Growth Rate Estimation in Batch Culture of Brevibacterium linens

Published by Else7'ier Science on behalf of IFAC

GROWTH RATE ESTIMATION IN BATCH CULTURE OF BREVIBACTERIUM LINENS K.

Preu~

and M.-V. Le Lanno

Ecole Nationale Superieure d'lngenieurs de Genie Chimique, INP Toulouse Laboratoire de Genie Chimique CNRS UMR 5503 18, Chemin de la Loge - 31078 Toulouse Cedex - France TeE. : +33 (0)5.62 .25.23.00, Fax: +33 (0)5.62.25.23.18 E-mail: Karlhein [email protected] °lAASI1NSA - CNRS UPR 8001 - 7, Av. du Colonel Roche - 31400 Toulouse , France E-mail: MVLeLann@laasIr

Abstract: Specific growth rate is estimated in batch culture of Brevibacterium linens in a 20 Jiters pilot bioreactor on lactic acid and amino acids as substrate. The estimation procedure is based on exhaust gas analysis and implemented in a MFCS/win (B. Braun Biotech) environment. Several batch runs with different initial substrate concentrations are presented. During further batch cultures multiple step changes of operation conditions (culture temperature and dissolved oxygen concentration) were applied . Their influence on kinetics are monitored by growth rate estimation. The parameters of a kinetic model are deduced from the experimental data. Keywords : Brevibacterium linens, estimation, kinetic model , specific growth rate

1. INTRODUCTION

known . This variable deals out to be very corrupted ' with noise , so that smoothing of the time derivative is inevitable. Unfortunately thi s renders the estimation insensitive to quick changes of operation conditions. These problems can be overcome by the estimation procedure described in sections 3.1 and 3.2 of this paper. Its experimental performance is shown in section 3.3. The considered process, batch growth of Brevibacterium linens in a 20 Jiters bioreactor, is described in section 2. By means of the growth rate estimation the influence of temperature and dissolved oxygen concentration on kinetics is examined experimentally in section 4. Finally some conclusions are drawn in section 5.

Estimating the specific growth rate (referred to as growth rate in the following) in microbial batch cul ture is of interest i.e. for monitoring and control purposes. For this goal a kinetic model is required in most cases. In general, several experiments have to be carried out in order to build the model. Substantial savings can be obtained by accelerating the modeling procedure. The proposed approach consists in applying multiple step changes of the operating conditions during batch culture. Their kinetic effects are indicated by an on-line growth rate estimation. In order to explore a large domain of operation conditions in one experiment, the duration of each step change will be rather short. For this reason the estimation procedure must provide an immediate response to these changes. As at the begjnning of the mode ling procedure kinetic and yield coefficients are not known, it is difficult to use observer-based [Bastin, Dochain 1990] or Kalman filtering [Shimizu et al. 1989] estimation procedures. Other approaches deduce the reaction rate of one component from gas phase measurements [Levisauskas et al. 1996], [Ljubenova, Ignatova 1994] . In these cases the time derivative of the respective reaction rate must be

2. PROCESS DESCRIPTION The pilot plant consists of a 20 Iiters stirred and aerated CHEMAP bioreactor. The considered process is batch growth of Brevibacterium linens, a bacterium used in the diary industry. It is grown on a synthetic culture medium containing lactic acid and amino acids as main substrates. Samples were taken at irregular intervals and the concentration of the following components was analyzed : biomass X (optical density), lactic acid L (enzymatic kid), amino acid A

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(HPLC). In fact, 16 amino acids were analyzed separately and regrouped to one pseudo-component. Exhaust gas composition (CO], O 2 ), pH, dissolved oxygen concentration (P02), reactor temperature (7), stirrer speed (v,) and inlet aeration rate (Fin) are measured on-line. Data acquisition, recording and visualization are performed by the MFCS/win-software (B. Braun Biotech). Its internal PID control reactor temperature and dissolved oxygen concentration . The latter is cascaded by stirrer speed control and regulation of the aeration rate if the maximum stirrer speed is reached . The entire process is operated via the MFCS/win operator interface. A macroscopic reaction scheme, describing some parts of the metabolism of Brevibacterium linens, was recently proposed by [Moreau 1999]. It can be roughly summarized as follows:

L + O 2 -> X + CO 2

Replacing biomass X and its derivative in equation I by equations 2 and 3, under the assumption of a constant yield Ywx , gives an expression for the growth rate :

Ji(t)

= vR .

u

(4)

(t)

Qu(t) The initial quantity of component a, Qito), is unknown. When calculating the growth rate for a terminated batch run a posteriori, the appropriate value can be found manually . In case of starting the estimation procedure during the course of a batch run, Qj1o) can hardly be determined a priori, neither manually , Hence an additional procedure, allowing for the on-line automatic determination of Qa(tO), is necessary. The description of thi s procedure can be found in [Preu· , Le Lann 2000].

(R,) 3.2 implementation

This representation implies that oxygen consumption and production of carbon dio xide are proportional to the production of bi omass. Generally both reactions take place simultaneously but R, is predominant at the beginning of a batch. The relation between reaction rates r, and r2 changes during the course of a batch run and depends on the concentration of the substrates lactic acid and amino acid.

In order to implement the estimation procedure described in the preceding section , the component whose reaction rate will be used has to be chosen. According to equation 2 the reacti o n rate of the chose n component has to be directly linked to growth. From the reaction scheme R, and R2 it can be seen that in the present case oxygen and carbon dioxide are possible candidates for growth rate estimation. Under the assumptions that (i) their concentration in the liquid phase remains constant and (ii) the gas volume between the culture surface and the exhaust gas analyzer is zero, the reaction rates are equivalent to the uptake / exhaust rate of the respective component : oxygen uptake rate OUR, carbon exhaust rate CER.

3. GROWTH RATE ESTIMATION

3.i General approach Due to the lack of appropriate sensors the growth rate can not directly be measured. Consequently it has to be calculated using the available on-line measurements. This procedure should work: - without measured state variables. - without a detailed kinetic model. - with few experimental data available a priori . Furthermore, as the estimation will be used for kinetic investigations and later on for control, it should react quickly to variations of the operation conditions. These conditions are fulfilled by the estimation procedure described in the following. Its basic equation is the differential equation for microbial growth with a neglected maintenance term:

dX _

*X

Tt- Ji

The reaction rate follows:

=y

v R..

.,X

CER(n) =

F.n(n) * (Yc02"uI(n) -

Y02"uI (n») YC02 .J

(5) (6)

Q02(n) = Q02(n -I ) + OUR * /!"'t

(7)

QC02(n) = QC02 (n -I) + CER * /!"'t

(8)

Then the growth rate can be estimated alternatively by the following equations:

OUR(n) Ji o2( n) = Q02( n)

(9)

of component a is defined as

*dX dt

CER(n) Ji c02(n) = Q () C02 n

(2)

1

Q. = v R ,. *dt +Q.(to) = Y.,x

*X

(l0)

In this case an on-line measurement that would have allowed for inferring on biomass was not available. Growth rate values deduced from off-line biomass analysis are very much corrupted with noise . Therefore the growth rate estimation was validated by

and its integral Qa being :

f

F." (n) * b 'o2;" -

The inlet concentrations are supposed to be constant parameters. Discrete integration of equation 3 leads to:

(1) VR,a

OU R(n ) =

(3)

10

calculating the biomass

344

X from

the estimated growth

rate and then comparing the estimated biomass with the off-line samples. Xu(n)

= X u(n-1)+X u(n-1)*J.l u(n)*L1t

Figure 1b shows the biomass estimation using the growth rate estimates with carbon dioxide (X{C02}) and oxygen (X{02}) as inputs. In both cases the estimated biomass corresponds well to its measured values. For this reason it is argued that the underlying growth rate estimates must be correct as well.

(11)

8.---------------------.

3.3 Experimental results Different experiments were carried out with different initial substrate concentrations. The substrate ratio rL is the fraction of lactic acid contained in the total initial substrate. rL

- - - - -

4

'0

XL,O =----'---

xL,o

6

§.

(12)

+ xA,o

2 • X{measured) [mol)

In all cases carbon dioxide and oxygen were used, according to equations 9 and 10, to estimate the growth rate. The quality of the resulting estimates was assessed by means of the biomass estimation procedure described above (equation 11).

O~-=~~~----r_---_+---~

10

20

Time [h)

30

40

50

Fig. 1b: Validation of estimated growth rate (rL=0.5). The batch run depicted in figure 2 was carried out with a reduced initial concentration of lactic acid . Consequently this substrate expires earlier than in the preceding case, after 28 hours.

0.3 . , - - - - - - - - - - - - - -- - - - -- ---,

0.2

0.3 . , - - - - - - - - - - - - - - - - -- - -

0.1

0.2

10

20

Time [hI 30

40

0.1

50

Fig. 1a: Estimated growth rate using carbon dioxide J.1{C02} and oxygen J.l{02} for an initial substrate ratio rL=OS

o+----~----_---

10

At the beginning of a batch run the quantity of biomass is very low so that the precision of exhaust gas analysis does not allow for reliable measurements right from the start. For this reason growth rate estimates become available after 10 to 16 hours of batch time have elapsed . Typically the estimated growth rate reaches its maximum value after 20 hours. Then it starts to decrease due to the sinking substrate concentration. Significant drops of growth rate are observed when a substrate expires. In figure 1a this happens after 32 hours (expiration of lactic acid) and 40 hours (expiration of amino acids). Finally the culture reaches a respiration regime where no new biomass is formed. At the beginning different estimates for growth rate are obtained depending on whether carbon dioxide or oxygen was used as inputs to the estimation. Generally the estimates converge to a common value during the course of the batch. But, expiration of lactic acid gives birth to further temporal differences of the estimates.

20

Time [hI

30

__

-~-~

40

50

Fig. 2a: Estimated growth rate using carbon dioxide J.1{C02} and oxygen J.1{02} for an initial substrate ratio rL=0.33 . 10 ~-----------------_,

8

6 '0

§. 4

X{C02) [mol] -X(02) [mol]

2

• X{measured) [mol]

o~~~~_+----_---~---~ 10

20

Time [hI

30

40

50

Fig. 2b: Validation of estimated growth rate (rL=0.33).

Again it can be observed that expiration of lactic acid Increases temporarily the difference between both

345

4. INFLUENCE OF TEMPERATURE AND DISSOLVED OXYGEN ON GROWTH RATE

growth rate estimates. However they generally converge to a common value. In comparison to figure la the growth rate is smaller: the reduced lactic acid concentration limits cell growth. As can be seen from figure 2b the estimated biomass is close to the measured values , which leads to the conclusion that the underlying growth rate estimates are realistic.

In order to examine the influence of temperature T and dissolved oxygen concentration P02 on the growth rate, step changes of these variables were applied during the course of a batch . The duration of each step was between 1.5 and 2 hours. For all batch runs mentioned in this section the initial substrate ration rL was 0.5 . As in the preceding section, the growth rate estimation was performed a posteriori and initialized manually. In this section the reaction rate of oxygen was used as input to the growth rate estimation. This estimate (}1 (02}) is less affected than the one resulting from carbon dioxide by disturbances generated by pH control. Figure 4 presents a batch run with repeated step changes of culture temperature. The resulting growth rate estimates were used to estimate biomass. As it can be seen from figure 4a, in a first time the temperature increase leads to a higher growth rate . But during the last temperature step (from 32.5 C to 34 QC) the optimal growth temperature is exceeded and the growth rate drops significantly . The estimated biomass (figure 4b) is close to the measured values which means that the underlying growth rate estimation is correct. Consequently it can be concluded that the growth rate estimation really represents the influence of temperature on growth.

In the following case the culture was grown on amino acids only. The growth rate estimates indicate that growth is slower without lactic acid and it takes more time until the batch reaches its end. After 25 hours the growth rate drops significantly. This event is likely to be related to expiration of an essential component in the fermentation broth. But the component in question is none of the 16 analyzed amino acids. During the first 30 hours of the batch run both growth rates lead to correct biomass estimation (figure 3b). Then, the biomass estimated from the exhausted carbon dioxide overestimates the real values . This corresponds to the higher growth rate, compared to the one estimated from oxygen uptake, between 30 and 40 hours (figure 3a). Apparently oxygen supplies better growth rate estimation in the case of amino acids as unique substrate. 0.3 .,.-- --

Q

- -- -- - -- - -- - - --,

0.25

35

0 .2 33

0.225

31 0.1

0.2 29

E 27

0.175

E

O +----~----_r----~---~

S

50

0.15

Fig. 3a: Estimated growth rate using carbon dioxide J.I{C02} and oxygen J.I{02} for an initial substrate ratio rL=O.

0.125

10

20

Time [h]

30

40

25 23 22

24

Time[h]

26

28

Fig. 4a: Growth rate estimation with repeated step change of culture temperature T. 6 6 X(C02) [mol] -X(02) [mol) • X(measured) [mol)

4

4

(;

• Bio {measured) [mol] - X(02) [mol]

.§. 2 2

10

20

Time [h)

30

40

o +---~-~-----~----~-~ 20 Time [h) 30 10 40

50

Fig. 3b: Validation of estimated growth rate (rL=O).

Fig. 4b: Validation of growth rate estimation.

346

rate afterwards is 7.S% too high. a corrected biomass estimation X{02.cor) can be calculated. The corrected growth rate estimation is depicted in figure Sc. The aim of this correction only is to illustrate the order of the error of the estimated growth rate in this specific experiment. It can of course not be used to correct estimates from other batch runs . During each step period the growth rate was approximated by a line (figure Sa). The distance between two lines. at the point of time when a step occurs. is a measure for the change of relative growth rate /1, generated by the reduction of dissolved oxygen concentration. Combining these relative changes from the reference value I at a dissolved oxygen concentration of SO% to the last step at 4% leads to the data shown in figure Sd. The relative change of growth rate in the case of dissolved oxygen concentration decreasing from 2S% to 17% could not be read because during this period the growth rate estimation was disturbed. Therefore it was assumed that the relative change is equal to the case of dissolved oxygen decrease from 17% to 10%. From figure Sd it can be seen that the influence of dissolved oxygen concentration on growth rate is small and only significant for values below 10%.

In order the explore the influence of low dissolved oxygen concentrations on growth rate several step changes from SO% to 4% P02 were applied during the batch depicted in figure S. It can be seen that the influence of dissolved oxygen concentration on growth rate is small. 0.25

60 50

0.225 40 0.2

30

~

~ ~

20

0.175 10 0.15

0 21

29

27

23 Time [hJ 25

Fig. Sa: Growth rate estimation with repeated step change of dissolved oxygen concentration P02 . 5,---------- - - - - - -- - - - ---------- - - - - - , • X (measured) [molJ - - X(02,cor} [molJ - - X(02} [molJ

4

3 o

0.95

oS 2

•

- 352-

•

•

0.9

•

H O +----------;-----------r----------r---~

10

Time [hJ

20

30

:~

0.85

40

Fig. Sb: Validation of estimated growth rate. 0 .8 +-------t-------+-------+--------+-------i

o 10 20 P02 [%J 30 40 50 Fig. Sd: Influence of dissolved oxygen concentration P02 on relative growth rate /1,.

The resulting estimated biomass overestimates the real values (figure Sb) . The source of this deviation Q might be the temperature reduction from 26 C to 12 QC that took place from 17 to 20.S hours. 0.3 , - - -- - - - - - - - -- -- -- - - -- - - - - - -- - - - - - - - -

1.5

,-------------------------------------~

-~(02,cor)

[II11J - - ~(02][1111]

0.2

H 0 .5

0.1

0+---------~+~10+~~o--------.7~.5~~~or:----------~ 10

20

Time [hJ

30

O+---~~--

o

40

__- -- - - - - -- -__- - - - - - - -__----L 10 Temperature 20 30 [OC]

Fig. 6: Influence of culture temperature T on relative growth rate /1,.

Fig. Sc: Estimated and corrected growth rate. It seems that in this case the estimated growth rate

does not represent the real values. Assuming (i) that the estimated influence of temperature on growth rate is 10% too high and that (ii) the estimated growth

Like in the case of dissolved oxygen. the experiments with step changes of temperature can be analyzed in the same way in order to determine the change of

347

relative growth rate when a temperature step change occurs. From the batch runs #1 (data not shown) and #2 (presented in figure 3) the influence of temperature on growth rate, as depicted in figure 6, can be deduced . This figure combines the relative growth rate, relative to the growth rate at a temperature of 26°C, obtained from both batches Ilr{#J} and Ilrf#2}. Rosso et al. 1995 proposed the following model for the influence of temperature on growth rate: ( ) /1 , ......

T

tration . Dissolved oxygen concentration has little influence on growth rate and only affects it significantly at very low values «10%). Above 50% no further increase of growth rate was found . When dissolved oxygen is decreased from 50% to 10 %, the growth rate diminishes by 7 %. On the other hand, temperature has a very strong influence. The highest growth rate was found at 32.2°C. A further temperature rise by two degrees (34.2°C) reduces growth rate by half due to thermal stress. As far as control of growth rate is concerned the results mentioned in this paper show that dissolved oxygen concentration can not be used as manipulated variable because its influence is too small. Temperature instead is an appropriate manipulated variable under the condition that its upper bound it strictly respected in order to avoid degradation of the culture.

1.39* eT - T,m )* eT - T,.J (r;~, - T~H(r.,p, - T~)·(T - T"",HT"", - T_, )-(r.,., + T_ -2 'T)]

(13)

In the present case the parameters of this law are Tmin=0.8 °C, Tmax=34 .2°C and Topr=32.2°C. They were calculated with the data presented in figure 6. 5. CONCLUSION It was shown that reaction rates of gaseous components can be used to estimate the growth rate in batch culture of bacteria. Generally, the described approach can be applied to cases where growth is directly linked to the respective reaction rates. A model, yield or kinetic parameters are not required. The estimation procedure contains one parameter that has to be ini tiali zed. In this paper recorded data was used to carry out estimation a posteriori and initialization was performed manually. Both available reaction rates, carbon dioxide and oxygen, give good estimates of growth rate. This is the case for different initial substrate concentrations. However for low initial concentrations of lactic acid the · oxygen reaction rate gives more precise estimates. This was proved indirectly by using the growth rate to estimate biomass. Good agreement between estimated and measured biomass is observed (mean relative error 5-10%). In practice, estimating biomass according to this procedure possesses the disadvantage of exponential evolution of error. For this reason the biomass estimate tends to diverge. Furthermore the biomass estimation procedure requires an initial value which is not available in the case of on-line estimation. Hence this biomass estimation procedure is limited to off-line applications. In order to explore the influence of culture temperature and dissolved oxygen concentration on growth rate, step changes of these operating conditions were applied during batch fermentations . The duration of these steps was between 1.5 and 2 hours, which allows for exploring a wide range of operating conditions in one batch run . The influence of these changes was indicated by the estimated growth rate. By means of biomass estimation based on the estimated growth rate it was proven that this procedure provides reliable results . It seems that in the case of step changes with high amplitude an error of about 10% appears in the estimated growth rate. As far as kinetics is concerned it was found that the cell metabolism reacts without measurable delay to a change of temperature or dissolved oxygen concen-

ACKNOWLEDGEMENT Technical support of this research by SOREDAB S.A . (Groupe Bongrain) is gratefully acknowledged. The authors wish to thank X. Meyer, A . Moreau and H. Pingaud for the experimental data of figures 1, 2 and 3. REFERENCES Bastin G ., Dochain D. (1990) : On-line Estimation and Adaptive Control of Bioreactors. Elsevier: Amsterdam . Levisauskas D., Simutis R., Borvitz D ., Liibbert A. ( 1996) : Automatic control of the specific growth

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Convenient Model to Describe the Combined Effects of Temperature and pH on Micobial Growth. Applied Environmental Biotechnology, Vol. 61, No. 2. Shimizu H ., Takamatsu T., Shioya S., Suga K.-I. (1989) : An Algorithmic Approach to Constructing

the On-line Estimation System for the specific growth rate. Biotech. Bioeng., 33, 354-364.

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