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In the past three decades, various computational frameworks for the modelling of the intracellular isotopic distribution have been proposed by different research groups. Among them the cascaded linear systems are the most popular approaches since they can transfer the nonlinear isotopomer labeling system into cascaded linear sub-systems. In this work, a novel two-step decomposition algorithm to model isotopomer labeling system is proposed. It can be utilized to decompose large metabolic networks. For convenience purpose, a new concept of isotopomer decomposition units (IDUs) is defined to distinguish the approach from others. Comparing to other cascaded linear systems, the IDU method follows a different decomposition procedure and results in another set of cascaded linear systems with different coefficients. Two variants of IDU algorithms are proposed, while one variant of them (IDU-B) has fewer number of balance equations than that of EMU balance equations. The efficiency of the IDU approach is demonstrated through two simulated examples.

The isotopically non-stationary 13C labelling experiments, as an emerging experimental technique, can estimate the intracellular fluxes of the cell culture under an isotopic transient period. However, to the best of our knowledge, the issue of the structural identifiability analysis of non-stationary isotope experiments is not well addressed in the literature. In this work, the local structural identifiability analysis for non-stationary cumomer balance equations is conducted based on the Taylor series approach. The numerical rank of the Jacobian matrices of the finite extended time derivatives of the measured fractions with respect to the free parameters is taken as the criterion. It turns out that only one single time point is necessary to achieve the structural identifiability analysis of the cascaded linear dynamic system of non-stationary isotope experiments. The equivalence between the local structural identifiability of the cascaded linear dynamic systems and the local optimum condition of the nonlinear least squares problem is elucidated in the work. Optimal measurements sets can then be determined for the metabolic network. Two simulated metabolic networks are adopted to demonstrate the utility of the proposed method.

Background Pichia pastoris is one of the most important cell factories for production of industrial enzymes and heterogenous proteins. The genome-scale metabolic model of high quality is crucial for comprehensive understanding of the P. pastoris metabolism. Methods In this paper, we upgraded P. pastoris genome-scale metabolic model based on the combination of latest genome annotations and literatures. Then the performance of the new model was evaluated using the Cobra Toolbox v2.0. Results Compared with the recently published model iMT1026, the reaction number in the new model iRY1243 was increased from 2035 to 2407 and the metabolite number was increased from 1018 to 1094. Accordingly, the unique ORF number was increased from 1026 to 1243. To improve the metabolic functions of P. pastoris genome-scale metabolic model, the biosynthesis pathways of vitamins and cofactors were carefully added. iRY1243 showed good performances when predicting the growth capability on most of the reported carbon and nitrogen sources, the metabolic flux distribution with glucose as a sole carbon source, the essential and partially essential genes, and the effects of gene deletion or overexpression on cell growth and S-adenosyl-l-methionine production. Conclusion iRY1243 is an upgraded P. pastoris genome-scale metabolic model with significant improvements in the metabolic coverage and prediction ability, and thus it will be a potential platform for further systematic investigation of P. pastoris metabolism. Electronic supplementary material The online version of this article (doi:10.1186/s40643-017-0152-x) contains supplementary material, which is available to authorized users.

Aimed at the determination of the number of mixtures for finite mixture models (FMMs), in this work, a new method called the penalized histogram difference criterion (PHDC) is proposed and evaluated with other criteria such as Akaike information criterion (AIC), the minimum message length (MML), the information complexity (ICOMP) and the evidence of data criterion (EDC). The new method, which calculates the penalized histogram difference between the data generated from estimated FMMs and those for modeling purpose, turns out to be better than others for data with complicate mixtures patterns. It is demonstrated in this work that the PHDC can determine the optimal number of clusters of the FMM. Furthermore, the estimated FMMs asymptotically approximate the true model. The utility of the new method is demonstrated through synthetic data sets analysis and the batch-wise comparison of citric acid fermentation processes.

Additional file 3. Non-growth-associated ATP maintenance (NGAM) requirement.

Pichia pastoris is a popular recombinant protein expression system for its accessibility of efficient gene manipulation and high protein production. Sufficient supply of precursors, energy, and redox cofactors is crucial for high recombinant protein production. In our present work, we found that the addition of glutamate improved the recombinant β-galactosidase (β-gal) production by P. pastoris G1HL. To elucidate the impacts of glutamate on the central metabolism in detail, a combined 13C-assisted metabolomics and 13C metabolic flux analysis was conducted based on LC–MS/MS and GC–MS data. The pool sizes of intracellular amino acids were obviously higher on glucose/glutamate (Glc/Glu). The fluxes in EMP entry reaction and in downstream TCA cycle were 50 and 67% higher on Glc/Glu than on Glc, respectively. While the fluxes in upstream TCA cycle kept almost unaltered, the fluxes in PPP oxidative branch decreased. The addition of glutamate leads to a remarkable change on the central metabolism of high β-galactosidase-producing P. pastoris G1HL. To meet the increased demands of redox cofactors and energy for higher β-galactosidase production on Glc/Glu, P. pastoris G1HL redistributes the fluxes in central metabolism through the inhibitions and/or activation of the enzymes in key nodes together with the energy and redox status.

Background Pichia pastoris is a popular recombinant protein expression system for its accessibility of efficient gene manipulation and high protein production. Sufficient supply of precursors, energy, and redox cofactors is crucial for high recombinant protein production. In our present work, we found that the addition of glutamate improved the recombinant β-galactosidase (β-gal) production by P. pastoris G1HL. Methods To elucidate the impacts of glutamate on the central metabolism in detail, a combined 13C-assisted metabolomics and 13C metabolic flux analysis was conducted based on LC–MS/MS and GC–MS data. Results The pool sizes of intracellular amino acids were obviously higher on glucose/glutamate (Glc/Glu). The fluxes in EMP entry reaction and in downstream TCA cycle were 50 and 67% higher on Glc/Glu than on Glc, respectively. While the fluxes in upstream TCA cycle kept almost unaltered, the fluxes in PPP oxidative branch decreased. Conclusion The addition of glutamate leads to a remarkable change on the central metabolism of high β-galactosidase-producing P. pastoris G1HL. To meet the increased demands of redox cofactors and energy for higher β-galactosidase production on Glc/Glu, P. pastoris G1HL redistributes the fluxes in central metabolism through the inhibitions and/or activation of the enzymes in key nodes together with the energy and redox status. Electronic supplementary material The online version of this article (doi:10.1186/s40643-016-0124-6) contains supplementary material, which is available to authorized users.

Multi-batch bioprocesses data, unlike the data from other industries, are highly correlated due to the operation characteristics of the industry. In this work, pairwise Fisher discriminant analysis (FDA) is successfully utilized to reveal the similarity between two batches. In order to handle the mixture pattern for the data projected into the reduced feature subspace represented by the first several generalized eigenvectors, the finite Gaussian mixture model is adopted here to calculate the confidence region of each mixture. There are several challenges facing application engineers when estimate finite mixture models (FMMs), such as initialization of the expectation-maximization (EM) algorithm and determination of number of mixtures. In this work, an initialization method based on the uniform prior distribution assumption and a new method to determine the number of components of FMMs based on estimated density histogram are proposed. The utility of the proposed method has been demonstrated in simulation studies. Combined with the pairwise FDA, the method has been successfully applied to a large scale multi-batch bioprocess data set.

Additional file 4. Trends of the MID of intracellular free amino acids during 13C labeling experiments on Glc and on Glc/Glu.

Subspace identification methods (SIMs) for estimating state-space models have been proven to be very useful and numerically efficient. They exist in several variants, but all have one feature in common: as a first step, a collection of high-order ARX models are estimated from vectorized input-output data. In order not to obtain biased estimates, this step must include future outputs. However, all but one of the submodels include non-causal input terms. The coefficients of them will be correctly estimated to zero as more data become available. They still include extra model parameters which give unnecessarily high variance, and also cause bias for closed-loop data. In this paper, a new model formulation is suggested that circumvents the problem. Within the framework, the system matrices (A,B,C,D) and Markov parameters can be estimated separately. It is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles.

In this paper, we analyze two recently proposed closed-loop subspace identification methods, referred to as innovation estimation method and whitening filter approach respectively. The similarity and difference between them are investigated in detail. It turns out that all closed-loop subspace identification methods can be classified as one-step, two-step, or multi-stage projection methods. A SISO closed-loop simulation shows that to identify a consistent model the whitening filter approach might require longer future and past horizons than the innovation estimation method.

The yeast Pichia pastoris GS115 is a widely used microbial cell factory for the production of heterologous protein. In order to reveal the impacts of high heterologous protein expression on the central metabolism of Pichia pastoris GS115 using glucose as sole carbon source, we engineered a high β-galactosidase expression strain P. pastoris G1HL and a low expression control strain P. pastoris GHL through controlling the initiation strength of constitutive promoter pGAP. The carbon flux distributions in these two strains were quantified via (13)C metabolic flux analysis. Compared to the control strain, G1HL showed a lower growth rate, a higher flux through glycolysis pathway, a higher flux through pentose phosphate pathway, and a lower flux through by-products secretion pathway. The metabolic flux redistribution in G1HL was thought to compensate the increased redox cofactors and energy demands caused by the high protein expression. Although the fluxes through Krebs cycle in two engineered strains were almost the same, they were significantly lower than those in wild strain. The enhanced expression of β-galactosidase by glutamate supplementation demonstrated the potential of P. pastoris GS115 to catabolize more carbon through the Krebs cycle for even higher protein expression. In conclusion, our work indicates that P. pastoris GS115 can readjusts the central metabolism for higher heterologous protein expression and provides strategies for strain development or process optimization for enhancing production of heterologous protein.

The mean activity coefficients of NaCl in (sodium chloride + sodium bicarbonate + water) were determined experimentally in the temperature range 293.15 K to 308.15 K at four NaHCO 3 molality fractions (0.1, 0.3, 0.5, and 0.7). The measurements were made with an electrochemical cell, using a Na + glass ion-selective electrode and a Cl − solid-state ion-selective electrode. The experimental values reported by Butler and Huston are found to be higher than those calculated from the Pitzer equation using the existing parameters while the experimental results of this work are close to the calculated values, up to an NaHCO 3 molality fraction of 0.5. At the NaHCO 3 molality fraction of 0.7, the experimental data are much lower than the calculated values, implying that the interference of HCO 3 − on the Na + glass ion-selective electrode can only be neglected up to a molality fraction of NaHCO 3 of 0.5, an observation which is consistent with that of Butler and Huston.

The mean activity coefficients of NaCl in the NaCl‐NH 4HCO3‐H2O system, measured by an electrochemical cell using ion-selective electrodes, were used to calculate the mean activity coefficients of NH 4HCO3 in the system through a thermodynamic model. The measurements were made at four temperatures from 293.15 to 308.15 K up to 1.8 mol kg 1 ,a t NH 4HCO3 molality fractions of 0.2 and 0.4. Both sets of values agree with those obtained from Pitzer equation incorporated with chemical reactions. This observation supports the applicability of the existing parameters for calculating mean activity coefficients of this system. © 2001 Elsevier Science B.V. All rights reserved.

A nonlinear dynamic principal component analysis (ND-PCA) approach is developed in this paper based on dynamic PCA and the sigmoid basis function feed forward neural network (SBFN). Through ND-PCA an integrated framework for on-line monitoring and root-cause diagnosis is developed. The approach is verified and illustrated on the Tennessee Eastman benchmark process as a case study while noises were added on sensor readings. Results show that the proposed ND-PCA approach performs good incipient diagnosis capability and overall diagnosis correctness rate.

This paper outlines an object/agent based system model for the Computer Integrated Process Operation System (CIPOS). Most previous studies have focused on the Computer Aided Process Operation system (CAPO), while they are standalone and not good at communication with each other. The system model proposed in this work can solve some key integrated problems in CIPOS, which are problem integration, task integration, tools integration and personnel involvement. An instantiated system, TE_CIPOS, is implemented to give further explanation and verification of the proposed object/agent based system model and its integrating environment.

In this paper, we show that the consistency of closed-loop subspace identification methods (SIMs) can be achieved through innovation estimation. Based on this analysis, a sufficient condition for the consistency of a new proposed closed-loop SIM is given. A consistent estimate of the Kalman gain under closed-loop conditions is also provided based on the algorithm. A multi-input-multi-output (MIMO) simulation shows that it is consistent under closed-loop condition, when traditional SIMs fail to provide consistent estimates.