Article pubs.acs.org/IECR
Optimal Control of Feeding in Fed-Batch Production of Xylitol Worasit Tochampa,† Sarote Sirisansaneeyakul,*,‡,§ Wirat Vanichsriratana,‡,§ Penjit Srinophakun,⊥ Huub H. C. Bakker,∥ Siwaporn Wannawilai,‡,§ and Yusuf Chisti∥ †
Department of Agro-Industry, Faculty of Agriculture, Natural Resources and Environment, Naresuan University, Phitsanulok 65000, Thailand ‡ Department of Biotechnology, Faculty of Agro-Industry, §Center for Advanced Studies in Tropical Natural Resources (CASTNAR), NRU-KU, and ⊥Department of Chemical Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10900, Thailand ∥ School of Engineering, Massey University, Private Bag 11 222, Palmerston North, New Zealand ABSTRACT: A model-based optimization involving a genetic algorithm was used to establish the optimal substrate feeding profiles in fed-batch fermentations for maximizing the average production rate of xylitol from xylose. The best-case feeding profiles were verified experimentally in fermentations fed with glucose and xylose. The model-predicted profiles agreed remarkably well with the measured data even though the model was based on parameter values derived from a batch fermentation.
1. INTRODUCTION This work is focused on the design of an optimal feeding strategy for production of xylitol by fed-batch fermentation of xylose. Xylitol, a five-carbon sugar alcohol, is an important commercial sweetener used in foods, pharmaceuticals, and oral hygiene products. Xylitol sells for $4−5 kg−1 and has a global market worth around $340 million per annum.1 Xylitol is produced via chemical transformation of xylose derived from wood hydrolysate. This process produces other undesired byproducts and, therefore, xylitol made by this method requires extensive and expensive purification. An alternative potentially attractive production method is via microbial conversion of xylose in a fermentation process.2−4 Yeasts of the genus Candida are some of the most effective microorganisms for producing xylitol. Candida mogii is an especially good producer.2,3 If xylose is used as the sole carbon source in the fermentation, some of the xylitol formed is further metabolized for cell growth and maintenance and this reduces the overall yield of xylitol on xylose. A better production strategy is to use a carbon source such as glucose for cell growth so that most of the xylose provided in the feed is transformed to xylitol with an improved yield.5 Xylitol is typically produced in a fed-batch fermentation so that the concentration of glucose in the bioreactor remains low: too high a concentration of glucose interferes with uptake of xylose into the cell. The fermentation broth and the feed generally contain more xylose than glucose. The feeding profiles of glucose and xylose need to be optimized to achieve maximum conversion of xylose to xylitol and achieve a high final titer of the product. Design of an optimal feeding strategy of xylitol production needs to consider the kinetics of cell growth, product formation, and the consumption of the carbon substrates. These kinetics are generally nonlinear. In optimization of highly nonlinear kinetics, the estimation of the kinetic parameters and the development of a substrate feeding strategy can be handled particularly well by the use of genetic algorithms.5,6 A genetic algorithm (GA) based approach was used in this work. The © XXXX American Chemical Society
basic concepts of genetic algorithms have been reviewed in the literature.6,7 In GA based optimization, a randomly generated population of strings, or chromosomes, is used to encode candidate solutions to the optimization problem. In subsequent cycles (or generations) of optimization, the population evolves toward an improved description of the system’s behavior. Optimization based on genetic algorithms is proving increasingly useful in bioprocesses.5,8,9
2. THE FERMENTATION MODEL The kinetic model used in the optimization was developed from a previously reported model for batch fermentation of xylose to xylitol (see Appendix).5 Thus, for a fed-batch fermentation involving separate feeds of xylose and glucose at flow rates of Fxyl and Fglc, respectively, the various material balances on the bioreactor can be written as follows: 1. For the biomass concentration: Fglc + Fxyl dCx =− ·Cx + μ·Cx dt VL (1) where Cx is the biomass concentration at time t, Fglc is volume flow rate of the glucose feed, Fxyl is the volume flow rate of the xylose feed, VL is the volume of the broth in the fermenter at time t, and μ is the specific growth rate. 2. For xylose concentration: dCxyl dt
=
Fxyl VL
f Cxyl −
Fglc + Fxyl VL
Cxyl − qxyl ·Cx
(2)
In the above equation, Cxyl is xylose concentration in the bioreactor, Cfxyl is xylose concentration in the feed medium and qxyl is the specific uptake rate of xylose. Received: August 19, 2014 Revised: January 13, 2015 Accepted: February 3, 2015
A
DOI: 10.1021/ie5032937 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
Table 1. Operator Options Used in the Optimization10
3. For glucose concentration: dCglc dt
=
Fglc VL
f Cglc −
Fglc + Fxyl VL
Cglc − qglc ·Cx
(3)
Cfglc
where Cglc is glucose concentration in the bioreactor, is glucose concentration in the feed medium, and qglc is the specific consumption rate of glucose. 4. For extracellular xylitol: ex Fglc + Fxyl ex dCxit ′ Cx Cxit + rt,xit =− dt VL
volumetric feed flow rates at each of the n steps, were the variable to be optimized and became the elements of the chromosome of the GA optimization (Figure 1a). If more than one control variables (e.g., multiple feeds) needed to be calculated, these were coded in a sequence on the chromosome (Figure 1b). The GA created N candidate solutions (N chromosomes) in the form of strings of variables. These candidate solutions were strings of random numbers within the search domain. For example, the feed flow rate F was constrained as Fmin ≤ F ≤ Fmax where Fmax is the maximum feed flow rate for a given component and Fmin is the minimum feed flow rate for the component. A numerical integration procedure was used to produce the simulated fermentation profiles for each chromosome. The feed rate varied with time in accordance with the sequence of values specified by the elements of the chromosome (Figure 1a). The resulting objective values for the different chromosomes were evaluated for selection for the next generation. The optimization was stopped once a specified maximum number of generations of 20 000 was reached,11 or there was no improvement in fitness of the objective function for a consecutive 500 generations.11 Xylitol production was optimized for a fed-batch fermentation involving two substrates, that is, xylose and glucose. The substrates were fed either mixed in a single-feed solution, or as two separate feed solutions. The goal of the optimization was to determine the optimal feeding profiles for maximizing the xylitol production in a fermentation of a minimum duration. This objective was described by the following performance function:
where is the extracellular concentration of xylitol and rt,xit ′ is mass flux of xylitol per unit cell dry mass. 5. For intracellular xylitol: (5)
where Cinxit is the intracellular concentration of xylitol, rf,xit is the specific rate of production of xylitol, ru,xit is the specific consumption rate of intracellular xylitol, and ρx is the density of a cell. 6. For the broth volume in the fermenter: dVL = Fxyl + Fglc dt
operator options 4 [6, max generation, 3] [4, max generation, 3] 4 2 [2, 3] 2 0.08
(4)
Cex xit
in dCxit in ′ ) ·ρx − μCxit = (rf,xit − ru,xit − rt,xit dt
operator name boundary mutation multinon-uniform mutation nonuniform mutation uniform mutation arithmetic crossover heuristic crossover simple crossover normalized geometric selection
(6)
If only a single-feed stream consisting of a mixture of the two substrates is used, the term on the right-hand-side of eq 6 is replaced by the mixed feed flow rate F.
3. EXPERIMENTAL SECTION 3.1. Microorganism, Culture Media, and Inoculum Preparation. The xylitol producing yeast Candida mogii ATCC 18364 (TISTR 5892) was used throughout. The yeast was maintained on a potato dextrose agar slant at 4 °C and transferred to fresh medium before preparation of the inoculum. The inoculum was prepared in a medium of the following composition (per liter of solution): 18.75 g of KH2PO4, 6 g of (NH4)2HPO4, 1.13 g of MgSO4·7H2O, 0.1 g of CaCl2, 36.5 mg of myo-inositol, 18.2 mg of calcium pantothenate, 3.66 mg of thiamine-HCl, 0.9 mg of pyridoxalHCl, 0.018 mg of biotin, 9.1 mg of FeCl3, 6.4 mg of MnSO4· H2O, 5.46 mg of ZnSO4·7H2O, 1.46 mg of CuSO4·5H2O and 20 g of glucose.5 The inoculum was grown at 30 °C for 24 h in a shake flask (20 mL culture medium in 250 mL flask) held on a rotary shaker at 250 rpm. 3.2. Optimization of the Feeding Profile. A real-valued genetic algorithm (GA) was used as a nonlinear optimizer to calculate an optimal feeding profile for the fed-batch production of xylitol.10 For this application, the GA was used in combination with MATLAB (www.mathworks.com) simulation software and constraint handling procedures. The GA options used in the optimization are specified in Table 1 and are based on published recommendations.10 The cultivation time was discretized into n steps of equal length. Prior experience5 with this fermentation suggested an anticipated culture duration of ≤20 h and therefore an n-value of 10 was used so that each constant feed flow step spanned no more than 10% of the total anticipated duration of the culture. Shorter steps may have improved the solution but were impractical in view of the computational time required. The control values, that is, the
max J =
Fi(t ), t f
(Cxit·VL)t f tf
(7)
where max J is the maximum value of the objective function, Cxit is the concentration of xylitol in the fermentation broth and (Cxit·VL)tf is the total mass of xylitol produced by the completion time tf of the fed-batch fermentation. The optimization was subjected to physical constraints on the feed flow rate and the final culture volume in the bioreactor. The feed flow rates of xylose and glucose were constrained such that 0 = Fmin ≤ Fi(t ) ≤ Fmax
(8)
Here Fi(t) is the feed rate of the component i (xylose or glucose) at time t. The values of Fmin and Fmax were constrained by the feed pump capacity or speed used. The maximum volume of the broth was constrained by the working volume of the bioreactor; thus: VL(tf ) ≤ VL,max B
(9) DOI: 10.1021/ie5032937 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
Figure 1. Chromosome structures with feed rate elements for a single-feed (a) and two-feed (b) optimization.
where VL(tf) is the broth volume in the bioreactor at the completion time tf of the fed-batch operation and VL,max is the maximum permissible working volume of the bioreactor. The maximum value of the feed rate was 0.3 L·h−1 and the maximum working volume of the bioreactor was 4.0 L. Therefore, the physical constraints on the feed rate and the culture volume were the following: 0 ≤ Fi(t) ≤ 0.3 L·h−1 and VL(tf) ≤ 4.0 L, where i is xylose or glucose and 0 ≤ t ≤ tf. A volume constraint was handled by a penalty strategy. This transformed the constrained problem into an unconstrained problem. The penalty term reflected a violation of the constraint and assigned a low fitness to the objective functions for the individuals that gave solutions that were far from the feasible. The fitness function was as follows: fitness = J − Jpen
profile. The feeding was terminated once the maximum working volume of 4 L had been attained. 3.4. Analytical Methods. The fermentation broth was sampled periodically. The dry biomass concentration in the broth was determined by recovering the cells by centrifugation (1700g, 15 min), washing twice in distilled water, drying to a constant weight at 105 °C, cooling in a desiccator, and weighing. The supernatant of the centrifuged broth samples was used to measure the concentrations of xylose, glucose, and xylitol. The concentrations were measured by HPLC (Knauer, Berlin, Germany). A VertiSep SUGAR CMP HPLC column (7.8 mm × 300 mm, 9 μm; Vertical Chromatography Co., Ltd., Thailand) was used. The column was held at 80 °C. The mobile phase was deionized water at a flow rate of 0.4 mL· min−1. A refractive index detector was used. The injection volume was 20 μL.
(10)
where Jpen
⎧ VL(tf ) ≤ VL,max ⎫ ⎪ 0; ⎪ ⎬ =⎨ ⎪ ⎪ ⎩ 0.5·(VL(tf ) − VL,max ); VL(tf ) > VL,max ⎭
4. RESULTS AND DISCUSSION 4.1. Fed-Batch Cultivation with a Constant Feed Rate and a Single Feed. This mode of operation was simulated as the base case for comparison with the other feeding regimes because it is a commonly used feeding strategy in fed-batch operations. The profiles of biomass production, xylose consumption, glucose consumption, and xylitol production for a fed-batch operation were first simulated for the initial conditions specified in section 3.2. The single-feed stream was a mixture of xylose (200 g·L−1) and glucose (20 g·L−1) to give a glucose/xylose concentration ratio of 10%. The cultivation time was fixed at 40 h. A constant feed rate value of 0.0375 L·h−1 was used so that after 40 h of operation, the final volume of the broth in the bioreactor was the maximum working volume of 4.0 L. The feed rate used in the simulation was based on prior empirical experience with this fermentation.3−5 This simulated fed-batch operation was designated as FB-1 and had the fermentation profiles shown in Figure 2. For this simulation, the values of μ, qxyl, qglc, rt,xit ′ , rf,xit, and ru,xit were calculated as previously reported and shown in the Appendix.5 On the basis of the simulated fed-batch operation with a constant feed rate (Figure 2), the maximum final concentration of xylitol was 25.16 g·L−1, or equivalent to an average production rate of 2.52 g·h−1. The xylitol yield was 0.56 g·g−1 (61% of theoretical yield) and the residual xylose concentration at the end of the fermentation was 30.26 g·L−1. For comparison with Figure 2, the profiles of a batch fermentation were simulated as shown in Figure 3. For the batch fermentation, designated as B-1, the working volume was
(11)
The penalty term varied during the optimization in accordance with the level of violation, depending on the distance from the feasible region. Therefore, any candidate individual that violated the constraint would inherit a low fitness value and find it difficult to survive to the next generation. At the start of the fed-batch operation, the initial concentrations of the various components in the bioreactor and the feed were as follows: Cx,0 = 6.0 g·L−1, Cxyl,0 = 0 g·L−1, Cglc,0 = 0 g·L−1, Cxit,0 = 0 g·L−1, Cfxyl = 200 g·L−1, and Cfglc = 20 g· L−1. The initial culture volume (VL,0) was 2.5 L. 3.3. Fed-Batch Cultivation. Fermentations were carried out in a 5 L stirred-tank bioreactor (Biostat B, B. Braun Biotech International, Germany) with an initial volume of 2.5 L of a minimal medium containing 10 g·L−1 glucose and 5 g·L−1 xylose. For the first 24 h, the conditions were aerobic with a dissolved oxygen concentration of >75% of air saturation. The temperature was controlled at 30 °C, and the pH was controlled at 4.5. Afterward, the dissolved oxygen concentration was controlled at 20% of air saturation value by automatic variation of the aeration rate and the agitation speed in the range of 600−800 rpm. The pH was now controlled at 6.0 by the automatic addition of 6 M NaOH solution or 6 M H3PO4 solution as needed. The glucose and xylose solutions were fed into the bioreactor in accordance with the optimized feeding C
DOI: 10.1021/ie5032937 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
concentration of biomass of 3.75 g·L−1 in the batch operation B-1. Therefore, except for the mode of operation, the batch fermentation simulated in Figure 3 was identical to the fedbatch fermentation simulated in Figure 2. The simulated profiles for the batch operation (Figure 3), showed a maximum xylitol concentration of 18.46 g·L−1 at 19.02 h. At this point, the average yield and production rate of xylitol were 0.35 g·g−1 and 3.88 g·h−1, respectively, and the residual xylose concentration was 21.99 g·L−1 (Figure 3). The batch operation B-1 and the fed-batch operation FB-1 are compared in Table 2. Although the maximum concentration of xylitol in the fed-batch operation was higher than in the batch (Table 2), the production rate of xylitol for the fed-batch was lower. Nevertheless, the fed-batch operation with a constant rate of feeding did substantially improve the xylitol yield on xylose, compared to the batch operation (Table 2). Clearly, in the batch fermentation more of the xylose was converted to biomass rather than to xylitol and this reduced the xylitol yield (Table 2). 4.2. Optimization of Feeding Profile for the Single Feed System. The substrate feeding profile for a fed-batch fermentation was optimized for a single-feed stream containing 200 g·L−1 of xylose and 20 g·L−1 of glucose. The initial conditions of the fermentation were as noted in section 3.2. The feed rate was discretized into a set of 10 steps of equal duration. A real-valued genetic algorithm with a population size of 80 was then used to determine the optimal feed rate profile to maximize xylitol production. The chromosome had 10 elements that represented the constant feed flow rates of the 10 steps (Figure 1a). Each optimization ran for five trials for each case (i.e., cases FB-2 and FB-3 discussed later). The run that showed the best performance (i.e., had the highest final concentration of xylitol) was deemed to be the most fit and was included in Table 2 for comparison with the other runs. This optimized single-feed fed-batch operation was designated as FB-2. The optimized feeding profile and resulting profiles of biomass concentration, glucose concentration, xylose concentration, and xylitol concentration are shown in Figure 4. The total duration of the FB-2 fed-batch operation (Figure 4) was fixed at 40 h. The maximum xylitol concentration attained in this operation was 25.59 g·L−1 (Figure 4), or equivalent to an average xylitol production rate of 2.56 g·h−1. Xylitol yield was 0.51 g·g−1 (55.8% of theoretical yield). The residual xylose concentration at the end of the fermentation was 25.30 g·L−1. The feeding profile established by the genetic optimization had feed rate steps that varied in flow rate between 0.0200 and 0.0655 L·h−1. The resulting concentration profiles for the biomass, xylose, glucose, and xylitol (Figure 4) were similar to those generated for the fed-batch fermentation FB-1 which had a constant feed rate. The optimized stepped
Figure 2. Fermentation profiles for biomass, xylose, glucose, and xylitol at a constant feed flow rate of 0.0375 L·h−1 for the single-feed system FB-1.
Figure 3. Simulated batch fermentation profiles for biomass, xylose, glucose and xylitol for an initial concentration ratio of glucose/xylose of 10% in batch culture B-1.
fixed at 4.0 L, or the same as the final volume for the fed-batch fermentation. In the fed-batch fermentation (Figure 2), the total amounts of glucose and xylose added to the fermenter were 30 and 300 g, respectively. These quantities were equivalent to the initial xylose concentrations of 75 g·L−1 and an initial glucose concentration of 7.5 g·L−1 in the batch operation. The initial amount of biomass in the fed-batch operation FB-1 was 15 g, corresponding to an initial
Table 2. Optimal Production Rates and Operation Times for the Various Cases final concentration (g·L−1)
tf
xylitol yield
production rate
case
feed mode
(h)
biomass
xylose
glucose
xylitol
xylose
glucose
(g·g−1)
(g·h−1)
B-1 FB-1 FB-2 FB-3 FB-4 FB-5 FB-6
batch single feed (constant) single feed single feed double feed double feed double feed
19.02 40.00 40.00 19.65 20.00 21.23 20.00
25.90 16.12 18.20 15.48 9.39 10.61 20.30
21.99 30.26 25.30 41.44 39.68 36.15 21.78
