Mathematical Modeling of Capsular Polysaccharide P
Mathematical Modeling of Capsular Polysaccharide P
Mathematical Modeling of Capsular Polysaccharide P
Vol. 22, No. 04, pp. 585 - 592, October - December, 2005
Abstract - In this work, the process of capsular polysaccharide production by Neisseria meningitidis
serogroup C was studied. Batch experimental runs were conducted in a set of one-liter bioreactors with 0.5 L
of Frantz cultivation medium. Cultivation temperature and pH were controlled at optimal pre-established
values. The dynamic behavior of the bacteria was analyzed based on biomass growth, glucose uptake,
polysaccharide production and dissolved oxygen time profile obtained in a set of experimental runs with
initial concentrations of glucose that varied from 5 to 13.5 g/L. Formulated hypotheses were then employed in
the construction of a phenomenological model of the bioprocess under study that successfully described the
dynamic behavior of the system and can be used in future control and optimization of the industrial process
of capsular polysaccharide production.
Keywords: Bioreactors; Capsular polysaccharide production; Optimization.
serogroup A and C have been produced by Bio- 450 mL Frantz medium in 2 L Erlenmeyer flasks
Manguinhos Institute (Fiocruz) since 1976 through a maintained under the previously described
technology transfer agreement with the Mérieux conditions. After this propagation procedure, growth
Institute of France. Since then various modifications suspension of 10% (v/v) inoculum was used for
in the vaccine production sector have been made, experiments conducted in bioreactors.
aiming to adpt this process to Good Manufacture
Practices rules. Bioreactor Experimental Conditions
Due to the importance of antimeningoccocal
vaccines for national public health, strategies to Experimental design runs were conducted in a set
optimize capsular polysaccharide production is an of four 1.0 L glass-vessel bioreactors (BIOSTAT Q,
extremely significant goal for achieving high B. Braun Biotech International Diessel GmbH,
productivity in the manufacture of purified or Germany) with a volume of 0.5 L. Bioreactors were
conjugated polysaccharide vaccines. Thus, the use of equipped with in situ sterilizable pH and
engineering techniques such as mathematical polarographic dissolved oxygen electrodes, pt-100-
modeling could be very important to design and temperature sensors and magnetic stirring speed
implement alternative industrial strategies in order to control. The fermentation conditions were controlled
improve the production of vaccines. according to the experimental design schedule.
In this work, the process of capsular Airflow rate was maintained at 0.8 L/min with an
polysaccharide production by Neisseria meningitidis upper aeration system. Temperature was maintained
serogroup C was studied, aiming to obtain a at 37 ºC, pH was automatically controlled by NaOH
mathematical model which could be used in future 5N at 7 and stirring speed was set to 1300 rpm. This
control and optimization in the industrial process. stirring speed resulted in an equivalent volumetric
oxygen transfer coefficient (kLa) of 36 h-1.
RESULTS AND DISCUSSION effect of dissolved oxygen was once more observed.
Limited availability of oxygen favored the specific
Aiming to develop a mathematical model that polysaccharide production, i.e., accumulation of
described the behavior of Neisseria meningitidis capsules per bacterial unit. Even after microbial
serogroup C in capsular polysaccharide production in growth stopped, production of the capsules
bioreactors, experimental runs were conducted in continued. Nevertheless, the hypothesis of the
one-liter glass vessels with 0.5 L of Frantz existence of a maximum quantity of surface
cultivation medium. Initial glucose concentration polysaccharide per bacterial unit was suggested.
was varied from 5 to 13.5 g/L. Samples of the Since capsular polysaccharide is not systematically
cultivation medium were collected at pre-established discarded as some bacterial exopolysaccharides, an
time intervals and analytical assays were conducted excessive accumulation of this structure on the
to obtain microbial growth, glucose uptake and bacterial surface may hinder interactions between
polysaccharide time profiles. cells and their surroundings and consequently there
Firstly, an analysis of the kinetics of capsular may be a maximum quantity of this structure per
polysaccharide production by Neisseria meningitidis bacterial unit.
serogroup C was conducted. Based on Based on the assumed hypothesis, a mathematical
microorganism behavior and transient characteristics model was developed for the process of capsular
common to processes operated in batch operation polysaccharide production by Neisseria meningitidis
mode, such as variations in glucose concentration, C. Equations 1 to 4 show the structure of this model,
accumulation of metabolic products and availability which is respectively composed of cell, glucose,
of dissolved oxygen, a set of modeling hypotheses polysaccharide and oxygen mass balance.
was formulated.
dX
= ( µX − µD ) X
In regard to microbial growth it was observed that (1)
the growth rate was highly dependent on oxygen dt
concentration in the cultivation medium. Two
different regions were delimited according to dS
= − ( σA + σM ) X (2)
availability of dissolved oxygen and the results show dt
that the specific microbial growth rate was directly
proportional to the concentration of dissolved dP
oxygen in the cultivation medium. Microbial growth = ( π1 + π2 ) X (3)
dt
was limited by concentration of glucose. Nevertheles
no growth substrate inhibition effects were observed dpO2
in the glucose concentration range studied in this = k L a (100 − pO 2 ) − φX (4)
dt
work.
Glucose consumption also seems to be affected where X, S and P are cell concentration (g/L),
by the availability of dissolved oxygen. At the glucose concentration (g/L) and capsular
beginning of cultivation, when oxygen concentration polysaccharide concentration (mg/L); pO2 is the
was higher, the rate of glucose uptake was shown to
percentage of oxygen saturation; µX and µD are
be much lower than the highest specific microbial
respectively biomass growth and death specific rates;
growth rates attained in this stage. On the other hand,
σA and σM are respectively specific rate of glucose
when oxygen concentration tended to values near
uptake under conditions of at higher and lower
zero, an increase in glucose uptake could be
observed in the complete range of initial substrate availability of oxygen; π1 is the specific rate of
concentration tested. This behavior could be growth associated with polysaccharide formation and
associated with a distinguished glucose metabolism π2 is the specific rate of accumulation of capsular
by Neisseria meningitidis according to higher or polysaccharide per bacterial unit; kLa is the global
lower availability of oxygen (Fu et al., 1995 oxygen transfer coefficient and φ is the specific rate
oxygen). of oxygen consumption. In Table 1 the kinetic
Accumulation of capsular polysaccharide expressions which compose the structure of the
accumulation occurred in two different ways: in part proposed phenomenological model are shown.
it was growth-associated, i.e., the number of capsules Equations 5 to 13 are functions that
increased due to the appearance of new cells and in mathematically describe all the phenomenological
part it was associated with the accumulation of characteristics formerly analyzed which compose the
polysaccharide on the surface of existing cells. The set of model hypotheses formulated through the
Brazilian Journal of Chemical Engineering Vol. 22, No. 04, pp. 585 - 592, October - December, 2005
588 A. W. S. Henriques, E. Jessouroun, E. L. Lima and T. L. M. Alves
experimental observation of the kinetics of capsular squares of the difference between predicted and
polysaccharide production by Neisseria menigitidis experimental values of biomass, glucose,
C. The model parameters were estimated using a polysaccharide and concentration of dissolved
computational routine based on the simplex method oxygen. The estimated values for phenomenological
of parameter estimation, which minimizes the sum of model parameters are presented in Table 2.
Specific rate of biomass growth: Specific rate of glucose consumption under conditions of higher
availability of oxygen:
pO2 (5)
µ max ⋅ S −
µX = − ko
σA max S (9)
k s X n + S
1 e
σA =
qA + S
Specific rate of biomass death: Specific rate of glucose consumption under conditions of lower
availability of oxygen:
− Sk
µD = k ee 1 (6)
S (10)
−
pO 2
σ M = σ M max 1 − e q M 1 − 100
Capsular polysaccharide formation
Specific rate of growth associated with polysaccharide formation:
Oxygen consumption
π1 = µ X YP / X (7)
Specific rate of oxygen consumption:
X qp + S YX / O
growth: (12)
pO 2
−
maintenance: φ 2 = m o e k mo (13)
In Figures 1 to 5 the results for predictions met by the fall in the specific rate of microbial growth
the proposed mathematical model are presented. As following the decrease in availability of dissolved
can be seen, the model was capable of predicting the oxygen. Glucose uptake for this system was also
experimental phenomena previously observed in a well described by the mathematical model, which
satisfactory manner. Results show that proposed successfully predicted both the reduced rate of
functions successfully described the kinetics of glucose consumption in region of the maximum
capsular polysaccharide production by N. oxygen concentration region and the increased
meningitidis C. consumption under conditions of limited availability
Figure 1 shows that the proposed model predicted of oxygen.
Figure 1: Mathematical Model Prediction () for Experimental Time Profiles for Biomass (υ),
Glucose (σ), Polysaccharide (λ) and pO2 (ν). Batch Run with S0 = 5 g/L
Figure 2: Mathematical Model Prediction () for Experimental Time Profiles for Biomass (υ),
Glucose (σ), Polysaccharide (λ) and pO2 (ν). Batch Run with S0 = 7.5 g/L
Figure 3: Mathematical Model Prediction () for Experimental Time Profiles for Biomass (υ),
Glucose (σ), Polysaccharide (λ) and pO2 (ν). Batch Run with S0 = 9 g/L
Brazilian Journal of Chemical Engineering Vol. 22, No. 04, pp. 585 - 592, October - December, 2005
590 A. W. S. Henriques, E. Jessouroun, E. L. Lima and T. L. M. Alves
Figure 4: Mathematical Model Prediction () for Experimental Time Profiles for Biomass (υ),
Glucose (σ), Polysaccharide (λ) and pO2 (ν). Batch Run with S0 = 11 g/L
Figure 5: Mathematical Model Prediction () for Experimental Time Profiles for Biomass (υ),
Glucose (σ), Polysaccharide (λ) and pO2 (ν). Batch Run with S0 = 13.5 g/L
Figures 4 and 5 contain the results for batch runs dissolved oxygen mass balance successfully
conducted with initial glucose concentrations greater predicted the dynamic behavior of capsular
than 10 g/L. As can be seen, the model developed polysaccharide production by Neisseria meningitidis
described the limited accumulation of polysaccharide C in the entire experimental range studied in this
due to the lack of new bacteria cell formation. The work. Therefore, the proposed model could be
model prediction indicated that although the glucose employed as an efficient tool for simulation and
was completely consumed, there was no significant implementation of future control and optimization
difference in the final concentration of schemes for this process of vaccine production.
polysaccharide between the batch runs. Since final
concentrations of biomass were very similar for both
experimental runs, this could be explained by one o CONCLUSIONS
the model assumptions, which assumed that there
was a maximum number of capsules per bacterial In this work, the process of capsular
unit. polysaccharide production by Neisseria meningitis
The mathematical model based on equations for sorogrupo C in bioreactors was studied. Based on
biomass, glucose, capsular polysacharide and experimental observations from five batch runs
Brazilian Journal of Chemical Engineering Vol. 22, No. 04, pp. 585 - 592, October - December, 2005
592 A. W. S. Henriques, E. Jessouroun, E. L. Lima and T. L. M. Alves