Supply-demand analysis a framework for exploring the regulatory design of metabolism

The impact of metabolism on the adaptation of organisms to environmental change

Since Jacob and Monod's discovery of the lac operon ∼1960, the explanations offered for most metabolic adaptations have been genetic. The focus has been on the adaptive changes in gene expression that occur, which are often referred to as "metabolic reprogramming." The contributions metabolism makes to adaptation have been largely ignored. Here we point out that metabolic adaptations, including the associated changes in gene expression, are highly dependent on the metabolic state of an organism prior to the environmental change to which it is adapting, and on the plasticity of that state. In support of this hypothesis, we examine the paradigmatic example of a genetically driven adaptation, the adaptation of E. coli to growth on lactose, and the paradigmatic example of a metabolic driven adaptation, the Crabtree effect in yeast. Using a framework based on metabolic control analysis, we have reevaluated what is known about both adaptations, and conclude that knowledge of the metabolic properties of these organisms prior to environmental change is critical for understanding not only how they survive long enough to adapt, but also how the ensuing changes in gene expression occur, and their phenotypes post-adaptation. It would be useful if future explanations for metabolic adaptations acknowledged the contributions made to them by metabolism, and described the complex interplay between metabolic systems and genetic systems that make these adaptations possible.

Gene expression regulates metabolite homeostasis during the Crabtree effect: Implications for the adaptation and evolution of Metabolism

A key issue in both molecular and evolutionary biology has been to define the roles of genes and phenotypes in the adaptation of organisms to environmental changes. The dominant view has been that an organism's metabolic adaptations are driven by gene expression and that gene mutations, independent of the starting phenotype, are responsible for the evolution of new metabolic phenotypes. We propose an alternate hypothesis, in which the phenotype and genotype together determine metabolic adaptation both in the lifetime of the organism and in the evolutionary selection of adaptive metabolic traits. We tested this hypothesis by flux-balance and metabolic-control analysis of the relative roles of the starting phenotype and gene expression in regulating the metabolic adaptations during the Crabtree effect in yeast, when they are switched from a low- to high-glucose environment. Critical for successful short-term adaptation was the ability of the glycogen/trehalose shunt to balance the glycolytic pathway. The role of later gene expression of new isoforms of glycolytic enzymes, rather than flux control, was to provide additional homeostatic mechanisms allowing an increase in the amount and efficiency of adenosine triphosphate and product formation while maintaining glycolytic balance. We further showed that homeostatic mechanisms, by allowing increased phenotypic plasticity, could have played an important role in guiding the evolution of the Crabtree effect. Although our findings are specific to Crabtree yeast, they are likely to be broadly found because of the well-recognized similarities in glucose metabolism across kingdoms and phyla from yeast to humans.

Workflow for Data Analysis in Experimental and Computational Systems Biology: Using Python as ‘Glue’

Bottom-up systems biology entails the construction of kinetic models of cellular pathways by collecting kinetic information on the pathway components (e.g., enzymes) and collating this into a kinetic model, based for example on ordinary differential equations. This requires integration and data transfer between a variety of tools, ranging from data acquisition in kinetics experiments, to fitting and parameter estimation, to model construction, evaluation and validation. Here, we present a workflow that uses the Python programming language, specifically the modules from the SciPy stack, to facilitate this task. Starting from raw kinetics data, acquired either from spectrophotometric assays with microtitre plates or from Nuclear Magnetic Resonance (NMR) spectroscopy time-courses, we demonstrate the fitting and construction of a kinetic model using scientific Python tools. The analysis takes place in a Jupyter notebook, which keeps all information related to a particular experiment together in one place and thus serves as an e-labbook, enhancing reproducibility and traceability. The Python programming language serves as an ideal foundation for this framework because it is powerful yet relatively easy to learn for the non-programmer, has a large library of scientific routines and active user community, is open-source and extensible, and many computational systems biology software tools are written in Python or have a Python Application Programming Interface (API). Our workflow thus enables investigators to focus on the scientific problem at hand rather than worrying about data integration between disparate platforms.

Genome-Scale Architecture of Small Molecule Regulatory Networks and the Fundamental Trade-Off between Regulation and Enzymatic Activity

Metabolic flux is in part regulated by endogenous small molecules that modulate the catalytic activity of an enzyme, e.g., allosteric inhibition. In contrast to transcriptional regulation of enzymes, technical limitations have hindered the production of a genome-scale atlas of small molecule-enzyme regulatory interactions. Here, we develop a framework leveraging the vast, but fragmented, biochemical literature to reconstruct and analyze the small molecule regulatory network (SMRN) of the model organism Escherichia coli, including the primary metabolite regulators and enzyme targets. Using metabolic control analysis, we prove a fundamental trade-off between regulation and enzymatic activity, and we combine it with metabolomic measurements and the SMRN to make inferences on the sensitivity of enzymes to their regulators. Generalizing the analysis to other organisms, we identify highly conserved regulatory interactions across evolutionarily divergent species, further emphasizing a critical role for small molecule interactions in the maintenance of metabolic homeostasis.

Control and regulation of pathways via negative feedback

The biochemical networks found in living organisms include a huge variety of control mechanisms at multiple levels of organization. While the mechanistic and molecular details of many of these control mechanisms are understood, their exact role in driving cellular behaviour is not. For example, yeast glycolysis has been studied for almost 80 years but it is only recently that we have come to understand the systemic role of the multitude of feedback and feed-forward controls that exist in this pathway. In this article, control theory is discussed as an approach to dissect the control logic of complex pathways. One of the key issues is distinguishing between the terms control and regulation and how these concepts are applied to regulated enzymes such as phosphofructokinase. In doing so, one of the paradoxes in metabolic regulation can be resolved where enzymes such as phosphofructokinase have little control but, nevertheless, possess significant regulatory influence.

Quantitative measures for redox signaling

Redox signaling is now recognized as an important regulatory mechanism for a number of cellular processes including the antioxidant response, phosphokinase signal transduction and redox metabolism. While there has been considerable progress in identifying the cellular machinery involved in redox signaling, quantitative measures of redox signals have been lacking, limiting efforts aimed at understanding and comparing redox signaling under normoxic and pathogenic conditions. Here we have outlined some of the accepted principles for redox signaling, including the description of hydrogen peroxide as a signaling molecule and the role of kinetics in conferring specificity to these signaling events. Based on these principles, we then develop a working definition for redox signaling and review a number of quantitative methods that have been employed to describe signaling in other systems. Using computational modeling and published data, we show how time- and concentration- dependent analyses, in particular, could be used to quantitatively describe redox signaling and therefore provide important insights into the functional organization of redox networks. Finally, we consider some of the key challenges with implementing these methods.

Shape shifting predicts ontogenetic changes in metabolic scaling in diverse aquatic invertebrates

Metabolism fuels all biological activities, and thus understanding its variation is fundamentally important. Much of this variation is related to body size, which is commonly believed to follow a 3/4-power scaling law. However, during ontogeny, many kinds of animals and plants show marked shifts in metabolic scaling that deviate from 3/4-power scaling predicted by general models. Here, we show that in diverse aquatic invertebrates, ontogenetic shifts in the scaling of routine metabolic rate from near isometry (bR = scaling exponent approx. 1) to negative allometry (bR < 1), or the reverse, are associated with significant changes in body shape (indexed by bL = the scaling exponent of the relationship between body mass and body length). The observed inverse correlations between bR and bL are predicted by metabolic scaling theory that emphasizes resource/waste fluxes across external body surfaces, but contradict theory that emphasizes resource transport through internal networks. Geometric estimates of the scaling of surface area (SA) with body mass (bA) further show that ontogenetic shifts in bR and bA are positively correlated. These results support new metabolic scaling theory based on SA influences that may be applied to ontogenetic shifts in bR shown by many kinds of animals and plants.

Tracing regulatory routes in metabolism using generalised supply-demand analysis

Background

Generalised supply-demand analysis is a conceptual framework that views metabolism as a molecular economy. Metabolic pathways are partitioned into so-called supply and demand blocks that produce and consume a particular intermediate metabolite. By studying the response of these reaction blocks to perturbations in the concentration of the linking metabolite, different regulatory routes of interaction between the metabolite and its supply and demand blocks can be identified and their contribution quantified. These responses are mediated not only through direct substrate/product interactions, but also through allosteric effects. Here we subject previously published kinetic models of pyruvate metabolism in Lactococcus lactis and aspartate-derived amino acid synthesis in Arabidopsis thaliana to generalised supply-demand analysis.

Results

Multiple routes of regulation are brought about by different mechanisms in each model, leading to behavioural and regulatory patterns that are generally difficult to predict from simple inspection of the reaction networks depicting the models. In the pyruvate model the moiety-conserved cycles of ATP/ADP and NADH/NAD ⁺ allow otherwise independent metabolic branches to communicate. This causes the flux of one ATP-producing reaction block to increase in response to an increasing ATP/ADP ratio, while an NADH-consuming block flux decreases in response to an increasing NADH/NAD ⁺ ratio for certain ratio value ranges.

In the aspartate model, aspartate semialdehyde can inhibit its supply block directly or by increasing the concentration of two amino acids (Lys and Thr) that occur as intermediates in demand blocks and act as allosteric inhibitors of isoenzymes in the supply block. These different routes of interaction from aspartate semialdehyde are each seen to contribute differently to the regulation of the aspartate semialdehyde supply block.

Conclusions

Indirect routes of regulation between a metabolic intermediate and a reaction block that either produces or consumes this intermediate can play a much larger regulatory role than routes mediated through direct interactions. These indirect routes of regulation can also result in counter-intuitive metabolic behaviour. Performing generalised supply-demand analysis on two previously published models demonstrated the utility of this method as an entry point in the analysis of metabolic behaviour and the potential for obtaining novel results from previously analysed models by using new approaches.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0236-1) contains supplementary material, which is available to authorized users.

Homeostasis and the glycogen shunt explains aerobic ethanol production in yeast

Aerobic glycolysis in yeast and cancer cells produces pyruvate beyond oxidative needs, a paradox noted by Warburg almost a century ago. To address this question, we reanalyzed extensive measurements from (13)C magnetic resonance spectroscopy of yeast glycolysis and the coupled pathways of futile cycling and glycogen and trehalose synthesis (which we refer to as the glycogen shunt). When yeast are given a large glucose load under aerobic conditions, the fluxes of these pathways adapt to maintain homeostasis of glycolytic intermediates and ATP. The glycogen shunt uses glycolytic ATP to store glycolytic intermediates as glycogen and trehalose, generating pyruvate and ethanol as byproducts. This conclusion is supported by studies of yeast with a partial block in the glycogen shunt due to the cif mutation, which found that when challenged with glucose, the yeast cells accumulate glycolytic intermediates and ATP, which ultimately leads to cell death. The control of the relative fluxes, which is critical to maintain homeostasis, is most likely exerted by the enzymes pyruvate kinase and fructose bisphosphatase. The kinetic properties of yeast PK and mammalian PKM2, the isoform found in cancer, are similar, suggesting that the same mechanism may exist in cancer cells, which, under these conditions, could explain their excess lactate generation. The general principle that homeostasis of metabolite and ATP concentrations is a critical requirement for metabolic function suggests that enzymes and pathways that perform this critical role could be effective drug targets in cancer and other diseases.

A detailed view on sulphur metabolism at the cellular and whole-plant level illustrates challenges in metabolite flux analyses

Understanding the dynamics of physiological process in the systems biology era requires approaches at the genome, transcriptome, proteome, and metabolome levels. In this context, metabolite flux experiments have been used in mapping metabolite pathways and analysing metabolic control. In the present review, sulphur metabolism was taken to illustrate current challenges of metabolic flux analyses. At the cellular level, restrictions in metabolite flux analyses originate from incomplete knowledge of the compartmentation network of metabolic pathways. Transport of metabolites through membranes is usually not considered in flux experiments but may be involved in controlling the whole pathway. Hence, steady-state and snapshot readings need to be expanded to time-course studies in combination with compartment-specific metabolite analyses. Because of species-specific differences, differences between tissues, and stress-related responses, the quantitative significance of different sulphur sinks has to be elucidated; this requires the development of methods for whole-sulphur metabolome approaches. Different cell types can contribute to metabolite fluxes to different extents at the tissue and organ level. Cell type-specific analyses are needed to characterize these contributions. Based on such approaches, metabolite flux analyses can be expanded to the whole-plant level by considering long-distance transport and, thus, the interaction of roots and the shoot in metabolite fluxes. However, whole-plant studies need detailed empirical and mathematical modelling that have to be validated by experimental analyses.

Multi-tasking of biosynthetic and energetic functions of glycolysis explained by supply and demand logic

After more than a century of research on glycolysis, we have detailed descriptions of its molecular organization, but despite this wealth of knowledge, linking the enzyme properties to metabolic pathway behavior remains challenging. These challenges arise from multi-layered regulation and the context and time dependence of component functions. However, when viewed as a system that functions according to the principles of supply and demand, a simplifying theoretical framework can be applied to study its regulation logic and to assess the coherence of experimental interpretations. These principles are universally applicable, as they emphasize the common metabolic tasks of glycolysis: the provision of free-energy carriers, and precursors for biosynthesis and stress-related compounds. Here we will review the regulation of multi-tasking by glycolysis and consider how an understanding of this central metabolic pathway can be pursued using general principles, rather than focusing on the biochemical details of constituent components.

A hierarchy of factors influence discontinuous gas exchange in the grasshopper Paracinema tricolor (Orthoptera: Acrididae)

The evolutionary origin and maintenance of discontinuous gas exchange (DGE) in tracheate arthropods are poorly understood and highly controversial. We investigated prioritization of abiotic factors in the gas exchange control cascade by examining oxygen, water and haemolymph pH regulation in the grasshopper Paracinema tricolor. Using a full-factorial design, grasshoppers were acclimated to hypoxic or hyperoxic (5% O2, 40% O2) gas conditions, or dehydrated or hydrated, whereafter their CO2 release was measured under a range of O2 and relative humidity (RH) conditions (5%, 21%, 40% O2 and 5%, 60%, 90% RH). DGE was significantly less common in grasshoppers acclimated to dehydrating conditions compared with the other acclimations (hypoxia, 98%; hyperoxia, 100%; hydrated, 100%; dehydrated, 67%). Acclimation to dehydrating conditions resulted in a significant decrease in haemolymph pH from 7.0±0.3 to 6.6±0.1 (mean ± s.d., P=0.018) and also significantly increased the open (O)-phase duration under 5% O2 treatment conditions (5% O2, 44.1±29.3 min; 40% O2, 15.8±8.0 min; 5% RH, 17.8±1.3 min; 60% RH, 24.0±9.7 min; 90% RH, 20.6±8.9 min). The observed acidosis could potentially explain the extension of the O-phase under low RH conditions, when it would perhaps seem more useful to reduce the O-phase to lower respiratory water loss. The results confirm that DGE occurrence and modulation are affected by multiple abiotic factors. A hierarchical framework for abiotic factors influencing DGE is proposed in which the following stressors are prioritized in decreasing order of importance: oxygen supply, CO2 excretion and pH modulation, oxidative damage protection and water savings.

A generic rate equation for catalysed, template-directed polymerisation

Biosynthetic networks link to growth and reproduction processes through template-directed synthesis of macromolecules such as polynucleotides and polypeptides. No rate equation exists that captures this link in a way that it can effectively be incorporated into a single computational model of the overall process. This paper describes the derivation of such a generic steady-state rate equation for catalysed, template-directed polymerisation reactions with varying monomer stoichiometry and varying chain length. The derivation is based on a classical Michaelis-Menten mechanism with template binding and an arbitrary number of chain elongation steps that produce a polymer composed of an arbitrary number of monomer types. The rate equation only requires the identity of the first dimer in the polymer sequence; for the remainder only the monomer composition needs be known. Further simplification of a term in the denominator yielded an equation requiring no positional information at all, only the monomer composition of the polymer; this equation still gave an excellent estimate of the reaction rate provided that either the monomer concentrations are at least half-saturating, or the polymer is very long.

Carbon partitioning in sugarcane (Saccharum species)

Focus has centered on C-partitioning in stems of sugarcane (Saccharum sp.) due to their high-sucrose accumulation features, relevance to other grasses, and rising economic value. Here we review how sugarcane balances between sucrose storage, respiration, and cell wall biosynthesis. The specific topics involve (1) accumulation of exceptionally high sucrose levels (up to over 500 mM), (2) a potential, turgor-sensitive system for partitioning sucrose between storage inside (cytosol and vacuole) and outside cells, (3) mechanisms to prevent back-flow of extracellular sucrose to xylem or phloem, (4) apparent roles of sucrose-P-synthase in fructose retrieval and sucrose re-synthesis, (5) enhanced importance of invertases, and (6) control of C-flux at key points in cell wall biosynthesis (UDP-glucose dehydrogenase) and respiration (ATP- and pyrophosphate-dependent phosphofructokinases). A combination of emerging technologies is rapidly enhancing our understanding of these points and our capacity to shift C-flux between sucrose, cell wall polymers, or other C-sinks.

Control limits for accumulation of plant metabolites: brute force is no substitute for understanding

Which factors limit metabolite accumulation in plant cells? Are theories on flux control effective at explaining the results? Many biotechnologists cling to the idea that every pathway has a rate limiting enzyme and target such enzymes first in order to modulate fluxes. This often translates into large effects on metabolite concentration, but disappointing small increases in flux. Rate limiting enzymes do exist, but are rare and quite opposite to what predicted by biochemistry. In many cases however, flux control is shared among many enzymes. Flux control and concentration control can (and must) be distinguished and quantified for effective manipulation. Flux control for several 'building blocks' of metabolism is placed on the demand side, and therefore increasing demand can be very successful. Tampering with supply, particularly desensitizing supply enzymes, is usually not very effective, if not dangerous, because supply regulatory mechanisms function to control metabolite homeostasis. Some important, but usually unnoticed, metabolic constraints shape the responses of metabolic systems to manipulation: mass conservation, cellular resource allocation and, most prominently, energy supply, particularly in heterotrophic tissues. The theoretical basis for this view shall be explored with recent examples gathered from the manipulation of several metabolites (vitamins, carotenoids, amino acids, sugars, fatty acids, polyhydroxyalkanoates, fructans and sugar alcohols). Some guiding principles are suggested for an even more successful engineering of plant metabolism.

Metabolic engineering of sugars and simple sugar derivatives in plants

Carbon captured through photosynthesis is transported, and sometimes stored in plants, as sugar. All organic compounds in plants trace to carbon from sugars, so sugar metabolism is highly regulated and integrated with development. Sugars stored by plants are important to humans as foods and as renewable feedstocks for industrial conversion to biofuels and biomaterials. For some purposes, sugars have advantages over polymers including starches, cellulose or storage lipids. This review considers progress and prospects in plant metabolic engineering for increased yield of endogenous sugars and for direct production of higher-value sugars and simple sugar derivatives. Opportunities are examined for enhancing export of sugars from leaves. Focus then turns to manipulation of sugar metabolism in sugar-storing sink organs such as fruits, sugarcane culms and sugarbeet tubers. Results from manipulation of suspected 'limiting' enzymes indicate a need for clearer understanding of flux control mechanisms, to achieve enhanced levels of endogenous sugars in crops that are highly selected for this trait. Outcomes from in planta conversion to novel sugars and derivatives range from severe interference with plant development to field demonstration of crops accumulating higher-value sugars at high yields. The differences depend on underlying biological factors including the effects of the novel products on endogenous metabolism, and on biotechnological fine-tuning including developmental expression and compartmentation patterns. Ultimately, osmotic activity may limit the accumulation of sugars to yields below those achievable using polymers; but results indicate the potential for increases above current commercial sugar yields, through metabolic engineering underpinned by improved understanding of plant sugar metabolism.