Path finding methods accounting for stoichiometry in metabolic networks

Graph-based methods have been widely used for the analysis of biological networks. Their application to metabolic networks has been much discussed, in particular noting that an important weakness in such methods is that reaction stoichiometry is neglected. In this study, we show that reaction stoichiometry can be incorporated into path-finding approaches via mixed-integer linear programming. This major advance at the modeling level results in improved prediction of topological and functional properties in metabolic networks.     

Herbivore metabolism and stoichiometry each constrain herbivory at different organizational scales across ecosystems

Plant-herbivore interactions mediate the trophic structure of ecosystems. We use a comprehensive data set extracted from the literature to test the relative explanatory power of two contrasting bodies of ecological theory, the metabolic theory of ecology (MTE) and ecological stoichiometry (ES), for per-capita and population-level rates of herbivory across ecosystems. We found that ambient temperature and herbivore body size (MTE) as well as stoichiometric mismatch (ES) both constrained herbivory, but at different scales of biological organization. Herbivore body size, which varied over 11 orders of magnitude, was the primary factor explaining variation in per-capita rates of herbivory. Stoichiometric mismatch explained more variation in population-level herbivory rates and also in per-capita rates when we examined data from within functionally similar trophic groups (e.g. zooplankton). Thus, predictions from metabolic and stoichiometric theories offer complementary explanations for patterns of herbivory that operate at different scales of biological organization.     

Mathematical description of microbiological reactions involving intermediates

Stoichiometric relationships for biological reactions involving intermediate formation are developed from microbial reaction fundamentals and thermodynamic principles. Biological reactions proceed through intermediates, which sequester carbon and electrons whenever their degradation is relatively slow. Modeling intermediate formation and subsequent utilization requires evaluation of the distribution of electrons, energy, and macronutrients (C and N) between energy-generating pathways and cell-synthesis pathways for each step in the mineralization of the primary electron-donor substrate. We describe how energy and electron balances are utilized to predict the stoichiometry for each step of a multi-step degradation process. Each stoichiometric relationship developed predicts substrate utilization, cell growth, and the formation of other products (e.g., H(2)CO(3) or H(+)) for one step in the pathway to full mineralization. A modeling example demonstrates how different kinetics for each step in the degradation of nitrilotriacetic acid (NTA) leads to observed patterns in experimental results, such as a delay in the release of H(2)CO(3) after NTA is removed from solution.     

A New Approach to Homeostatic Regulation: Towards a Unified View of Physiological and Ecological Concepts

Stoichiometric homeostasis is the ability of an organism to keep its body chemical composition constant, despite varying inputs. Stoichiometric homeostasis therefore constrains the metabolic needs of consumers which in turn often feed on resources not matching these requirements. In a broader context, homeostasis also relates to the capacity of an organism to maintain other biological parameters (e.g. body temperature) at a constant level over ambient environmental variations. Unfortunately, there are discrepancies in the literature and ecological and physiological definitions of homeostasis are disparate and partly contradictory. Here, we address this matter by reviewing the existing knowledge considering two distinct groups, regulators and conformers and, based on examples of thermo- and osmoregulation, we propose a new approach to stoichiometric homeostasis, unifying ecological and physiological concepts. We suggest a simple and precise graphical way to identify regulators and conformers: for any given biological parameter (e.g. nutrient stoichiometry, temperature), a sigmoidal relation between internal and external conditions can be observed for conformers while an inverse sigmoidal response is characteristic of regulators. This new definition and method, based on well-studied physiological mechanisms, unifies ecological and physiological approaches and is a useful tool for understanding how organisms are affected by and affect their environment.     

Ab initio prediction of thermodynamically feasible reaction directions from biochemical network stoichiometry

Analysis of the stoichiometric structure of metabolic networks provides insights into the relationships between structure, function, and regulation of metabolic systems. Based on knowledge of only reaction stoichiometry, certain aspects of network functionality and robustness can be predicted. Current theories focus on breaking a metabolic network down into non-decomposable pathways able to operate in steady state. The physics underlying these theories is based on mass balance and the laws of thermodynamics. However, due to the inherent nonlinearity of the thermodynamic constraints on metabolic fluxes, computational analysis of large-scale biochemical systems can be expensive. In this study, it is shown how the feasible reaction directions may be determined by either computing the allowable ranges under the mass-balance and thermodynamic constraints or by analyzing the stoichiometric structure of the network. The computed reaction directions translate into a set of linear constraints necessary for thermodynamic feasibility. This set of necessary linear constraints is shown to be sufficient to guarantee feasibility in certain cases, thus translating the nonlinear thermodynamic constraints to linear. We show that for a reaction network of 44 internal reactions representing energy metabolism, the computed linear inequality constraints represent necessary and sufficient conditions for thermodynamic feasibility.     

Unifying elemental stoichiometry and metabolic theory in predicting species abundances

While metabolic theory predicts variance in population density within communities depending on population average body masses, the ecological stoichiometry concept relates density variation across communities to varying resource stoichiometry. Using a data set including biomass densities of 4959 populations of soil invertebrates across 48 forest sites we combined these two frameworks. We analyzed how the scaling of biomass densities with population‐averaged body masses systematically interacts with stoichiometric variables. Simplified analyses employing either only body masses or only resource stoichiometry are highly context sensitive and yield variable and often misleading results. Our findings provide strong evidence that analyses of ecological state variables should integrate allometric and stoichiometric variables to explain deviations from predicted allometric scaling and avoid erroneous conclusions. In consequence, our study provides an important step towards unifying two prominent ecological theories, metabolic theory and ecological stoichiometry.     

植物生态化学计量内稳性特征

化学计量内稳性是生态化学计量学研究的核心概念之一,是指生物在面对外界变化的时候保持自身化学组成相对稳定的能力,其反映了生物对周围环境变化作出的生理和生化响应与适应。通过研究植物生态化学计量内稳性,有助于深入了解植物对环境的适应策略和生态适应性,以及植物化学计量内稳性与生态系统功能的关系,但目前关于植物生态化学计量内稳性的研究较少。已有的研究结果表明:不同物种或功能群由于其生长策略不同而具有不同的生态化学计量内稳性特征;同一物种的不同器官、不同生长阶段以及不同元素的内稳性存在较大的差异。该文对植物生态化学计量内稳性概念、内稳性指数的测算方法,不同植物物种或功能群、不同器官、不同生长阶段内稳性特征,以及植物内稳性与生态系统结构、功能和稳定性的关系等方面进行了综述,并结合现已开展的工作,对有待进一步拓展的相关植物生态化学计量内稳性研究领域进行了展望,以期为促进国内相关研究工作的开展提供参考。     

Branch-point stoichiometry can generate weak links in metabolism: the case of glycine biosynthesis

Although the metabolic network permits conversion between almost any pair of metabolites, this versatility fails at certain sites because of chemical constraints (kinetic, thermodynamic and stoichiometric) that seriously restrict particular conversions. We call these sites weak links in metabolism, as they can interfere harmfully with management of matter and energy if the network as a whole does not include adequate safeguards. A critical weak link is created in glycine biosynthesis by the stoichiometry of the reaction catalyzed by glycine hydroxymethyltransferase (EC 2.1.2.1), which converts serine into glycine plus one C₁ unit: this produces an absolute dependence of the glycine production flux on the utilization of C₁ units for other metabolic pathways that do not work coordinately with glycine use. It may not be possible, therefore, to ensure that glycine is always synthesized in sufficient quantities to meet optimal metabolic requirements.     

MetRxn: a knowledgebase of metabolites and reactions spanning metabolic models and databases

Background  

Increasingly, metabolite and reaction information is organized in the form of genome-scale metabolic reconstructions that describe the reaction stoichiometry, directionality, and gene to protein to reaction associations. A key bottleneck in the pace of reconstruction of new, high-quality metabolic models is the inability to directly make use of metabolite/reaction information from biological databases or other models due to incompatibilities in content representation (i.e., metabolites with multiple names across databases and models), stoichiometric errors such as elemental or charge imbalances, and incomplete atomistic detail (e.g., use of generic R-group or non-explicit specification of stereo-specificity).     

Functional shifts in lake zooplankton communities with hypereutrophication

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Optimal path-finding through mental exploration based on neural energy field gradients

Rodent animal can accomplish self-locating and path-finding task by forming a cognitive map in the hippocampus representing the environment. In the classical model of the cognitive map, the system (artificial animal) needs large amounts of physical exploration to study spatial environment to solve path-finding problems, which costs too much time and energy. Although Hopfield’s mental exploration model makes up for the deficiency mentioned above, the path is still not efficient enough. Moreover, his model mainly focused on the artificial neural network, and clear physiological meanings has not been addressed. In this work, based on the concept of mental exploration, neural energy coding theory has been applied to the novel calculation model to solve the path-finding problem. Energy field is constructed on the basis of the firing power of place cell clusters, and the energy field gradient can be used in mental exploration to solve path-finding problems. The study shows that the new mental exploration model can efficiently find the optimal path, and present the learning process with biophysical meaning as well. We also analyzed the parameters of the model which affect the path efficiency. This new idea verifies the importance of place cell and synapse in spatial memory and proves that energy coding is effective to study cognitive activities. This may provide the theoretical basis for the neural dynamics mechanism of spatial memory.     

Integrating thermodynamic and enzymatic constraints into genome-scale metabolic models

Stoichiometric genome-scale metabolic network models (GEMs) have been widely used to predict metabolic phenotypes. In addition to stoichiometric ratios, other constraints such as enzyme availability and thermodynamic feasibility can also limit the phenotype solution space. Extended GEM models considering either enzymatic or thermodynamic constraints have been shown to improve prediction accuracy. In this paper, we propose a novel method that integrates both enzymatic and thermodynamic constraints in a single Pyomo modeling framework (ETGEMs). We applied this method to construct the EcoETM (E. coli metabolic model with enzymatic and thermodynamic constraints). Using this model, we calculated the optimal pathways for cellular growth and the production of 22 metabolites. When comparing the results with those of iML1515 and models with one of the two constraints, we observed that many thermodynamically unfavorable and/or high enzyme cost pathways were excluded from EcoETM. For example, the synthesis pathway of carbamoyl-phosphate (Cbp) from iML1515 is both thermodynamically unfavorable and enzymatically costly. After introducing the new constraints, the production pathways and yields of several Cbp-derived products (e.g. L-arginine, orotate) calculated using EcoETM were more realistic. The results of this study demonstrate the great application potential of metabolic models with multiple constraints for pathway analysis and phenotype prediction.     

Chemostat cultures of yeasts, continuous culture fundamentals and simple unstructured mathematical models.

Fundamental aspects of chemostat cultures are reviewed. Using yeast cultures as examples, it is shown that steady states in chemostats may be predicted quantitatively by combining the correct number of unstructured kinetic models with expressions for existing stoichiometric constraints. The necessary number of such kinetic models corresponds to the number of limiting substrates and increases with the number of different metabolic pathways available to the strain. This is demonstrated by an experimental comparison of yeast growth limited by glucose alone for which metabolism is oxidative, and growth doubly limited by both glucose and oxygen, which occurs according to an oxido-reductive metabolism. The steady state data for such experiments can in principle be predicted based on a minimal amount of information by a simple stoichiometric model. It represents the overall stoichiometry of growth by a superposition of a fully oxidative and a fully reductive growth reaction and uses the concept of "aerobicity" to characterize the relative importance of the two reactions.     

Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism.

Analysis of metabolic networks using linear optimization theory allows one to quantify and understand the limitations imposed on the cell by its metabolic stoichiometry, and to understand how the flux through each pathway influences the overall behavior of metabolism. A stoichiometric matrix accounting for the major pathways involved in energy and mass transformations in the cell was used in our analysis. The auxiliary parameters of linear optimization, the so-called shadow prices, identify the intermediates and cofactors that cause the growth to be limited on each nutrient. This formalism was used to examine how well the cell balances its needs for carbon, nitrogen, and energy during growth on different substrates. The relative values of glucose and glutamine as nutrients were compared by varying the ratio of rates of glucose to glutamine uptakes, and calculating the maximum growth rate. The optimum value of this ratio is between 2-7, similar to experimentally observed ratios. The theoretical maximum growth rate was calculated for growth on each amino acid, and the amino acids catabolized directly to glutamate were found to be the optimal nutrients. The importance of each reaction in the network can be examined both by selectively limiting the flux through the reaction, and by the value of the reduced cost for that reaction. Some reactions, such as malic enzyme and glutamate dehydrogenase, may be inhibited or deleted with little or no adverse effect on the calculated cell growth rate.     

Hybrid metabolic flux analysis: combining stoichiometric and statistical constraints to model the formation of complex recombinant products

Background  

Stoichiometric models constitute the basic framework for fluxome quantification in the realm of metabolic engineering. A recurrent bottleneck, however, is the establishment of consistent stoichiometric models for the synthesis of recombinant proteins or viruses. Although optimization algorithms for in silico metabolic redesign have been developed in the context of genome-scale stoichiometric models for small molecule production, still rudimentary knowledge of how different cellular levels are regulated and phenotypically expressed prevents their full applicability for complex product optimization.     

Metabolic networks: enzyme function and metabolite structure

Metabolism is one of the most complex cellular processes. Connections between biochemical reactions via substrate and product metabolites create complex metabolic networks that may be analyzed using network theory, stoichiometric analysis, and information on protein structure/function and metabolite properties. These frameworks take into consideration different aspects of enzyme chemistry, enzyme structure and metabolite structure, and demonstrate the impact of metabolic biochemistry on the systemic properties of metabolism. The integration of these approaches and the systematic classification of enzyme function and the chemical structure of metabolites will enhance our understanding of metabolism, and could improve our ability to predict enzyme function and novel metabolic pathways.     

A Strategy to Calculate the Patterns of Nutrient Consumption by Microorganisms Applying a Two-Level Optimisation Principle to Reconstructed Metabolic Networks

Bacterial responses to environmental changes rely on a complex network of biochemical reactions. The properties of the metabolic network determining these responses can be divided into two groups: the stoichiometric properties, given by the stoichiometry matrix, and the kinetic/thermodynamic properties, given by the rate equations of the reaction steps. The stoichiometry matrix represents the maximal metabolic capabilities of the organism, and the regulatory mechanisms based on the rate laws could be considered as being responsible for the administration of these capabilities. Post-genomic reconstruction of metabolic networks provides us with the stoichiometry matrix of particular strains of microorganisms, but the kinetic aspects of in vivo rate laws are still largely unknown. Therefore, the validity of predictions of cellular responses requiring detailed knowledge of the rate equations is difficult to assert. In this paper, we show that by applying optimisation criteria to the core stoichiometric network of the metabolism of Escherichia coli, and including information about reversibility/irreversibility only of the reaction steps, it is possible to calculate bacterial responses to growth media with different amounts of glucose and galactose. The target was the minimisation of the number of active reactions (subject to attaining a growth rate higher than a lower limit) and subsequent maximisation of the growth rate (subject to the number of active reactions being equal to the minimum previously calculated). Using this two-level target, we were able to obtain by calculation four fundamental behaviours found experimentally: inhibition of respiration at high glucose concentrations in aerobic conditions, turning on of respiration when glucose decreases, induction of galactose utilisation when the system is depleted of glucose and simultaneous use of glucose and galactose as carbon sources when both sugars are present in low concentrations. Preliminary results of the coarse pattern of sugar utilisation were also obtained with a genome-scale E. coli reconstructed network, yielding similar qualitative results.     

Pathway engineering for production of aromatics in Escherichia coli: Confirmation of stoichiometric analysis by independent modulation of AroG, TktA, and Pps activities

The synthesis of 3-deoxy-D-arabino-heptulosonate-7-phosphate (DAHP) is the first commitment of resources toward aromatics production in Escherichia coli. DAHP is produced during a condensation reaction between phosphoenolpyruvate (PEP) and erythrose 4-phosphate (E4P) catalyzed by DAHP synthases (coded by aroF, aroG, and aroH). Stoichiometric analysis has shown a severe PEP limitation in the theoretical yield of DAHP production from glucose due to the phosphotransferase system (PTS) for sugar uptake. This limitation can be relieved by (i) the recycling of pyruvate from PEP using PEP synthase (Pps) or (ii) use of non-PTS sugars such as xylose. Previous studies have shown the usefulness of overexpressing tktA (encoding transketolase), aroG, and pps (PEP synthase) for DAHP production in an aroB strain unable to utilize DAHP further. In the present study we confirm the predictions of the stoichiometric analysis by introducing pps, tktA, and aroG into vectors under independently controlled promoters. In glucose medium, although TktA has some positive effect on the final DAHP concentration, it has no effect on the yield (percent conversion). With Pps overexpression, the DAHP concentration produced from glucose is increased almost twofold and the yield is approaching the theoretical maximum, as predicted by the stoichiometric analysis. However, this Pps effect is observed only in the presence of both increased AroG and TktA. In xylose mimimal medium, the final DAHP concentration and the yield are completely determined by the AroG activity. TktA and Pps play no or insignificant roles, and the yield can reach the theoretical maximum without overexpression of these two enzymes. The results shown here are important for both rational design of metabolic pathways and industrial production of aromatics such as tryptophan, phenylalanine, indigo, quinic acid, and catechol.     

Rapid evolution of a consumer stoichiometric trait destabilizes consumer–producer dynamics

Recent studies have shown that adaptive evolution can be rapid enough to affect contemporary ecological dynamics in nature (i.e. ‘rapid evolution’). These studies tend to focus on trait functions relating to interspecific interactions; however, the importance of rapid evolution of stoichiometric traits has been relatively overlooked. Various traits can affect the balance of elements (carbon, nitrogen, and phosphorus) of organisms, and rapid evolution of such stoichiometric traits will not only alter population and community dynamics but also influence ecosystem functions such as nutrient cycling. Multiple environmental changes may exert a selection pressure leading to adaptation of stoichiometrically important traits, such as an organism's growth rate. In this paper, we use theoretical approaches to explore the connections between rapid evolution and ecological stoichiometry at both the population and ecosystem level. First, we incorporate rapid evolution into an ecological stoichiometry model to investigate the effects of rapid evolution of a consumer's stoichiometric phosphorus:carbon ratio on consumer–producer population dynamics. We took two complementary approaches, an asexual clonal genotype model and a quantitative genetic model. Next, we extended these models to explicitly track nutrients in order to evaluate the effect of rapid evolution at the ecosystem level. Our model results indicate rapid evolution of the consumer stoichiometric trait can cause complex dynamics where rapid evolution destabilizes population dynamics and rescues the consumer population from extinction (evolutionary rescue). The model results also show that rapid evolution may influence the level of nutrients available in the environment and the flux of nutrients across trophic levels. Our study represents an important step for theoretical integration of rapid evolution and ecological stoichiometry.     

An experimental test of the hypothesis of non‐homeostatic consumer stoichiometry in a plant litter–microbe system

Stoichiometric homeostasis of heterotrophs is a common, but not always well‐examined premise in ecological stoichiometry. We experimentally evaluated the relationship between substrate (plant litter) and consumer (microorganisms) stoichiometry for a tropical terrestrial decomposer system. Variation in microbial C : P and N : P ratios tracked that of the soluble litter fraction, but not that of bulk leaf litter material. Microbial N and P were not isometrically related, suggesting higher rates of P than N sequestration in microbial biomass. Shifts in microbial stoichiometry were related to changes in microbial community structure. Our results indicate that P in dissolved form is a major driver of terrestrial microbial stoichiometry, similar to aquatic environments. The demonstrated relative plasticity in microbial C : P and N : P and the critical role of P have important implications for theoretical modelling and contribute to a process‐based understanding of stoichiometric relationships and the flow of elements across trophic levels in decomposer systems.