A New Temperature Control Shifting Strategy for Enhanced Triterpene Production by Ganoderma lucidum G0119 Based on Submerged Liquid Fermentation

Transcription

1 Appl Bochem Botechnol (2016) 180: DOI /s A New Temperature Control Shftng Strategy for Enhanced Trterpene Producton by Ganoderma lucdum G0119 Based on Submerged Lqud Fermentaton Je Feng 1,2,3 & Na Feng 1,2,3 & Jng-Song Zhang 1,2,3 & Yan Yang 1,2,3 & We Ja 1,2,3 & Ch-Chung Ln 1,2,3 Receved: 25 February 2016 / Accepted: 6 May 2016 / Publshed onlne: 6 June 2016 # Sprnger Scence+Busness Meda New York 2016 Abstract Temperature control s a very mportant factor on trterpene productvty n submerged lqud fermentaton. Temperature effects from 23 to 32 C on trterpene producton by Ganoderma lucdum G0119 were nvestgated n 6-L strred fermentor. Logstc and Luedekng-Pret equatons were used to estmate the mycelal growth and trterpene producton knetcs by regresson analyss. On that bass, a temperatureshftng fermentaton control strategy was establshed. From 0 to 61 h, culturng was performed at 32 C to get hgh specfc mycelal growth rate. Between 62 and 127 h, the temperature was decreased stepwse from 31 to 30 C to mantan hgh trterpene productvty. After 128 h, temperature was mantaned at 29 C to mnmze trterpene producton nhbton and sustan hgh productvty. Elevated trterpene level (0.269 g L 1 ), yeld ( g g 1 ), and productvty ( g (L h) 1 ) were acheved representng 27.32, 13.94, and % hgher than submerged lqud fermentaton at constant temperature of 29 C, respectvely, feasble for the ndustral scale. Keywords Ganoderma lucdum. Mycelum. Trterpenes. Knetcs model. Temperature-shftng strategy * Jng-Song Zhang syja16@saas.sh.cn Key Laboratory of Edble Fung Resources and Utlzaton (South) of Mnstry of Agrculture, Shangha, Chna Natonal Engneerng Research Center of Edble Fung, Key Laboratory of Agrcultural Genetcs and Breedng of Shangha, Shangha, Chna Insttute of Edble Fung, Shangha Academy of Agrcultural Scences, 1000 Jnq Road, Fengxan Dstrct, Shangha , Chna

2 Appl Bochem Botechnol (2016) 180: Introducton Ganoderma lucdum (Fr.) Karst (Polyporaceae) s a famous tradtonal Chnese medcnal mushroom. Polysacchardes and trterpenes are two of ts major boactve components [1, 2]. Interestngly, recent studes show that trterpenes have new bologcal actvtes ncludng anttumor and ant-hiv-1 [3 6]. Latest report demonstrates that G. lucdum s capable of reducng obesty n mce by nfluencng the content of mcrobota n the gut [7]. As t usually takes several months to cultvate G. lucdum and the trterpene yeld s rather low n sol cultvaton, the submerged fermentaton s consdered to be the promsng alternatve for effcent producton of trterpenes [8, 9]. It has been a major concern that the trterpenes n the submerged fermentaton of G. lucdum are qute low as recent studes dentfed many physologcally actve G. lucdum metaboltes for potental nutraceutcal applcatons. Many prevous studes were centered on the nfluence of varous factors on the shake flask culture of G. lucdum mycelum, such as the optmzaton of the culture medum and the choce of the cultvaton condtons [10, 11]. Recently publshed reports studed the key factors affectng the bosynthess of trterpenes systematcally [12, 13]. As an mportant envronmental factor, the fermentaton temperature affects the producton effcency of trterpenes concernng energy metabolsm of the mycelum. In spte of the effect of temperature on the fermentaton of trterpenes, the temperature control strategy was generally gnored n recent studes [14]. We recently publshed our studes on the mprovement of trterpene fermentaton producton by G. lucdum G0119 based on our knetc model on the effect of ntrogen source [15]. In order to further mprove the productvty and effcency of trterpene producton n submerged fermentatons and on the bass of the detaled analyss of the relatonshp between the knetc model, the temperature and the modeled parameters n the trterpene fermentaton process were undertaken to optmze the temperature control strategy as well as to further enhance the yeld and productvty of trterpenes. Ths study was based on lqud submerged fermentaton knetc modelng under varous fermentaton temperatures wth G. lucdum G0119. The nternal relatonshp of the temperature and the model parameters was smulated, calculated, and analyzed to establsh the best temperature control strategy for trterpene submerged fermentaton to develop the sgnfcantly more effcent trterpene fermentaton producton process. Materals and Methods Strans and Materals Stran: G. lucdum G0119 (Hunong Lngzh No. 1 varety) preserved by the Agrcultural Culture Collecton of Chna (Edble Fung Branch). It was mantaned on potato dextrose agar (PDA) slants. The slants were noculated and ncubated at 26 C for 10 days then stored at 4 C for about 2 months. Meda and Culture Condtons The seed medum contaned the followng: potato 200 g, glucose 20 g, dstlled water 1000 ml, and natural ph. For the seed culture, three peces of pea sze agar culture from

3 742 Appl Bochem Botechnol (2016) 180: a slant culture were noculated nto a 250-mL flask wth 100 ml seed medum and then cultvated for 10 days on a recprocal shaker at 150 rpm and 26 C. The fermentaton medum contaned (g L 1 ) the followng: glucose 30, yeast extract 3, KH 2 PO 4 2, and MgSO 4 7H 2 O 2. For lqud submerged fermentaton, the seed culture was noculated at 10 % (by volume, equvalent 0.45 g DCW L 1, DCW = dry cell weght) nto 4.5 L of the fermentaton medum n 6-L fermentor (model Botech-5BGZ-50JS; Shangha Baoxng Bo-engneerng Equpment Co., Ltd., Shangha, Chna). The noculated fermentor was agtated at 100 rpm and 26 C. Analytcal Methods Determnaton of Mycelal Bomass The mycelal bomass of G. lucdum was determned by weghng the dry cell. Samples collected at varous tmes were centrfuged for 20 mn at 10,000 g. The resultng pellet was washed repeatedly wth dstlled water and dred at 60 C untl a constant weght was reached [15]. Determnaton of Glucose Twenty-mrolter cultures were dluted to 2 ml wth dstlled water. 1.5 ml 3,5-dntrosalcylc acd reagent was added [16]. Samples were dluted to 25 ml. Glucose level was determned wth UV spectrometer (model UV-2000; Shangha Precson Scentfc Instrument Co., Ltd., Shangha, Chna) at 520 nm. Determnaton of Trterpenes ThemethodofFengetal.[17] was used. The dred mycela (1 g) were heat reflux extracted by absolute ethanol 50 ml for 2 h (repeated three tmes). After removal of mycela by centrfugaton, the supernatants were dred at 50 C under vacuum. The resdues were suspended n water followed by extracton wth 15 ml chloroform (repeated twce). The trterpenes n the chloroform extract were further extracted wth 5%(w/v) NaHCO 3 (repeated four tmes). After addng 2 mol L 1 HCltoadjustthepH of the NaHCO 3 phase to about , the trterpenes n the NaHCO 3 phase were agan extracted wth 15 ml chloroform (repeated four tmes). After removng chloroform by evaporaton at 40 C, trterpenes were dssolved n absolute ethanol and constant volume to 5 ml. One hundred-mcrolter sample was dluted to 0.2 ml wth 5%(w/v) vanllc aldehyde. 0.5 ml perchlorc acd reagent was added. After 20 mn at the 60 C water bath, the sample was dluted to 5 ml wth acetc acd and the resultng absorbance at 550 nm was determned wth a spectrophotometer usng ursolc acd as standard. Knetc Models The knetc models for trterpene submerged fermentaton nclude temporal varatons of bomass (X, dry mycelal weght, g L 1 ), product (P, trterpenes yeld, g L 1 ), and substrate (S, glucose,gl 1 ).

4 Appl Bochem Botechnol (2016) 180: Mcrobal Growth: the Logstc Equaton Knetc models of mcrobal growth were based on ether the Monod equaton [18] orthe logstc equaton. Mcrobal growth s governed by a hyperbolc relatonshp lmted by maxmum attanable cell mass concentraton as descrbed by the logstc equaton (Eq. (1)). μ ¼ μ max 1 X ð1þ X max where μ max s the maxmum specfc growth rate, X s the dry mycelal concentraton, and X max s the maxmum cell concentraton. Product Formaton: the Luedekng-Pret Equaton The knetcs of trterpene producton was based on the Luedekng-Pret equatons [19]. Accordng to ths model, the product formaton rate depends on both the nstantaneous bomass concentraton and growth rate (Eq. (2)): dp dt ¼ α dx dt þ βx where P represents product concentraton, α s the growth-assocated constant for the Luedekng-Pret equaton, and β s the non-growth-assocated constant. Carbon Source Uptake: the Luedekng-Pret Equaton There s a classcal knetc model of substrate uptake proposed by Luedekng and Pret [19] (Eq. (3)). ð2þ ds dt ¼ 1 dx Y X =S dt þ mx þ 1 dp Y P=S dt ð3þ where Y X/S s the factor for cells on carbon substrate, X s the bomass concentraton, m s the carbon substrate mantenance coeffcent, Y P/S s the product on carbon substrate yeld, and P s the product concentraton. Model Fttng and Computatonal Method To evaluate the fttng accuracy of the knetc models, the relatve error sum of squares (Ø) was employed. Parameters μ max, X max, α, β, Y X/S, m,andy P/S have been estmated to mnmze the objectve functon, Ø: ϕ ¼ X X exp X calc X calc 2 þ X S exp S calc S calc! 2 þ X P exp P calc 2 ð4þ P calc where X exp, S exp, and P exp are the observed value of bomass, substrate, and product concentraton, respectvely. X calc, S calc,andp calc are the correspondng ftted value by the knetc models. Ø s employed because the statstc s not dependent on the magntude of the measurements. Estmates for the model parameters were obtaned by mnmzng Ø.

5 744 Appl Bochem Botechnol (2016) 180: Parameters n these dfferental equatons were estmated by a non-lnear least-squares routne n the optmzaton toolbox of the MATLAB envronment [20]. As mnmzaton of the sum of squares for a general non-lnear problem s qute dependent on the ntal guesses for the parameters, varous startng ponts were provded and the fnal parameter set wth the lowest sum-squared error was chosen. The fourth-order Runge-Kutta genetc algorthm method was used to solve the dfferental equaton. Smplex method was used to search the parameter value. All the numercal calculatons were performed by the MATLAB 7.1 software. Results and Dscusson Study on the Mycelal Growth, Glucose Consumpton, and Trterpene Bosynthess Under Varous Temperatures Varatons on the fermentaton-controlled temperature affect the growth of G. lucdum mycelum, the bosynthess, and metabolsm of trterpenes accordngly. The actvty of varous key metabolc enzymes durng the process n the mycela can also be sgnfcantly affected. The nfluence of temperature on the mycela durng submerged lqud fermentaton was the result of varous factors nfluencng fermentaton performance. Consequently, durng the fermentaton process, the optmal temperature envronment at varous fermentaton tmes must be determned. As shown n Fg. 1, wthn the range of 23 to 32 C, the changes n mycelal growth, glucose consumpton, and Fg. 1 Knetcs of mycelal growth (a), glucose consumpton (b), and trterpene producton (c) under varous temperatures. Each value s presented as mean ± standard devaton (n =3). (whte trangle) 23 o C; (black damond) 26 o C; (whte crcle) 29 o C; (black pentacle) 32 o C

6 Appl Bochem Botechnol (2016) 180: trterpene bosynthess were determned durng the process of G. lucdum G0119 submerged fermentaton. Temperature has sgnfcant nfluence on the mycelal growth, glucose consumpton, and trterpene bosynthess. Wth ncreasng temperature, the rate of glucose consumpton was concomtantly accelerated together wth the rate of mycelal growth. The tme for reachng the growth phase was notably shortened. When glucose was exhausted, maxmal mycelal dry weght was reached. The rate of mycelal growth vared at dfferent temperatures. As shown n Fg. 1a, the maxmum mycelal dry weght at the fermentaton temperatures of 23, 26, 29, and 32 C was 3.66, 5.31, 8.31, and 7.04 g L 1, respectvely. At the early stage of fermentaton, the concentratons of trterpenes ncreased gradually concomtant wth the growth of the mycela. However, after enterng nto the growth perod, trterpenes contnued to be produced by the mycela and attaned the maxmum level at the end of the fermentaton process. The resultng maxmum concentratons of trterpenes were 0.82 mg (100 mg) 1,1.54 mg (100 mg) 1, 2.54 mg (100 mg) 1, and 1.42 mg (100 mg) 1, respectvely, as shown n Fg. 1c. Wth ncreasng temperature, the mycelal growth rate was hgher. As a result, the rate of mycelal growth entered nto the logarthmc phase rather quckly. However, the trterpene producton was negatvely mpacted by hgher than the optmal temperature. At 32 C, the fermentaton producton yeld of trterpenes was and % of that under 26 and 29 C condtons, respectvely. Consequently, wthn ths range, the hgher temperature was conducve to entry nto the logarthmc phase of mycelal growth earler, but the relatvely lower temperature was more sutable for trterpene bosynthess. Development and Verfcaton of the Knetc Model for Mycelal Growth, Glucose Consumpton, and Trterpene Bosynthess at Varous Temperatures At temperatures of 23, 26, 29, and 32 C, based on our G. lucdum G0119 lqud submerged fermentaton data μ max, X max, α, β, Y X/S, m,andy P/S for trterpenes bosynthess by the combned knetc model parameter fttng method has been developed. The relatonshp of the model parameters wth the temperature descrbed by polynomal s shown n Fg. 2 and Table 1. The relatonal expresson of Table 1 was compled on the bass of Eqs. (1) to(3) presented n the BMaterals and Methods^ secton. The knetc model dependng on the controllng temperature was obtaned from the actual lqud submerged fermentaton data wth G. lucdum G0119. The results are shown n Eqs. (5) to(7). dx dt ¼ 0:0008T 2 X 0:0386T þ 0:4579 X 1 0:0762T 2 : ð5þ þ 4:5624T 60:449 dp dt ¼ 0:0028T 2 dx þ 0:1557T 1:9279 dt þ T 2 þ 0:0007T 0:0086 X :ð6þ ds dt ¼ 1 0:0089T 2 0:5229T þ 7:9924 dx dt þ T 2 þ T X þ 1 0:21T 2 11:029T þ 323:75 dp dt : ð7þ

7 746 Appl Bochem Botechnol (2016) 180: Fg. 2 Relatonshp between the model parameters and temperature. Each value s presented as mean ± standard devaton (n = 3). (black square) μ m ;(black crcle) X max ;(black upper trangle) α; (black lower trangle) β; (black damond) Y X/S ;(whte left trangle) m; (whte pentacle) Y P/S ;(black sold) model value

8 Appl Bochem Botechnol (2016) 180: Table 1 Results of parameters estmated from the models Parameters Ftted equaton R 2 μ max μ max = T T X max X max = T T α α= T T β β= T T Y X/S Y X/S = T T m m= T T Y P/S Y P/S =0.21T T In order to verfy the applcablty of Eqs. (5)to(7) at 23 to 32 C, the equatons were ntegral of at 26 and 29 C and the resultng trterpene fermentaton knetcs graphs were compled. Subsequently, these graphs were compared wth the actual expermental results (Fg. 3). The calculated data based on the current model and the actual expermental results were consstent wth the trterpene submerged fermentaton process. At 26 C, the maxmum relatve error was 0.51 %, and average relatve error was 0.19 %. At 29 C, the maxmum relatve error was 1.08 %, and average relatve error was 0.67 %. The results were n agreement wth the fttng of the model concernng the process of the trterpene submerged fermentaton between 26 C and 29 C. Effects of Temperature on the Knetc Parameters of Trterpene Fermentaton The knetc fttng model and the relevant parameters were analyzed as follows: 1. Wthn the controlled temperature range, μ max was ncreasng wth the rse of temperature (Fg. 2a). Based on Eq. (1), at the begnnng of the fermentaton, X <<X max,thus1 X/X max 1. dx ¼ μ dt max 1 X X μ X max X ¼ 0:0008T 2 0:0386T þ 0:4579 X max dp ¼ α dx : þ β X ðαμ dt dt max þ βþ X ¼ ρ max X Wthn the temperature range from 23 to 32 C, the ntal mycelal dry weght value X was the same. Thus, the rate of mycelal growth was proportonal to μ max. That means the lag phase of mycelal growth was shortened wth the temperature ncrease. Smlarly, ρ max obtaned by calculaton based on Table 1 and the value ncreased wth temperature ncrease wthn 24 and 32 C ndcatve of that the lag phase for trterpene bosynthess was shortened wth ncreasng temperature. 2. When the temperature was below 29 C, X max ncreased wth the hgher temperature. When the temperature exceeded 29 C, X max was lower wth ncreasng temperature. At 29 C, X max ncreased by 88.95, 26.67, and 8.88 % as compared wth the 24, 26, and 32 C condtons, respectvely. The theoretcal mnmum growth temperature of G. lucdum G0119 was calculated to be C. 3. Intally, the α value ncreased and subsequently declned wth the ncrease of temperature. Y X/S and Y P/S ntally decreased and then ncreased wth the elevaton of temperature. These results ndcate that the optmal temperature was benefcal to the bosynthess of trterpenes.

9 748 Appl Bochem Botechnol (2016) 180: Fg. 3 Comparson of the results predcted by the knetc model wth expermental results of trterpene producton by G. lucdum G0119 n submerged lqud fermentaton. Each value s presented as mean ± standard devaton (n = 3). (whte trangle) mycelum; (black square) glucose; (black pentacle) trterpenes; (black sold) model value 4. The β and m values ncreased at the begnnng and then declned wth the ncreasng temperature. The results show that the hgher temperature accelerates per mycelum consumpton of glucose wth gradual decrease n trterpene producton n the late fermentaton stage. Formulaton of the Optmal Temperature Control Strategy for Enhanced Trterpene Submerged Lqud Fermentaton Producton On the bass of the above analyses and combned wth Eqs. (4)to(6) and Table 1, the objectve functon of optmal control s the concentraton of trterpene P value. Other numercal condtons are as follows: The ntal mycelal concentraton X 0 =0.3gL 1, the ntal trterpene concentraton P 0 = 0, the ntal glucose concentraton S 0 =30 g L 1, the resdual glucose concentraton S end 6gL 1, the fermentaton tme t 240 h, the fermentaton temperature 23 C T 32 C (take an nteger), and ntegraton tme step s 1 h. A proposed temperature control profle to enhance trterpene producton s shown n Fg. 4. The results ndcate that (1) durng the early stage of fermentaton (0 61 h) ncrease the fermentaton temperature leadng to the lag phase of mycelal growth to be shortened. The hgher mycelal growth rate leads to the ncrease of trterpene productvty. (2) At the fermentaton metaphase ( h) gradual reducton of the fermentaton temperature from 31 to 30 C, the mycelal growth rate and the trterpene productvty can be mantaned at a hgher level for a longer perod of tme. (3) At the statonary phase of fermentaton (128 h), mantan the temperature at 29 C to mprove the β and m values wth resultng mprovement of the cellular bosynthess of trterpenes. The resultng optmal temperature control strategy s shown n Fg. 4. The new temperature control strategy s from 0 to 61 h durng the early stage of fermentaton, the temperature s controlled at 32 C. From 62 to 86 h n the fermentaton metaphase, the temperature s controlled at 31 C. From 87 to 127 h durng the fermentaton metaphase, the temperature s controlled by 30 C. After 128 h n the statonary phase of fermentaton, the temperature s controlled at 29 C, untl the end of the fermentaton. The above formulated temperature control strategy was used n the submerged fermentaton producton process of trterpenes. The results are compared wth the fermentaton control at 29 C (Fg. 5). At the begnnng of the fermentaton, the temperature was mantaned at a hgher level, and the G. lucdum mycela had a short lag phase and then rapdly entered nto the growth phase. After applyng our shftng temperature control strategy, the rate of trterpene bosynthess has been mantaned at

10 Appl Bochem Botechnol (2016) 180: Fg. 4 The proposed temperature control profle to enhance trterpene producton a hgher rate untl the end of the fermentaton process. The rate of glucose consumpton was accelerated n the entre process. The specfc results are shown n Table 2. Fnally, the fermentaton tme was shortened by 10 h. The yeld of trterpenes was (0.269 g L 1 ), trterpenes yeld per unt glucose was ( g g 1 ), and the resultng trterpene productvty Fg. 5 Comparson of submerged lqud fermentaton wth the optmzed temperature control strategy (as shown n Fg. 4) and wth constant temperature of 29 C. Each value s presented as mean ± standard devaton (n = 3). (whte trangle) 23 o C; (black trangle) optmzaton strategy; (whte crcle) 23 o C; (black crcle) optmzaton strategy; (whte pentacle) 23 o C; (black pentacle) optmzaton strategy

11 750 Appl Bochem Botechnol (2016) 180: Table 2 Comparson of the parameters n submerged lqud trterpene fermentaton under varous temperatures Parameter Temperature ( C) Temperature strategy Intal glucose concentraton (g L 1 ) e Resdual glucose concentraton (g L 1 ) ± ± ± ± ± 0.21 Fermentaton tme (h) a Dry cell weght (g L 1 ) 3.66 ± ± ± ± ± 0.22 Trterpene yeld (mg (100 mg) 1 ) 0.82 ± ± ± ± ± 0.12 Trterpene concentraton (g L 1 ) b ± ± ± ± ± Glucose consumpton rate (g (L h) 1 ) ± ± ± ± ± Mycelal yeld on glucose (g g 1 ) ± ± ± ± ± Trterpene yeld on glucose (g g 1 ) c ± ± ± ± ± Mycelal productvty (g (L h) 1 ) d ± ± ± ± ± Trterpene productvty (g (L h) 1 ) d ± ± ± ± ± a Fermentaton tme s defned as the tme when the glucose s exhausted b Trterpene producton (unt: g L 1 ) s defned as trterpene yeld (unt: g kg 1 ) multpled by dry cell weght (unt: g L 1 ) c Trterpene yeld on glucose s defned as total trterpene producton (unt: g L 1 ) dvded by glucose concentraton (unt: g L 1 ) d Productvty (unt: g (L h) 1 ) s defned as producton per unt tme per unt volume of mycela/trterpenes e Each value s presented as mean ± standard devaton (n =3)

12 Appl Bochem Botechnol (2016) 180: was g(lh) 1, whch were sgnfcantly mproved by 27.32, 13.94, and %, respectvely. Ths consderably enhanced trterpene fermentaton producton process could feasbly be scaled up to the ndustral level. Concluson Durng the lqud submerged fermentaton producton process of trterpenes by G. lucdum,the temperature s a very mportant control parameter. Proper temperature control strategy s the requrement that can guarantee better growth of the mycelum and hgh yeld of metaboltes, partcularly for the fermentaton wth flamentous fung. Few studes have analyzed how temperature affects the trterpene fermentaton of G. lucdum strans. Changng the temperatures clearly mproved mycelal growth and trterpene producton of the G. lucdum strans. In the submerged fermentaton process of trterpene producton by G. lucdum G0119, hgh fermentaton temperature accelerates the accumulaton of trterpenes n the early fermentaton stage. However, the lower temperature apparently enhances the mycelal growth and subsequent trterpene producton at the late fermentaton stage. The logstc equaton was used to smulate the fermentaton process. The parameters of the fermentaton knetcs were calculated at varous temperatures. Subsequently, the optmal temperature control strategy was formulated by usng the quadratc polynomal to ft the knetc parameters. Usng ths strategy, the producton of trterpenes was acheved by the unfcaton of hgh productvty, hgh yeld, and hgh producton ntensty. Such shftng temperature control strategy has been proven n actual submerged fermentaton experments reproducbly to enhance trterpene producton. It s concevable that such sgnfcantly mproved fermentaton of trterpene strategy could be mplemented at the large ndustral producton scale. dp/dt, productvty (g (L h) 1 ); ds/dt, the carbon source consumpton rate (g (L h) 1 ); dx/ dt, growthrate(g(lh) 1 ); m, mantenance coeffcent (g substrate (g cells h) 1 ); max, maxmum; o, ntal; P, trterpene concentraton (g L 1 ); P calc, the correspondng ftted value of product concentraton by knetc models (g L 1 ); P exp, observed product concentraton (g L 1 ); r 2, correlaton coeffcent (dmensonless); S, glucose concentraton (g L 1 ); S calc,the correspondng ftted value of carbon substrate concentraton by knetc models (g L 1 ); S exp, observed carbon substrate concentraton (g L 1 ); t, tme (h); X, bomass concentraton (g L 1 ); X calc, the correspondng ftted value of bomass by knetc models (g L 1 ); X exp,observed bomass concentraton (g L 1 ); Y P/S, product yeld per carbon substrate (g product (g substrate) 1 ); Y X/S, cellular yeld per substrate (g cells (g substrate) 1 ); μ max, maxmum specfc growth rate for the logstc equaton (h 1 ); α, growth-assocated constant for the Luedekng- Pret equaton (g product (g bomass) 1 ); β, non-growth-assocated constant for the Luedekng- Pret equaton (g h 1 ); Ø, mnmzng objectve functon of the dscrepancy between expermental data and smulated results (dmensonless) Acknowledgments Ths work was supported by the Shangha Muncpalty Agrcultural Research Project Grant for Career Development of Young Talents (Shangha Agrcultural Research Youth 2015 No. 1 7) and Shangha Academy of Agrcultural Scences Young Scentst Career Development Grant (No. ZP06).

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