Mixing control as a device to increase PHB production in batch fermentations with co-cultures of Lactobacillus delbrueckii and Ralstonia eutropha

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1 Process Biochemistry 40 (2005) Mixing control as a device to increase PHB production in batch fermentations with co-cultures of Lactobacillus delbrueckii and Ralstonia eutropha V.S.R.K. Ganduri a, S. Ghosh a, P.R. Patnaik b, a Department of Biotechnology, Anna University, Chennai , India b Institute of Microbial Technology, Sector 39-A, Chandigarh , India Received 10 November 2003; accepted 1 January 2004 Abstract Poly( -hydroxybutyric acid) or PHB is a bacterial polymer whose biocompatability, biodegradability and versatile properties make it an eco-friendly substitute for synthetic polymers. It is synthesized by Ralstonia eutropha from glucose as the main carbon source. However, better productivity is obtained through co-cultures of Lactobacillus delbrueckii and R. eutropha. PHB concentrations of 12 g/l have been reported in laboratory experiments and up to 40 g/l are theoretically achievable by fed-batch fermentation with programmable control of carbon and nitrogen feed rates. In this analysis, it is shown that equally high yields are possible in simpler batch fermentations by controlling the mixing intensity. Since mixing in large bioreactors is inherently incomplete, the present approach allows this nonideal feature to be gainfully utilized Elsevier Ltd. All rights reserved. Keywords: PHB; Bacterial co-culture; Batch fermentation; Controlled mixing 1. Introduction Fermentations employing two or more microorganisms sometimes offer benefits over single culture fermentations. Commensalism and neutralism are two well-known classes of such cultures. In another situation, one microorganism converts a substrate A into a metabolite B, which the second organism utilizes this to generate the final product P. Although the second microorganism can also grow on A, this process is slow and inefficient, whereas B is more easily metabolized. There are many examples of the purposeful use of mixed cultures of this kind [1 3]. The present study is of the production of poly( -hydroxybutyric acid) or PHB by a co-culture of Lactobacillus delbrueckii and Ralstonia eutropha. PHB is a member of the family of poly(hydroxyalkanoic acids) and is synthesized and accumulated inside cells when the cultivation medium has an excess of carbon and is deficient in nitrogen, usually as ammonia [4]. It has properties IMTECH communication no. 049/2003. Corresponding author. Fax: /632. address: pratap@imtech.res.in (P.R. Patnaik). superior to those of commercial synthetic polymers and, in addition, it is biodegradable, biocompatible, nontoxic and piezoelectric. This makes PHB attractive for many medical, cosmetic, chemical and electronic applications [5]. Although single cultures, mainly Alcaligenes eutrophus, have been used for PHB production, better efficiency and higher productivity have been achieved recently by co-cultures of A. eutrophus with either Lactococcus lactis [6] or L. delbrueckii [7 9]. In mixed culture fermentations, control of the carbon and nitrogen concentrations in the broth and appropriate staggering of inoculations by the component cultures are key factors determining the efficiency of the process. To do this, fed-batch operation has been preferred in many laboratory-scale fermentations, and final (peak) PHB concentrations up to 12 g/l have been reported [9]. It has also been shown that this may be increased more than three-fold by more complex control of the ammonia feed rate [10]. The possibility of PHB concentrations up to 40 g/l raises two interesting questions. First, are such high productivities possible under more realistic industrial conditions? Secondly, can complex fed-batch operation be replaced by simpler batch operation? The present study explores these /$ see front matter 2004 Elsevier Ltd. All rights reserved. doi: /j.procbio

2 258 V.S.R.K. Ganduri et al. / Process Biochemistry 40 (2005) two questions against the background of supporting work. In studies with other fermentations using either two kinds of cells [11,12] or two substrates [13,14], it has been shown that optimizing the degree of (macro-)mixing can result in higher product concentrations than in well-mixed bioreactors. These studies open the possibility of exploiting the inherent imperfect mixing in large bioreactors to achieve high PHB concentrations in batch operations. 2. Modeling of PHB synthesis in a mixed culture 2.1. Kinetic model To overcome the sluggish utilization of glucose by A. eutrophus (later renamed R. eutropha), Katoh et al. [7] used L. delbrueckii initially to convert glucose to lactic acid, which is easily metabolized by R. eutropha. These experiments were followed by others by Shimizu and coworkers [8 10], who proposed the model presented below for batch fermentation in a perfectly mixed vessel. The rate of growth of L. delbrueckii is r X 1 = dx 1 = µ 1 (S, P, DO)X 1 (1) The rate of glucose consumption is similarly r S = ds = ν 1 (S, P, DO)X 1 (2) and the rate of lactate accumulation is r P = σ 1 (S, P, DO)X 1 ν 2 (P, DO, N)X 2 (3) The specific rates, defined in Appendix A, follow the equations given below: µ 1 (S, P, DO) µ ( m 1 (DO)S 1 P ) n (4) K S + S P m ν 1 (S, P, DO) µ 1(S, P, DO) Y X1 /S(DO) + σ 1(S, P, DO) Y P/S (DO) σ 1 (S, P, DO) αµ 1 (S, P, DO) + β(s, DO) (6) where β(s, DO) β m(do)s (7) K S + S The second term on the right-hand side of Eq. (3) is the rate of substrate consumption by R. eutropha, and it was considered to be of the following form: ν 2 (P, DO,N) µ 2(P, DO,N) (8) Y X2 /P(DO) R. eutropha is introduced after a reasonable amount of glucose has been metabolized, and in Tohyama et al. s [9,10] experiments this was done 4 h after inoculation by L. delbrueckii. Then the rate of growth of R. eutropha is r X 2 = dx 2 (5) = µ 2 (P, DO, N)X 2 (9) The rate of nitrogen consumption is likewise r N = dn = ν 3 (P, DO, N)X 2 (10) and the rate of formation of PHB is r Q = dq = σ 2 (N)X 2 (11) Tohyama et al. [10] considered µ 2, σ 2 and ν 3 to be of the following form: ( )( ) µ m2 (DO)P N µ 2 (P, DO,N) K P + P + (P 2 (12) /K i ) K N + N ν 3 (P, DO,N) µ 2(P, DO,N) (13) Y X2 /N(DO) ( ) kn σ 2 (N) q m (14) k N + N It may be noted that, unlike µ 2, no dependence of µ 1 on N was considered. This was based on their experimental observation that ammonia concentration changed little during L. delbrueckii cultivation as compared with that of R. eutropha. Two critical factors control PHB production. One is the C:N ratio, whose optimum range is [7]. The other is the dissolved oxygen (DO) concentration. Since L. delbrueckii is anaerobic whereas R. eutropha is aerobic, initially a low concentration of 0.5 ppm was maintained for 4 h, then increased to 3.0 ppm, followed by alternate hourly periods of 0.5 and 3.0 ppm. Tohyama et al. [10] studied both constant and variable durations for the two phases but their results do not show any significant difference in bioreactor performance. So a constant time interval of 1 h, employed by them, was used in our theoretical study since this easier to maintain Imperfectly mixed bioreactor Imperfect mixing of broth in a bioreactor generates non-uniform spatial distribution of cells, substrates and products, which affect the relative growth rates of biomass, the rate of oxygen uptake, and the stability of the reactor [13]. Earlier studies by Patnaik [11 13] showed that better performances could be elicited through controlled imperfect mixing rather than by hypothetical perfect mixing. Although both micromixing and macromixing occur simultaneously, the dominance of the latter increases with the volume of the reactor and as fermentation progresses [15]. Most models of macromixing are based on the classical concept that a linear train of perfectly mixed reactor approaches plug-flow behavior. By modifying a model originally proposed by Tanner et al. [16], Patnaik [13] constructed a model comprising two reactors with a closed loop recycle (Fig. 1). The model visualizes two mixing regions in the broth and the recycle streams represent internal circulation. Each reactor in the model functions with a continuous throughput but there is no overall inflow or outflow.

3 V.S.R.K. Ganduri et al. / Process Biochemistry 40 (2005) dn 2 = D 2 (N 1 N 2 ) + r N 2 (25) Fig. 1. Two-region model of macromixing in a batch fermentation (from Tanner et al. [16]). For each reactor a dilution rate can be defined in the normal way. Tanner et al. [16] interpreted this as a measure of the degree of macromixing. They also considered the reactors to be of the same size and hence of the same dilution rate. Patnaik [13] relaxed this restriction, thus allowing two dilution rates, D 1 and D 2, to be different. If D 1 or D 2, that region is perfectly mixed, while D 1 or D 2 0 indicates complete regional segregation. For complete mixing throughout the broth, both D 1 and D 2, and similarly complete spatial segregation occurs when D 1 and D 2 0. Most real fermentations will of course have dilution rates between these limits. Without loss of generality, let reactor 1 represent the upper (non-inoculated) region in Fig. 1 and reactor 2 the lower (inoculated) region. Then mass balances may be written for each region as given below. Reactor 1: dx 11 dx 21 ds 1 dp 1 dn 1 dq 1 Reactor 2: dx 12 = D 1 (X 12 X 11 ) + r X 1 1 (15) = D 1 (X 22 X 21 ) + r X 2 1 (16) = D 1 (S 2 S 1 ) + r S 1 (17) = D 1 (P 2 P 1 ) + r P 1 (18) = D 1 (N 2 N 1 ) + r N 1 (19) = D 1 (Q 2 Q 1 ) + r Q 1 (20) = D 2 (X 11 X 12 ) + r X 1 2 (21) dq 2 = D 2 (Q 1 Q 2 ) + r Q 2 (26) To specify the initial conditions for Eqs. (15) (26), itwas considered that inoculum is introduced in the lower region of the broth, as in the design of most bioreactors. In terms of the model, a change in the inoculated region merely interchanges the initial conditions. If the reactor is perfectly mixed, synthesis of lactate begins throughout the broth immediately after inoculation of L. delbrueckii. But, with imperfect mixing, the cells migrate at finite speeds from the inoculated region (region 2 in Fig. 1) into the upper region. So, at exactly t = 0 there are finite concentrations of L. delbrueckii and lactate in region 2 but zero concentrations in region 1. The same argument applies to R. eutropha and its product (PHB) at t = 4 h. Since glucose and ammonia are present even before the first inoculation and cell-free broth may be agitated intensely without any risk of damaging the cells, the initial concentrations of these two may be assumed to be uniform in both the regions. Since the other concentrations are generated after the inoculations, their initial values will be zero in the upper (non-inoculated) region. This means at t = 0 the inocula and their products, lactic acid and PHB, are confined to the inoculated region. So, if w is the initial concentration of any of these variables in the broth as a whole, this translates to ( ) D1 + D 2 w 2 = w (27) D 1 in the inoculated region. Thus, with the same starting conditions, the inoculated region is initially richer than for a perfectly mixed broth and the other region is leaner. The overall initial concentrations and the values of the kinetic parameters were taken from Tohyama et al. [9,10] and are listed in Table 1. Since in real terms one is interested in the broth as a whole, the concentrations in the two model reactors of Fig. 1 have to be averaged. By simple material balances, these averages may be shown to be L. delbureckii cell concentration,x 1 = X 11D 2 + X 12 D 1 (28) R. eutropha cell concentration,x 2 = X 21D 2 +X 22 D 1 (29) Glucose concentration,s = S 1D 2 + S 2 D 1 (30) dx 22 = D 2 (X 21 X 22 ) + r X 2 2 (22) Lactate concentration,p = P 1D 2 + P 2 D 1 (31) ds 2 dp 2 = D 2 (S 1 S 2 ) + r S 2 (23) = D 2 (P 1 P 2 ) + r P 2 (24) Ammonia concentration,n = N 1D 2 + N 2 D 1 (32) PHB concentration,q= Q 1D 2 + Q 2 D 1 (33)

4 260 V.S.R.K. Ganduri et al. / Process Biochemistry 40 (2005) Table 1 List of kinetic parameter values and initial conditions (from Tohyama et al. [10]) Variable Value α 1.23 β m (h 1 ) 1.8 µ m1 (h 1 ) µ m2 (h 1 ) K i (g/l) 2.5 k N (g/l) 0.05 K N (g/l) K P (g/l) 6.0 K S (g/l) 35.8 n 1.0 P m (g/l) 42.9 q m (h 1 ) Y P/S Y X2 /N 2.41 Y X2 /P Y X1 /S 1.0 X X a S 0 10 P N Q a The initial concentration of R. eutropha inoculated at 4.0 h. 3. Results and discussion Eqs. (1) (26) were solved for dilution rates D 1 and D 2 from 0.1 to 2.0 h 1 to represent different combinations of poor mixing and good mixing. Although theoretically perfect mixing implies D 1, D 2, beyond D i (i = 1, 2) > 2.0h 1 there are only marginal changes in the performance [11,13]. Typical time-domain plots characterizing the fermentation at four representative combinations of D 1 and D 2 are shown in Figs. 2 7 for the same duration (30 h) as Fig. 3. Evolution of R. eutropha concentration with time for different combinations of mixing intensities (D 1, D 2 ). in the work of Tohyama et al. [9,10]. Plots for the combination (D 1 = 0.1h 1, D 2 = 1.0h 1 ) are not shown because here the specific growth rates of both cultures became negative within 3.0 h. This implies that poor mixing in the non-inoculated region and good mixing in the inoculated region does not sustain the fermentation. For the feasible combinations of D 1 and D 2 there is an interesting dichotomy among the plots. For all the concentrations, the profiles can be separated into two pairs. When the mixing intensities are unequal (i.e. D 1 D 2 ), the growth of both bacteria is poor (Figs. 2 and 3) and correspondingly there is late consumption of glucose (plot not shown) and low production of both lactate (Fig. 4) and PHB (Fig. 5). Fig. 2. Evolution of L. delbrueckii concentration with time for different combinations of mixing intensities (D 1, D 2 ). Fig. 4. Evolution of lactate concentration with time for different combinations of mixing intensities (D 1, D 2 ).

5 V.S.R.K. Ganduri et al. / Process Biochemistry 40 (2005) Fig. 5. Evolution of ammonia concentration with time for different combinations of mixing intensities (D 1, D 2 ). If the degrees of mixing are equal (i.e. D 1 = D 2 ), there is substantial growth of both organisms and, as expected, high concentrations of both lactate and PHB. It may be noted that PHB concentration is high in both volumetric terms (g/l) and per unit mass of cells (g/g biomass) when D 1 = D 2. Fig. 4 also shows that lactate production is higher for these conditions than when D 1 D 2. Since lactate is an inhibitor of the growth of both organisms [4,7,8], it might seem paradoxical that when its concentration is high there is actually better growth and greater PHB synthesis. To explain this, we refer to the quantitative expressions of the effect of lactate on L. delbrueckii (Eq. (4)) and R. eutropha (Eq. (12)). Increasing lactate concentration monotonically inhibits the growth Fig. 6. Evolution of PHB concentration (g/l) with time for different combinations of mixing intensities (D 1, D 2 ). Fig. 7. Evolution of PHB concentration (g/g biomass) with time for different combinations of mixing intensities (D 1, D 2 ). of L. delbrueckii, which stops growing when P exceeds P m, the maximum sustainable value. However, the effect of lactate on R. eutropha is somewhat different. At low concentrations of lactate, as Eq. (12) shows, µ 2 is a nearly linear function of P, whereas high values of P are inhibitory. This dependence implies the existence of an optimum concentration of lactate, P, that maximizes the specific growth rate, µ 2,ofR. eutropha. Itis important to realize that P may be different from P m, the threshold concentration for L. delbrueckii. With this framework, it is possible to understand why a low concentration of lactate when D 1 = D 2 is not necessarily favorable and why the larger concentrations generated when D 1 D 2 are not necessarily detrimental. These results are in conformity with the metabolic control of lactate concentration by balancing its production by R. eutropha with its consumption by L. delbrueckii. This balance is linked in a complex, and not fully understood, way to ammonia concentrations and is a key to maximization of PHB production [9,10]. A high concentration of nitrogen promotes the growth of R. eutropha while PHB synthesis is favored by low concentrations. However, the mechanisms of these two processes seem to be more complex than has been envisaged [8,9] and this inference is supported by the observation that the ammonia profiles (Fig. 5) intersect whereas none of the other profiles (Figs. 2-4, 6 and 7) do. Now, Eqs. (27) (32) show that the spatially averaged value of any variable w is given by ( ) ( ) D2 D1 w = w 1 + w 2 (34) where w j is its value in the jth model reactor. So the dilution ratio D 2 /D 1 rather than D 1 or D 2 alone seems to determine the performance. The effect of this ratio on the final

6 262 V.S.R.K. Ganduri et al. / Process Biochemistry 40 (2005) Fig. 8. Effect of the dilution ratio (D 2 /D 1 ) on the final (30 h) average concentrations of L. delbrueckii and R. eutropha. (30 h) concentrations have been plotted in Figs for 0 < D 2 /D 1 < 2. The lower limit is decided by the fact that both D 1 and D 2 have to be positive. The upper limit was fixed from our observation that for ratios larger than 2.0 the lactate concentration soon exceeded the maximum allowable limit of P m = 42.9 g/l [17], causing a negative growth rate, µ 1, for L. delbrueckii. The duration of fermentation (30 h) was chosen to facilitate comparison with previous studies [7 10]. Within the range 0 <D 2 /D 1 < 2, we observe that the concentrations of both organisms increase monotonically (Fig. 8), as does lactate concentration (Fig. 9). Glucose (plots not shown) and ammonia (in solution) (Fig. 9) decrease Fig. 9. Effect of the dilution ratio (D 2 /D 1 ) on the final (30 h) average concentrations of lactate and ammonia. Fig. 10. Effect of the dilution ratio (D 2 /D 1 ) on the final (30 h) average volumetric (g/l) and gravimetric (g/g biomass) concentrations of PHB. as the ratio increases and are almost completely exhausted around D 2 /D 1 = 1, i.e. D 2 = D1. The concentration of primary interest, PHB, has a more unusual variation. Both volumetrically and per unit biomass, PHB passes through peak values. The volumetric peak occurs at D 2 /D 1 = 1.43 (Fig. 10), and the gravimetric peak occurs at 1.0 (Fig. 10). This difference is due to the biomass concentrations X 1 and X 2 increasing at rates different from each other and from that of PHB. The maximization of PHB concentration at D 2 = 1.43D 1 might seem to contradict the inference from Figs. 2 7 that D 1 = D 2 is more favorable for PHB synthesis. However, these plots are for only four specific combinations of D 1 and D 2 covering D 2 /D 1 = 0.05, 0.1 and 1.0. Since D 2 /D 1 is the determining factor, it is now understandable why the plots are in two close pairs, one for D 1 = D 2 = 0.1 and D 1 = D 2 = 1.0, for both of which this ratio is 1.0, and the other for D 1 = 1.0, D 2 = 0.1 and D 1 = 2.0, D 2 = 0.1, whose ratios 0.1 and 0.05 are much smaller and nearly equal. On the other hand, the plots in Figs explore a wider range of the ratio in finer detail, which has revealed that combinations of D 1 and D 2 that were not covered in Figs. 2 7 turn out to be better than D 1 = D 2. The superior performance seen here for D 1 D 2, i.e. a departure from perfect mixing, reinforces similar observations reported earlier [11 13] for other fermentations and strengthens the general validity of exploiting controlled imperfect mixing as a tool to increase the fermentation efficiency of large bioreactors. It may be clarified here that D 2 /D 1 does not fix D 1 and D 2 uniquely. Furthermore, although for nearly perfect mixing this ratio equals 1.0 since both D 1 and D 2 tend toward large equal values, the converse is not true, i.e. D 2 /D 1 = 1 does not necessarily imply nearly perfect mixing. (At truly perfect

7 V.S.R.K. Ganduri et al. / Process Biochemistry 40 (2005) mixing, the ratio is indeterminate since D 1 and D 2 but this is hypothetical situation.) Fig. 10 shows that at the optimum value of D 2 /D 1 = 1.43 the maximum attainable concentration of PHB is 36.6 g/l after 30 h. To place this in proper prospective, we observe that with a constant DO, Tohyama and Shimizu [8] obtained 7 g/l PHB after 35 h. Tohyama et al. [9] enhanced this to 12 g/l by employing a square wave DO profile. Later Tohyama et al. [10] showed theoretically that it is possible to achieve 40.6 g/l by using bang-bang control of ammonia concentration and 38.8 g/l by optimizing the starting concentration of ammonia. All these studies were in fed-batch operation with small well-mixed bioreactors. In this study we have shown that by simply controlling the mixing intensity in batch fermentation it is possible to obtain equally high concentrations of PHB. 4. Concluding observations Previous studies of bacterial fermentations with single or lumped substrates have indicated that macromixing in the broth can have a significant effect on cell growth and product formation. The present work has extended those studies to batch fermentation for the production of poly( -hydroxybutyric acid), using a mixed culture of L. delbrueckii and R. eutropha. Unlike the earlier systems, here one organism (L. delbrueckii) is anaerobic and other is aerobic. So to promote the growth of both, the DO concentration was varied during alternate hours between 0.5 and 3.0 ppm. Macromixing was modeled by a combination of two continuous flow reactors connected by a closed loop recycle. The reactors were of unequal volumes and thus had unequal dilution rates D 1 and D 2. It was observed that the final (peak) concentration of PHB depended on the ratio D 2 /D 1 rather than on their individual values. The value of D 2 /D 1 that maximized the PHB concentration was found to be 1.43, which departs from 1.0 for complete mixing. At this ratio, the batch yield of PHB was 36.6 g/l and 4.12 g/(g biomass), which are three times the best experimental values reported in small, well-mixed, fed-batch fermentations and comparable to the theoretically maximum yields possible in such reactors. The present study thus indicates that by suitably regulating the inherent incomplete mixing in large bioreactors it is possible to achieve in simple batch operation productivities comparable to those possible in fed-batch fermentations with more elaborate controls. The present results and those of Patnaik [11 13] also suggest that the incomplete mixing in large bioreactors may be profitably harnessed for productivities even higher than achievable in laboratory-scale vessels. The accuracy of our simulation results is limited by the accuracy of the underlying kinetic model. Tohyama et al. [10] have alluded to two limitations of their model. One is the absence of the inclusion of a progressive decrease in cellular enzyme activity; the other is the lack of a uniquely best control strategy for lactate concentration. A third limitation not mentioned them is the absence of any effect of DO concentration on the specific PHB production rate σ 2 in Eq. (14). A Luedking Piret form similar to Eq. (6) might have improved the model. Nevertheless, given that Tohyama et al. s [9,10] kinetic framework has a plausible mechanistic basis and fits their experimental data satisfactorily, its application to imperfect mixing provides reliable indicators of real bioreactor performance. Appendix A D 1, D 2 dilution rates in reactors (1) and (2) (h 1 ) DO dissolved oxygen concentration (ppm) k N reaction rate constant (g/l) K i, K N, K P, K S equilibrium constants (g/l) n order of inhibition of the specific growth rate of L. delbrueckii N average ammonia concentration (g/l) N 1, N 2 ammonia concentrations in reactors (1) and (2) (g/l) P average lactate concentration (g/l) P 1, P 2 lactate concentrations in reactors (1) and (2) (g/l) P m maximum sustainable lactate concentration (g/l) P optimum constant lactate concentration (g/l) q m maximum specific PHB production rate (h 1 ) Q average PHB concentration (g/l) Q 1, Q 2 PHB concentrations in reactors (1) and (2) (g/l) ri N rate of consumption of ammonia in the ith reactor (g/(l h)) ri P rate of formation of lactate in the ith reactor (g/(l h)) r Q i rate of formation of PHB in the ith reactor (g/(l h)) ri S rate of consumption of glucose in the ith reactor (g/(l h)) r x j i rate of synthesis of X i in the jth reactor (g/(l h)) S average glucose concentration (g/l) S 1, S 2 glucose concentrations in reactors 1 and 2 (g/l) w spatially averaged value of any variable, defined by Eq. (34) w j concentration of any variable w in the jth model reactor (g/l) X 1 average biomass concentration of L. delbrueckii (g/l)

8 264 V.S.R.K. Ganduri et al. / Process Biochemistry 40 (2005) X 2 average biomass concentration of R. eutropha (g/l) X ij concentration of ith species in jth reactor of the model (g/l) Y X1 /S, Y P/S, Y X1 /P, Y Q/P, Y X2 /N yield coefficients Greek symbols α Luedking Piret rate constant β defined by Eq. (7) (h 1 ) β m maximum value of β (h 1 ) µ 1 specific growth rate of L. delbrueckii (h 1 ) µ 2 specific growth rate of R. eutropha (h 1 ) µ m1 maximum value of µ 1 (h 1 ) µ m2 maximum value of µ 2 (h 1 ) ν 1 specific glucose consumption rate (h 1 ) ν 2 specific lactate consumption rate (h 1 ) ν 3 specific ammonia consumption rate (h 1 ) σ 1 specific lactate production rate (h 1 ) σ 2 specific PHB production rate (h 1 ) References [1] Grootjen DRJ, Meijlink HHM, van der Lans RGJM, Luyben KChAM. Cofermentation of glucose and xylose with immobilized Pichia stipitis and Saccharomyces cerevisiae. Enzyme Microbiol Technol 1990;12: [2] Kondo T, Kondo M. Efficient production of acetic acid from glucose in a mixed culture of Zymomonas mobilis and Acetobacter sp. J Ferment Bioeng 1996;81:42 6. [3] Shimizu H, Mizuguchi T, Tanak E, Shioya S. Nisin production by a mixed culture system consisting of L. lactis and K. marxians. Appl Environ Microbiol 1999;65: [4] Anderson AJ, Dawes EA. Occurrence, metabolism, metabolic role and industrial uses of bacterial polyhydroxyalkanoates. Microbiol Rev 1990;54: [5] Lee SY, Chang HN. Production of poly(hydroxyalkanoic acid). Adv Biochem Eng Biotechnol 1995;52: [6] Tanaka K, Katamune K, Ishizaki A. Fermentative production of poly( -hydroxybutyric acid) from xylose via l-lactate by a two-stage culture method employing Lactobacillus lactis IO-1 and Ralstonia eutropha. Can J Microbiol 1995;41: [7] Katoh T, Yuguchi D, Yoshii H, Shi H, Shimizu K. Dynamics and modelling on fermentative production of poly( -hydroxybutyric acid) from sugars via lactate by a mixed culture of Lactobacillus delbrueckii and Alcaligenes eutrophus. J Biotechnol 1999;67: [8] Tohyama M, Shimizu K. Control of a mixed culture of Lactobacillus delbrueckii and Ralstonia eutropha for the production of PHB from glucose via lactate. Biochem Eng J 1999;4: [9] Tohyama M, Takagi S, Shimizu K. Effect of controlling lactate concentration and periodic change in DO concentration on fermentation characteristics of a mixed culture of Lactobacillus delbrueckii and Ralstonia eutropha for PHB production. J Biosci Bioeng 2000;89: [10] Tohyama M, Patarinska T, Qiang Z, Shimizu K. Modeling of the mixed culture and periodic control for PHB production. Biochem Eng J 2002;10: [11] Patnaik PR. Incomplete mixing in large bioreactors a study of its role in the fermentative production of streptokinase. Bioprocess Eng 1996;14:91 6. [12] Patnaik PR. Influence of macromixing on plasmid stability during batch fermentation with recombinant bacteria. Ind J Chem Technol 1997;4: [13] Patnaik PR. On the improvement of bacterial growth on complementary substrates by partial segregation in the broth. J Chem Technol Biotechnol 2000;75: [14] Patnaik PR. Effect of fluid dispersion on cybernetic control of microbial growth on substitutable substrates. Bioprocess Biosyst Eng 2003;25: [15] Ruggeri B, Sassi G. On the modeling approaches of biomass behavior in bioreactor. Chem Eng Commun 1993;122:1 56. [16] Tanner RD, Dunn IJ, Bourne JR, Klu MK. The effect of imperfect mixing on an idealised kinetic fermentation model. Chem Eng Sci 1985;40: [17] Yoo S, Kim W-S. Cybernetic model for synthesis of poly- -hydroxybutyric acid in Ralstonia eutropha. Biotechnol Bioeng 1994; 43: