Kinetic Modeling of Ethanol Production
by Scheffersomyces stipitis from Xylose
Daniele Farias & Rafael R. de Andrade &
Received: 16 April 2013 /Accepted: 17 September 2013 /
Published online: 1 October 2013
#Springer Science+Business Media New York 2013
Abstract This work focuses on the kinetics of ethanol production by Scheffersomyces
stipitis on xylose with the development of a mathematical model considering the effect of
substrate and product concentrations on growth rate. Experiments were carried out in batch
and continuous modes, with substrate concentration varying from 7.2 to 145 g L−1. Inhib-
itory effects on cell growth, substrate uptake, and ethanol production rates were found to be
considerable. Kinetic parameters were obtained through linear and non-linear regression
methods. Experiments in continuous mode were performed at different dilution rates to
evaluate the inhibitory effect of ethanol. A mixed mathematical model which combined
Andrews and Levenspiel's models, combining substrate and product inhibition, was used. A
quasi-Newton routine was applied to obtain a more accurate fitting of kinetic parameters. The
parameters such as cell to product factor (YP/X) and limiting cell yield (YX) were shown to be
dependent on substrate concentration. The kinetic model fitted satisfactorily the experimental data.
List of symbols
Acetic acid concentration (g L−1)
Substrate inhibition coefficient (g L−1)
Substrate saturation parameter (g L−1)
Maintenance coefficient (g g−1h−1)
Parameter describing product inhibition
Product concentration (g L−1)
Final ethanol concentration (g L−1)
Maximal product concentration when cell growth ceases (g L−1)
Substrate concentration (g L−1)
Appl Biochem Biotechnol (2014) 172:361–379
D. Farias (*):F. Maugeri-Filho
School of Food Engineering, University of Campinas, CEP 13083-862 Campinas, SP, Brazil
R. R. de Andrade
Department of Exact and Earth Sciences, Federal University of São Paulo, UNIFESP, Diadema,
São Paulo, Brazil
Initial substrate concentration (g L−1)
Final substrate concentration (g L−1)
Substrate concentration at which the measured specific growth rate is maximum
Biomass concentration (g L−1)
Xylitol concentration (g L−1)
Final xylitol concentration (g L−1)
Fermentation total time (h)
Initial biomass concentration (g L−1)
Final biomass concentration (g L−1)
Dilution rate (h−1)
Ethanol production rate (g L−1h−1)
Substrate uptake rate (g L−1h−1)
Cell growth rate (g L−1h−1)
Cell to product conversion factor (g g−1)
Limiting cell yield (g g−1)
Biomass yield (g g−1)
Ethanol yield (g g−1)
Maximum specific growth rate as described by Monod's model (h−1)
The maximum specific growth rate related to each initial substrate concentration
Specific growth rate (h−1)
Specific substrate uptake rate (h−1)
Specific ethanol production rate (h−1)
Ethanol can be produced from different substrates containing fermentable sugars, such as
agricultural products and food processing wastes. However, the cost of substrates must be
low to increase the economic viability of the process in a large scale . Lignocellulosic
biomass represents an abundant renewable energy source, besides the fact that it does not
compete with food supply, thus being considered an ideal substrate for bioethanol produc-
tion [2–4]. However, while technologies for first-generation ethanol (from sugarcane juice,
molasses, or starch) are well established, the ones for second-generation ethanol are still
under development around the world [5, 6].
Lignocellulosic raw material is composed by cellulose, hemicellulose, and lignin. Xylose
is the main sugar obtained from the hydrolysis of hemicellulosic portion, and the efficient
conversion of this component is one of the major issues in the use of lignocellulosic raw
material for second-generation ethanol production, leading to an estimated increase of 25 %
in ethanol production [5, 7]. Thus, appropriated microorganism cultivation for each type of
sugar must be considered, taking into account that Saccharomyces cerevisiae, the yeast most
commonly applied in ethanol production, is unable to ferment xylose, which limits its use for
biofuel production from lignocellulosic material [3, 4].
Scheffersomyces stipitis (formerly Pichia stipitis) is considered a promising microorgan-
ism for industrial applications due to its capability to ferment xylose and other important
hexoses (glucose, mannose, galactose, and cellobiose) found in lignocellulosic material [5, 8],
with relatively high yield. The main drawback is its low ethanol tolerance [9, 10]. It is well
362Appl Biochem Biotechnol (2014) 172:361–379
conditionsand that different strainsrequire specific nutrient sources to efficiently convert sugar
into target products. Nutrients such as nitrogen, trace elements, or vitamins can be required to
achieve rapid fermentation and high levels of ethanol, which are desired to reduce capital costs
and energy requirement in the distillation step . For S. stipitis, oxygen availability is
considered the major factor that affects the efficiency of xylose conversion into ethanol. The
ability of S. stipitis to metabolize xylose is strongly related to oxygen concentration in the
medium, which must be controlled at microaerophilic conditions to avoid the deviation of the
carbon flux to cellular growth (in detriment of ethanol formation), which makes the process
There is an intensified interest in the study of all the steps involved in ethanol production
to obtain cost reduction, and the kinetic modeling of the process in helps the understanding
of the process as well as its optimization . Besides, modeling may reduce the process
costs of alcoholic fermentation development, eliminating unnecessary experimental work
because it allows the study of operational conditions and related conversion and kinetic
parameters through simulations. It may help also in the understanding of the whole process,
which is useful to define operational conditions. Four main factors affect the fermentative
process of ethanol production: substrate limitation, substrate inhibition, ethanol inhibition,
and cellular death. However, nowadays, no proposed model in the literature takes into
account all of these factors simultaneously, but only each factor separately . Due to this,
the main goal of this work was to develop a mixed mathematical model capable of
describing cell, substrate, and ethanol concentrations during microaerophilic fermentation
conditions in a fermentative process for ethanol production from xylose by S. stipitis NRRL-
Materials and Methods
Microorganism and Culture Media
The microorganism used was S. stipitis NRRL-Y7124, stored for long periods in glycerol
at −80 °C . The strain maintenance for short periods was performed through propagation
in slants, composed of GYMP media: 20 g L−1agar nutrient (NA), 10 g L−1glucose, 5 g L−1
yeast extract, 20 g L−1malt extract, and 2 g L−1monobasic sodium phosphate. The slants
were stored in a refrigerator. The culture media for microorganism activation consists of two
Medium I: GYMP, during 24 h for reactivation of microorganism maintained in slants.
Medium II: medium composed of xylose, 20 g L−1; yeast extract, 3 g L−1; malt extract,
3 g L−1; (NH4)2HPO4, 2 g L−1; KH2PO4, 4 g L−1; MgSO4·7H2O, 0.5 gL−1, and trace
elements, 1 mL.L−1; pH 4.5. The solution of trace elements is composed of (g L−1)
H3B3, 0.05; CaCl2·2H2O, 1.25; ZnSO4·7H2O, 0.3; MnSO4·H2O, 0.19; CoCl2·6H2O,
0.025; CuSO4·5H2O, 0.025, NaMoO4·2H2O, 0.035; and FeSO4·7H2O, 0.9.
The media were sterilized in an autoclave for 15 min at 121 °C. The solutions of xylose,
(NH4)2HPO4, and KH2PO4were sterilized separately and aseptically added to the system
according to each defined concentration. S. stipitis was incubated in shaken flasks at 150 rpm
for 24 h, at 28 °C in GYMP medium (medium I), and during 24 h at 28 °C in mineral medium
(medium II). The assays were performed using a defined medium containing pure xylose in
order to study the fermentation performance and to perform kinetic modeling.
Appl Biochem Biotechnol (2014) 172:361–379 363
The study about the effect of substrate concentration on the kinetic parameters (μmax, KS, and
KI) was carried out in batch mode. The xylose concentration ranged from 7.2 to 145 g L−1.
Mini-bioreactors of 1 L, with 800-mL working volume, at 28 °C, 150 rpm, and microaerated at
0.05 vvm,wereused.The media pH was adjusted to 4.5using previously sterilized solutionsof
NaOH 2 N and HCl 2 N. Samples were taken periodically for analytical determination. The
mini-fermentors were autoclaved for 15 min at 121 °C.
Continuous fermentation was carried out in a Bioflo III System bioreactor (New Brunswick
Co.), with 3-L total volume and 2.5 L working volume at 28 °C, pH 4.5, 150 rpm, and
0.05 vvm, with dilution rates varying from 0.008 to 0.150 h−1.
Xylose concentration in the bioreactor feed stream was 95 g L−1. Samples were taken
routinely to check the steady state. Fermentation was considered in a steady-state condition
when the cell concentration reached a permanent value. Besides, a turbidimeter coupled to
the fermentation vessel was also an important source of information for this purpose. After
steady state had been reached, samples were taken periodically. Cell viability, measured by
methylene blue staining technique , was higher than 90 % for all experiments.
The measurement of cell growth was performed by (a) optical density measurement (OD) at
600 nm and (b) gravimetric determination of biomass concentration (dry weight) after
centrifuging the cells at 10,000 rpm for 10 min in Eppendorfs tubes and washing and drying
the precipitate at 70 °C to obtain constant weight. The biomass concentration was calculated
by the weight difference divided by the sample volume.
Concentrations of xylose, xylitol, acetic acid, glycerol, and ethanol were measured by an
ultra-high-performance liquid chromatograph (UPLC), model Accela, ThermoScientific. The
column was a HyperREXXPmodel, maintained at 30 °C. The eluent was a solution of H2SO4,
pH 2.6, 1.0 mL min−1. Sugars and alcohols were detected by refractive index (RI) and acetic
acid by UV at wavelength 205 nm. For standards, a mixed solution of the components for
concentrations ranging from 0.01 to 4 % was used. The software Chromoquest was used to
integrate and quantify the results.
In fermentation processes, the determination of specific rates of growth (μX), production (μP),
and consumption (μS) was taken into consideration and calculated according to Eqs. 1 to 3:
364Appl Biochem Biotechnol (2014) 172:361–379
To evaluate the influence of substrate in microorganism growth, the values of KSand
μmaxwere calculated according to Monod equation, applying the linearization method of
Lineweaver–Burk (Eq. 4).
To evaluate the kinetics of substrate inhibition, given by KIparameter, Eq. 5 (Andrews'
model) and Eq. 6 were applied:
KSþ S þ
The biomass yield based on substrate (YX/S) and ethanol yield based on substrate (YP/S)
were defined by Eqs. 7 and 8:
In this work, a deterministic approach was considered on the base of unstructured models
such as the Levenspiel and Andrews' ones. Such approach is very convenient for process
control and scale-up because it is simple, it does not demand intensive computing work, and
is useful for a variety of processes, mainly for bioethanol production.
More recently, other approaches have been proposed for ethanol production modeling by
S. stipitis, such as the genome scale metabolic models (GEMs), which represents the link
between the genotype and phenotype of the microorganism based on the genome sequence
annotation and relevant biochemical and physiological information. These models have the
ability to provide a holistic view of the metabolism of a microorganism. Once experimen-
tally validated, these models can be used to characterize the metabolic resource allocation,
generate experimentally testable predictions of cellular phenotypes, elucidate metabolic
network evolution scenarios, design experiments that most effectively reveal the genotype–
phenotyperelationships,and design microorganismwithdesiredpropertieslikeoverproduction
of ethanol .
Moreover, the use of dynamic flux balance models is a technique based on the metabolic
fluxes of the cells and uses linear programming subjected to constraints to find an optimal
condition through an objective function . This technique enables, through computer
Appl Biochem Biotechnol (2014) 172:361–379365
simulation, the evaluation of the impact of several strategies to increase ethanol production,
such as genetic modification, metabolic engineering, co-culture of strains, different substrate
composition, and others. Dynamic flux balance models could also help, together with kinetic
models and GEMs, in describing S. sipitis metabolism assisting in the estimation of substrate
uptake kinetic parameters by estimating the best microaerobic growth conditions and can
reveal the key metabolic details of how different oxygen supplies caused metabolism shift,
providing efficient utilization of xylose and high ethanol yields .
Although dynamic flux balance models have been considered a powerful technique, it
can require deep knowledge about the metabolic pathways (if a genome scale modeling is
used) and models which can be sufficient complex depending on the biological systems and
number of reactions defined by the model . Also, it is well known that complexes
models can lead to great computation efforts for simulation. In addition, simpler approaches
in kinetic models can lead to valuable results and aid in decision making in industrial plants.
On the other hand, the dynamic description of ethanol fermentation using unstructured
models can be carried out basically with three differential equations for microorganism
growth, substrate uptake, and ethanol formation (Eqs. 9–11), which can be obtained from the
mass balance in the reactor.
where X, S, and P are the concentrations of cells, substrate, and ethanol, respectively.
The rates of cell growth, rx(g L−1h−1), substrate uptake, rS(g L−1h−1), and product
formation, rP(g L−1h−1), can be expressed by a non-structured model for the process in
batch mode as it was performed in this work. The dead cells were not taken into account due
to the high viability of cells in the experiments. Experimental data have shown that in
fermentations with S. stipitis, the cell growth is affected by the initial substrate concentration
as well as the produced ethanol. In this study, the proposed model, composed by Andrews
and Levenspiel equations, expresses the cellular growth rate, rX,as a function of cell,
substrate, and product (ethanol) concentrations, as shown in Eq. 12.
S þ KSþ S2=KI
where μ is the specific cellular growth rate, μmaxis the maximum specific growth rate, X is
the cell concentration (g L−1), S is the substrate concentration (g L−1), KSis the substrate
saturation constant (g L−1), KIis the substrate inhibition constant (g L−1), P is the product
concentration (g L−1), Pmaxis the product concentration at which cell growth ceases (g L−1),
and n is a parameter related to product inhibition.
The rate of substrate uptake is described by Eq. 13:
366 Appl Biochem Biotechnol (2014) 172:361–379
where YXand mXrepresent the limit cellular yield and the maintenance coefficient,
The Luedking–Piret expression was applied to represent the ethanol formation rate, rP,
which is proportional to the cell concentration (X) and to the cellular growth rate, as defined
by Eq. 14, where α and β are constants:
rP¼ αrXþ βX
According to Eq. 9 to 14, the parameters to be estimated using quasi-Newton (QN)
algorithm were mx, YP/X, YX, and n, while the others (μmax, KS, KI, and Pmax) were obtained
from experimental data, from batch and continuous fermentations as previously described,
and were kept fixed.
The parameter estimation procedure consisted in finding values which minimize an
objective function, formed by experimental data and results generated by the model simu-
lation. The relevant kinetic parameters were adjusted according to experimental results for
substrate consumption and ethanol production.
Considering that θ specifies a vector, which contains all the parameters to be estimated,
the objective of mathematical estimation is to find θ by the minimization of objective
function E(θ), defined by Eqs. 15 and 16:
E θ ð Þ ¼
nθ ð Þð16Þ
where Xen, Sen, and Penare the experimental values of cell, substrate, and ethanol concen-
trations, respectively, for each sampling time, n. Xn, Sn, and Pnare the concentrations
computed by the model at each time, n. Xemax, Semax, and Pemaxare the maximum measured
concentrations, and the term np is the number of sampling points. εn(θ) is the error due to the
The determination of a feasible region of the search space in a multiparameter estimation
of deterministic models is a complex task. Thus, for the solution of Eqs. 9 to 14, a
FORTRAN routine with integration based on fouth-order Runge–Kutta method was used.
For fitting the proposed model to the experimental data, the parameters mx, YP/X, YX, and n
were estimated through the minimization of Eq. 16 using a QN algorithm.
Results and Discussion
The results from batch runs are presented in Table 1, which are initial substrate concentration
(S0), final ethanol (Pf), xylitol (Xyf), and biomass (Xf) concentrations, fermentation time (tT),
and calculated values of ethanol yield (YP/S), biomass yield (YX/S), and maximum specific
growth rate related to each initial substrate concentration (μmax
According to Table 1, S. stipitis practically consumed all the xylose in all assays, except
when the initial substrate concentration was 125.2 and 145.6 g L−1, where incomplete
Appl Biochem Biotechnol (2014) 172:361–379 367
consumption of xylose was observed. Roberto et al.  also reported incomplete xylose
utilization when 99 or 145 g L−1initial xylose was employed, even after 100 h of
fermentation, using the same strain of S. stipitis. Moreover, the xylose consumption rate
was lower in assays with high substrate concentrations, which can be verified by the low
specific growth rate. Consequently, for higher substrate concentrations, extra fermentation
time was required to achieve total or quasi-total sugar consumption due to both substrate and
Glycerol and acetic acid production was not detected at the investigated conditions. For
the assay performed with an initial substrate concentration of 9.2 g L−1, the final xylitol
concentration was lower than 0.05 g L−1. For experiments at a higher initial substrate
concentration, the xylitol production increased, which can be associated with a decrease in
ethanol yield (YP/S). This occurs because xylitol is an intermediate product in the metabolism
of xylose to ethanol, and also it can be present at different concentrations, depending on the
aerobiosis conditions, and can be converted into ethanol afterward. Roberto et al. ,
Barbosa et al. , Amaral Collaço et al. , and Parajó et al.  studied the bioconver-
sion of xylose into xylitol by several yeasts and found out that when carbon source limitation
occurs, the xylitol produced is consumed. Thus, the presence of xylitol in the fermentation
does not reduce the ethanol conversion in an expressive way since it can be partially or
completely converted into ethanol. However, the culture conditions can be optimized to
maximize the xylose conversion into ethanol to achieve higher yields and productivities.
It was also observed that the assays performed at the highest xylose concentrations (nominal
which is predictable. Nevertheless, this result suggests that, although a low maximum specific
growth rate was observed (Table 1), the strain showed good ethanol tolerance (Pfof 54.9 g L−1).
Slininger et al.  and Linko et al.  also reported higher ethanol concentration in media
containing 100 or 150 g L−1of initial xylose concentration using S. stipitis NRRL-Y7124. They
also reported for the whole range of initial xylose concentration (7 to 150 g L−1) high yields of
ethanol from xylose (YP/S=0.39 to 0.42). Therefore, this microorganism, under microaerophilic
conditions, can produce high ethanol yields.
Table 1 Data for the conversion of xylose into ethanol in batch mode at different initial substrate concen-
trations by S. stipitis
S0(g L−1)tT(h)Xf(g L−1)Pf(g L−1) Xyf(g L−1)YP/S(g g−1)YX/S(g g−1)
bResidual substrate concentration was 4.4 g L−1
cResidual substrate concentration was 26.1 g L−1
368Appl Biochem Biotechnol (2014) 172:361–379
The ethanol yield coefficient was shown to be dependent on xylose concentration, as can
be seen in Table 1, where YP/Svaried from 0.36 up to yields as high as 0.504 g g−1, which is
practically 100 % of the theoretical value for ethanol production from sugars by S. stipitis.
However, these high yields were obtained at low initial substrate concentration, and in such
situation, the alcohol concentration is quite low at the end of the fermentation, so that other
sugar sources in the medium, like the yeast extract, may contribute significantly with the
final amount of ethanol, consequently increasing the yield coefficient. Others workers also
reported high yields with S. stipitis for lower substrate concentration, as Calleja et al. 
and Dellweg et al.  who reported yields as high as 97 and 96 %, respectively. The
authors reported that the ethanol yield coefficient (YP/S) is inversely proportional to the initial
xylose concentration and reaches nearly the theoretical value of 0.51 when substrate
concentration is very low. Also, according to Hinman et al. , the substrate concentration
presents a great impact on xylose-to-ethanol yield. In this present work, lower substrate
concentrations resulted also in higher xylose conversion into ethanol, and this result is of
vital importance for the fermentative process with S. stipitis, indicating that low substrate
concentrations may be the most suitable fermentation procedure, as it may be the case, for
example, of the continuous operation mode or fed-batch fermentation.
It is also of practical interest to determine the extent to which inhibition occurs and what
causes it. Substrate influence over the microorganism growth was studied as shown in Fig. 1.
It can be seen that there is a strong inhibition effect of the substrate over the specific growth
rate (Fig. 1a), which decreases from xylose concentration higher than around 30 g L−1. The
double inverse procedure (1/μ as function of 1/S0), as depicted in Fig. 1b and according to
Lineweaver–Burk's equation (Eq. 4), shows that only the first four data are aligned, which
correspond to the lower substrate concentrations. In this range, the microorganism follows
Monod kinetics. Therefore, from this part of the curve the constants of Monod equation
could be determined, being KS=1.67 g L−1and μmax=0.232 h−1. In addition, in order to
obtain the substrate inhibition constant (KI), Eqs. 5 and 6 were applied. The inhibition
constant was found as KI=24.4 g L−1. These parameters were calculated using the experi-
mental data obtained in batch mode and will be used as initial estimate to obtain the final
values by quasi-Newton method.
Du Preez et al.  and Slininger et al.  suggested that the fermentative process of
xylose consumption by S. stipitis is totally inhibited at ethanol concentrations from 42 to
45 g L−1. However, in this work, this strain reached higher ethanol concentration than those
reported, which correspond to about 55 g L−1for initial xylose concentration of 120 g L−1.
However, the fermentation time was quite long, about 240 h, which hampered productivity.
The ethanol concentrations at the end of fermentations were satisfactory and above the
values found in literature. This limiting ethanol tolerance is mainly related to a specific
strain, mode of operation of fermenters, and cultivation conditions, which may explain these
differences found in the literature.
To determine the effects ofethanol inhibition and the ethanol-limiting concentration (parameter
Pmax), eight runs in continuous fermentation at different dilution rates were performed. The results
are shown in Table 2 and Fig. 2. The dilution rate (D) varied from 0.008 to 0.150 h−1. The xylose
concentration in feed stream was fixed at 95 g L−1. Analysis of biomass, substrate, and ethanol
concentrations in the reactor was performed after the steady state has been reached. It can be seen
from Fig. 2 that the ethanol and cellular concentrations rapidly decreased and the xylose concen-
tration increased when the dilution rate increased. The ethanol and biomass concentrations tend to
stabilize at lower values for higher dilution rates, whereas for xylose a small decrease in its
concentration in the same operating conditions is observed. The maximum ethanol concentration
was 41.9 g L−1for a dilution rate of 0.008 h−1.
Appl Biochem Biotechnol (2014) 172:361–379369
Operation at low dilution rates is thus shown to be necessary to minimize the inhibitory
effect of substrate, and in this condition a more efficient xylose conversion was possible,
although alcohol inhibition was considerable.
The mathematical model to be computed consisted of Eqs. 9 to 14. The system is formed by
eight parameters, four of which were fitted by quasi-Newton algorithm (YP/X, YX, mx, and n)
and the remaining ones, μmax, KS, KI, and Pmax, were kept fixed according to experimental
The parameters of Andrews equation (Eq. 5), μmax, KS, and KI, were determined using
experimental data from batch assays and by performing the linearization of Eqs. 4 and 5 as
Fig. 1 Data from batch fermentations: a influence of initial xylose concentration (S0) on specific growth rate
(μ) and b linearization according to Lineweaver–Burk method to obtain KSand μmaxparameters
370Appl Biochem Biotechnol (2014) 172:361–379
previously described. The parameter for substrate inhibition, KI, was calculated through a
mix of graphical and algebraic procedures, as shown by Eq. 6, which was obtained by the
derivation of Eq. 5 in relation to substrate (dμ/dS=0). In Eq. 6, S* denotes the substrate
concentration at maximum point in curve μ vs. S (Fig. 1a). Values of n and Pmaxwere based
on experimental data from continuous modes, performing the linearization of data according
to the curve Ln(D/μmax) vs Ln(1−P/Pmax), as shown in Fig. 3 as an example, where n was
obtained from the curve slope for the best alignment achieved according to a trial-and-error
procedure with different Pmaxvalues. Data of n were fine-tuned afterwards by the Fortran
routine using the QN approach. All the remaining parameters varied with initial substrate
concentration, except mx, the maintenance coefficient, which changed lightly between
experiments so that it was kept constant in all situations and equivalent to the average of
Table 2 Data for the conversion of xylose into ethanol by S. stipitis in continuous fermentation at different
D (h−1) P (g L−1) Xy (g L−1) AA (g L−1) X (g L−1) Productivity
YP/S(g g−1) YX/S(g g−1) Viability
— not detected, AA acetic acid
Fig. 2 Data from continuous fermentation for xylose uptake, biomass accumulation, and ethanol production
for different dilution rates. Filled square, substrate; filled circle, ethanol; and filled triangle, cells
Appl Biochem Biotechnol (2014) 172:361–379 371
Variation in parameter n with S0, as found here, is unusual, and it was attributed to
changes in the microorganism metabolism at higher substrate concentrations, which was
supported by the increase in xylitol production as S0increased (Table 1). However, meta-
bolic models, such as the genome-scale metabolic models (GEMs), can be used to under-
stand this effect and to predict metabolic capabilities of cells so as to analyze metabolite
connectivity and pathway redundancy . GEMs can also be used to predict genotypic–
phenotypic relationships and for identification of metabolic engineering targets on S. stipitis
[18, 31]. A complete model describing the kinetics and stoichiometry of the xylose
fermenting process is not found in the literature; however, it would be a valuable tool for
predicting optimum reactor configuration strategies as well as scale-up procedures. A similar
study using Levenspiel's model to evaluate ethanol inhibition in alcoholic fermentation from
glucose by S. cerevisiae was carried out by Atala et al. , who found an n value of about
1.5, lower than those found here for S. stipitis. As n is related to the ethanol inhibition effect,
a higher n means that the microorganism is more sensitive to the ethanol concentrations, as is
the case of S. stipitis compared to S. cerevisiae. However, they are different strains of yeast
using different substrates and metabolic routes such that it is difficult to compare kinetic
For initial estimation of YP/X, values of μP(Eq. 3) calculated from experimental data (for
several substrate concentrations) were plotted against μX(Eq. 1), as shown in Fig. 4a. The
angular coefficient corresponds to parameter α and the linear coefficient to β. As β is
practically zero, α was considered equivalent to the parameter YP/X. The initial values for YX
and mXwere also estimated by graphical method, plotting 1/YX/Svs. 1/μ (Fig. 4b). The
angular coefficient corresponds to mX(maintenance coefficient) and the linear one to 1/YX.
All experimental data for YP/X, mx, and YXare shown in Table 3, together with the fitted
Figure 5a shows the values of YX(limiting cellular yield) as estimated by the model fitting
(through quasi-Newton routine) as a function of initial substrate concentration using data in
batch mode. It can be noted that YXvalues decreased linearly with increasing initial substrate
concentration. Opposite behavior was obtained for the conversion factor, YP/X(Fig. 5b),
which increased linearly with the increase of substrate concentration, which means that the
Fig. 3 Calculation of parameter n
372Appl Biochem Biotechnol (2014) 172:361–379
cells are more effective in ethanol production at higher substrate concentration. The values
of YP/Xand YXwere written as functions of initial substrate concentration, according to
Eqs. 17 and 18, respectively, and used in simulations of the process.
YX¼ −0:0007S0þ 0:1366 R2¼ 0:9515
YP=X¼ 0:05167S0þ 3:772 R2¼ 0:9699
Through the simulations of the model formed by Eqs. 9 to 14, 17, and 18 and the kinetic
parameters in Table 3 (fixed parameters: μmax=0.232 h−1; KS=1.67 g L−1; KI=24.4 g L−1and
Pmax=56 g L−1), the concentration profiles of ethanol (P), substrate (S), and biomass (X)
Fig. 4 Determination of the kinetic parameters YP/X(a) and mXand YX(b) for batch experiments. Data from
fermentation with 50 g L−1initial substrate concentration, as an example
Appl Biochem Biotechnol (2014) 172:361–379 373
were obtained. These data are plotted against time in Fig. 6 for some of the batch assays, as
example: 9.2, 49.6, 82.6, 125.0, and 145.6 g L−1of initial substrate concentration. It can be
seen that the proposed model fitted well the experimental data, whose standard residual
deviations (RSD) are put together with the other simulations in Table 4.
The standard residual deviations, given by Eq. 19, describes the average percentage
deviation of experimental and predicted values and is used to characterize the quality of
ð Þ ¼
where RSD ¼1
model andexperimentaldata,dp istheaverageofexperimentalvalues,and np isthenumberof
experimental points. It can be noticed that biomass concentration, substrate, and ethanol
presented deviations from 4.0 to 25.1 %. Higher RSDs were obtained for biomass data
(25.1 % for the experiment at an initial substrate concentration of 125 g L−1). This can be
explained due to the difficulty in measuring the biomass concentration in medium as a result of
the increased flocculating characteristic of the microorganism at high ethanol concentrations.
In order to validate the model, experiments with 7.2 and 36.0 g L−1initial xylose
concentration were used. The results are shown in Fig. 7. The RSD (%) values between
the model prediction and experimental values for biomass concentration, substrate, and
ethanol for validations test were low. The relatively low RSD for validation suggests a good
fitting performance of the model proposed. Therefore, the model can be used for optimiza-
tion and process control. However, it can be stressed that the kinetic parameters are valid for
the specific conditions used in these experiments. When operational conditions change, such
as pH, temperature, fermentation medium, or salt concentration, the kinetic parameters need
to be re-estimated. According to Andrade et al. , although a time-consuming task,
parameter re-estimation is necessary to obtain an accurate description of processes when
changes in operational conditions/raw material composition occur.
??2, xpand dpare respectively the values predicted by the
Table 3 Kinetic and conversion parameters before and after fitting procedure for different initial substrate
concentrations for experiments in batch mode (fixed remaining parameters: μmax=0.232 h−1, KS=1.67 g L−1,
KI=24.4 g L−, and Pmax=56 g L−1)
S0(g L−1)YP/X(g g−1), before/afterYX(g g−1), before/aftermxa(g g−1h−1)nb, after
aAverage of n values
bInitial value was 3.62
374 Appl Biochem Biotechnol (2014) 172:361–379
Atala et al. , Andrade et al. , and Rivera et al.  also used Levenspiel model to
evaluate ethanol inhibition in alcoholic fermentation by S. cerevisiae, and they found that the
model fitted satisfactorily the experimental data for all cases. In our work, the Andrews–
Levenspiel mixed model was applied in alcoholic fermentation by S. stipitis NRRL-Y7124 at
different xylose and ethanol concentrations to evaluate and describe the microorganism inhibi-
tion as well to fit the kinetic parameters. It was also found that although the microorganisms are
can be used for different processes where substrate and product inhibition is found.
The formulation of optimization criteria (objective function) basing on process simulation
is one of the essential steps in model parameter estimation. The determination of a feasible
region in a multiparameter search of a deterministic model is a complex task . For this
reason, the optimization was evaluated using QN algorithm. From computational results, it
was found that the QN algorithm presented a good performance, and the parameters were
estimated for each concentration. The curves of estimated parameters as a function of
substrate concentration presented a regression coefficient above 96 %. Lower coefficients
could lead to additional errors in the model.
0.0 25.050.0 75.0100.0 125.0150.0
0.025.0 50.0 75.0100.0125.0150.0
Fig. 5 Dependence of parameters YX(a) and YP/X(b) on initial substrate concentration
Appl Biochem Biotechnol (2014) 172:361–379 375
It is important to mention that although raw material or media composition may change
and parameters should be re-estimated, some of them can be fixed because they do not
present a significant impact on model fitting performance. Thus, the results presented in this
work can aid in future modeling of processes in which biomass hydrolysates will be used as
0.0 5.010.0 15.020.0
P and X (g.L-1)
P and X (g.L-1)
0.0 50.0 100.0150.0 200.0250.0
P and X (g.L-1)
P and X (g.L-1)
0.0 50.0 100.0150.0 200.0250.0
P and X (g.L
Fig. 6 Experimental (symbols) and model prediction (lines) data for batch mode fermentations at different
substrate concentrations (a–e). Filled square, substrate; filled circle, ethanol; and filled triangle, cells
Table 4 Residual standard deviations (%RSD) for X, S, and P at different initial substrate concentrations
Substrate concentration (g L−1)
Variable9.2 22.949.671.482.1120.0125.2145.6 7.2a
376Appl Biochem Biotechnol (2014) 172:361–379
substrate. The kinetic model can also be used in process design, control, and optimization,
which may aid to reduce the developing costs of second-generation bioethanol.
In this way, with knowledge obtained through the coupling of different modeling
techniques, experiments with optimal metabolic fluxes can be designed, and kinetic param-
eters for xylose uptake and ethanol production, as well as the evaluation of the correlations
between gene expression and metabolic changes in response to environmental perturbation
can be determined.
S. stipitis consumed xylose efficiently, reaching high conversion rates near the theoretically
possible maximum at low substrate concentrations. High ethanol contents were achieved for
both batch and continuous mode, presenting double inhibitory effect by substrate and
ethanol. A simple mechanicist non-structured model for yeast growth taking into account
double inhibitory effect was proposed, and the model predictions were in good agreement
with experimental observations, thus allowing us to systematically investigate the kinetics
characteristics and describe xylose consumption and ethanol yield of this yeast under
microaerobic conditions. The kinetic parameters determined can be quite different from
those found for traditional alcohol-producing microorganisms, such as S. cerevisiae, what
the model used cannot explain. Perhaps more recent model propositions, such as the
genome-scale metabolic models (GEMs), would be useful in this respect.
The QN methodology associated with the model of Andrews–Levenspiel was suc-
cessful to estimate the kinetic parameters of xylose fermentation. The parameters Yx
decreased, and Yp/xincreased, probably due to the higher inhibitory effect caused by the
ethanol accumulated and by the high xylose concentration. The approach used in this
work can be useful for process prediction and control, as well as for simulation and
optimization of the fermentative process. Moreover, the evaluation of their impacts on
yield, conversion, and productivity can also be assessed, and useful insights were drawn
on kinetic parameters estimation of S. stipitis from model simulations. These insights can
be applied for efficient xylose utilization and high ethanol yields, promoting cost
reduction in an industrial scale.
Acknowledgments The authors acknowledge Fundação de Amparo à Pesquisa do Estado de São Paulo
(FAPESP) for financial support.
P and X (g.L-1)
P and X (g.L-1)
Fig. 7 Validation of the model. Experimental (symbols) and model prediction (lines) data for batch mode
fermentation performed at 7 g L−1(a) and 36.0 g L−1(b) of initial xylose concentration. Filled square,
substrate; filled circle, ethanol; and filled triangle, cells
Appl Biochem Biotechnol (2014) 172:361–379 377
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