Modeling lipid accumulation in oleaginous fungi in chemostat cultures. II: Validation of the chemostat model using yeast culture data from literature
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Abstract
A model that predicts cell growth, lipid accumulation and substrate consumption of oleaginous fungi in chemostat cultures (Meeuwse et al. in Bioproc Biosyst Eng. doi: 10.1007/s0044901105458, 2011) was validated using 12 published data sets for chemostat cultures of oleaginous yeasts and one published data set for a polyhydroxyalkanoate accumulating bacterial species. The model could describe all data sets well with only minor modifications that do not affect the key assumptions, i.e. (1) oleaginous yeasts and fungi give the highest priority to Csource utilization for maintenance, second priority to growth and third priority to lipid accumulation, and (2) oleaginous yeasts and fungi have a growth rate independent maximum specific lipid production rate. The analysis of all data showed that the maximum specific lipid production rate is in most cases very close to the specific production rate of membrane and other functional lipids for cells growing at their maximum specific growth rate. The limiting factor suggested by Ykema et al. (in Biotechnol Bioeng 34:1268–1276, 1989), i.e. the maximum glucose uptake rate, did not give good predictions of the maximum lipid production rate.
Keywords
Model validation Chemostat Oleaginous yeast Lipid production rateIntroduction
In part I [1], we presented a mathematical model for lipid accumulation in oleaginous fungi growing in chemostat cultures. This model describes our chemostat cultures of U. isabellina growing on glucose as Csource and NH_{4} ^{+} as Nsource well. In the current paper, we show that the model can also describe data obtained with oleaginous yeasts cultivated in chemostats using a large range of C/N ratios and dilution rates, including the low dilution rates that could not be realized with U. isabellina. With the large set of data from literature, we also test hypotheses about the limiting factor for the specific lipid production rate. One of these hypotheses comes from the chemostat model published by Ykema et al. [2]. Finally, we show that our model for lipid accumulation can also predict accumulation of polyhydroxyalkanoates (PHA), another carbonbased storage material.
Model

The first priority of the fungus is to use the supplied Csource to satisfy its maintenance requirements, then to produce lipidfree biomass including functional lipids, and finally, only if there is still Csource available, to accumulate storage lipids.

If sufficient Csource is available, the specific lipid production rate will increase up to a maximum value q _{ L,max}. This maximum specific lipid production rate is independent of the specific growth rate.

Single nitrogen limitation, where the Nsource limits the lipidfree biomass formation and the specific lipid production rate has its maximum value;

Dual limitation of Csource and Nsource, where the Nsource limits the lipidfree biomass formation and the Csource limits the lipid production;

Single carbon limitation, where the Csource limits the lipidfree biomass formation and only membrane lipids are produced.
Literature data used to validate the model as is described in the text
Data set no.  References  Organisms  Medium Csource/Nsource^{a}  Number of datapoints^{b}  C/N ratio (Cmol/Nmol)  Dilution rates (h^{−1})  Reported μ _{max} (h^{−1}) 

Fungi  
1  Hansson et al. [3]  Mucor rouxii ^{c}  Glucose/NH_{4}Cl + YE  15  11–29  0.03–0.14  – 
2  Meeuwse et al. [1]  Umbelopsis isabellina  Glucose/(NH_{4})_{2}SO_{4}  6 + 6  16 + 20  0.04–0.19  0.23 
3  Song et al. [4]  Mucor circinelloides  Glucose/NH_{4}Cl + YE  5  43  0.04–0.18  – 
Yeast  
4  Alvarez et al. [5]  Rhodotorula glutinis  Molasses (both C and N)  7  25–35  0.04–0.1  – 
5  Brown et al. [6]  Candida curvata  Glucose/YE  20^{d}  71  0.025–0.29  0.305 
6  Choi et al. [7]  Rhodotorula gracilis  Glucose/(NH_{4})_{2}SO_{4} + YE  6  53  0.02–0.09  – 
7  Evans and Ratledge [8]  Candida cruvata  Sugars^{e}/NH_{4}Cl + YE  16 + 16^{f}  17 + 50–52 ^{g}  0.02–0.3^{f}  0.3^{f} 
8  Gill et al. [9]  Candida 107  Glucose/NH_{4}Cl + YE  7 + 7  6 + 26  0.03–0.21  0.21 
9  Hansson and Dostalek [10]  Cryptococcus albidus  Glucose/NH_{4}Cl + YE  5 + 4  10 + 58  0.031–0.107  0.11 
10  Hassan et al. [11]  Apiotrichum curvatum UfaM3^{h,i}  Glucose/NH_{4}Cl + YE  11  44  0.04–0.4  – 
11  Papanikolaou and Aggelis [12]  Yarrowia lipolytica  Glycerol/(NH_{4})_{2}SO_{4} + YE  5  147  0.03–0.13  0.21 
12  Ratledge and Hall [13]  Rhodotorula glutinis  Glucose/NH_{4}Cl + YE  5 + 4  6 + 25  0.02–0.1  0.12 
13  Ykema et al. [2]  Apiotrichum curvatum ^{f}  Glucose/NH_{4}Cl + YE  11  7–68  0.02  0.2 
14  Yoon and Rhee [14]  Rhodotorula glutinis  Glucose/(NH_{4})_{2}SO_{4} + YE  7  62  0.01–0.1  0.13 
Results and discussion
Table 1 shows an overview of chemostat cultures with more than four dilution rates or C/N ratios found in literature. In most studies one or two constant C/N ratios and various dilution rates were used. In most studies, a high C/N ratio in the feed (>20 Cmol/Nmol) was used to promote lipid accumulation. Some studies also included a low C/N ratio, which does not lead to lipid production in most cases.
Model parameters were determined for all data sets in Table 1, in most cases using all data within a set, independent of the C/N ratio or dilution rate. Because of the large number of studies used, we will not describe all studies separately. We will discuss the fitting procedure and the predictions for all studies in general and point out some exceptions. Graphs showing the measured data points together with the model predictions for all studies are shown in the electronic supplementary material; parity plots and an example of measured data when compared with model predictions are included this article.
Chemostat cultures with filamentous fungi
The results from submerged chemostat studies with oleaginous fungi are hardly described in the literature: we only found three papers on this topic. The first (Data set 1) uses the filamentous fungus Mucor rouxii [3]. This fungus has a filamentous and a yeastlike morphology, and the yeastlike form was observed during most of the experiments. The filamentous form of Mucor rouxii is able to accumulate lipids up to 30% w/w [15], but in the yeastlike form <10% w/w lipids was found, even in the presence of residual glucose. Therefore, Data set 1 was not suitable to fit the model. In our studies with U. isabellina (Data set 2 [1]) we also observed that the filamentous fungus transformed to a yeastlike morphology when it was cultivated at a high dilution rate and exposed to the shear forces of the stirrer for at least 7 days. This yeastlike form also did not accumulate lipids and was not included in the model validation. Data set 2 has been discussed extensively in part I [1] and will therefore not be discussed here. Data set 3 uses Mucor circinelloides [4] and will be discussed together with the yeast cultures. Kendrick and Ratledge [16] used the fungus Entomophtora exitalis in chemostat culture, but only used one C/N ratio and dilution rate. As our model needs at least four data points for the determination of parameter values, this data set was not used.
Chemostat cultures with oleaginous yeasts
All studies in Table 1 report total biomass concentrations and lipid concentrations or lipid fractions in the cells, but they do not always report all substrate concentrations required to find the model parameters. For Data sets 2, 4–6 and 8–11, the Csource and Nsource concentrations are reported, or the limiting (=depleted) substrate is indicated and the concentration of the nonlimiting substrate is reported. For Data sets 3, 7 and 12–14, however, one or both substrate concentrations are not reported. Therefore, these data sets could not be completely described by the model, as will be discussed later. None of the studies reports CO_{2} production or O_{2} consumption. Data set 13 was obtained under nonsteady state conditions in a continuous culture with a changing Csource concentration in the feed. To describe this data set, changes in time have to be taken into consideration, which makes the model and the fitting procedure for this data set different from the other data sets. Therefore, we decided not to use this data set for the validation of the model; however, we will discuss nonsteady state situations later in this article.
Determination of parameter values
Model parameters found for the literature data
Data set no.  f _{ L0} (Cmol Cmol^{−1})  Y _{ XN } ^{a} ± SD (Cmol Nmol^{−1})  q _{ L,max} ± SD (Cmol Cmol^{−1} h^{−1})  Y _{ XS } ± SD (Cmol Cmol^{−1})  Y _{ LS } ± SD (Cmol Cmol^{−1})  m _{S} ± SD (Cmol Cmol^{−1 } h^{−1}) 

2  0.079  6.1 ± 0.7  0.023 ± 0.005  0.92 ± 0.10  0.59^{b}  0.05 ± 0.01 
3  0.15  (12.1 ± 0.7)(37 ± 5)*D  0.032 ± 0.007^{c}  ND^{d}  ND^{d}  ND^{d} 
4  0.15  (13.7 ± 1.4)(71 ± 23)*D^{e}  0.039 ± 0.006  0.56 ± 0.07  0.99 ± 0.36  0^{b} 
5  0.12  (15.3 ± 0.6)(41 ± 4)*D  0.040 ± 0.008  0.86 ± 0.11  0.65 ± 0.27  0^{b} 
6  0.15  (8.5 ± 0.7)(70 ± 15)*D  0.027 ± 0.006  0.25 ± 0.02  0.59^{b}  0^{b} 
7a^{f}  0.19  (22 ± 1)(84 ± 11)*D  0.037 ± 0.010^{c,g}  0.55 ± 0.02 ^{g,h}  0.59^{b}  0^{b} 
7b^{f}  ND^{d}  
8a^{f}  0.15  (13.8 ± 0.7)(38 ± 6)*D  0.069 ± 0.009  0.62 ± 0.03  0.88 ± 0.14  0^{b} 
8b^{f}  5.8 ± 0.3  
9a^{f}  0.15  (18 ± 2)(83 ± 30)*D  0.041 ± 0.004  0.75 ± 0.05  0.47 ± 0.04  0^{b} 
9b^{f}  6.4 ± 0.5  0.032 ± 0.002  
10  0.12  (16.5 ± 0.4)(34 ± 2)*D  0.065 ± 0.015  0.73 ± 0.04  0.88 ± 0.18  0^{b} 
11  0.12  (16.9 ± 0.8)(37 ± 10)*D  0.030 ± 0.013  0.16 ± 0.01  0.97 ± 0.34  0^{b} 
12a^{f}  0.21  (9.8 ± 0.4)(62 ± 6)*D  0.031 ± 0.004^{c}  0.56 ± 0.04 ^{h}  0.77 ± 0.41 ^{h}  0^{b} 
12b^{f}  ND^{d}  
14  0.15  (8.1 ± 0.4)(60 ± 8)*D  0.028 ± 0.006^{c}  ND^{d}  ND^{d}  ND^{d} 
Basal lipid content of the cells (f _{ L0})
If available, we used the reported lipid fraction in the Climitation regime as the basal lipid content of the cells. However, not all studies report results in this regime. For these studies, we used either an estimated value of 10% w/w = 0.015 Cmol Cmol^{−1}, which is the average measured value found in literature, or the lowest reported lipid fraction if this was below 10% w/w (see Table 2).
Yield of lipidfree biomass on Nsource
If present, yeast extract (YE) was taken into consideration as Nsource; it was assumed to contain 10% N w/w, unless another fraction was reported in the study.
Only very few studies applied Climitation and reported values for the Nsource concentration in the fermenter (C _{N}). Reported Nsource concentrations are compared with the predicted values in Fig. 2c. The few data points that are depicted in this parity plot are close to the correlation line, so from this plot and Fig. 2b we can conclude that the values found for Y _{ XN } are suitable for use in the model.
Maximum specific lipid production rate
Because we assume that the specific lipid production rate is constant when the Csource is not limiting, the value for the maximum specific lipid production rate (q _{ L,max}) was calculated by taking the average specific lipid production rate for all data points with C _{N} = 0 and C _{S} > 0. For Data sets 3, 7, 12 and 14, the Csource concentration (C _{S}) was not reported, but the occurrence of Nlimitation (C _{N} = 0) was reported. Therefore, for the data points with C _{N} = 0, we did not know if the cells were subjected to single Nlimitation (C _{S} > 0) or to dual limitation (C _{S} = 0). Because single Nlimitation usually occurs at a higher dilution rate than dual limitation, we calculated the maximum specific lipid production rate using only data points with Nlimitation and a high dilution rate for which the specific lipid production rate appeared to be constant.
All values for the maximum specific lipid production rate (q _{ L,max}) are shown in Table 2. The standard deviation for most values is quite small, indicating that the value of the specific lipid production rate was indeed constant for the used data points. No dependency on the dilution rate or the C/N ratio was found. The maximum specific lipid production rate (q _{ L,max}) predicts the lipid concentration in the fermenter and the lipid fraction in the cells when the Csource is in abundance (Eq. 15, Table 1 in part I). The parity plot in Fig. 2d shows that the lipid fraction in the cells is predicted very well.
The constant minimum specific lipid production rate (q _{ L,min}) for Data set 9 was calculated by taking the average of the specific lipid production rates during single Climitation. This allowed accurate modeling of this data set, as shown in Fig. 2d.
Yields of lipidfree biomass and lipids on Csource and maintenance coefficient
Multiple linear regression analysis using Eq. 23 was applied to find Y _{ XS }, Y _{ LS } and m _{S}. However, for none of the data sets from literature, this gave a reliable value for the maintenance coefficient. In all cases, the obtained value for m _{S} was negative or had such a large standard deviation that it was not significantly different from zero. Therefore, the maintenance coefficient (m _{S}) was set to zero and values for Y _{ XS } and Y _{ LS } were obtained (Table 2). For Data sets 2, 6 and 7, a theoretical value of Y _{ LS } = 0.59 Cmol Cmol^{−1} was used as was published by Ratledge [18]. The fitting of Data set 2 was discussed extensively in part I. Fitting of Y _{ LS } for Data set 6 and 7 gave unrealistic values of Y _{ LS } ± SD = 9 × 10^{3} ± 6 × 10^{7} Cmol Cmol^{−1} and Y _{ LS } ± SD = 7 × 10^{3} ± 9 × 10^{7} Cmol Cmol^{−1}, respectively, and therefore we replaced Y _{ LS } with the literature value of 0.59 Cmol Cmol^{−1}.
All values found for the yield of lipidfree biomass on Csource (Y _{ XS }) are in the expected range when the inaccuracy is taken into consideration. Only the value for Data set 2 is very high; this was discussed in detail in part I. Data sets 6 and 11 have a very low value for Y _{ XS }. This could be caused by the use of Csource for the production of extra products that were not measured. Data set 11 does report production of small amounts of citrate, but taking this product into consideration did not increase the value for Y _{ XS }. Therefore, other byproducts may have been present. The values found for Y _{ LS } are generally above the theoretical value of 0.59 Cmol Cmol^{−1}, but several values are not very accurate as is indicated by a large standard deviation, so no conclusions can be drawn here.
Because all data sets lack CO_{2}production data, the carbon balance and therefore the assumption that no other products besides biomass, lipids and CO_{2} were formed, could not be checked. The parameter values found are based on this assumption and are, therefore, only valid if the model is not extended with byproduct formation.
For most data points, the parameters Y _{ XS }, Y _{ LS } and m _{S} predict the concentration of Csource in the fermenter well (Eq. 10, Table 1 in part I); a parity plot is shown in Fig. 2e. For some data points that experience Climitation, the parameters Y _{ XS }, Y _{ LS } and m _{S} are needed to predict the specific lipid production rate (Eq. 16, Table 1 in part I) or the lipidfree biomass concentration (Eq. 13, Table 1 in part I), as was explained in part I. Parity plots for these variables were already shown in Fig. 2b and d.
Fit of the model to the data sets
All parity plots in Fig. 2b–e show that the model gives a good fit for all data sets with the parameter values from Table 2. So far, we have not been able to find chemostat results for oleaginous yeast or fungi in literature that cannot be described with the model, unless there was a clear reason for it, as was the case with Data set 1.
Comparison with previously published model

carbohydrates stored in the cells are included as an extra product

the maximum specific lipid production rate of the cells is not constant, but is given by the difference between their maximum specific glucose uptake rate (\( {\frac{{\mu_{\max } }}{{Y_{XS} }}} + {\frac{{q_{L,\min } }}{{Y_{LS} }}} + m_{S}\)) and their actual specific glucose requirement for growth and maintenance (\( {\frac{D}{{Y_{XS} }}} + m_{S}\))
Ykema et al. [2] validated their model using a continuous culture of Apiotrichum curvatum with a constant dilution rate and a changing C/N ratio of the feed. As the change in C/N ratio was quite fast, this continuous culture was not in steady state, while all mass balances used in the model require steady state to be valid. Furthermore, a theoretical glucose concentration in the reactor was used for validation instead of the glucose concentration in the feed. This theoretical glucose concentration in the reactor was calculated assuming no consumption of glucose in the reactor, but only supply and washout by the ingoing and outgoing flow, respectively. Because in reality there is consumption in the reactor, the outgoing flow will contain less glucose than is assumed using this theoretical glucose concentration in the reactor. This leads to an underestimation of the glucose consumption. We doubt that this model was properly validated; this triggered us to develop our model and to check if the assumptions used in the model of Ykema et al. [2] are indeed valid.
Regulation of the maximum lipid production rate
Although the metabolic pathway and the enzymes involved in lipid production in oleaginous yeast and fungi are known [19], nothing is known about the regulation of the maximum specific lipid production rate. We showed before that the maximum glucose uptake rate, as used in the model of Ykema et al. [2], is not limiting for the maximum specific lipid production rate. Therefore, we propose another hypothesis.
Broader use of the model
Culture properties and parameter values for PHA production
Reference  Durner et al. [20] 

Organism  Pseudomonas oleovorans 
Medium Csource/Nsource  Octanoate/(NH_{4})_{2}SO_{4} 
Number of datapoints  50 
C/N ratio (Cmol/Nmol)  133 
Dilution rates (h^{−1})  0.05, 0.1, 0.2, 0.3, 0.4 
Y _{ XN } ± SD (Cmol Nmol^{−1}l)  4.0 ± 0.8 
q _{ P,max} ± SD (Cmol Cmol^{−1} h^{−1})  0.20 ± 0.04 
Y _{ XS } ± SD (Cmol Cmol^{−1})  0.82 ± 0.04 
Y _{ PS } ± SD (Cmol Cmol^{−1})  0.45 ± 0.02 
m _{S} ± SD (Cmol Cmol^{−1} h^{−1})  0.11 ± 0.02 
Use of the model for nonsteady state conditions
Conclusions
The model that was developed and partly validated in part I of this article [1] was further validated using 11 published data sets for chemostat cultures of oleaginous yeasts and one data set for PHA accumulating microorganisms. All data sets except one could be described well with the model, if a growth rate dependent yield of lipidfree cell mass on Nsource was incorporated (Eq. 27). One data set required another modification, i.e. the incorporation of a constant instead of a growth rate dependent minimum specific lipid production rate (Eq. 28). This shows that the main assumptions in the model are valid: (1) oleaginous yeasts and fungi give the highest priority to Csource utilization for maintenance, second priority to growth and third priority to lipid accumulation, and (2) oleaginous yeasts and fungi have a growth rate independent maximum specific lipid production rate. The maximum specific lipid production rate was in most cases very close to the lipid production rate required for synthesis of the basal (membrane and functional) lipids in cells growing at their maximum specific growth rate. This indicates that the cells use the same pathway for lipid accumulation and for production of membrane and functional lipids, and that no special pathway is switched on for lipid accumulation in chemostat cultures. The assumption that the maximum specific lipid production rate is dictated by the maximum glucose uptake rate, postulated by Ykema et al. [2], was shown not to be correct for the tested data sets. Finally, the model proved also to be able to predict the production of PHA, another carbonbased storage product.
Notes
Acknowledgments
This work was financially supported by the DEN program of SenterNovem under project number 2020031214006. The authors would like to thank Sebastiaan Haemers and Fred van den End for their technical support.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Supplementary material
References
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