Mathematical Modeling of Acetone-Butanol-Ethanol Fermentation with

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Biofuels and Biomass

Mathematical Modeling of Acetone-Butanol-Ethanol Fermentation with Simultaneous Utilization of Glucose and Xylose by Recombinant Clostridium Acetobutylicum Jongkoo Lim, Ha-Eun Byun, Boeun Kim, Hyerin Park, and Jay Lee Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.9b01007 • Publication Date (Web): 06 Aug 2019 Downloaded from pubs.acs.org on August 9, 2019

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A systematic approach for parameter identification of the co-fermentation kinetic model 121x74mm (300 x 300 DPI)

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Model fits to the experimental data of the specific growth rates (A) on glucose and (B) on xylose 152x57mm (300 x 300 DPI)


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Experimental and predicted concentration profiles of fed-batch fermentation with ISBR-by-adsorption in glucose-based medium with glucose feed concentration of (A) 200 g/L and (B) 700 g/L respectively 165x129mm (300 x 300 DPI)


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Comparison of the simulation result after the model adjustment and experimental data of fed-batch fermentation with ISBR in glucose/xylose-based medium at three glucose-to-xylose initial ratios: (A) 9:1 and (B) 3:7 with feed concentration of 200 g/L, and (C) 8:2 with feed concentration of 700 g/L 152x182mm (300 x 300 DPI)


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Model validation with experimental data of fed-batch fermentation with ISBR in glucose/xylose-based medium at three glucose-to-xylose initial ratios: (A) 7:3, (B) 4:6 with feed concentration of 200 g/L, and (C) 9:1 with feed concentration of 700 g/L 152x182mm (300 x 300 DPI)


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Mathematical Modeling of Acetone-Butanol-Ethanol Fermentation with Simultaneous Utilization of Glucose and Xylose by Recombinant Clostridium Acetobutylicum Jongkoo Lim†, ‡, Ha-Eun Byun†, Boeun Kim†, Hyerin Park‡, Jay H. Lee†, *

† Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291, Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea ‡ R&D Center, GS Caltex Corporation, 359, Expo-ro, Yuseong-gu, Daejeon, 34122, Republic of Korea

KEYWORDS Acetone-butanol-ethanol fermentation; Co-fermentation kinetic modeling; Glucose and xylose; Clostridium acetobutylicum; Model parameter identification


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ABSTRACT Studies on acetone-butanol-ethanol (ABE) fermentation of sugars from lignocellulosic biomass have been actively carried out in recent years, and recombinant strains have been developed to efficiently co-utilize glucose and xylose, which are the dominant sugar types in most lignocellulosic biomass. However, there is a lack of mathematical models for describing and predicting the simultaneous utilization of glucose and xylose in ABE fermentation, particularly for the purpose of supporting optimization and control of the process. This study proposes a kinetic model for ABE fermentation with co-utilization of glucose and xylose by recombinant Clostridium acetobutylicum. The model is developed based on unstructured models, i.e., the Monod equation and the Luedeking-Piret model, and a modified concentration-dependent weighting factor is suggested to describe the simultaneous utilization of glucose and xylose based on the experimental analysis. A systematic identification approach is employed to obtain reliable estimates of model parameters for the co-fermentation process, which involves highly nonlinear and correlated kinetics. The glucose- and xylose-associated parameter groups are sequentially estimated using single substrate- and co-fermentation data, respectively, and in the combined model, a subset of the parameters are selected through an identifiability analysis for further refinement.

The

developed model is shown to accurately predict the dynamics of the co-fermentation of glucose and xylose in ABE production at various glucose-to-xylose ratios, feeding rates, and feed concentrations.


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1. INTRODUCTION As concerns about climate change deepen, interest in biofuels has been growing rapidly. Biobutanol, produced from acetone-butanol-ethanol (ABE) fermentation by Clostridia1, has received much attention in recent years owing to its advantages over bioethanol, including the high energy content, low volatility and corrosiveness, good miscibility with gasoline, and of the ability to use the existing transportations infrastructures without any modification2-4. Despite the superior properties of biobutanol, the biobutanol production has faced several problems in commercialization due to the high cost of feedstock, and low product yield and productivity caused by the toxicity of produced butanol1, 5. Major ways to overcome these problems are i) selection of cheaper feedstock; ii) genetic engineering of microorganisms for increasing the yield, productivity or tolerance for inhibitors in lignocellulosic biomass hydrolysates; and iii) product recovery during fermentation for mitigating the product toxicity problem2, 6. Recently, biobutanol produced from ABE fermentation of lignocellulosic (i.e., the secondgeneration) biomass has been actively investigated as an alternative to the first-generation biofuels, in an effort to lower the feedstock cost2, 6-7. The lignocellulosic biomass contains various types of hexose and pentose, including glucose, xylose, mannose, and arabinose. The wild-type Clostridium can utilize different types of sugars on an individual basis, but not simultaneously. For example, the strain consumes a negligible amount of less preferred xylose in the presence of more preferred glucose. This regulatory mechanism is known as carbon catabolite repression (CCR)8, and leads to the accumulation and waste of the less-preferred sugars when the mixture of sugars obtained from the lignocellulosic biomass is used in a continuous fermentation process. Thus, genetic engineering of the strain for enhancing pentose utilization has been conducted to


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facilitate a more effective co-utilization of glucose and other fermentable sugars, especially xylose8-9. The co-utilization of glucose and xylose by the recombinant strain increases the nonlinearity and complexity of the fermentation kinetics, presenting significant challenges in process design and operation. Thus, a reliable model that can describe and predict the cofermentation kinetics is essential. Particularly, for model-based optimization and control studies, the model should be validated over various possible operating conditions. In addition, since a typical fermentation process exhibits significant batch-to-batch variations even with a same type of strains due to the natural variabilities of living organisms, on-line model adaptation and optimization may be necessary to ensure stable operation as well as consistent performance 10. For such purposes, a simple rather than complex model is suitable. There have been several modeling studies on single substrate ABE fermentation, but studies on the co-fermentation modeling are scarce in the literature. Recently, Diaz and Willis11 proposed a kinetic model of ABE fermentation applicable to both the single substrate fermentations of glucose and xylose as well as their co-fermentation. The authors modified Shinto's model12 to account for the CCR, and the model parameters were estimated with previously reported experimental data. However, only a single experimental data set obtained from a cofermentation experiment with the initial glucose to xylose ratio of 1:1 was used for the parameter estimation, so the predictive capability of the proposed model at other initial glucose to xylose ratios is questionable. Moreover, the model proposed by Diaz and Willis is a structured model based on a metabolic pathway that considers a total of 13 components including intermediate products (acetyl-CoA, butyryl-CoA, etc.) as well as products and sugars. Such a model may be


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able to enhance our fundamental understandings of the microbial metabolism, but may not be best suited to the purpose of directing on-line optimization and control studies. The aim of this study is to develop a mathematical model capable of describing and predicting the kinetics of the ABE fermentation by recombinant strains utilizing glucose and xylose simultaneously, for the purpose of supporting optimization and control efforts. To this end, we perform lab-scale batch and fed-batch experiments using recombinant Clostridium acetobutylicum and develop a model with certain assumptions based on the literature and our analysis of the experimental data. The model combines the well-known unstructured models, i.e., the Monod and Luedeking-Piret models, which have relatively simple structures with a smaller number of parameters compared to those based on metabolic networks. In particular, a new index, which weights the relative sugar concentrations and relative preference for glucose, is proposed to predict the kinetics of co-fermentation of glucose and xylose at various ratios. The developed model is validated under diverse medium and feeding conditions to ensure its applicability to optimization and control studies. In this study, we also propose a systematic approach to estimate the model parameters. Since the consumption kinetics of glucose and xylose in the co-fermentation are complex and highly correlated, it is difficult to identify the model parameter values accurately with cofermentation data alone. Therefore, this study proposes to estimate the kinetic parameters associated with the glucose and xylose using single substrate- and co-fermentation data, respectively, and then readjust a subset of their values.

2. MATHEMATICAL MODELING


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A kinetic model of ABE fermentation with simultaneous utilization of glucose and xylose is developed based on previous unstructured models, which have been employed to describe the kinetics of the ABE fermentation13-15. The rate equations for cell growth on glucose and xylose (𝜇𝑔,𝐺𝑙 and 𝜇𝑔,𝑋𝑙 ) are constructed from the modified Monod equation. The rate equations for sugar consumption and product formation ( 𝑟𝐺𝑙 , 𝑟𝑋𝑙 , 𝑟𝐵 , 𝑟𝐸 , and 𝑟𝐴 ) are established based on the Luedeking-Piret model16 as it has been shown that the Luedeking-Piret model can describe the kinetics of the ABE fermentation in many previous studies17. The main assumptions in the model development are as follows: (i)

The fermenter is well-mixed so that its content is homogeneous.

(ii)

The pH and temperature in the fermenter are controlled to be constant around their optimal values. Therefore, the proposed model does not include the terms with respect to varying pH and temperature.

(iii)

Since the inhibitory effects of ethanol and acetone are relatively negligible compared to that of butanol, only the inhibitory effect of butanol is considered in the model. According to some previous experimental reports7, 18-19, there exist the butanol inhibition effects on cell growth, sugar consumption, and butanol production.

(iv)

The cell growth can be inhibited by high concentrations of substrate and cell as well as butanol in the ABE fermentation18, 20-21.

(v)

The threshold levels of butanol toxicity for cell growth on glucose and xylose (𝑃𝐵,𝐺𝑙 and 𝑃𝐵,𝑋𝑙 ) are assumed to have different values based on the observation by Bowles et al.18 and Ounine et al.19. Also, the threshold levels of butanol toxicity for glucose consumption ′ ′ and xylose consumption (𝑃𝐵,𝐺𝑙 and 𝑃𝐵,𝑋𝑙 ) are assumed to have different values.


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(vi)

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Quantity of each sugar consumed depends on the sugar ratio but the total amount of sugar consumed is almost identical regardless of the glucose-to-xylose ratio for a same amount of initial sugar medium. This assumption is made based on observations from the batch fermentation experiments with several initial glucose-to-xylose ratios (i.e., 8:2, 7:3 and 6:4) by recombinant Clostridium acetobutylicum (see Section 4.1). Although the strain is manipulated to alleviate the CCR and utilizes the two sugar types simultaneously as shown in the experimental results (see Section 4.1), the preference for the glucose utilization still remains.

(vii)

The production rates (𝑟𝐵 , 𝑟𝐸 , 𝑟𝐴 ) do not depend on the sugar type explicitly. This is based on the experimental observation that the produced amount of ABE is almost identical regardless of the glucose-to-xylose ratio when the same amount of sugar is consumed (Section 4.1).

In this study, fed-batch fermentation with in situ butanol recovery by adsorption (referred to as “ISBR-by-adsorption” hereafter, where adsorbents are contained inside the fermenter to recover the products) as well as conventional batch fermentation runs are carried out to obtain data for an accurate model parameter estimation. The conventional batch fermentation without product recovery has a short production time since the cell growth becomes rapidly inhibited by the butanol inhibition effect at a low cell concentration. This results in the lack of information on the inhibitory effect of high cell concentration on cell growth (see Supporting Information). On the other hand, in the fed-batch fermentation with product recovery by adsorption, the production time increases due to the product recovery by the adsorption so the cell growth inhibition by high cell concentration can be experimentally observed. In addition, the model developed considering the


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dilution effect by feeding and the adsorption effect is expected to be more widely applicable, especially in optimization and control studies22. Section 2.1 presents the rate equations for cofermentation of glucose and xylose in the ABE production, and Section 2.2 introduces the dynamic model of fed-batch fermentation with ISBR-by-adsorption.

2.1 Rate equations for the ABE fermentation using glucose and xylose Based on the assumptions (iii), (iv) and (v), the specific rates of cell growth from glucose and xylose, 𝜇𝑔,𝐺𝑙 and 𝜇𝑔,𝑋𝑙 respectively, are formulated as the modified Monod equations that include three inhibition terms. They are represented as follows: 𝑖

𝜇𝑔,𝐺𝑙

𝑚𝑎𝑥 𝜇𝐺𝑙 𝐺𝑙 𝐶𝐵 𝐵,𝐺𝑙 𝑋 𝑖𝑋 = (1 − ) (1 − ) 𝐾𝑆,𝐺𝑙 + 𝐺𝑙 + 𝐺𝑙2 ⁄𝐾𝐼,𝐺𝑙 𝑃𝐵,𝐺𝑙 𝑃𝑋

𝜇𝑔,𝑋𝑙

𝑚𝑎𝑥 𝜇𝑋𝑙 𝑋𝑙 𝐶𝐵 𝐵,𝑋𝑙 𝑋 𝑖𝑋 = (1 − ) − (1 ) 𝐾𝑆,𝑋𝑙 + 𝑋𝑙 + 𝑋𝑙2 ⁄𝐾𝐼,𝑋𝑙 𝑃𝐵,𝑋𝑙 𝑃𝑋

(1)

𝑖

(2)

Exact definitions of the parameters are given in the Nomenclature section. To describe the contribution of glucose and xylose to the cell growth in co-fermentation, several modeling methods have been proposed: a method to modify the Monod equation by introducing a competitive sugar consumption term into the denominator23-25 and a method to represent the overall growth rate as a weighted sum of the growth rates on individual substrates with constant weighting coefficients26. In this study, the overall specific growth rate from a mixture of glucose and xylose is obtained by a weighted sum of the specific growth rates 𝜇𝑔,𝐺𝑙 and 𝜇𝑔,𝑋𝑙 with the time-varying weighting factors (𝑗1 , 𝑗2 ) as below: 𝜇𝑔 = 𝑗1 𝜇𝑔,𝐺𝑙 + 𝑗2 𝜇𝑔,𝑋𝑙 and 𝑗1 + 𝑗2 = 1

(3)


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𝑋𝑙 𝐾 𝑗2 = { 𝐺𝑙 + 𝑋𝑙 1

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𝑖𝑓 𝐺𝑙 > 0

(4)

𝑖𝑓 𝐺𝑙 = 0

Based on the assumption (vi), the suggested weighting factor is the relative sugar concentrations in the fermentation broth multiplied by the relative preference for sugars as expressed in Eq 4 and the weighting factors sum up to unity. The parameter 𝐾 represents the relative preference for glucose over xylose; a smaller 𝐾 indicates higher glucose preference. The value of 𝐾 can vary depending on the extent to which CCR is alleviated in the genetically manipulated strain. Note that 𝐾 equals to zero if glucose and xylose are sequentially consumed (i.e., strong CCR without any genetic manipulation). When the glucose in the fermentation broth is completely consumed, the weighting factor for the xylose-consuming growth (𝑗2 ) becomes unity. The rate equations for sugar consumption (𝑟𝐺𝑙 and 𝑟𝑋𝑙 ) and product formation (𝑟𝐵 , 𝑟𝐸 , and 𝑟𝐴 ) are established based on the Luedeking-Piret model, composed of a growth-associated part (𝛼𝑖 ) and a nongrowth-associated part (𝛽𝑖 ), as follows: 𝑖′

1 𝑑𝐺𝑙 𝐶𝐵 𝐵,𝐺𝑙 𝑟𝐺𝑙 = − = 𝛼𝐺𝑙 𝑗1 𝜇𝑔,𝐺𝑙 + 𝛽𝐺𝑙 𝑗1 (1 − ′ ) 𝑋 𝑑𝑡 𝑃𝐵,𝐺𝑙

(5)

𝑖′

1 𝑑𝑋𝑙 𝐶𝐵 𝐵,𝑋𝑙 𝑟𝑋𝑙 = − = 𝛼𝑋𝑙 𝑗2 𝜇𝑔,𝑋𝑙 + 𝛽𝑋𝑙 𝑗2 (1 − ′ ) 𝑋 𝑑𝑡 𝑃𝐵,𝑋𝑙

(6)

𝑖

1 𝑑𝐶𝐵 𝐶𝐵 𝐵,𝐵 𝑟𝐵 = = 𝛼𝐵 𝜇𝑔 + 𝛽𝐵 (1 − ) 𝑋 𝑑𝑡 𝑃𝐵,𝐵

(7)

𝑟𝐸 =

1 𝑑𝐶𝐸 = 𝛼𝐸 𝜇𝑔 + 𝛽𝐸 𝑋 𝑑𝑡

(8)

𝑟𝐴 =

1 𝑑𝐶𝐴 = 𝛼𝐴 𝜇𝑔 + 𝛽𝐴 𝑋 𝑑𝑡

(9)


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Based on the assumption (iii) and (v), the butanol inhibition term is added to each nongrowthassociated part in 𝑟𝐺𝑙 , 𝑟𝑋𝑙 and 𝑟𝐵 since the specific growth rates in their growth-associated parts already account for the butanol inhibition effect as represented in Eqs 1 and 2. The production rates, 𝑟𝐵 , 𝑟𝐸 and 𝑟𝐴 , depend only on the overall growth rate and the cell concentration regardless of the sugar type, according to the assumption (vii).

2.2 Model for the fed-batch fermentation with ISBR-by-adsorption In the fed-batch fermentation with ISBR-by-adsorption, both fermentation and adsorption take place in the fermenter. The sugar medium is continuously fed into the fermenter to prevent a shortage of the substrates. The overall mass balance equations for the concentrations of cell (𝑋), glucose (𝐺𝑙), xylose (𝑋𝑙), butanol (𝐶𝐵 ), ethanol (𝐶𝐸 ) and acetone (𝐶𝐴 ) can be derived based on the rate equations in Section 2.1 as follows: 𝑑𝑋 = (𝜇𝑔 − 𝑘𝑑 − 𝐷)𝑋 𝑑𝑡

(5)

𝑑𝐺𝑙 = (𝐺𝑙𝑓 − 𝐺𝑙)𝐷 − 𝑟𝐺𝑙 𝑋 𝑑𝑡

(6)

𝑑𝑋𝑙 = (𝑋𝑙𝑓 − 𝑋𝑙)𝐷 − 𝑟𝑋𝑙 𝑋 𝑑𝑡

(7)

𝑑𝐶𝐵 𝑑𝐴𝐵 = 𝑟𝐵 𝑋 + − 𝐶𝐵 𝐷 𝑑𝑡 𝑑𝑡

(8)

𝑑𝐶𝐸 𝑑𝐴𝐸 = 𝑟𝐸 𝑋 + − 𝐶𝐸 𝐷 𝑑𝑡 𝑑𝑡

(9)


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𝑑𝐶𝐴 𝑑𝐴𝐴 = 𝑟𝐴 𝑋 + − 𝐶𝐴 𝐷 𝑑𝑡 𝑑𝑡

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(10)

where 𝑘𝑑 is the specific rate constant of cell death, and 𝐺𝑙𝑓 and 𝑋𝑙𝑓 are the concentrations of glucose and xylose in the feed media, respectively. The dilution rate D is defined as D=F/V, where F is the feeding rate and V is the liquid volume in the fermenter. The rate of change in the concentration of product i by adsorption (𝑑𝐴𝑖 ⁄𝑑𝑡) is described using the adsorption kinetic model developed by Eom et al.27 which is derived based on the external mass-transfer equation and the adsorption equilibrium from the extended Langmuir model as below: 𝑑𝐴𝑖 𝑚 𝑑𝑞𝑖 𝑚 =− = − 𝑘𝑖 (𝑞𝑖,𝑒𝑞 − 𝑞𝑖 ) 𝑑𝑡 𝑉 𝑑𝑡 𝑉 𝑞𝑖,𝑒𝑞 =

𝑞𝑖,𝑚 𝐵𝑖 𝐶𝑖 1 + ∑𝑛𝑖=1 𝐵𝑖 𝐶𝑖

(11)

(12)

where 𝑚 is the amount of adsorbents in the fermenter. The values of adsorption kinetic parameters reported in Eom et al.27 are used here.

2.3 Model parameter identification Since the proposed kinetic model contains a large number of parameters that need to be estimated (30 in total), it is difficult to identify all of them at once using solely the experimental data of co-fermentation. When using the co-fermentation data alone, the over-parameterization problem may occur, where the model contains more parameters than estimable by the available data, resulting in inaccurate parameter estimates. In particular, the consumption kinetics of glucose and xylose in the co-fermentation are highly correlated and thus can lead to the poor identifiability and ill-conditioning problem. Therefore, a systematic approach is essential to obtain reliable


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parameter estimates for the co-fermentation process which involves highly nonlinear and correlated kinetics. In this study, we first perform several experiments with different fermentation modes and conditions, e.g., batch fermentation in glucose- and xylose-based medium, fed-batch fermentation with ISBR-by-adsorption in glucose/xylose-based medium. Based on the collected data from these experiments, the Monod parameters, kinetic parameters associated with glucose utilization, and those associated with xylose utilization are estimated separately. The separately estimated values are then fine-tuned through re-estimation of an identifiable subset to improve the fidelity of the model. The detailed procedure of model parameter identification is as follows: Step 1:

The Monod parameters of cell growth on glucose are estimated by fitting the

measured specific growth rates from the batch fermentation experiments with various initial glucose concentrations. In the same manner, the Monod parameters of cell growth on xylose are estimated using the experimental results of the batch fermentation in the xylose-based medium. Step 2:

The parameters related to the glucose utilization and product formation are

estimated by fitting the experimental data (i.e., concentration profiles of the cell, glucose and products) of the fed-batch fermentation with ISBR-by-adsorption in glucose-based medium, with the predetermined Monod parameters fixed. The cell growth-related parameters, i.e., cell death rate constant, inhibitory thresholds and inhibition constants, are also estimated in this step. Step 3:

The parameters related to the xylose utilization and the coefficient for the substrate

preference are estimated by fitting the experimental data (i.e., concentration profiles of cell, glucose, xylose and products) of the fed-batch fermentation with ISBR-by-adsorption in


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glucose/xylose-based medium, while keeping the predetermined parameters in step 1 and step 2 fixed. Step 4:

An identifiable parameter subset obtained through an identifiability analysis is re-

estimated with the same data used in step 3. Finally, the validity of the model is checked with a new data set obtained from different initial glucose-to-xylose ratios and operating conditions.

Figure 1. A systematic approach for parameter identification of the co-fermentation kinetic model. 𝑚𝑎𝑥 𝑚𝑎𝑥 𝜃𝐺𝑙𝑢.𝑀𝑜𝑛𝑜𝑑 = {𝜇𝐺𝑙 , 𝐾𝑆,𝐺𝑙 , 𝐾𝐼,𝐺𝑙 }, 𝜃𝑋𝑦𝑙.𝑀𝑜𝑛𝑜𝑑 = {𝜇𝑋𝑙 , 𝐾𝑆,𝑋𝑙 , 𝐾𝐼,𝑋𝑙 }, 𝜃𝐶𝑒𝑙𝑙.𝐺𝑙𝑢 = ′ ′ {𝑘𝑑 , 𝑃𝐵,𝐺𝑙 , 𝑖𝐵,𝐺𝑙 , 𝑃𝑋 , 𝑖𝑋 }, 𝜃𝐺𝑙𝑢.𝐶𝑜𝑛𝑠 = {𝛼𝐺𝑙 , 𝛽𝐺𝑙 , 𝑃𝐵,𝐺𝑙 , 𝑖𝐵,𝐺𝑙 }, 𝜃𝐴𝐵𝐸.𝑃𝑟𝑜𝑑 =

{𝛼𝐵 , 𝛽𝐵 , 𝑃𝐵,𝐵 , 𝑖𝐵,𝐵 , 𝛼𝐸 , 𝛽𝐸 , 𝛼𝐴 , 𝛽𝐴 }, 𝜃𝐶𝑒𝑙𝑙.𝑋𝑦𝑙 = {𝑃𝐵,𝑋𝑙 , 𝑖𝐵,𝑋𝑙 }, 𝜃𝑋𝑦𝑙.𝐶𝑜𝑛𝑠 = ′ ′ {𝛼𝑋𝑙 , 𝛽𝑋𝑙 , 𝑃𝐵,𝑋𝑙 , 𝑖𝐵,𝑋𝑙 }, 𝜃𝑊 = {𝐾}

The parameter estimation is performed using the conventional least-squares estimation (LSE) method. Lower and upper bounds on each parameter are decided based on our previous study17 and insights gathered from the literature and experiments. The ode45 solver in MATLAB is used to integrate the differential mass balance equations, and lsqnonlin function in MATLAB


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R2017a Optimization Toolbox is employed for solving the nonlinear regression problem. Confidence intervals (CIs) of the parameter estimates are obtained through Monte Carlo simulations using assumed distributions of the measured outputs 28-29. In step 4, in order to readjust the separately estimated parameter values, only an identifiable subset of the parameters, which can be reliably estimated with given data, is re-estimated rather than the entire set. The identifiable parameter subset satisfies the following conditions30: i) the model outputs, such as concentrations of cells, substrates, and products, should be sufficiently sensitive to a change in each parameter of the subset; ii) a variation(s) in the model output(s) due to a change in a certain parameter cannot be canceled out by a change(s) in another parameter(s) in the subset. Many studies30-32 have suggested ways to select an identifiable parameter subset satisfying these conditions. This study employed a sensitivity matrix based method proposed by Brun et al.30 and used two parameter identifiability measures, i.e., collinearity index and determinant measure. For this, a sensitivity matrix (of the outputs) with respect to the parameters is obtained through the central difference approximation. Then the collinearity indices 𝛾𝑘 of all possible subsets of the parameters are computed using the equations in Table 1. 𝛾𝑘 indicates the degree of near-linear dependency of the sensitivity matrix of each subset: If the sensitivity measures of a subset are independent, 𝛾𝑘 is equal to unity, and 𝛾𝑘 approaches infinity as they become linearly dependent. The parameter subsets with 𝛾𝑘 values higher than a threshold level are deemed poorly identifiable, and a reasonable threshold value for 𝛾𝑘 is found to be between 10 – 15 according to the literatures30, 33

. Among the candidates having the largest dimension with a 𝛾𝑘 value below the threshold level,

a parameter subset with the highest determinant measure 𝜌𝑘 (see Table 1) is chosen for the model adjustment. Note that a high value of 𝜌𝑘 indicates that the parameters in the subset are more


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influential and less correlated, i.e., the subset with the highest 𝜌𝑘 is deemed the most identifiable parameter subset.

Table 1. Measures of identifiability analysis30 Notation

Description

Non-dimensional sensitivity matrixa

𝐒 = {𝑠𝑖𝑗 } where 𝑠𝑖𝑗 =

𝜕𝜂𝑖 𝜃𝑗 𝜕𝜃𝑗 𝑠𝑐𝑖

𝐒̃ = {𝑠̃𝑖𝑗 } where 𝑠̃𝑖𝑗 =

Normalized sensitivity matrix

𝑠𝑖𝑗 ‖𝐬𝑗 ‖

𝑁

𝑚𝑠𝑞𝑟 𝛿𝑗

Sensitivity measure

1 2 = √ ∑ 𝑠𝑖𝑗 𝑁 𝑖=1

𝛾𝑘 = 1⁄√min 𝜆̃𝑘 where 𝜆̃𝑘 = 𝑒𝑖𝑔𝑒𝑛(𝐒̃𝑘𝑇 𝐒̃𝑘 )

Collinearity indexb

𝑛

1⁄2𝑛

𝜌𝑘 = det(𝐒𝑘𝑇 𝐒𝑘 )1⁄2𝑛 = (∏ 𝜆𝑗 )

Determinant measureb

𝑗=1 a

th

th

𝜂𝑖 , 𝜃𝑗 and 𝑠𝑐𝑖 denote the i model output, j model parameter, and a scale factor for the model output 𝜂𝑖 , respectively. b

k denotes the index of the parameter subset and n is the number of columns of 𝐒𝑘

3. MATERIALS AND METHODS 3.1 Bacterial strains Recombinant Clostridium acetobutylicum, obtained from American Type Culture Collection, was used as the bacterial strain in this study. In order to disrupt the genes encoding the enzymes responsible for acid formation, both the pta and buk genes were knocked out by using


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the TargeTron Gene Knockout System34-35. In general, this microbe can hardly grow in the lignocellulosic hydrolysates that contain fermentation inhibitors, such as hydroxymethyl furfural (HMF), furfural, and phenolic compounds, and has limited ability to consume glucose and xylose simultaneously. Therefore, optimization of the microbe was performed to increase the tolerance against various unknown inhibitors and the xylose consumption rate by applying forward genetic manipulation with N-Methyl-N-nitro-N-nitrosoguanidine (NTG)-treated mutagenesis as described in Otte et al.36. The mutated colonies were isolated from the total mixture to select the best strain after growing them on a plate containing 1 % of corn steep liquor (CSL) and a mixed sugar solution from lignocellulosic biomass hydrolysate including the inhibitors. The adhE1 and ctfAB genes encoding aldehyde/alcohol dehydrogenase and coenzyme A transferase were overexpressed to increase the butanol yield and selectivity.

3.2 Culture medium and Inoculation The strain was first cultured in an anaerobic chamber (Coy Laboratory products, Glass Lake, MI) containing 90 % (v/v) N2, 5 % (v/v) H2 and 5 % (v/v) CO2 at 37 °C. For a plate culture, 2×YTG (Yeast extract/Tryptone/Glucose) medium (pH 5.8) was used and it contained 20 g/L Glucose, 16 g/L Tryptone, 10 g/L Yeast extract, 4 g/L NaCl and 1.5 % (w/v) agar. Erythromycin was added to the media at the final concentration of 40 μg/mL for the recombinant strains. For tube and flask culture, Clostridial Growth Medium (CGM, pH 5.8) was used and it contained 10 g/L Glucose, 5 g/L Yeast Extract, 2.3 g/L Asparagine, 2 g/L (NH4)2SO4, 1.252 g/L KH2PO4, 1 g/L NaCl, 0.71 g/L MgSO4·7H2O, 0.14 g/L K2HPO4, 0.014 g/L MnSO4·5H2O, 0.01 g/L FeSO4·7H2O and erythromycin was also added to the media at the final concentration of 40 μg/mL in the tube or flask. For the main culture in a 7 L Bioflow fermentor, CSL modified media


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containing several sugars (glucose and xylose), 30 g/L CSL (DAESANG Corporation, Korea), 1 g/L NaCl, 0.71 g/L MgSO4·7H2O, 0.05 g/L FeSO4·7H2O and 0.014 g/L MnSO4·5H2O was used. After adding all components, pH was adjusted to 5.5 by using ammonia. To prepare the inoculums, a 1 mL from a stock culture frozen in 20% (v/v) glycerol was thawed at 22 – 25 °C and was streaked on 2×YTG agar medium. It grew in an anaerobic chamber at 37 °C over 30 hours. And then a 50 mL Falcon tube filled with 40 mL of CGM was prepared for inoculation of a single colony of the Clostridium stain to be cultured in anaerobic condition up to an absorbance of 1.0 at 600 nm. This seed culture was transferred to a flask containing 360 mL of CGM. The 400 mL flask culture was inoculated into the fermenter after the cell density in the flask reached an absorbance of 1.0 at 600 nm.

3.3 Analytical methods Concentrations of glucose and xylose in the fermentation broth were analyzed using highperformance liquid chromatography (HPLC) (Agilent Technologies 1260 Infinity) equipped with a refractive index detector. The analytic separation was achieved on an Aminex® HPX-87H anion exchange column (Bio-Rad Laboratories, Hercules, CA). Concentrations of butanol, ethanol, and acetone were measured by gas chromatography (Agilent 6890N; Agilent Technologies, Santa Clara, CA) with a flame ionization detector (GC–FID). Cell concentration was monitored through measuring absorbance at 600 nm by an Ultrospec 5000 spectrophotometer (Pharmacia Biotech, Uppsala, Sweden).

3.4 Adsorbent


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Dowex optipore L-493, purchased from Dow Korea, was used for as a part of the experimental ISBR-by-adsorption system. This is a hydrophobic poly (styrene-co-divinylbenzene) resin, which has a high surface area and adsorption capacity for 1-butanol27, 37.

3.5 Experiments 3.5.1 Batch fermentation A 7 L Bioflo 310 fermenter (New Brunswick Scientific Co., Enfield, CT) with 2 L working volume was used for the batch fermentation. The pH in the fermenter was maintained at 5.0 by adding ammonia solution (28 %, w/v) at 37 ℃. The culture was agitated at 200 rpm and flushed with oxygen-free nitrogen at a flow rate of 50 mL/min to maintain anaerobic condition17. Several batch fermentation experiments were conducted using the medium supplemented with different initial glucose concentrations (i.e., 2.53, 4.23, 8.86, 18.83, 28.75, 43.5, 51.44, and 69.38 g/L) and different initial xylose concentrations (i.e., 1.88, 5.83, 11.02, 20.1, 40.95, 61.54, and 83.59 g/L), respectively. Here, initial concentrations of glucose and xylose are measured by using HPLC after transferring the fermentation medium from the flask to the batch fermenter. In addition, batch fermentation experiments using glucose and xylose at different initial glucose-toxylose ratios (i.e., 8:2, 7:3, and 6:4) were conducted to confirm the simultaneous utilization of glucose and xylose and to provide a basis for the assumptions in the model development.

3.5.2 Fed-Batch fermentation with ISBR-by-adsorption Lab-scale fed-batch fermentation experiments were carried out using the same strain, equipment, and media as in the batch fermentation. A 200 g of adsorbent was added to the fermenter, and the feed media was continuously injected through the peristaltic pump to prevent


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sugar depletion in the fermentation broth. Also, a small amount of antifoam (Antifoam 204; SigmaAldrich) was added to the fermenter. The fed-batch fermentation with ISBR-by-adsorption in the glucose-based medium was conducted for two different glucose feeding conditions: feeding with a low glucose concentration of 200 g/L and a high feeding rate of 0.12 L/h, and with a high glucose concentration of 700g/L and a low feeding rate of 0.027L/h. In both cases, the initial glucose concentration was 60 g/L. The fed-batch fermentation with ISBR-by-adsorption in glucose/xylose-based medium was carried out for six different glucose-to-xylose ratios and feeding conditions: 9:1, 7:3, 4:6 and 3:7 for the feed concentration of 200 g/L, and 9:1 and 8:2 for the feed concentration of 700 g/L. Three sets were used for parameter estimation, and three other sets were used for model validation. In all fermentation experiments, samples were taken at 1.5 h intervals, and the concentrations of cell, substrates, and products were measured at each sampling time.

4. RESULTS AND DISCUSSION 4.1 Simultaneous utilization of glucose and xylose In this study, Clostridium acetobutylicum was manipulated to increase xylose consumption rate, resulting in the effective co-utilization of glucose and xylose for biobutanol production. The experimental data of the batch fermentation using both glucose and xylose as substrates at various initial glucose-to-xylose ratios show that the recombinant strain consumes glucose and xylose simultaneously and xylose is consumed even in the presence of glucose at high concentration (Supporting Information). According to the results of batch co-fermentation experiments, CCR seems to be alleviated sufficiently in the manipulated strain. The ratio of xylose consumed increases as the initial xylose ratio increases as reported in Table 2, indicating that


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relative consumptions of the sugars are dependent on the ratio of sugar concentrations. In addition, for all initial sugar ratios, the batch co-fermentation experiments show similar total amounts of consumed sugars and produced ABE, as shown in Table 2. These experimental results support the assumptions (vi) and (vii) made in the model development (see Section 2). The ratio of the glucose consumed to the total sugar consumed is slightly higher than the initial glucose ratio in the medium (Table 2) since the preference for glucose remains to a certain extent even after the genetic manipulation. This is why the parameter 𝐾, which represents the strain’s preference for glucose, should be included in the suggested weighting factor.

Table 2. Experimental results of the batch fermentation Initial sugar ratio (glucose:xylose)

Sugar consumption [g]

Product concentration [g/L]

Glucose (ratio)

Xylose (ratio)

Total

Acetone

Butanol

Ethanol

Total ABE

8:2

88.4 (8.2)

18.9 (1.8)

107.3

1.604

16.022

2.145

19.771

7:3

80.9 (7.7)

23.8 (2.3)

104.7

1.709

16.709

1.968

20.386

6:4

76.4 (7.2)

29.1 (2.8)

105.5

1.630

16.493

1.916

20.039

4.2 Model development 4.2.1 Model fitting to the batch fermentation data In the early exponential growth phase of batch fermentation where the concentrations of cell and products are low, the inhibition terms for the cell and butanol concentrations in Eqs 1 and


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Page 26 of 43

2 can be excluded. Thus, 𝜇𝑔,𝐺𝑙 and 𝜇𝑔,𝑋𝑙 can be simplified under substrate-limiting conditions as below: 𝜇𝑔,𝐺𝑙

𝑚𝑎𝑥 𝜇𝐺𝑙 𝐺𝑙 = 𝐾𝑆,𝐺𝑙 + 𝐺𝑙 + 𝐺𝑙2 ⁄𝐾𝐼,𝐺𝑙

(18)

𝑚𝑎𝑥 𝜇𝑋𝑙 𝑋𝑙 𝐾𝑆,𝑋𝑙 + 𝑋𝑙 + 𝑋𝑙2 ⁄𝐾𝐼,𝑋𝑙

(19)

𝜇𝑔,𝑋𝑙 =

and the Monod parameters of cell growth can be estimated using the batch fermentation data as described in step 1 of Section 2.5. The batch fermentation experiments were carried out at initial sugar concentration ranging between 2.5 and 70 g/L for glucose, and 1.5 and 85 g/L for xylose, respectively. The experimental value of the specific growth rate for each initial concentration was derived from the experimental data of dry cell mass (DCM) at the early growth phase, and the Monod equations in Eqs 18 and 19 were fitted to the experimental values. Figure 2 shows a graph of the fitted Monod equations, and the estimated values of the Monod parameters are reported in Table 3. According to the result, the 𝑚𝑎𝑥 𝑚𝑎𝑥 maximum specific growth rate on xylose (𝜇𝑋𝑙 ) is slightly smaller than that on glucose (𝜇𝐺𝑙 ).

Also, the substrate saturation constant for cell growth on xylose (𝐾𝑆.𝑋𝑙 ) is approximately 1.9 times that on glucose (𝐾𝑆.𝐺𝑙 ), indicating a higher affinity of the strain for glucose than for xylose. On the other hand, the inhibitory effect of glucose on the cell growth is much stronger than that of xylose as 𝐾𝐼,𝐺𝑙 has a much lower value than 𝐾𝐼,𝑋𝑙 .


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Figure 2. Model fits to the experimental data of the specific growth rates (A) on glucose and (B) on xylose

Table 3 Monod parameters estimated from experimental data of batch fermentation Glucose

Xylose

Estimated value

95% CI

Estimated value

95% CI

𝜇𝑖𝑚𝑎𝑥 (h−1 )

0.3612

[0.2316, 0.4908]

0.3081

[0.2082, 0.4081]

𝐾𝑆.𝑖 (g/L)

3.0079

[0.2958, 5.7201]

5.5935

[1.2549, 9.9322]

𝐾𝐼,𝑖 (g/L)

73.629

[2.225, 145.033]

107.78

[0.164, 215.399]

4.2.2 Model fitting to fed-batch fermentation with ISBR In steps 2 and 3, based on the Monod parameters determined in step 1, the remaining parameter values were estimated using the experimental data of fed-batch fermentation with ISBRby-adsorption. The ABE production proceeds mostly in the solventogenic phase of ABE fermentation. Since the strain used in this study was particularly engineered to restrain the acid formation, the batch experiment data show that the fermentation process enters the solventogenic phase from the acidogenic phase after about 3 h (see Supporting Information). Thus, the experimental data obtained after 3 h from the start-up were used for the parameter estimation in step 2 and 3. The estimation results are summarized in Table 4 (2nd and 3rd columns).


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Table 4. Kinetic parameters estimated from experimental data of fed-batch fermentation with ISBR-by-adsorption Parameter

Estimated value

95% CI

Re-estimated value (Identifiable subset)

95% CI

Cell / Glucose / Products associated parameters 𝑘𝑑 (h−1 )

0.0086

[0.0000, 0.0217]

𝑃𝐵,𝐺𝑙 (g⁄L)

14.0032

[12.1606, 15.0000]

𝑖𝐵,𝐺𝑙

0.5163

[0.0993, 0.8052]

𝑃𝑋 (g⁄L)

9.1453

[8.0000, 10.9991]

𝑖𝑋

0.4471

[0.2464, 0.8467]

′ 𝑃𝐵,𝐺𝑙 (g⁄L)

17.2562

[14.0350, 19.9995]

′ 𝑖𝐵,𝐺𝑙

𝛼𝐺𝑙 𝛽𝐺𝑙 (h−1 ) 𝛼𝐵

0.9012 3.7980 1.5103 2.2837

[0.5947, 1.3260] [1.0016, 4.9640] [1.3311, 2.0939] [1.0276, 3.1611]

𝛽𝐵 (h−1 )

0.1589

[0.0077, 0.3826]

𝑃𝐵,𝐵 (g⁄L)

14.8310

[12.9513, 19.9998]

𝑖𝐵,𝐵

0.4684

[0.0000, 0.9978]

𝛼E

0

-

𝛽𝐸 (h−1 ) 𝛼𝐴 𝛽𝐴 (h−1 )

0.0393 0 0.0400

[0.0362, 0.0422] [0.0364, 0.0434]

0.7490

[0.3570, 1.1580]

0.3761

[0.1658, 0.5841]

0.9898

[0.8205, 1.2052]

1.7392 2.4063

[1.6319, 1.8371] [2.2765, 2.5463]

0.0329

[0.0302, 0.0353]

0.0414

[0.0383, 0.0445]

Xylose / Weighting factor associated parameters 𝑃𝐵,𝑋𝑙 (g⁄L)

13.3434

[10.6661, 15.0000]

𝑖𝐵,𝑋𝑙

0.1563

[0.0029, 0.3679]

′ 𝑃𝐵,𝑋𝑙 (g⁄L)

17.8553

[12.6652, 20.0000]

′ 𝑖𝐵,𝑋𝑙

𝛼𝑋𝑙 𝛽𝑋𝑙 (h−1 )

0.0113 3.3240 0.5629

𝐾

0.6226

0.1340

[0.0005, 0.3910]

[0.0000, 0.5220] [0.0000, 4.6960] [0.4094, 1.1519]

3.1032 0.4805

[1.1868, 4.7427] [0.2444, 0.7568]

[0.6061, 0.6403]

0.6336

[0.6104, 0.6541]


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In step 2, the kinetic parameters related to the glucose utilization and product formation were estimated by fitting the model parameters without the xylose utilization term to the experimental data obtained from the fed-batch fermentation with ISBR-by-adsorption in the glucose-based medium. Figure 3 shows experimental and simulated concentration profiles as results of step 2, and there exists a steep rise in the glucose concentration around 15 h since the feeding of the media was started at that time. As shown in Figure 3, the cell growth becomes completely inhibited, and the butanol production is restrained when the butanol concentration reaches value around 14.0032 g/L (𝑃𝐵,𝐺𝑙 ). The growth- and nongrowth-associated coefficients for the glucose utilization, 𝛼𝐺𝑙 and 𝛽𝐺𝑙 , were estimated to be 3.798 and 1.510 ℎ−1 , respectively. The growth and nongrowth-associated coefficients for butanol production (𝛼𝐵 and 𝛽𝐵 ) were estimated as 2.284 and 0.1589, respectively; the growth-associated pattern is dominant in the production of butanol. The butanol concentration at which the butanol production is completely inhibited (𝑃𝐵,𝐵 ) is higher than the butanol concentration at which the cell growth is completely inhibited (𝑃𝐵,𝐺𝑙 ). Contrary to the butanol production, the productions of ethanol and acetone mostly follow the nongrowth-associated pattern: the estimated values of the growth- and nongrowthassociated coefficients were 0 and 0.0393 for the ethanol production (𝛼E and 𝛽𝐸 ), respectively, and were 0 and 0.04 for the acetone production (𝛼𝐴 and 𝛽𝐴 ), respectively.


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Figure 3. Experimental and predicted concentration profiles of fed-batch fermentation with ISBRby-adsorption in glucose-based medium with glucose feed concentration of (A) 200 g/L and (B) 700 g/L respectively

In step 3, keeping the predetermined parameters in steps 1 and 2 fixed, the remaining kinetic parameters related to the xylose utilization and the relative preference for glucose were estimated by fitting the whole model parameters to the experimental data of the fed-batch fermentation with ISBR-by-adsorption in glucose/xylose-based medium. Table 4 represents the estimation results using the experimental data executed for several combinations of the initial glucose-to-xylose ratios and feed concentrations, i.e., 9:1 and 3:7 for the feed concentration of 200g/L, and 8:2 for the feed concentration of 700g/L. The threshold values of butanol toxicity for ′ the cell growth on xylose 𝑃𝐵,𝑋𝑙 and the xylose consumption 𝑃𝐵,𝑋𝑙 are almost similar to those for


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′ the cell growth on glucose 𝑃𝐵,𝐺𝑙 and the glucose consumption 𝑃𝐵,𝐺𝑙 , respectively. In general, the

utilization of xylose is known to be much more vulnerable to butanol toxicity

7, 19

; however, this

recombinant strain shows improved butanol tolerance. The growth- and nongrowth-associated coefficients for the xylose utilization, 𝛼𝑋𝑙 and 𝛽𝑋𝑙 , were estimated as 3.324 and 0.5629 h−1 , respectively. As a result of step 3, the parameter 𝐾 corresponding to the relative preference for glucose was estimated to be 0.6226, and it slightly increased to 0.6336 in the subsequent model adjustment step. When glucose and xylose are present in the same amount in the fermentation broth, the weighting factors (𝑗1 and 𝑗2 ) are 0.683 and 0.317, respectively. This indicates that the recombinant strain used in this study prefers glucose over xylose about 2.2 times more when the same amounts of glucose and xylose exist in the medium.

4.2.3 Model adjustment and validation In step 4, the separately estimated values of the model parameters in step 2 and 3 were adjusted to improve the fidelity of the model by re-estimation. Only the identifiable parameter subset selected through the identifiability analysis was re-estimated rather than the entire set. The ′ ′ Monod parameters and the coefficients for the inhibitory effects (𝑃𝐵,𝐺𝑙 , 𝑃𝐵,𝑋𝑙 , 𝑃𝐵,𝐺𝑙 , 𝑃𝐵,𝑋𝑙 , 𝑃𝑋 and

𝑃𝐵,𝐵 ) determined in steps 1-3 were excluded from the model adjustment because they are considered to be intrinsic parameters, and the coefficients for the inhibitory effects have reasonable values compared to the experimental data and literature

17, 19

. Therefore, a full parameter set

considered for the identifiability analysis was composed of 16 parameters, except for 𝛼𝐸 and 𝛼𝐴 , which were estimated to be zero.


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Using the separately determined parameter values as nominal values, collinearity indices 𝛾𝑘 of all possible parameter subsets were calculated as described in Section 2.3. As a result, the maximum size of parameter subset (𝑛) satisfying 𝛾𝑘 ≤ 10 (corresponding to the threshold for 𝛾𝑘 ) was 11, which means that 11 parameters can be reliably identified at most for the given data. This also confirms that the estimation of all model parameters using the co-fermentation data alone leads to an over-parameterization problem resulting in unreliable parameter estimates. To select the most identifiable subset among the potentially identifiable subsets of which dimension is 11, their determinant measures 𝜌𝑘 were analyzed, and the parameter subsets were ranked based on 𝜌𝑘 values. The top five parameter subsets are summarized in Table 5. The parameters of the top-ranked subset were re-estimated to refine the model parameter values obtained sequentially in step 2 and 3. The re-estimation result is given in Table 4 (4th and 5th columns) and Figure 4.

Table 5. Top five identifiable parameter subsets ranked according to 𝜌𝑘 among the potentially identifiable subsets of size 11 Set index

𝛾𝑘

𝜌𝑘

Subset 𝑘

1

9.513

1.895

′ 𝑖𝐵,𝐺𝑙 , 𝑖𝑋 , 𝑖𝐵,𝐺𝑙 , 𝛽𝐺𝑙 , 𝛼𝑋𝑙 , 𝛽𝑋𝑙 , 𝛼𝐵 , 𝛽𝐸 , 𝛽𝐴 , 𝑖𝐵,𝑋𝑙 , 𝐾

2

9.219

1.874

′ 𝑘𝑑 , 𝑖𝑋 , 𝑖𝐵,𝐺𝑙 , 𝛽𝐺𝑙 , 𝛼𝑋𝑙 , 𝛽𝑋𝑙 , 𝛼𝐵 , 𝑖𝐵,𝐵 , 𝛽𝐸 , 𝛽𝐴 , 𝐾

3

8.484

1.865

′ 𝑘𝑑 , 𝑖𝐵,𝐺𝑙 , 𝑖𝑋 , 𝑖𝐵,𝐺𝑙 , 𝛽𝐺𝑙 , 𝛼𝑋𝑙 , 𝛽𝑋𝑙 , 𝛼𝐵 , 𝛽𝐸 , 𝛽𝐴 , 𝐾

4

8.367

1.804

′ 𝑘𝑑 , 𝑖𝐵,𝐺𝑙 , 𝑖𝐵,𝐺𝑙 , 𝛽𝐺𝑙 , 𝛼𝑋𝑙 , 𝛽𝑋𝑙 , 𝛼𝐵 , 𝑖𝐵,𝐵 , 𝛽𝐸 , 𝛽𝐴 , 𝐾

5

9.168

1.798

′ 𝑘𝑑 , 𝑖𝐵,𝐺𝑙 , 𝑖𝐵,𝐺𝑙 , 𝛽𝐺𝑙 , 𝛼𝑋𝑙 , 𝛽𝑋𝑙 , 𝛼𝐵 , 𝛽𝐵 , 𝛽𝐸 , 𝛽𝐴 , 𝐾


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Figure 4. Comparison of the simulation result after the model adjustment and experimental data of fed-batch fermentation with ISBR in glucose/xylose-based medium at three glucose-to-xylose initial ratios: (A) 9:1 and (B) 3:7 with feed concentration of 200 g/L, and (C) 8:2 with feed concentration of 700 g/L

Figure 4 shows the simulation results of the model after the model adjustment. The total sum of squared relative errors (SSRE) of the three data sets decreases from 13.8 to 10.7 by the


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model adjustment. To confirm the validity of the developed model, we compared the simulation results of the model with a new set of experimental data from fed-batch fermentation runs with ISBR-by-adsorption in glucose/xylose-based medium at different glucose-to-xylose ratios, i.e., 7:3 and 4:6 for the feed concentration of 200g/L, and 9:1 for the feed concentration of 700g/L. As shown in Figure 5, the predicted results using the developed model are in good agreement with the experimental results. Even under different conditions of initial glucose-to-xylose ratios and injected feeding conditions, the developed model can reliably describe and predict the dynamic behavior of ABE fermentation simultaneously utilizing the glucose and xylose including the overall ABE production as well as the inhibition effects by butanol and biomass itself. Since the model can predict the phenomena of dilution by feeding and adsorption as well, it can be extended to different types of fed-batch or continuous fermentation processes (e.g., fermentation process combined with ex-situ butanol recovery by adsorption). Furthermore, we compared the simulation results of a previously published model using the constant weighting with those of the proposed model using the suggested concentrationdependent weighting factors. The model with the constant weighting factors was proposed by Leksawasdi et al.25 to describe the fermentation kinetics using a mixture of glucose and xylose in ethanol production, and was shown to provide good prediction performance for the case where the initial glucose-to-xylose ratio was 1:1. For a fair comparison, we used the model with the exact same structure as our proposed model except for the weighting factors in Eq 4, and the model parameters were identified in the same way as in Section 2.3. Note that 𝑗2 was estimated instead of 𝐾, and 𝑗1 = 1 − 𝑗2 . The results showed that the co-fermentation kinetic model with the constant weighting factors failed to predict the simultaneous consumption kinetics of glucose and xylose at various initial glucose-to-xylose ratios (see Supporting Information). It significantly under- or


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Energy & Fuels

over-estimated the glucose concentration as shown in Figure S2, and its total SSRE of the three data sets was 15.9, which is about 1.5 times higher than that of the model with the suggested weighting factors. This supports that the concentration-dependent weighting factors proposed in this study greatly improve the accuracy of the prediction in regard to the simultaneous consumption of glucose and xylose in the ABE fermentation under diverse medium and feeding conditions.


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Figure 5. Model validation with experimental data of fed-batch fermentation with ISBR in glucose/xylose-based medium at three glucose-to-xylose initial ratios: (A) 7:3, (B) 4:6 with feed concentration of 200 g/L, and (C) 9:1 with feed concentration of 700 g/L


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Energy & Fuels

5. CONCLUSIONS An unstructured kinetic model of ABE fermentation with simultaneous utilization of glucose and xylose by recombinant Clostridium acetobutylicum was developed for the purpose of supporting process optimization and control studies. Batch and fed-batch fermentation experiments were carried out on a lab-scale using a genetically modified strain showing alleviated carbon catabolite repression (CCR). Based on the experimental observations, a weighting factor depending on the relative concentrations of sugar and preference for glucose was introduced into the calculation of the overall rate of cell growth in the co-fermentation. For reliable identification of a large number of model parameters that result, a systematic approach was introduced, rather than estimating all parameters simultaneously using co-fermentation experimental data alone. Glucose and xylose-associated kinetic parameters were separately estimated with single substrateand co-fermentation data, respectively, and then the best identifiable parameter subset given the data were selected and fine-tuned through re-estimation. The developed model successfully predicted the co-fermentation dynamics at various glucose-to-xylose ratios and feeding conditions. In addition, the model can describe the effects of dilution and adsorption in fed-batch fermentation with in situ product recovery by adsorption, as well as the inhibitory effects by substrates, product, and cell. The model is expected to serve as a basis for further model-based optimization and control studies involving various process setups for lignocellulosic biobutanol production. Furthermore, the proposed approach for model parameter identification can be applied to other co-fermentation modeling studies.


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NOMENCLATURE 𝑋 = concentration of biomass [g⁄𝐿] 𝐺𝑙 = concentration of glucose [g⁄𝐿] 𝑋𝑙 = concentration of xylose [g⁄𝐿] 𝐶𝐵 = concentration of butanol [g⁄𝐿] 𝐶𝐸 = concentration of ethanol [g⁄𝐿] 𝐶𝐴 = concentration of acetone [g⁄𝐿] 𝑟𝐵 = specific rate of butanol production [ℎ−1 ] 𝑟𝐸 = specific rate of ethanol production [ℎ−1 ] 𝑟𝐴 = specific rate of acetone production [ℎ−1 ] 𝑟𝐺𝑙 = specific rate of glucose consumption [ℎ−1 ] 𝑟𝑋𝑙 = specific rate of xylose consumption [ℎ−1 ] 𝑚𝑎𝑥 𝜇𝐺𝑙 = maximum growth rate of biomass on glucose [ℎ−1 ]

𝜇𝑔,𝐺𝑙 = growth rate of biomass on glucose [ℎ−1 ] 𝐾𝑆,𝐺𝑙 = substrate saturation constant of the growth on glucose [g⁄𝐿] 𝐾𝐼,𝐺𝑙 = substrate inhibition constant of the growth on glucose [g⁄𝐿] 𝑚𝑎𝑥 𝜇𝑋𝑙 = maximum growth rate of biomass on xylose [ℎ−1 ]

𝜇𝑔,𝑋𝑙 = growth rate of biomass on xylose [ℎ−1 ] 𝐾𝑆,𝑋𝑙 = substrate saturation constant of the growth on xylose [g⁄𝐿] 𝐾𝐼,𝑋𝑙 = substrate inhibition constant of the growth on xylose [g⁄𝐿] 𝑘𝑑 = specific cell death rate [ℎ−1 ] 𝑃𝐵,𝐺𝑙 = butanol concentration at which cell growth on glucose stops [g⁄𝐿] 𝑖𝐵,𝐺𝑙 = product inhibition constant to cell growth on glucose 𝑃𝐵,𝑋𝑙 = butanol concentration at which cell growth on xylose stops [g⁄𝐿] 𝑖𝐵,𝑋𝑙 = product inhibition constant to cell growth on xylose 𝑃𝑋 = cell concentration at which cell growth stops [g⁄𝐿]


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Energy & Fuels

𝑖𝑋 = cell concentration inhibition constant to cell growth ′ 𝑃𝐵,𝐺𝑙 = butanol concentration at which glucose consumption stops [g⁄𝐿] ′ 𝑖𝐵,𝐺𝑙 = product inhibition constant to glucose consumption ′ 𝑃𝐵,𝑋𝑙 = butanol concentration at which xylose consumption stops [g⁄𝐿] ′ 𝑖𝐵,𝑋𝑙 = product inhibition constant to xylose consumption

𝑃𝐵,𝐵 = butanol concentration at which butanol production stops [g⁄𝐿] 𝑖𝐵,𝐵 = product inhibition constant to butanol production 𝛼𝐺𝑙 = growth related effect of the cell mass on the glucose consumption 𝛽𝐺𝑙 = nongrowth related effect of the cell mass on the glucose consumption [ℎ−1 ] 𝛼𝑋𝑙 = growth related effect of the cell mass on the xylose consumption 𝛽𝑋𝑙 = nongrowth related effect of the cell mass on the xylose consumption [ℎ−1 ] 𝛼𝐵 = growth related effect of the cell mass on the butanol production 𝛽𝐵 = nongrowth related effect of the cell mass on the butanol production [ℎ−1 ] 𝛼𝐸 = growth related effect of the cell mass on the ethanol production 𝛽𝐸 = nongrowth related effect of the cell mass on the ethanol production [ℎ−1 ] 𝛼𝐴 = growth related effect of the cell mass on the acetone production 𝛽𝐴 = nongrowth related effect of the cell mass on the acetone production [ℎ−1 ] 𝐾 = relative preference for glucose over xylose 𝐴𝑖 = concentration of component 𝑖 by adsorption [g⁄𝐿] 𝑞𝑖 = amount of adsorbed component 𝑖 per unit mass of adsorbent [g⁄𝑘𝑔𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑛𝑡 ] 𝑞𝑖,𝑒𝑞 = amount of adsorbed component 𝑖 per unit mass of adsorbent at equilibrium [g⁄𝑘𝑔𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑛𝑡 ] 𝑞𝑖,𝑚 = maximum adsorption capacity for component 𝑖 per unit mass of adsorbent [g⁄𝑘𝑔𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑛𝑡 ] 𝑘𝑖 = adsorption kinetic parameter for component 𝑖 [ℎ−1 ] 𝐵𝑖 = adsorption equilibrium constant for component 𝑖 [L⁄𝑔] 𝐶𝑖 = concentration of component 𝑖 [g⁄𝐿]


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ASSOCIATED CONTENT Supporting Information Experimental data of batch fermentation in glucose/xylose-based medium with various initial glucose-to-xylose ratios, Comparison of the simulation result using the fermentation kinetic model with constant weighting factors and experimental data of fed-batch fermentation with ISBR in glucose/xylose-based medium at three glucose-to-xylose initial ratios, Estimated kinetic parameters of the model with constant weighting factors (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This project (Project No. : 2013001580001) is supported by the Ministry of Environment, Republic of Korea as "The Wastes to Energy Technology Development Program".


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Mathematical Modeling of Acetone-Butanol-Ethanol Fermentation with

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