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A kinetic model for growth and biosynthesis of medium-chain-length poly-(3-hydroxyalkanoates) in Pseudomonas putida


A kinetic model is presented giving a mathematical description of batch culture of Pseudomonas putida PGA1 grown using saponified palm kernel oil as carbon source and ammonium as the limiting nutrient. The growth of the micro-organism is well-described using Tessier-type model which takes into account the inhibitory effect of ammonium at high concentrations. The ammonium consumption rate by the cells is related in proportion to the rate of growth. The intracellular production of medium-chain-length poly-(3-hydroxyalkanoates) (PHA MCL) by P. putida PGA1 cells is reasonably modeled by the modified Luedeking-Piret kinetics, which incorporate a function of product synthesis inhibition (or reduction) by ammonium above a threshold level.

Ammonium; Kinetic; Medium-chain-length PHA; P. putida; Substrate-inhibition


A kinetic model for growth and biosynthesis of medium-chain-length poly-(3-hydroxyalkanoates) in Pseudomonas putida

M. S. M. AnnuarI,* * Tho whom correspondence should be addressed ; I. K. P. TanI; S. IbrahimII; K. B. RamachandranIII

IInstitute of Biological Sciences, University of Malaya, Phone: 603-7967-6740, Fax: 603-7967-4178, Zip Code: 50603, Kuala Lumpur, Malaysia. E-mail:

IIDepartment of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

IIIDepartment of Biotechnology, Indian Institute of Technology (IIT) Madras, Chennai-600036, India


A kinetic model is presented giving a mathematical description of batch culture of Pseudomonas putida PGA1 grown using saponified palm kernel oil as carbon source and ammonium as the limiting nutrient. The growth of the micro-organism is well-described using Tessier-type model which takes into account the inhibitory effect of ammonium at high concentrations. The ammonium consumption rate by the cells is related in proportion to the rate of growth. The intracellular production of medium-chain-length poly-(3-hydroxyalkanoates) (PHAMCL) by P. putida PGA1 cells is reasonably modeled by the modified Luedeking-Piret kinetics, which incorporate a function of product synthesis inhibition (or reduction) by ammonium above a threshold level.

Keywords: Ammonium; Kinetic; Medium-chain-length PHA; P. putida; Substrate-inhibition.


Poly-(3-hydroxyalkanoates) (PHA) are natural polyesters accumulated intracellularly by various types of microorganisms. When nutrient supplies such as nitrogen, oxygen, phosphorus, sulfur or magnesium are imbalanced, it is advantageous for bacteria to store excess carbon by polymerizing soluble carbon intermediates into water-insoluble molecules like PHA inside their cells (Madison and Huisman, 1999). PHA is classified into two major families, i.e., short-chain-length PHA (PHASCL) and medium-chain-length PHA (PHAMCL). Typical examples of PHASCL are poly-(3-hydroxybutyrate) (PHB) and poly-(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV). A well known producer of PHASCL is Wautersia eutropha (formerly known as Alcaligenes eutrophus). The class of PHAMCL is characterized by monomers with a carbon atom length ranging from 6 to 18, and is primarily produced by the fluorescent pseudomonads (Huisman et al. , 1989). More than 100 different monomers have been reported to occur in PHAMCL (Steinbuchel and Valentin, 1995). The PHAMCL are also targeted for specific uses where chirality and elastomeric properties are important. The constituent monomers that display different functional groups in their side chain are a valuable source of chiral synthons yet to be exploited (Kessler et al. , 2001).

Only the PHASCL have been commercially produced up to 500 tons year-1, which was manufactured by Monsanto (Kellerhals et al., 2000). The PHAMCL are yet to make a significant impact as a viable choice due to the fact that it is very expensive to produce this polymer in bulk amounts even for material testing purposes. The final PHAMCL yield and content obtained are lower compared to those of PHASCL, which hampered development of its applications (Lee et al. , 2000). Much of the research effort was directed to improve its yield and productivity using fermentation processes. Several PHAMCL production strategies in the bioreactor such as batch and continuous (Durner et al. , 2001; Jung et al., 2001), fed-batch (Beom, 2002) and high-cell-density processes (Lee et al., 2000) under various cultivation conditions have been described.

For the production of PHAMCL, one of the most preferred feedstocks is highly reduced and long carbon chain molecules such as animal or vegetable oils or their free fatty acids. These substrates have high energy content, which is excellent for good cell growth and energy metabolism. It is suggested that these oils in the semi-purified form can be a cheaper substrate for PHAMCL fermentation as compared to the purified, single-type fatty acids. However, most of the studies on PHAMCL fermentation employed the latter as the carbon source, which gives more defined fermentation components. Relatively high yield and productivity have been reported for the use of pure, single type fatty acids as the fermentation feedstock (Durner et al., 2001). The usage of crude fatty acid mixtures or their oils, however, has not been a popular choice.

One of the pioneering studies on the utilization of crude mixture of fatty acids from plant oils for microbial PHAMCL production was reported by Tan et al. (1997). Using ammonium-limited culture of Pseudomonas putida PGA1 in shake-flasks, they have shown that saponified palm kernel oil (SPKO) and its major free fatty acids, when used as the sole carbon and energy source in the fermentation, gave good biomass growth and PHAMCL yield. Subsequently, kinetics of ammonium uptake and growth of P. putida PGA1 using SPKO as the sole carbon and energy source with ammonium as the limiting nutrient was studied by Annuar et al. (2006). They reported that the ammonium uptake by P. putida PGA1 cells can be described using a first-order kinetic model, indicating that the micro-organism’s specific uptake rate of ammonium and its growth should increase as the ammonium ion concentrations become higher (< 0.1-0.2 gL-1). Further increase in the ammonium ion concentration above 0.2 g L-1 resulted in slightly lower specific growth rates of P. putida PGA1 (Annuar et al., 2006, 2007).

In cultivations using an automated bioreactor, PHAMCL accumulation by P. putida PGA1 is encouraged under ammonium-limited conditions with SPKO as the sole carbon and energy source (Annuar et al., 2007). The amount of PHAMCL accumulated and its specific production rate, qPHA, were influenced by the residual ammonium concentration level in the culture medium. It was observed in both batch and fed-batch fermentations that when the residual ammonium becomes exhausted (<0.05 g L-1), the PHAMCL accumulation and qPHA were significantly reduced (Annuar et al., 2007). However, this effect can be reversed by feeding low amount of ammonium to the culture, resulting in significantly improved PHAMCL yield and productivity. It is concluded that the feeding of residual ammonium concentration in the culture medium during the PHAMCL accumulation has a positive effect on sustaining the PHAMCL biosynthetic capability of the organism. Uptake of SPKO by the micro-organism follows zero-order kinetics, indicating a mass transfer limitation of the free fatty acids by the P. putida PGA1 cells (Annuar et al., 2007).

Several kinetic models have been proposed for the growth and PHASCL production by strains of W. eutropha under chemolithoautotrophic and heterotrophic growth conditions using laboratory-scale automated bioreactor (Heinzle and Lafferty, 1980; Mulchandani et al., 1989; Belfares et al., 1995). On the other hand, no formal kinetic models have been reported for growth and PHAMCL production by microorganisms, especially by the main producer of PHAMCL, i.e., Pseudomonas sp.

In this short communication, a kinetic model for growth and PHAMCL production by P. putida PGA1 is presented which complements the earlier studies of Annuar et al. (2007). The present study evaluated several kinetic models for growth of P. putida PGA1 on SPKO with ammonium as a limiting nutrient. Two classes of growth models were tested on published experimental data of Annuar et al. (2006), i.e., models incorporating a substrate inhibition parameter and models that consist of only growth parameters. This was followed by the development of a simple mathematical model via partial adoption of a published model of Heinzle and Lafferty (1980), which reasonably describes the limiting substrate consumption (i.e., ammonium) and PHAMCL production in P. putida PGA1 in a batch fermentation. The simulation results for growth, ammonium consumption and PHAMCL biosynthesis in P. putida PGA1 were compared with the published experimental data (Annuar et al., 2007).



Pseudomonas putida PGA1 strain was a gift from Professor G. Eggink of the Agrotechnological Research Institute, Wageningen, The Netherlands.

Medium Composition

In all studies, a defined mineral medium was used with NaNH4HPO4.H2O providing the limiting ammonium nutrient. SPKO was supplied as the sole carbon and energy source. The exact composition of the mineral medium and trace elements used was detailed in Annuar et al. (2007). Saponification of palm kernel oil (PKO) was carried out according to Tan et al. (1997). PKO is the extract from the nut of the oil palm (Elaeis guineensis Jacq.) fruit. The oil consists of a mixture of C6–C18:2 fatty acids with approximately 82% saturated fatty acids and 18% unsaturated fractions. Detailed fatty acid composition of palm kernel oil was reported by Elson (1992).

Shake-Flasks Studies

The different growth models for P. putida PGA1 were evaluated using experimental data obtained from shake-flasks cultivation. The corresponding data and details of the experimental conditions for this cultivation which include the cultivation conditions, growth and ammonium assays, data analyses and numerical calculations have been described elsewhere (Annuar et al., 2006).

Bioreactor Studies

Experimental data for comparison with simulation results were obtained from published work of Annuar et al. (2007), which also elaborated on the bioreactor specifications and experimental conditions (fatty acid compositions of SPKO, cultivation conditions, analytical methods, data analyses and calculations). Data from batch fermentation was used for comparison with the simulation results. The main geometric characteristics of the stirred tank bioreactor and the initial conditions of the experiment are reproduced in Tables 1 and 2, respectively. In the bioreactor studies, the temperature and the pH were maintained at 30 (± 0.5) °C and 7.0 (± 0.05), respectively, with an agitation rate of 600 rpm and an aeration rate of 0.5 vvm of filtered air. Silicone anti-foaming agent (BDH) was included in the aqueous medium at 1.0 g L-1.

Experimental Data Regression and Estimation of Growth Model Kinetic Parameters

Mathematical models describing growth only and those that incorporated growth inhibitions by the substrate were fitted to the shake-flask cultivation data using non-linear regression function of Polymath 6.0 software. The program uses the Levenberg-Marquardt (LM) algorithm, a technique that uses an iterative solution method to calculate the kinetic parameter values.

Simulation of Batch Fermentation

Simulation of the batch fermentation in the bioreactor was performed using the differential equations solver of Polymath 6.0 software. A set of ordinary differential equations (ODE) (eqs. 1, 8 and 9, see Results and Discussion section) was solved using the Runge-Kutta-Fehlberg (RKF45) algorithm.


Simple models are necessary in order to have a solid basis for the design of fermentation processes, for economic calculations, and for the control of fermentation processes. Modeling requires simplifications of the complex biological system, which are at the same time a major goal of modeling. In this study, a semi-empirical model proposed on the basis of a simple mechanistic description from the work of Heinzle and Lafferty (1980) was partially adopted. They presented a structured model describing batch culture of Wautersia eutropha strain H16 (formerly classified as Alcaligenes eutrophus H16) under chemolithoautotrophic growth conditions. In their work, growth and storage of poly-b-hydroxybutyrate (PHB), i.e., PHASCL are described as a function of the limiting substrate S (i.e., ammonium), the residual biomass R (i.e., PHA-free biomass), and the product P (PHB). Their bacterial ammonium consumption and PHASCL biosynthesis models were fitted to the experimental data obtained from the reported work of Annuar et al. (2007); which details the dynamics of the PHAMCL fermentation of P. putida PGA1 grown on 6.8 g L-1 SPKO and 0.4 g L-1 ammonium as carbon and nitrogen sources, respectively. The growth, ammonium consumption, and PHAMCL production profiles are reproduced in Figure 1.

Rate of Cell Growth (rR)

The total dry biomass (X) of P. putida PGA1 consists of two parts, namely PHAMCL (P) and residual biomass (R), where R is calculated as the difference between the total dry biomass and PHAMCL concentration (X=R+P). R is the catalytically active fraction of biomass, which includes proteins and nucleic acid.

The limiting substrate ammonium (S) is essential to produce R and limits its synthesis at low concentrations. The synthesis of R is described as follows,

where rR is the rate of synthesis of R and µ is the specific rate of synthesis of R.

The maintenance requirement for the limiting substrate is assumed to be small enough to be neglected. Several growth models were tested to describe the specific growth rate of P. putida PGA1 (Table 3). The growth models were divided into those that incorporate limiting substrate-inhibition kinetics and those that contained only growth kinetic parameters. All the models were fitted to the experimental data from shake-flask culture with varying initial ammonium concentrations (Annuar et al., 2006). The estimated values for the model kinetic parameters and fitting constant as returned by the fitting algorithm are shown in Table 3, along with the post-regression statistics. It is clear that growth models that incorporate the substrate inhibition parameter (R2: 0.9867-0.9955) gave better fits to the experimental data compared to the models with only growth parameters (R2: 0.9094-0.9569). Among the three models that take into account the substrate inhibition factor, the Tessier-type model showed the best fit of the experimental data (R2: 0.9955), as compared to the Andrews (R2: 0.9901) and Aiba (R2:0.9867) models. The graphical outputs showing the fits of the experimental data by the models with growth kinetic parameters only and by the growth models incorporating the substrate-inhibition kinetic are shown in Figure 2(a) and 2(b), respectively.

The R2 (correlation coefficient) is frequently used to judge whether the model represents correctly the data, implying that, if the correlation coefficient is close to one, then the regression model is correct. However, many examples exist where the correlation coefficient is close enough to one but the model is still not appropriate. Hence, the residual plot should be used together with R2 for judging the appropriateness of the model, while R2 can be used for comparing various models representing the same dependent variable. The residual plot shows the difference between the calculated and measured values of the dependent variable as a function of the measured values. This is shown in Figure 3 for the fitting of a Tessier-type model to the experimental data. The residuals are randomly distributed around the line of error=0 with zero mean, indicating that the Tessier-type model represents the data correctly (Figure 3). The residual plots for other tested growth models also showed similar random nature of their residuals distribution (data not shown). If the residuals show a clear trend, this indicates that an inappropriate model is being used. This information combined with the high R2 showed that Tessier-type model describes best the growth of P. putida PGA1 with ammonium as the limiting substrate. Another useful indicator for the comparison of various models representing the same dependent variable is the variance (s). A model with smaller variance represents the data more accurately than a model with larger variance. It is also found that all the models representing substrate inhibition kinetics have consistently much lower s as compared to those representing the growth kinetics as a function of substrate concentration only (Table 3). This indicated that the substrate-inhibition kinetic model should be able to represent growth data more accurately. Different levels of high ammonium concentration in the aqueous medium were found to exert a substrate-inhibition effect towards growth of W. eutropha strains (Suzuki et al., 1986; Mulchandani et al., 1989; Belfares et al., 1995; Beaulieu et al., 1995) and P. putida PGA1 (Annuar et al., 2006, 2007).

On the other hand, for the regression model to be stable and statistically valid, the confidence intervals must be much smaller (or at least smaller) than the respective parameter values (in absolute values). The confidence intervals at 95% for all tested growth models are less than the estimated parameter values returned by the fitting algorithm (Table 3). The Tessier-type model has significantly much smaller confidence intervals for all its kinetic parameters.

Rate of Ammonium Consumption (rS)

An examination of the experimental data (Figure 1) indicated that ammonium concentration was almost completely consumed in the growth phase due to the bacterial metabolism and this corresponded to an increase in the residual biomass growth rate. Furthermore, specific ammonium uptake rates were found to be positively correlated with specific growth rates of the micro-organism, with the optimal rates occurring at 0.1 g L-1 ammonium ion in aqueous medium (Annuar et al., 2006). The rate of ammonium consumption is related to the rate of growth as shown in following equation

which is adequate to describe the relationship between the rate of synthesis of R (rR) and the rate of consumption of the limiting substrate S (rS). The value of biomass yield coefficient on ammonium (YR/S) is taken from the work of Heinzle and Lafferty (1980) at 1.48 ± 0.14 (Table 4). In their work, W. eutropha H16 was grown on fully synthetic medium containing ammonium (in the form of (NH4)2SO4) as nitrogen source and gaseous CO2 as the sole carbon and energy source.

Rate of PHAMCL Production (rP)

The rate of synthesis of PHAMCL (rP) is assumed to be the sum of a growth associated term (rP,1) and a biomass associated term (rP,2), following the suggestion of Heinzle and Lafferty (1980). They formulated a rate expression for P as:

As shown in Figure 1, the rP is correlated with rR during the growth phase. The first term in the expression of the rate of synthesis of P, i.e., rP,1, is a function of PHAMCL yield coefficient on residual biomass (YP/R) and rR (Eq. 10).

The value of YP/R is determined to be within a range of 0.105-0.16 (Heinzle and Lafferty, 1980). For the purpose of the modeling exercise in this work, average YP/R value were used, i.e., 0.13.

The non-growth associated term of the synthesis of P (rP,2) is assumed to be a function of the limiting substrate S, of the residual biomass R, and of the product P (Heinzle and Lafferty, 1980). At high contents of PHAMCL in the cells, the rate of synthesis of P is decreased, which can be formally described as an inhibition. Following this, the second term in the expression of the rate of synthesis of P , rP,2 , is given by equation (11).

The values of k1 and k2 fall within the range of 0.045-0.048 h-1 and 0.18-0.176 h-1, respectively, as determined by Heinzle and Lafferty (1980). For the purpose of simulation in the present work, the average values of both (k1=0.047 and k2=0.18) were used in the rate expression (Eq. 11).

The crucial aspect of the model is the initialization of the non-growth associated production of P, and the inhibition of it by the limiting substrate ammonium. Heinzle and Lafferty (1980) proposed that this inhibition can be incorporated into the model by multiplying Eq. (11) by a function that is used to describe allosteric substrate inhibition, which yields the following equation:

KI,P is the inhibition constant representing the substrate concentration at half maximum rate of production of P. KI,P was determined to be between 0.036 and 0.047 g L-1 (NH4)2SO4 (Table 4). Again here, the average value of 0.042 g L-1 for KI,P was employed in the simulation exercise.

Table 4 summarizes all the kinetic parameters required to solve the final set of equations [Eqs (1), (8), (9), (10), (11), and (12)].


Figure 4 shows the results of a numerical integration of the model with one set of parameters as given in Table 4. The time course of calculated concentrations is compared with experimental values. The comparisons demonstrate a good agreement between the data from simulations of the model with the experimental data. Thus, alongside the Tessier-type model incorporating substrate-inhibition kinetics to describe the batch growth of P. putida PGA1, the models for ammonium utilization and accumulation of PHASCL (PHB), initially proposed by Heinzle and Lafferty (1980) for W. eutropha under chemolithoautotrophic growth conditions, are equally applicable to simulate the ammonium consumption and PHAMCL accumulation in P. putida under heterotrophic conditions. Ammonium utilization kinetics by P. putida PGA1 in a chemically defined medium can be modeled quite simply using a rate equation related directly by a yield coefficient to the growth kinetic model. The PHAMCL formation rate can be described reasonably well by using a model that takes into account the growth-associated and non-growth associated product formation simultaneously. Using this general form of Luedeking-Piret kinetics, Heinzle and Lafferty (1980) modified the non-growth product formation rate equation to include a function of PHAMCL biosynthesis inhibition by a certain level of ammonium in the medium; when the ammonium concentration exceeds the 0.036-0.047 g L-1 range, the rate of PHAMCL biosynthesis in the cells is reduced. This is not an unfounded modification, as it is well known that PHA accumulation is increased significantly under threshold ammonium concentration in the medium. This ammonium level differs between different types of micro-organisms. The accumulation and storing of the intracellular polymer is the bacterial culture’s response to the deficiency conditions (e.g. ammonium limitation) that do not permit continuation of its exponential growth. In this case, the intracellular stored carbon in the form of polymer helps the bacterial population to survive the starvation period until favorable growth conditions are restored in its environment.

Ammonium consumption and PHASCL (PHB) production models proposed by Mulchandani et al. (1989) were also compared to the current experimental data. Using W. eutropha ATCC 17697 culture grown in fructose as carbon substrate, their ammonium consumption rate equation took a form similar to the model of Heinzle and Lafferty (1980) with the biomass yield coefficient with respect to ammonium (YR/S) estimated at 1.46 g g-1, which is essentially the same as the value in the current model. Hence, the ammonium utilization model of Muchandani et al. (1989) also describes well the experimental data (Figure 5). Their PHB production model, on the other hand, over-estimated the biosynthesis of PHAMCL by P. putida PGA1 cells. Although their rate equation also adopts the Luedeking-Piret kinetics, it does not take into account the possibility of PHAMCL biosynthesis inhibition above a certain level of residual ammonium in the aqueous medium (Figure 5). Their product synthesis equation is solely a function of the culture’s growth rate and biomass concentration, each related to the product balance by a constant (Mulchandani et al., 1989).

Alternative ammonium consumption and PHASCL (PHB) production models for W. eutropha DSM545 grown in mineral salts medium containing glucose as carbon source and (NH4)2SO4 as nitrogen source were reported by Belfares et al. (1995). Their ammonium utilization rate equation also took a similar form to the two models tested earlier. However, due to significantly higher difference in the biomass yield coefficient with respect to ammonium (equivalent to YR/S), which was estimated at 6.25 g g-1 , in comparison to other YR/S values used in this study, the rate of ammonium consumption was grossly over-estimated compared to the experimental data (Figure 5). On the other hand, the PHB production rate proposed by these authors was solely a function of cell growth with a biomass product yield coefficient (equivalent to YP/R) estimated at 0.13. As a result, it predicted a very much lower PHAMCL production rate in P. putida PGA1 batch culture (Figure 5).


The batch growth of P. putida PGA1 culture in a defined aqueous medium with a fatty acid mixture as carbon source can be described by using a Tessier-type model which incorporates the limiting substrate (ammonium) inhibition kinetics. Utilization of the ammonium is related vis-à-vis to growth kinetics. The PHAMCL accumulation by P. putida PGA1 cells can be reasonably modeled using Luedeking-Piret kinetics that take into account the product synthesis inhibition (or reduction) by ammonium concentrations above a threshold level.







medium-chain-length poly-(3-hydroxyalkanoates)



short-chain-length poly-(3-hydroxyalkanoates)









palm kernel oil



saponified palm kernel oil






ordinary differential equations






product concentration

g L-1


residual biomass concentration

g L-1


limiting substrate concentration

g L-1


total biomass concentration

g L-1

k 1

constant 1


k 2

constant 2



substrate-inhibition constant

g L-1


product-inhibition constant

g L-1


substrate constant

g L-1


fitting constant


r R

rate of R synthesis

g L-1 h-1

r S

rate of S consumption

g L-1 h-1

r P

rate of P formation

g L-1 h-1

r P,1

first term of rP equation

g L-1 h-1

r P,2

second term of rP equation

g L-1 h-1

R 2

coefficient of correlation



growth yield coefficient



product yield coefficient


Greek Symbols


specific growth rate



maximum specific growth rate






This study was funded by University of Malaya research, grant no. Vot F0156/2001A.

(Received: June 19, 2007 ; Accepted: November 26, 2007)

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  • Publication Dates

    • Publication in this collection
      03 July 2008
    • Date of issue
      June 2008


    • Accepted
      26 Nov 2007
    • Received
      19 June 2007
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