Optimal control of batch processes involving simultaneous enzymatic and microbial reactions

Optimal enzyme feed rate profiles have been calculated, based on a model for a fed-batch simultaneous enzymatic and microbial reaction (SEMR) process. The model parameters corresponded to a relatively slow citric acid fermentation. The profiles were calculated using an iterative algorithm based on the minimum principle. Penalty functions were used to enforce inequality constraints on the enzyme feed rate. Significant improvements in the objective function relative to that for the best constant enzyme feed rate were found. The effect on the optimal profiles of changes in the parameters of the model and the objective function were investigated, as was the effect of introducing the stationary state assumption to eliminate glucose concentration as a state variable. Major differences between bang-bang control variable profiles and singular arcs were found, with the singular arc solution slightly better than the optimal bang-bang control.List of Symbols a N-vector of initial conditions - b ₁–b₁₀ parameters defined in Table 2 - c vector of cost parameters - c ₁–c₆ penalty function parameters - E enzyme concentration (U/l) - f N-vector of functions - F enzyme feed rate (U/l-h) - g N-vector of functions - G glucose concentration (g/l) - H Hamiltonian - J objective function - J ^* modified objective function - L number of integration steps per time interval - L number of control variables - M number of time intervals - n iteration index - N number of state variables - P product concentration (g/l) - r ₁ glucose formation rate (g/l-h) - r ₂ product formation rate (g/l-h) - t time (h) - T final time (h) - u L-vector of control variables - x N-vector of state variables - z N-vector of adjoint variables - Z total enzyme fed (U/l) Greek convergence parameter The support of one of the authors by the National Science Foundation (Grant CBT-84-20552) is gratefully acknowledged.     

微生物转谷氨酰胺酶的纯化方法和酶学性质研究

由Streptoverticillium mobaTaense发酵生产的转谷氨酰胺酶经过除茵体、超滤浓缩、乙醇沉淀、干燥后得到粗酶产品,其活力回收率约70％。又经Superdex-75凝胶过滤和Source 30S阳离子交换两步纯化后得到纯酶,最终酶活力收率约37％。酶最适温度为50℃,在40℃以下稳定性良好;最适pH为6．0,pH4．0～8．0时比较稳定。离子强度对酶影响很小。     

Kinetics of microbial product formation and its consequences for the optimization of fermentation processes

Different types of product formation kinetics are discussed with respect to their significance for fermentation process economics. Microbial products belonging to various classes are formed in a growth-coupled manner. It is often found that the specific rate of product formation increases with the specific growth rate, approaching a maximum at higher growth rates. It is illustrated that for such types of relationship between the product formation rate and the growth rate process conditions are optimal when the specific rate of product formation is about half-maximal.     

一株产低温碱性脂肪酶菌株的发酵条件优化

对一株产低温碱性脂肪酶细菌（Pseudoalteromonas sp．BJ17）的发酵条件进行了优化,研究各种碳源及氮源对产酶的影响,应用正交实验优化其发酵培养基组成。结果表明：最佳培养基组成为淀粉12g／L,蛋白胨12g／L,酵母膏3g／L,酪蛋白2g/L。最佳培养温度为25℃,发酵时间为16h。     

Evaluation of nanoparticle-immobilized cellulase for improved ethanol yield in simultaneous saccharification and fermentation reactions

Ethanol yields were 2.1 (P = 0.06) to 2.3 (P = 0.01) times higher in simultaneous saccharification and fermentation (SSF) reactions of microcrystalline cellulose when cellulase was physisorbed on silica nanoparticles compared to enzyme in solution. In SSF reactions, cellulose is hydrolyzed to glucose by cellulase while yeast simultaneously ferments glucose to ethanol. The 35°C temperature and the presence of ethanol in SSF reactions are not optimal conditions for cellulase. Immobilization onto solid supports can stabilize the enzyme and promote activity at non-optimum reaction conditions. Mock SSF reactions that did not contain yeast were used to measure saccharification products and identify the mechanism for the improved ethanol yield using immobilized cellulase. Cellulase adsorbed to 40 nm silica nanoparticles produced 1.6 times (P = 0.01) more glucose than cellulase in solution in 96 h at pH 4.8 and 35°C. There was no significant accumulation (<250 μg) of soluble cellooligomers in either the solution or immobilized enzyme reactions. This suggests that the mechanism for the immobilized enzyme's improved glucose yield compared to solution enzyme is the increased conversion of insoluble cellulose hydrolysis products to soluble cellooligomers at 35°C and in the presence of ethanol. The results show that silica-immobilized cellulase can be used to produce increased ethanol yields in the conversion of lignocellulosic materials by SSF.     

Perspectives of data analysis of enzyme inhibition and activation,Part 3: Equations for calculation of the initial rates of enzymatic reactions

Equations for calculation of the initial rates of activated enzymatic reactions and the inhibited enzymatic reactions, unavailable in experimental enzymology, were obtained. Examples of practically using of these equations are given. © 2009 Wiley Periodicals, Inc. J Biochem Mol Toxicol 23:108–118, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jbt.20271     

Multifractality in intracellular enzymatic reactions

Enzymatic kinetics adjust well to the Michaelis-Menten paradigm in homogeneous media with dilute, perfectly mixed reactants. These conditions are quite different from the highly structured cell plasm, so applications of the classic kinetics theory to this environment are rather limited. Cytoplasmic structure produces molecular crowding and anomalous diffusion of substances, modifying the mass action kinetic laws. The reaction coefficients are no longer constant but time-variant, as stated in the fractal kinetics theory. Fractal kinetics assumes that enzymatic reactions on such heterogeneous media occur within a non-Euclidian space characterized by a certain fractal dimension, this fractal dimension gives the dependence on time of the kinetic coefficients. In this work, stochastic simulations of enzymatic reactions under molecular crowding have been completed, and kinetic coefficients for the reactions, including the Michaelis-Menten parameter KM, were calculated. The simulations results led us to confirm the time dependence of michaelian kinetic parameter for the enzymatic catalysis. Besides, other chaos related phenomena were pointed out from the obtained KM time series, such as the emergence of strange attractors and multifractality.     

木质纤维素原料酶水解产乙醇工艺的研究进展

木质纤维素原料预处理后,经水解、发酵等过程,可生产乙醇作为清洁燃料,这大大提高了农业和林业废弃物的利用率,减轻了环境污染,并为经济的可持续发展提供了保证。目前木质纤维素酶水解因其具有明显优势而受到重视,被普遍研究和采用。综述了近年来木质纤维素原料的预处理方法、酶与水解技术、发酵工艺以及发酵耦合分离技术的最新研究成果。     

谷氨酸流加发酵过程的神经网络优化研究

采用神经网络的方法,将模拟网络与优化网络结合组成双网系统,用于谷氨酸流加生产过程的模拟与优化分析。模拟网络中设置瓶颈结构．以加强网络的数据过滤与压缩能力,滤除工业数据中的噪音。利用训练算法本身,优化网络方便地实现了单变量、多变量优化,获得令人满意的结果。     

Design of coupled reactions for simplification of bioluminescence analysis

Luminescence analysis may be applied to many substances by arranging a prior reaction producing a species entering the light-emitting reaction. Under favourable conditions the two consecutive reactions are carried out simultaneously as a one-step procedure. In a bioluminescence assay, luciferase stability is frequently a problem, making it desirable to develop analytical schemes where the analytical response becomes largely independent of any impaired luciferase activity. The value of maximal emission or an approached steady-state level is a convenient and usually well-defined analytical parameter. When recording this level it is important to design the participating reactions in a way that compensates for changes in luciferase activity.     

Multi-objective optimization of glycopeptide antibiotic production in batch and fed batch processes

Fermentation optimization involves potentially conflicting multiple objectives such as product concentration and production media cost. Simultaneous optimization of these objectives would result in a multiobjective optimization problem, which is characterized by a set of multiple solutions, knows as pareto optimal solutions. These solutions gives flexibility in evaluating the trade-offs and selecting the most suitable operating policy. Here, ε-constraint approach was used to generate the pareto solutions for two objectives: product concentration and product per unit cost of media, for batch and fed batch operations using process model for Amycolatopsis balhimycina, a glycopeptide antibiotic producer. This resulted in a set of several pareto optimal solutions with the two objectives ranging from (0.75 g l⁻¹, 3.97 g $^-1) to (0.44 g l⁻¹, 5.19 g $^-1) for batch and from (1.5 g l⁻¹, 5.46 g $^-1) to (1.1 g l⁻¹, 6.34 g $^-1) for fed batch operations. One pareto solution each for batch and for fed batch mode was experimentally validated.     

种植转Bt基因抗虫棉对土壤生物学活性的影响

采用温室盆栽实验,研究了种植转Bt基因棉（苏抗103）和同源常规棉（苏棉12）对根际土壤生物学活性的影响。结果表明：与对照常规棉相比,种植转Bt基因棉对根际土壤脱氢酶、碱性磷酸酶、蔗糖酶和土壤呼吸的影响因生育期而异,土壤脲酶、蛋白酶和微生物量C在各生育期均没有显著差异;土壤蔗糖酶、土壤脱氢酶和土壤呼吸分别只在苗期（苏抗103〉苏棉12,增幅为25．5％）、花铃期（苏抗103〉苏棉12,增幅为21．6％）、花铃期（苏抗103〉苏棉12,增幅为36．1％）存在显著差异;土壤磷酸酶在花铃期和吐絮期活性显著下降（降幅分别为22．1％和32．9％）。     

Economic impact of total solids loading on enzymatic hydrolysis of dilute acid pretreated corn stover

In process integration studies of the biomass-to-ethanol conversion process, it is necessary to understand how cellulose conversion yields vary as a function of solids and enzyme loading and other key operating variables. The impact of solids loading on enzymatic cellulose hydrolysis of dilute acid pretreated corn stover slurry was determined using an experimental response surface design methodology. From the experimental work, an empirical correlation was obtained that expresses monomeric glucose yield from enzymatic cellulose hydrolysis as a function of solids loading, enzyme loading, and temperature. This correlation was used in a technoeconomic model to study the impact of solids loading on ethanol production economics. The empirical correlation was used to provide a more realistic assessment of process cost by accounting for changes in cellulose conversion yields at different solids and enzyme loadings as well as enzyme cost. As long as enzymatic cellulose conversion drops off at higher total solids loading (due to end-product inhibition or other factors), there is an optimum value for the total solids loading that minimizes the ethanol production cost. The optimum total solids loading shifts to higher values as enzyme cost decreases.     

Impact of enzymatic pre-hydrolysis on batch activated sludge systems dealing with oily wastewaters

Dairy wastewater containing different oil and grease contents was treated in batch activated sludge systems with and without (control) an enzymatic pre-hydrolysis stage [with 0.2% (w/v) of fermented babassu cake containing Penicillium restrictum lipases]. When the oil and grease concentration in the control bioreactor was increased (400, 600 and 800 mg l^–1), the COD removal efficiency fell (86%, 75% and 0%). However, in the reactor fed with pre-hydrolysed wastewater, COD removal efficiency was maintained (93%, 92% and 82%). At an oil and grease concentration of 800 mg l^–1, the control bioreactor presented final volatile suspended solids (VSS) values ten times greater (2225 mg l^–1) than those obtained for bioreactor fed with pre-hydrolysed wastewater (200 mg l^–1).     

Optimization of batch fermentation processes by graphical method

A graphical method is proposed for batch fermentation process optimization. Its objective function is the maximum output of the product when the time of process is fixed or free. The technique of optimization is based on Bellman's dynamic programming concepts and the assumption that the process can be described by mathematical models of generalized structure. An example of the proposed technique's application is presented.     

Reduced models of networks of coupled enzymatic reactions

The Michaelis-Menten equation has played a central role in our understanding of biochemical processes. It has long been understood how this equation approximates the dynamics of irreversible enzymatic reactions. However, a similar approximation in the case of networks, where the product of one reaction can act as an enzyme in another, has not been fully developed. Here we rigorously derive such an approximation in a class of coupled enzymatic networks where the individual interactions are of Michaelis-Menten type. We show that the sufficient conditions for the validity of the total quasi-steady state assumption (tQSSA), obtained in a single protein case by Borghans, de Boer and Segel can be extended to sufficient conditions for the validity of the tQSSA in a large class of enzymatic networks. Secondly, we derive reduced equations that approximate the network's dynamics and involve only protein concentrations. This significantly reduces the number of equations necessary to model such systems. We prove the validity of this approximation using geometric singular perturbation theory and results about matrix differentiation. The ideas used in deriving the approximating equations are quite general, and can be used to systematize other model reductions.     

The effects of fermentation and enzymatic treatment of pea on nutrient digestibility and growth performance of broilers

The present study examined the impacts of native, fermented or enzymatically treated peas (Pisum sativum L.) inclusion in broiler diets, on growth performance and nutrient digestibility. For the fermentation process, Madonna pea was mixed with water (1/1) containing 2.57×10⁸ Bacillus subtilis (GalliPro®) spores/kg pea and then, incubated for 48 h at 30 °C. For the enzymatic treatment process, the used water for dough production contained three enzymes, AlphaGal^TM (α-galactosidase), RONOZYME® ProAct and VP (protease and pectinases respectively – DSM, Switzerland) and the pea dough incubated for 24 h at 30°C. Nine corn-wheat-soybean diets were formulated by supplying 10%, 20% and 30% of the required CP with either native, fermented or enzymatically treated peas. Performance was recorded weekly and at the end of the experiment (day 35), apparent ileal digestibility (AID) of CP, amino acids (AA), crude fat, starch, Ca, P and K were determined. Data were subjected to ANOVA using GLM procedure with a 3×3 factorial arrangement of treatments. Both processes reduced α-galactosides, phytate, trypsin inhibitor activity and resistant starch in peas. Increasing levels of pea products up to 300 g/kg diet, reduced BW gain and feed intake (P⩽0.05). Broilers fed diets containing enzymatically treated pea had the best feed conversion ratio at day 35. Different types of pea product and their inclusion levels had no effect on AID of all nutrients. The interaction between type of the pea products and inclusion levels was significant for AID of starch. For native pea diets, 10% group showed similar AID of starch to 20% native pea but it had higher AID than 30% native pea. For fermented and enzymatically treated groups, all three levels displayed similar AID of starch. In conclusion, enzymatic treatment and fermentation could improve the nutritional quality of pea. Inclusion of enzymatically treated pea in broiler diets could improve broiler performance compared with other pea products while, it displayed neither positive nor negative impact on nutrient digestibility. The present findings indicate the feasibility of these processes, particularly enzymatic treatment, for improving the nutritional quality of pea as a protein source for broiler nutrition.     

赖氨酸流加发酵最优控制的研究

在赖氨酸发酵动力学模型和庞特里金明小值原理的基础上,得出流加发酵的最优化底物流加方式。并进一步对流加发酵的全过程进行了分析,得出了在实际控制中较为可行的流加发酵全过程的总控制策略,实际控制表明在小型反应器中赖氨酸产生菌FB42的发酵水平为81．6g／l。、转化率为0．418％、生产强度为1．16g／h·L,和分批发酵相比分别提高了45．4％、9．7％和28．4％。     

Comparative metabolomic analysis on industrial continuous and batch ethanol fermentation processes by GC-TOF-MS

The intracellular metabolic profile characterization of Saccharomyces cerevisiae throughout industrial ethanol fermentation was investigated using gas chromatography coupled to time-of-flight mass spectrometry. A total of 143 and 128 intracellular metabolites in S. cerevisiae were detected and quantified in continuous and batch fermentations, respectively. The two fermentation processes were both clearly distinguished into three main phases by principal components analysis. Furthermore, the levels of some metabolites involved in central carbon metabolism varied significantly throughout both processes. Glycerol and phosphoric acid were principally responsible for discriminating seed, main and final phases of continuous fermentation, while lactic acid and glycerol contributed mostly to telling different phases of batch fermentation. In addition, the levels of some amino acids such as glycine varied significantly during both processes. These findings provide new insights into the metabolomic characteristics during industrial ethanol fermentation processes. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On the thermodynamics of microbial growth processes

In this article, we provide a rigorous thermodynamic analysis of microbial growth process, clarify the role of the generalized degree of reduction concept as it is used in both stoichiometric equations and as a characterizing factor for thermophysical properties, and introduce a classification method to account for errors when using the generalized degree of reduction to estimate the energy and free energy contents of molecules. We maintain the advantages of using the generalized degree of reduction while correcting for the large errors in the principle of energy regularity, especially for small molecules and for nitrogen-source compounds. As a result, we obtain more accurate energy balances (heat loads) and second law constraints, and are able to clarify contradictory statements in the literature as to whether nonphotosynthesis fermentation process can produce oxygen or absorb rather than produce heat. Indeed, the answers to such questions become evident using the classification system introduced here.