Thermodynamic efficiency of microbial growth is low but optimal for maximal growth rate

Arsenic Contamination of Groundwater Is Determined by Complex Interactions between Various Chemical and Biological Processes

At a great many locations worldwide, the safety of drinking water is not assured due to pollution with arsenic. Arsenic toxicity is a matter of both systems chemistry and systems biology: it is determined by complex and intertwined networks of chemical reactions in the inanimate environment, in microbes in that environment, and in the human body. We here review what is known about these networks and their interconnections. We then discuss how consideration of the systems aspects of arsenic levels in groundwater may open up new avenues towards the realization of safer drinking water. Along such avenues, both geochemical and microbiological conditions can optimize groundwater microbial ecology vis-à-vis reduced arsenic toxicity.

On paradoxes between optimal growth, metabolic control analysis, and flux balance analysis

In Microbiology it is often assumed that growth rate is maximal. This may be taken to suggest that the dependence of the growth rate on every enzyme activity is at the top of an inverse-parabolic function, i.e. that all flux control coefficients should equal zero. This might seem to imply that the sum of these flux control coefficients equals zero. According to the summation law of Metabolic Control Analysis (MCA) the sum of flux control coefficients should equal 1 however. And in Flux Balance Analysis (FBA) catabolism is often limited by a hard bound, causing catabolism to fully control the fluxes, again in apparent contrast with a flux control coefficient of zero. Here we resolve these paradoxes (apparent contradictions) in an analysis that uses the 'Edinburgh pathway', the 'Amsterdam pathway', as well as a generic metabolic network providing the building blocks or Gibbs energy for microbial growth. We review and show that (i) optimization depends on so-called enzyme control coefficients rather than the 'catalytic control coefficients' of MCA's summation law, (ii) when optimization occurs at fixed total protein, the former differ from the latter to the extent that they may all become equal to zero in the optimum state, (iii) in more realistic scenarios of optimization where catalytically inert biomass is compensating or maintenance metabolism is taken into consideration, the optimum enzyme concentrations should not be expected to equal those that maximize the specific growth rate, (iv) optimization may be in terms of yield rather than specific growth rate, which resolves the paradox because the sum of catalytic control coefficients on yield equals 0, (v) FBA effectively maximizes growth yield, and for yield the summation law states 0 rather than 1, thereby removing the paradox, (vi) furthermore, FBA then comes more often to a 'hard optimum' defined by a maximum catabolic flux and a catabolic-enzyme control coefficient of 1. The trade-off between maintenance metabolism and growth is highlighted as worthy of further analysis.

Gear Shifting in Biological Energy Transduction

Confronted with thermodynamically adverse output processes, free-energy transducers may shift to lower gears, thereby reducing output per unit input. This option is well known for inanimate machines such as automobiles, but unappreciated in biology. The present study extends existing non-equilibrium thermodynamic principles to underpin biological gear shifting and identify possible mechanisms. It shows that gear shifting differs from altering the degree of coupling and that living systems may use it to optimize their performance: microbial growth is ultimately powered by the Gibbs energy of catabolism, which is partially transformed into Gibbs energy ('output force') in the ATP that is produced. If this output force is high, the cell may turn to a catabolic pathway with a lower ATP stoichiometry. Notwithstanding the reduced stoichiometry, the ATP synthesis flux may then actually increase as compared to that in a system without gear shift, in which growth might come to a halt. A 'variomatic' gear switching strategy should be optimal, explaining why organisms avail themselves of multiple catabolic pathways, as these enable them to shift gears when the growing gets tough.

Bacterial functional redundancy and carbon metabolism potentials in soil, sediment, and water of thermokarst landscapes across the Qinghai-Tibet Plateau: Implications for the fate of permafrost carbon

Permafrost thaw create widespread thermokarst landscapes. As a result, distinct habitats are provided to harbor different bacterial communities in degraded permafrost soil (PBCs), thermokarst lake sediment (SBCs), and lake water (WBCs), driving carbon metabolism differentially. In this study, we investigated functional diversity and redundancy, and carbon metabolism potentials of PBCs, SBCs, and WBCs in thermokarst landscapes across the Qinghai-Tibet Plateau. The results showed that PBCs and SBCs had higher taxonomic and functional alpha diversity than WBCs, while WBCs had lower functional redundancy. WBCs had the highest beta diversity followed by SBCs and PBCs, suggesting strong determination of taxonomic variations on functional differences. Community assembly processes also had significant influences on beta diversity, especially for SBCs. Metabolism pathways of carbohydrate metabolism, methane metabolism, and carbon fixation were enriched differentially in PBCs, SBCs, and WBCs, suggesting different C fate in distinct habitats. Carbohydrate metabolism data suggested that PBCs might have stronger potentials to mineralize a greater diversity of organic carbon substrate than SBCs and WBCs, promoting degradation of organic carbon stocks in degraded permafrost soils. Methane metabolism data showed that SBCs had a stronger methanogenesis potential followed by PBCs and WBCs, while PBCs had a stronger methane oxidation potential. High abundance of genes involving in formaldehyde assimilation might suggested that a large proportion of produced methane might be assimilated by methanotrophs in the thermokarst landscapes. Both aerobic and anaerobic carbon fixation pathways were enriched in PBCs. The results added our understanding of functional properties and biogeochemical carbon cycles in thermokarst landscapes, improving our abilities in accurate modeling of carbon dynamics and the ultimate fate of permafrost carbon in a warming world.

Applying the Nernst Equation to Control ORP in Denitrification Process for Uranium-Containing Nuclear Effluent with High Loads of Nitrogen and COD

Several reviews of denitrification have shown it to be an efficient process for treating high nitrate-loaded effluents from nuclear industries. However, stressful conditions adversely affect biological kinetic parameters and performance. Additionally, actual nuclear effluents contain multiple pollutants and radioactive emissions that could render implementation difficult. The objective of this study was to treat and recycle water from nuclear industries by using a mixture of blended real nuclear wastewater (BRNW). The process was carried out under physicochemical parameters control in a biological model to established a technical setup and to model the denitrification process in a real nuclear wastewater effluent. Denitrification processes were carried out in the wastewater sample under controlled ORP conditions by the Hill model to establish the kinetic model. The results show a complete elimination of nitrate by the bacteria. Indicators of biochemical reactions were used to obtain a model based on Monod and controlled ORP. The good fit of the proposed model was verified under empirical and simulated conditions. To establish optimal performance, it was necessary to add 3% v/v of methanol, as a carbon source, to remove the nitrate in BRNW. Isolation techniques confirmed that Pseudomonas spp. was the dominant bacteria. Gene expression demonstrated the lack of inhibition of the NosZ gene responsible for the reduction in nitric oxide, a “greenhouse gas”. Finally, COD and uranium were removed from the liquid by precipitation. At the end of the process, the treated effluent could potentially be reused in industrial processes, recycling most of the wastewater effluents.

Thermodynamic selection: mechanisms and scenarios

Thermodynamic selection is an indirect competition between agents feeding on the same energy resource and obeying the laws of thermodynamics. We examine scenarios of this selection, where the agent is modeled as a heat-engine coupled to two thermal baths and extracting work from the high-temperature bath. The agents can apply different work-extracting, game-theoretical strategies, e.g. the maximum power or the maximum efficiency. They can also have a fixed structure or be adaptive. Depending on whether the resource (i.e. the high-temperature bath) is infinite or finite, the fitness of the agent relates to the work-power or the total extracted work. These two selection scenarios lead to increasing or decreasing efficiencies of the work-extraction, respectively. The scenarios are illustrated via plant competition for sunlight, and the competition between different ATP production pathways. We also show that certain general concepts of game-theory and ecology-the prisoner's dilemma and the maximal power principle-emerge from the thermodynamics of competing agents. We emphasize the role of adaptation in developing efficient work-extraction mechanisms.

A Game Theoretic Analysis of the Dual Function of Antibiotics

There are two major views toward the role of antibiotics in microbial social interactions. The classical view is that antibiotics serve as weapons, produced by a bacterial species, at a significant cost, to inhibit the growth of its competitors. This view is supported by observations that antibiotics are usually upregulated by stress responses that infer the intensity of ecological competition, such as nutrient limitation and cellular damage, which point out to a competitive role for antibiotics. The other ecological function frequently assigned to antibiotics is that they serve as signaling molecules which regulate the collective behavior of a microbial community. Here, we investigate the conditions at which a weapon can serve as a signal in the context of microbial competition. We propose that an antibiotic will serve as a signal whenever a potential alteration of the growth behavior of the signal receiver, in response to a subinhibitory concentration (SIC) of the antibiotic, reduces the competitive pressure on the signal producer. This in turn would lead to avoiding triggering the stress mechanisms of the signal producer responsible for further antibiotics production. We show using individual-based modeling that this reduction of competitive pressure on the signal producer can happen through two main classes of responses by the signal recipient: competition tolerance, where the recipient reduces its competitive impact on the signal producer by switching to a low growth rate/ high yield strategy, and niche segregation, where the recipient reduces the competitive pressure on the signal producer by reducing their niche overlap. Our hypothesis proposes that antibiotics serve as signals out of their original function as weapons in order to reduce the chances of engaging in fights that would be costly to both the antibiotic producer as well as to its competitors.

Energetic scaling in microbial growth

Microbial growth is a clear example of organization and structure arising in nonequilibrium conditions. Due to the complexity of the microbial metabolic network, elucidating the fundamental principles governing microbial growth remains a challenge. Here, we present a systematic analysis of microbial growth thermodynamics, leveraging an extensive dataset on energy-limited monoculture growth. A consistent thermodynamic framework based on reaction stoichiometry allows us to quantify how much of the available energy microbes can efficiently convert into new biomass while dissipating the remaining energy into the environment and producing entropy. We show that dissipation mechanisms can be linked to the electron donor uptake rate, a fact leading to the central result that the thermodynamic efficiency is related to the electron donor uptake rate by the scaling law [Formula: see text] and to the growth yield by [Formula: see text] These findings allow us to rederive the Pirt equation from a thermodynamic perspective, providing a means to compute its coefficients, as well as a deeper understanding of the relationship between growth rate and yield. Our results provide rather general insights into the relation between mass and energy conversion in microbial growth with potentially wide application, especially in ecology and biotechnology.

Intelligent host engineering for metabolic flux optimisation in biotechnology

Optimising the function of a protein of length N amino acids by directed evolution involves navigating a 'search space' of possible sequences of some 20N. Optimising the expression levels of P proteins that materially affect host performance, each of which might also take 20 (logarithmically spaced) values, implies a similar search space of 20P. In this combinatorial sense, then, the problems of directed protein evolution and of host engineering are broadly equivalent. In practice, however, they have different means for avoiding the inevitable difficulties of implementation. The spare capacity exhibited in metabolic networks implies that host engineering may admit substantial increases in flux to targets of interest. Thus, we rehearse the relevant issues for those wishing to understand and exploit those modern genome-wide host engineering tools and thinking that have been designed and developed to optimise fluxes towards desirable products in biotechnological processes, with a focus on microbial systems. The aim throughput is 'making such biology predictable'. Strategies have been aimed at both transcription and translation, especially for regulatory processes that can affect multiple targets. However, because there is a limit on how much protein a cell can produce, increasing kcat in selected targets may be a better strategy than increasing protein expression levels for optimal host engineering.

The view of microbes as energy converters illustrates the trade-off between growth rate and yield

The application of thermodynamics to microbial growth has a long tradition that originated in the middle of the 20th century. This approach reflects the view that self-replication is a thermodynamic process that is not fundamentally different from mechanical thermodynamics. The key distinction is that a free energy gradient is not converted into mechanical (or any other form of) energy but rather into new biomass. As such, microbes can be viewed as energy converters that convert a part of the energy contained in environmental nutrients into chemical energy that drives self-replication. Before the advent of high-throughput sequencing technologies, only the most central metabolic pathways were known. However, precise measurement techniques allowed for the quantification of exchanged extracellular nutrients and heat of growing microbes with their environment. These data, together with the absence of knowledge of metabolic details, drove the development of so-called black-box models, which only consider the observable interactions of a cell with its environment and neglect all details of how exactly inputs are converted into outputs. Now, genome sequencing and genome-scale metabolic models (GEMs) provide us with unprecedented detail about metabolic processes inside the cell. However, mostly due to computational complexity issues, the derived modelling approaches make surprisingly little use of thermodynamic concepts. Here, we review classical black-box models and modern approaches that integrate thermodynamics into GEMs. We also illustrate how the description of microbial growth as an energy converter can help to understand and quantify the trade-off between microbial growth rate and yield.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells

Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.

Architecture of bacterial respiratory chains

Bacteria power their energy metabolism using membrane-bound respiratory enzymes that capture chemical energy and transduce it by pumping protons or Na⁺ ions across their cell membranes. Recent breakthroughs in molecular bioenergetics have elucidated the architecture and function of many bacterial respiratory enzymes, although key mechanistic principles remain debated. In this Review, we present an overview of the structure, function and bioenergetic principles of modular bacterial respiratory chains and discuss their differences from the eukaryotic counterparts. We also discuss bacterial supercomplexes, which provide central energy transduction systems in several bacteria, including important pathogens, and which could open up possible avenues for treatment of disease.

Metabolic Engineering of Bacterial Respiration: High vs. Low P/O and the Case of Zymomonas mobilis

Respiratory chain plays a pivotal role in the energy and redox balance of aerobic bacteria. By engineering respiration, it is possible to alter the efficiency of energy generation and intracellular redox state, and thus affect the key bioprocess parameters: cell yield, productivity and stress resistance. Here we summarize the current metabolic engineering and synthetic biology approaches to bacterial respiratory metabolism, with a special focus on the respiratory chain of the ethanologenic bacterium Zymomonas mobilis. Electron transport in Z. mobilis can serve as a model system of bacterial respiration with low oxidative phosphorylation efficiency. Its application for redox balancing and relevance for improvement of stress tolerance are analyzed.

Metabolism, bioenergetics and thermal physiology: influences of the human intestinal microbiota

The micro-organisms which inhabit the human gut (i.e. the intestinal microbiota) influence numerous human biochemical pathways and physiological functions. The present review focuses on two questions, 'Are intestinal microbiota effects measurable and meaningful?' and 'What research methods and variables are influenced by intestinal microbiota effects?'. These questions are considered with respect to doubly labelled water measurements of energy expenditure, heat balance calculations and models, measurements of RMR via indirect calorimetry, and diet-induced energy expenditure. Several lines of evidence suggest that the intestinal microbiota introduces measurement variability and measurement errors which have been overlooked in research studies involving nutrition, bioenergetics, physiology and temperature regulation. Therefore, we recommend that present conceptual models and research techniques be updated via future experiments, to account for the metabolic processes and regulatory influences of the intestinal microbiota.

Consistent microbial dynamics and functional community patterns derived from first principles

Microbial communities are key engines that drive earth's biogeochemical cycles. However, existing ecosystem models have only limited ability to predict microbial dynamics and require the calibration of multiple population-specific empirical equations. In contrast, we build on a new kinetic "Microbial Transition State" (MTS) theory of growth derived from first principles. We show how the theory coupled to simple mass and energy balance calculations provides a framework with intrinsically important qualitative properties to model microbial community dynamics. We first show how the theory can simultaneously account for the influence of all the resources needed for growth (electron donor, acceptor, and nutrients) while still producing consistent dynamics that fulfill the Liebig rule of a single limiting substrate. We also show consistent patterns of energy-dependent microbial successions in mixed culture without the need for calibration of population-specific parameters. We then show how this approach can be used to model a simplified activated sludge community. To this end, we compare MTS-derived dynamics with those of a widely used activated sludge model and show that similar growth yields and overall dynamics can be obtained using two parameters instead of twelve. This new kinetic theory of growth grounded by a set of generic physical principles parsimoniously gives rise to consistent microbial population and community dynamics, thereby paving the way for the development of a new class of more predictive microbial ecosystem models.

Energetic evolution of cellular Transportomes

BACKGROUND

Transporter proteins mediate the translocation of substances across the membranes of living cells. Many transport processes are energetically expensive and the cells use 20 to 60% of their energy to power the transportomes. We hypothesized that there may be an evolutionary selection pressure for lower energy transporters.

RESULTS

We performed a genome-wide analysis of the compositional reshaping of the transportomes across the kingdoms of bacteria, archaea, and eukarya. We found that the share of ABC transporters is much higher in bacteria and archaea (ca. 27% of the transportome) than in primitive eukaryotes (13%), algae and plants (10%) and in fungi and animals (5-6%). This decrease is compensated by an increased occurrence of secondary transporters and ion channels. The share of ion channels is particularly high in animals (ca. 30% of the transportome) and algae and plants with (ca. 13%), when compared to bacteria and archaea with only 6-7%. Therefore, our results show a move to a preference for the low-energy-demanding transporters (ion channels and carriers) over the more energy-costly transporter classes (ATP-dependent families, and ABCs in particular) as part of the transition from prokaryotes to eukaryotes. The transportome analysis also indicated seven bacterial species, including Neorickettsia risticii and Neorickettsia sennetsu, as likely origins of the mitochondrion in eukaryotes, based on the phylogenetically restricted presence therein of clear homologues of modern mitochondrial solute carriers.

CONCLUSIONS

The results indicate that the transportomes of eukaryotes evolved strongly towards a higher energetic efficiency, as ATP-dependent transporters diminished and secondary transporters and ion channels proliferated. These changes have likely been important in the development of tissues performing energetically costly cellular functions.

Bioenergetic Controls on Microbial Ecophysiology in Marine Sediments

Marine sediments constitute one of the most energy-limited habitats on Earth, in which microorganisms persist over extraordinarily long timescales with very slow metabolisms. This habitat provides an ideal environment in which to study the energetic limits of life. However, the bioenergetic factors that can determine whether microorganisms will grow, lie dormant, or die, as well as the selective environmental pressures that determine energetic trade-offs between growth and maintenance activities, are not well understood. Numerical models will be pivotal in addressing these knowledge gaps. However, models rarely account for the variable physiological states of microorganisms and their demand for energy. Here, we review established modeling constructs for microbial growth rate, yield, maintenance, and physiological state, and then provide a new model that incorporates all of these factors. We discuss this new model in context with its future application to the marine subsurface. Understanding the factors that regulate cell death, physiological state changes, and the provenance of maintenance energy (i.e., endogenous versus exogenous metabolism), is crucial to the design of this model. Further, measurements of growth rate, growth yield, and basal metabolic activity will enable bioenergetic parameters to be better constrained. Last, biomass and biogeochemical rate measurements will enable model simulations to be validated. The insight provided from the development and application of new microbial modeling tools for marine sediments will undoubtedly advance the understanding of the minimum power required to support life, and the ecophysiological strategies that organisms utilize to cope under extreme energy limitation for extended periods of time.

Metabolic enzyme cost explains variable trade-offs between microbial growth rate and yield

Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off between growth rate and biomass yield has been proposed to explain this. We studied growth rate/yield trade-offs by using a novel modeling framework, Enzyme-Flux Cost Minimization (EFCM) and by assuming that the growth rate depends directly on the enzyme investment per rate of biomass production. In a comprehensive mathematical model of core metabolism in E. coli, we screened all elementary flux modes leading to cell synthesis, characterized them by the growth rates and yields they provide, and studied the shape of the resulting rate/yield Pareto front. By varying the model parameters, we found that the rate/yield trade-off is not universal, but depends on metabolic kinetics and environmental conditions. A prominent trade-off emerges under oxygen-limited growth, where yield-inefficient pathways support a 2-to-3 times higher growth rate than yield-efficient pathways. EFCM can be widely used to predict optimal metabolic states and growth rates under varying nutrient levels, perturbations of enzyme parameters, and single or multiple gene knockouts.

Light-Enhanced Microbial Organic Carbon Yield

Molecular evidence for proteorhodopsin- and bacteriochlorophyll-based photoheterotrophy is widespread in oligotrophic marine microbial community metagenomes, and has been implicated in light-enhanced growth rates, substrate uptake rates, and anapleurotic carbon fixation, thus complicating the web of interactions within the ‘microbial loop.’ We quantified photoheterotrophic metabolism of the oxidized organic acid glycolate, a fast-turnover and exclusively phytoplankton-derived substrate at an oligotrophic site in the subtropical North Pacific Ocean. As expected, concentration-dependent changes in uptake rates were observed over the diel cycle, with maxima occurring at midday. Although no light-enhanced substrate uptake rates were observed, samples exposed to light altered the balance between assimilation and respiration, resulting in an approximately four-fold increase in glycolate-specific assimilation efficiency. Energy demand for such a metabolic adjustment was linearly related to light, consistent with photoheterotrophy.

The metabolome 18 years on: a concept comes of age

BACKGROUND

The term 'metabolome' was introduced to the scientific literature in September 1998.

AIM AND KEY SCIENTIFIC CONCEPTS OF THE REVIEW

To mark its 18-year-old 'coming of age', two of the co-authors of that paper review the genesis of metabolomics, whence it has come and where it may be going.

Global microbialization of coral reefs

Microbialization refers to the observed shift in ecosystem trophic structure towards higher microbial biomass and energy use. On coral reefs, the proximal causes of microbialization are overfishing and eutrophication, both of which facilitate enhanced growth of fleshy algae, conferring a competitive advantage over calcifying corals and coralline algae. The proposed mechanism for this competitive advantage is the DDAM positive feedback loop (dissolved organic carbon (DOC), disease, algae, microorganism), where DOC released by ungrazed fleshy algae supports copiotrophic, potentially pathogenic bacterial communities, ultimately harming corals and maintaining algal competitive dominance. Using an unprecedented data set of >400 samples from 60 coral reef sites, we show that the central DDAM predictions are consistent across three ocean basins. Reef algal cover is positively correlated with lower concentrations of DOC and higher microbial abundances. On turf and fleshy macroalgal-rich reefs, higher relative abundances of copiotrophic microbial taxa were identified. These microbial communities shift their metabolic potential for carbohydrate degradation from the more energy efficient Embden-Meyerhof-Parnas pathway on coral-dominated reefs to the less efficient Entner-Doudoroff and pentose phosphate pathways on algal-dominated reefs. This 'yield-to-power' switch by microorganism directly threatens reefs via increased hypoxia and greater CO2 release from the microbial respiration of DOC.

Enzyme oscillation can enhance the thermodynamic efficiency of cellular metabolism: consequence of anti-phase coupling between reaction flux and affinity

Cells generally convert nutrient resources to products via energy transduction. Accordingly, the thermodynamic efficiency of this conversion process is one of the most essential characteristics of living organisms. However, although these processes occur under conditions of dynamic metabolism, most studies of cellular thermodynamic efficiency have been restricted to examining steady states; thus, the relevance of dynamics to this efficiency has not yet been elucidated. Here, we develop a simple model of metabolic reactions with anabolism-catabolism coupling catalyzed by enzymes. Through application of external oscillation in the enzyme abundances, the thermodynamic efficiency of metabolism was found to be improved. This result is in strong contrast with that observed in the oscillatory input, in which the efficiency always decreased with oscillation. This improvement was effectively achieved by separating the anabolic and catabolic reactions, which tend to disequilibrate each other, and taking advantage of the temporal oscillations so that each of the antagonistic reactions could progress near equilibrium. In this case, anti-phase oscillation between the reaction flux and chemical affinity through oscillation of enzyme abundances is essential. This improvement was also confirmed in a model capable of generating autonomous oscillations in enzyme abundances. Finally, the possible relevance of the improvement in thermodynamic efficiency is discussed with respect to the potential for manipulation of metabolic oscillations in microorganisms.

Proton pumping complex I increases growth yield in Candida utilis

In living cells, growth is the result of coupling between substrate catabolism and multiple metabolic processes that take place during net biomass formation and cellular maintenance processes. A crucial parameter for growth evaluation is its yield, i.e. the efficiency of the transformation processes. The yeast Candida utilis is of peculiar interest since its mitochondria exhibit a complex I that is proposed to pump protons but also an external NADH dehydrogenase that do not pump protons. Here, we show that in C. utilis cells grown on non-fermentable media, growth yield is 30% higher as compared to that of Saccharomyces cerevisiae that do not exhibit a complex I. Moreover, ADP/O determination in C. utilis shows that electrons coming from internal NADH dehydrogenase go through proton pumping complex I, whereas electrons coming from external NADH dehydrogenases do not go through proton pumping complex I. Furthermore, we show that electron competition strictly depends on extra-mitochondrial NADH concentration, i.e. the higher the extra-mitochondrial NADH concentration, the higher the competition process with a right way for electrons coming from external NADH dehydrogenases. Such a complex regulation in C. utilis allows an increase in growth yield when cytosolic NADH is not plentiful but still favors the cytosolic NADH re-oxidation at high NADH, favoring biomass generation metabolic pathways.

Bacterial growth laws reflect the evolutionary importance of energy efficiency

We are interested in the balance of energy and protein synthesis in bacterial growth. How has evolution optimized this balance? We describe an analytical model that leverages extensive literature data on growth laws to infer the underlying fitness landscape and to draw inferences about what evolution has optimized in Escherichia coli. Is E. coli optimized for growth speed, energy efficiency, or some other property? Experimental data show that at its replication speed limit, E. coli produces about four mass equivalents of nonribosomal proteins for every mass equivalent of ribosomes. This ratio can be explained if the cell's fitness function is the the energy efficiency of cells under fast growth conditions, indicating a tradeoff between the high energy costs of ribosomes under fast growth and the high energy costs of turning over nonribosomal proteins under slow growth. This model gives insight into some of the complex nonlinear relationships between energy utilization and ribosomal and nonribosomal production as a function of cell growth conditions.

Concerted evolution of life stage performances signals recent selection on yeast nitrogen use

Exposing natural selection driving phenotypic and genotypic adaptive differentiation is an extraordinary challenge. Given that an organism's life stages are exposed to the same environmental variations, we reasoned that fitness components, such as the lag, rate, and efficiency of growth, directly reflecting performance in these life stages, should often be selected in concert. We therefore conjectured that correlations between fitness components over natural isolates, in a particular environmental context, would constitute a robust signal of recent selection. Critically, this test for selection requires fitness components to be determined by different genetic loci. To explore our conjecture, we exhaustively evaluated the lag, rate, and efficiency of asexual population growth of natural isolates of the model yeast Saccharomyces cerevisiae in a large variety of nitrogen-limited environments. Overall, fitness components were well correlated under nitrogen restriction. Yeast isolates were further crossed in all pairwise combinations and coinheritance of each fitness component and genetic markers were traced. Trait variations tended to map to quantitative trait loci (QTL) that were private to a single fitness component. We further traced QTLs down to single-nucleotide resolution and uncovered loss-of-function mutations in RIM15, PUT4, DAL1, and DAL4 as the genetic basis for nitrogen source use variations. Effects of SNPs were unique for a single fitness component, strongly arguing against pleiotropy between lag, rate, and efficiency of reproduction under nitrogen restriction. The strong correlations between life stage performances that cannot be explained by pleiotropy compellingly support adaptive differentiation of yeast nitrogen source use and suggest a generic approach for detecting selection.

Entropy production of a steady-growth cell with catalytic reactions

Cells generally convert external nutrient resources to support metabolism and growth. Understanding the thermodynamic efficiency of this conversion is essential to determine the general characteristics of cellular growth. Using a simple protocell model with catalytic reaction dynamics to synthesize the necessary enzyme and membrane components from nutrients, the entropy production per unit-cell-volume growth is calculated analytically and numerically based on the rate equation for chemical kinetics and linear nonequilibrium thermodynamics. The minimal entropy production per unit-cell growth is found to be achieved at a nonzero nutrient uptake rate rather than at a quasistatic limit as in the standard Carnot engine. This difference appears because the equilibration mediated by the enzyme exists only within cells that grow through enzyme and membrane synthesis. Optimal nutrient uptake is also confirmed by protocell models with many chemical components synthesized through a catalytic reaction network. The possible relevance of the identified optimal uptake to optimal yield for cellular growth is also discussed.

Methods for integration of transcriptomic data in genome-scale metabolic models

Several computational methods have been developed that integrate transcriptomic data with genome-scale metabolic reconstructions to infer condition-specific system-wide intracellular metabolic flux distributions. In this mini-review, we describe each of these methods published to date with categorizing them based on four different grouping criteria (requirement for multiple gene expression datasets as input, requirement for a threshold to define a gene's high and low expression, requirement for a priori assumption of an appropriate objective function, and validation of predicted fluxes directly against measured intracellular fluxes). Then, we recommend which group of methods would be more suitable from a practical perspective.

A thermodynamic theory of microbial growth

Our ability to model the growth of microbes only relies on empirical laws, fundamentally restricting our understanding and predictive capacity in many environmental systems. In particular, the link between energy balances and growth dynamics is still not understood. Here we demonstrate a microbial growth equation relying on an explicit theoretical ground sustained by Boltzmann statistics, thus establishing a relationship between microbial growth rate and available energy. The validity of our equation was then questioned by analyzing the microbial isotopic fractionation phenomenon, which can be viewed as a kinetic consequence of the differences in energy contents of isotopic isomers used for growth. We illustrate how the associated theoretical predictions are actually consistent with recent experimental evidences. Our work links microbial population dynamics to the thermodynamic driving forces of the ecosystem, which opens the door to many biotechnological and ecological developments.

Toward quantitative understanding on microbial community structure and functioning: a modeling-centered approach using degradation of marine oil spills as example

Molecular ecology approaches are rapidly advancing our insights into the microorganisms involved in the degradation of marine oil spills and their metabolic potentials. Yet, many questions remain open: how do oil-degrading microbial communities assemble in terms of functional diversity, species abundances and organization and what are the drivers? How do the functional properties of microorganisms scale to processes at the ecosystem level? How does mass flow among species, and which factors and species control and regulate fluxes, stability and other ecosystem functions? Can generic rules on oil-degradation be derived, and what drivers underlie these rules? How can we engineer oil-degrading microbial communities such that toxic polycyclic aromatic hydrocarbons are degraded faster? These types of questions apply to the field of microbial ecology in general. We outline how recent advances in single-species systems biology might be extended to help answer these questions. We argue that bottom-up mechanistic modeling allows deciphering the respective roles and interactions among microorganisms. In particular constraint-based, metagenome-derived community-scale flux balance analysis appears suited for this goal as it allows calculating degradation-related fluxes based on physiological constraints and growth strategies, without needing detailed kinetic information. We subsequently discuss what is required to make these approaches successful, and identify a need to better understand microbial physiology in order to advance microbial ecology. We advocate the development of databases containing microbial physiological data. Answering the posed questions is far from trivial. Oil-degrading communities are, however, an attractive setting to start testing systems biology-derived models and hypotheses as they are relatively simple in diversity and key activities, with several key players being isolated and a high availability of experimental data and approaches.

The role of mitochondrial biogenesis and ROS in the control of energy supply in proliferating cells

In yeast, there is a constant growth yield during proliferation on non-fermentable substrate where the ATP generated originates from oxidative phosphorylation. This constant growth yield is due to a tight adjustment between the growth rate and the cellular mitochondrial amount. We showed that this cellular mitochondrial amount is strictly controlled by mitochondrial biogenesis. Moreover, the Ras/cAMP pathway is the cellular signaling pathway involved in the regulation of mitochondrial biogenesis, with a direct relationship between the activity of this pathway and the cellular amount of mitochondria. The cAMP protein kinase Tpk3p is the catalytic subunit specifically involved in the regulation of mitochondrial biogenesis through regulation of the mitochondrial ROS production. An overflow of mitochondrial ROS decreases mitochondrial biogenesis through a decrease in the transcriptional co-activator Hap4p, which can be assimilated to mitochondria quality control. Moreover, the glutathione redox state is shown as being an intermediate in the regulation of mitochondrial biogenesis. This article is part of a Special Issue entitled: 18th European Bioenergetic Conference.

Adaptation of Phaeobacter inhibens DSM 17395 to growth with complex nutrients

Phaeobacter inhibens DSM 17395, a member of the Roseobacter clade, was studied for its adaptive strategies to complex and excess nutrient supply, here mimicked by cultivation with Marine Broth (MB). During growth in process-controlled fermenters, P. inhibens DSM 17395 grew faster (3.6-fold higher μmax ) and reached higher optical densities (2.2-fold) with MB medium, as compared to the reference condition of glucose-containing mineral medium. Apparently, in the presence of MB medium, metabolism was tuned to maximize growth rate at the expense of efficiency. Comprehensive proteomic analysis of cells harvested at ½ ODmax identified 1783 (2D DIGE, membrane and extracellular protein-enriched fractions, shotgun) different proteins (50.5% coverage), 315 (based on 2D DIGE) of which displayed differential abundance profiles. Moreover, 145 different metabolites (intra- and extracellular combined) were identified, almost all of which (140) showed abundance changes. During growth with MB medium, P. inhibens DSM 17395 specifically formed the various proteins required for utilization of phospholipids and several amino acids, as well as for gluconeogenesis. Metabolic tuning on amino acid utilization is also reflected by massive discharge of urea to dispose the cell of excess ammonia. Apparently, P. inhibens DSM 17395 modulated its metabolism to simultaneously utilize diverse substrates from the complex nutrient supply.

Tropical freshwater ecosystems have lower bacterial growth efficiency than temperate ones

Current models and observations indicate that bacterial respiration should increase and growth efficiency (BGE) should decrease with increasing temperatures. However, these models and observations are mostly derived from data collected in temperate regions, and the tropics are under-represented. The aim of this work was to compare bacterial metabolism, namely bacterial production (BP) and respiration (BR), bacterial growth efficiency (BGE) and bacterial carbon demand (BCD) between tropical and temperate ecosystems via a literature review and using unpublished data. We hypothesized that (1) tropical ecosystems have higher metabolism than temperate ones and, (2) that BGE is lower in tropical relative to temperate ecosystems. We collected a total of 498 coupled BP and BR observations (N_total = 498; N_temperate = 301; N_tropical = 197), calculated BGE (BP/(BP+BR)) and BCD (BP+BR) for each case and examined patterns using a model II regression analysis and compared each parameter between the two regions using non-parametric Mann–Whitney U test. We observed a significant positive linear regression between BR and BP for the whole dataset, and also for tropical and temperate data separately. We found that BP, BR and BCD were higher in the tropics, but BGE was lower compared to temperate regions. Also, BR rates per BP unit were at least two fold higher in the tropics than in temperate ecosystems. We argue that higher temperature, nutrient limitation, and light exposure all contribute to lower BGE in the tropics, mediated through effects on thermodynamics, substrate stoichiometry, nutrient availability and interactions with photochemically produced compounds. More efforts are needed in this study area in the tropics, but our work indicates that bottom-up (nutrient availability and resource stoichiometry) and top-down (grazer pressure) processes, coupled with thermodynamic constraints, might contribute to the lower BGE in the tropics relative to temperate regions.

Uncoupling of substrate-level phosphorylation in Escherichia coli during glucose-limited growth

The respiratory chain of Escherichia coli contains three different cytochrome oxidases. Whereas the cytochrome bo oxidase and the cytochrome bd-I oxidase are well characterized and have been shown to contribute to proton translocation, physiological data suggested a nonelectrogenic functioning of the cytochrome bd-II oxidase. Recently, however, this view was challenged by an in vitro biochemical analysis that showed that the activity of cytochrome bd-II oxidase does contribute to proton translocation with an H(+)/e(-) stoichiometry of 1. Here, we propose that this apparent discrepancy is due to the activities of two alternative catabolic pathways: the pyruvate oxidase pathway for acetate production and a pathway with methylglyoxal as an intermediate for the production of lactate. The ATP yields of these pathways are lower than those of the pathways that have so far always been assumed to catalyze the main catabolic flux under energy-limited growth conditions (i.e., pyruvate dehydrogenase and lactate dehydrogenase). Inclusion of these alternative pathways in the flux analysis of growing E. coli strains for the calculation of the catabolic ATP synthesis rate indicates an electrogenic function of the cytochrome bd-II oxidase, compatible with an H(+)/e(-) ratio of 1. This analysis shows for the first time the extent of bypassing of substrate-level phosphorylation in E. coli under energy-limited growth conditions.

Improving metabolic flux predictions using absolute gene expression data

Background

Constraint-based analysis of genome-scale metabolic models typically relies upon maximisation of a cellular objective function such as the rate or efficiency of biomass production. Whilst this assumption may be valid in the case of microorganisms growing under certain conditions, it is likely invalid in general, and especially for multicellular organisms, where cellular objectives differ greatly both between and within cell types. Moreover, for the purposes of biotechnological applications, it is normally the flux to a specific metabolite or product that is of interest rather than the rate of production of biomass per se.

Results

An alternative objective function is presented, that is based upon maximising the correlation between experimentally measured absolute gene expression data and predicted internal reaction fluxes. Using quantitative transcriptomics data acquired from Saccharomyces cerevisiae cultures under two growth conditions, the method outperforms traditional approaches for predicting experimentally measured exometabolic flux that are reliant upon maximisation of the rate of biomass production.

Conclusion

Due to its improved prediction of experimentally measured metabolic fluxes, and of its lack of a requirement for knowledge of the biomass composition of the organism under the conditions of interest, the approach is likely to be of rather general utility. The method has been shown to predict fluxes reliably in single cellular systems. Subsequent work will investigate the method’s ability to generate condition- and tissue-specific flux predictions in multicellular organisms.

Redox balance is key to explaining full vs. partial switching to low-yield metabolism

BACKGROUND

Low-yield metabolism is a puzzling phenomenon in many unicellular and multicellular organisms. In abundance of glucose, many cells use a highly wasteful fermentation pathway despite the availability of a high-yield pathway, producing many ATP molecules per glucose, e.g., oxidative phosphorylation. Some of these organisms, including the lactic acid bacterium Lactococcus lactis, downregulate their high-yield pathway in favor of the low-yield pathway. Other organisms, including Escherichia coli do not reduce the flux through the high-yield pathway, employing the low-yield pathway in parallel with a fully active high-yield pathway. For what reasons do some species use the high-yield and low-yield pathways concurrently and what makes others downregulate the high-yield pathway? A classic rationale for metabolic fermentation is overflow metabolism. Because the throughput of metabolic pathways is limited, influx of glucose exceeding the pathway's throughput capacity is thought to be redirected into an alternative, low-yield pathway. This overflow metabolism rationale suggests that cells would only use fermentation once the high-yield pathway runs at maximum rate, but it cannot explain why cells would decrease the flux through the high-yield pathway.

RESULTS

Using flux balance analysis with molecular crowding (FBAwMC), a recent extension to flux balance analysis (FBA) that assumes that the total flux through the metabolic network is limited, we investigate the differences between Saccharomyces cerevisiae and L. lactis that downregulate the high-yield pathway at increasing glucose concentrations, and E. coli, which keeps the high-yield pathway functioning at maximal rate. FBAwMC correctly predicts the metabolic switching mode in these three organisms, suggesting that metabolic network architecture is responsible for differences in metabolic switching mode. Based on our analysis, we expect gradual, "overflow-like" switching behavior in organisms that have an additional energy-yielding pathway that does not consume NADH (e.g., acetate production in E. coli). Flux decrease through the high-yield pathway is expected in organisms in which the high-yield and low-yield pathways compete for NADH. In support of this analysis, a simplified model of metabolic switching suggests that the extra energy generated during acetate production produces an additional optimal growth mode that smoothens the metabolic switch in E. coli.

CONCLUSIONS

Maintaining redox balance is key to explaining why some microbes decrease the flux through the high-yield pathway, while other microbes use "overflow-like" low-yield metabolism.

Systems analysis of microbial adaptations to simultaneous stresses

Microbes live in multi-factorial environments and have evolved under a variety of concurrent stresses including resource scarcity. Their metabolic organization is a reflection of their evolutionary histories and, in spite of decades of research, there is still a need for improved theoretical tools to explain fundamental aspects of microbial physiology. Using ecological and economic concepts, this chapter explores a resource-ratio based theory to elucidate microbial strategies for extracting and channeling mass and energy. The theory assumes cellular fitness is maximized by allocating scarce resources in appropriate proportions to multiple stress responses. Presented case studies deconstruct metabolic networks into a complete set of minimal biochemical pathways known as elementary flux modes. An economic analysis of the elementary flux modes tabulates enzyme atomic synthesis requirements from amino acid sequences and pathway operating costs from catabolic efficiencies, permitting characterization of inherent tradeoffs between resource investment and phenotype. A set of elementary flux modes with competitive tradeoffs properties can be mathematically projected onto experimental fluxomics datasets to decompose measured phenotypes into metabolic adaptations, interpreted as cellular responses proportional to the experienced culturing stresses. The resource-ratio based method describes the experimental phenotypes with greater accuracy than other contemporary approaches and further analysis suggests the results are both statistically and biologically significant. The insight into metabolic network design principles including tradeoffs associated with concurrent stress adaptation provides a foundation for interpreting physiology as well as for rational control and engineering of medically, environmentally, and industrially relevant microbes.

Growth states of catalytic reaction networks exhibiting energy metabolism

All cells derive nutrition by absorbing some chemical and energy resources from the environment; these resources are used by the cells to reproduce the chemicals within them, which in turn leads to an increase in their volume. In this study we introduce a protocell model exhibiting catalytic reaction dynamics, energy metabolism, and cell growth. Results of extensive simulations of this model show the existence of four phases with regard to the rates of both the influx of resources and cell growth. These phases include an active phase with high influx and high growth rates, an inefficient phase with high influx but low growth rates, a quasistatic phase with low influx and low growth rates, and a death phase with negative growth rate. A mean field model well explains the transition among these phases as bifurcations. The statistical distribution of the active phase is characterized by a power law, and that of the inefficient phase is characterized by a nearly equilibrium distribution. We also discuss the relevance of the results of this study to distinct states in the existing cells.

Systems biochemistry in practice: experimenting with modelling and understanding, with regulation and control

Biology and medicine have become ‘big science’, even though we may not always like this: genomics and the subsequent analysis of what the genomes encode has shown that interesting living organisms require many more than 300 gene products to interact. We once thought that somewhere in this jungle of interacting macromolecules was hidden the molecule that constitutes the secret of Life, and therewith of health and disease. Now we know that, somehow, the secret of Life is the jungle of interactions. Consequently, we need to find the Rosetta Stones, i.e. interpretations of this jungle of systems biology. We need to find, perhaps convoluted, paths of understanding and intervention. Systems biochemistry is a good place to start, as it has the foothold that what goes in must come out. In the present paper, we review two strategies, which look at control and regulation. We discuss the difference between control and regulation and prove a relationship between them.

New patterns of mixed-substrate utilization during batch growth of Escherichia coli K12

Microbial growth on mixtures of substrates is of considerable engineering and biological interest. Most of the work until now has dealt with microbial growth on binary mixtures of sugars or polyols. In these cases, it is often found that no matter how the inoculum is precultured, only one of the two substrates is consumed in the first growth phase, leading to the diauxic growth pattern. The goal of the experiments reported here is to investigate growth on mixtures containing at least one organic acid. These experiments show that the substrate utilization patterns in such mixtures are qualitatively different from the diauxic growth pattern. For instance, during growth of Escherichia coli K12 on certain binary mixtures of organic acids, the two substrates are utilized simultaneously, and the mixed-substrate maximum specific growth rate exceeds the single-substrate maximum specific growth rate on either one of the two constituent substrates. Furthermore, the very same mixed-substrate maximum specific growth and substrate uptake rates are observed no matter how the inoculum is precultured. On the other hand, in a mixture of glucose and pyruvate, the maximum specific growth rate seems to depend on the preculturing conditions, thus suggesting the existence of multiple physiological quasi-steady states. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 747-757, 1997.

Thermodynamic evaluation of energy metabolism in mixed substrate catabolism: modeling studies of stationary and oscillatory states

Thermodynamic and kinetic calculations were performed in a model of mixed substrate metabolism. The model simulates the catabolic breakdown of a first substrate, glucose (S(1)), in the presence of a second substrate, formate (S(2)), which acts as an additional source of free energy. The principal results obtained with different relative rates of uptake of S(2) allow to predict and interpret the following experimental observations: (1) the existence of increased ATP yields by mixed substrate utilization with a maximum ATP yield and optimum input (or molar) ratio for both substrates; (2) a greater assimilation of S(1) which may be interpreted as a decreasing fraction of energy required for assimilation; (3) a decrease in ATP yields due to increasing energy demand for transport; (4) an increased assimilation of the carbon source (S(1)) as a function of increasing inputs of the additional energy source; (5) thermodynamic efficiency (eta) defined as the ratio between the output power of ATP synthesis and the input catabolic power, increases for S(2)/S(1) ratios ranging between 0.08 and 2 while for ratios higher than two a slight decrease of eta was noticed; and (6) the observed maximum in ATP yield for optimum molar ratio of the two substrates corresponds to high eta predicting that higher biomass yields may be obtained through a variable, high, eta by chanelling fluxes through catabolic pathways with different ATP yields. During oscillatory behavior, maxima in fluxes were almost coincident with maxima in forces. Thus, the pattern of dissipation was not so advantageous as in the single substrate model under starvation conditions.

Network thermodynamics in the post-genomic era

Network models have been used to study the underlying processes and principles of biological systems for decades, providing many insights into the complexity of life. Biological systems require a constant flow of free energy to drive these processes that operate away from thermodynamic equilibrium. With the advent of high-throughput omics technologies, more and more thermodynamic knowledge about the biological components, processes and their interactions are surfacing that we can integrate using large-scale biological network models. This allows us to ask many fundamental questions about these networks, such as, how far away from equilibrium must the reactions in a network be displaced in order to allow growth, or what are the possible thermodynamic objectives of the cell.

Control of glycolytic flux in Zymomonas mobilis by glucose 6-phosphate dehydrogenase activity

Glycolytic genes in Zymomonas mobilis are highly expressed and constitute half of the cytoplasmic protein. The first four genes (glf, zwf, edd, glk) in this pathway form an operon encoding a glucose permease, glucose 6-phosphate dehydrogenase (G6-P dehydrogenase), 6-phosphogluconate dehydratase, and glucokinase, respectively. Each gene was overexpressed from a tac promoter to investigate the control of glycolysis during the early stages of batch fermentation when flux (qCO(2)) is highest. Almost half of flux control appears to reside with G6-P dehydrogenase (C(J) (G6-P dehydrogenase) = 0.4). Although Z. mobilis exhibits one of the highest rates of glycolysis known, recombinants with elevated G6-P dehydrogenase had a 10% to 13% higher glycolytic flux than the native organism. A small increase in flux was also observed for recombinants expressing glf. Results obtained did not allow a critical evaluation of glucokinase and this enzyme may also represent an important control point. 6-Phosphogluconate dehydratase appears to be saturating at native levels. With constructs containing the full operon, growth rate and flux were both reduced, complicating interpretations. However, results obtained were also consistent with G6-P dehydrogenase as a primary site of control. Flux was 17% higher in operon constructs which exhibited a 17% increase in G6-P dehydrogenase specific activity, relative to the average of other operon constructs which contain a frameshift mutation in zwf. It is unlikely that all flux control residues solely in G6-P dehydrogenase (calculated C(J) (G6-P dehydrogenase) = 1.0) although these results further support the importance of this enzyme. As reported in previous studies, changes in flux were not accompanied by changes in growth rate providing further evidence that ATP production does not limit biosynthesis in rich complex medium.

Stoichiometry of energy coupling by proton-translocating ATPases: a history of variability

One of the central energy-coupling reactions in living systems is the intraconversion of ATP with a transmembrane proton gradient, carried out by proton-translocating F- and V-type ATPases/synthases. These reversible enzymes can hydrolyze ATP and pump protons, or can use the energy of a transmembrane proton gradient to synthesize ATP from ADP and inorganic phosphate. The stoichiometry of these processes (H(+)/ATP, or coupling ratio) has been studied in many systems for many years, with no universally agreed upon solution. Recent discoveries concerning the structure of the ATPases, their assembly and the stoichiometry of their numerous subunits, particularly the proton-carrying proteolipid (subunit c) of the F(O) and V(0) sectors, have shed new light on this question and raise the possibility of variable coupling ratios modulated by variable proteolipid stoichiometries.

Flux balance analysis: a geometric perspective

Advances in the field of bioinformatics have led to reconstruction of genome-scale networks for a number of key organisms. The application of physicochemical constraints to these stoichiometric networks allows researchers, through methods such as flux balance analysis, to highlight key sets of reactions necessary to achieve particular objectives. The key benefits of constraint-based analysis lie in the minimal knowledge required to infer systemic properties. However, network degeneracy leads to a large number of flux distributions that satisfy any objective; moreover, these distributions may be dominated by biologically irrelevant internal cycles. By examining the geometry underlying the problem, we define two methods for finding a unique solution within the space of all possible flux distributions; such a solution contains no internal cycles, and is representative of the space as a whole. The first method draws on typical geometric knowledge, but cannot be applied to large networks because of the high computational complexity of the problem. Thus a second method, an iteration of linear programs which scales easily to the genome scale, is defined. The algorithm is run on four recent genome-scale models, and unique flux solutions are found. The algorithm set out here will allow researchers in flux balance analysis to exchange typical solutions to their models in a reproducible format. Moreover, having found a single solution, statistical analyses such as correlations may be performed.