Balancing biomass reaction stoichiometry and measured fluxes in flux balance analysis.

MOTIVATION: Flux balance analysis (FBA) is widely recognized as an important method for studying metabolic networks. When incorporating flux measurements of certain reactions into an FBA problem, it is possible that the underlying linear program may become infeasible, e.g. due to measurement or modeling inaccuracies. Furthermore, while the biomass reaction is of central importance in FBA models, its stoichiometry is often a rough estimate and a source of high uncertainty. RESULTS: In this work, we present a method that allows modifications to the biomass reaction stoichiometry as a means to (i) render the FBA problem feasible and (ii) improve the accuracy of the model by corrections in the biomass composition. Optionally, the adjustment of the biomass composition can be used in conjunction with a previously introduced approach for balancing inconsistent fluxes to obtain a feasible FBA system. We demonstrate the value of our approach by analyzing realistic flux measurements of E.coli. In particular, we find that the growth-associated maintenance (GAM) demand of ATP, which is typically integrated with the biomass reaction, is likely overestimated in recent genome-scale models, at least for certain growth conditions. In light of these findings, we discuss issues related to the determination and inclusion of GAM values in constraint-based models. Overall, our method can uncover potential errors and suggest adjustments in the assumed biomass composition in FBA models based on inconsistencies between the model and measured fluxes. AVAILABILITY AND IMPLEMENTATION: The developed method has been implemented in our software tool CNApy available from https://github.com/cnapy-org/CNApy.

Toward a modeling, optimization, and predictive control framework for fed-batch metabolic cybergenetics.

Biotechnology offers many opportunities for the sustainable manufacturing of valuable products. The toolbox to optimize bioprocesses includes extracellular process elements such as the bioreactor design and mode of operation, medium formulation, culture conditions, feeding rates, and so on. However, these elements are frequently insufficient for achieving optimal process performance or precise product composition. One can use metabolic and genetic engineering methods for optimization at the intracellular level. Nevertheless, those are often of static nature, failing when applied to dynamic processes or if disturbances occur. Furthermore, many bioprocesses are optimized empirically and implemented with little-to-no feedback control to counteract disturbances. The concept of cybergenetics has opened new possibilities to optimize bioprocesses by enabling online modulation of the gene expression of metabolism-relevant proteins via external inputs (e.g., light intensity in optogenetics). Here, we fuse cybergenetics with model-based optimization and predictive control for optimizing dynamic bioprocesses. To do so, we propose to use dynamic constraint-based models that integrate the dynamics of metabolic reactions, resource allocation, and inducible gene expression. We formulate a model-based optimal control problem to find the optimal process inputs. Furthermore, we propose using model predictive control to address uncertainties via online feedback. We focus on fed-batch processes, where the substrate feeding rate is an additional optimization variable. As a simulation example, we show the optogenetic control of the ATPase enzyme complex for dynamic modulation of enforced ATP wasting to adjust product yield and productivity.

A new Zymomonas mobilis platform strain for the efficient production of chemicals.

BACKGROUND: Zymomonas mobilis is well known for its outstanding ability to produce ethanol with both high specific productivity and with high yield close to the theoretical maximum. The key enzyme in the ethanol production pathway is the pyruvate decarboxylase (PDC) which is converting pyruvate to acetaldehyde. Since it is widely considered that its gene pdc is essential, metabolic engineering strategies aiming to produce other compounds derived from pyruvate need to find ways to reduce PDC activity. RESULTS: Here, we present a new platform strain (sGB027) of Z. mobilis in which the native promoter of pdc was replaced with the IPTG-inducible PT7A1, allowing for a controllable expression of pdc. Expression of lactate dehydrogenase from E. coli in sGB027 allowed the production of D-lactate with, to the best of our knowledge, the highest reported specific productivity of any microbial lactate producer as well as with the highest reported lactate yield for Z. mobilis so far. Additionally, by expressing the L-alanine dehydrogenase of Geobacillus stearothermophilus in sGB027 we produced L-alanine, further demonstrating the potential of sGB027 as a base for the production of compounds other than ethanol. CONCLUSION: We demonstrated that our new platform strain can be an excellent starting point for the efficient production of various compounds derived from pyruvate with Z. mobilis and can thus enhance the establishment of this organism as a workhorse for biotechnological production processes.

A Cell-Free Multi-enzyme Cascade Reaction for the Synthesis of CDP-Glycerol.

CDP-glycerol is a nucleotide-diphosphate-activated version of glycerol. In nature, it is required for the biosynthesis of teichoic acid in Gram-positive bacteria, which is an appealing target epitope for the development of new vaccines. Here, a cell-free multi-enzyme cascade was developed to synthetize nucleotide-activated glycerol from the inexpensive and readily available substrates cytidine and glycerol. The cascade comprises five recombinant enzymes expressed in Escherichia coli that were purified by immobilized metal affinity chromatography. As part of the cascade, ATP is regenerated in situ from polyphosphate to reduce synthesis costs. The enzymatic cascade was characterized at the laboratory scale, and the products were analyzed by high-performance anion-exchange chromatography (HPAEC)-UV and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS). After the successful synthesis had been confirmed, a design-of-experiments approach was used to screen for optimal operation conditions (temperature, pH value and MgCl2 concentration). Overall, a substrate conversion of 89 % was achieved with respect to the substrate cytidine.

StrainDesign: a comprehensive Python package for computational design of metabolic networks.

SUMMARY: Various constraint-based optimization approaches have been developed for the computational analysis and design of metabolic networks. Herein, we present StrainDesign, a comprehensive Python package that builds upon the COBRApy toolbox and integrates the most popular metabolic design algorithms, including nested strain optimization methods such as OptKnock, RobustKnock and OptCouple as well as the more general minimal cut sets approach. The optimization approaches are embedded in individual modules, which can also be combined for setting up more elaborate strain design problems. Advanced features, such as the efficient integration of GPR rules and the possibility to consider gene and reaction additions or regulatory interventions, have been generalized and are available for all modules. The package uses state-of-the-art preprocessing methods, supports multiple solvers and provides a number of enhanced tools for analyzing computed intervention strategies including 2D and 3D plots of user-selected metabolic fluxes or yields. Furthermore, a user-friendly interface for the StrainDesign package has been implemented in the GUI-based metabolic modeling software CNApy. StrainDesign provides thus a unique and rich framework for computational strain design in Python, uniting many algorithmic developments in the field and allowing modular extension in the future. AVAILABILITY AND IMPLEMENTATION: The StrainDesign package can be retrieved from PyPi, Anaconda and GitHub (https://github.com/klamt-lab/straindesign) and is also part of the latest CNApy package.

CNApy: a CellNetAnalyzer GUI in Python for analyzing and designing metabolic networks.

SUMMARY: Constraint-based reconstruction and analysis (COBRA) is a widely used modeling framework for analyzing and designing metabolic networks. Here, we present CNApy, an open-source cross-platform desktop application written in Python, which offers a state-of-the-art graphical front-end for the intuitive analysis of metabolic networks with COBRA methods. While the basic look-and-feel of CNApy is similar to the user interface of the MATLAB toolbox CellNetAnalyzer, it provides various enhanced features by using components of the powerful Qt library. CNApy supports a number of standard and advanced COBRA techniques and further functionalities can be easily embedded in its GUI facilitating modular extension in the future. AVAILABILITY AND IMPLEMENTATION: CNApy can be installed via conda and its source code is freely available at https://github.com/cnapy-org/CNApy under the Apache 2 license.

Characterizing and utilizing oxygen-dependent promoters for efficient dynamic metabolic engineering.

Promoters adjust cellular gene expression in response to internal or external signals and are key elements for implementing dynamic metabolic engineering concepts in fermentation processes. One useful signal is the dissolved oxygen content of the culture medium, since production phases often proceed in anaerobic conditions. Although several oxygen-dependent promoters have been described, a comprehensive and comparative study is missing. The goal of this work is to systematically test and characterize 15 promoter candidates that have been previously reported to be induced upon oxygen depletion in Escherichia coli. For this purpose, we developed a microtiter plate-level screening using an algal oxygen-independent flavin-based fluorescent protein and additionally employed flow cytometry analysis for verification. Various expression levels and dynamic ranges could be observed, and six promoters (nar-strong, nar-medium, nar-weak, nirB-m, yfiD-m, and fnrF8) appear particularly suited for dynamic metabolic engineering applications. We demonstrate applicability of these candidates for dynamic induction of enforced ATP wasting, a metabolic engineering approach to increase productivity of microbial strains that requires a narrow level of ATPase expression for optimal function. The selected candidates exhibited sufficient tightness under aerobic conditions while, under complete anaerobiosis, driving expression of the cytosolic F1-subunit of the ATPase from E. coli to levels that resulted in unprecedented specific glucose uptake rates. We finally utilized the nirB-m promoter to demonstrate the optimization of a two-stage lactate production process by dynamically enforcing ATP wasting, which is automatically turned on in the anaerobic (growth-arrested) production phase to boost the volumetric productivity. Our results are valuable for implementing metabolic control and bioprocess design concepts that use oxygen as signal for regulation and induction.

Cell-Free Multi-Enzyme Synthesis and Purification of Uridine Diphosphate Galactose.

High costs and low availability of UDP-galactose hampers the enzymatic synthesis of valuable oligosaccharides such as human milk oligosaccharides. Here, we report the development of a platform for the scalable, biocatalytic synthesis and purification of UDP-galactose. UDP-galactose was produced with a titer of 48 mM (27.2 g/L) in a small-scale batch process (200 µL) within 24 h using 0.02 genzyme /gproduct . Through in-situ ATP regeneration, the amount of ATP (0.6 mM) supplemented was around 240-fold lower than the stoichiometric equivalent required to achieve the final product yield. Chromatographic purification using porous graphic carbon adsorbent yielded UDP-galactose with a purity of 92 %. The synthesis was transferred to 1 L preparative scale production in a stirred tank bioreactor. To further reduce the synthesis costs here, the supernatant of cell lysates was used bypassing expensive purification of enzymes. Here, 23.4 g/L UDP-galactose were produced within 23 h with a synthesis yield of 71 % and a biocatalyst load of 0.05 gtotal_protein /gproduct . The costs for substrates per gram of UDP-galactose synthesized were around 0.26 €/g.

Enabling anaerobic growth of Escherichia coli on glycerol in defined minimal medium using acetate as redox sink.

Glycerol has become an attractive substrate for bio-based production processes. However, Escherichia coli, an established production organism in the biotech industry, is not able to grow on glycerol under strictly anaerobic conditions in defined minimal medium due to redox imbalance. Despite extensive research efforts aiming to overcome these limitations, anaerobic growth of wild-type E. coli on glycerol always required either the addition of electron acceptors for anaerobic respiration (e.g. fumarate) or the supplementation with complex and relatively expensive additives (tryptone or yeast extract). In the present work, driven by model-based calculations, we propose and validate a novel and simple strategy to enable fermentative growth of E. coli on glycerol in defined minimal medium. We show that redox balance could be achieved by uptake of small amounts of acetate with subsequent reduction to ethanol via acetyl-CoA. Using a directed laboratory evolution approach, we were able to confirm this hypothesis and to generate an E. coli strain that shows, under anaerobic conditions with glycerol as the main substrate and acetate as co-substrate, robust growth (µ = 0.06 h-1), a high specific glycerol uptake rate (10.2 mmol/gDW/h) and an ethanol yield close to the theoretical maximum (0.92 mol per mol glycerol). Using further stoichiometric calculations, we also clarify why complex additives such as tryptone used in previous studies enable E. coli to achieve redox balance. Our results provide new biological insights regarding the fermentative metabolism of E. coli and offer new perspectives for sustainable production processes based on glycerol.

Deciphering the physiological response of Escherichia coli under high ATP demand.

One long-standing question in microbiology is how microbes buffer perturbations in energy metabolism. In this study, we systematically analyzed the impact of different levels of ATP demand in Escherichia coli under various conditions (aerobic and anaerobic, with and without cell growth). One key finding is that, under all conditions tested, the glucose uptake increases with rising ATP demand, but only to a critical level beyond which it drops markedly, even below wild-type levels. Focusing on anaerobic growth and using metabolomics and proteomics data in combination with a kinetic model, we show that this biphasic behavior is induced by the dual dependency of the phosphofructokinase on ATP (substrate) and ADP (allosteric activator). This mechanism buffers increased ATP demands by a higher glycolytic flux but, as shown herein, it collapses under very low ATP concentrations. Model analysis also revealed two major rate-controlling steps in the glycolysis under high ATP demand, which could be confirmed experimentally. Our results provide new insights on fundamental mechanisms of bacterial energy metabolism and guide the rational engineering of highly productive cell factories.

Designing microbial communities to maximize the thermodynamic driving force for the production of chemicals.

Microbial communities have become a major research focus due to their importance for biogeochemical cycles, biomedicine and biotechnological applications. While some biotechnological applications, such as anaerobic digestion, make use of naturally arising microbial communities, the rational design of microbial consortia for bio-based production processes has recently gained much interest. One class of synthetic microbial consortia is based on specifically designed strains of one species. A common design principle for these consortia is based on division of labor, where the entire production pathway is divided between the different strains to reduce the metabolic burden caused by product synthesis. We first show that classical division of labor does not automatically reduce the metabolic burden when metabolic flux per biomass is analyzed. We then present ASTHERISC (Algorithmic Search of THERmodynamic advantages in Single-species Communities), a new computational approach for designing multi-strain communities of a single-species with the aim to divide a production pathway between different strains such that the thermodynamic driving force for product synthesis is maximized. ASTHERISC exploits the fact that compartmentalization of segments of a product pathway in different strains can circumvent thermodynamic bottlenecks arising when operation of one reaction requires a metabolite with high and operation of another reaction the same metabolite with low concentration. We implemented the ASTHERISC algorithm in a dedicated program package and applied it on E. coli core and genome-scale models with different settings, for example, regarding number of strains or demanded product yield. These calculations showed that, for each scenario, many target metabolites (products) exist where a multi-strain community can provide a thermodynamic advantage compared to a single strain solution. In some cases, a production with sufficiently high yield is thermodynamically only feasible with a community. In summary, the developed ASTHERISC approach provides a promising new principle for designing microbial communities for the bio-based production of chemicals.

An extended and generalized framework for the calculation of metabolic intervention strategies based on minimal cut sets.

The concept of minimal cut sets (MCS) provides a flexible framework for analyzing properties of metabolic networks and for computing metabolic intervention strategies. In particular, it has been used to support the targeted design of microbial strains for bio-based production processes. Herein we present a number of major extensions that generalize the existing MCS approach and broaden its scope for applications in metabolic engineering. We first introduce a modified approach to integrate gene-protein-reaction associations (GPR) in the metabolic network structure for the computation of gene-based intervention strategies. In particular, we present a set of novel compression rules for GPR associations, which effectively speedup the computation of gene-based MCS by a factor of up to one order of magnitude. These rules are not specific for MCS and as well applicable to other computational strain design methods. Second, we enhance the MCS framework by allowing the definition of multiple target (undesired) and multiple protected (desired) regions. This enables precise tailoring of the metabolic solution space of the designed strain with unlimited flexibility. Together with further generalizations such as individual cost factors for each intervention, direct combinations of reaction/gene deletions and additions as well as the possibility to search for substrate co-feeding strategies, the scope of the MCS framework could be broadly extended. We demonstrate the applicability and performance benefits of the described developments by computing (gene-based) Escherichia coli strain designs for the bio-based production of 2,3-butanediol, a chemical, that has recently received much attention in the field of metabolic engineering. With our extended framework, we could identify promising strain designs that were formerly unpredictable, including those based on substrate co-feeding.

Increasing ATP turnover boosts productivity of 2,3-butanediol synthesis in Escherichia coli.

BACKGROUND: The alcohol 2,3-butanediol (2,3-BDO) is an important chemical and an Escherichia coli producer strain was recently engineered for bio-based production of 2,3-BDO. However, further improvements are required for realistic applications. RESULTS: Here we report that enforced ATP wasting, implemented by overexpressing the genes of the ATP-hydrolyzing F1-part of the ATPase, leads to significant increases of yield and especially of productivity of 2,3-BDO synthesis in an E. coli producer strain under various cultivation conditions. We studied aerobic and microaerobic conditions as well as growth-coupled and growth-decoupled production scenarios. In all these cases, the specific substrate uptake and 2,3-BDO synthesis rate (up to sixfold and tenfold higher, respectively) were markedly improved in the ATPase strain compared to a control strain. However, aerobic conditions generally enable higher productivities only with reduced 2,3-BDO yields while high product yields under microaerobic conditions are accompanied with low productivities. Based on these findings we finally designed and validated a three-stage process for optimal conversion of glucose to 2,3-BDO, which enables a high productivity in combination with relatively high yield. The ATPase strain showed again superior performance and finished the process twice as fast as the control strain and with higher 2,3-BDO yield. CONCLUSIONS: Our results demonstrate the high potential of enforced ATP wasting as a generic metabolic engineering strategy and we expect more applications to come in the future.

Automatic construction of metabolic models with enzyme constraints.

BACKGROUND: In order to improve the accuracy of constraint-based metabolic models, several approaches have been developed which intend to integrate additional biological information. Two of these methods, MOMENT and GECKO, incorporate enzymatic (kcat) parameters and enzyme mass constraints to further constrain the space of feasible metabolic flux distributions. While both methods have been proven to deliver useful extensions of metabolic models, they may considerably increase size and complexity of the models and there is currently no tool available to fully automate generation and calibration of such enzyme-constrained models from given stoichiometric models. RESULTS: In this work we present three major developments. We first conceived short MOMENT (sMOMENT), a simplified version of the MOMENT approach, which yields the same predictions as MOMENT but requires significantly fewer variables and enables direct inclusion of the relevant enzyme constraints in the standard representation of a constraint-based model. When measurements of enzyme concentrations are available, these can be included as well leading in the extreme case, where all enzyme concentrations are known, to a model representation that is analogous to the GECKO approach. Second, we developed the AutoPACMEN toolbox which allows an almost fully automated creation of sMOMENT-enhanced stoichiometric metabolic models. In particular, this includes the automatic read-out and processing of relevant enzymatic data from different databases and the reconfiguration of the stoichiometric model with embedded enzymatic constraints. Additionally, tools have been developed to adjust (kcat and enzyme pool) parameters of sMOMENT models based on given flux data. We finally applied the new sMOMENT approach and the AutoPACMEN toolbox to generate an enzyme-constrained version of the E. coli genome-scale model iJO1366 and analyze its key properties and differences with the standard model. In particular, we show that the enzyme constraints improve flux predictions (e.g., explaining overflow metabolism and other metabolic switches) and demonstrate, for the first time, that these constraints can markedly change the spectrum of metabolic engineering strategies for different target products. CONCLUSIONS: The methodological and tool developments presented herein pave the way for a simplified and routine construction and analysis of enzyme-constrained metabolic models.

Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks.

BACKGROUND: The concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing and (re)designing metabolic networks. However, the calculation of MCS in genome-scale metabolic models is a complex computational problem. The development of duality-based algorithms in the last years allowed the enumeration of thousands of MCS in genome-scale networks by solving mixed-integer linear problems (MILP). A recent advancement in this field was the introduction of the MCS2 approach. In contrast to the Farkas-lemma-based dual system used in earlier studies, the MCS2 approach employs a more condensed representation of the dual system based on the nullspace of the stoichiometric matrix, which, due to its reduced dimension, holds promise to further enhance MCS computations. RESULTS: In this work, we introduce several new variants and modifications of duality-based MCS algorithms and benchmark their effects on the overall performance. As one major result, we generalize the original MCS2 approach (which was limited to blocking the operation of certain target reactions) to the most general case of MCS computations with arbitrary target and desired regions. Building upon these developments, we introduce a new MILP variant which allows maximal flexibility in the formulation of MCS problems and fully leverages the reduced size of the nullspace-based dual system. With a comprehensive set of benchmarks, we show that the MILP with the nullspace-based dual system outperforms the MILP with the Farkas-lemma-based dual system speeding up MCS computation with an averaged factor of approximately 2.5. We furthermore present several simplifications in the formulation of constraints, mainly related to binary variables, which further enhance the performance of MCS-related MILP. However, the benchmarks also reveal that some highly condensed formulations of constraints, especially on reversible reactions, may lead to worse behavior when compared to variants with a larger number of (more explicit) constraints and involved variables. CONCLUSIONS: Our results further enhance the algorithmic toolbox for MCS calculations and are of general importance for theoretical developments as well as for practical applications of the MCS framework.

Characterizing and ranking computed metabolic engineering strategies.

MOTIVATION: The computer-aided design of metabolic intervention strategies has become a key component of an integrated metabolic engineering approach and a broad range of methods and algorithms has been developed for this task. Many of these algorithms enforce coupling of growth with product synthesis and may return thousands of possible intervention strategies from which the most suitable strategy must then be selected. RESULTS: This work focuses on how to evaluate and rank, in a meaningful way, a given pool of computed metabolic engineering strategies for growth-coupled product synthesis. Apart from straightforward criteria, such as a preferably small number of necessary interventions, a reasonable growth rate and a high product yield, we present several new criteria useful to pick the most suitable intervention strategy. Among others, we investigate the robustness of the intervention strategies by searching for metabolites that may disrupt growth coupling when accumulated or secreted and by checking whether the interventions interrupt pathways at their origin (preferable) or at downstream steps. We also assess thermodynamic properties of the pathway(s) favored by the intervention strategy. Furthermore, strategies that have a significant overlap with alternative solutions are ranked higher because they provide flexibility in implementation. We also introduce the notion of equivalence classes for grouping intervention strategies with identical solution spaces. Our ranking procedure involves in total ten criteria and we demonstrate its applicability by assessing knockout-based intervention strategies computed in a genome-scale model of E.coli for the growth-coupled synthesis of l-methionine and of the heterologous product 1,4-butanediol. AVAILABILITY AND IMPLEMENTATION: The MATLAB scripts that were used to characterize and rank the example intervention strategies are available at http://www2.mpi-magdeburg.mpg.de/projects/cna/etcdownloads.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

RedCom: A strategy for reduced metabolic modeling of complex microbial communities and its application for analyzing experimental datasets from anaerobic digestion.

Constraint-based modeling (CBM) is increasingly used to analyze the metabolism of complex microbial communities involved in ecology, biomedicine, and various biotechnological processes. While CBM is an established framework for studying the metabolism of single species with linear stoichiometric models, CBM of communities with balanced growth is more complicated, not only due to the larger size of the multi-species metabolic network but also because of the bilinear nature of the resulting community models. Moreover, the solution space of these community models often contains biologically unrealistic solutions, which, even with model linearization and under application of certain objective functions, cannot easily be excluded. Here we present RedCom, a new approach to build reduced community models in which the metabolisms of the participating organisms are represented by net conversions computed from the respective single-species networks. By discarding (single-species) net conversions that violate a minimality criterion in the exchange fluxes, it is ensured that unrealistic solutions in the community model are excluded where a species altruistically synthesizes large amounts of byproducts (instead of biomass) to fulfill the requirements of other species. We employed the RedCom approach for modeling communities of up to nine organisms involved in typical degradation steps of anaerobic digestion in biogas plants. Compared to full (bilinear and linearized) community models, we found that the reduced community models obtained with RedCom are not only much smaller but allow, also in the largest model with nine species, extensive calculations required to fully characterize the solution space and to reveal key properties of communities with maximum methane yield and production rates. Furthermore, the predictive power of the reduced community models is significantly larger because they predict much smaller ranges of feasible community compositions and exchange fluxes still being consistent with measurements obtained from enrichment cultures. For an enrichment culture for growth on ethanol, we also used metaproteomic data to further constrain the solution space of the community models. Both model and proteomic data indicated a dominance of acetoclastic methanogens (Methanosarcinales) and Desulfovibrionales being the least abundant group in this microbial community.

OptMDFpathway: Identification of metabolic pathways with maximal thermodynamic driving force and its application for analyzing the endogenous CO2 fixation potential of Escherichia coli.

Constraint-based modeling techniques have become a standard tool for the in silico analysis of metabolic networks. To further improve their accuracy, recent methodological developments focused on integration of thermodynamic information in metabolic models to assess the feasibility of flux distributions by thermodynamic driving forces. Here we present OptMDFpathway, a method that extends the recently proposed framework of Max-min Driving Force (MDF) for thermodynamic pathway analysis. Given a metabolic network model, OptMDFpathway identifies both the optimal MDF for a desired phenotypic behavior as well as the respective pathway itself that supports the optimal driving force. OptMDFpathway is formulated as a mixed-integer linear program and is applicable to genome-scale metabolic networks. As an important theoretical result, we also show that there exists always at least one elementary mode in the network that reaches the maximal MDF. We employed our new approach to systematically identify all substrate-product combinations in Escherichia coli where product synthesis allows for concomitant net CO2 assimilation via thermodynamically feasible pathways. Although biomass synthesis cannot be coupled to net CO2 fixation in E. coli we found that as many as 145 of the 949 cytosolic carbon metabolites contained in the genome-scale model iJO1366 enable net CO2 incorporation along thermodynamically feasible pathways with glycerol as substrate and 34 with glucose. The most promising products in terms of carbon assimilation yield and thermodynamic driving forces are orotate, aspartate and the C4-metabolites of the tricarboxylic acid cycle. We also identified thermodynamic bottlenecks frequently limiting the maximal driving force of the CO2-fixing pathways. Our results indicate that heterotrophic organisms like E. coli hold a possibly underestimated potential for CO2 assimilation which may complement existing biotechnological approaches for capturing CO2. Furthermore, we envision that the developed OptMDFpathway approach can be used for many other applications within the framework of constrained-based modeling and for rational design of metabolic networks.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering.

BACKGROUND: The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing. RESULTS: We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli. CONCLUSIONS: We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements.

Temperature-dependent dynamic control of the TCA cycle increases volumetric productivity of itaconic acid production by Escherichia coli.

Based on the recently constructed Escherichia coli itaconic acid production strain ita23, we aimed to improve the productivity by applying a two-stage process strategy with decoupled production of biomass and itaconic acid. We constructed a strain ita32 (MG1655 ΔaceA Δpta ΔpykF ΔpykA pCadCs), which, in contrast to ita23, has an active tricarboxylic acid (TCA) cycle and a fast growth rate of 0.52 hr-1 at 37°C, thus representing an ideal phenotype for the first stage, the growth phase. Subsequently we implemented a synthetic genetic control allowing the downregulation of the TCA cycle and thus the switch from growth to itaconic acid production in the second stage. The promoter of the isocitrate dehydrogenase was replaced by the Lambda promoter (pR ) and its expression was controlled by the temperature-sensitive repressor CI857 which is active at lower temperatures (30°C). With glucose as substrate, the respective strain ita36A grew with a fast growth rate at 37°C and switched to production of itaconic acid at 28°C. To study the impact of the process strategy on productivity, we performed one-stage and two-stage bioreactor cultivations. The two-stage process enabled fast formation of biomass resulting in improved peak productivity of 0.86 g/L/hr (+48%) and volumetric productivity of 0.39 g/L/hr (+22%) in comparison to the one-stage process. With our dynamic production strain, we also resolved the glutamate auxotrophy of ita23 and increased the itaconic acid titer to 47 g/L. The temperature-dependent activation of gene expression by the Lambda promoters (pR /pL ) has been frequently used to improve protein or, in a few cases, metabolite production in two-stage processes. Here we demonstrate that the system can be as well used in the opposite direction to selectively knock-down an essential gene (icd) in E. coli to design a two-stage process for improved volumetric productivity. The control by temperature avoids expensive inducers and has the potential to be generally used to improve cell factory performance.