Kinetics of the selective fermentation of glucose from glucose/fructose mixtures using Saccharomyces cerevisiae ATCC 36859

The kinetics of batch fermentation during the growth of S. cerevisiae ATCC 36859 was studied in various glucose/fructose mixtures. It was found that the growth is inhibited equally by glucose and fructose even though fructose is not consumed to any large extent by the yeast under the conditions tested here. The inhibition of growth by the substrate and ethanol is represented by linear equations. These equations were combined with the MONOD expression in order to formulate equations for the biomass growth, glucose and fructose consumption and ethanol production. Parameter estimates were obtained by fitting these equations to batch fermentation data and so developing models which indicate that the growth is completely inhibited when 62 g/l ethanol is produced by the yeast, while glucose consumption and ethanol production continue up to an ethanol concentration of 152 g/l. Products containing a high concentration of fructose are best produced by using a high initial biomass concentration.     

Parameter estimation techniques for interaction and redistribution models: a predator-prey example

Summary The use of parameter estimation techniques for partial differential equations is illustrated using a predatorprey model. Whereas ecologists have often estimated parameters in models, they have not previously been able to do so for models that describe interactions in heterogeneous environments. The techniques we describe for partial differential equations will be generally useful for models of interacting species in spatially complex environments and for models that include the movement of organisms. We demonstrate our methods using field data from a ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interaction. Our parameter estimation algorithms can be employed to identify models that explain better than 80% of the observed variance in aphid and ladybird densities. Such parameter estimation techniques can bridge the gap between detail-rich experimental studies and abstract mathematical models. By relating the particular bestfit models identified from our experimental data to other information on Coccinella behavior, we conclude that a term describing local taxis of ladybirds towards prey (aphids in this case) is needed in the model.     

Ph control and the "shoulder" effect in parallel fermentation pathways

In an effort, to develop comprehensive mathematical models for use in optimizing fermentation processes, product rate data taken at constant pH's for the lactic acid fermentation (Lactobacillus delbrueckii) were analyzed. It was observed that the rate of acid synthesis-time trajectories exhibited a “shoulder” effect at pH's less than 5. That is, a nearly constant rate of synthesis for up to 10 hr in the late growth phase, out of a maximum total fermentation time of 70 hr. This effect was used as a clue from which to structure the proposed model with parallel pathways. Simulating shunting pathways does, in fact, demonstrate that, the notion of parallelism is consistent with the expression of a shoulder. It is postulated, therefore, that a differential pH effect between two parallel pathways can account for the presence of a shoulder when both routes prevail, and no shoulder when either pathway predominates.     

拉曼光谱分析技术在资源微生物发酵性能评价中的应用

微生物发酵过程是细胞新陈代谢进行物质转化的过程,为了提高目标产物的转化率,需要对微生物发酵动态特性进行实时分析,以便实时优化发酵过程。拉曼光谱(Raman spectroscopy)量化测试作为一种有应用前景的在线过程分析技术,可以在避免微生物污染的条件下,实现精准监测,进而用于优化控制微生物发酵过程。【目的】以运动发酵单胞菌(Zymomonas mobilis)为例,建立微生物发酵过程中葡萄糖、木糖、乙醇和乳酸浓度拉曼光谱预测模型,并进行准确性验证。【方法】采用浸入式在线拉曼探头,收集运动发酵单胞菌发酵过程中多个组分的拉曼光谱,采用偏最小二乘法对光谱信号进行预处理和多元数据分析,结合离线色谱分析数据,对拉曼光谱进行建模分析和浓度预测。【结果】针对运动发酵单胞菌,首先实现拉曼分析仪对单一产品乙醇发酵过程的精准检测,其次基于多元变量分析,建立葡萄糖、乙醇和乳酸浓度变化的预测模型,实现对发酵过程中各成分浓度变化的准确有效分析。【结论】成功建立了一种评价资源微生物尤其是工业菌株发酵液多种组分的拉曼光谱分析方法。该方法为运动发酵单胞菌等工业菌株利用多组分底物工业化生产不同产物的实时检测,以及其他微生物尤其工业菌株的选育和过程优化提供了新方法。     

Kolmogorov’s Differential Equations and Positive Semigroups on First Moment Sequence Spaces

Spatially implicit metapopulation models with discrete patch-size structure and host-macroparasite models which distinguish hosts by their parasite loads lead to infinite systems of ordinary differential equations. In several papers, a this-related theory will be developed in sufficient generality to cover these applications. In this paper the linear foundations are laid. They are of own interest as they apply to continuous-time population growth processes (Markov chains). Conditions are derived that the solutions of an infinite linear system of differential equations, known as Kolmogorov’s differential equations, induce a C ₀-semigroup on an appropriate sequence space allowing for first moments. We derive estimates for the growth bound and the essential growth bound and study the asymptotic behavior. Our results will be illustrated for birth and death processes with immigration and catastrophes. An erratum to this article can be found at     

A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay

 We consider a two-dimensional model of cell-to-cell spread of HIV-1 in tissue cultures, assuming that infection is spread directly from infected cells to healthy cells and neglecting the effects of free virus. The intracellular incubation period is modeled by a gamma distribution and the model is a system of two differential equations with distributed delay, which includes the differential equations model with a discrete delay and the ordinary differential equations model as special cases. We study the stability in all three types of models. It is shown that the ODE model is globally stable while both delay models exhibit Hopf bifurcations by using the (average) delay as a bifurcation parameter. The results indicate that, differing from the cell-to-free virus spread models, the cell-to-cell spread models can produce infective oscillations in typical tissue culture parameter regimes and the latently infected cells are instrumental in sustaining the infection. Our delayed cell-to-cell models may be applicable to study other types of viral infections such as human T-cell leukaemia virus type 1 (HTLV-1). Received: 18 November 2000 / Published online: 28 February 2003 RID="*" ID="*" Research was partially supported by the NSERC and MITACS of Canada and a start-up fund from the College of Arts and Sciences at the University of Miami. On leave from Dalhousie University, Halifax, Nova Scotia, Canada. Current address: Department of Mathematics, Clarke College, Dubuque, Iowa 52001, USA Key words or phrases: HIV-1 – Cell-to-cell spread – Time delay – Stability – Hopf bifurcation – Periodicity     

A kinetic model for methanogenesis from whey permeate in a packed bed immobilized cell bioreactor

The fermentation kinetics of methane production from whey permeate in a packed bed immobilized cell bioreactor at mesophilic temperatures and pHs around neutral was studied. Propionate and acetate were the only two major organic intermediates found in the methanogenic fermentation of lactose. Based on this finding, a three-step reaction mechanism was proposed: lactose was first degraded to propionate, acetate, CO(2), and H(2) by fermentative bacteria; propionate was then converted to acetate by propionate-degrading bacteria; and finally, CH(4) and CO(2) were produced from acetate, H(2), and CO(2) by methanogenic bacteria. The second reaction step was found to be the rate-limiting step in the overall methanogenic fermentation of lactose. Monod-type mathematical equations were used to model these three step reactions. The kinetic constants in the models were sequentially determined by fitting the mathematical equations with the experimental data on acetate, propionate, and lactose concentrations. A mixed-culture fermentation model was also developed. This model simulates the methanogenic fermentation of whey permeate very well.     

Retrospective optimization of time-dependent fermentation control strategies using time-independent historical data

We have previously shown the usefulness of historical data for fermentation process optimization. The methodology developed includes identification of important process inputs, training of an artificial neural network (ANN) process model, and ultimately use of the ANN model with a genetic algorithm to find the optimal values of each critical process input. However, this approach ignores the time-dependent nature of the system, and therefore, does not fully utilize the available information within a database. In this work, we propose a method for incorporating time-dependent optimization into our previously developed three-step optimization routine. This is achieved by an additional step that uses a fermentation model (consisting of coupled ordinary differential equations (ODE)) to interpret important time-course features of the collected data through adjustments in model parameters. Important process variables not explicitly included in the model were then identified for each model parameter using automatic relevance determination (ARD) with Gaussian process (GP) models. The developed GP models were then combined with the fermentation model to form a hybrid neural network model that predicted the time-course activity of the cell and protein concentrations of novel fermentation conditions. A hybrid-genetic algorithm was then used in conjunction with the hybrid model to suggest optimal time-dependent control strategies. The presented method was implemented upon an E. coli fermentation database generated in our laboratory. Optimization of two different criteria (final protein yield and a simplified economic criteria) was attempted. While the overall protein yield was not increased using this methodology, we were successful in increasing a simplified economic criterion by 15% compared to what had been previously observed. These process conditions included using 35% less arabinose (the inducer) and 33% less typtone in the media and reducing the time required to reach the maximum protein concentration by 10% while producing approximately the same level of protein as the previous optimum.     

葡萄糖酸促进氧化亚铁硫杆菌磁小体合成的发酵动力学

【目的】明确不同种类有机物对氧化亚铁硫杆菌(Acidithiobacillus ferrooxidans) BYM磁小体形成的促进作用,为安全有效提升细菌磁小体产量提供新思路。【方法】以A. ferrooxidans BYM为目的菌株,采用单因素试验分析10种有机物对A. ferrooxidans BYM亚铁氧化的影响,通过4 L发酵体系进一步筛选促进磁小体合成的有机物;通过分批发酵实验基于经典发酵动力学模型(Logistic、Luedeking-Piret、底物消耗动力学方程)分别构建A. ferrooxidans BYM菌体生长、磁小体合成以及亚铁消耗动力学模型。【结果】筛选得到10 mmol/L葡萄糖酸能使磁小体产量最高达到2.00×10⁻³ g/L,葡萄糖酸使A. ferrooxidans BYM细胞呈椭圆形,表面光滑;在葡萄糖酸作用下,A. ferrooxidans BYM的发酵符合Logistic、Luedeking-Piret、底物消耗动力学方程。【结论】添加10 mmol/L葡萄糖酸能够使A. ferrooxidans BYM磁小体产量提升8倍,葡萄糖酸通过改变细胞形态和表面结构促进磁小体合成,菌体生长、产物生成以及底物消耗动力学模型可以阐明A. ferrooxidans BYM在葡萄糖酸存在下的分批发酵过程。     

Process analysis and optimal design of a fermentation process based upon elemental balance equations: Generalized semitheoretical equations for estimating rates of oxygen demand and heat evolution

Based upon elemental balance equations, generalized semitheoretical equations are developed for estimating the rates of oxygen demand and heat evolution of a fermentation process. The results estimated by these equations are in good agreement with data obtained from yeast–hydrocarbon and yeast–carbohydrate fermentation processes for citric acid production. Furthermore, a direct relationship between rates of oxygen demand and heat evolution is derived with a correlation constant of 0.18 kcal/mM O₂.The relationship has been verified by data of citric acid fermentation processes and also confirmed by published data. These derived equations would be useful for process design and optimization.     

Maximum Likelihood Estimation of Long‐Term HIV Dynamic Models and Antiviral Response

Summary HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short‐term dynamic models, recent works considered more complex long‐term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation‐maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long‐term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2–ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between‐patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.     

Optimizing medium constituents and fermentation conditions for citric acid production from palmyra jaggery using response surface method

The quantitative effects of pH, temperature, time of fermentation, sugar concentration, nitrogen concentration and potassium ferrocyanide on citric acid production were investigated using a statistical experimental design. It was found that palmyra jaggery (sugar syrup from the palmyra palm) is a suitable substrate for increasing the yield of citric acid using Aspergillus niger MTCC 281 by submerged fermentation. Regression equations were used to model the fermentation in order to determine optimum fermentation conditions. Higher yields were obtained after optimizing media components and conditions of fermentation. Maximum citric acid production was obtained at pH 5.35, 29.76 °C, 5.7 days of fermentation with 221.66 g of substrate/l, 0.479 g of ammonium nitrate/l and 2.33 g of potassium ferrocyanide/l.     

Model Construction and Analysis of Respiration in Halobacterium salinarum

The archaeon Halobacterium salinarum can produce energy using three different processes, namely photosynthesis, oxidative phosphorylation and fermentation of arginine, and is thus a model organism in bioenergetics. Compared to its bacteriorhodopsin-driven photosynthesis, less attention has been devoted to modeling its respiratory pathway. We created a system of ordinary differential equations that models its oxidative phosphorylation. The model consists of the electron transport chain, the ATP synthase, the potassium uniport and the sodium-proton antiport. By fitting the model parameters to experimental data, we show that the model can explain data on proton motive force generation, ATP production, and the charge balancing of ions between the sodium-proton antiporter and the potassium uniport. We performed sensitivity analysis of the model parameters to determine how the model will respond to perturbations in parameter values. The model and the parameters we derived provide a resource that can be used for analytical studies of the bioenergetics of H. salinarum.     

Evaluation of Various Unstructured Kinetic Models for the Production of Protease by Bacillus sphaericus MTTC511

Bacillus sphaericus MTCC511 was used for the production of protease in submerged batch fermentation. Maximum protease activity of 1010 U/L was obtained during a fermentation period of 24 h under optimized conditions of 30 °C in a medium with an initial pH of 7 and at a shaking rate of 120 rpm. The maximum biomass obtained in the batch fermentation was 2.55 g/L after 16 h. Various unstructured models were analyzed to simulate the experimental values of microbial growth, protease activity and substrate concentration. The unstructured models, i.e. the Monod model for microbial growth, the Monod incorporated Luedeking‐Piret model for the production of protease and the Monod‐incorporated modified Luedeking‐Piret model for the utilization of substrate were capable of predicting the fermentation profile with high coefficient of determination (R²) values of 0.9967, 0.9402 and 0.9729, respectively. The results indicated that the unstructured models were able to describe the fermentation kinetics more effectively.     

Continuous and discrete mathematical models of tumor-induced angiogenesis

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial-cell migration, and organize themselves into a dendritic structure. Subsequent cell proliferation near the sprout tip permits further extension of the capillary and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumors. In this paper we present both continuous and discrete mathematical models which describe the formation of the capillary sprout network in response to chemical stimuli (tumor angiogenic factors, TAF) supplied by a solid tumor. The models also take into account essential endothelial cell-extracellular matrix interactions via the inclusion of the matrix macromolecule fibronectin. The continuous model consists of a system of nonlinear partial differential equations describing the initial migratory response of endothelial cells to the TAF and the fibronectin. Numerical simulations of the system, using parameter values based on experimental data, are presented and compared qualitatively with in vivo experiments. We then use a discretized form of the partial differential equations to develop a biased random-walk model which enables us to track individual endothelial cells at the sprout tips and incorporate anastomosis, mitosis and branching explicitly into the model. The theoretical capillary networks generated by computer simulations of the discrete model are compared with the morphology of capillary networks observed in in vivo experiments.     

Modeling of yeast metabolism and process dynamics in batch fermentation

Much is known about yeast metabolism and the kinetics of industrial batch fermentation processes. In this study, however, we provide the first tool to evaluate the dynamic interaction that exists between them. A stoichiometric model, using wine fermentation as a case study, was constructed to simulate batch cultures of Saccharomyces cerevisiae. Five differential equations describe the evolution of the main metabolites and biomass in the fermentation tank, while a set of underdetermined linear algebraic equations models the pseudo-steady-state microbial metabolism. Specific links between process variables and the reaction rates of metabolic pathways represent microorganism adaptation to environmental changes in the culture. Adaptation requirements to changes in the environment, optimal growth, and homeostasis were set as the physiological objectives. A linear programming routine was used to define optimal metabolic mass flux distribution at each instant throughout the process. The kinetics of the process arise from the dynamic interaction between the environment and metabolic flux distribution. The model assessed the effect of nitrogen starvation and ethanol toxicity in wine fermentation and it was able to simulate fermentation profiles qualitatively, while experimental fermentation yields were reproduced successfully as well.     

Reverse engineering: A model for T-cell vaccination

A class of minimal models is constructed that can exhibit several salient phenomena associated with T-cell inoculations that prevent and cure autoimmune disease. The models consist of differential equations for the magnitude of two populations, the effectorsE (which cause the disease), and an interacting regulator populationR. In these models, normality, vaccination and disease are identified with stable steady-states of the differential equations. Thereby accommodated by the models are a variety of findings such as the induction of vaccination or disease, depending on the size of the effector inoculant. Features such as spontaneous acquisition of disease and spontaneous cure require that the models be expanded to permit slow variation of their coefficients and hence slow shifts in the number of steady-states. Other extensions of the basic models permit them to be relevant to vaccination by killed cells or by antigen, or to the interaction of a larger number of cell types. The discussion includes an indication of how the highly simplified approach taken here can serve as a first step in a modeling program that takes increasing cognizance of relevant aspects of known immunological physiology. Even at its present stage, the theory leads to several suggestions for experiments.     

Real‐time monitoring of high‐gravity corn mash fermentation using in situ raman spectroscopy

In situ Raman spectroscopy was employed for real‐time monitoring of simultaneous saccharification and fermentation (SSF) of corn mash by an industrial strain of Saccharomyces cerevisiae. An accurate univariate calibration model for ethanol was developed based on the very strong 883 cm^?1 C–C stretching band. Multivariate partial least squares (PLS) calibration models for total starch, dextrins, maltotriose, maltose, glucose, and ethanol were developed using data from eight batch fermentations and validated using predictions for a separate batch. The starch, ethanol, and dextrins models showed significant prediction improvement when the calibration data were divided into separate high‐ and low‐concentration sets. Collinearity between the ethanol and starch models was avoided by excluding regions containing strong ethanol peaks from the starch model and, conversely, excluding regions containing strong saccharide peaks from the ethanol model. The two‐set calibration models for starch (R² = 0.998, percent error = 2.5%) and ethanol (R² = 0.999, percent error = 2.1%) provide more accurate predictions than any previously published spectroscopic models. Glucose, maltose, and maltotriose are modeled to accuracy comparable to previous work on less complex fermentation processes. Our results demonstrate that Raman spectroscopy is capable of real time in situ monitoring of a complex industrial biomass fermentation. To our knowledge, this is the first PLS‐based chemometric modeling of corn mash fermentation under typical industrial conditions, and the first Raman‐based monitoring of a fermentation process with glucose, oligosaccharides and polysaccharides present. Biotechnol. Bioeng. 2013; 110: 1654–1662. © 2013 Wiley Periodicals, Inc.     

In situ near infrared spectroscopy for analyte‐specific monitoring of glucose and ammonium in streptomyces coelicolor fermentations

There are many challenges associated with in situ collection of near infrared (NIR) spectra in a fermentation broth, particularly for highly aerated and agitated fermentations with filamentous organisms. In this study, antibiotic fermentation by the filamentous bacterium Streptomyces coelicolor was used as a model process. Partial least squares (PLS) regression models were calibrated for glucose and ammonium based on NIR spectra collected in situ. To ensure that the models were calibrated based on analyte‐specific information, semisynthetic samples were used for model calibration in addition to data from standard batches. Thereby, part of the inherent correlation between the analytes could be eliminated. The set of semisynthetic samples were generated from fermentation broth from five separate fermentations to which different amounts of glucose, ammonium, and biomass were added. This method has previously been used off line but never before in situ. The use of semisynthetic samples along with validation on an independent batch provided a critical and realistic evaluation of analyte‐specific models based on in situ NIR spectroscopy. The prediction of glucose was highly satisfactory resulting in a RMSEP of 1.1 g/L. The prediction of ammonium based on NIR spectra collected in situ was not satisfactory. A comparison with models calibrated based on NIR spectra collected off line suggested that this is caused by signal attenuation in the optical fibers in the region above 2,000 nm; a region which contains important absorption bands for ammonium. For improved predictions of ammonium in situ, it is suggested to focus efforts on enhancing the signal in that particular region. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010