A model-based method for investigating bioenergetic processes in autotrophically growing eukaryotic microalgae: Application to the green algae Chlamydomonas reinhardtii

Chromosome-scale assembly and population diversity analyses provide insights into the evolution of Sapindus mukorossi

Sapindus mukorossi is an environmentally friendly plant and renewable energy source whose fruit has been widely used for biomedicine, biodiesel, and biological chemicals due to its richness in saponin and oil contents. Here, we report the first chromosome-scale genome assembly of S. mukorossi (covering ~391 Mb with a scaffold N50 of 24.66 Mb) and characterize its genetic architecture and evolution by resequencing 104 S. mukorossi accessions. Population genetic analyses showed that genetic diversity in the southwestern distribution area was relatively higher than that in the northeastern distribution area. Gene flow events indicated that southwest species may be the donor population for the distribution areas in China. Genome-wide selective sweep analysis showed that a large number of genes are involved in defense responses, growth and development, including SmRPS2, SmRPS4, SmRPS7, SmNAC2, SmNAC23, SmNAC102, SmWRKY6, SmWRKY26, and SmWRKY33. We also identified several candidate genes controlling six agronomic traits by genome-wide association studies, including SmPCBP2, SmbHLH1, SmCSLD1, SmPP2C, SmLRR-RKs, and SmAHP. Our study not only provides a rich genomic resource for further basic research on Sapindaceae woody trees but also identifies several economically significant genes for genomics-enabled improvements in molecular breeding.

Insights into salvianolic acid B biosynthesis from chromosome-scale assembly of the Salvia bowleyana genome

Salvia bowleyana is a traditional Chinese medicinal plant that is a source of nutritional supplements rich in salvianolic acid B and a potential experimental system for the exploration of salvianolic acid B biosynthesis in the Labiatae. Here, we report a high-quality chromosome-scale genome assembly of S. bowleyana covering 462.44 Mb, with a scaffold N50 value of 57.96 Mb and 44,044 annotated protein-coding genes. Evolutionary analysis revealed an estimated divergence time between S. bowleyana and its close relative S. miltiorrhiza of ~3.94 million years. We also observed evidence of a whole-genome duplication in the S. bowleyana genome. Transcriptome analysis showed that SbPAL1 (PHENYLALANINE AMMONIA-LYASE1) is highly expressed in roots relative to stem and leaves, paralleling the location of salvianolic acid B accumulation. The laccase gene family in S. bowleyana outnumbered their counterparts in both S. miltiorrhiza and Arabidopsis thaliana, suggesting that the gene family has undergone expansion in S. bowleyana. Several laccase genes were also highly expressed in roots, where their encoded proteins may catalyze the oxidative reaction from rosmarinic acid to salvianolic acid B. These findings provide an invaluable genomic resource for understanding salvianolic acid B biosynthesis and its regulation, and will be useful for exploring the evolution of the Labiatae.

A review on photobioreactor design and modelling for microalgae production

From the cell to the photobioreactor and to the industrial exploitation of microalgae, through the controlled experiments and modelling.

Towards model-driven characterization and manipulation of plant lipid metabolism

Plant lipids have versatile applications and provide essential fatty acids in human diet. Therefore, there has been a growing interest to better characterize the genetic basis, regulatory networks, and metabolic pathways that shape lipid quantity and composition. Addressing these issues is challenging due to context-specificity of lipid metabolism integrating environmental, developmental, and tissue-specific cues. Here we systematically review the known metabolic pathways and regulatory interactions that modulate the levels of storage lipids in oilseeds. We argue that the current understanding of lipid metabolism provides the basis for its study in the context of genome-wide plant metabolic networks with the help of approaches from constraint-based modeling and metabolic flux analysis. The focus is on providing a comprehensive summary of the state-of-the-art of modeling plant lipid metabolic pathways, which we then contrast with the existing modeling efforts in yeast and microalgae. We then point out the gaps in knowledge of lipid metabolism, and enumerate the recent advances of using genome-wide association and quantitative trait loci mapping studies to unravel the genetic regulations of lipid metabolism. Finally, we offer a perspective on how advances in the constraint-based modeling framework can propel further characterization of plant lipid metabolism and its rational manipulation.

A high-quality genome provides insights into the new taxonomic status and genomic characteristics of Cladopus chinensis (Podostemaceae)

The Podostemaceae are ecologically and morphologically unusual aquatic angiosperms that survive only in rivers with pristine hydrology and high water quality and are at a relatively high risk of extinction. The taxonomic status of Podostemaceae has always been controversial. Here, we report the first high-quality genome assembly for Cladopus chinensis of Podostemaceae, obtained by incorporating Hi-C, Illumina and PacBio sequencing. We generated an 827.92 Mb genome with a contig N50 of 1.42 Mb and 27,370 annotated protein-coding genes. The assembled genome size was close to the estimated size, and 659.42 Mb of the assembly was assigned to 29 superscaffolds (scaffold N50 21.22 Mb). A total of 59.20% repetitive sequences were identified, among which long terminal repeats (LTRs) were the most abundant class (28.97% of the genome). Genome evolution analysis suggested that the divergence time of Cladopus chinensis (106 Mya) was earlier than that of Malpighiales (82 Mya) and that this taxon diverged into an independent branch of Podestemales. A recent whole-genome duplication (WGD) event occurred 4.43 million years ago. Comparative genomic analysis revealed that the expansion and contraction of oxidative phosphorylation, photosynthesis and isoflavonoid metabolism genes in Cladopus chinensis are probably related to the genomic characteristics of this growing submerged species. Transcriptome analysis revealed that upregulated genes in the shoot group compared to the root group were enriched in the NAC gene family and transcription factors associated with shoot development and defense responses, including WUSCHEL (WUS), ASYMMETRIC LEAVES (ASL), SHOOT MERISTEMLESS (STM), NAC2, NAC8, NAC29, NAC47, NAC73, NAC83 and NAC102. These findings provide new insights into the genomic diversity of unusual aquatic angiosperms and serve as a valuable reference for the taxonomic status and unusual shoot apical meristem of Podostemaceae.

INDISIM-Denitrification, an individual-based model for study the denitrification process

Denitrification is one of the key processes of the global nitrogen (N) cycle driven by bacteria. It has been widely known for more than 100 years as a process by which the biogeochemical N-cycle is balanced. To study this process, we develop an individual-based model called INDISIM-Denitrification. The model embeds a thermodynamic model for bacterial yield prediction inside the individual-based model INDISIM and is designed to simulate in aerobic and anaerobic conditions the cell growth kinetics of denitrifying bacteria. INDISIM-Denitrification simulates a bioreactor that contains a culture medium with succinate as a carbon source, ammonium as nitrogen source and various electron acceptors. To implement INDISIM-Denitrification, the individual-based model INDISIM was used to give sub-models for nutrient uptake, stirring and reproduction cycle. Using a thermodynamic approach, the denitrification pathway, cellular maintenance and individual mass degradation were modeled using microbial metabolic reactions. These equations are the basis of the sub-models for metabolic maintenance, individual mass synthesis and reducing internal cytotoxic products. The model was implemented in the open-access platform NetLogo. INDISIM-Denitrification is validated using a set of experimental data of two denitrifying bacteria in two different experimental conditions. This provides an interactive tool to study the denitrification process carried out by any denitrifying bacterium since INDISIM-Denitrification allows changes in the microbial empirical formula and in the energy-transfer-efficiency used to represent the metabolic pathways involved in the denitrification process. The simulator can be obtained from the authors on request.

Advances in metabolic modeling of oleaginous microalgae

Production of biofuels and bioenergy precursors by phototrophic microorganisms, such as microalgae and cyanobacteria, is a promising alternative to conventional fuels obtained from non-renewable resources. Several species of microalgae have been investigated as potential candidates for the production of biofuels, for the most part due to their exceptional metabolic capability to accumulate large quantities of lipids. Constraint-based modeling, a systems biology approach that accurately predicts the metabolic phenotype of phototrophs, has been deployed to identify suitable culture conditions as well as to explore genetic enhancement strategies for bioproduction. Core metabolic models were employed to gain insight into the central carbon metabolism in photosynthetic microorganisms. More recently, comprehensive genome-scale models, including organelle-specific information at high resolution, have been developed to gain new insight into the metabolism of phototrophic cell factories. Here, we review the current state of the art of constraint-based modeling and computational method development and discuss how advanced models led to increased prediction accuracy and thus improved lipid production in microalgae.

Leveraging algal omics to reveal potential targets for augmenting TAG accumulation

Ongoing global efforts to commercialize microalgal biofuels have expedited the use of multi-omics techniques to gain insights into lipid biosynthetic pathways. Functional genomics analyses have recently been employed to complement existing sequence-level omics studies, shedding light on the dynamics of lipid synthesis and its interplay with other cellular metabolic pathways, thus revealing possible targets for metabolic engineering. Here, we review the current status of algal omics studies to reveal potential targets to augment TAG accumulation in various microalgae. This review specifically aims to examine and catalog systems level data related to stress-induced TAG accumulation in oleaginous microalgae and inform future metabolic engineering strategies to develop strains with enhanced bioproductivity, which could pave a path for sustainable green energy.

A systems-wide understanding of photosynthetic acclimation in algae and higher plants

The ability of phototrophs to colonise different environments relies on robust protection against oxidative stress, a critical requirement for the successful evolutionary transition from water to land. Photosynthetic organisms have developed numerous strategies to adapt their photosynthetic apparatus to changing light conditions in order to optimise their photosynthetic yield, which is crucial for life on Earth to exist. Photosynthetic acclimation is an excellent example of the complexity of biological systems, where highly diverse processes, ranging from electron excitation over protein protonation to enzymatic processes coupling ion gradients with biosynthetic activity, interact on drastically different timescales from picoseconds to hours. Efficient functioning of the photosynthetic apparatus and its protection is paramount for efficient downstream processes, including metabolism and growth. Modern experimental techniques can be successfully integrated with theoretical and mathematical models to promote our understanding of underlying mechanisms and principles. This review aims to provide a retrospective analysis of multidisciplinary photosynthetic acclimation research carried out by members of the Marie Curie Initial Training Project, AccliPhot, placing the results in a wider context. The review also highlights the applicability of photosynthetic organisms for industry, particularly with regards to the cultivation of microalgae. It intends to demonstrate how theoretical concepts can successfully complement experimental studies broadening our knowledge of common principles in acclimation processes in photosynthetic organisms, as well as in the field of applied microalgal biotechnology.

Engineering central metabolism - a grand challenge for plant biologists

The goal of increasing crop productivity and nutrient-use efficiency is being addressed by a number of ambitious research projects seeking to re-engineer photosynthetic biochemistry. Many of these projects will require the engineering of substantial changes in fluxes of central metabolism. However, as has been amply demonstrated in simpler systems such as microbes, central metabolism is extremely difficult to rationally engineer. This is because of multiple layers of regulation that operate to maintain metabolic steady state and because of the highly connected nature of central metabolism. In this review we discuss new approaches for metabolic engineering that have the potential to address these problems and dramatically improve the success with which we can rationally engineer central metabolism in plants. In particular, we advocate the adoption of an iterative 'design-build-test-learn' cycle using fast-to-transform model plants as test beds. This approach can be realised by coupling new molecular tools to incorporate multiple transgenes in nuclear and plastid genomes with computational modelling to design the engineering strategy and to understand the metabolic phenotype of the engineered organism. We also envisage that mutagenesis could be used to fine-tune the balance between the endogenous metabolic network and the introduced enzymes. Finally, we emphasise the importance of considering the plant as a whole system and not isolated organs: the greatest increase in crop productivity will be achieved if both source and sink metabolism are engineered.

Determination of Gibbs energies of formation in aqueous solution using chemical engineering tools

Standard Gibbs energies of formation are of primary importance in the field of biothermodynamics. In the absence of any directly measured values, thermodynamic calculations are required to determine the missing data. For several biochemical species, this study shows that the knowledge of the standard Gibbs energy of formation of the pure compounds (in the gaseous, solid or liquid states) enables to determine the corresponding standard Gibbs energies of formation in aqueous solutions. To do so, using chemical engineering tools (thermodynamic tables and a model enabling to predict activity coefficients, solvation Gibbs energies and pKa data), it becomes possible to determine the partial chemical potential of neutral and charged components in real metabolic conditions, even in concentrated mixtures.

A reductionist approach to model photosynthetic self-regulation in eukaryotes in response to light

Along with the development of several large-scale methods such as mass spectrometry or micro arrays, genome wide models became not only a possibility but an obvious tool for theoretical biologists to integrate and analyse complex biological data. Nevertheless, incorporating the dynamics of photosynthesis remains one of the major challenges while reconstructing metabolic networks of plants and other photosynthetic organisms. In this review, we aim to provide arguments that small-scale models are still a suitable choice when it comes to discovering organisational principles governing the design of biological systems. We give a brief overview of recent modelling efforts in understanding the interplay between rapid, photoprotective mechanisms and the redox balance within the thylakoid membrane, discussing the applicability of a reductionist approach in modelling self-regulation in plants and outline possible directions for further research.

Elucidating temporal resource allocation and diurnal dynamics in phototrophic metabolism using conditional FBA

The computational analysis of phototrophic growth using constraint-based optimization requires to go beyond current time-invariant implementations of flux-balance analysis (FBA). Phototrophic organisms, such as cyanobacteria, rely on harvesting the sun’s energy for the conversion of atmospheric CO2 into organic carbon, hence their metabolism follows a strongly diurnal lifestyle. We describe the growth of cyanobacteria in a periodic environment using a new method called conditional FBA. Our approach enables us to incorporate the temporal organization and conditional dependencies into a constraint-based description of phototrophic metabolism. Specifically, we take into account that cellular processes require resources that are themselves products of metabolism. Phototrophic growth can therefore be formulated as a time-dependent linear optimization problem, such that optimal growth requires a differential allocation of resources during different times of the day. Conditional FBA then allows us to simulate phototrophic growth of an average cell in an environment with varying light intensity, resulting in dynamic time-courses for all involved reaction fluxes, as well as changes in biomass composition over a diurnal cycle. Our results are in good agreement with several known facts about the temporal organization of phototrophic growth and have implications for further analysis of resource allocation problems in phototrophic metabolism.

Obstructions to Sampling Qualitative Properties

Background

Sampling methods have proven to be a very efficient and intuitive method to understand properties of complicated spaces that cannot easily be computed using deterministic methods. Therefore, sampling methods became a popular tool in the applied sciences.

Results

Here, we show that sampling methods are not an appropriate tool to analyze qualitative properties of complicated spaces unless RP = NP. We illustrate these results on the example of the thermodynamically feasible flux space of genome-scale metabolic networks and show that with artificial centering hit and run (ACHR) not all reactions that can have variable flux rates are sampled with variables flux rates. In particular a uniform sample of the flux space would not sample the flux variabilities completely.

Conclusion

We conclude that unless theoretical convergence results exist, qualitative results obtained from sampling methods should be considered with caution and if possible double checked using a deterministic method.

Establishing Chlamydomonas reinhardtii as an industrial biotechnology host

Microalgae constitute a diverse group of eukaryotic unicellular organisms that are of interest for pure and applied research. Owing to their natural synthesis of value-added natural products microalgae are emerging as a source of sustainable chemical compounds, proteins and metabolites, including but not limited to those that could replace compounds currently made from fossil fuels. For the model microalga, Chlamydomonas reinhardtii, this has prompted a period of rapid development so that this organism is poised for exploitation as an industrial biotechnology platform. The question now is how best to achieve this? Highly advanced industrial biotechnology systems using bacteria and yeasts were established in a classical metabolic engineering manner over several decades. However, the advent of advanced molecular tools and the rise of synthetic biology provide an opportunity to expedite the development of C. reinhardtii as an industrial biotechnology platform, avoiding the process of incremental improvement. In this review we describe the current status of genetic manipulation of C. reinhardtii for metabolic engineering. We then introduce several concepts that underpin synthetic biology, and show how generic parts are identified and used in a standard manner to achieve predictable outputs. Based on this we suggest that the development of C. reinhardtii as an industrial biotechnology platform can be achieved more efficiently through adoption of a synthetic biology approach.

A state of the art of metabolic networks of unicellular microalgae and cyanobacteria for biofuel production

The most promising and yet challenging application of microalgae and cyanobacteria is the production of renewable energy: biodiesel from microalgae triacylglycerols and bioethanol from cyanobacteria carbohydrates. A thorough understanding of microalgal and cyanobacterial metabolism is necessary to master and optimize biofuel production yields. To this end, systems biology and metabolic modeling have proven to be very efficient tools if supported by an accurate knowledge of the metabolic network. However, unlike heterotrophic microorganisms that utilize the same substrate for energy and as carbon source, microalgae and cyanobacteria require light for energy and inorganic carbon (CO2 or bicarbonate) as carbon source. This double specificity, together with the complex mechanisms of light capture, makes the representation of metabolic network nonstandard. Here, we review the existing metabolic networks of photoautotrophic microalgae and cyanobacteria. We highlight how these networks have been useful for gaining insight on photoautotrophic metabolism.

Generic flux coupling analysis

Flux coupling analysis (FCA) has become a useful tool for aiding metabolic reconstructions and guiding genetic manipulations. Originally, it was introduced for constraint-based models of metabolic networks that are based on the steady-state assumption. Recently, we have shown that the steady-state assumption can be replaced by a weaker lattice-theoretic property related to the supports of metabolic fluxes. In this paper, we further extend our approach and develop an efficient algorithm for generic flux coupling analysis that works with any kind of qualitative pathway model. We illustrate our method by thermodynamic flux coupling analysis (tFCA), which allows studying steady-state metabolic models with loop-law thermodynamic constraints. These models do not satisfy the lattice-theoretic properties required in our previous work. For a selection of genome-scale metabolic network reconstructions, we discuss both theoretically and practically, how thermodynamic constraints strengthen the coupling results that can be obtained with classical FCA. A prototype implementation of tFCA is available at http://hoverboard.io/L4FC.

Modelling of Microalgae Culture Systems with Applications to Control and Optimization

Mathematical modeling is becoming ever more important to assess the potential, guide the design, and enable the efficient operation and control of industrial-scale microalgae culture systems (MCS). The development of overall, inherently multiphysics, models involves coupling separate submodels of (i) the intrinsic biological properties, including growth, decay, and biosynthesis as well as the effect of light and temperature on these processes, and (ii) the physical properties, such as the hydrodynamics, light attenuation, and temperature in the culture medium. When considering high-density microalgae culture, in particular, the coupling between biology and physics becomes critical. This chapter reviews existing models, with a particular focus on the Droop model, which is a precursor model, and it highlights the structure common to many microalgae growth models. It summarizes the main developments and difficulties towards multiphysics models of MCS as well as applications of these models for monitoring, control, and optimization purposes.

Modelling central metabolic fluxes by constraint-based optimization reveals metabolic reprogramming of developing Solanum lycopersicum (tomato) fruit

Modelling of metabolic networks is a powerful tool to analyse the behaviour of developing plant organs, including fruits. Guided by our current understanding of heterotrophic metabolism of plant cells, a medium-scale stoichiometric model, including the balance of co-factors and energy, was constructed in order to describe metabolic shifts that occur through the nine sequential stages of Solanum lycopersicum (tomato) fruit development. The measured concentrations of the main biomass components and the accumulated metabolites in the pericarp, determined at each stage, were fitted in order to calculate, by derivation, the corresponding external fluxes. They were used as constraints to solve the model by minimizing the internal fluxes. The distribution of the calculated fluxes of central metabolism were then analysed and compared with known metabolic behaviours. For instance, the partition of the main metabolic pathways (glycolysis, pentose phosphate pathway, etc.) was relevant throughout fruit development. We also predicted a valid import of carbon and nitrogen by the fruit, as well as a consistent CO2 release. Interestingly, the energetic balance indicates that excess ATP is dissipated just before the onset of ripening, supporting the concept of the climacteric crisis. Finally, the apparent contradiction between calculated fluxes with low values compared with measured enzyme capacities suggest a complex reprogramming of the metabolic machinery during fruit development. With a powerful set of experimental data and an accurate definition of the metabolic system, this work provides important insight into the metabolic and physiological requirements of the developing tomato fruits.

DRUM: a new framework for metabolic modeling under non-balanced growth. Application to the carbon metabolism of unicellular microalgae

Metabolic modeling is a powerful tool to understand, predict and optimize bioprocesses, particularly when they imply intracellular molecules of interest. Unfortunately, the use of metabolic models for time varying metabolic fluxes is hampered by the lack of experimental data required to define and calibrate the kinetic reaction rates of the metabolic pathways. For this reason, metabolic models are often used under the balanced growth hypothesis. However, for some processes such as the photoautotrophic metabolism of microalgae, the balanced-growth assumption appears to be unreasonable because of the synchronization of their circadian cycle on the daily light. Yet, understanding microalgae metabolism is necessary to optimize the production yield of bioprocesses based on this microorganism, as for example production of third-generation biofuels. In this paper, we propose DRUM, a new dynamic metabolic modeling framework that handles the non-balanced growth condition and hence accumulation of intracellular metabolites. The first stage of the approach consists in splitting the metabolic network into sub-networks describing reactions which are spatially close, and which are assumed to satisfy balanced growth condition. The left metabolites interconnecting the sub-networks behave dynamically. Then, thanks to Elementary Flux Mode analysis, each sub-network is reduced to macroscopic reactions, for which simple kinetics are assumed. Finally, an Ordinary Differential Equation system is obtained to describe substrate consumption, biomass production, products excretion and accumulation of some internal metabolites. DRUM was applied to the accumulation of lipids and carbohydrates of the microalgae Tisochrysis lutea under day/night cycles. The resulting model describes accurately experimental data obtained in day/night conditions. It efficiently predicts the accumulation and consumption of lipids and carbohydrates.

Flux balance analysis as an alternative method to estimate fluxes without labeling

The analysis of plant metabolic networks essentially contributes to the understanding of the efficiency of plant systems in terms of their biotechnological usage. Metabolic fluxes are determined by biochemical parameters such as metabolite concentrations as well as enzyme properties and activities, which in turn are the result of various regulatory events at various levels between control of transcription and posttranslational regulation of enzyme protein activity. Thus, knowledge about metabolic fluxes on a large scale provides an integrated view on the functional state of a metabolically active cell, organ, or system. In this chapter, we introduce flux balance analysis as a constraint-based method for the prediction of optimal metabolic fluxes in a given metabolic network. Furthermore, we provide a step-by-step protocol for metabolic network reconstruction and constraint-based analysis using the COBRA Toolbox.

Model-driven elucidation of the inherent capacity of Geobacter sulfurreducens for electricity generation

Background

G. sulfurreducens is one of the commonest microbes used in microbial fuel cells (MFCs) for organic-to-electricity biotransformation. In MFCs based on this microorganism, electrons can be conveyed to the anode via three ways: 1) direct electron transfer (DET) mode, in which electrons of reduced c-type cytochromes in the microbial outer membrane are directly oxidized by the anode; 2) mediated electron transfer (MET) mode, in which the reducing potential available from cell metabolism in the form of NADH is targeted as an electron source for electricity generation with the aid of exogenous mediators; and 3) a putative mixed operation mode involving both electron transfer mechanisms described above (DET and MET). However, the potential of G. sulfurreducens for current output in these three operation modes and the metabolic mechanisms underlying the extraction of the reducing equivalents are still unknown.

Results

In this study, we performed flux balance analysis (FBA) of the genome-scale metabolic network to compute the fundamental metabolic potential of G. sulfurreducens for current output that is compatible with reaction stoichiometry, given a realistic nutrient uptake rate. We also developed a method, flux variability analysis with target flux minimization (FATMIN) to eliminate futile NADH cycles. Our study elucidates the possible metabolic strategies to sustain the NADH for current production under the MET and Mixed modes. The results showed that G. sulfurreducens had a potential to output current at up to 3.710 A/gDW for DET mode, 2.711 A/gDW for MET mode and 3.272 A/gDW for a putative mixed MET and DET mode. Compared with DET, which relies on only one contributing reaction, MET and Mixed mode were more resilient with ten and four reactions respectively for high current production.

Conclusions

The DET mode can achieve a higher maximum limit of the current output than the MET mode, but the MET has an advantage of higher power output and more flexible metabolic choices to sustain the electric current. The MET and DET modes compete with each other for the metabolic resource for the electricity generation.

Fast thermodynamically constrained flux variability analysis

MOTIVATION

Flux variability analysis (FVA) is an important tool to further analyse the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. For many constraint-based models, FVA identifies unboundedness of the optimal flux space. This reveals that optimal flux solutions with net flux through internal biochemical loops are feasible, which violates the second law of thermodynamics. Such unbounded fluxes may be eliminated by extending FVA with thermodynamic constraints.

RESULTS

We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analysing genome-scale metabolic networks. We first show that FBA with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast FVA with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30-300 is achieved. In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 of 716 networks, additional irreversible or fixed reactions could be detected.

AVAILABILITY AND IMPLEMENTATION

Fast-tFVA is written in C++ and published under GPL. It uses the open source software SCIP and libSBML. There also exists a Matlab interface for easy integration into Matlab. Fast-tFVA is available from page.mi.fu-berlin.de/arnem/fast-tfva.html.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A proof for loop-law constraints in stoichiometric metabolic networks

Background

Constraint-based modeling is increasingly employed for metabolic network analysis. Its underlying assumption is that natural metabolic phenotypes can be predicted by adding physicochemical constraints to remove unrealistic metabolic flux solutions. The loopless-COBRA approach provides an additional constraint that eliminates thermodynamically infeasible internal cycles (or loops) from the space of solutions. This allows the prediction of flux solutions that are more consistent with experimental data. However, it is not clear if this approach over-constrains the models by removing non-loop solutions as well.

Results

Here we apply Gordan’s theorem from linear algebra to prove for the first time that the constraints added in loopless-COBRA do not over-constrain the problem beyond the elimination of the loops themselves.

Conclusions

The loopless-COBRA constraints can be reliably applied. Furthermore, this proof may be adapted to evaluate the theoretical soundness for other methods in constraint-based modeling.

Network reduction in metabolic pathway analysis: elucidation of the key pathways involved in the photoautotrophic growth of the green alga Chlamydomonas reinhardtii

Metabolic pathway analysis aims at discovering and analyzing meaningful routes and their interactions in metabolic networks. A major difficulty in applying this technique lies in the decomposition of metabolic flux distributions into elementary mode or extreme pathway activity patterns, which in general is not unique. We propose a network reduction approach based on the decomposition of a set of flux vectors representing adaptive microbial metabolic behavior in bioreactors into a minimal set of shared pathways. Several optimality criteria from the literature were compared in order to select the most appropriate objective function. We further analyze photoautotrophic metabolism of the green alga Chlamydomonas reinhardtii growing in a photobioreactor under maximal growth rate conditions. Key pathways involved in its adaptive metabolic response to changes in light influx are identified and discussed using an energetic approach.

Flux-balance modeling of plant metabolism

Flux-balance modeling of plant metabolic networks provides an important complement to (13)C-based metabolic flux analysis. Flux-balance modeling is a constraints-based approach in which steady-state fluxes in a metabolic network are predicted by using optimization algorithms within an experimentally bounded solution space. In the last 2 years several flux-balance models of plant metabolism have been published including genome-scale models of Arabidopsis metabolism. In this review we consider what has been learnt from these models. In addition, we consider the limitations of flux-balance modeling and identify the main challenges to generating improved and more detailed models of plant metabolism at tissue- and cell-specific scales. Finally we discuss the types of question that flux-balance modeling is well suited to address and its potential role in metabolic engineering and crop improvement.