Substrate uptake,phosphorus repression,and effect of seed culture on glycopeptide antibiotic production: Process model development and experimental validation

Actinomycetes, the soil borne bacteria which exhibit filamentous growth, are known for their ability to produce a variety of secondary metabolites including antibiotics. Industrial scale production of such antibiotics is typically carried out in a multi‐substrate medium where the product formation may experience catabolite repression by one or more of the substrates. Availability of reliable process models is a key bottleneck in optimization of such processes. Here we present a structured kinetic model to describe the growth, substrate uptake and product formation for the glycopeptide antibiotic producer strain Amycolatopsis balhimycina DSM5908. The model is based on the premise that the organism is an optimal strategist and that the various metabolic pathways are regulated via key rate limiting enzymes. Further, the model accounts for substrate inhibition and catabolite repression. The model is also able to predict key phenomena such as simultaneous uptake of glucose and glycerol but with different specific uptake rates, and inhibition of glycopeptide production by high intracellular phosphate levels. The model is successfully applied to both production and seed medium with varying compositions and hence has good predictive ability over a variety of operating conditions. The model parameters are estimated via a well‐designed experimental plan. Adequacy of the proposed model was established via checking the model sensitivity to its parameters and confidence interval calculations. The model may have applications in optimizing seed transfer, medium composition, and feeding strategy for maximizing production. Biotechnol. Bioeng. 2010;105: 109–120. © 2009 Wiley Periodicals, Inc.     

A dynamic fed batch strategy for a Pichia pastoris mixed feed system to increase process understanding

Mixed substrate feeding strategies are frequently investigated to enhance the productivity of recombinant Pichia pastoris processes. For this purpose, numerous fed batch experiments or time-consuming continuous cultivations are required to optimize control parameters such as the substrate mixing ratio and the applied methanol concentration. In this study, we decoupled the feeding of methanol and glycerol in a mixed substrate fed batch environment to gain process understanding for a recombinant P. pastoris Muts strain producing the model enzyme horseradish peroxidase. Specific substrate uptake rates (qs) were controlled separately, and a stepwise increased qGly-control scheme was applied to investigate the effect of various substrate fluxes on the culture. The qs-controlled strategy allowed a parallel characterization of the metabolism and the recombinant protein expression in a fed batch environment. A critical-specific glycerol uptake rate was determined, where a decline of the specific productivity occurred, and a time-dependent acceleration of protein expression was characterized with the dynamic fed batch approach. Based on the observations on recombinant protein expression, propositions for an optimal feeding design to target maximal productivities were stated. Thus, the dynamic fed batch strategy was found to be a valuable tool for both process understanding and optimization of product formation for P. pastoris in a mixed substrate environment.     

On the influence of oxygen and cell concentration in an SFPR whole cell biocatalytic Baeyer-Villiger oxidation process

Efficient whole cell biotransformations, in particular microbial whole cell Baeyer-Villiger oxidation with molecular oxygen, demand comprehension and optimization of the process details involved. Optimal provision of oxygen and control of bioprocess parameters are pivotal for their success. The interrelation of cell density and oxygen supply in an in situ substrate feeding and product removal (SFPR) whole cell Baeyer-Villiger oxidation process was investigated in detail. Both parameters were optimized with respect to practical considerations. The outcome of this study supports a schematic process model, allows estimation of optimum process conditions and exploration of its limits.     

Kinetic modeling of lipase‐catalyzed esterification reaction between oleic acid and trimethylolpropane: A simplified model for multi‐substrate multi‐product ping–pong mechanisms

Kinetic models are among the tools that can be used for optimization of biocatalytic reactions as well as for facilitating process design and upscaling in order to improve productivity and economy of these processes. Mechanism pathways for multi‐substrate multi‐product enzyme‐catalyzed reactions can become very complex and lead to kinetic models comprising several tens of terms. Hence the models comprise too many parameters, which are in general highly correlated and their estimations are often prone to huge errors. In this study, Novozym^®435 catalyzed esterification reaction between oleic acid (OA) and trimethylolpropane (TMP) with continuous removal of side‐product (water) was carried out as an example for reactions that follow multi‐substrate multi‐product ping‐pong mechanisms. A kinetic model was developed based on a simplified ping‐pong mechanism proposed for the reaction. The model considered both enzymatic and spontaneous reactions involved and also the effect of product removal during the reaction. The kinetic model parameters were estimated using nonlinear curve fitting through unconstrained optimization methodology and the model was verified by using empirical data from different experiments and showed good predictability of the reaction under different conditions. This approach can be applied to similar biocatalytic processes to facilitate their optimization and design. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29:1422–1429, 2013     

Optimal substrate feeding policy for a fed batch fermentation with substrate and product inhibition kinetics

The optimal substrate feeding policy for the fed batch fermentation which is governed by product and substrate inhibited kinetics is presented. The conjunction point between nonsingular and singular arcs and the feeding policy along the singular arc are derived analytically in terms of the concentrations of substrate and product and the liquid volume. Thus, it is possible to determine the feeding rate by monitoring the state variables (i.e., closed loop control). As a specific example, an optimization study of the fed batch fermentation for ethanol production by Saccharomyces cerevisiae is presented. It is shown that the optimal feeding patterns are heavily dependent upon the initial conditions. The point selectivity provides the guideline for predicting the optimal feeding patterns and explaining the results of rigorous mathematical analysis.     

Identifyability measures to select the parameters to be estimated in a solid‐state fermentation distributed parameter model

Process modeling can lead to of advantages such as helping in process control, reducing process costs and product quality improvement. This work proposes a solid‐state fermentation distributed parameter model composed by seven differential equations with seventeen parameters to represent the process. Also, parameters estimation with a parameters identifyability analysis (PIA) is performed to build an accurate model with optimum parameters. Statistical tests were made to verify the model accuracy with the estimated parameters considering different assumptions. The results have shown that the model assuming substrate inhibition better represents the process. It was also shown that eight from the seventeen original model parameters were nonidentifiable and better results were obtained with the removal of these parameters from the estimation procedure. Therefore, PIA can be useful to estimation procedure, since it may reduce the number of parameters that can be evaluated. Further, PIA improved the model results, showing to be an important procedure to be taken. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:905–917, 2016     

Simultaneous versus sequential optimal experiment design for the identification of multi-parameter microbial growth kinetics as a function of temperature

Optimal experiment design for parameter estimation (OED/PE) has become a popular tool for efficient and accurate estimation of kinetic model parameters. When the kinetic model under study encloses multiple parameters, different optimization strategies can be constructed. The most straightforward approach is to estimate all parameters simultaneously from one optimal experiment (single OED/PE strategy). However, due to the complexity of the optimization problem or the stringent limitations on the system's dynamics, the experimental information can be limited and parameter estimation convergence problems can arise. As an alternative, we propose to reduce the optimization problem to a series of two-parameter estimation problems, i.e., an optimal experiment is designed for a combination of two parameters while presuming the other parameters known. Two different approaches can be followed: (i) all two-parameter optimal experiments are designed based on identical initial parameter estimates and parameters are estimated simultaneously from all resulting experimental data (global OED/PE strategy), and (ii) optimal experiments are calculated and implemented sequentially whereby the parameter values are updated intermediately (sequential OED/PE strategy).This work exploits OED/PE for the identification of the Cardinal Temperature Model with Inflection (CTMI) (Rosso et al., 1993). This kinetic model describes the effect of temperature on the microbial growth rate and encloses four parameters. The three OED/PE strategies are considered and the impact of the OED/PE design strategy on the accuracy of the CTMI parameter estimation is evaluated. Based on a simulation study, it is observed that the parameter values derived from the sequential approach deviate more from the true parameters than the single and global strategy estimates. The single and global OED/PE strategies are further compared based on experimental data obtained from design implementation in a bioreactor. Comparable estimates are obtained, but global OED/PE estimates are, in general, more accurate and reliable.     

Structured modeling and state estimation in a fermentation process: Lipase production by Candida rugosa

A simple structured mathematical model coupled with a methodology of state and parameter estimation is developed for lipase production by Candida rugosa in batch fermentation. The model describes the system according to the following qualitative observations and hypothesis: Lipase production is induced by extracellular oleic acid present in the medium. The acid is transported into the cell where it is consumed, transformed, and stored. Lipase is excreted to the medium where it is distributed between the available oil-water interphase and aqueous phase. Cell growth is modulated by the intracellular substrate concentration. Model parameters have been determined and the whole model validated against experiments not used in their determination. The estimation problem consists in the estimation of three state variables (biomass, intra- and extracellular substrate) and two kinetic parameters by using only the on-line measurement provided by exhaust gas analysis. The presented estimation strategy divides the complex problem into three subproblems that can be solved by stable algorithms. The estimation of biomass (X) and the specific growth rate (mu), is achieved by a recursive prediction error algorithm using the on-line measurement of the carbon dioxide evolution rate. mu is then used to perform an estimation of intracellular substrate and the other kinetic parameter related to substrate transport (A) by an adaptive observer. Extracellular substrate is then evaluated by means of the estimated values of intracellular substrate and biomass through the material balance of the reactor. Simulation and experimental tests showed good performance of the developed estimator, which appears suitable to be used for process control and monitoring. (c) 1995 John Wiley & Sons, Inc.     

Control of the specific growth rate of Bacillus subtilis for the production of biosurfactant lipopeptides in bioreactors with foam overflow

This paper formulates a feeding law for a bioprocess dedicated to the production of an antibiotic surfactant using Bacillus subtilis. The specificity of the process relies on the use of the surface active property of the product to extract it by foaming. The control law is designed to maintain a constant specific biomass growth rate while taking into account the particularity of the process. This law can be regarded as a generalization of the conventional exponential feeding strategy and is generic enough to encompass the case of continuous processes with partial recycling. Conventional exponential feeding strategies indeed fail to account for the loss of biomass induced by the foaming. Previous experiments have provided a model of the process and values for its parameters. From this information, a feeding rate law was computed using the feeding strategy proposed in this paper and applied to an experimental culture. This experiment allows discussion of the modeling of the biomass extraction method used in this study. The results on the estimated specific growth rate highlight the complete agreement between the expected and experimental features. Further process optimization studies can now be performed on the basis of the constant specific biomass growth rate.     

单纯形加速法拟合生态学中的非线性模型

本文以Logistic模型,Taylor幂法则模型,Holling功能反应模型,以及种群内禀增长力Rm等模型的拟合和参数估计为例,探讨单纯形加速法在生态模型优化拟合和参数估计中的应用.结果表明,单纯形加速法拟合生态学中的非线性模型不仅适用广泛,而且拟合过程是直接求原来非线性模型的最优拟合,因而优于生态学中通常使用的将原模型“线性化后再拟合”的方法,而与其它一些最优化方法,如:麦夸方法、枚举选优法等比较,由于单纯形法不需计算目标函数的偏导数,因而计算不受目标函数及其偏导函数复杂程度的限制,而且对于各种模型其求优计算过程十分相似,可以编制统一的计算程序.本研究所编制的计算机程序对于本文未提到的其它一些模型也是完全适用的,在应用时仅需修改定义目标函数的自定义函数语句即可.研究也发现,在求优过程中,只要搜索系数选择适当和实际数据合理,是可以保证寻优成功的.     

Structured kinetic model to represent the utilization of multiple substrates in complex media during rifamycin B fermentation

Industrial fermentations typically use media that are balanced with multiple substitutable substrates including complex carbon and nitrogen source. Yet, much of the modeling effort to date has mainly focused on defined media. Here, we present a structured model that accounts for growth and product formation kinetics of rifamycin B fermentation in a multi-substrate complex medium. The phenomenological model considers the organism to be an optimal strategist with an in-built mechanism that regulates the sequential and simultaneous uptake of the substrate combinations. This regulatory process is modeled by assuming that the uptake of a substrate depends on the level of a key enzyme or a set of enzymes, which may be inducible. Further, the fraction of flux through a given metabolic branch is estimated using a simple multi-variable constrained optimization. The model has the typical form of Monod equation with terms incorporating multiple limiting substrates and substrate inhibition. Several batch runs were set up with varying initial substrate concentrations to estimate the kinetic parameters for the rifamycin overproducer strain Amycolatopsis mediterranei S699. Glucose and ammonium sulfate (AMS) demonstrated significant substrate inhibition toward growth as well as product formation. The model correctly predicts the experimentally observed regulated simultaneous uptake of the substitutable substrate combinations under different fermentation conditions. The modeling results may have applications in the optimization and control of rifamycin B fermentation while the modeling strategy presented here would be applicable to other industrially important fermentations.     

Modelling and optimization of a recombinant BHK-21 cultivation process using hybrid grey-box systems

In this work a model-based optimization study of fed-batch BHK-21 cultures expressing the human fusion glycoprotein IgG1-IL2 was performed. It was concluded that due to the complexity of the BHK metabolism it is rather difficult to develop a kinetic model with sufficient accuracy for optimization studies. Many kinetic expressions and a large number of parameters are involved resulting in a complex identification problem. For this reason, an alternative more cost-effective methodology based on hybrid grey-box models was adopted. Several model structures combining the a priori reliable first principles knowledge with black-box models were investigated using data from batch and fed-batch experiments. It has been reported in previous studies that the BHK metabolism exhibits modulation particularities when compared to other mammalian cell lines. It was concluded that these mechanisms were effectively captured by the hybrid model, this being of crucial importance for the successful optimization of the process operation. A method was proposed to monitor the risk of hybrid model unreliability and to constraint the optimization results to acceptable risk levels. From the optimization study it was concluded that the process productivity may be considerably increased if the glutamine and glucose concentrations are maintained at low levels during the growth phase and then glutamine feeding is increased.     

Mixed-feed exponential feeding for fed-batch culture of recombinant methylotrophic yeast

A simple, accurate model capable of predicting cell growth and methanol utilization during the mixed substrate fed-batch fermentation of Mut^S recombinant Pichia pastoris was developed and was used to design an exponential feeding strategy for mixed substrate fed-batch fermentation at a constant specific growth rate. Mixed substrate feeding has been shown to boost productivity in recombinant fed-batch culture of P. pastoris, while fixed growth rate exponential feeding during fed-batch culture is a useful tool in process optimization and control.     

Mathematical and kinetic modeling of biofilm reactor based on ant colony optimization

Inverse estimation of model parameters via mathematical modeling route, known as inverse modeling (IM), is an attractive alternative approach to the experimental methods. This approach makes use of efficient optimization techniques in the course of solution of an inverse problem with the aid of measured data. In this study, a novel optimization method based on ant colony optimization (ACO), denoted by ACO-IM, is presented for inverse estimation of kinetic and film thickness parameters of biofilm models that describe an experimental fixed bed anaerobic reactor. The proposed optimization method for parameter estimation emulates the fact that ants are capable of finding the shortest path from a food source to their nest by depositing a trial of pheromone during their walk. The efficacy of the ACO-IM for numerical estimation of bio-kinetic parameters is demonstrated through its application for the anaerobic treatment of industry wastewater in a fixed bed biofilm process. The results explain the rigorousness of mathematical models, the form of kinetic and film thickness models and the type of packing to be used with the biofilm process for accurate determination of kinetic and film thickness parameters so as to ensure reliable predictive performance of the biofilm reactor models.     

Packed-Bed Bioreactors Under the Influence of Chemical Modulators

This report considers the behaviour of packed-bed immobilized enzyme reactors operating in the presence of substrate and/or product sequestrators. In some cases, enzyme inhibition by the reaction product and presence of chemical modulators are also considered. For each case, an appropriate analytical model is developed. Using numerical simulations, it is shown that reactor performance is impaired by substrate sequestration. This effect can be partially reversed when competitive sequestration by product or modulator is operational.

In addition, a comparison is made between some of the predicted characteristics of the reactor and experimental data. It reveals the capabilities and limitations of the models employed.     

A kinetic model for energy spilling-associated product formation in substrate-sufficient continuous culture

It has been demonstrated that excess substrate can cause uncoupling between anabolism and catabolism, which leads to energy spilling. However, the Luedeking-Piret equation for product formation does not account for the energy spilling-associated product formation due to substrate excess. Based on the growth yield and energy uncoupling models proposed earlier, a kinetic model describing energy spilling-associated product formation in relation to residual substrate concentration was developed for substrate-sufficient continuous culture and was further verified with literature data. The parameters in the proposed model are well defined and have their own physical meanings. From this model, the specific productivity of unit energy spilling-associated substrate consumption, and the maximum product yield coefficient, can be determined. Results show that the majority of energy spilling-associated substrate consumption was converted to carbon dioxide and less than 6% was fluxed into the metabolites, while it was found that the maximum product yield coefficients varied markedly under different nutrient limitations. The results from this research can be used to develop the optimized bioprocess for maximizing valuable product formation.     

ConvAn: a convergence analyzing tool for optimization of biochemical networks

Dynamic models of biochemical networks usually are described as a system of nonlinear differential equations. In case of optimization of models for purpose of parameter estimation or design of new properties mainly numerical methods are used. That causes problems of optimization predictability as most of numerical optimization methods have stochastic properties and the convergence of the objective function to the global optimum is hardly predictable. Determination of suitable optimization method and necessary duration of optimization becomes critical in case of evaluation of high number of combinations of adjustable parameters or in case of large dynamic models. This task is complex due to variety of optimization methods, software tools and nonlinearity features of models in different parameter spaces. A software tool ConvAn is developed to analyze statistical properties of convergence dynamics for optimization runs with particular optimization method, model, software tool, set of optimization method parameters and number of adjustable parameters of the model. The convergence curves can be normalized automatically to enable comparison of different methods and models in the same scale. By the help of the biochemistry adapted graphical user interface of ConvAn it is possible to compare different optimization methods in terms of ability to find the global optima or values close to that as well as the necessary computational time to reach them. It is possible to estimate the optimization performance for different number of adjustable parameters. The functionality of ConvAn enables statistical assessment of necessary optimization time depending on the necessary optimization accuracy. Optimization methods, which are not suitable for a particular optimization task, can be rejected if they have poor repeatability or convergence properties. The software ConvAn is freely available on www.biosystems.lv/convan.     

Mathematical modelling and process optimization of a continuous 5-stage bioreactor cascade for production of poly[-(R)-3-hydroxybutyrate] by Cupriavidus necator

A multistage system for poly(hydroxyalkanoate) (PHA) production consisting of five continuous stirred tank reactors in series (5-CSTR) with Cupriavidus necator DSM 545 as production strain was modelled using formal kinetic relations. Partially growth-associated production of PHA under nitrogen limited growth was chosen as modelling strategy, thus the Luedeking-Piret’s model of partial growth-associated product synthesis was applied as working hypothesis. Specific growth rate relations adjusted for double substrate (C and N source) limited growth according to Megee et al. and Mankad-Bungay relation were tested. The first stage of the reactor cascade was modelled according to the principle of nutrient balanced continuous biomass production system, the second one as two substrate controlled process, while the three subsequent reactors were adjusted to produce PHB under continuous C source fed and nitrogen deficiency. Simulated results of production obtained by the applied mathematical models and computational optimization indicate that PHB productivity of the whole system could be significantly increased (from experimentally achieved 2.14 g L^?1 h^?1 to simulated 9.95 g L^?1 h^?1) if certain experimental conditions would have been applied (overall dilution rate, C and N source feed concentration). Additionally, supplemental feeding strategy for switching from batch to continuous mode of cultivation was proposed to avoid substrate inhibition.     

Kinetic modeling of cellulosic biomass to ethanol via simultaneous saccharification and fermentation: Part II. Experimental validation using waste paper sludge and anticipation of CFD analysis

A kinetic model of cellulosic biomass conversion to ethanol via simultaneous saccharification and fermentation (SSF) developed previously was validated experimentally using paper sludge as the substrate. Adsorption parameters were evaluated based on the data obtained at various values for fractional cellulose conversion. The adsorption model was then combined with batch SSF data to evaluate the cellulose hydrolysis parameters. With the parameters evaluated for the specific substrate, the discrete model was able to predict SSF successfully both with discrete addition of cellulase only and with discrete feeding of substrate, cellulase, and media. The model tested in this study extends the capability of previous SSF models to semi-continuous feeding configurations, and invites a mechanistic interpretation of the recently observed trend of increasing conversion with decreasing feeding frequency [Fan et al. (2007a) Bioprocess Biosyst Eng 30(1):27-34]. Our results also support the feasibility and utility of determining adsorption parameters based on data obtained at several conversions, particularly when the model is to be applied to extended reaction times rather than only initial hydrolysis rates. The revised model is considerably more computationally efficient than earlier models, and appears for many conditions to be within the capability of simulation using computational fluid dynamics.     

Kinetics of <Emphasis Type="SmallCaps">l</Emphasis>-lysine fermentation: a continuous culture model incorporating oxygen uptake rate

For process design and optimization, it is essential to have a mathematical model that represents the system well. Many past studies do not go beyond empirically fitting experimental data. In the present study, an unstructured model incorporating oxygen uptake and dissolved oxygen concentration was developed for a continuous culture of L-lysine. Specific rate expressions of cell growth, substrate consumption, product formation, and oxygen uptake were developed and incorporated in the model. The model predicts very well the effects of operational parameters, such as the dilution rate and the feed substrate concentration. It is also able to predict the unsteady-state dynamics of continuous L-lysine fermentation.