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RESEARCH PAPER New Biotechnology � Volume 27, Number 4 � September 2010

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A combined metabolic/polymerizationkinetic model on the microbialproduction of poly(3-hydroxybutyrate)Giannis Penloglou1,2, Avraam Roussos2, Christos Chatzidoukas2 andCostas Kiparissides1,2

1Department of Chemical Engineering, Aristotle University of Thessaloniki, P.O. Box 472, 54124 Thessaloniki, Greece2Chemical Process Engineering Research Institute, P.O. Box 60361, 57001 Thermi, Thessaloniki, Greece

Abstract

In the present work, an integrated dynamic metabolic/polymerization kinetic model is developed for

the prediction of the intracellular accumulation profile and the molecular weight distribution of poly(3-

hydroxybutyrate) (P(3HB) or PHB) produced in microbial cultures. The model integrates two different

length/time scales by combining a polymerization kinetic model with a metabolic one. The bridging

point between the two models is the concentration of the monomer unit (i.e. 3-hydroxybutyryl-CoA)

produced during the central aerobic carbon metabolism. The predictive capabilities of the proposed

model are assessed by the comparison of the calculated biopolymer concentration and number average

molecular weight with available experimental data obtained from batch and fed-batch cultures of

Alcaligenes eutrophus and Alcaligenes latus. The accuracy of the proposed model was found to be

satisfactory, setting this model a valuable tool for the design of the process operating profile for the

production of different polymer grades with desired molecular properties.

IntroductionPolyhydroxyalkanoates (PHAs) are microbial polyesters produced

in a variety of microorganisms, under nutrient limiting condi-

tions, as intracellular carbon and energy storage compounds [1].

PHAs exhibit significant advantages compared to conventional

polymeric materials as they are produced from renewable sources,

they are non-toxic and 100% biodegradable [2]. Poly(3-hydroxy-

butyrate) (PHB) represents the most important member of the

PHAs, since it was the first PHA discovered and is still the most

studied one. It is a biopolymer with an extensive range of applica-

tions since its mechanical properties are similar to conventional

commercial polymers, such as polypropylene [3]. In spite of the

potential of the PHAs, their introduction to the world-wide market

is currently limited due to a series of economic and engineering

considerations [4]. Presently, commercially available biopolymers

are significantly more expensive than their synthetic alternatives

Corresponding author: Kiparissides, C. ([email protected]), ([email protected])

358 www.elsevier.com/locate/nbt 1871-6784/$

[5] and, therefore, represent only a small portion of the total

polymer volume capacity. The increased production cost of PHAs

as well as their efficient separation and subsequent downstream

processing are some of the problems that hinder their applicabil-

ity. Therefore, there is a growing need for the development of

novel microbial processes in order to maximize the overall process

efficiency and reduce the total production cost [6]. To this end,

advanced mathematical models can provide the means first to

understand and then to control the underlying biochemical phe-

nomena, leading to the production of biopolymers with desirable

molecular and end-use properties, in a competitive way.

The traditional approach for modeling a PHA-producing micro-

bial process is based on the assumption that an unstructured, non-

segregated biophase is growing in a spatially homogeneous envir-

onment [7–9]. The specific biomass growth rate is commonly

described by an empirical equation and, consequently, these

so-called ‘macroscopic’ models cannot predict the process beha-

vior under a wide range of fermentation conditions. Despite the

- see front matter � 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nbt.2010.02.001

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New Biotechnology �Volume 27, Number 4 � September 2010 RESEARCH PAPER

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importance of the central carbon metabolism, responsible for the

accumulation of biopolymers in bacterial cells, only a limited

number of publications have dealt with the detailed (i.e. struc-

tured) mathematical modeling of metabolic pathways in cells. The

main reasons are the lack of information regarding the reaction

kinetics, the metabolic regulation as well as the variations intro-

duced by changes in the physiological conditions of the culture.

Leaf and Srienc [10], presented a metabolic model for the

description of the intracellular PHB synthesis in Alcaligenes eutro-

phus that accounted for the regulatory behavior of the cells. The

authors showed that complex, mechanistic reaction rate expres-

sions (i.e. derived from a ping-pong Bi-Bi reaction mechanism)

resulted in significantly more accurate results than the simplified,

irreversible Michaelis–Menten kinetic model. A similar kinetic

model was employed by van Wegen et al. [11] for the investigation

of PHB accumulation in Escherichia coli. The authors concluded

that the PHB accumulation rate was highly sensitive to parameters

such as the culture’s pH and the intracellular concentrations of the

acetyl-coenzyme A and coenzyme A. Dias et al. [12] developed a

mathematical model for the prediction of PHB and residual bio-

mass concentrations in mixed microbial cultures based on a

simplified metabolic network comprising seven reactions. In con-

sistency with experimental observations, the model predicted that

the specific PHB productivity rate increased under nitrogen-lim-

ited conditions as well as that the PHB accumulation exhibited a

self-inhibiting behavior. In a follow-up work, the authors pre-

sented a segregated model, accounting for a number of cell popu-

lations characterized by different kinetic growth rates [13].

Despite the extensive studies on the metabolism of biopolymer-

producing bacteria [14–16], the detailed mechanisms of polymer

accumulation and the associated molecular weight distribution

(MWD) are not sufficiently understood [17]. It should be noted

that the MWD is, to a large extent, responsible for the end-use

properties of biopolymers, including their physical, chemical,

mechanical and rheological characteristics. For example, the

mechanical properties of biopolymers considerably deteriorate

when the weight average molecular weight (Mw) is lower than

4 � 105 Da [18]. Moreover, for thermoplastic applications the

value of Mw should be higher than 6 � 105 Da [19]. The molecular

weight distribution of biopolymers is affected by a variety of

variables, including the host microorganism, the substrate type

and concentration, the nutritional (e.g. nitrogen source concen-

tration) and operating conditions (e.g. pH and temperature), as

well as the downstream polymer separation and processing. Typi-

cal values of the number average molecular weight (Mn) of PHB,

range from 8 � 104 to 1 � 106 Da [3,6,20] although extreme values

as high as 2 � 107 have also been reported in mutant strains

[21,22].

Due to a number of unknown factors (e.g. the lack of informa-

tion on key aspects of the intracellular polymerization-degrada-

tion mechanisms) and limited number of accurate experimental

measurements on MWD, only few studies have dealt with the

prediction of the molecular weight of biopolymers in bacterial

cultures. Bradel and Reichert [23] developed a mathematical

model for the prediction of the molecular weight distribution of

PHB produced in flask cultures of A. eutrophus under different pH

values. The applicability of the proposed model was limited to the

special case where the fructose (as carbon source) concentration

remained constant, assuming in addition a constant monomer

concentration. Moreover, chain transfer and polymer degradation

reactions were assumed to be negligible, an assumption that does

not hold true in wild-type bacteria. Mantzaris and coworkers

[24,25] presented a rigorous population balance model in contin-

uous form based on steady-state experimental data that accounted

for either a constant or a chain length dependent propagation rate.

However, their calculations were based on a subjective and arbi-

trary assumption for the average propagation rate of PHB chains

(i.e. 2 monomer units/chain/s). Moreover, the kinetic model did

not include a biopolymer degradation mechanism.

The present paper deals with the development of an integrated

metabolic/polymerization kinetic model for the prediction of the

concentration and molecular weight distribution of PHB in bac-

terial cultures. The proposed approach combines a realistic

description of cell metabolism (i.e. monomer concentration is

not assumed to be constant) with a polymerization kinetic model

comprising initiation, propagation, chain transfer and degrada-

tion reactions. The proposed modeling framework is developed

and tested in a system of A. eutrophus utilizing fructose as carbon

source; however, it can be adjusted accordingly to describe the

behavior of different microbial systems. This means that the

proposed approach is generic enough to be applied to any PHA

production system, regardless of the choice of bacterial strain or

operating conditions. Demonstrating further the applicability of

the model, the latter is employed for the dynamic simulation of

the Alcaligenes latus fermentative production of PHB, using sucrose

as carbon source.

In what follows, the metabolic mechanism for the synthesis and

degradation of PHB is described and the differential equations

regarding the mass conservation of the various intracellular spe-

cies are derived. Subsequently, model predictions are compared

with experimental measurements on PHB concentration and

number average molecular weight obtained from batch and fed-

batch cultures of A. eutrophus (later known as Ralstonia eutropha,

Wautersia eutropha, Cupriavidus necator, etc.).

Model developmentDepending on the bacterium type and carbon source utilized,

different metabolic pathways can be established to describe the

microbial production of PHAs [2]. Carbohydrates constitute a very

common carbon source for the fermentative production of PHB in

Alcaligenes species bacteria. The central aerobic carbon metabolism

that leads to the production of PHB in Alcaligenes species bacteria is

depicted in Fig. 1 [26,27]. The carbon source (e.g. a carbohydrate,

fructose in this case) is initially converted into acetyl-coenzyme A

(AcCoA) through the Entner–Doudoroff pathway. The AcCoA is an

intermediate metabolite for the synthesis of PHB via a sequence of

three enzymatic reactions. In the first reaction, two AcCoA mole-

cules are condensed by the catalytic action of the enzyme 3-

ketothiolase (phaA) to form one molecule of acetoacetyl-coen-

zyme A (Ac-AcCoA). Subsequently, Ac-AcCoA is reduced by acet-

oacetyl-CoA reductase (phaB) to 3-hydroxybutyryl-CoA (3-

HBCoA) at the expense of NADH. In the third enzymatic reaction,

the monomer unit 3-HBCoA is polymerized into PHB following a

polymerization mechanism catalyzed by synthase (phaC). Finally,

under the action of depolymerase (phaZ) the accumulated PHB is

hydrolyzed into 3-hydroxybutyrate (3-HB). Subsequently,

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FIG. 1

Metabolic pathway for the intracellular synthesis and degradation of PHB in Alcaligenes species.

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3-hydroxybutyrate is converted to AcCoA which is utilized as

carbon and energy source under carbon starvation conditions

(i.e. substrate depletion). Notice that while a simplified pathway

of the central aerobic carbon metabolism of A. eutrophus is con-

sidered here, any other metabolic pathway belonging to a different

strain can be employed. By the selection of the appropriate

detailed metabolic model it is possible to apply the proposed

mathematical framework to different microbial systems or/and

different carbon sources (e.g. carbohydrates or fatty acids).

The last two enzymatic steps described above, can be further

analyzed into a set of comprehensive reactions catalyzed by the

presence of PHA synthase and depolymerase that control the mole-

cular formation and degradation of PHB polymer chains (see Fig. 2).

The above kinetic mechanism is representative of both micellar and

budding models have been identified in bacteria regarding the

formation of PHB granules. In both theories, two PHA synthase

molecules, via their two thiol groups (i.e. active sites), derived from

two cysteine residues of the enzyme subunits, form a homodimer

with two catalytic active sides (i.e. two thiol groups) [28–30]. The

catalytic mechanism of the PHB synthesis is initiated by the addi-

tion of a monomer (3-HBCoA) molecule to one of the two active

sites. Chain propagation occurs via the reaction of the anchored

PHB chain on one thiol group of a synthase dimer with to the 3-

HBCoA molecule, which is bound to the other active site of the same

homodimer. Active polymer chains undergo a chain transfer reac-

tion to an agent (X) (e.g. water – in this case – or an enzyme with a

water molecule in its active from) resulting in the formation of an

inactive (dead) polymer chain with simultaneous release of a

synthase molecule. Finally, inactive polymer chains may undergo

chain-end degradation catalyzed by depolymerase. The cyclic nat-

ure of the PHB metabolism (i.e. simultaneous accumulation and

turnover) in bacterial cells under nitrogen limitation conditions has

been demonstrated by Doi et al. [31] and Taidi et al. [32]. Notice that

by appropriate modifications to the polymerization kinetic

mechanism, it is possible to apply the proposed framework to

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systems with more than one carbon sources in order to predict

the formation of copolymer chains.

In the present study, the following polymerization–depolymer-

ization kinetic scheme was employed based on the work of Kawa-

guchi and Doi [33]:

Initiation

E-SHþM#�!km1E-SH-M#�!ki

P1-ESþ CoA-SH (1)

Propagation

Pn-ESþM#�!km2Pn-ES-M#�!

kp

Pnþ1-ESþCoA-SH (2)

Chain Transfer

Pn-ESþH2O�!ktDn þ E-SH (3)

Degradation

Dn þ E-OH�!kdDn�1 þD1 þ E-OH (4)

where E-SH, M#, CoA-SH and E-OH denote the concentrations of

synthase dimer, monomer coenzyme A complex (M-SCoA), coen-

zyme A and depolymerase, respectively. Furthermore, Pn-ES (Pn),

Pn-ES-M# (P�n) and Dn are the corresponding concentrations of

active, intermediate and inactive polymer chains with a degree

of polymerization equal to n. In contrast to the original polymer-

ization model proposed by Kawaguchi and Doi [33], initiation is

assumed to occur in two steps with the formation of an inter-

mediate ‘synthase–monomer’ complex (E-SH-M#). Similarly, a

two-step reaction is also considered for polymer chain propagation

where an intermediate ‘active polymer–monomer’ complex (Pn-

ES-M#) is initially formed.

In the following mathematical model developments, it is

assumed that the polymerase (PhaC), depolymerase (PhaZ) and

chain transfer agent concentrations are constant throughout the

course of polymerization [33,34]. Since the enzyme activity is

known to depend on the total cell concentration [35], the above


FIG. 2

Detailed kinetic mechanism of the intracellular polymerization-degradation of PHB in Alcaligenes species.

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assumption will be realistic when the concentration of residual

biomass remains constant (e.g. under nitrogen limitation condi-

tions). Moreover, it is considered that the rate-limiting step in the

degradation mechanism is the binding of the inactive polymer

chain to depolymerase. Finally, the effects of population hetero-

geneity (i.e. segregation of cells) and mass-transfer limitation

phenomena are not taken into account. Based on the postulated

kinetic scheme and model assumptions, the net production rates

for the various intracellular molecular species will be given by the

following equations:

Active polymer chains of length ‘‘n’’

d Pn½ �dt¼ ki E-SH-M#

� �dðn� 1Þ � km2 Pn½ � M#

� �þ kp P�n�1

� �Hðn� 1Þ � k�t Pn½ � n ¼ 1;2; :::;1 (5)

Intermediate polymer chains of length ‘‘n’’

d P�n� �dt¼ km2 Pn½ � M#

� �� kp P�n

� �n ¼ 1; 2; :::;1 (6)

Inactive polymer chains of length ‘‘n’’



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d Dn½ �dt¼ k�t Pn½ � � k�d Dn½ � þ k�d Dnþ1½ � n ¼ 2;3; :::;1 (7)

Monomer

d M#� �dt

¼ JM tð Þ � k�m1 M#� �

� km2 M#� �X1

n¼1

Pn½ � (8)

Synthase–Monomer complex

d E-SH-M#� �

dt¼ k�m1 M#

� �� ki E-SH-M#

� �(9)

where k�m1 ¼ km1 E-SH½ �, k�d ¼ kd E-OH½ � and k�t ¼ kt H2O½ �. The Kro-

necker delta function, d(x), and the Heaviside step function, HðxÞ,are defined by the following equations:

d xð Þ ¼ 1; if x ¼ 00; otherwise

�(10)

TABLE 1

Point estimates and 95% confidence limits for the parameters ofthe polymerization–depolymerization model.

Parameter Point Estimate 95% confidence interval

ki (h�1) 0.62 � 104 0.53–0.71 � 104

kp (h�1) 0.46 � 105 0.41–0.51 � 105

k�t (h�1) 0.14 � 101 0.13–0.15 � 101

k�m1 (h�1) 0.11 � 10�3 0.09–0.13 � 10�3

km2 (l/mol/h) 0.86 � 107 0.71–1.01 � 107

k�d (h�1) 0.83 � 102 0.76–0.90 � 102

YM=S 0.35 � 10�2 0.33–0.37 � 10�2

HðxÞ ¼ 1; if x>00; if x � 0

�(11)

Finally, JM ðtÞ denotes the monomer production rate (flux) from

upstream metabolic steps. Notice that polymer chains with length

n equal to one (i.e. 3-hydroxybutyrate) are assumed to be instan-

taneously transformed to AcCoA and, therefore, are not included

in the respective population balance (i.e. Eq. (7)). The system of

differential Eqs. (5)–(9) can be integrated in time provided that the

monomer production rate term, JM ðtÞ, is known. This rate can be

calculated by either a kinetic model of cell metabolism or by

metabolic flux analysis. In general, JM ðtÞ will depend on the

metabolic pathway, the assimilated carbon source and, moreover,

the vectors k, Y, C and J denoting the reaction kinetic constants,

the yield coefficients and the upstream metabolite concentrations

and fluxes, respectively:

JM tð Þ ¼ g k;Y;C; J; tð Þ (12)

It should be noted that the number of population balance

equations for the active, intermediate and inactive polymer chains

in Eqs. (5)–(7) depend on the maximum degree of polymerization

that typically ranges from 106 to 107. Consequently, the computa-

tional effort associated with the solution of the complete set of

differential equations becomes prohibitively high even for the

contemporary high-end processors. To deal with this limitation

and reduce the dimensionality of the problem a numerical method

(i.e. the fixed pivot technique) was employed. Following the

developments of Kumar and Ramkrishna [36], polymer chains

can only exist at predefined discrete chain lengths xi, called pivots.

If a polymer chain is formed at a length u between two pivots then

it is assigned to the two adjacent pivots with appropriate fractions

so that any two moments of the chain length distribution are

conserved. A more detailed description of the fixed pivot techni-

que is presented in Appendix A and in the original work of Saliakas

et al. [37]. In this work, a mixed uniform-logarithmic discretization

rule was adopted so that the number of continuous-discrete dif-

ferential equations per polymer chain population was reduced to

80-100.

Results and discussionThe proposed metabolic/polymerization kinetic model of this

study was validated against experimental data reported by Kawa-

guchi and Doi [33] that correspond to the fermentation of


Alcaligenes eutrophus H16 (ATCC 17699), in non-growth condi-

tions. According to that work, a two-stage cultivation profile was

employed. Firstly, the bacterial cells were grown in a nutrient-rich

medium without accumulating any amount of PHB. Subsequently,

once a high-density cell population was obtained, cells were

harvested and transferred into a nitrogen source free mineral

medium that favored the PHB accumulation, while the residual

biomass remained constant. In the case that the biomass concen-

tration is constant, the monomer production rate, JM ðtÞ, can be

assumed to be proportional to the fructose consumption rate,

JFðtÞ:JM tð Þ ¼ YM=F � JF tð Þ (13)

where YM=F (mol of monomer produced/mol of fructose con-

sumed) is a monomer to substrate yield coefficient. The latter is

considered constant throughout the second stage of cultivation.

The kinetic rate constants (i.e. ki, k�m1, km2, kp, k�t , k�d) and the yield

coefficient YM=F appearing in the system of differential and alge-

braic Eqs. (5)–(13) were estimated based on a set of experimental

data of Kawaguchi and Doi [33], using a general non-linear para-

meter estimator (M. Caracotsios, Model parametric sensitivity

analysis and nonlinear parameter estimation. Theory and applica-

tions, PhD thesis, University of Wisconsin, Madison, WI, 1986).

The values of the estimated parameters as well as their respective

95% confidence intervals are reported in Table 1. Note that the

values of these parameters are strongly affected by the metabolic

pathway and the experimental conditions (i.e. the Entner–

Doudoroff pathway occurring under non-growth conditions

due to nitrogen limitation). Subsequently, the model was

employed for the calculation of the PHB concentration, MWD

and Mn for three different cases, specifically: (i) a batch culture with

an initial fructose concentration SF(0) = 5 g/l, (ii) a batch culture

with an initial fructose concentration SF(0) = 10 g/l and (iii) a fed-

batch culture with initial fructose concentration SF(0) = 5 g/l and a

pulse feeding of 5 g fructose per liter of culture volume at time

t = 24 h.

Batch fermentation: cases (i) and (ii)The dynamic evolution of the fructose concentration for cases (i)

and (ii) is depicted in Fig. 3. As can be seen, the fructose concen-

tration decreases linearly with time, at a rate equal to

JF ’0:85 g=l=h, independently of its initial concentration. As a

result, the carbon source is completely depleted in 6 and 12 h

(twofold time in case (ii)), respectively. In Fig. 4, the model

predictions are compared with experimental measurements on

PHB production. Apparently, there is a good agreement between


FIG. 3

Comparison of model predictions with experimental measurements of thefructose concentration for cases (i) and (ii).

FIG. 5

Dynamic evolution of the molecular weight distribution of PHB for case (i).

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model and experimental results. Notice that during the ‘‘feast’’

phase (i.e. the first 6 and 12 h of cultivation, for cases (i) and (ii),

respectively), the rate of polymer accumulation is approximately

independent of the initial fructose concentration. However, by the

time that the fructose concentration has been depleted, the mono-

mer production is terminated and the PHB concentration starts

decreasing due to the dominant action of the PHB depolymerase.

The inactive monomer (3-hydroxybutyrate), produced by the PHB

degradation reaction, is rapidly transformed into AcCoA. It is

pointed out that the maximum PHB concentrations, achieved

in both cases at the time point where the carbon source is depleted,

are 1.50 and 3.10 g/l, resulting in a polymer to fructose yield, YP/S,

equal to 0.300 and 0.310 g/g, respectively.

The predicted molecular weight distributions of PHB for the two

different initial fructose concentrations are depicted in Figs. 5 and

6. As can be seen, the MWDs evolve rapidly to a maximum peak

FIG. 4

Comparison of model predictions with experimental measurements of thePHB concentration for cases (i) and (ii).

value (i.e. at 7 h and 13 h for cases (i) and (ii), respectively) that

corresponds to the respective maximum value for the number

average molecular weight, Mn. From this point onward, the peak

value of the MWD decreases reflecting the respective decreases in

the PHB concentration and Mn. In Fig. 7, model predictions are

compared with experimental measurements for Mn. Apparently,

for both cases there is a satisfactory agreement of model results

with the corresponding experimental data. Notice that for case (ii),

the final value of Mn is slightly higher than the respective one for

case (i) (i.e. approximately 640,000 and 850,000 g/mol, respec-

tively). This is attributed to the early cease of the molecular

development of the polymer chains in case (i), due to the faster

monomer exhaustion under lower initial fructose concentration.

Moreover, the predicted maximum values of Mn (i.e. approxi-

mately 900,000 and 950,000 g/mol) appear in both cases when

the fructose concentration is depleted.

FIG. 6

Dynamic evolution of the molecular weight distribution of PHB for case (ii).



FIG. 7

Comparison of model predictions with experimental measurements of the

PHB number average molecular weight of PHB for cases (i) and (ii). FIG. 9


PHB concentration in case (iii).

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Fed-batch fermentation: case (iii)The time evolution of fructose concentration for case (iii) is

depicted in Fig. 8. Note that the consumption rate of both the

initially loaded fructose and the fructose pulse (occurred after the

complete consumption of the first one) is the same in the batch

case (i.e. equal to 0.85 g/l). After the second pulse, the concentra-

tion of fructose reached its initial value (5 g/l) and once again the

consumption rate was identical. In Fig. 9, a good agreement

between the model predictions and the experimental measure-

ments on the PHB concentration is depicted. The maximum

amount of PHB, 2.55 g/l, is attained at about 7 h after the intro-

duction of the fructose pulse, corresponding to a polymer to

fructose yield, YP/S, equal to 0.255 g/g. It should be noted that

the PHB concentration in this case did not increase beyond the

maximum value attained in case (ii), since the total PHB accumu-

lation for a given amount of substrate depends on the amount of

the residual biomass. Moreover, the bacterial culture remained in

‘‘famine’’ conditions for approximately 17 h, where the accumu-

FIG. 8


fructose concentration in case (iii).


lated PHB was intracellularly consumed (around 0.3 g/l) as carbon

and energy source for maintenance.

The dynamic evolution of the respective molecular weight

distribution is presented in Fig. 10. As can be seen, the MWD

reaches an initial maximum peak value at about t = 7 h. At that

time, the substrate concentration is approximately equal to zero.

Subsequently, polymer degradation dominates over the develop-

ment of the polymer chains. However, after the introduction of

the fructose pulse feeding at t = 24 h, the polymer chains start

growing again and the MWD reaches a new peak value at, approxi-

mately t = 31 h. As can be seen in Fig. 11, the maximum value for

Mn, 950,000 g/mol, is attained at about t = 7 h. Notice that this

maximum value is not exceeded after the introduction of the

second fructose pulse and is almost the same to the maximum

Mn value obtained under batch fermentation conditions (see case

(ii)).

FIG. 10

Dynamic evolution of the molecular weight distribution of PHB for case (iii).


FIG. 11


PHB number average molecular weight for case (iii).

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Application to other PHA production systemsIn order to make evident that the present modeling approach can

be efficiently applied to other microbial systems under different

conditions, the proposed model was revised for the growth-asso-

ciated PHB production by Alcaligenes latus and tested against

experimental data produced in a 2-l batch culture (BioFlo 110-

New Brunswick Scientific). The fermentation conditions are

described in the original work of Wang and Lee [38]. In this case,

FIG. 12

Comparison of model predictions with experimental measurements of (a)

sucrose, ammonium sulfate and residual biomass concentrations and (b) PHB

concentration and number average molecular weight for the cultivation of

Alcaligenes latus.

the metabolic pathway toward the PHB production starts from

sucrose. The mathematical model was expanded to account for the

simultaneous growth of the residual biomass in parallel with the

PHB accumulation and the consumption of ammonium sulfate,

while the part of the model that describes the polymerization

kinetics remained the same. In Fig. 12(a), the dynamic evolution of

the nutrient concentrations (i.e. sucrose and ammonium sulfate)

and the respective production of the residual biomass are pre-

sented. Along the time evolution of the culture, the PHB accu-

mulation rate and the built up of the PHB are shown in Fig. 12(b).

The model parameters were properly tuned to make the model

consistent with the new conditions. The excellent agreement of

the model predictions with the respective experimental measure-

ments proves the general applicability of the model to various

PHAs production systems.

ConclusionsAn integrated metabolic/polymerization model was developed for

the prediction of the PHB concentration and molecular weight

distribution in bacterial cultures. A cell metabolism model was

employed to calculate the monomer unit production rate from the

carbon substrate. The calculated rate was then employed as input

to the polymerization kinetic model to predict the PHB concen-

tration and MWD. The combined model was applied to the

investigation of Alcaligenes species fermentation under different

operating policies. It was found that the fed-batch operating policy

did not result in an increase of either the total PHB concentration

or the corresponding maximum value of Mn, as compared to the

batch operation for the same total fructose consumption. This

behavior can be explained by the absence of residual biomass

growth. In view of the above conclusions and the model-based

interpretation of the experimental results, it is evident that the

present metabolic/kinetic modeling approach can be further

improved to capture additional phenomena of different length

and time scales in order to successfully address the problem of the

optimal operation of the microbial processes for the production of

desired PHA grades.

AcknowledgementsThis work was carried out with the financial support of EC under

the IP-project titled ‘Sustainable Microbial and Biocatalytic

Production of Advanced Functional Materials’

(BIOPRODUCTION/NMP-2-CT-2007-026515).

Appendix AIn the present work the fixed pivot technique (FPT) of Kumar and

Ramkrishna [36] was properly adapted for solving Eqs. (5)–(7).

Assuming that the ‘active’, ‘intermediate’ and ‘inactive’ polymer

chain concentrations remain constant in the discrete chain length

domain x j�1; x j

h i, one can define the following lumped ‘active’,

‘intermediate’ and ‘inactive’ polymer chain concentrations, P j, P�j

and D j, corresponding to the ‘j’ element:

P j ¼Zx j

x j�1

Pn½ � dx; P�j ¼

Zx j

x j�1

P�n� �

dx; D j ¼Zx j

x j�1

Dn½ � dx (A1)

Accordingly, the chain length domain is discretized into a num-

ber of nt node points (pivots) using a logarithmic discretization rule.



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If the length of a new polymer chain, u, lies in a position between

two pivots, it is assigned to the two adjacent pivots with the

appropriate weights so that two moments of the chain length

distribution (i.e. number and mass of polymer chains) are con-

served. Notice that polymer chains formed via chain initiation

and chain transfer reactions always correspond to the defined node

points. From the application of the FPT to Eqs. (5)–(7), the following

system of continuous-discrete differential equations is obtained:

Lumped molar balance equations for the ‘active’ polymer

chains

dP j

dt¼ ki½E-SH-M#�dð j� 1Þ � km2P j½M#� þ kpHð j� 1Þ

Xj

k¼1

P�kA j;k � k�t P j

j ¼ 1;2; . . . ;nt (A2)

Lumped molar balance equations for the ‘intermediate’ polymer

chains

dP�j

dt¼ km2P j M#

� �� kpP

�j j ¼ 1;2; . . . ;1 (A3)

Lumped molar balance equations for the ‘inactive’ polymer chains

dD j

dt¼ k�t P j � kdD j þ k�d

Xjþ1

k¼ j

DkB j;k j ¼ 2;3; . . . ; nt (A4)


The matrices Aj;k and B j;k are defined as follows:

Aj;k ¼

x jþ1 � xt

x jþ1 � x jx j � xt � x jþ1

xt � x j�1

x j � x j�1x j�1 � xt � x j

8>><>>: where xt ¼ xk þ x1 (A5)

Bj;k ¼

x jþ1 � xt

x jþ1 � x jx j � xt � x jþ1

xt � x j�1

x j � x j�1x j�1 � xt � x j

8>><>>: where xt ¼ xk � x1 (A6)

The total polymer chain length distribution of polymer chains is

calculated from the sum of the individual ‘active’, ‘intermediate’

and ‘inactive’ polymer chain distributions:

T j ¼ P j þ P�j þD j (A7)

Finally, the number average molecular weight was calculated by

the following equation:

Mn ¼Pnt

j¼1 xjT jPntj¼1 T j

!MW (A8)

where MW is the molecular weight of the repeating unit.

References

[1] Reddy, C.S.K. et al. (2003) Polyhydroxyalkanoates: an overview. Bioresour.

Technol. 87, 137–146

[2] Madison, L.L. and Huisman, G.W. (1999) Metabolic engineering of poly(3-

hydroxyalkanoates): from DNA to plastic. Microbiol. Mol. Biol. Rev. 63,

21–53

[3] Anderson, A.J. and Dawes, E.A. (1990) Occurrence, metabolism, metabolic

role, and industrial uses of bacterial polyhydroxyalkanoates. Microbiol. Rev. 54,

450–472

[4] Lee, S.Y. et al. (1999) Recent advances in polyhydroxyalkanoate production by

bacterial fermentation: mini-review. Int. J. Biol. Macromol. 25, 31–36

[5] Philip, S. et al. (2007) Polyhydroxyalkanoates biodegradable polymers with a

range of applications. J. Chem. Technol. Biotechnol. 82, 233–247

[6] Verlinden, R.A.J. et al. (2007) Bacterial synthesis of biodegradable

polyhydroxyalkanoates. J. Appl. Microbiol. 102, 1437–1449

[7] Heinzle, E. and Lafferty, R.M. (1980) A kinetic model for growth and synthesis of

poly-b-hydroxybutyric acid (PHB) in Alcaligenes eutrophus H 16. Eur. J. Appl.

Microbiol. Biotechnol. 11, 8–16

[8] Mulchandani, A. et al. (1989) Substrate inhibition kinetics for microbial growth

and synthesis of poly-b-hydroxybutyric acid by Alcaligenes eutrophus ATCC

17697. Appl. Microbiol. Biotechnol. 30, 11–17

[9] Shahhoseini, S. (2004) Simulation and optimisation of PHB production in fed-

batch culture of Ralstonia eutropha. Proc. Biochem. 39, 963–969

[10] Leaf, T.A. and Srienc, F. (1998) Metabolic modeling of polyhydroxybutyrate

biosynthesis. Biotechnol. Bioeng. 57, 557–570

[11] van Wegen, R.J. et al. (2001) Metabolic and kinetic analysis of poly(3-

hydroxybutyrate) production by recombinant Escherichia coli. Biotechnol. Bioeng.

74, 70–80

[12] Dias, J.M.L. et al. (2005) Mathematical modelling of a mixed culture cultivation

process for the production of polyhydroxybutyrate. Biotechnol. Bioeng. 92,

209–222

[13] Dias, J.M.L. et al. (2008) Segregated population balance model of microbial

cultures for the production of PHA. Sustainable Microbial and Biocatalytic

Production of Advanced Functional Materials: 2nd Annual Meeting Proceedings,

Thessaloniki, 2–3 October. pp. 288–292

[14] Byrom, D. (1993) The synthesis and biodegradation of polyhydroxyalkanoates

from bacteria. Int. Biodeter. Biodegr. 31, 199–208

[15] Kidwell, H.E. et al. (1995) Regulated expression of the Alcaligenes eutrophus

pha biosynthesis genes in Escherichia coli. Appl. Environ. Microbiol. 61,

1391–1398

[16] Wieczorek, R. et al. (1996) Occurrence of polyhydroxyalkanoic acid granule-

associated proteins related to the Alcaligenes eutrophus H16 GA24 protein in other

bacteria. FEMS Microbiol. Lett. 135, 23–30

[17] Steinbuchel, A. and Hein, S. (2001) Biochemical and molecular basis of microbial

synthesis of polyhydroxyalkanoates in microorganisms. Adv. Biochem. Eng.

Biotechnol. 71, 81–123

[18] Cox, M.K. (1995) Recycling Biopol – composting and material recycling. Pure

Appl. Chem. 32, 607–612

[19] Luzier, W.D. (1992) Materials derived from biomass/biodegradable materials.

Proc. Natl. Acad. Sci. U.S.A. 89, 839–842

[20] Khanna, S. and Srivastava, A.K. (2005) Recent advances in microbial

polyhydroxyalkanoates. Process Biochem. 40, 607–619

[21] Kusaka, S. et al. (1997) Molecular mass of poly[(R)-3-hydroxybutyric acid]

produced in a recombinant Escherichia coli. App. Microbiol. Biotechnol. 47,

140–143

[22] Choi, J. and Lee, S.Y. (2004) High level production of supra molecular weight

poly(3-hydroxybutyrate) by metabolically engineered Escherichia coli. Biotechnol.

Bioprocess Eng. 9, 196–200

[23] Bradel, R. and Reichert, K.-H. (1993) Modeling of molar mass distribution of

poly(D-(�)-3-hydroxybutyrate) during bacterial synthesis. Makromol. Chem. 194,

1983–1990

[24] Mantzaris, N.V. et al. (2002) A population balance model describing the

dynamics of molecular weight distributions and the structure of PHA copolymer

chains. Chem. Eng. Sci. 57, 4643–4663

[25] Iadevaia, S. and Mantzaris, N.V. (2006) Genetic network driven control of PHBV

copolymer composition. J. Biotechnol. 122, 99–121

[26] Sudesh, K. et al. (2000) Synthesis, structure and properties of

polyhydroxyalkanoates biological polyesters. Prog. Polym. Sci. 25, 1503–1555

[27] Lutke-Eversloh, T. et al. (2001) Identification of a new class of biopolymer:

bacterial synthesis of a sulfur-containing polymer with thioester linkages.

Microbiology 147, 11–19

[28] Muh, U. et al. (1999) PHA synthase from Chromatium vinosum: cysteine 149 is

involved in covalent catalysis. Biochemistry 38, 826–837

[29] Rehm, B.H.A. and Steinbuchel, A. (1999) Biochemical and genetic analysis of

PHA synthases and other proteins required for PHA synthesis. Int. J. Biol.

Macromol. 25, 3–19

[30] Zhang, S. et al. (2000) Kinetic and mechanistic characterization of the

polyhydroxybutyrate synthase from Ralstonia eutropha. Biomacromolecules 1,

244–251


[31] Doi, Y. et al. (1990) Cyclic nature of poly(3-hydroxyalkanoate) metabolism in

Alcaligenes eutrophus. FEMS Microbiol. Lett. 67, 165–170

[32] Taidi, B. et al. (1995) Turnover of poly(3-hydroxybutyrate) (PHB) and its

influence on the molecular mass of the polymer accumulated by Alcaligenes

eutrophus during batch culture. FEMS Microbiol. Lett. 129, 201–205

[33] Kawaguchi, Y. and Doi, Y. (1992) Kinetics and mechanism of synthesis and

degradation of poly(3-hydroxybutyrate) in Alcaligenes eutrophus. Macromolecules

25, 2324–2329

[34] Haywood, G.W. et al. (1989) The importance of PHB-synthase substrate

specificity in polyhydroxyalkanoate synthesis by Alcaligenes eutrophus. FEMS

Microbiol. Lett. 57, 1–6

[35] Lee, Y.-H. et al. (2000) Construction of transformant Alcaligenes latus enforcing its

own cloned phbC gene and characterization of poly-b-hydroxybutyrate

biosynthesis. Biotechnol. Lett. 22, 961–967

[36] Kumar, S. and Ramkrishna, D. (1996) On the solution of population balance

equationsby discretization. I.Afixedpivot technique.Chem.Eng.Sci.51,1311–1332

[37] Saliakas, V. et al. (2007) Dynamic optimization of molecular weight distribution

using orthogonal collocation on finite elements and fixed pivot methods: an

experimental and theoritical investigation. Macromol. React. Eng. 1, 119–136

[38] Wang, F. and Lee, S.Y. (1997) Poly(3-hydroxybutyrate) production with high

productivity and high polymer content by a fed-batch culture of Alcaligenes latus

under nitrogen limitation. Appl. Environ. Microbiol. 63, 3703–3706


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