A Possible Mechanism of Metabolic Regulation in Gibberella fujikuroi Using a

Mixed Carbon Source of Glucose and Corn Oil Inferred from Analysis of the

Kinetics Data Obtained in a Stirrer Tank Bioreactor

Erika Y. Rios-IribePrograma Regional del Noroeste para el Doctorado en Biotecnolog�ıa, Facultad de Ciencias Qu�ımico Biol�ogicas, Universidad Aut�onomade Sinaloa, Av. de las Am�ericas y Blvd. Universitarios, Ciudad Universitaria, CP 80000, Culiac�an, Sinaloa, M�exico

Oscar M. Hern�andez-Calder�onFacultad de Ciencias Qu�ımico Biol�ogicas, Universidad Aut�onoma de Sinaloa, Av. de las Am�ericas y Blvd. Universitarios, CiudadUniversitaria, CP 80000, Culiac�an, Sinaloa, M�exico

C. Reyes-MorenoPrograma Regional del Noroeste para el Doctorado en Biotecnolog�ıa, Facultad de Ciencias Qu�ımico Biol�ogicas, Universidad Aut�onomade Sinaloa, Av. de las Am�ericas y Blvd. Universitarios, Ciudad Universitaria, CP 80000, Culiac�an, Sinaloa, M�exico

I. Contreras-AndradeFacultad de Ciencias Qu�ımico Biol�ogicas, Universidad Aut�onoma de Sinaloa, Av. de las Am�ericas y Blvd. Universitarios, CiudadUniversitaria, CP 80000, Culiac�an, Sinaloa, M�exico

Luis B. Flores-CoteraDept. de Biotecnolog�ıa y Bioingenier�ıa, CINVESTAV, Av. Polit�ecnico 2508, C.P. 07360, M�exico, D.F., M�exico

Eleazar M. Escamilla-SilvaDept. de Ingenier�ıa Qu�ımica, Instituto Tecnol�ogico de Celaya, Av. Tecnol�ogico y Antonio Garc�ıa Cubas S/N, C.P. 38010 Celaya,Guanajuato, M�exico

DOI 10.1002/btpr.1775Published online June 12, 2013 in Wiley Online Library (wileyonlinelibrary.com)

A nonstructured model was used to study the dynamics of gibberellic acid production in astirred tank bioreactor. Experimental data were obtained from submerged batch cultures ofGibberella fujikuroi (CDBB H-984) grown in varying ratios of glucose-corn oil as the car-bon source. The nitrogen depletion effect was included in mathematical model by consider-ing the specific kinetic constants as a linear function of the normalized nitrogenconsumption rate. The kinetics of biomass growth and consumption of phosphate and nitro-gen were based on the logistic model. The traditional first-order kinetic model was used todescribe the specific consumption of glucose and corn oil. The nitrogen effect was solelyincluded in the phosphate and corn oil consumption and biomass growth. The model fit wassatisfactory, revealing the dependence of the kinetics with respect to the nitrogen assimila-tion rate. Through simulations, it was possible to make diagrams of specific growth rate andspecific rate of substrate consumptions, which was a powerful tool for understanding themetabolic interactions that occurred during the various stages of fermentation process. Thiskinetic analysis provided the proposal of a possible mechanism of regulation on growth, sub-strate consumptions, and production of gibberellic acid (GA3) in G. fujikuroi. VC 2013 Amer-ican Institute of Chemical Engineers Biotechnol. Prog., 29:1169–1180, 2013Keywords: kinetic analysis, mixed carbon source, nitrogen depletion effect, Gibberellafujikuroi

Introduction

Gibberella fujikuroi is a gibberellin-producing fungus. Themost important gibberellin from an industrial perspective isthe gibberellic acid (GA3), which can be produced by fer-mentation at relatively high concentrations. The gibberellicacid is a phytohormone that affects plant development proc-

esses such as seed germination root and shoots growth, andeven mitosis in some plants. Various strategies have beenused to improve GA3 production including: (a) varyingmedium composition, (b) strain selection,1 (c) using differentculture modes such as submerged, solid-state, fed-batch sys-tem,2–4 (d) optimization of the culture conditions such astemperature, aeration, and pH, and (e) using different reactorconfigurations such as stirred tank, airlift, fluidized, orpacked bed arrangements.5–7 To find the best productionconditions, most research studies have been carried out

Correspondence concerning this article should be addressed toE. M. Escamilla-Silva at eleazar@iqcelaya.itc.mx.

VC 2013 American Institute of Chemical Engineers 1169

following a protocol of cause and effect. In previous work,in our laboratory, we conducted a series of experimentswhere different oils were used: rice, safflower, sesame, soy-bean, sunflower, and maize. The resulting best inducers forthe production of Gibberellins were found to be safflower,rice, and corn oil. However, the time to reach the start ofproduction of gibberellins was found to be highly variable.Thus, the idea emerged of making a mixture of glucose andvegetable oils to reduce the time to achieve the maximumgibberellic acid production and this resulted in finding thatcorn oil exerted more influence (Unpublished results so far).The production of GA3 by G. fujikuroi using only glucose oroil as the carbon source has been extensively studied.8 More-over, Rios-Iribe et al.6 reported that using a mixture of car-bon sources increases the production of gibberellic acid incomparison with using only glucose as a carbon source inthe medium under the same process conditions. Also, wefound that both carbon sources are metabolized quickly,which means that glucose does not exert catabolic repressionon the assimilation of corn oil or some kind of metaboliccontrol on the transport of fatty acids into cells ofG. fujikuroi.

On other hand, the quality and quantity of nitrogen sourceplay a significant role on GA3 production. All describedmedia that guarantee high yields of gibberellins have lowconcentration of nitrogen. Nitrogen-limited growth condi-tions are needed to induce the highest concentrations of GA3

as its formation is that of a typical secondary metabolite inrequiring unbalanced growth.3,6,9

The depletion of nitrogen not only influences the produc-tion of GA3, it also affects growth and substrate metabolism.Candau et al.10 found that increased mycelial dry weight inthe presence of glucose and the absence of a nitrogen sourceis due to the accumulation of carbohydrates and fats. Thiswas also confirmed by Jacklin et al.9 In addition, they alsofound that sesamol (2.5 mM) inhibited the growth of Fusar-ium moniliforme by about 40% and lipid accumulation by35%, but GA3 accumulation was increased by 20-fold. Thismay imply that the acetyl-CoA originally used for fatty acidbiosynthesis was instead directed to secondary metaboliteGA3 accumulation. Cohen and Drucker11 reported thatexponential-phase cells of Neurospora crassa require thecontinued presence of a protein inducer and nitrogen starva-tion to induce exocellular protease under conditions whereprotein is the sole nitrogen source. In N. crassa, proteasebiosynthesis is inducible by a protein substrate when cellsare starved for carbon, nitrogen, or sulfur; substrate concen-trations of carbon, nitrogen, or sulfur repress enzyme biosyn-thesis, with catabolite repression occurring when substratelevels of a carbon source are provided, when cells ofN. crassa are starved for nitrogen, both amount of proteasesynthesized and rates of synthesis decrease linearly as afunction of the period of starvation before the cells areinduced with protein as the sole N-source.

These systems use exponential-phase cells, as such,parameters of substrate and culture condition can be manipu-lated over short periods of time, and general analyses ofoptimal conditions can be performed quickly, perhaps yield-ing a mechanistic basis for future studies in G. fujikuroi.

N. crassa is a gibberellin-producing fungus.12 F. monili-forme (asexual stage, some isolates of which produce theperfect stage called G. fujikuroi) produces two types ofextracellular proteolytic enzymes, one active in acidic mediaand the second under neutral conditions.13

Several mathematical structures have been proposed todescribe the behavior of microorganisms.14–20 Among theprior efforts to understand and predict the behavior ofG. fujikuroi, Shukla et al.21 proposed a mathematical modelfor the first time for submerged cultivation to describe bio-mass growth, substrate consumption and product formation.Later, this model was extrapolated to computer simulationand design (offline on computer) of nutrient feeding strat-egies for fed-batch cultivation aimed at achieving high con-centration and productivity of GA3. Using this model-basednutrient feeding strategy, a volumetric productivity of 0.0168g L21 h21 for GA3 was obtained, which was �2.9 timeshigher than that obtained in conventional batch cultures.22

In this work, it is proposed that the nitrogen assimilationrate affects the biomass growth and the substrate consump-tion. It was assumed that the nitrogen uptake rate is the rate-limiting step in the growth of G. fujikuroi. The nitrogendepletion effect was included in the mathematical model byconsidering the specific kinetic constants to be a linear func-tion of the normalized nitrogen consumption rate. Thisapproach yielded model predictions that were fully consistentwith experimental data reported by Rios-Iribe6,8 and it wassuperior to the traditional models used. Based on a kineticanalysis of the culture, a possible metabolic regulatory mech-anism was inferred for G. fujikuroi when growth occurs on amixed carbon source. The specific uptake of corn oil wasindicated to be more closely related to the biomass specificproduction than the glucose specific uptake. In previous stud-ies,8 lipolytic activity was investigated for the first time byG. fujikuroi two cases very importants: When not used as acarbon source vegetable oils such lipolytic activity decreaseddrastically and the second that the proteolytic activity startsbefore running out the source of nitrogen, but surprisinglyincreases lipolytic activity after the nitrogen is depleted asshown in Figure 2. This phenomenon allows inferring theinsersion of free fatty acids in the secondary metabolism inparticular gibberellin biosynthesis. Finally, the zero-orderkinetics of GA3 production suggests that the concentration ofthe enzymes involved in the biosynthesis of gibberellinsremain constant during the production period.

Materials and Methods

G. fujikuroi strain CDBB H-984 was obtained from theNational Collection of Microbial and Cellular Cultures of theCINVESTAV-IPN, Mexico, maintained on potato dextroseagar slants at 4�C and subcultured every 2 months. Fullydeveloped mycelia from a slant were resuspended in isotonicNaCl solution (0.9%) and the suspension (2 mL) used toinoculate Erlenmeyer flasks containing 250 mL of fresh cul-ture medium. The flask was incubated in a radial shaker, 280rev min21 (Labconco, Lenexa, KS) for 38 h at 29�C 6 2�C.Subsequently, 200 mL taken from the flask were used toinoculate 3,800 mL of culture medium contained in thestirred tank bioreactor. The culture medium used for inocu-lum preparations was previously reported.3 A Stirred TankBioreactor (Applikon, Schiedam, The Netherlands; 7 L) wasused. The Bio-expert (Applikon, Schiedam, The Netherlands)software was used to record all the parameters throughoutthe fermentation time. Moreover, it allows material to be fedor removed from the bioreactor by using peristaltic pumps.

Three different culture mediums were used, in whichsolely the ratio of glucose to corn oil was varied in a waythat kept the concentration of carbon constant at 40 g L21.

1170 Biotechnol. Prog., 2013, Vol. 29, No. 5

The glucose carbon to corn oil carbon ratios used were: 1:2ratio, with a concentration of 33.25 g L21 of glucose and36.4 g L21 of corn oil; 1:1 ratio, with a concentration of 50g L21 of glucose and 27.4 g L21 of corn oil; and 2:1 ratio,with a concentration of 66.5 g L21 of glucose and 18.2 gL21 of corn oil. The typical culture medium also contained2 g L21 NH4Cl, 3 g L21 KH2PO4, 1.5 g L21 MgSO4�7H2O,and 2 mL L21 of trace elements. A stock solution of thetrace elements used contained (g L21) 1.0 FeSO4�7H2O, 1.5Na2MoO4�2H2O, 0.2 MnSO4�H2O, and 1.0 ZnSO4�7H2O. ApH value of 3.5, 29�C, 600 rev min21 agitation, and 1 vvmaeration were maintained and controlled with a biocontrollerconnected to the bioreactor, throughout the culture time.Samples were taken over a 360 h period and stored at 4�Cbefore analysis.

Fungi were harvested by filtration (under reduced pres-sure) through preweighed oven-dried nitrocellulose mem-branes (0.45-mm pore size; Millipore; Billerica, MA). Afterdrying at 90�C to constant weight, the biomass was quanti-fied by the dry weight method. Lipids were determined grav-imetrically after extraction with hexane and were rota-evaporated for hexane recuperation in a rota-evaporator(B€uchi, Postfach, Switzerland) and dried for 12 h in vacuumoven at 60�C (Felisa, M�exico). Residual NH4

1 in the fer-mentation broth was assayed by the Kjeldahl method(A.O.A.C.).23 The residual glycerol was determined by a col-orimetric Hantzsch condensation method.24

Determination of gibberellic acid

The GA3 in the culture fluid was quantified by HPLCusing a Varian 9012 Chromatograph (Varian; Palo Alto, CA)after extracting 10 mL samples of culture filtrate with three10 mL portions of ethyl acetate before adjusting to pH 2.0with 0.1 M HCl. The organic fractions were rotary evapo-rated and the residue taken up in 3 mL of methanol. GA3

was identified and quantified by reference to a GA3 standard(Sigma–Aldrich, Toluca, M�exico).25

Determination of free fatty acids

Fatty acids were quantified by gas chromatography using aVarian 3800 Gas Chromatograph equipped with an autosam-pler connected with a CP-FFAP CB (Varian, Palo Alto, CA)column (25 m 3 0.53 mm I.D., 1.0 mm film thickness). Theflame ionization detection system was operated at 270�C withan injector temperature of 260�C. The oven temperature pro-gramming used was to first isothermally hold at 200�C for 5min and then increase to 230�C at 1�C min21. The carrier gas(N2) flow was maintained constant at 5 mL min21. The fattyacids were extracted with 3 mL absolute methanol from hex-anic extract used to quantify lipids. The resuspension was leftstanding at 0�C for at least 12 h. An aliquot of 1 mL solutionwas twice filtered through a 0.45-lm nylon membrane (Milli-pore, Billerica, MA) at room temperature and 1 mL wasinjected onto the column.6,8

Results and Discussion

Kinetics of biomass growth, substrate consumptions, andGA3 production in batch cultures of G. fujikuroi

Figure 1 shows the kinetics of biomass growth, gibberellicacid production, and consumption of glucose, corn oil, nitro-gen, and phosphate by G. fujikuroi using a mixed carbon

source at different glucose/corn oil ratios [(a) 1:2, (b) 1:1and (c) 2:1]. The maximum production of GA3 occurred at288 h regardless of the ratio of glucose to corn oil used.However, the variation in the ratio of glucose to corn oil didsignificantly affect the production of GA3. It was observedthat maximum values of gibberellic acid concentration were430, 380, and 280 mg L21 of GA3 for glucose/corn oil ratiosof 1:2, 1:1, and 2:1, respectively. There was a rapid con-sumption of nitrogen and phosphate during the exponentialgrowth phase. In all experiments, the presence of ammonianitrogen in the culture medium was not significantly detectedafter 36 h, gibberellic acid production began at 48 h, and themaximum uptake of phosphate was reached at about 48 h.

We performed the quantification of the major fatty acidsin the corn oil: linoleic, oleic, palmitic, and stearic acids.

Figure 1. Kinetics of biomass growth, production of gibberellicacid, and consumption of glucose, corn oil, nitrogen,and phosphate in cultures of G. fujikuroi usingdifferent mixtures of carbon source of glucose andcorn oil on basis of 40 g L21 of total carbon.

Biotechnol. Prog., 2013, Vol. 29, No. 5 1171

Figure 2 shows the history of the concentration of total fattyacids (TFA) and glycerol. Only the medium with a glucose/corn oil ratio of 1:2 presented accumulation of TFA with amaximum concentration peak of 926 mg L21 at 96 h. Con-cerning the kinetics of glycerol, similar behavior was foundat the beginning of the fermentation process for all themedia used. The maximum concentration values of glycerolwere similar to each other, but not the duration of transientperiods. The glycerol concentration remained constant afterabout 48, 96, and 144 h for the glucose/corn oil ratios of1:2, 1:1, and 2:1, respectively.

Model development

A preliminary analysis applied to the normalized nitrogenconcentration indicated that the behavior observed in all theexperiments was highly similar; hence, the dynamics wereconcluded to be independent of the proportion of glucose/corn oil used. The trends shown by experimental data indi-cated a logistic behavior (Figure 3a). The nitrogen uptakemodel26 was, therefore, fitted by following equation:

2dSN

dt5kNðSN2SN;resÞ 12

SN2SN;res

SN;0

� �; SNðt50Þ5 SN;0

(1)

A variant of the classic logistic model, Eq. 2, was used todescribe biomass growth,27 in which the effect of nitrogenassimilation was introduced through the growth coefficientas a linear function of the normalized uptake rate of nitro-gen, Eq. 3; this follows from the assumption of growth islinked to N uptake.

1

X

dX

dt5lX 12

X

Xmax

� �; Xðt50Þ5 X0 (2)

lX5aX 21

SN;0

dSN

dt

� �1bX (3)

Free glucose in the medium is generally available to bedirectly assimilated by most organisms. Under this scenario,

the prospect that a limiting mechanism exists for the trans-port of glucose is low. Thus, based on this assumption, thespecific consumption rate of glucose, Eq. 4, solely dependson the availability in the medium (SG) and the metabolicrequirements of growth (kG).

21

X

dSG

dt5kGSG; SGðt50Þ5 SG;0 (4)

Figure 3c shows a sharp drop in normalized corn oil con-centration occurs during the first 24 h where the dynamicsare independent of the glucose/corn oil mixture used. How-ever, the profiles of corn oil concentration diverged there-after with a smaller slope. Specifically, two behaviorsemerge: a sudden and similar normalized-consumption until24 h followed by a slower consumption rate that is approxi-mately first-order in corn oil concentration. Because triacyl-glycerols cannot pass through the cell membrane,enzymatic hydrolysis to partial acylglycerols and free fattyacids (by lipases and esterases) is necessary for cellularuptake.28,29 Hence, corn oil consumption minimally consistsof two processes in series: the oil hydrolysis and the cellu-lar absorption of fatty acids. The nature of this kind ofmechanism might suggest the existence of a limiting step.The following mechanism is proposed for the uptake offatty acids:

HL!kHLFA!kFA

M

where HL represents the hydrolysable lipids, FA correspondsto the TFAs in the culture medium, and M refers to the fattyacids assimilated by the organism. Regarding the kineticsassociated with this mechanism, the specific consumptionrate of TFA was represented by Eq. 5 in a manner similar toglucose consumption (Eq. 4).

21

X

dSFA

dtjcons5kFASFA (5)

The generation rate of TFA, Eq. 6, was related stoichio-metrically to rate of lipid hydrolysis by the yield factorYFA/HL.

dSFA

dtjgen52YFA=HL

dSHL

dt(6)

Thus, the overall rate of TFA production was obtainedfrom the balance between the generation and consumptionrates. Because the accumulation of TFA was experimentallyobserved to be low in the culture medium, the overall ratewas considered to be negligible,

dSFA=dt50: (7)

dSFA

dt5

dSFA

dtjgen1

dSFA

dtjcons (8)

The rate of TFA consumption is assumed to be con-trolled by the rate of lipid hydrolysis. Then later, it can beconsidered to be a first-order kinetic process. Additionally,it was dependent on the instantaneous lipolytic activity(KLA), which was defined as the product of two effects: thebiomass concentration (high biomass concentrationsincrease the formation or denaturalization of lipase in themedium) as shown in Figure 6a and to induce exocellularproteolytic enzyme from carbon-starved exponential phasecells of G. fujikuroi like as Neurospora crassa, both a pro-tein substrate and an activating protease of certain specificproperties must be present at the same time and the effect

Figure 2. Time course of glycerol and total fatty acid (linoleic1 oleic 1 palmitic 1 stearic acids) in cultures ofG. fujikuroi grown in different mixtures of glucoseand corn oil on basis of 40 g L21 of total carbon.

1172 Biotechnol. Prog., 2013, Vol. 29, No. 5

of nitrogen assimilation may be it considered in the coeffi-cient kO as can be discerned in Figures 7 and 8, thereforekLA 5 kOX

2dSHL

dt5kLASHL; SHLðt50Þ5 SHL;0 (9)

It is proposed that the nitrogen assimilation affected thesynthesis and degradation of lipolytic enzymes. This influ-ence was included by Eq. 9, as a linear function of the nor-malized uptake rate of nitrogen.

kO5aO 21

SN;0

dSN

dt

� �1bO (10)

With this, the specific consumption of TFA, Eq. 10, isstructured as a function of the availability of oil in themedium and the effect of nitrogen assimilation on lipolyticcapacity, but only when the lipid hydrolysis is a limitingstep.

21

X

dSFA

dtjcons5YFA=HLkOSHL (11)

In this case, the corn oil was considered practically ashydrolysable lipids, because of the low concentration ofTFA. This consideration leads to SLH 5 SO.

It is assumed that phosphate consumption is uniquelyrelated to cell growth with constant cell yield coefficient, Yn/

P (cell production for phosphate consumption). Cell growthwas described by the logistic model, Eq. 11, and was consid-ered influenced by the nitrogen assimilation, Eq. 12.

1

n

dn

dt5ln 12

n

nmax

� �; nðt50Þ5 n0 (12)

ln5an 21

SN;0

dSN

dt

� �1bn (13)

A constant yield coefficient of phosphate (SP) to cells (n),implies that n5n01Yn=PðSP;02SPÞ. Substituting this relation

Figure 3. Normalized model and experimental data of nitrogen, glucose, corn oil, and phosphate uptake by G. fujikuroi using differentmixtures of glucose and corn oil.

Biotechnol. Prog., 2013, Vol. 29, No. 5 1173

into Eq. 5 yields Eq. 13, which represents the model usedfor the uptake of phosphate,

2dSP

dt5lnðSP;02SP1dSPÞ 12

dSP1SP;02SP

dSP1SP;02SP;min

� �;

SPðt50Þ5 SP;0 (14)

where dSP5n0=Yn=P and SP;min is the minimum phosphateconcentration reached when the cell concentration reaches itsmaximum value. The parameter dSP is a measure of the ini-tial cell concentration inoculated to the medium. The hypoth-esis of a constant cell yield coefficient of phosphate is notrestricted to this work. Thomas and Dodson30 measured theeffect of the phosphate concentration on the growth in anartificial medium for the cultivation of Chaetoceros gracilis.They found that the final cell numbers were a linear functionof initial phosphate concentration up to 0.8 mg atom/L, andthe amount of phosphorus per cell is 2 3 1029 mg atom/cell.

Figure 5 indicates that the GA3 accumulation occurred lin-early with time, i.e., it follows zero-order kinetics (Eq. 14),only during the period of time from 48 to 288 h.

dP

dt50; t < ts;

dP

dt5kGA; t0 < t

< tf ;dP

dt50; t > tf (15)

To estimate the optimal model parameters, a nonlinearregression technique assisted by a code developed in Matlab

VR

(The MathWorks, Natick, MA) was used to minimize the devi-ation between the model and experimental data. For calcula-tion of the model predictions, the system of differentialequations describing the batch cultivation kinetics was solvedby an integration program based on Runge-Kutta-Fehlberg.31

The optimization program for the direct search of the mini-mum of a multivariable function was based on the Broyden-Fletcher-Goldfarb-Shanno variable metric method.32 The min-imization criteria used in the program was as follows:

SSWR5Xn

i51

Xm

j51

dij

Wj

� �2

(16)

where SSWR represents the sum of squares of the weighedresidues, i and j represents the number of experimental data

points and the number of variables respectively, Wj repre-sents the weight of each variable (maximum value of eachvariable), and dij denotes the difference between the modeland the experimental value.

Validation of the proposed model for the dynamic study ofnutrient uptake, biomass, and gibberellic acid production

The proposed model was fitted to the experimental data sat-isfactorily as can bee seen in Figures 3–5; the results of param-eter estimation as well as the corresponding values of theSSWR are summarized in Table 1. In general, the model pre-sented a good correlation between the experimental data andmodel predictions. The Xmax and Pmin parameters are not opti-mized values, but average values of the stationary phase. Thedeath phase was not taken into account in the model.

Figure 3 shows the nitrogen consumption and has a similarbehavior between the experimental data and the proposedmodel regardless of the mixed carbon sources used. However,the dynamics of nitrogen assimilation did affect the consump-tion of the substrates; specifically, corn oil and phosphate.Something interesting that is worth noting that our proposedmodel represents well the literature reports on gibberellin bio-synthesis, which mention that gibberellin production beginswhen the concentration of the nitrogen source is depleted andmicrobial growth reached the stationary phase as shown inFigures 3–5. This in conjunction with the consumption of thecarbon source can establish a steady-state fermentation systemthat is controlling the rate of growth and the carbon source,so that only further production gibberellins, especially gibber-ellic acid during a longer period. Biomass experimental datawere fitted to a logistic considering mx constant and adjust-ment was robust; however, no such adjustment was reported.For that model has a correlation factor of r2 5 0.981 (2:1),0.971 (1:1), and 0.992 (1:2), respectively. mx variation inactual fact not constant due to the disturbances that presentmicroorganism-substrate relations; however, this variation isminimal so that the validity falls within experimental error.

However, the proposed model was superior (Figure 4) andthe growth was very well simulated, especially during 0–48

Figure 4. Normalized model and experimental data of biomassproduction by G. fujikuroi using three different mix-tures of glucose and corn oil as carbon source (glu-cose/corn oil ratios of 1:2, 1:1, and 2:1).

Table 1. Model Parameters for Batch Cultivation of G. fujikuroiUsing Different Mixtures of Glucose and Corn Oil as Carbon Source

Model Parameters

Glucose/corn

oil ratioof 1:1

Glucose/corn

oil ratioof 1:2

Glucose/corn

oil ratioof 2:1

Nitrogen kN (h21) 0.6505 0.5573 0.4654SN,res (g L21) 0.0000013 0.00005 0.000102SSWR 0.0033 0.00008 0.0008

Biomass Xmax (g L21) 20.9320* 20.8351* 18.9731*

aX 2.0848 1.6098 1.3979bX (h21) 0.0715 0.0982 0.0539SSWR 0.0041 0.0041 0.0023

Glucose kG (L g21 h21) 0.0026 0.0062 0.0020SSWR 0.0171 0.0064 0.0049

Corn oil aO (L g21) 0.0796 0.0868 0.1385bO (L g21 h21) 0.0004 0.0002 0.0005SSWR 0.0211 0.0420 0.0068

Phosphate Pmin (g L21) 0.6559* 0.7474* 0.9666*

an 1.0693 1.9457 0.7760bn (h21) 0.1419 0.1237 0.1108dSP (g L21) 0.0227 0.0239 0.0363SSWR 0.0005 0.0006 0.0018

GA3 kP (g L21 h21) 0.0015 0.0016 0.0012SSWR 0.0061 0.0071 0.0075

*These parameters are not optimized values.

1174 Biotechnol. Prog., 2013, Vol. 29, No. 5

h. According to the model, biomass growth was significantlyaffected by nitrogen assimilation. When adjusted glucoseuptake model, we used the same model as that used adjust-ment in corn oil consumption, whereas the rate constant waslinear function of the relative depletion of nitrogen; however,the linear coefficient was so small that lost their dependenceon such term and the model is reduced to the modeldescribed by Eq. 1. This report is very important becausespecific glucose uptake was not controlled by the nitrogenconsumption as can seen in Figure 3b.

Table 1 shows the kinetic parameters obtained with themodel proposed in this article. These data are very interest-ing and will be very useful in dynamic studies of the fer-mentation process for the production of GA3. KG is observedthat increases with decreasing initial concentration of glucoseand otherwise increasing the initial glucose concentrationdecreases KG and this fact is very important because conven-tional lag phase is by-passed in large scale fermentations ifinitial high glucose concentrations (more than 20%) or theuse of complex ammonium compounds as a nitrogen sourceis avoided, and if vigorously growing inoculum is used tocommence a fast mycelium development. This fact is con-firmed by nitrogen consumption and reduced biomass pro-duction in the same table. The kinetic analysis of corn oiluptake showed that uptake of this substrate was stronglyaffected by nitrogen assimilation. In all three cases, thebehavior of normalized consumption rate was similar beforeexhaustion of nitrogen, indicating almost identical lipolyticcapacity (enzyme concentration). A sensitivity analysis wasapplied in order to investigate the effect of the aO parameter(which introduces the effect of nitrogen depletion) on themodel. It was found that this parameter is indispensable fora proper prediction of the corn oil uptake (Figure 3c).

Phosphate was supplied in excess of the culture needs.Furthermore, the assumption that consumption is mainlyrelated to cell growth was adequate. The model successfullyfit that data (Figure 3d). If the premise on which the phos-phate model is formulated is correct, then the cell growthceased around 48 h (Figure 4).

In all the experiments, after 48 h the GA3 concentrationincreased linearly with time as shown in Figure 5, while thesubsequent increase in biomass did not affect the kineticbehavior of GA3 despite the significant relative increase of26.1% in biomass for the glucose/corn oil ratio of 2:1(Figure 4). In this case, the increase in biomass should influ-ence the production kinetics of GA3, deviating from the lin-ear behavior observed, unless the cell concentration and thecell productivity have remained constant. If the latter is true,then the increase in biomass could be due to intracellularlipid accumulation and the cell growth should have ceasedbefore or coincidently with the onset of GA3 production.This is consistent with observations in many fungi that thesecondary metabolism is activated following the phase ofrapid biomass proliferation (or from fast nutrient consump-tion), i.e., once the growth slows.33–37 The experimental dataof phosphate concentration also strengthen the hypothesisthat cell growth ceased after 48 h. Subsequent to that time,the assumption that there was cell growth has a major draw-back: the main component of the cell membrane is phospho-lipids, whose synthesis demands the use of phosphoruscompounds. The consideration of cell growth after the stabi-lization of the culture phosphate concentration would requirethe recycling of phosphorus, which is metabolically ineffi-cient when the medium is still rich in phosphates.

The increase in GA3 concentration ceased after 288 hregardless of the glucose/corn oil ratio used (Figure 5). Toconsider glucose as responsible for the end of this metabolicprocess is inadequate because in all cases, the GA3 produc-tion continued even after the depletion of this substrate (Fig-ure 3b). The oil was not a limiting factor in GA3 productionbecause in two experiments (glucose/corn oil ratio of 1:1and 1:2), oil was apparently present in culture medium insignificant concentrations at the end of the runs as seen inFigure 3c. It could be possible to assume that the end-timeof GA3 production was caused by the exhaustion of intracel-lular lipid (data not reported), which resulted in cell death.In the oil-contained medium (1:1 and 1: 2 ratios), signifi-cantly more biomass was formed than glucose alone, and theproduction phase continued for a long time by high myce-lium productivity, according to the observed experimentaldata (Figures 3c and 4).

Kinetic analysis and simulation of batch cultivation

Equation 16 is the classical model, in which substrate isconsumed by both growth and maintenance mechanisms.

21

X

dS

dt5

1

YX=S

1

X

dX

dt1m (17)

The parameter YX/S is the yield coefficient of biomass onsubstrate, and m is the maintenance coefficient of substrate. Inthis research, the mathematical model expressed by Eq. 15was avoided despite its prior use by others.21,38 It is wellknown that besides substrate uptake for growth, organismsrequire a certain amount of energy for their maintenance.39

However, it is not true that these requirements are constantduring the lifetime of the organism. A batch culture is aclosed system where growth typically ceases due to the accu-mulation of metabolic waste products or when a limitingnutrient is depleted. The biological and environmental changesaffect the metabolism of the microorganisms and cause

Figure 5. Experimental and model data for the production ofgibberellic acid by G. fujikuroi using three differentmixtures of glucose and corn oil as carbon source(glucose/corn oil ratios of 1:2, 1:1, and 2:1).

Biotechnol. Prog., 2013, Vol. 29, No. 5 1175

metabolic stress and finally cell death. Inevitably, these con-tinuous variations of environmental conditions led to variablerequirements for growth and maintenance. Therefore, the priorestablishment of constant metabolic requirements can restricta model’s predictive capability. Unfortunately, the model usedin this investigation also has weak points. It does not allowfor predicting the maximum biomass achieved in the culturemedium, and the specific growth rates, substrate consumption,and product formation were proposed independently of eachother. On the other hand, two of the greatest advantages ofthe used model were its simplicity and the excellent fitobtained between the experimental and simulated data,although the medium is a combination of two carbon sources,slow and rapid assimilation, the model allows analyzing thekinetic behavior of G. fujikuroi via simulation. Fact allowedchoosing how will feed these carbon sources in the process,

allowing extending the production time and maximizing theconcentration of GA3, as previously reported.

Figure 6 shows the specific substrate consumption rate vs.specific growth rate behavior of the complex nature of themetabolism of G. fujikuroi. The model expressed by Eq. 15is valid only if applied piecewise in time. That is, the spe-cific glucose consumption rate is not linearly correlated withthe specific growth rate before 36 h, but it is after 36 h, i.e.,it can be modeled by Eq. 15. Additionally, the specific cornoil consumption rate is linearly correlated with the specificgrowth rate before 36 h, but not after 36 h. This could indi-cate that growth was strongly related to corn oil uptakebefore 36 h and to glucose uptake after 36 h. But, it is notpossible to affirm that growth was sustained uniquely bycorn oil alone before 36 h and by glucose alone after 36 h,at least not with the data reported here.

Figure 6. Simulated behavior of the specific rate of substrate consumption (glucose and corn oil) as a function of specific growth rate(a) Period 0-24 h, (b) Period 24-192 h.

1176 Biotechnol. Prog., 2013, Vol. 29, No. 5

The time histories of the specific rates of growth and con-sumption of glucose and corn oil revealed finer details of themetabolic interaction between growth and substrate con-sumption. This is shown by Figure 7a–c (semilogarithmicplots). The three culture mediums studied showed a verysimilar behavior. The analysis was conducted in three stages.In the first stage, according to the behavior exhibited duringthe first 12 h, the biomass growth was maintained by glu-cose. The specific rates of growth and glucose uptakeremained practically constant during 0–12 h. There was avast difference between the specific consumption specificrate of glucose and corn oil. Besides the growth, glucoseuptake could have been maybe used for the synthesis ofextracellular metabolites. At the end of this stage, oil con-sumption contributed significantly to the growth of the fungi.At the second stage, this coincides with increased nitrogenuptake rate (12–24 h); where should one look for N uptake(see Figure 3a), the specific biomass growth rate was higherthan the specific consumption rate of glucose indicating thatthe fungi physiology changed to secondary metabolism. Bio-mass growth was mainly maintained by corn oil. This couldbe an indication that G. fujikuroi has a greater affinity forcorn oil than glucose during this period of high growth. Twotendencies were observed in the specific growth rate: anaccelerated exponentially phase followed by a deacceleratedexponentially phase. In the third stage, after nitrogen starva-tion (after 24 h), the specific rates of growth and glucoseconsumption decreased exponentially, and showed a some-what similar decaying (presented a somewhat similar slope),which might suggest that the growth and glucose uptakecould be regulated by the same metabolic mechanism in thisstage. The deaccelerated exponentially phase of specific cornoil consumption rate in the second stage continued until 36h; after this time, the decay constant of the specific corn oilconsumption rate dramatically decreased.

At 48 h, the specific growth rate showed a scarcely percepti-ble change. Therefore, considering that cell growth ended at48 h, we can express that growth is not a simple mechanism tobe modeled with a constant growth coefficient. In fact, bio-mass growth using glucose and corn oil as carbon source underconditions of nitrogen depletion is composed of four phasesfor the cell growth and a later lipogenic phase. This approachsuggests that there is cell growth in the absence of nitrogen in

the medium. Cohen and Drucker11 found N. crassa myceliatransferred to N-free Vogel’s medium can continue to increasein dry weight without any lag period. These unexpected resultswere found to be a reflection of the unbalanced growth. Simi-lar behavior has also been reported for P. griseofulvum.40

Regarding the argument that growth was mainly supportedby corn oil in the period 12–24 h, there is evidence that thelipid consumption is strongly linked to cell growth. Yoshidaet al.41 investigated effect of lipid materials on the produc-tion of lipase by Torulopsis ernobii. They found that theaddition of substrates such as stearic, palmitic, and oleicacids to the basal peptone medium stimulated the lipolyticactivity with a relative increase of 170% and led to a viablecell count three times greater than when the basal peptonemedium without added substrate was used. Under thisapproach, it is quite possible that the low corn oil consump-tion at the beginning of fermentation was due to a low activ-ity of hydrolases in the medium, and a subsequent increasein hydrolytic activity was at the expense of glucose con-sumption Then, it could be argued that glucose does notexert catabolic repression on the uptake of corn oil.

During the period of 12–24 h, two tendencies wereobserved in the specific consumption rate of corn oil: anaccelerated uptake rate followed by an abrupt transition to adecelerated uptake rate. This behavior could be due to thehigh availability of nitrogen promoted the synthesis andsecretion of extracellular lipases with the unique aim toaccelerate growth, because the consumption of lipid isstrongly linked to cell growth.41 However, the depletion ofnitrogen led to an increase in extracellular protease activity,which affected the activity of lipases in the medium.11 Lipo-lytic activity decreased rapidly and dramatically, in a veryshort period of time (in 6 h approximately). The latter wasinferred from the time history of the specific consumptionrate of corn oil and latter was confirmed by simulation.

It was observed that the glucose/corn oil ratio of 2:1showed a slightly longer period of hydrolysis. The overallspecific consumptions ð2˚SN=˚XÞ were calculated for theperiod 0–24 h, which yielded the following values: 0.057,0.039, and 0.041 g of N consumed/g of biomass producedfor glucose/corn oil ratios of 2:1, 1:1, and 1:2, respectively.This result could suggest that G. fujikuroi grown on mediumwith a glucose/corn oil ratio of 2:1 may have accumulated

Figure 7. Simulation of the time histories of the specific rates of growth and consumption of glucose and corn oil for the three cul-tures of G. fujikuroi using different mixtures of glucose and corn oil on basis of 40 g L21 of total carbon.

Biotechnol. Prog., 2013, Vol. 29, No. 5 1177

greater pools of nitrogen (amino acids), which caused repres-sion of the synthesis of extracellular proteases under a mech-anism similar to the one reported by Cohen and Drucker,11

and it extended the duration of the lipolytic activity.

From the good fit of the model of oil consumption, it wasinferred that the specific consumption rate of fatty acids wasnot constant, but regulated by the corn oil concentration ofthe culture medium. This was an inevitable consequence ofpossibly being limited by the oil hydrolysis rate.

The experiment with glucose/corn oil ratio of 1:2 offeredthe possibility of determining the coefficient of absorption ofTFA, but only when the concentration of TFA in themedium was significant (48–360 h). Substitution of Eq. 5and Eq. 6 into Eq. 7 yields Eq. 17, which was used to calcu-late the coefficient of absorption.

dSFA

dt52YFA=HL

dSHL

dt2kFAXSFA (18)

In this case, the rate of hydrolysis was not affected by theuptake of nitrogen. Therefore, in Eq. 7, the coefficient kLA

was replaced by a constant parameter, kHL, and its solutionis given by SHL5SHL;0expð2kHLtÞ. The proposed model wasexpressed by the Eq. 18.

dSFA

dt5YFA=HLkHLSHL;0exp 2kHLtð Þ2kFAXSFA (19)

The fit of the model is shown in Figure 2. The values ofthe optimized parameters are: hydrolysis rate constant,kHL50:0279 h21; and coefficient of absorption of TFA,kFA50:0008311 g L 21h21; with SSWR 5 0.0977.

The lipolytic activity in the medium was determined basedon the simulation of the corn oil consumption rate. One activ-ity unit (U) was defined as the amount of the enzyme requiredto break 1 mmol of ester bonds in glycerides per minute. Itwas assumed that 1 mmol of ester bonds equals about 280 mgof corn oil (based on molecular mass of linoleic acid). Figure8 shows the results of this calculation. It was found that thelipolytic activity was negligible in the beginning, butincreased rapidly to a maximum (of 138, 114, and 71 U L21

for glucose/corn oil ratios of 1:2, 1:1, and 2:1, respectively)after about 20 h, and then decreased exponentially to a smallvalue of 0.004 U L21. The lipolytic activity was likely

slightly overestimated, because the number of ester bonds pergram of glycerides is less than the previously used (because itis an average value determined indirectly by means of indexesof acidity (AI) and saponification (SI): EI 5 SI 2 AI). Thismethodology, in conjunction with the proper knowledge ofthe glyceride distribution, could be useful for the calculationof instant lipolytic activity in the culture medium.

The specific cell growth rate was simulated (Figure 8b).This result was inferred from the experimental kinetics ofphosphate concentration by use of the Eq. 11. The use of aglucose/corn oil ratio of 2:1 provided a lower rate of cellgrowth in comparison with other ratios.

1

n

dn

dt52

1

ðSP;02SP1dSPÞdSP

dt(20)

It is possible that the rate of hydrolysis was influenced bycorn oil concentration, which in turn controlled the cellulargrowth. Thus, hydrolysis acted as a rate-limiting step in thegrowth of G. fujikuroi. The less rapid growth achieved byglucose/corn oil ratio of 2:1 led to higher specific consump-tion of nitrogen (2˚SN=˚X). Probably as a consequence ofthis: (a) the proteolytic response was less intense, whichextended the period of the lipolytic activity; (b) and the geneexpression for the production of GA3 was also diminished.This is why it is very important for gibberellin fermentationthe quality and quantity of nitrogen used.

In fact, hydrolysis of corn oil also acted indirectly as arate-limiting step in the glucose consumption. Some studiesreported on the outcome of cultivating Streptomyces lividansin medium containing glucose and oil as carbon sources.42

They found that there was neither b-oxidation nor fatty acidbiosynthesis, indicating that glucose provided all the inter-mediates down to the level of acetate and that the trioleinprovided the majority of the straight-chain fatty acyl groupsin the lipids. Thus, the cells use both substrates simultane-ously, evidently by mutually exclusive mechanisms, therebyachieving increased growth. Applying this principle of mutu-ally exclusive mechanisms, the specific glucose consumptionwas regulated by the hydrolysis-limited growth rate. Thisraises the possibility that the consumption of glucose mayincrease by increasing the lipolytic activity of the medium,and thus accelerate the cell growth.

Figure 8. Simulation of the lipolytic activity, (a) calculated from the consumption rate of corn oil, and (b) simulation of specific rateof cell growth, assuming a constant yield (Yn/P) during the whole growth phase.

1178 Biotechnol. Prog., 2013, Vol. 29, No. 5

A possible metabolic regulatory mechanism in G. fujikuroi

using a mixed carbon source

This kinetic analysis suggests a possible mechanism of meta-bolic regulation in the production of GA3 by G. fujikuroi usinga mixed carbon source. At the beginning of cultivation, glucoseis used as the main carbon source in order to sustain a constantcell growth rate and to synthesize hydrolases, whose productionis induced by the presence of oil substrate. Hydrolytic activityis rapidly expressed and the specific rate of corn oil consump-tion increases concomitantly with accelerated biomass growthuntil the nitrogen in the medium is depleted. During this expo-nential growth period, the specific rate of glucose consumptionis kept constant, which at first glance suggests that the glucoseuptake is not associated with cell growth. However, it couldalso be simply that initially glucose is high and transport is sat-urated leading to apparently constant specific uptake of the glu-cose. Nitrogen starvation leads to a reduced growth rate andpromotes the formation of extra- and intra-cellular proteases.The extracellular proteolytic activity adversely affects theextracellular hydrolytic activity and the rate of corn oil uptakeis slowed. Moreover, amino acids released by intracellular pro-teolysis and subsequently translocated support the cell growthbetween nitrogen depletion and gibberellic acid production(36–48 h). The recycling of nitrogenous compounds reaches acritical level, then the cell growth ceases and lipogenic phaseand secondary metabolite production of GA3 begin in the cul-ture. Although these last two metabolic mechanisms competewith each other because they share a common precursor, ace-tyl-CoA,9,42 in this case when a mixed carbon source is used,competition may not occur.43

The maximum cell concentration reached during growthplays a fundamental role in the production of GA3. First, ahigh cell concentration leads a higher rate of production ofGA3. It is very possible that cell concentration remains con-stant after cessation of cell growth. Otherwise, it is difficultto understand the linear behavior of the GA3 concentrationas function of time. Second, a high cell concentration resultsin nutrient depletion. G. fujikuroi is stressed due to lowintake of nutrients and its secondary metabolism is activatedpossibly as a survival mechanism in response to insufficientnutrient availability. The expression of the enzyme activityinvolved in the biosynthesis of gibberellins may be depend-ent of the level of nitrogen depletion.

The zero-order kinetics of GA3 production also suggeststhat the concentration of the enzymes involved in the biosyn-thesis of gibberellins had to remain constant during the pro-duction period. This means that the period of biosynthesis ofthese enzymes should be very short (a few hours), after thecessation of cell growth according to experimental data. It ispossible that the metabolic mechanism involved in the stop-ping of cell growth is also responsible of the activation ofsecondary metabolism.

Conclusions

The effect of using a mixed carbon source on the produc-tion of GA3 by G. fujikuroi was studied. Three different mix-tures of glucose and corn oil were used as a carbon source onbasis of 40g L21 of total carbon. A mathematical structurewas formulated to describe biomass growth, substrate con-sumption and product formation, in which the nitrogen deple-tion effect was included in model by considering the specifickinetic constants as linear function of normalized nitrogenconsumption rate. The model fit was satisfactory. The simula-

tions allowed computing estimates of the specific growth rateand the specific rate of substrate consumptions, which was apowerful tool for understanding the metabolic interactions thatoccurred during the various stages of cultivation. The simula-tions allowed predicting the likely behavior of the lipolyticactivity of the medium. This kinetic analysis provided the pro-posal of a possible mechanism of regulation on growth, sub-strate consumptions, and production of GA3 in G. fujikuroiusing a mixed carbon source of glucose and corn oil.

Acknowledgments

Direcci�on General de Estudios Superiores Tecnol�ogicos(DGEST) grant-4258.11-P. We acknowledge the fellowshipsgranted by the Programa de Doctores J�ovenes of the Univer-sidad Aut�onoma de Sinaloa to E.Y. R�ıos-Iribe and O.M.Hern�andez-Calder�on.

Notation

dij = difference between the model and experimentalvalues for ith data points and jth process variables

k = specific rate constant of substrate assimilation orhydrolysis (h21 or g L21 h21 or L g21 h21)

m = cell maintenance constant (h21)n = active cell concentration (cell L21)S = substrate concentration (g L21)P = GA3 concentration (g L21)

SSWR = sum of squares of the weighted residuest = time (h)

Wj = weight of each variable (usually the maximumvalue of each variable)

X = biomass concentration (g L21)Yi/j = yield of product i with j as substrate

Greek letters

a = nitrogen-assimilation associated parameter (L g21)b = nitrogen-assimilation nonassociated parameter (L

g21 h21)m = maximum-specific growth rate of logistic model

(h21)

Subscripts

0 = initialmax = maximummin = minimum

n = cellres = residual

Total = total fatty acidsG = glucose

GA = gibberellic acidHL = hydrolysable lipidLA = lipolytic activity

N = nitrogenO = corn oilP = phosphateX = biomass

Literature Cited

1. Escamilla Silva EM, Dendooven L, Uscanga-Reynell JA,Monroy-Ram�ırez AI, Gonz�alez-Alatorre G, De la Torre MM.Morphological development and gibberellin production by dif-ferent Straits of Gibberella fujikuroi in shake flasks and bioreac-tor. World J Microbiol Biotechnol. 1999;15:753-755.

Biotechnol. Prog., 2013, Vol. 29, No. 5 1179

2. Tomasini A, Fajardo C, Barrios-Gonzalez J. Gibberellic acidproduction using different solid state fermentation systems.World J Microbiol Biotechnol. 1997;13:203–206.

3. Escamilla EM, Dendooven L, Maga~na IP, Parra R, De la TorreMM. Optimization of gibberellic acid production by immobi-lized Gibberella fujikuroi mycelium in fluidized bioreactors. JBiotechnol. 2000;76:147-155.

4. Shukla R, Chand S, Srivastava AK. Improvement of gibberellicacid production using a model based fed-batch cultivation ofGibberella fujikuroi. Process Biochem. 2005b;40:2045-2050.

5. Ch�avez-Parga MC, Gonz�alez-Ortega O, Negrete-Rodr�ıguezMLX, Medina-Torres L, Escamilla-Silva EM. Hydrodynamics,mass transfer and rheological studies of gibberellic acid produc-tion in an airlift bioreactor. World J Microbiol Biotechnol.2007;23:615-623.

6. Rios-Iribe EY, Flores-Cotera LB, Gonz�alez-Ch�avira MM,Gonz�alez-Alatorre G, Escamilla-Silva EM. Inductive effect pro-duced by a mixture of carbon source in the production of gib-berellic acid by Gibberella fujikuroi. World J MicrobiolBiotechnol. 2011;27:1499–1505.

7. Tudzynski B. Biosynthesis of gibberellins in Gibberella fuji-kuroi: biomolecular aspects. Appl Microbiol Biotechnol. 1999;52:298-310.

8. Rios Iribe EY. Expresi�on gen�etica del hongo Gibberella fuji-kuroi bajo dos diferentes fuentes de carbono mediante la t�ecnicade despliegue diferencial. MSc Thesis. M�exico: UniversidadAut�onoma de Quer�etaro; 2003.

9. Jacklin A, Ratledge C, Wynn JP. Lipid-to-gibberellin metabolicswitching in Fusarium moniliforme via the action of sesamol.Biotechnol Lett. 2000;22:1983-1986.

10. Candau R, Avalos J, Cerda-Olmedo E. Gibberellins and carote-noids in the wild type and mutants of Gibberella fujikuroi. ApplEnviron Microbiol. 1991;57:3378-3382.

11. Cohen BL, Drucker H. Regulation of exocellular protease inNeurospora crassa: induction and repression under conditions ofnitrogen starvation. Arch Biochem Biophys. 1977;182:601–613.

12. Kawanabe Y, Yamane H, Murayama T, Takahashi N, NakamuraT. Identification of gibberellin A3 in mycelia of Neurosporacrassa. Agric Biol Chem. 1983;47:1693-1694.

13. Kolaczkowska M, Polanowski A, Czaplinska S. Extracellularproteinases of Fusarium moniliforme. Hodowla Rosl AklimNasienn. 1980;24:1-7.

14. Monod J. The growth of bacterial cultures. Annu Rev Microbiol.1949;3:371-393.

15. Fredickson AG, Magee RD, Tsuchiya HM. Mathematical mod-els for fermentation processes. Adv Appl Microbiol. 1970;13:419–465.

16. Humphrey AE. Fermentation process modelling. An overview.Ann N Y Acad Sci. 1979;32:17–33.

17. Gutke R. Theoretical basis of kinetics growth, metabolism andproduct formation of microorganisms. In: UNEP/UNESCO/ICRO Training Course. Jena: Science Academy of East Ger-many, Central Institute for Microbiology and ExperimentalTherapy (ZIMET); 1980;1:30–112.

18. Nielsen J, Villadsen J. Modelling of microbial kinetics. ChemEng Sci. 1992;47:4225–4270.

19. Larralde-Corona CP, Gonz�alez-Blanco PC, Viniegra-Gonz�alezG. Comparison of alternative kinetic models for estimating thespecific growth rate of Gibberella fujikuroi by image analysistechniques. Biotechnol Tech. 1994;8:261–266.

20. Escamilla-Silva EM. Aplicaci�on del modelo de Gompertz parael estudio cin�etico de crecimiento del hongo Gibberella fujikuroien cultivo sumergido. In: VII Congreso Nacional de Bio-tecnolog�ıa y Bioingenier�ıa. M�exico: Mazatl�an Sin; 1997.

21. Shukla R, Chand S, Srivastava AK. Batch kinetics and modelingof gibberellic acid production by Gibberella fujikuroi. EnzymeMicrob Technol. 2005;36:492-497.

22. Shukla R, Chand S, Srivastava AK. Improvement of gibberellicacid production using a model based fed-batch cultivation ofGibberella fujikuroi. Process Biochem. 2005;40:2045-2050.

23. A.O.A.C. Official Methods of Analysis, 15th ed. of the Associa-tion of Official Chemists. Washington, D.C.: A.O.A.C.; 1990.

24. Foster LB, Dunn RT. Stable reagents for determination of serumtriglycerides by a colorimetric Hantzsch condensation method.Clin Chem. 1973;19:338-340.

25. Negrete-Rodr�ıguez X. Producci�on de �acido giber�elico en bio-rreactor de tanque agitado con Gibberella fujikuroi empleandoaceite de ma�ız como fuente de carbono. MSc Thesis. InstitutoTecnol�ogico de Celaya; 2002. Celaya, Gto. M�exico.

26. Ayati F, Aziza M, Maachi R, Amrane A. The substrate carbonconsumption and metabolite production to describe the growthof Geotrichum candidum and Penicillium camemberti on glu-cose and amino acids. Food Technol Biotechnol. 2010;48:79-85.

27. Monteiro-Machado CM, Soccol CR. Gibberellic acid production,Chapter 13. In: Pandey A, Soccol CR, Larroche C, editors. Cur-rent Developments in Solid-State Fermentation. 2007:277-301.Springer, API, New Delhi.

28. Diniz-Maia MM, Camargo-de-Morais MM, De-Morais MA,Magalh~aes-Melo EH, De-Lima-Filho JL. Production of extracel-lular lipase by the phytopathogenic fungus Fusarium solaniFS1. Rev Microbiol. 1999;30:304-309.

29. Voigt CA, Sch€afer W, Salomon S. A secreted lipase of Fusar-ium graminearum is a virulence factor required for infection ofcereals. Plant J. 2005;42:364-375.

30. Thomas WH, Dodson AN. Effects of phosphate concentrationon cell division rates and yield of a tropical oceanic diatom.Biol Bull Mar Biol Lab Woods Hole. 1968;134:199-208.

31. Mathews JH, Fink KK. Numerical Methods Using Matlab, 4thed. Upper Saddle River, New Jersey: Prentice-Hall Inc.; 2004.

32. Rao SS. Engineering Optimization: Theory and Practice, 4th ed.Wiley; 2009. Hoboken, New Jersey.

33. Borrow A, Brown S, Jefferys EG, Kessel RHJ, Lloyd EC, LloydPB, Rothwell A, Rothwell B, Swait JC. The kinetics of metabo-lism of Gibberella fujikuroi in stirred culture. Can J Microbiol.1964;10:407-444.

34. Bu’Lock JD, Detroy RW, Hostalek Z, Munim-al-Shakarchi A.Regulation of secondary biosynthesis in Gibberella fujikuroi.Trans Br Mycol Soc. 1974;62:377-384.

35. Drew SW, Demain AL. Effect of primary metabolites on sec-ondary metabolism. Ann Rev Microbiol. 1977;31:343-356.

36. Luckner M, Nover L, Bohm H. Secondary Metabolism and CellDifferentiation. Berlin: Springer-Verlag; 1977:37-102.

37. Wang DIC, Cooney CL, Demain AL, Dunnill P, Humphrey AE,Lilly MD. Fermentation and Enzyme Technology. Wiley-Inter-science Publication; 1979:6-8. United States of America andCanada.

38. Chavez-Parga MC, Gonzalez-Ortega O, Negrete-Rodr�ıguezMLX, Galindo-Vallarino I, Gonz�alez-Alatorre G, Escamilla-Silva EM. Kinetic of the gibberellic acid and bikaverin produc-tion in an airlift bioreactor. Process Biochem. 2008;43:855-860.

39. Krahe M. Biochemical Engineering. Ullmann’s Encyclopedia ofIndustrial Chemistry. 2003. Wiley-VCH Verlag GmbH & Co.KGaA.

40. Bent J, Morton AG. Amino acid composition of fungi duringdevelopment in submerged culture. Biochem J. 1964;92:260–269.

41. Yoshida F, Motai H, Ichishima E. Effect of lipid materials onthe production of lipase by Torulopsis ernobii. Appl EnvironMicrobiol. 1968;16:845-847.

42. Giordano W, Domenech CE. Aeration affects acetate destinationin Gibberella fujikuroi. FEMS Microbiol Lett. 1999;180:111-116.

43. Peacock L, Ward J, Ratledge C, Dickinson FM, Ison A. HowStreptomyces lividans uses oils and sugars as mixed substrates.Enzyme Microb Technol. 2003;32:157-166.

Manuscript received Oct. 15, 2012, and revision received Mar. 28,

2013.

1180 Biotechnol. Prog., 2013, Vol. 29, No. 5