The Unscented Kalman Filter estimates the plasma insulin from glucose measurement

Understanding the simultaneous interaction within the glucose and insulin homeostasis in real-time is very important for clinical treatment as well as for research issues. Until now only plasma glucose concentrations can be measured in real-time. To support a secure, effective and rapid treatment e.g. of diabetes a real-time estimation of plasma insulin would be of great value. A novel approach using an Unscented Kalman Filter that provides an estimate of the current plasma insulin concentration is presented, which operates on the measurement of the plasma glucose and Bergman's Minimal Model of the glucose insulin homeostasis. We can prove that process observability is obtained in this case. Hence, a successful estimator design is possible. Since the process is nonlinear we have to consider estimates that are not normally distributed. The symmetric Unscented Kalman Filter (UKF) will perform best compared to other estimator approaches as the Extended Kalman Filter (EKF), the simplex Unscented Kalman Filter (UKF), and the Particle Filter (PF). The symmetric UKF algorithm is applied to the plasma insulin estimation. It shows better results compared to the direct (open loop) estimation that uses a model of the insulin subsystem.     

Real‐time model based process monitoring of enzymatic biodiesel production

In this contribution we extend our modelling work on the enzymatic production of biodiesel where we demonstrate the application of a Continuous‐Discrete Extended Kalman Filter (a state estimator). The state estimator is used to correct for mismatch between the process data and the process model for Fed‐batch production of biodiesel. For the three process runs investigated, using a single tuning parameter, q_x = 2 × 10^?2 which represents the uncertainty in the process model, it was possible over the entire course of the reaction to reduce the overall mean and standard deviation of the error between the model and the process data for all of the five measured components (triglycerides, diglycerides, monoglycerides, fatty acid methyl esters, and free fatty acid). The most significant reduction for the three process runs, were for the monoglyceride and free fatty acid concentration. For those components, there was over a ten‐fold decrease in the overall mean error for the state estimator prediction compared with the predictions from the pure model simulations. It is also shown that the state estimator can be used as a tool for detection of outliers in the measurement data. For the enzymatic biodiesel process, given the infrequent and sometimes uncertain measurements obtained we see the use of the Continuous‐Discrete Extended Kalman Filter as a viable tool for real time process monitoring. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:585–595, 2015     

Reconstructing Mammalian Sleep Dynamics with Data Assimilation

Data assimilation is a valuable tool in the study of any complex system, where measurements are incomplete, uncertain, or both. It enables the user to take advantage of all available information including experimental measurements and short-term model forecasts of a system. Although data assimilation has been used to study other biological systems, the study of the sleep-wake regulatory network has yet to benefit from this toolset. We present a data assimilation framework based on the unscented Kalman filter (UKF) for combining sparse measurements together with a relatively high-dimensional nonlinear computational model to estimate the state of a model of the sleep-wake regulatory system. We demonstrate with simulation studies that a few noisy variables can be used to accurately reconstruct the remaining hidden variables. We introduce a metric for ranking relative partial observability of computational models, within the UKF framework, that allows us to choose the optimal variables for measurement and also provides a methodology for optimizing framework parameters such as UKF covariance inflation. In addition, we demonstrate a parameter estimation method that allows us to track non-stationary model parameters and accommodate slow dynamics not included in the UKF filter model. Finally, we show that we can even use observed discretized sleep-state, which is not one of the model variables, to reconstruct model state and estimate unknown parameters. Sleep is implicated in many neurological disorders from epilepsy to schizophrenia, but simultaneous observation of the many brain components that regulate this behavior is difficult. We anticipate that this data assimilation framework will enable better understanding of the detailed interactions governing sleep and wake behavior and provide for better, more targeted, therapies.     

Unscented Kalman filter with parameter identifiability analysis for the estimation of multiple parameters in kinetic models

In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison.     

A robust soft sensor to monitor 1,3-propanediol fermentation process by Clostridium butyricum based on artificial neural network

With the aggravation of environmental pollution and energy crisis, the sustainable microbial fermentation process of converting glycerol to 1,3-propanediol (1,3-PDO) has become an attractive alternative. However, the difficulty in the online measurement of glycerol and 1,3-PDO creates a barrier to the fermentation process and then leads to the residual glycerol and therefore, its wastage. Thus, in the present study, the four-input artificial neural network (ANN) model was developed successfully to predict the concentration of glycerol, 1,3-PDO, and biomass with high accuracy. Moreover, an ANN model combined with a kinetic model was also successfully developed to simulate the fed-batch fermentation process accurately. Hence, a soft sensor from the ANN model based on NaOH-related parameters has been successfully developed which cannot only be applied in software to solve the difficulty of glycerol and 1,3-PDO online measurement during the industrialization process, but also offer insight and reference for similar fermentation processes.     

Use of an Extended Kalman Filter and development of an automated system for xylose fermentation by a recombinantEscherichia coli

Summary An automated system was developed for on-line monitoring and control of xylose fermentation by a recombinantEscherichia coli. A 7-L fermenter was interfaced with a personal computer. Control circuits were constructed and a software was developed to estimate the states of the fermentation using an Extended Kalman Filter. The automated system combined with the Extended Kalman Filter provided a satisfactory way to obtain on-line information regarding estimation of fermentation parameters.     

Determination of kinetic parameters of 1,3-propanediol fermentation by Clostridium diolis using statistically optimized medium

1,3-propanediol (1,3-PD) is a chemical compound of immense importance primarily used as a raw material for fiber and textile industry. It can be produced by the fermentation of glycerol available abundantly as a by-product from the biodiesel plant. The present study was aimed at determination of key kinetic parameters of 1,3-PD fermentation by Clostridium diolis. Initial experiments on microbial growth inhibition were followed by optimization of nutrient medium recipe by statistical means. Batch kinetic data from studies in bioreactor using optimum concentration of variables obtained from statistical medium design was used for estimation of kinetic parameters of 1,3-PD production. Direct use of raw glycerol from biodiesel plant without any pre-treatment for 1,3-PD production using this strain investigated for the first time in this work gave results comparable to commercial glycerol. The parameter values obtained in this study would be used to develop a mathematical model for 1,3-PD to be used as a guide for designing various reactor operating strategies for further improving 1,3-PD production. An outline of protocol for model development has been discussed in the present work.     

Biodiesel biorefinery: opportunities and challenges for microbial production of fuels and chemicals from glycerol waste

ABSTRACT: The considerable increase in biodiesel production worldwide in the last 5 years resulted in astoichiometric increased coproduction of crude glycerol. As an excess of crude glycerol hasbeen produced, its value on market was reduced and it is becoming a "waste-stream" insteadof a valuable "coproduct". The development of biorefineries, i.e. production of chemicals andpower integrated with conversion processes of biomass into biofuels, has been singled out asa way to achieve economically viable production chains, valorize residues and coproducts,and reduce industrial waste disposal. In this sense, several alternatives aimed at the use ofcrude glycerol to produce fuels and chemicals by microbial fermentation have beenevaluated. This review summarizes different strategies employed to produce biofuels andchemicals (1,3-propanediol, 2,3-butanediol, ethanol, n-butanol, organic acids, polyols andothers) by microbial fermentation of glycerol. Initially, the industrial use of each chemical isbriefly presented; then we systematically summarize and discuss the different strategies toproduce each chemical, including selection and genetic engineering of producers, andoptimization of process conditions to improve yield and productivity. Finally, the impact ofthe developments obtained until now are placed in perspective and opportunities andchallenges for using crude glycerol to the development of biodiesel-based biorefineries areconsidered. In conclusion, the microbial fermentation of glycerol represents a remarkablealternative to add value to the biodiesel production chain helping the development ofbiorefineries, which will allow this biofuel to be more competitive.     

Metabolomics: quantification of intracellular metabolite dynamics

The rational improvement of microbial strains for the production of primary and secondary metabolites ('metabolic engineering') requires a quantitative understanding of microbial metabolism. A process by which this information can be derived from dynamic fermentation experiments is presented. By applying a substrate pulse to a substrate-limited, steady state culture, cellular metabolism is shifted away from its metabolic steady state. With the aid of a rapid sampling and quenching routine it is possible to take 4-5 samples per second during this process, thus capturing the metabolic response to this stimulus. Over 30 metabolites, nucleotides and cofactors from Escherichia coli metabolism can be extracted and analysed using a range of different techniques, for example enzymatic assays, HPLC and LC-MS methods. Using different substrates as limiting and pulse-substrates (glucose, glycerol), different metabolic pathways and substrate uptake systems are investigated. The resulting plots of intracellular metabolite concentrations against time serve as a data basis for modelling microbial metabolic networks.     

Anaerobic fermentation of glycerol by Escherichia coli: a new platform for metabolic engineering

The worldwide surplus of glycerol generated as inevitable byproduct of biodiesel fuel and oleochemical production is resulting in the shutdown of traditional glycerol-producing/refining plants and new applications are needed for this now abundant carbon source. In this article we report our finding that Escherichia coli can ferment glycerol in a pH-dependent manner. We hypothesize that glycerol fermentation is linked to the availability of CO(2), which under acidic conditions is produced by the oxidation of formate by the enzyme formate hydrogen lyase (FHL). In agreement with this hypothesis, glycerol fermentation was severely impaired by blocking the activity of FHL. We demonstrated that, unlike CO(2), hydrogen (the other product of FHL-mediated formate oxidation) had a negative impact on cell growth and glycerol fermentation. In addition, supplementation of the medium with CO(2) partially restored the ability of an FHL-deficient strain to ferment glycerol. High pH resulted in low CO(2) generation (low activity of FHL) and availability (most CO(2) is converted to bicarbonate), and consequently very inefficient fermentation of glycerol. Most of the fermented glycerol was recovered in the reduced compounds ethanol and succinate (93% of the product mixture), which reflects the highly reduced state of glycerol and confirms the fermentative nature of this process. Since glycerol is a cheap, abundant, and highly reduced carbon source, our findings should enable the development of an E. coli-based platform for the anaerobic production of reduced chemicals from glycerol at yields higher than those obtained from common sugars, such as glucose.     

Human faecal microbiota display variable patterns of glycerol metabolism

Significant amounts of glycerol reach the colon microbiota daily through the diet and/or by in situ microbial production or release from desquamated epithelial cells. Some gut microorganisms may anaerobically reduce glycerol to 1,3-propanediol (1,3-PDO), with 3-hydroxypropanal as an intermediate. Accumulation of the latter intermediate may result in the formation of reuterin, which is known for its biological activity (e.g. antimicrobial properties). To date, glycerol metabolism in mixed cultures from the human colon has received little attention. Using in vitro batch incubations of faeces from 10 human individuals, we demonstrated that glycerol addition (140 mM) significantly affects the metabolism and composition of the microbial community. About a third of the samples exhibited rapid glycerol conversion, yielding proportionally higher levels of acetate and 1,3-PDO. In contrast, a slower glycerol metabolism resulted in higher levels of propionate. Furthermore, rapid glycerol metabolism correlated with significant shifts in the Lactobacillus-Enterococcus community, which were not observed in slower glycerol-metabolizing samples. As the conversion of glycerol to 1,3-PDO is a highly reducing process, we infer that the glycerol metabolism may act as an effective hydrogen sink. Given the importance of hydrogen-consuming processes in the gut, this work suggests that glycerol may have potential as a tool for modulating fermentation kinetics and profiles in the gastrointestinal tract.     

重组毕赤酵母产青霉素G酰化酶的分批发酵动力学研究

构建了重组毕赤酵母产青霉素G酰化酶的分批发酵动力学模型。实验考察了分批发酵过程中甘油消耗、甲醇浓度、菌体浓度、溶氧、补料时间对青霉素G酰化酶活力的影响。应用Matlab软件,对菌体生长、基质消耗和产物生成方程进行最优参数估算和非线性拟合,得到相应的动力学模型。模型的计算值与实验值能较好地拟合,表明所建模型能较好反映重组毕赤酵母产青霉素G酰化酶的分批发酵过程。     

Nonlinear Dual Reconstruction of SPECT Activity and Attenuation Images

In single photon emission computed tomography (SPECT), accurate attenuation maps are needed to perform essential attenuation compensation for high quality radioactivity estimation. Formulating the SPECT activity and attenuation reconstruction tasks as coupled signal estimation and system parameter identification problems, where the activity distribution and the attenuation parameter are treated as random variables with known prior statistics, we present a nonlinear dual reconstruction scheme based on the unscented Kalman filtering (UKF) principles. In this effort, the dynamic changes of the organ radioactivity distribution are described through state space evolution equations, while the photon-counting SPECT projection data are measured through the observation equations. Activity distribution is then estimated with sub-optimal fixed attenuation parameters, followed by attenuation map reconstruction given these activity estimates. Such coupled estimation processes are iteratively repeated as necessary until convergence. The results obtained from Monte Carlo simulated data, physical phantom, and real SPECT scans demonstrate the improved performance of the proposed method both from visual inspection of the images and a quantitative evaluation, compared to the widely used EM-ML algorithms. The dual estimation framework has the potential to be useful for estimating the attenuation map from emission data only and thus benefit the radioactivity reconstruction.     

Impurities of crude glycerol and their effect on metabolite production

Glycerol is a valuable raw material for the production of industrially useful metabolites. Among many promising applications for the use of glycerol is its bioconversion to high value-added compounds, such as 1,3-propanediol (1,3-PD), succinate, ethanol, propionate, and hydrogen, through microbial fermentation. Another method of waste material utilization is the application of crude glycerol in blends with other wastes (e.g., tomato waste hydrolysate). However, crude glycerol, a by-product of biodiesel production, has many impurities which can limit the yield of metabolites. In this mini-review we summarize the effects of crude glycerol impurities on various microbial fermentations and give an overview of the metabolites that can be synthesized by a number of prokaryotic and eukaryotic microorganisms when cultivated on glycerol.     

Physiological predisposition of various Clostridium species to synthetize 1,3-propanediol from glycerol

1,3-Propanediol (1,3-PD) production by fermentation of glycerol was first described in 1881 but little attention was paid to this biosynthesis for over a century. An increasing interest in microbial 1,3-PD production is observed since late 1980s. The high growth rate of the biofuel market and the perspective of glycerol becoming abundant attract even more attention to this valuable chemical.Glycerol conversion to 1,3-PD is known to occur in Clostridia, Enterobacteriaceae and Lactobacillaceae. Some clostridial species are among the best 1,3-PD producers.This work is a review of the current state of research on Clostridium spp. strains that ferment glycerol to 1,3-PD. It focuses on the metabolic pathways and factors that influence the production of this diol. The effects of different environmental stresses on the process of 1,3-PD synthesis are also covered. Moreover, various genetic engineering methods utilized in order to improve the capabilities of bacteria used in this process are presented.     

A hybrid asymptotic-Kalman observer for bioprocesses

The exponential observers (extended Kalman or Luenberger observers, high gain observers) allow the use of a tuning parameter for managing the rate of convergence of the state estimate towards the true state. But their results are strongly dependent on the model quality (especially the kinetic model in bioprocesses). On the other hand, asymptotic observers (like the observer of Bastin and Dochain) have a rate of convergence which is a function of the experimental conditions (namely the dilution rate). However, this lack of tuning parameter is compensated by the absence of need for any kinetic model. In this paper, a hybrid technique is proposed which allows to jointly estimate the state and identify on-line the confidence on the kinetic model. The two limit cases (100 and 0 confidence) allow to recover rigorously the extended Kalman filter and the asymptotic observer of Bastin and Dochain. A simulation example (a fed-batch bacterial culture) is proposed and exhibits very satisfactory results.     

A comparative study of solvent-assisted pretreatment of biodiesel derived crude glycerol on growth and 1,3-propanediol production from Citrobacter freundii

The rapidly growing biodiesel industry has created a scenario, where it is both important and challenging to deal with the enormous amount of crude glycerol generated as an inherent by-product. With every 100 gallons of biodiesel produced, 5-10 gallons of the crude glycerol is left behind containing several impurities which makes its disposal difficult. The objective of the present investigation was to evaluate the impact of biodiesel-derived crude glycerol upon microbial growth and production of 1,3-propanediol by Citrobacter freundii. Five different grades of crude glycerol (obtained from biodiesel preparation using jatropha, soybean, sunflower, rice bran and linseed oils) were used. Crude glycerol caused significant inhibition of microbial growth and subsequently 1,3-propanediol production as compared to pure glycerol. Therefore, a process was developed for the treatment of crude glycerol using solvents before fermentation wherein four different non-polar solvents were examined yielding different grades of pretreated glycerol. Subsequently, the potential toxic effects of pretreated glycerol on the growth and 1,3-propanediol production by C. freundii was evaluated. In case of petroleum ether-treated crude glycerol obtained from jatropha & linseed and hexane-treated crude glycerol obtained from rice bran, the yields obtained were comparable to the pure glycerol. Similarly, soybean-derived glycerol gave comparable results after treatment with either hexane or petroleum ether.     

Microbial production of D-mannitol and D-fructose from glycerol

In view of the recent development that some petrochemical products are efficiently available as substrates for the fermentation industry, glycerol manufactured from propylene by chemical synthesis would also be hoped for the purpose. This paper describes some of the factors influencing mannitol production from glycerol by Torulopsis yeasts and a microbial conversion of glycerol to D -fructose via mannitol, in which two sequential steps of yeast and Acetobacter fermentation are involved. Torulopsis mannitofaciens CBS 5981 and Torulopsis vcrsatilis CBS 1752, exceptionally good mannitol producers, were selected for the study. High concentrations of nitrogen sources and KH₂PO₄ in the medium markedly decreased mannitol yield in spite of good utilization of the substrate. T. mannitofaciens produced mannitol in yield of 31% of the glycerol consumed at optimal condition. The fermentation by washed yeast cells gave much higher mannitol yield of more than 50%. A sequential fermentation process was carried out without isolation and purification of the intermediate and yielded.51.7%. D -fructose from the glycerol.