-1) and low (250 mol·m^-2·s^-1) photosynthetic photon flux density at 350, 675 and 1000 l·l^-1 CO₂. At 8 weeks of age, half the seedlings in each CO₂-irradiance treatment were subjected to a drying cycle which reduced plant water potential to about -2.5 MPa in the most stressed plants, while control plants remained well-watered (water potentials of -0.3 and -0.7 MPa for sweetgum and loblolly pine, respectively). During this stress cycle, whole seedling net photosynthesis, transpiration and stomatal conductance of plants from each CO₂-irradiance-water treatment were measured under respective growth conditions.For both species, water stress effects on gas exchange were greatest under high irradiance conditions. Waterstressed plants had significantly lower photosynthesis rates than well-watered controls throughout most of the drying cycle, with the most severe inhibition occurring for low CO₂, high irradiance-grown sweetgum seedlings. Carbon dioxide enrichment had little effect on gas exchange rates of either water-stressed or well-watered loblolly pine seedlings. In contrast, water stress effects were delayed for sweetgum seedlings grown at elevated CO₂, particularly in the 1000 l·l^-1 CO₂, high irradiance treatment where net photosynthesis, transpiration and conductance of stressed plants were 60, 36 and 33% of respective control values at the end of the drying cycle. Development of internal plant water deficits was slower for stressed sweetgum seedlings grown at elevated CO₂. As a result, these seedlings maintained higher photosynthetic rates over the drying cycle than stressed sweetgum seedlings grown at 350 l·l^-1 CO₂ and stressed loblolly pine seedlings grown at ambient and enriched CO₂ levels. In addition, water-stressed sweetgum seedlings grown at elevated CO₂ exhibited a substantial increase in water use efficiency.The results suggest that with the future increase in atmospheric CO₂ concentration, sweetgum seedlings should tolerate longer exposure to low soil moisture, resulting in greater first year survival of seedlings on drier sites of abandoned fields in the North Carolina piedmont.     

Permeabilization of elicited suspension culture of madder (Rubia akane Nakai) cells for release of anthraquinones

To enhance the productivity of anthraquinone colorants during madder (Rubia akane Nakai) cell cultures, the effects of permeabilizing agents on the production of anthraquinone colorants were investigated. Tween 80 was the best among the permeabilizing agents tested. Addition of 1% Tween 80 increased the total and released concentrations of anthraquinones about 1.6 times (159 mg l–1) and 14 times (71 mg l–1), respectively. In addition, anthraquinone production was increased to 220 mg l–1, 2.2 times as the level of control culture by simultaneous use of 1% Tween 80, 5 mg chitosan/l and 2% (w/v) XAD-7. Also, 47% (105 mg l–1) of total anthraquinones was released to medium or adsorbed on XAD-7.     

Factors which influence the sedimentation characteristics of Torulopsis glabrata after growth in a recirculation system

Summary Some environmental affects on cell aggregation described in the literature are briefly summarized. By means of a biomass recirculation culture (Contact system), using the yeast Torulopsis glabrata, the aggregation behavior of cells in static and in dynamic test systems is described. Sedimentation times required to obtain 50 g · l^–1 yeast dry matter in static systems were always higher than in dynamic ones.In addition to, influencing the biomass yield, the specific growth rate of the yeast also affected cell aggregation. The specific growth rate and therefore the aggregation could be regulated by the biomass recirculation rate as well as by the sedimenter volume.Abbreviations f_o Overflow flow rate (l·h^–1) - f_R Recycle flow rate (l·h^–1) - f_t0t Total flow rate through the fermenter (l·h^–1) - g Gram - h Hour - D_R Fermenter dilution rate due to recycle (h^–1) - D_S Fermeter dilution rate due to substrate (h^–1) - D_tot Total fermenter dilution rate (h^–1) - l Liter - Specific growth rate (h^–1) - P_F Fermenter productivity (g·l^–1·h^–1) - P_FS Overall productivity (g·l^–1·h^–1) - R_pM Rates per minute - RS Residual sugar content in the effluent with respect to the substrate concentration (%) - Y Yield of biomass with respect to sugar concentration (%) - Sed 50 Sedimentation time to reach a YDM of 50 g·l^–1 (min) - V Volume (l) - V_F Fermenter volume (l) - V_Sed Sedimenter volume (l) - VVM Volumes per volume and minute - X_F YDM in the fermenter (g·l^–1) - X_F YDM in the recycle (g·l^–1) - X_S Yeast dry matter due to substrate concentration (g·l^–1) - YDM Yeast dry matter (g·l^–1)     

Improvement of very high gravity ethanol fermentation by media supplementation using Saccharomyces cerevisiae

The final ethanol concentration achieved was increased by 17% (to 103 g ethanol/l) when excess assimilable nitrogen was added to the batch very high gravity (VHG) ethanolic fermentations by Saccharomyces cerevisiae. The supplementation of the media with 12 g yeast extract l–1, 0.3 g cell walls l–1, 3 g glycine l–1 and 20 g soya flour l–1 led to halving reduction of the fermentation time to 28 h. The ethanol productivity was enhanced by more than 50% (to achieved value 3.3 g l–1 h–1).     

Continuous culture of Candida boidinii variant 60 growing on methanol

Summary A new variant, Candida boidinii variant 60, which is less sensitive to methanol and formaldehyde shocks was grown in continuous cultures with methanol as sole carbon source. The substrate concentration in the feeding medium was either 1% methanol or 3% methanol. Biomass production, methanol consumption, the formation of formaldehyde and gas exchange were measured at different dilution rates. With low methanol feeding (10 g/l) maximal productivity of 0.44 g biomass/l·h is obtained at a dilution rate of 0.14 h^–1. Maximal specific growth rate is 0.18 h^–1. A yield of 0.32 g biomass/g methanol was obtained and the respiration quotient was determined as 0.55. Independently of initial substrate concentration, biomass decreases if methanol and formaldehyde are accumulating in the culture broth.In the culture with high methanol feeding (30 g/l) cell concentratioon increases up to 9 g/l at D=0.04 h^–1. At higher dilution rates methanol and form-aldehyde appear in the medium. Formaldehyde is then preferably oxidized without energy advantages for the cells. It seems that this enables the cells to overcome toxic effects caused by methanol and formaldehyde.     

Continuous production of itaconic acid by Aspergillus terreus immobilized in a porous disk bioreactor

Summary Aspergillus terreus NRRL 1960 was grown on porous disks rotating intermittently in and out of the liquid phase. This immobilized fungal cell bioreactor was used to produce itaconic acid from glucose in a continuous operation. The effect of temperature, pH, disk rotation speed, and feed rate on the itaconic acid concentration and volumetric productivity were studied. The highest itaconic acid concentration and volumetric productivity obtained were 18.2 g/l and 0.73 g/l·h, respectively, under the following conditions: temperature at 36°C, pH 3.0, disk rotation speed at 8 rpm, and feed rate at 60 ml/h. These results are better than those by conventional fermentation or by other immobilized method.Nomenclature F feed rate (l/h) - K _1s saturation constant for immobilized cells (g/l) - K _2s saturation constant for suspended cells (g/l) - M ₁ increased mass of immobilized cells (g) - M ₂ total mass of immobilized cells (g) - P concentration of itaconic acid (g/l) - S substrate concentration in and out of the reactor (g/l) - S ₀ substrate concentration in the feed (g/l) - V liquid volume of the reactor (1) - X concentration of the suspended cells (g/l) - Y ₁ apparent yield of the immobilized cells (g cells/g substrate) - Y ₂ apparent yield of the suspended cells (g cell/g substrate) - Y ₃ apparent yield of itaconic acid (g itaconic acid/g substrate) - m ₁ maintenance and by-products coefficient of the immobilized cells (g substrate/g cell·h) - m ₂ maintenance and by-products coefficient of the suspended cells (g substrate/g cell·h) - µ_1max maximum specific growth rate of the immobilized cells (h^-1) - µ_2max maximum specific growth rate of the suspended cells (h^-1)     

Simulation of glucose isomerase reactor: optimum operating temperature

A design equation for immobilized glucose isomerase (IGI) packed bed reactor is developed assuming enzyme deactivation and substrate protection. The developed equation is used to simulate the performance of the reactor at various temperatures (50–80 °C). Enzyme deactivation is significant at high temperature. Substrate protection showed to have significant effect in reducing enzyme deactivation and increasing the enzyme half-life. Factors affecting the optimum operating temperature are discussed. The optimum operating temperature is greatly influenced by the operating period and to a lesser extent with both initial glucose concentration and glucose conversion.Two modes of reactor operation are tested i.e., constant feed flow rate and constant conversion. Reactor operating at constant conversion is more productive than reactor operating at constant flow rate if the working temperature is higher than the optimum temperature. Although at lower temperatures than the optimum, the two modes of operation give the same result.List of Symbols a residual enzyme activity - E [mg/l] concentration of active enzyme - E _a [kJ/mole] activation energy - E ₀ [mg/l] initial concentration of active enzyme - k [Specific] kinetic parameter - k _d [h^–1] first order thermal deactivation rate constant - k _e equilibrium constant - k _m [mole/l] apparent Michaelis constant - k _p [mole/l] Michaelis constant for product - k _s [mole/l] Michaelis constant for substrate - k ₀ [Specific] pre-exponential factor - Q [1/h] volumetric flow rate - ¯Q [1/h] average volumetric flow rate - R [kJ/mol·k] ideal gas constant - s [mole/l] apparent substrate concentration - s [mole/l] substrate concentration - s _e [mole/l] substrate concentration at equilibrium - s ₀ [mole/l] substrate concentration at reactor inlet - p [mole/l] product concentration - p _e [mole/l] product concentration at equilibrium - P _r [mole fructose/l·h] reactor productivity - T [k] temperature - t [h] time - t _p [h] operating time - V [l] reactor volume - v [mole/l·h] reaction rate - v [mole/l] reaction rate under enzyme deactivation and substrate protection - v _m [mole/l·h] maximum apparent reaction rate - v _p [mole/l·h] maximum reaction rate for product - v _s [mole/l·h] maximum reaction rate for substrate - x substrate fractional conversion - x _e substrate fractional conversion at equilibrium Greek Symbols effectiveness factor - mean effectiveness factor - substrate protection factor - [h] residence time - [h] average residence time - ₀ [h] initial residence time     

The role of vanadium in green plants

Cells of Chlorella pyrenoidosa, derived from vanadium free agar slants, respond with great sensitivity to microamounts of vanadium, added as NH₄VO₃ to autotrophic liquid cultures. Between 0.01 and 1 g V per litre nutrient medium (2·10^-10-2·10^-8g-at/l), the algae respond with a continuous increase in dry weight. At higher V-concentrations, further enhancement in biomass is accompanied by a additional increase in chlorophyll content. Maximum V-effect on both parameters was found to be at 500g V/l (10^-5 g-at/l). Dry weight as well as chlorophyll content of Chlorella are decreased by concentrations above 25 mg V/l; 100 mg V/l (2·10^-3 g-at/l) stop growth and cause death of the cells. The toxic threshold for the V-content in the algae was determined to be at 150–200 g V/g (3–4·10^-6 g-at/g) dry weight.Two different pH-optima for a positive vanadium action on dry weight and chlorophyll biosynthesis were established, the first at pH 7, the other in the range pH 7.5–8. Two sites of vanadium action in green algae are discussed.Part I: Arch. Microbiol. 105, 77–82 (1975)     

Immobilization of yeast cells on various supports for ethanol production

An immobilization technique has been developed for a packed bed fermenter which is being considered as one stage of a process for the production of fuel-grade ethanol from sugar solutions. Relatively inexpensive beech wood chips have been successfully used as the support material and relatively high cell loadings of 188 mg DW cells/g DW support have been achieved for a test system of Saccharomyces cerevisiae cultures.No washout of adsorbed cells occurs below a superficial liquid velocity of 8.9 × 10^-2 cm/s which can be increased to 9.7 × 10^-2 cm/s by including up to 1% Hercofloc solution in the reactor medium during the immobilization procedure. The immobilization procedure is practically unaffected by pH and temperature in the range 3.5 to 5.0 and 22 °C to 37 °C respectively.Typical ethanol productivity of 21.8g/l·hr has been obtained with wood-chip-adsorbed cells, which compares well with optimal values of 18 to 32g/l·hr obtained using free-suspension cultures in stirred-tank fermenters with cell recycle.     

Production of ethanol from cellulose,Solka Floc BW 200, in a fedbatch mixed culture of Trichoderma reesei,C 30, and Saccharomyces cerevisiae

Summary Solka floc BW 200 was converted to ethanol in a multistep conversion using Saccharomyces cerevisiae in combination with Trichoderma reesei, C 30. Up to 40 g/l ethanol was obtained with these mixed cultures and a maximum yield of 83% and productivity of 0.2 g/l·h was achieved. The limiting factor in the process was the activity of the cellulolytic enzymes produced by T. reesei, C 30. It is suggested that oxygen can be used in this type of a mixed culture as an external regulator for maintaining an optimal cellulolytic enzyme activity in the system, thus giving an overall optimal conversion of cellulose to ethanol.     

Dichloromethane utilized by an anaerobic mixed culture: acetogenesis and methanogenesis

Dichloromethane (8.9 mg/l) was eliminated from industrially polluted, anaerobic groundwater in a fixed-bed reactor (43 m³) which was packed with activated charcoal and operated continuously for over three years. The elimination of dichloromethane over this period was some ten-fold in excess of the sorptive capacity of the charcoal, and the elimination (3.7 mg/h·[kg of charcoal]: residence time, 49 h) was tentatively attributed to dehalogenative microorganisms immobilized on the charcoal. Anaerobic enrichment cultures, with dichloromethane as the sole added source of carbon and energy, were inoculated with material from the reactor. Reproducibly complete substrate disappearance in subcultures was observed when traces of groundwater (1%) or yeast extract (0.01%) were supplied. Fed-batch experiments under an atmosphere of CO₂ plus N₂ led to the conversion in 11 days of 11 mM dichloromethane to 3 mM acetate and 2 mM methane, with a growth yield of 0.4 g of protein/mol of dichloromethane; insignificant amounts (<1 M) of chloromethane accumulated. Methanogenesis could be inhibited by 50 mM 2-bromoethane sulfonate without any effect on the dehalogenation rate. The maximum dehalogenation rate was 0.13 mmol dichloromethane/h·l (2.6 mkat/kg of protein).Abbreviation DCM dichloromethane     

Analysis of immobilized cell bioreactors for desulfurization of flue gases and sulfite/sulfate-laden wastewater

Sulfur dioxide (SO₂) is one of the major pollutantsin the atmosphere that cause acid rain. Microbialprocesses for reducing SO₂ to hydrogen sulfide(H₂S) have previously been demonstrated byutilizing mixed cultures of sulfate-reducing bacteria(SRB) with municipal sewage digest as the carbon andenergy source. To maximize the productivity of theSO₂-reducing bioreactor in this study, variousimmobilized cell bioreactors were investigated: a stirredtank with SRB flocs and columnar reactors with cellsimmobilized in either -carrageenan gel matrix orpolymeric porous BIO-SEP^TM beads. Themaximum volumetric productivity for SO₂reduction in the continuous stirred-tank reactor (CSTR)with SRB flocs was 2.1 mmol SO₂/h·l. The-carrageenan gel matrix used for cellimmobilization was not durable at feed sulfiteconcentrations greater than 2000 mg/l or at sulfite feedrate of 1.7 mmol/h·l. A columnar reactor withmixed SRB cells that had been allowed to grow intohighly stable BIO-SEP polymeric beads exhibited thehighest sulfite conversion rates, in the range of16.5 mmol/h·l (with 100% conversion) to20 mmol/h·l (with 95% conversion). In addition toflue gas desulfurization, potential applications of thismicrobial process include the treatment ofsulfate/sulfite-laden wastewater from the pulp and paper,petroleum, mining, and chemical industries.     

On-line biomass estimation using a modified oxygen utilization rate

A procedure for estimating biomass during batch fermentation from on-line gas analysis is presented. First, the respiratory quotient was used to determine the fraction of the total oxygen utilization rate required for cell maintenance and growth versus product synthesis. The modified oxygen utilization rate was then used to estimate biomass on-line by integrating the oxygen balance for cell synthesis-maintenance. The method is illustrated for the case of L-lysine synthesis by Corynebacterium glutamicum.List of Symbols CER mmol CO₂/l · h carbon dioxide evolution rate - M _{O 2}/x mmol O₂/h · g cells maintenance coefficient - OUR mmol O₂/l · h oxygen utilization rate - OUR _X mmol O₂/l · h OUR fraction for cell maintenance and growth - RQ mmol CO₂/mmol O₂ respiratory quotient(CER/OUR) - X g cells/l biomass concentration - Y _X/O₂ yield coefficients