Optimal re-design of primary metabolism in Escherichia coli using linlog kinetics

This paper examines the validity of the linlog approach, which was recently developed in our laboratory, by comparison of two different kinetic models for the metabolic network of Escherichia coli. The first model is a complete mechanistic model; the second is an approximative model in which linlog kinetics are applied. The parameters of the linlog model (elasticities) are derived from the mechanistic model. Three different optimization cases are examined. In all cases, the objective is to calculate the enzyme levels that maximize a certain flux while keeping the total amount of enzyme constant and preventing large changes of metabolite concentrations. For an average variation of metabolite levels of 10% and individual changes of a factor 2, the predicted enzyme levels, metabolite concentrations and fluxes of both models are highly similar. This similarity holds for changes in enzyme level of a factor 4-6 and for changes in fluxes up to a factor 6. In all three cases, the predicted optimal enzyme levels could neither have been found by intuition-based approaches, nor on basis of flux control coefficients. This demonstrates that kinetic models are essential tools in Metabolic Engineering. In this respect, the linlog approach is a valuable extension of MCA, since it allows construction of kinetic models, based on MCA parameters, that can be used for constrained optimization problems and are valid for large changes of metabolite and enzyme levels.     

Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics

This paper presents a new mathematical framework for modeling of in vivo dynamics and for metabolic re-design: the linlog approach. This approach is an extension of metabolic control analysis (MCA), valid for large changes of enzyme and metabolite levels. Furthermore, the presented framework combines MCA with kinetic modeling, thereby also combining the merits of both approaches. The linlog framework includes general expressions giving the steady-state fluxes and metabolite concentrations as a function of enzyme levels and extracellular concentrations, and a metabolic design equation that allows direct calculation of required enzyme levels for a desired steady state when control and response coefficients are available. Expressions giving control coefficients as a function of the enzyme levels are also derived. The validity of the linlog approximation in metabolic modeling is demonstrated by application of linlog kinetics to a branched pathway with moiety conservation, reversible reactions and allosteric interactions. Results show that the linlog approximation is able to describe the non-linear dynamics of this pathway very well for concentration changes up to a factor 20. Also the metabolic design equation was tested successfully.     

Translating biochemical network models between different kinetic formats

Mechanistic biochemical network models describe the dynamics of intracellular metabolite pools in terms of substance concentrations, stoichiometry and reaction kinetics. Data from stimulus response experiments are currently the most informative source for in-vivo parameter estimation in such models. However, only a part of the parameters of classical enzyme kinetic models can usually be estimated from typical stimulus response data. For this reason, several alternative kinetic formats using different “languages” (e.g. linear, power laws, linlog, generic and convenience) have been proposed to reduce the model complexity. The present contribution takes a rigorous “multi-lingual” approach to data evaluation by translating biochemical network models from one kinetic format into another. For this purpose, a new high-performance algorithm has been developed and tested. Starting with a given model, it replaces as many kinetic terms as possible by alternative expressions while still reproducing the experimental data. Application of the algorithm to a published model for Escherichia coli's sugar metabolism demonstrates the power of the new method. It is shown that model translation is a powerful tool to investigate the information content of stimulus response data and the predictive power of models. Moreover, the local and global approximation capabilities of the models are elucidated and some pitfalls of traditional single model approaches to data evaluation are revealed.     

A new framework for the estimation of control parameters in metabolic pathways using lin-log kinetics.

The control properties of biochemical pathways can be described by control coefficients and elasticities, as defined in the framework of metabolic control analysis. The determination of these parameters using the traditional metabolic control analysis relationships is, however, limited by experimental difficulties (e.g. realizing and measuring small changes in biological systems) and lack of appropriate mathematical procedures (e.g. when the more practical large changes are made). In this paper, the recently developed lin-log approach is proposed to avoid the above-mentioned problems and is applied to estimate control parameters from measurements obtained in steady state experiments. The lin-log approach employs approximative linear-logarithmic kinetics parameterized by elasticities and provides analytical solutions for fluxes and metabolite concentrations when large changes are made. Published flux and metabolite concentration data are used, obtained from a reconstructed section of glycolysis converting 3-phosphoglycerate to pyruvate [Giersch, C. (1995) Eur. J. Biochem. 227, 194-201]. With the lin-log approach, all data from different experiments can be combined to give realistic elasticity and flux control coefficient estimates by linear regression. Despite the large changes, a good agreement of fluxes and metabolite concentrations is obtained between the measured and calculated values according to the lin-log model. Furthermore, it is shown that the lin-log approach allows a rigorous statistical evaluation to identify the optimal reference state and the optimal model structure assumption. In conclusion, the lin-log approach addresses practical problems encountered in the traditional metabolic control analysis-based methods by introducing suitable nonlinear kinetics, thus providing a novel framework with improved procedures for the estimation of elasticities and control parameters from large perturbation experiments.     

Model reduction and a priori kinetic parameter identifiability analysis using metabolome time series for metabolic reaction networks with linlog kinetics

In this work, we present a time-scale analysis based model reduction and parameter identifiability analysis method for metabolic reaction networks. The method uses the information obtained from short term chemostat perturbation experiments. We approximate the time constant of each metabolite pool by their turn-over time and classify the pools accordingly into two groups: fast and slow pools. We performed a priori model reduction, neglecting the dynamic term of the fast pools. By making use of the linlog approximative kinetics, we obtained a general explicit solution for the fast pools in terms of the slow pools by elaborating the degenerate algebraic system resulting from model reduction. The obtained relations yielded also analytical relations between a subset of kinetic parameters. These relations also allow to realize an analytical model reduction using lumped reaction kinetics. After solving these theoretical identifiability problems and performing model reduction, we carried out a Monte Carlo approach to study the practical identifiability problems. We illustrated the methodology on model reduction and theoretical/practical identifiability analysis on an example system representing the glycolysis in Saccharomyces cerevisiae cells.     

RankAggreg, an R package for weighted rank aggregation

Background

Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems.

Results

In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters.

Conclusion

The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.     

Identification of a Metabolic Reaction Network from Time-Series Data of Metabolite Concentrations

Recent development of high-throughput analytical techniques has made it possible to qualitatively identify a number of metabolites simultaneously. Correlation and multivariate analyses such as principal component analysis have been widely used to analyse those data and evaluate correlations among the metabolic profiles. However, these analyses cannot simultaneously carry out identification of metabolic reaction networks and prediction of dynamic behaviour of metabolites in the networks. The present study, therefore, proposes a new approach consisting of a combination of statistical technique and mathematical modelling approach to identify and predict a probable metabolic reaction network from time-series data of metabolite concentrations and simultaneously construct its mathematical model. Firstly, regression functions are fitted to experimental data by the locally estimated scatter plot smoothing method. Secondly, the fitted result is analysed by the bivariate Granger causality test to determine which metabolites cause the change in other metabolite concentrations and remove less related metabolites. Thirdly, S-system equations are formed by using the remaining metabolites within the framework of biochemical systems theory. Finally, parameters including rate constants and kinetic orders are estimated by the Levenberg–Marquardt algorithm. The estimation is iterated by setting insignificant kinetic orders at zero, i.e., removing insignificant metabolites. Consequently, a reaction network structure is identified and its mathematical model is obtained. Our approach is validated using a generic inhibition and activation model and its practical application is tested using a simplified model of the glycolysis of Lactococcus lactis MG1363, for which actual time-series data of metabolite concentrations are available. The results indicate the usefulness of our approach and suggest a probable pathway for the production of lactate and acetate. The results also indicate that the approach pinpoints a probable strong inhibition of lactate on the glycolysis pathway.     

Dependence of control coefficient distribution on the boundaries of a metabolic system: a generalized analysis of the effects of additional input and output reactions to a linear pathway

Both experimental and theoretical studies of metabolism are likely to relate to a segment that has been isolated for analytical purposes. In practice, it will be embedded in the whole of cellular metabolism. Thus, it is necessary to consider how conclusions about the control of an isolated pathway may be modified in this wider context where the input and output metabolites are considered as variables of cellular metabolism. Here, we analyse the effect of expanding a linear metabolic pathway by adding an extra input or an extra output. In particular, we analyse the effect of the elasticities of the extra steps on control coefficients. We derive matrix algebraic relationships for obtaining flux and concentration control coefficients from expressions depending on these extra elasticities and on parameters (elasticities and control coefficients) of the original pathway. These equations can be shown in certain cases to be generalized versions of earlier rescaling relationships and to be related to top-down analysis, but also apply where the new variable metabolite of the expanded pathway is an effector of more than one step of the original pathway. We use our relationships to analyse the dependence or independence of control coefficients upon these extra elasticities for the published analyses of the pathway of mammalian serine biosynthesis (Fell & Snell, 1988) and Escherischia coli threonine biosynthesis (Chassagnole et al., 2001). The same analysis can be applied to determine whether the transport reactions of substrates and products of a pathway in and out of a cell need to be included in estimations of the control coefficients of the enzymes.     

Something from nothing: bridging the gap between constraint-based and kinetic modelling

Two divergent modelling methodologies have been adopted to increase our understanding of metabolism and its regulation. Constraint-based modelling highlights the optimal path through a stoichiometric network within certain physicochemical constraints. Such an approach requires minimal biological data to make quantitative inferences about network behaviour; however, constraint-based modelling is unable to give an insight into cellular substrate concentrations. In contrast, kinetic modelling aims to characterize fully the mechanics of each enzymatic reaction. This approach suffers because parameterizing mechanistic models is both costly and time-consuming. In this paper, we outline a method for developing a kinetic model for a metabolic network, based solely on the knowledge of reaction stoichiometries. Fluxes through the system, estimated by flux balance analysis, are allowed to vary dynamically according to linlog kinetics. Elasticities are estimated from stoichiometric considerations. When compared to a popular branched model of yeast glycolysis, we observe an excellent agreement between the real and approximate models, despite the absence of (and indeed the requirement for) experimental data for kinetic constants. Moreover, using this particular methodology affords us analytical forms for steady state determination, stability analyses and studies of dynamical behaviour.     

Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method

MOTIVATION: Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. RESULTS: In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.     

The elucidation of metabolic pathways and their improvements using stable optimization of large-scale kinetic models of cellular systems

Metabolic engineering of cellular systems to maximize reaction fluxes or metabolite concentrations still presents a significant challenge by encountering unpredictable instabilities that can be caused by simultaneous or consecutive enhancements of many reaction steps. It can therefore be important to select carefully small subsets of key enzymes for their subsequent stable modification compatible with cell physiology. To address this important problem, we introduce a general mixed integer non-linear problem (MINLP) formulation to compute automatically which enzyme levels should be modulated and which enzyme regulatory structures should be altered to achieve the given optimization goal using non-linear kinetic models of relevant cellular systems. The developed MINLP formulation directly employs a stability analysis constraint and also includes non-linear biophysical constraints to describe homeostasis conditions for metabolite concentrations and protein machinery without any preliminary model simplification (e.g. linlog kinetics approximation). The framework is demonstrated on a well-established large-scale kinetic model of the Escherichia coli central metabolism used for the optimization of the glucose uptake through the phosphotransferase transport system (PTS) and serine biosynthesis. Computational results show that substantial stable improvements can be predicted by manipulating only small subsets of enzyme levels and regulatory structures. This means that while more efforts can be required to elucidate larger stable optimal enzyme level/regulation choices, no further significant increase in the optimized fluxes can be obtained and, therefore, such choices may not be worth the effort due to the potential loss of stability properties. The source for instability through saddle-node and Hopf bifurcations is identified, and all results are contrasted with predictions from metabolic control analysis.     

Quantitative assessment of the glyoxalase pathway in Leishmania infantum as a therapeutic target by modelling and computer simulation

The glyoxalase pathway of Leishmania infantum was kinetically characterized as a trypanothione-dependent system. Using time course analysis based on parameter fitting with a genetic algorithm, kinetic parameters were estimated for both enzymes, with trypanothione derived substrates. A K(m) of 0.253 mm and a V of 0.21 micromol.min(-1).mg(-1)for glyoxalase I, and a K(m) of 0.098 mm and a V of 0.18 micromol.min(-1).mg(-1) for glyoxalase II, were obtained. Modelling and computer simulation were used for evaluating the relevance of the glyoxalase pathway as a potential therapeutic target by revealing the importance of critical parameters of this pathway in Leishmania infantum. A sensitivity analysis of the pathway was performed using experimentally validated kinetic models and experimentally determined metabolite concentrations and kinetic parameters. The measurement of metabolites in L. infantum involved the identification and quantification of methylglyoxal and intracellular thiols. Methylglyoxal formation in L. infantum is nonenzymatic. The sensitivity analysis revealed that the most critical parameters for controlling the intracellular concentration of methylglyoxal are its formation rate and the concentration of trypanothione. Glyoxalase I and II activities play only a minor role in maintaining a low intracellular methylglyoxal concentration. The importance of the glyoxalase pathway as a therapeutic target is very small, compared to the much greater effects caused by decreasing trypanothione concentration or increasing methylglyoxal concentration.     

Determination of in vivo oxygen uptake and carbon dioxide evolution rates from off-gas measurements under highly dynamic conditions

In vivo kinetics of Saccharomyces cerevisiae are studied, in a time window of 150 s, by analyzing the response of O(2) and CO(2) in the fermentor off-gas after perturbation of chemostat cultures by metabolite pulses. Here, a new mathematical method is presented for the estimation of the in vivo oxygen uptake rate (OUR) and carbon dioxide evolution rate (CER) directly from the off-gas data in such perturbation experiments. The mathematical construction allows effective elimination of delay and distortion in the off-gas measurement signal under highly dynamic conditions. A black box model for the fermentor off-gas system is first obtained by system identification, followed by the construction of an optimal linear filter, based on the identified off-gas model. The method is applied to glucose and ethanol pulses performed on chemostat cultures of S. cerevisiae. The estimated OUR is shown to be consistent with the independent dissolved oxygen measurement. The estimated in vivo OUR and CER provide valuable insights into the complex dynamic behavior of yeast and are essential for the establishment and validation of in vivo kinetic models of primary metabolism.     

Determination of two mebeverine metabolites, mebeverine alcohol and desmethylmebeverine alcohol, in human plasma by a dual stable isotope-based gas chromatographic-mass spectrometric method

A dual stable isotope-based GC-MS method was developed for the simultaneous determination of two metabolites of mebeverine, mebeverine alcohol and desmethylmebeverine alcohol, in human plasma. Plasma samples were treated with β-glucuronidase to cleave the glucuronide conjugates of both compounds prior to analysis. The treated plasma was prepared for analysis by solid-phase extraction using octadecylsilane cartridges. The isolated metabolites were derivatized and analyzed by GC-MS using selected-ion monitoring. Plots of peak-area ratio were linear with metabolite concentration from 2 to 200 ng/ml and the limit of detection for both metabolites was 0.5 ng/ml. The GC-MS methodology was applied to the analysis of plasma from human subjects following peroral administration of mebeverine. Pharmacokinetic parameters for both metabolites were determined and suggest that relative systemic mebeverine exposure may potentially be assessed using metabolite kinetics, if the latter subsequently are demonstrated to be linear with mebeverine dose.     

Metabolic control analysis of Aspergillus niger L-arabinose catabolism

A mathematical model of the L-arabinose/D-xylose catabolic pathway of Aspergillus niger was constructed based on the kinetic properties of the enzymes. For this purpose L-arabinose reductase, L-arabitol dehydrogenase and D-xylose reductase were purified using dye-affinity chromatography, and their kinetic properties were characterized. For the other enzymes of the pathway the kinetic data were available from the literature. The metabolic model was used to analyze flux and metabolite concentration control of the L-arabinose catabolic pathway. The model demonstrated that flux control does not reside at the enzyme following the intermediate with the highest concentration, L-arabitol, but is distributed over the first three steps in the pathway, preceding and following L-arabitol. Flux control appeared to be strongly dependent on the intracellular L-arabinose concentration. At 5 mM intracellular L-arabinose, a level that resulted in realistic intermediate concentrations in the model, flux control coefficients for L-arabinose reductase, L-arabitol dehydrogenase and L-xylulose reductase were 0.68, 0.17 and 0.14, respectively. The analysis can be used as a guide to identify targets for metabolic engineering aiming at either flux or metabolite level optimization of the L-arabinose catabolic pathway of A. niger. Faster L-arabinose utilization may enhance utilization of readily available organic waste containing hemicelluloses to be converted into industrially interesting metabolites or valuable enzymes or proteins.     

Application of a new structured model to tobacco cell cultures

A new structured kinetic model has been formulated and applied to batch suspensions of Nicotiana tabacum. This model has been developed by representing culture interactions with pathways designated for structural component production, secondary metabolite synthesis, and cellular respiration. Additional provisions were made to distinguish growth-competitive secondary metabolite production from non-growth-competitive secondary metabolite production. Parameters for kinetic rate expressions within the model were estimated based upon experimental observations utilized in conjunction with numerical optimization techniques. Using these parameters, culture growth, substrate uptake, cell respiration, and total phenolics production were all successfully correlated to experimenta data from shake flask cultures of N. tabacum.     

GC-EI-TOF-MS analysis of in vivo carbon-partitioning into soluble metabolite pools of higher plants by monitoring isotope dilution after 13CO2 labelling

The established GC-EI-TOF-MS method for the profiling of soluble polar metabolites from plant tissue was employed for the kinetic metabolic phenotyping of higher plants. Approximately 100 typical GC-EI-MS mass fragments of trimethylsilylated and methoxyaminated metabolite derivatives were structurally interpreted for mass isotopomer analysis, thus enabling the kinetic study of identified metabolites as well as the so-called functional group monitoring of yet non-identified metabolites. The monitoring of isotope dilution after (13)CO(2) labelling was optimized using Arabidopsis thaliana Col-0 or Oryza sativa IR57111 plants, which were maximally labelled with (13)C. Carbon isotope dilution was evaluated for short (2h) and long-term (3 days) kinetic measurements of metabolite pools in root and shoots. Both approaches were shown to enable the characterization of metabolite specific partitioning processes and kinetics. Simplifying data reduction schemes comprising calculation of (13)C-enrichment from mass isotopomer distributions and of initial (13)C-dilution rates were employed. Metabolites exhibited a highly diverse range of metabolite and organ specific half-life of (13)C-label in their respective pools ((13)C-half-life). This observation implied the setting of metabolite specific periods for optimal kinetic monitoring. A current experimental design for the kinetic metabolic phenotyping of higher plants is proposed.     

Parameter optimization by using differential elimination: a general approach for introducing constraints into objective functions

Background

The investigation of network dynamics is a major issue in systems and synthetic biology. One of the essential steps in a dynamics investigation is the parameter estimation in the model that expresses biological phenomena. Indeed, various techniques for parameter optimization have been devised and implemented in both free and commercial software. While the computational time for parameter estimation has been greatly reduced, due to improvements in calculation algorithms and the advent of high performance computers, the accuracy of parameter estimation has not been addressed.

Results

We propose a new approach for parameter optimization by using differential elimination, to estimate kinetic parameter values with a high degree of accuracy. First, we utilize differential elimination, which is an algebraic approach for rewriting a system of differential equations into another equivalent system, to derive the constraints between kinetic parameters from differential equations. Second, we estimate the kinetic parameters introducing these constraints into an objective function, in addition to the error function of the square difference between the measured and estimated data, in the standard parameter optimization method. To evaluate the ability of our method, we performed a simulation study by using the objective function with and without the newly developed constraints: the parameters in two models of linear and non-linear equations, under the assumption that only one molecule in each model can be measured, were estimated by using a genetic algorithm (GA) and particle swarm optimization (PSO). As a result, the introduction of new constraints was dramatically effective: the GA and PSO with new constraints could successfully estimate the kinetic parameters in the simulated models, with a high degree of accuracy, while the conventional GA and PSO methods without them frequently failed.

Conclusions

The introduction of new constraints in an objective function by using differential elimination resulted in the drastic improvement of the estimation accuracy in parameter optimization methods. The performance of our approach was illustrated by simulations of the parameter optimization for two models of linear and non-linear equations, which included unmeasured molecules, by two types of optimization techniques. As a result, our method is a promising development in parameter optimization.

     

Metabolic control and its analysis. Additional relationships between elasticities and control coefficients

Existing theorems from the analysis of metabolic control have been taken and embedded in a simple matrix algebra procedure for calculating the flux control coefficients of enzymes (formerly known as sensitivities) in a metabolic pathway from their kinetic properties (their elasticities). New theorems governing the flux control coefficients of branched pathways and substrate cycles have been derived to allow the procedure to be applied to complex pathway configurations. Modifications to the elasticity terms used in the equations have been theoretically justified so that the method remains valid for pathways with conserved metabolites (for example, the adenine nucleotide pool or the intermediates of a catalytic cycle such as the tricarboxylic acid cycle) or with pools of metabolites kept very near to equilibrium by very rapid reactions. The matrix equations generated using these theorems and relationships may be solved algebraically or numerically. Algebraic solutions have been used to determine the factors responsible for the degree of amplification of flux control coefficients by substrate cycles and to show that it is possible to derive expressions for the elasticities of a group of enzymes.     

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.