Empirical Modeling of Batch FermentationKinetics for Poly(glutamic acid) Productionand Other Microbial Biopolymers

Andrew Richard, Argyrios Margaritis

Department of Chemical and Biochemical Engineering, The University ofWestern Ontario, London, Ontario, Canada, N6A 5B9; telephone: (519)661-2146; fax: (519) 661-3498; e-mail: amarg@uwo.ca

Received 29 July 2003; accepted 23 March 2004

Published online 23 July 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bit.20156

Abstract: An empirical kinetic model is proposed for thebatch production of poly(glutamic acid) from Bacillussubtilis IFO 3335. In addition, the proposed model wasused to fit the kinetic data of poly(glutamic acid) pro-duction from other bacterial strains using different media,as well as kinetic data from different strains for the pro-duction of the exocellular biopolymers dextran, hyaluronicacid, xanthan, alginate, and the endocellular biopolymerpolyhydroxybutyrate. The empirical model treats the bio-polymer as a component of the biomass and fits the ex-perimental biomass data using a sigmoidal relationship thatincludes the maximum specific growth rate, Amax, and thesubstrate saturation parameter, KS. An empirical param-eter, the relative coefficient (r), quantifies, in relativeterms, the degree of nongrowth-associated biopolymerformation. B 2004 Wiley Periodicals, Inc.

Keywords: kinetic model; microbial biopolymer; fermenta-tion; relative coefficient; poly(glutamic acid)

INTRODUCTION

Microbial biopolymers have found use in diverse applica-

tions. They are used as stabilizers, emulsifiers, thickeners,

and excipients in the food, industrial, and health care

markets (Sutherland, 1998). Poly(glutamic acid) (PGA) is a

water-soluble, biodegradable biopolymer that is produced

by microbial fermentation. Recent research has shown that

PGA can be used in drug delivery for the controlled release

of the anticancer drug paclitaxel (Taxol) (Multani et al.,

1997; Li et al., 2000).

In order to optimize the production of PGA for

biomedical applications, a fundamental understanding of

the key fermentation parameters is necessary. We have

previously reviewed PGA for biomedical applications

(Richard and Margaritis, 2001), optimized PGA production

in batch culture (Richard and Margaritis, 2003a), and

quantified the key oxygen mass transfer parameters (OUR,

Qo2, kLa) and the key broth rheology parameters (flow

index, consistency index, apparent viscosity) as a function

of fermentation time for the batch production of PGA by B.

subtilis IFO 3335 (Richard and Margaritis, 2003b). There is

also a need to develop a kinetic model for this process in

order to further understand and optimize PGA production.

Kinetic models are important tools for understanding,

controlling, and optimizing fermentation processes. Micro-

bial processes are inherently complex, and it is of critical

importance in practical applications to develop models that

provide an accurate description of the process without

unnecessary complexity (Luong et al., 1988). Unstructured

kinetic models are frequently used because of their

simplicity and adequacy for technical purposes (Garcıa-

Ochoa et al., 1995).

Biopolymer fermentation processes are of particular

interest because, in certain cases, these microbial processes

do not follow the classical kinetic model of substrate-

limited biomass growth and product formation proposed by

Monod in 1949 (Garcıa-Ochoa et al., 1995; Quinlan, 1986;

Schweickart and Quinlan, 1989). Several unstructured

kinetic models have been proposed to describe the kinetics

of microbial systems where biopolymers are produced

(Garcıa-Ochoa et al., 1995; Quinlan, 1986; Schweickart

and Quinlan, 1989; Weiss and Ollis, 1980; Santos et al.,

2000). These models have been thoroughly reviewed

(Margaritis and Pace, 1985; Garcıa-Ochoa et al., 1995;

Luong et al., 1988; Kovarova-Kovar and Egli, 1998).

In general, these models use a form of the logistical

equation to describe biomass growth (Eq. 1) and a form of

the Luedeking-Piret model (1959) to describe biopolymer

formation as a function of biomass (Eq. 2):

dX

dt¼ AmaxX ð1:0� X=XmaxÞ ð1Þ

dP

dt¼ nXþm

dX

dtð2Þ

In order to fit their experimental data, several researchers

have also used Monod-type equations to better describe

B 2004 Wiley Periodicals, Inc.

Correspondence to: A. Margaritis

Contract grant sponsors: Natural Sciences and Engineering Research

Council of Canada (NSERC); NSERC (Ph.D. Canada Graduate Scholar-

ship A.R.)

Contract grant number: A4388 (to A.M.)

biomass growth and product formation in terms of the

limiting substrate (Moraine and Rogovin, 1966; Moraine

and Rogovin, 1971; Garcıa-Ochoa et al., 1995) and others

have proposed substrate dependent equations which are not

of the Monod type (Quinlan, 1986; Schweickart and

Quinlan, 1989) (Eqs. 3, 4):

dX

dt¼ kXNX ð3Þ

dP

dt¼ kPSX ð4Þ

The current unstructured models have several limita-

tions. Models that are dependent on biomass concentration

only do not take into account substrate-limited product

formation. Models that employ several equations for

substrate-limited growth are complicated and require

numerical techniques in order to determine a solution.

None of the previously proposed unstructured models

consider the formation of the biopolymer as a component of

the biomass. In this work, we present an empirical model

for biopolymer fermentations that is simple to use and

based on the assumption that the biopolymer is a

component of the biomass.

THEORETICAL ASPECTS AND EMPIRICALMODEL DEVELOPMENT

Modeling of Biomass and ‘‘Extended-Biomass’’

All of the unstructured kinetic models presented in the

literature treat the biopolymer as a fermentation product,

Table I. Maximum biomass and biopolymer concentrations (Xmax, Pmax) for various biopolymer fermentations.

Biopolymer Microorganism Xmax (g/L) Pmax (g/L) Reference

Xanthan X. campestris NRRL-B1459 1.7 29 Garcıa-Ochoa et al., 1995

Pullulan A. pullulans ATCC 9348 9.2 11.3 Gibbs and Seviour, 1996

Pullulan A. pullulans P56 6 23 Roukas and Mantzouridou, 2001

Dextran L. mesenteroides NRRL B512(f) 5.1 8.5 Santos et al., 2000

PGA B. subtilis IFO 3335 4.7 23 Richard and Margaritis, 2003b

PGA B. subtilis IFO 3335 3.5 8.1 Kunioka and Goto, 1994

PGA B. licheniformis ATCC 9945A 3.2 23.2 Yoon et al., 2000

Hyaluronic acid S. zooepidemicus ATCC 35246 1.8 1.6 Armstrong and Johns, 1997

Alginate A. vinlandii ATCC 9046 3.5 4.5 Pena et al., 2000

Figure 1. Biomass specific growth rate (A) vs. citric acid concentration (S) during batch fermentation of B. subtilis IFO 3335 (Richard and Margaritis,

2003b). Experimental data (.); Eq. 8 (—).

502 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 87, NO. 4, AUGUST 20, 2004

which constitutes a major component of substrate con-

version, as shown in Table I. While the specific growth rate

of biomass production may not fit the Monod model

(Garcıa-Ochoa et al., 1995; Quinlan, 1986; Schweickart

and Quinlan, 1989), we propose the concept of extended-

biomass (XV) that includes the biopolymer, which results in

an empirical model that fits the Monod equation, as shown

in Eq. 7. Although it is well accepted that the biopolymer

is a product of cell metabolism, the inclusion of the

biopolymer may be regarded as ‘‘pseudo-biomass,’’ or

Figure 2. Effect of relative coefficient (r) on biomass specific growth rate/substrate curve (So = 20 g/L, Ks = 7 g/L, Amax = 0.1275 h�1).

Table II. Proposed empirical kinetic model for biopolymer fermentations.

Parameter Equation Equation number

AV A0maxS

K 0S þ S

(7)

A AmaxSr

KrS þ S r

(8)

X Amaxt ¼ lnðX=XoÞ þK rS Y r

X=S

�lnXar � ln ð�aþXÞ

ar � ð�aþXÞ�1

aðr�1Þ þ ð�aþXÞ�2

2aðr�2Þ � � � � � �ð�aþXÞ�ðr�1Þ

ðr�1Þa�

a ¼ YX=SSo þ Xo

(14)

XV A0maxt ¼ðK 0

SYX0=S þ So YX0=S þXoÞðYX0=S So þX 0

o Þln ðX0=X0

oÞ �ðK 0

SYX0=SÞ

ðYX0=S So þX0oÞln½ðYX0=S So þ X 0

o � X0ÞYX0=S So�

(13)

S ðX�XoÞ ¼ YX=S ðSo � SÞ or;

(11)

ðX0 �X 0oÞ ¼ YX0=S ðSo � SÞ

(10)

P P ¼ X0 �X (12)

Input data: Xo, So, Po, AVmax, Amax, YXV/S, YX/S.

Calculated parameters from input data: r, KSV, KS.

RICHARD AND MARGARITIS: BATCH PRODUCTION OF POLY(GLUTAMIC ACID) 503

extended-biomass, solely for the purposes of fitting data to

an empirical model.

The extended-biomass is defined as:

X0 ¼ Xþ P ð5Þ

The specific growth rate of the extended-biomass is then

defined as:dX0

dt¼ A0X0 ð6Þ

Interestingly, the specific growth rate of the extended-

biomass follows the Monod equation:

A0 ¼ A0maxS

K0s þ S

ð7Þ

This is a simple way to look at the biomass formation and

biopolymer production together. As such, the specific

growth rate of the extended biomass is limited by a single

substrate (S). The extended-biomass specific growth rate

over time is determined graphically from Eq. 6 and a plot of

ln (XV) vs. fermentation time.

It is now necessary to model the biomass formation and

specific growth rate of the biomass (A) separately as a

function of substrate concentration. Figure 1 shows the

biomass specific growth rate (A) as a function of citric acid

concentration (S) for PGA production (Richard and

Margaritis, 2003b). The resulting curve has a sigmoidal

shape. At high substrate concentrations, the specific growth

rate is at its maximum (Amax). As the substrate is consumed,

the specific growth rate falls, but at a faster rate of decline

Table III. Model parameters for PGA production.

Parameters Richard and Margaritis (2003b) Kunioka and Goto (1994)a Yoon et al. (2000)b

For XV: AVmax 0.314 0.311 0.416

KVS 2.95 9.00 3.00

YVXS 1.405 0.577 2.183

R2 0.99 0.97 0.98

For X: Amax 0.281 0.129 0.3608

r 29 3 7

KS 15.1 6.89 7.09

YXS 0.630 0.189 0.334

R2 0.99 0.98 0.99

aUsing B. subtilis IFO 3335, So = 20 g/L citric acid.bUsing B. lichenformis ATCC 9945A, So = 12 g/L citric acid.

Figure 3. Batch fermentation kinetics of B. subtilis IFO 3335 during poly(glutamic acid) production (Richard and Margaritis, 2003b). Biomass, X (.);poly(glutamic acid) concentration, P (o); citric acid concentration, S (

E

); Eq. 14 (—), Eq. 12 (�����), Eq. 10 (. . .. . .).

504 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 87, NO. 4, AUGUST 20, 2004

than would be expected for a Monod relationship. As the

specific growth rate approaches zero, there is still consider-

able substrate remaining for biopolymer formation. At this

point in the fermentation, no other substrates are limiting

growth. In other words, there is only one growth-limiting

substrate (citric acid).

There are several mathematical expressions that could

be used to describe this sigmoidal relationship between Aand S. In Monod’s original work, he stated that ‘‘several

different mathematical formulations could be made to fit

the data. But it is convenient and logical to adopt a

hyperbolic equation’’ (Monod, 1949). As in Monod’s

Figure 4. Batch fermentation kinetics of B. subtilis IFO 3335 during poly(glutamic acid) production (Kunioka and Goto, 1994). Biomass, X (.);poly(glutamic acid) concentration, P (o); citric acid concentration, S (z); Eq. 14 (—), Eq. 12 (�����), Eq. 10 (. . . . . .).

Figure 5. Batch fermentation kinetics of B. licheniformis ATCC 9945A during poly(glutamic acid) production (Yoon et al., 2000). Biomass, X (.);poly(glutamic acid) concentration, P (o); citric acid concentration, S (z); Eq. 14 (—), Eq. 12 (�����), Eq. 10 (. . .. . .).

RICHARD AND MARGARITIS: BATCH PRODUCTION OF POLY(GLUTAMIC ACID) 505

equation, which describes the specific growth rate in terms

of Amax, we choose a sigmoidal equation that also contains

Amax:

A ¼ AmaxSr

K rs þ Sr

ð8Þ

The specific growth rate of the biomass can also be de-

fined by:dX

dt¼ AX ð9Þ

The biomass specific growth rate over time is determined

graphically from Eq. 9 and a plot of ln (X) vs. fermenta-

Figure 6. Plot of P(t) – Po – nB(t) (Eq. 15) vs. A(t) (Eq. 16) for the determination of ‘‘m’’ during batch fermentation of B. subtilis IFO 3335 for the data

from Richard and Margaritis (2003b).

Figure 7. Plot of P(t) – Po – nB(t) (Eq. 15) vs. A(t) (Eq. 16) for the determination of ‘‘m’’ during batch fermentation of B. subtilis IFO 3335 for the data

from Kunioka and Goto (1994).

506 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 87, NO. 4, AUGUST 20, 2004

tion time. The relationship described in Eq. 8 is conven-

ient because it contains Amax and KS, describes the spe-

cific growth rate as a function of substrate concentration,

and contains the relative coefficient, ‘‘r,’’ which is de-

scribed below.

Relative Coefficient, r

In Eq. 8 we incorporate the ‘‘relative coefficient,’’ r. The

relative coefficient is necessary in order to produce a

sigmoidal fit of the data, but it also describes another

Figure 8. Biomass specific growth rate (A) vs. substrate concentration (S) during batch biopolymer fermentations (Published data, .; Eq. 8, —); a:

Dextran (Santos et al., 2000), b: Xanthan (Serrano-Carreon et al., 1998), c: Alginate (Pena et al., 2000), d: PHB (Yoo and Kim, 1994), e: Hyaluronic acid

(Armstrong and Johns, 1997).

RICHARD AND MARGARITIS: BATCH PRODUCTION OF POLY(GLUTAMIC ACID) 507

phenomenon of the process, which is the relative amount of

nongrowth-associated biopolymer formation. As ‘‘r’’ ap-

proaches unity, Eq. 8 becomes the Monod equation,

meaning that no substrate is available for further biopoly-

mer formation after biomass growth has stopped. As a

result, the biopolymer formation is completely growth-

associated. As ‘‘r’’ increases, there is more substrate

available for biopolymer formation after biomass growth

has stopped. Hence, there is relatively more nongrowth-

associated biopolymer formation. This is depicted in

Figure 2.

Modeling of Substrate and Product (Biopolymer)

From Eqs. 5–7, the extended-biomass concentration as a

function of fermentation time is fully defined. The most

convenient way to describe the substrate concentration is

given by the extended-biomass yield:

ðX0 � X 0oÞ ¼ YX0=SðSo � SÞ ð10Þ

Note that in most instances the initial extended-biomass

concentration, XVo, will be equal to the initial biomass

concentration, Xo, if the initial biopolymer concentration is

Table IV. Model parameters for various biopolymer fermentations.

Santos et al. (2000) Armstrong and Johns (1997) Serrano-Carreon et al. (1998) Pena et al. (2000) Yoo and Kim (1994)

Biopolymer Dextran Hyaluronic acid Xantan Alginate PHB

Microorganism L. mesenteroides

NRRL B512(f)

S. zooepidemicus

ATCC 35246

X. campestris

NRRL-B1459

A. vinlandii

ATCC 9046

A. eutrophus

NCIB 11599

AVmax (h�1) 0.89 0.46 0.17 0.25 0.17

KVS (g/L) 3.2 1.8 11.0 2.7 5.5

YVXS 0.74 0.149 0.932 0.405 0.435

R2 0.97 0.97 0.95 0.98 0.96

Amax (h�1) 1.31 0.37 0.14 0.18 0.19

r 4 9 14 2 6

KS (g/L) 6.2 7.0 16.0 1.1 15

YXS 0.328 0.084 0.108 0.155 0.110

R2 0.99 0.99 0.99 0.99 0.99

Figure 9. Batch fermentation kinetics of L. mesenteroides NRRL B512(f) during dextran production (Santos et al., 2000). Biomass, X (.); Dextranconcentration, P (o); Sucrose concentration, S (z); Eq. 14 (—), Eq. 12 (�����), Eq. 10 (. . .. . .).

508 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 87, NO. 4, AUGUST 20, 2004

zero. The initial biomass concentration is the biomass con-

centration after inoculation and is easily determined.

The substrate concentration can also be described in

terms of the biomass yield:

ðX� XoÞ ¼ YX=SðSo � SÞ ð11Þ

Since XV is known from Eqs. 6, 7, and 10, and X can be

determined from Eqs. 8, 9, and 11, the biopolymer

concentration is given by:

P ¼ X0 � X ð12Þ

Solving the Model

One of the advantages of the proposed model is that it can

be easily solved in a sequential manner and converted to a

practical form describing all of the components as a

function of fermentation time.

Figure 10. Batch fermentation kinetics of S. zooepidemicus ATCC 35246 during hyaluronic acid production (Armstrong and Johns, 1997). Biomass, X

(.); Hyaluronic acid concentration, P (o); Glucose concentration, S (z); Eq. 14 (—), Eq. 12 (�����), Eq. 10 (. . . . . .).

Figure 11. Batch fermentation kinetics of X. campestris NRRL-B1459 during xanthan production (Serrano-Carreon et al., 1998). Biomass, X (.);Xanthan concentration, P (o); Glucose concentration, S (z); Eq. 14 (—), Eq. 12 (�����), Eq. 10 (. . .. . .).

RICHARD AND MARGARITIS: BATCH PRODUCTION OF POLY(GLUTAMIC ACID) 509

First, for the extended-biomass Eqs. 6, 7, and 10 can be

combined and integrated to yield an expression for XV andfermentation time:

A0maxt ¼ðK 0

SYX0=S þ SoYX0=S þ XoÞðYX0=S So þ X 0

oÞlnðX0=X 0

oÞ

�ðK 0

S YX0=SÞðYX0=SSo þ X 0

oÞln½ðYX0=S SoþX0

o

� X0ÞYX0=S So� ð13Þ

By combining Eqs. 8, 9, and 11, a similar expression for X

and fermentation time can be derived:

Amaxt ¼ lnðX=XoÞ þ K rS Y

rX=S

�ln X

ar� lnð�aþ XÞ

ar

� ð�aþ XÞ�1

aðr�1Þ

þ ð�aþ XÞ�2

2aðr�2Þ � � � � � � ð�aþ XÞ�ðr�1Þ

ðr� 1Þa

�XXo

ð14Þ

Figure 12. Batch fermentation kinetics of A. vinlandii ATCC 9046 during alginate production (Pena et al., 2000). Biomass, X (.); Alginate

concentration, P (o); Sucrose concentration, S (z); Eq. 14 (—), Eq. 12 (�����), Eq. 10 (. . . . . .).

Figure 13. Batch fermentation kinetics of A. eutrophus NCIB 11599 during PHB production (Yoo and Kim, 1994). Biomass, X (.); PHB concentration,

P (o); Glucose concentration, S (z); Eq. 14 (—), Eq. 12 (�����), Eq. 10 (. . . . . .).

510 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 87, NO. 4, AUGUST 20, 2004

where a = YX/S So + Xo. The equations for the proposed

model are summarized in Table II.

RESULTS AND DISCUSSION

In order to establish the use of the empirical model for

poly(glutamic acid) production and for other biopolymers,

the model was used to fit literature data reported for several

biopolymer fermentations. Batch kinetic data were ana-

lyzed for the production of poly(glutamic acid), dextran,

hyaluronic acid, xanthan, alginate, and polyhydroxybu-

tyrate (PHB). In total, 24 different datasets were analyzed

to demonstrate the fit of the empirical model. (Refer to the

original articles for a detailed analysis of the fermentation

results for each of these systems.)

Empirical Fit of Data for Poly(glutamic acid)

The values for Amax, AVmax, KS, KSV, and r for several PGA

fermentations are summarized in Table III. The extended-

biomass yield, YXV/S, and the biomass yield, YX/S, were also

determined and the initial biomass concentration, Xo, is

known. Using the equations from Table II, the model can

be solved for XV, X, P, and S according to the method

outlined above.

The proposed empirical model provides an accurate

approximation of the experimental PGA data from Richard

and Margaritis (2003b) (Fig. 3), as well as for PGA

production from B. subtilis IFO 3335 using a different

medium (Kunioka and Goto, 1994) (Fig. 4), and from

B. licheniformis using a different medium (Yoon et al.,

2000) (Fig. 5).

Of particular interest from Table III are the different

values of the relative coefficient, ‘‘r.’’ The relative

coefficient from Richard and Margaritis (2003b) is high

(r = 29) compared to that of Kunioka and Goto (r = 3) or

Yoon et al. (r = 7). This would suggest that PGA production

in this study is more nongrowth-associated than for the

other two sets of data. This is in fact the case, as can be

seen by comparing Figure 3 with Figures 4 and 5.

Table V. Model parameters for xanthan fermentations.

Garcıa-Ochoa et al.

(1990)

Moraine and Rogovin

(1971)

Shu and Yang

(1990)aShu and Yang

(1990)bLetisse et al.

(2003)

Pinches and Pallent

(1986)

Microorganism X. campestris

NRRL-B1459

X. campestris

NRRL-B1459

X. campestris

NRRL-B1459

X. campestris

NRRL-B1459

X. campestris

ATCC 13951

X. campestris

NRRL-B1459-4L II

Limiting substrate Sucrose Glucose Glucose Glucose Sucrose Glucose

AVmax (h�1) 0.059 0.11 0.272 0.098 0.102 0.281

KVS (g/L) 8.5 35.0 18.5 7.1 7.8 23.5

YVXS 0.64 0.632 0.844 0.608 0.656 0.811

R2 0.98 0.97 0.94 0.95 0.96 0.96

Amax (h�1) 0.040 0.178 0.232 0.147 0.084 0.244

r 17 36 14 49 8 16

KS (g/L) 9.1 37.0 20.9 22.9 21.8 18.2

YX/S 0.052 0.158 0.214 0.489 0.115 0.343

R2 0.99 0.99 0.99 0.99 0.99 0.99

aFermentation temperature 31jC.bFermentation temperature 22jC.

Table VI. Model parameters for alginate fermentations.

Parente et al. (1998) Parente et al. (2000) Brivonese and Sutherland (1989) Conti et al. (1994) Clementi et al. (1999)

Microorganism A. vinelandii DSM576 A. vinelandii DSM576 A. vinelandii AX P. fluorescens 1586 A. vinelandii DSM576

Limiting substrate Glucose Glucose Glucose Fructose Glucose

AVmax (h�1) 0.224 0.118 0.095 0.0568 0.135

KVS (g/L) 7.0 3.2 21.0 0.49 13.6

YVXS 0.29 0.245 0.278 0.401 0.492

R2 0.98 0.96 0.92 0.94 0.91

Amax (h�1) 0.187 0.13 0.156 0.0571 0.133

r 7 3 3 2 8

KS (g/L) 10.3 6.9 13.1 0.94 11.0

YXS 0.229 0.18 0.143 0.111 0.327

R2 0.99 0.99 0.98 0.99 0.97

RICHARD AND MARGARITIS: BATCH PRODUCTION OF POLY(GLUTAMIC ACID) 511

In order to test the accuracy of the empirical model, the

data from Richard and Margaritis (2003b) and the results

reported by Kunioka and Goto (1994) were analyzed

according to the Luedeking-Piret model and the method of

Weiss and Ollis (1980). Equations 1 and 2 are combined

and integrated to give the following (see Weiss and Ollis,

1980, for the step by step derivation):

PðtÞ ¼ Po þmXo

�eAt

1� ðXo=XmaxÞð1:0� eAÞ � 1:0

�

þ ðnXmax=AÞln�1� ðXo=XmaxÞð1:0� eAtÞ

�ð15Þ

A plot of P(t) – Po – nB(t) vs. A(t) gives the value of m,

where:

AðtÞ ¼ Xo

�eAt�

1� ðXo=XmaxÞð1:0� eAtÞ� � 1:0Þ ð16Þ

BðtÞ ¼ ðXmax=AÞln�1� ðXo=XmaxÞð1:0� eAtÞ

�ð17Þ

The straight line plot for the determination of the parameter

‘‘m’’ for Richard and Margaritis (2003b) is presented in

Figure 6. The straight line plot for the determination of

‘‘m’’ for the data from Kunioka and Goto (1994) is

presented in Figure 7. It can be seen from the plots that the

Luedeking-Piret model and the method of Weiss and Ollis

(1980) do not provide an accurate approximation of the

experimental data.

Empirical Fit of Data for Other Biopolymers

In order to establish the use of the empirical model beyond

poly(glutamic acid) production, the model was used to fit

literature data for other biopolymer fermentations. Figure 8

Table VII. Model parameters for PHB fermentations.

Lee et al. (2001) Grothe et al. (1999) Park et al. (1995) Park et al. (1995) Knee et al. (1990)

Microorganism P. fluorescens BM-07 A. latus ATCC 29714 A. eutrophus AER5 transformant A. eutrophus ATCC 17699 P. oleovorans

Limiting substrate Ammonium sulfate Ammonium (NH4+) Fructose Fructose Octanoate

AVmax (h�1) 0.209 0.059 0.244 0.213 0.67

KVS 0.47 g/L 0.094 g/L 3.5 g/L 2.3 g/L 5.5 mM

YVXS 14.7 19.02 0.44 0.44 0.209

R2 0.93 0.93 0.98 0.95 0.97

Amax (h�1) 0.153 0.073 0.201 0.202 0.335

r 2 3 4 8 2

KS 0.26 g/L 0.28 g/L 5.5 g/L 8.5 g/L 3.57 mM

YXS 4.1 8.9 0.234 0.291 0.189

R2 0.97 0.98 0.99 0.99 0.99

Figure 14. Published vs. empirical model values for X, S, and P for

xanthan production from X. campestris ATCC 13951 (Letisse et al., 2003);

a: Biomass, X; b: Sucrose, S; c: Xanthan, P.

512 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 87, NO. 4, AUGUST 20, 2004

shows the sigmoidal relationship between A and S for

dextran from Leuconostoc mesenteroides NRRL B512(f)

(Santos et al., 2000), hyaluronic acid from Streptococcus

zooepidemicus (Armstrong and Johns, 1997), xanthan from

Xanthomonas campestris NRRL-B1459 (Serrano-Carreon

et al., 1998), alginate from Azotobacter vinelandii ATCC

9046 (Pena et al., 2000), and polyhydroxybutyrate (PHB)

from Alcaligenes eutrophus NCIB 11599 (Yoo and Kim,

1994). The values for Amax, AVmax, KS, KSV, and r were

determined (Table IV) and the model was solved for XV,X, P, and S for each biopolymer fermentation according

the method outlined above.

The proposed model provides an accurate approximation

of the experimental data for dextran (Fig. 9), hyaluronic

acid (Fig. 10), xanthan (Fig. 11), alginate (Fig. 12), and

PHB (Fig. 13), as can be seen from the figures and from the

R2 values in Table IV.

From Table IV, it is interesting to note the different

values of the relative coefficient, ‘‘r.’’ For xanthan

production (Fig. 11) the r coefficient was relatively high

(r = 14), suggesting that the biopolymer formation in this

fermentation was largely nongrowth-associated. This can

be seen from Figure 11, where the xanthan concentration

was still increasing during the stationary phase. The

xanthan concentration increased from 15 g/L at the

beginning of the stationary phase to a maximum concen-

tration of 33 g/L.

For dextran (r = 4) and alginate (r = 2) production, the

relatively low r coefficients suggest that biopolymer for-

mation was largely growth-associated in these systems,

which can be seen from the fermentation curves (Figs. 9, 12).

For hyaluronic acid (r = 9) and PHB (r = 6), there was

more nongrowth-associated biopolymer formation

(Figs. 10, 13) than for dextran or alginate, but less than

that of xanthan.

Analysis of Multiple Datasets

In order to demonstrate the accuracy of the empirical

model, multiple datasets were analyzed for xanthan (6),

alginate (5), and PHB (5). Model parameters are presented

in Tables V, VI, and VII. The goodness of fit for each

dataset that was analyzed here was then determined by

calculating the correlation coefficient for the model

(predicted) values vs. the actual (experimental) values for

X, S, and P. For example, Figure 14 shows a plot of

experimental vs. model values and correlation coefficients

for X, S, and P for xanthan production from X. campestris

ATCC 13951 (Letisse et al., 2003). All correlation coeffi-

cients are presented in Table VIII and show a good corre-

lation between experimental andmodel values of X, S, and P.

CONCLUSIONS

The proposed empirical kinetic model provides an accurate

approximation of the microbial production of PGA from

B. subtilis IFO 3335. The proposed model can also be

used to provide an accurate approximation of the micro-

bial production of PGA from other bacterial strains and

other biopolymers, such as dextran, hyaluronic acid,

xanthan, alginate, and PHB. The model incorporates the

concept of extended biomass, which can be used to

Table VIII. Goodness of fit of empirical model to experimental kinetic data using R2.

Biopolymer Reference R2 Substrate, S R2 Biomass, X R2 Biopolymer, P

Alginate Parente et al. (1998) 0.987 0.996 0.956

Alginate Parente et al. (2000) 0.990 0.983 0.957

Alginate Brivonese and Sutherland (1989) 0.999 0.967 0.993

Alginate Conti et al. (1994) 0.947 0.946 0.964

Alginate Clementi et al. (1999) 0.865 0.987 0.954

Alginate Pena et al., 2000 0.982 0.989 0.970

Dextran Santos et al., 2000 0.959 0.993 0.996

Hyaluronic acid Armstrong and Johns, 1997 0.994 0.989 0.979

PGA Richard and Margaritis, 2003b 0.971 0.987 0.949

PGA Kunioka and Goto., 1994 0.958 0.989 0.949

PGA Yoon et al., 2000 0.988 0.997 0.991

PHB Yoo and Kim (1994) 0.990 0.998 0.992

PHB Lee et al. (2001) 0.947 0.967 0.934

PHB Grothe et al. (1999) 0.958 0.945 0.959

PHB Park et al. (1995) A. eutrophus AER5 transformant 0.964 0.992 0.977

PHB Park et al. (1995) A. eutrophus ATCC 17699 0.956 0.989 0.992

PHB Knee et al. (1990) 0.979 0.961 0.906

Xanthan Serrano-Carreon et al. (1998) 0.986 0.995 0.955

Xanthan Garcıa-Ochoa et al. (1990) 0.989 0.969 0.986

Xanthan Moraine and Rogovin (1971) 0.978 0.917 0.960

Xanthan Shu and Yang (1990) (31jC) 0.960 0.996 0.989

Xanthan Shu and Yang (1990) (22jC) 0.954 0.994 0.982

Xanthan Pinches and Pallent (1986) 0.984 0.982 0.993

Xanthan Letisse et al. (2003) 0.971 0.978 0.983

RICHARD AND MARGARITIS: BATCH PRODUCTION OF POLY(GLUTAMIC ACID) 513

determine Monod-type kinetic parameters for the com-

bined biomass-biopolymer extended biomass. The model

also incorporates the concept of fitting the experimental

biomass data using a sigmoidal relationship that includes

Amax and KS, as well as ‘‘r,’’ the relative coefficient. The

relative coefficient quantifies, in relative terms, the

amount of nongrowth-associated biopolymer formation.

More work is needed to further refine the model and to

test the model with other microbial fermentations.

NOMENCLATURE

kP Rate constant

KS Biomass substrate affinity constant (g/L)

KSV Extended biomass substrate affinity constant (g/L)

kX Rate constant

m Parameter of Weiss and Ollis (1980) model referring to

biopolymer production due to biomass (g P g X�1h�1)

N Nitrogen concentration (g/L)

n Parameter of Weiss and Ollis (1980) model referring to

biopolymer production due to growth (g P g X�1)

P Biopolymer concentration (g/L)

Pmax Maximum biopolymer concentration (g/L)

Po Initial biopolymer concentration (g/L)

r Relative coefficient

S Limiting substrate concentration (g/L)

So Initial substrate concentration (g/L)

t Fermentation time (h)

X Biomass concentration (g/L)

XV Extended biomass concentration (g/L)

Xmax Maximum biomass concentration (g/L)

Xo Initial biomass concentration (g/L)

XVo Initial extended biomass concentration (g/L)

YX/S Biomass yield

YXV/S Extended biomass yield

A Biomass specific growth rate (h�1)

AV Extended biomass specific growth rate (h�1)

AVmax Extended biomass maximum specific growth rate (h�1)

Amax Biomass maximum specific growth rate (h�1)

References

Armstrong D, Johns M. 1997. Culture conditions affect the molecular

weight properties of hyaluronic acid produced by Streptococcus

zooepidemicus. Appl Environ Microbiol 63:2759–2764.

Brivonese A, Sutherland I. 1989. Polymer production by a mucoid strain of

Azotobacter vinelandii in batch culture. Appl Microbiol Biotechnol

30:97–102.

Clementi F, Crudele M, Parente E, Mancini M, Moresi M. 1999.

Production and characterization of alginate from Azotobacter vine-

landii. J Sci Food Agric 79:602–610.

Conti E, Flaibani A, O’Regan M, Sutherland I. 1994. Alginate from

Pseudomonas fluorescens and P. putida: production and properties.

Microbiology 140:1125–1132.

Garcıa-Ochoa F, Garcia-Leon M, Romero A. 1990. Kinetic modeling of

xanthan production from sucrose. Chem Biochem Eng Q 4:15–20.

Garcıa-Ochoa F, Santos V, Alcon A. 1995. Xanthan gum production: an

unstructured kinetic model. Enzyme Microbiol Technol 17:206–217.

Gibbs P, Seviour R. 1996. Does the agitation rate and/or oxygen saturation

influence exopolysaccharide production by Aureobasidium pullulans

in batch culture? Appl Microbiol Biotechnol 46:503–510.

Grothe E, Moo-Young M, Chisti Y. 1999. Fermentation optimization for

the production of poly(h-hydroxybutyric acid) microbial thermo-

plastic. Enzyme Microbiol Technol 25:132–141.

Knee E Jr, Wolf M, Lenz R, Fuller R. 1990. Influence of growth conditions

on production and composition of PHA by Pseudomonas oleovorans.

In: Dawes EA, editor. Novel biodegradable microbial polymers.

Dordrecht: Kluwer. p 439–440.

Kovarova-Kovar K, Egli T. 1998. Growth kinetics of suspended microbial

cells: from single substrate-controlled growth to mixed-substrate ki-

netics. Microbiol Mol Biol Rev 62:646–666.

Kunioka M, Goto A. 1994. Biosynthesis of poly(g-glutamic acid) from L-

glutamic acid, citric acid, and ammonium sulfate in Bacillus subtilis

IFO3335. Appl Microbiol Biotechnol 40:867–872.

Lee H-J, Choi M, Kim T-U, Yoon S. 2001. Accumulation of poly-

hydroxyalkanoic acid containing large amounts of unsaturated mono-

mers in Pseudomonas fluorescens BM07 utilizing saccharides and its

inhibition by 2-bromooctanoic acid. Appl Environ Microbiol 67:

4963–4974.

Letisse F, Lindley N, Roux G. 2003. Development of a phenomenological

modeling approach for prediction of growth and xanthan gum pro-

duction using Xanthomonas campestris. Biotechnol Prog 19:822–827.

Li C, Ke S, Wu Q-P, Tansey W, Hunter N, Buchmiller L, Milas L,

Chamsangavej C, Wallace S. 2000. Experimental therapeutics, pre-

clinical pharmacology — tumor irradiation enhances the tumor-

specific distribution of poly(L-glutamic acid)-conjugated paclitaxel

and its antitumor efficacy. Clin Cancer Res 6:2829–2834.

Luedeking R, Piret E. 1959. A kinetic study of the lactic acid fermentation.

J Biochem Microbiol Technol Eng 1:393–412.

Luong J, Mulchandani A, LeDuy A. 1988. Kinetics of biopolymer

synthesis: a revisit. Enzyme Microb Technol 10:326–332.

Margaritis A, Pace G. 1985. Microbial polysaccharides. In: Comprehen-

sive biotechnology — the principles, applications and regulations of

biotechnology in industry, agriculture and medicine. Oxford: Perga-

mon Press. p 1005–1044.

Monod J. 1949. The growth of bacterial cultures. Annu Rev Microbiol

3:371–394.

Moraine R, Rogovin P. 1966. Kinetics of polysaccharide B-1459 fer-

mentation. Biotechnol Bioeng 8:511–524.

Moraine R, Rogovin P. 1971. Xanthan biopolymer production at increased

concentration by pH control. Biotechnol Bioeng 13:381–391.

Multani A, Li C, Ozen M, Yadav M, Yuu D-F, Wallace S, Pathak S. 1997.

Paclitaxel and water-soluble poly(L-glutamic acid)-paclitaxel, induce

direct chromosomal abnormalities and cell death in a murrine meta-

static melanoma cell line. Anticancer Res 17:4269–4274.

Parente E, Crudele M, Aquino M, Clemente F. 1998. Alginate production

by Azotobacter vinelandii DSM576 in batch fermentation. J Ind

Microbiol Biotechnol 20:171–176.

Parente E, Crudele M, Ricciardi A, Mancini M, Clemente F. 2000. Effect

of ammonium sulphate concentration and agitation speed on the

kinetics of alginate production by Azotobacter vinelandii DSM576 in

batch fermentation. J Ind Microbiol Biotechnol 25:242–248.

Park J-S, Park H-C, Huh T-L, Lee Y-H. 1995. Production of poly-h-hydroxybutyrate by Alcaligenes eutrophus transformants harbouring

cloned phbCAB genes. Biotech Lett 17:735–740.

Pena C, Trujillo-Roldan M, Galindo E. 2000. Influence of dissolved

oxygen tension and agitation speed on alginate production and its

molecular weight in cultures of Azotobacter vinelandii. Enzyme

Microbiol Technol 27:390–398.

Pinches A, Pallent L. 1986. Rate and yield relationships in the production

of xanthan gum by batch fermentations using complex and chemically

defined growth media. Biotechnol Bioeng 28:1484–1496.

Quinlan A. 1986. Kinetics of secondary metabolite synthesis in batch

culture when two different substrates limit cell growth and metabolite

production: xanthan synthesis by Xanthomonas campestris. Biochem

Eng 469:259–269.

Richard A, Margaritis A. 2001. Poly(glutamic acid) for biomedical

applications. CRC Crit Rev Biotechnol 21:219–232.

Richard A, Margaritis A. 2003a. Optimization of cell growth and poly

(glutamic acid) production in batch fermentation by Bacillus subtilis.

Biotechnol Lett 25:465–468.

Richard A, Margaritis A. 2003b. Rheology, oxygen transfer and molecular

514 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 87, NO. 4, AUGUST 20, 2004

weight characteristics of poly(glutamic acid) fermentation by Bacillus

subtilis. Biotechnol Bioeng 82:299–305.

Roukas T, Mantzouridou F. 2001. Effect of the aeration rate on pullulan

production and fermentation broth rheology in an airlift reactor.

J Chem Technol Biotechnol 76:371–376.

Santos M, Teixeira J, Rodrigues A. 2000. Production of dextransucrase,

dextran and fructose from sucrose using Leuconostoc mesenteroides

NRRL B512(f). Biochem Eng J 4:177–188.

Schweickart R, Quinlan A. 1989. Kinetics of xanthan production when

NH4+ limits biomass synthesis and glucose limits polysaccharide

synthesis. J Biomech Eng 111:166–171.

Serrano-Carreon L, Corona R, Sanchez A, Galindo E. 1998. Prediction of

xanthan fermentation development by a model linking kinetics, power

drawn and mixing. Proc Biochem 33:133–146.

Shu C-H, Yang S-T. 1990. Effects of temperature on cell growth and

xanthan production in batch cultures of Xanthomonas campestris.

Biotechnol Bioeng 35:454–468.

Sutherland I. 1998. Novel and established applications of microbial

polysaccharides. Trends Biotechnol 16:41–46.

Weiss R, Ollis D. 1980. Extracellular microbial polysaccharides. I.

Substrate, biomass, and product kinetic equations for batch xanthan

gum fermentation. Biotechnol Bioeng 22:859–873.

Yoo S, Kim W. 1994. Cybernetic model for synthesis of poly-a-

hydroxybutyric acid in Alcaligenes eutrophus. Biotechnol Bioeng 43:

1043–1051.

Yoon S, Do J, Lee S, Chang H. 2000. Production of poly-g-glutamic acid

by fed-batch culture of Bacillus licheniformis. Biotechnol Lett

22:585–588.

RICHARD AND MARGARITIS: BATCH PRODUCTION OF POLY(GLUTAMIC ACID) 515