Channelling can decrease pool size

Personalised modelling of clinical heterogeneity between medium-chain acyl-CoA dehydrogenase patients

BACKGROUND

Monogenetic inborn errors of metabolism cause a wide phenotypic heterogeneity that may even differ between family members carrying the same genetic variant. Computational modelling of metabolic networks may identify putative sources of this inter-patient heterogeneity. Here, we mainly focus on medium-chain acyl-CoA dehydrogenase deficiency (MCADD), the most common inborn error of the mitochondrial fatty acid oxidation (mFAO). It is an enigma why some MCADD patients-if untreated-are at risk to develop severe metabolic decompensations, whereas others remain asymptomatic throughout life. We hypothesised that an ability to maintain an increased free mitochondrial CoA (CoASH) and pathway flux might distinguish asymptomatic from symptomatic patients.

RESULTS

We built and experimentally validated, for the first time, a kinetic model of the human liver mFAO. Metabolites were partitioned according to their water solubility between the bulk aqueous matrix and the inner membrane. Enzymes are also either membrane-bound or in the matrix. This metabolite partitioning is a novel model attribute and improved predictions. MCADD substantially reduced pathway flux and CoASH, the latter due to the sequestration of CoA as medium-chain acyl-CoA esters. Analysis of urine from MCADD patients obtained during a metabolic decompensation showed an accumulation of medium- and short-chain acylcarnitines, just like the acyl-CoA pool in the MCADD model. The model suggested some rescues that increased flux and CoASH, notably increasing short-chain acyl-CoA dehydrogenase (SCAD) levels. Proteome analysis of MCADD patient-derived fibroblasts indeed revealed elevated levels of SCAD in a patient with a clinically asymptomatic state. This is a rescue for MCADD that has not been explored before. Personalised models based on these proteomics data confirmed an increased pathway flux and CoASH in the model of an asymptomatic patient compared to those of symptomatic MCADD patients.

CONCLUSIONS

We present a detailed, validated kinetic model of mFAO in human liver, with solubility-dependent metabolite partitioning. Personalised modelling of individual patients provides a novel explanation for phenotypic heterogeneity among MCADD patients. Further development of personalised metabolic models is a promising direction to improve individualised risk assessment, management and monitoring for inborn errors of metabolism.

From Protein Film Electrochemistry to Nanoconfined Enzyme Cascades and the Electrochemical Leaf

Protein film electrochemistry (PFE) has given unrivalled insight into the properties of redox proteins and many electron-transferring enzymes, allowing investigations of otherwise ill-defined or intractable topics such as unstable Fe-S centers and the catalytic bias of enzymes. Many enzymes have been established to be reversible electrocatalysts when attached to an electrode, and further investigations have revealed how unusual dependences of catalytic rates on electrode potential have stark similarities with electronics. A special case, the reversible electrochemistry of a photosynthetic enzyme, ferredoxin-NADP⁺ reductase (FNR), loaded at very high concentrations in the 3D nanopores of a conducting metal oxide layer, is leading to a new technology that brings PFE to myriad enzymes of other classes, the activities of which become controlled by the primary electron exchange. This extension is possible because FNR-based recycling of NADP(H) can be coupled to a dehydrogenase, and thence to other enzymes linked in tandem by the tight channelling of cofactors and intermediates within the nanopores of the material. The earlier interpretations of catalytic wave-shapes and various analogies with electronics are thus extended to initiate a field perhaps aptly named "cascade-tronics", in which the flow of reactions along an enzyme cascade is monitored and controlled through an electrochemical analyzer. Unlike in photosynthesis where FNR transduces electron transfer and hydride transfer through the unidirectional recycling of NADPH, the "electrochemical leaf" (e-Leaf) can be used to drive reactions in both oxidizing and reducing directions. The e-Leaf offers a natural way to study how enzymes are affected by nanoconfinement and crowding, mimicking the physical conditions under which enzyme cascades operate in living cells. The reactions of the trapped enzymes, often at very high local concentration, are thus studied electrochemically, exploiting the potential domain to control rates and direction and the current-rate analogy to derive kinetic data. Localized NADP(H) recycling is very efficient, resulting in very high cofactor turnover numbers and new opportunities for controlling and exploiting biocatalysis.

Mechanisms and Effects of Substrate Channelling in Enzymatic Cascades

Substrate or metabolite channelling is a transfer of intermediates produced by one enzyme to the sequential enzyme of a reaction cascade or metabolic pathway, without releasing them entirely into bulk. Despite an enormous effort and more than three decades of research, substrate channelling remains the subject of continuing debates and active investigation. Herein, we review the benefits and mechanisms of substrate channelling in vivo and in vitro. We discuss critically the effects that substrate channelling can have on enzymatic cascades, including speeding up or slowing down reaction cascades and protecting intermediates from sequestration and enzymes' surroundings from toxic or otherwise detrimental intermediates. We also discuss how macromolecular crowding affects substrate channelling and point out the galore of open questions.

Pre-analytic Considerations for Mass Spectrometry-Based Untargeted Metabolomics Data

Metabolomics is the science of characterizing and quantifying small molecule metabolites in biological systems. These metabolites give organisms their biochemical characteristics, providing a link between genotype, environment, and phenotype. With these opportunities also come data challenges, such as compound annotation, missing values, and batch effects. We present the steps of a general pipeline to process untargeted mass spectrometry data to alleviate the latter two challenges. We assume to have a matrix with metabolite abundances, with metabolites in rows and samples in columns. The steps in the pipeline include summarizing technical replicates (if available), filtering, imputing, transforming, and normalizing the data. In each of these steps, a method and parameters should be chosen based on assumptions one is willing to make, the question of interest, and diagnostic tools. Besides giving a general pipeline that can be adapted by the reader, our goal is to review diagnostic tools and criteria that are helpful when making decisions in each step of the pipeline and assessing the effectiveness of normalization and batch correction. We conclude by giving a list of useful packages and discuss some alternative approaches that might be more appropriate for the reader's data.

Tissue and serum metabolite profiling reveals potential biomarkers of human hepatocellular carcinoma

BACKGROUND AND AIMS

Metabolomics serves as an important tool in distinguishing changes in metabolic pathways and the diagnosis of human disease. Hepatocellular carcinoma (HCC) is a malignance present of heterogeneous metabolic disorder and lack of effective biomarker for surveillance and diagnosis. In this study, we searched for potential metabolite biomarkers of HCC using tissue and serum metabolomics approach.

METHODS

A total of 30 pairs of matched liver tissue samples from HCC patients and 90 serum samples (30 HCC patients, 30 liver cirrhosis patients, and 30 healthy individuals) were assessed. Metabolomics was performed through ultra performance liquid chromatography-mass spectrometry in conjunction with multivariate and univariate statistical analyses.

RESULTS

A total of six differential metabolites including chenodeoxycholic acid (CDCA), glycocholic acid (GCA), LPC20:5, LPE18:0, succinyladenosine and uridine were present in HCC tissue and serum samples. CDCA, LPC20:5, succinyladenosine and uridine were used to construct a diagnostic model based on logistic regression. The four-metabolite panel discriminated HCC from liver cirrhosis with an AUC score of 0.938, sensitivity of 93.3% and specificity of 86.7%. For all HCC and cirrhosis patients, the diagnostic accuracy increased to 96.7% and 90.0%, respectively.

CONCLUSION

The combination of CDCA, LPC20:5, succinyladenosine and uridine can be used as a biomarker panel to improve HCC sensitivity and specificity. This panel significantly benefits HCC diagnostics and reveals new insight into HCC pathogenesis.

Does metabolite channeling accelerate enzyme-catalyzed cascade reactions?

Metabolite or substrate channeling is a direct transfer of metabolites from one enzyme to the next enzyme in a cascade. Among many potential advantages of substrate channeling, acceleration of the total reaction rate is considered as one of the most important and self-evident. However, using a simple model, supported by stochastic simulations, we show that it is not always the case; particularly at long times (i.e. in steady state) and high substrate concentrations, a channeled reaction cannot be faster, and can even be slower, than the original non-channeled cascade reaction. In addition we show that increasing the degree of channeling may lead to an increase of the metabolite pool size. We substantiate that the main advantage of channeling likely lies in protecting metabolites from degradation or competing side reactions.

Metabolomics in plants and humans: applications in the prevention and diagnosis of diseases

In the recent years, there has been an increase in the number of metabolomic approaches used, in parallel with proteomic and functional genomic studies. The wide variety of chemical types of metabolites available has also accelerated the use of different techniques in the investigation of the metabolome. At present, metabolomics is applied to investigate several human diseases, to improve their diagnosis and prevention, and to design better therapeutic strategies. In addition, metabolomic studies are also being carried out in areas such as toxicology and pharmacology, crop breeding, and plant biotechnology. In this review, we emphasize the use and application of metabolomics in human diseases and plant research to improve human health.

Clustering and optimal arrangement of enzymes in reaction-diffusion systems

Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.

Metabolic adaptation and protein complexes in prokaryotes

Protein complexes are classified and have been charted in several large-scale screening studies in prokaryotes. These complexes are organized in a factory-like fashion to optimize protein production and metabolism. Central components are conserved between different prokaryotes; major complexes involve carbohydrate, amino acid, fatty acid and nucleotide metabolism. Metabolic adaptation changes protein complexes according to environmental conditions. Protein modification depends on specific modifying enzymes. Proteins such as trigger enzymes display condition-dependent adaptation to different functions by participating in several complexes. Several bacterial pathogens adapt rapidly to intracellular survival with concomitant changes in protein complexes in central metabolism and optimize utilization of their favorite available nutrient source. Regulation optimizes protein costs. Master regulators lead to up- and downregulation in specific subnetworks and all involved complexes. Long protein half-life and low level expression detaches protein levels from gene expression levels. However, under optimal growth conditions, metabolite fluxes through central carbohydrate pathways correlate well with gene expression. In a system-wide view, major metabolic changes lead to rapid adaptation of complexes and feedback or feedforward regulation. Finally, prokaryotic enzyme complexes are involved in crowding and substrate channeling. This depends on detailed structural interactions and is verified for specific effects by experiments and simulations.

Compartmentation of glycogen metabolism revealed from 13C isotopologue distributions

Background

Stable isotope tracers are used to assess metabolic flux profiles in living cells. The existing methods of measurement average out the isotopic isomer distribution in metabolites throughout the cell, whereas the knowledge of compartmental organization of analyzed pathways is crucial for the evaluation of true fluxes. That is why we accepted a challenge to create a software tool that allows deciphering the compartmentation of metabolites based on the analysis of average isotopic isomer distribution.

Results

The software Isodyn, which simulates the dynamics of isotopic isomer distribution in central metabolic pathways, was supplemented by algorithms facilitating the transition between various analyzed metabolic schemes, and by the tools for model discrimination. It simulated ¹³C isotope distributions in glucose, lactate, glutamate and glycogen, measured by mass spectrometry after incubation of hepatocytes in the presence of only labeled glucose or glucose and lactate together (with label either in glucose or lactate). The simulations assumed either a single intracellular hexose phosphate pool, or also channeling of hexose phosphates resulting in a different isotopic composition of glycogen. Model discrimination test was applied to check the consistency of both models with experimental data. Metabolic flux profiles, evaluated with the accepted model that assumes channeling, revealed the range of changes in metabolic fluxes in liver cells.

Conclusions

The analysis of compartmentation of metabolic networks based on the measured ¹³C distribution was included in Isodyn as a routine procedure. The advantage of this implementation is that, being a part of evaluation of metabolic fluxes, it does not require additional experiments to study metabolic compartmentation. The analysis of experimental data revealed that the distribution of measured ¹³C-labeled glucose metabolites is inconsistent with the idea of perfect mixing of hexose phosphates in cytosol. In contrast, the observed distribution indicates the presence of a separate pool of hexose phosphates that is channeled towards glycogen synthesis.

Towards a matrix mechanics framework for dynamic protein network

Protein–protein interaction networks are currently visualized by software generated interaction webs based upon static experimental data. Current state is limited to static, mostly non-compartmental network and non time resolved protein interactions. A satisfactory mathematical foundation for particle interactions within a viscous liquid state (situation within the cytoplasm) does not exist nor do current computer programs enable building dynamic interaction networks for time resolved interactions. Building mathematical foundation for intracellular protein interactions can be achieved in two increments (a) trigger and capture the dynamic molecular changes for a select subset of proteins using several model systems and high throughput time resolved proteomics and, (b) use this information to build the mathematical foundation and computational algorithm for a compartmentalized and dynamic protein interaction network. Such a foundation is expected to provide benefit in at least two spheres: (a) understanding physiology enabling explanation of phenomenon such as incomplete penetrance in genetic disorders and (b) enabling several fold increase in biopharmaceutical production using impure starting materials.

Clinical applications of metabolomics in oncology: a review

Metabolomics, an omic science in systems biology, is the global quantitative assessment of endogenous metabolites within a biological system. Either individually or grouped as a metabolomic profile, detection of metabolites is carried out in cells, tissues, or biofluids by either nuclear magnetic resonance spectroscopy or mass spectrometry. There is potential for the metabolome to have a multitude of uses in oncology, including the early detection and diagnosis of cancer and as both a predictive and pharmacodynamic marker of drug effect. Despite this, there is lack of knowledge in the oncology community regarding metabolomics and confusion about its methodologic processes, technical challenges, and clinical applications. Metabolomics, when used as a translational research tool, can provide a link between the laboratory and clinic, particularly because metabolic and molecular imaging technologies, such as positron emission tomography and magnetic resonance spectroscopic imaging, enable the discrimination of metabolic markers noninvasively in vivo. Here, we review the current and potential applications of metabolomics, focusing on its use as a biomarker for cancer diagnosis, prognosis, and therapeutic evaluation.

Stochastic reaction-diffusion simulation of enzyme compartmentalization reveals improved catalytic efficiency for a synthetic metabolic pathway

We have demonstrated the accuracy of a spatial stochastic model of Escherichia coli central carbon metabolism using the next subvolume method (NSM), an efficient implementation of the Gillespie direct method of stochastic simulation. Using this model, we demonstrate that compartmentalization of the enzymes comprising an engineered pathway for biosynthesis of R-1,2-propanediol leads to improved kinetic properties for the pathway enzymes, especially when substrate diffusivities are low. Our results suggest that enzyme compartmentalization is a powerful approach for improving the catalytic turnover of a channeled carbon substrate and should be particularly useful when applied to synthetic metabolic pathways that suffer from poor translation efficiency, are present in highly variable copy numbers, and have low turnover for new substrates. Furthermore, this approach represents a generic modeling framework for simultaneously analyzing spatial and stochastic events in cellular metabolism and should enable quantitative evaluation of the effect of enzyme compartmentalization on virtually any recombinant pathway.

Steady-state kinetic behaviour of functioning-dependent structures

A fundamental problem in biochemistry is that of the nature of the coordination between and within metabolic and signalling pathways. It is conceivable that this coordination might be assured by what we term functioning-dependent structures (FDSs), namely those assemblies of proteins that associate with one another when performing tasks and that disassociate when no longer performing them. To investigate a role in coordination for FDSs, we have studied numerically the steady-state kinetics of a model system of two sequential monomeric enzymes, E(1) and E(2). Our calculations show that such FDSs can display kinetic properties that the individual enzymes cannot. These include the full range of basic input/output characteristics found in electronic circuits such as linearity, invariance, pulsing and switching. Hence, FDSs can generate kinetics that might regulate and coordinate metabolism and signalling. Finally, we suggest that the occurrence of terms representative of the assembly and disassembly of FDSs in the classical expression of the density of entropy production are characteristic of living systems.

Regulation of metabolic networks: understanding metabolic complexity in the systems biology era

Metabolism is one of the best recognised networks within biological systems, but our understanding of metabolic regulation has been limited by a failure to consider regulation within the context of the whole network. With recent advances in theoretical aspects of network thinking and a postgenomic landscape in which our ability to quantify molecular changes at a systems level is unsurpassed, the time is ripe for the development of a new level of understanding of the regulation of plant metabolic networks. Theoretical advances such as the formal description of 'scale-free' networks have provided explanations for network behaviour (such as robustness). In parallel, the appreciation of the importance of new levels of the metabolic regulatory hierarchy (such as protein-protein interaction) and the continuing development of global profiling technologies is generating a system-wide molecular data set of increasing resolution. In this review we will argue that the integration of these different aspects of metabolic research will bring about a step change in our understanding of the regulation of metabolic networks in plants.

Enzyme co-localization in pea leaf chloroplasts: glyceraldehyde-3-P dehydrogenase, triose-P isomerase, aldolase and sedoheptulose bisphosphatase

Nearest neighbor analysis of immunocytolocalization experiments indicates that the enzymes glyceraldehyde-3-P dehydrogenase, triose-P isomerase and aldolase are located close to one another in the pea leaf chloroplast stroma, and that aldolase is located close to sedoheptulose bisphosphatase. Direct transfer of the triose phosphates between glyceraldehyde-3-P dehydrogenase and triose-P isomerase, and from glyceraldehyde-3-P dehydrogenase and triose-P isomerase to aldolase, is then a possibility, as is direct transfer of sedoheptulose bisphosphate from aldolase to sedoheptulose bisphosphatase. Spatial organization of these enzymes may be important for efficient CO(2) fixation in photosynthetic organisms. In contrast, there is no indication that fructose bisphosphatase is co-localized with aldolase, and direct transfer of fructose bisphosphate from aldolase to fructose bisphosphatase seems unlikely.

Current status and challenges in connecting models of erythrocyte metabolism to experimental reality

Detailed kinetic models of human erythrocyte metabolism have served to summarize the vast literature and to predict outcomes from laboratory and "Nature's" experiments on this simple cell. Mathematical methods for handling the large array of nonlinear ordinary differential equations that describe the time dependence of this system are well developed, but experimental methods that can guide the evolution of the models are in short supply. NMR spectroscopy is one method that is non-selective with respect to analyte detection but is highly specific with respect to their identification and quantification. Thus time courses of metabolism are readily recorded for easily changed experimental conditions. While the data can be simulated, the systems of equations are too complex to allow solutions of the inverse problem, namely parameter-value estimation for the large number of enzyme and membrane-transport reactions operating in situ as opposed to in vitro. Other complications with the modelling include the dependence of cell volume on time, and the rates of membrane transport processes are often dependent on the membrane potential. These matters are discussed in the light of new modelling strategies.

Discrete event, multi-level simulation of metabolite channeling

Typically differential equations are employed to simulate cellular dynamics. To develop a valid continuous model based on differential equations requires accurate parameter estimations; an accuracy which is often difficult to achieve, due to the lack of data. In addition, processes in metabolic pathways, e.g. metabolite channeling, seem to be of a rather qualitative and discrete nature. With respect to the available data and to the perception of the underlying system, a discrete rather than a continuous approach to modeling and simulation seems more adequate. A discrete approach does not necessarily imply a more abstract view on the system. If we move from macro to micro and multi-level modeling, aspects of subsystems and their interactions, which have been only implicitly represented, become an explicit part of the model. To start exploring discrete event phenomena within metabolite channeling we choose the tryptophan synthase. Based on a continuous macro model, a discrete event, multi-level model is developed which allows us to analyze the interrelation between structural and functional characteristics of the enzymes.

Evolution of cross-feeding in microbial populations

Although limited by a single resource, microbial populations that grow for long periods in continuous culture (chemostat) frequently evolve stable polymorphisms. These polymorphisms may be maintained by cross-feeding, where one strain partially degrades the primary energy resource and excretes an intermediate that is used as an energy resource by a second strain. It is unclear what selective advantage cross-feeding strains have over a single competitor that completely degrades the primary resource. Here we show that cross-feeding may evolve in microbial populations as a consequence of the following optimization principles: the rate of ATP production is maximized, the concentration of enzymes of the pathway is minimized, and the concentration of intermediates of the pathway is minimized.

Mathematical modelling of the urea cycle. A numerical investigation into substrate channelling

Metabolite channelling, the process in which consecutive enzymes have confined substrate transfer in metabolic pathways, has been proposed as a biochemical mechanism that has evolved because it enhances catalytic rates and protects unstable intermediates. Results from experiments on the synthesis of radioactive urea [Cheung, C., Cohen, N.S. & Raijman, L (1989) J. Biol. Chem.264, 4038-4044] have been interpreted as implying channelling of arginine between argininosuccinate lyase and arginase in permeabilized hepatocytes. To investigate this interpretation further, a mathematical model of the urea cycle was written, using Mathematica it simulates time courses of the reactions. The model includes all relevant intermediates, peripheral metabolites, and subcellular compartmentalization. Analysis of the output from the simulations supports the argument for a high degree of, but not absolute, channelling and offers insights for future experiments that could shed more light on the quantitative aspects of this phenomenon in the urea cycle and other pathways.

Biochemical engineering: cues from cells

Engineering principles are used in the exploitation of biocatalysts derived from cells. The purity of reagents, catalysts and maintenance of operation variables are extremely important for bioengineering systems. Any change in the purity of reagents or in operation variables usually leads to a dramatic decrease in productivity. Cellular systems, however, are able to work with relatively high impure conditions and increase their productivity in response to external signals. Thus the seemingly disordered 'bag of juice' or cytoplasm has more order and much higher order of integration than first appears. Learning the semantics of this paradoxical ability of order and integration would help bioengineers to understand and enhance productivity even using impure reagents.

Elastic extension and jump of the flagellar nexin links: a theoretical mechanical cycle

The functions of the nexin links of a flagellar axoneme have not been clearly demonstrated. Taking into account both the elastic (Hookean) characteristics and the possible jump of the nexin links, we calculated the sliding to bending conversion of a theoretical model in a tip-ward direction step by step, according to the essential principles proposed by the geometric clutch hypothesis [Lindemann, 1994: J Theoret Biol 168:175-189]: the activity of the dynein arms depends on the transverse forces induced by the axonemal curvature. In our calculations, however, the transverse forces that are involved in the regulation of the activities of the dynein arms were due to the extension of the nexin links located upstream of a given abscissa. This allowed us to define a bent segment as the axonemal portion at whose proximal and distal ends the nexin links were relaxed, and as fully extended as possible, respectively. The model creates an apparent disorder in the orientation of the nexin links as already observed [Bozkurt and Wooley, 1993: Cell Motil Cytoskeleton 24:109-118; Wooley, 1997: J Cell Sci 110:85-94]. We propose that the nexin links are involved in a mechanical cycle, whose 3 stages are (1) rapid extension, (2) slow relaxation, and (3) stand-by. The rapid extension is compatible with the mechanical interactions between the nexin links and the inner dynein arms with which they form the dynein regulatory complex. This was correlated with the oscillating properties of the nexin links along the axoneme that allow them to be one of the regulatory elements of the local ATPase activity of the dynein arms.

Mechanisms for cytoplasmic organization: an overview

One of the basic characteristics of life is the intrinsic organization of cytoplasm, yet we know surprisingly little about the manner in which cytoplasmic macromolecules are arranged. It is clear that cytoplasm is not the homogeneous "soup" it was once envisioned to be, but a comprehensive model for cytoplasmic organization is not available in modern cell biology. The premise of this volume is that phase separation in cytoplasm may play a role in organization at the subcellular level. Other mechanisms for non-membrane-bounded intracellular organization have previously been proposed. Some of these will be reviewed in this chapter. Multiple mechanisms, involving phase separation, specific intracellular targeting, formation of macromolecular complexes, and channeling, all could well contribute to cytoplasmic organization. Temporal and spatial organization, as well as composition, are likely to be important in defining the characteristics of cytoplasm.

A simple mechanism decreasing free metabolite pool size in static spatial channelling

We propose a simple mechanism which enables decrease of the free pool of channelled metabolite in static spatial channelling, when the concentration of the enzyme consuming the channelled metabolite is greater than the concentration of the enzyme producing this metabolite. Spatial channelling occurs between two enzymes when the common metabolite is released to a small space between these enzymes and does not from a ternary covalent complex with them, as is the case in covalent (dynamic or static) channelling. The mechanism proposed is qualitatively independent of rate constants, metabolite concentrations as well as other kinetic properties and is quantitatively significant for all physiologically relevant conditions. Calculations show that the free metabolite pool must decrease, when the concentration of the enzyme consuming the channelled metabolite is greater than the enzyme producing it. This mechanism is much more effective than increase in the concentration (or rate constant) of the enzyme consuming the metabolite in the absence of spatial channelling.

19F NMR measurements of the rotational mobility of proteins in vivo

Three glycolytic enzymes, hexokinase, phosphoglycerate kinase, and pyruvate kinase, were fluorine labeled in the yeast Saccharomyces cerevisiae by biosynthetic incorporation of 5-fluorotryptophan. 19F NMR longitudinal relaxation time measurements on the labeled enzymes were used to assess their rotational mobility in the intact cell. Comparison with the results obtained from relaxation time measurements of the purified enzymes in vitro and from theoretical calculations showed that two of the labeled enzymes, phosphoglycerate kinase and hexokinase, were tumbling in a cytoplasm that had a viscosity approximately twice that of water. There were no detectable signals from pyruvate kinase in vivo, although it could be detected in diluted cell extracts, indicating that there was some degree of motional restriction of the enzyme in the intact cell.

Why and when channelling can decrease pool size at constant net flux in a simple dynamic channel

Cornish-Bowden and Cárdenas (Cornish-Bowden, A. and Cárdenas M.L. (1993) Eur. J. Biochem. 213, 87-92) have suggested that simulation results peviously published by us (Mendes, P., Kell, D.B. and Westerhoff, H.V. (1992) Eur. J. Biochem. 204, 255-266) which had demonstrated that large reductions of intermediate pool sizes could be accompanied by increasing channel flux in a model metabolic pathway, were an artefact of changes in the pathway's overall flux of the order of 0.0075%, or of inappropriate alterations of enzyme activities. They also asserted to prove that the "channelling of an intermediate cannot affect its free concentration at constant net flux". We consider the co-response of the intermediate metabolite concentration ('pool') and the channel flux to changes in kinetic (or thermodynamic) parameters. Both by analytical proofs and by numerical examples we show that this co-response can be positive, negative or null, depending on the parameter change. In particular, we prove that there is always a number of ways of changing parameters such that the intermediate metabolite concentration decreases with increasing channel flux, whether the total flux varies or is constant. We also show that increased stability of the (dynamic) enzyme-intermediate-enzyme complex, as well as a single parameter change that similarly displays no cross-over effects, can lead to decreased intermediate metabolite concentration and increased channel flux at constant total flux. In general, a non-zero co-response of the intermediate metabolite concentration ('pool') and the channel flux to changes in kinetic (or other) parameters is the rule rather than the exception. More specifically: (i) The algebraic analysis ('general proof') given in Cornish-Bowden and Cárdenas (1993) contains the constraint that the elasticities of various steps to the modulation parameters which were used to vary the channel flux at constant net flux were unity. This is an unfortunate and unnecessary constraint which, when lifted, means that the concentration of the pool in the general case can indeed change at constant net flux. A 'simplified proof' given in Cornish-Bowden and Cárdenas (1993) also fails, due in addition to the consequent failure to include mass conservation relations for some of the enzymes. (ii) In the systems studied by Cornish-Bowden and Cárdenas (1993), flux is properly to be considered as a variable (since it varies during the transition to the steady state), and not a parameter, and as such cannot per se affect the magnitude of other variables in the steady state. (iii) By relaxing the constraint referred to in (i), above, and by making dual modulations (i.e., of more than one parameter at once) which are different from those carried out in Cornish-Bowden and Cárdenas (1993) we find many instances in which channelling (described by a parameter p) does significantly affect the concentration of the pool intermediate C at constant total flux. (iv) In the same pathways, but in which the flux is held constant by setting it via a zero-order flux-generating reaction, the addition of a channel is also able to significantly to modulate the size of the pool at constant total flux. Our results show that the effectiveness of channelling in decreasing a pool, even at constant flux, is very much a reality.

Effect of channelling on the concentration of bulk-phase intermediates as cytosolic proteins become more concentrated

This paper shows that metabolic channelling can provide a mechanism for decreasing the concentration of metabolites in the cytoplasm when cytosolic proteins become more concentrated. A dynamic complex catalysing the direct transfer of an intermediate is compared with the analogous pathway lacking a channel (an "ideal" pathway). In an ideal pathway a proportional increase in protein content does not result in a change in the steady-state concentration of the bulk-phase intermediate, whereas in a channelling pathway the bulk-phase intermediate either decreases or increases depending on the elemental rate constants within the enzyme mechanisms. When the concentration of the enzymes are equal, the pool size decreases with increasing protein concentration if the elemental step depleting the bulk-phase intermediate exerts more control on its concentration than the step supplying the intermediate. Results are illustrated numerically, and a simplified dynamic channel is analysed in which the concentration of the enzyme-enzyme forms. For such a "hit-and-run" channel it is shown that, when the product-releasing step of the enzyme located upstream is close to equilibrium, the pool size decreases as the concentrations of the enzymes increase in proportion, regardless of the rate, equilibrium constants and concentration ratios of the two sequential enzymes.

Elusive control

The concept of a single rate-limiting step was proven to be too simplistic for understanding control and regulation of metabolism. Consequently, searches have identified relatively few steps with high control. Here we review a number of such searches and indicate what mechanisms may be responsible for this elusiveness of control. It turns out that this elusiveness of control has itself led to increased understanding of the roles played in metabolic control and regulation of such diverse factors as distributiveness of control, condition dependence, enzyme elasticity, homeostasis, control hierarchies, the input into a pathway, coenzyme sequestration, and redundancy and diversity of control function.

The molecular biology of multidomain proteins. Selected examples

The aim of this review is to give an overview of the contribution molecular biology can make to an understanding of the functions and interactions within multidomain proteins. The contemporary advantages ascribed to multidomain proteins include (a) the potential for metabolite channelling and the protection of unstable intermediates; (b) the potential for interactions between domains catalysing sequential steps in a metabolic pathway, thereby giving the potential for allosteric interactions; and (c) the facility to produce enzymic activities in a fixed stoichiometric ratio. The alleged advantages in (a) and (b) however apply equally well to multi-enzyme complexes; therefore, specific examples of these phenomena are examined in multidomain proteins to determine whether the proposed advantages are apparent. Some transcription-regulating proteins active in the control of metabolic pathways are composed of multiple domains and their control is exerted and modulated at the molecular level by protein-DNA, protein-protein and protein-metabolite interactions. These complex recognition events place strong constraints upon the proteins involved, requiring the recognition of and interaction with different classes of cellular metabolites and macromolecules. Specific examples of transcription-regulating proteins are examined to probe how their multidomain nature facilitates a general solution to the problem of multiple recognition events. A general unifying theme that emerges from these case studies is that a basic unitary design of modules provided by enzymes is exploited to produce multidomain proteins by a complex series of gene duplication and fusion events. Successful modules provided by enzymes are co-opted to new function by selection apparently acting upon duplicated copies of the genes encoding the enzymes. In multidomain transcription-regulating proteins, former enzyme modules can be recruited as molecular sensors that facilitate presumed allosteric interactions necessary for the molecular control of transcription.

Control in channelled pathways. A matrix method calculating the enzyme control coefficients

The usual equations expressing the enzyme control coefficients (quantitative indicators of 'global' control properties of a pathway) via the elasticity coefficients (reflecting local kinetic properties of an enzyme reaction), cannot be applied to a variety of 'non-ideal' pathways, in particular to pathways with metabolic channelling. Here we show that the relationship between the control and elasticity coefficients can be obtained by considering such a metabolic pathway as a network of elemental chemical conversions (steps). To calculate the control coefficients of enzymes one should first determine the elasticity coefficients of such elemental steps and then take their appropriate combinations. Although the method is illustrated for a channelled pathway it can be used for any non-ideal pathway including those with high enzyme concentrations where the sequestration of metabolites by enzymes cannot be neglected.

Metabolic channeling versus free diffusion: transition-time analysis

Metabolic channeling is the term used to describe the restricted flow of substrates and products in multienzyme systems. It has been argued for some time that free diffusion is sufficiently rapid to obviate the need for channeling and, furthermore, that it is also fast enough to prevent competing side reactions from interfering with the metabolic flow. In this article we argue that a thorough consideration of the temporal behavior of metabolite pools suggests that channeling is important in many cases.

Enzyme-enzyme interactions and metabolite channelling: alternative mechanisms and their evolutionary significance

Metabolite channelling may result from different kinetic mechanisms in which enzyme-enzyme interactions occur, so that intermediates are not released into the bulk solution and cannot be used by enzymes outside the channel. From an evolutionary point of view, the emergence of such mechanisms may provide new functional possibilities for the system, which would result in a selective advantage. Hence, it would be useful to evaluate the objective advantages provided by the various options by considering different criteria for functional effectiveness. Following this strategy, the goal of this paper is to compare a model for a free-diffusion two-enzyme system with two different models with inclusion of enzyme-enzyme interactions. In addition, models with simultaneous free and interacting branches are also analysed, and their advantages or disadvantages are presented. Basic guidelines are suggested that help in predicting the occurrence of specific mechanisms in different circumstances, and provide theoretical evidence in support of the hypothesis that no single solution simultaneously optimizes all the possible desired properties of the system.

Structural and functional properties of a multi-enzyme complex from spinach chloroplasts. 2. Modulation of the kinetic properties of enzymes in the aggregated state

The carboxylase activity of free ribulose 1,5-bisphosphate carboxylase-oxygenase has been compared to that of the five-enzyme complex present in chloroplasts. Kinetic results have shown that the V/active site is lower for the free enzyme than for the complex. Conversely the Km is smaller for the complex than for the free enzyme. This implies that the catalytic activity of the enzyme is enhanced when it is embedded in the complex. Under reducing conditions and in the presence of reduced thioredoxin, inactive oxidized phosphoribulokinase, free in solution or inserted in the multi-enzyme complex, becomes active. The kinetics of this activation process has been studied and shown to be exponential. The time constant of this exponential decreases, for the free enzyme, as thioredoxin concentration is increased. Alternatively, for the enzyme embedded in the complex, this time constant increases with thioredoxin concentration almost in a linear fashion. This implies that the complex is much more rapidly activated by reduced thioredoxin than is the free phosphoribulokinase. The variation of the amplitude of this activation process as a function of thioredoxin concentration is a hyperbola. The concentration of thioredoxin which results in half the asymptotic value of this hyperbola is smaller for the complex than for the free enzyme. A kinetic model has been proposed and the dynamic equations resulting from this model have been derived. They fit the experimental results exactly. From the variation of the amplitude of the activation process one may derive the binding constants of thioredoxin on either the oxidized enzyme or on a partly dithiothreitol-reduced enzyme (both of them free or inserted in the complex). In either case, the affinity of reduced thioredoxin is larger for the complex than for the free enzyme. The individual values of some of the rate constants have also been estimated from the variation of the time constants as a function of thioredoxin concentration. Taken together, these results show that at least two enzymes, ribulose 1,5-bisphosphate carboxylase-oxygenase and phosphoribulokinase, have quite different kinetic properties depending on whether they are in free solution or embedded in the multi-enzyme complex.

Channelling can affect concentrations of metabolic intermediates at constant net flux: artefact or reality?

We show that if a metabolic intermediate is directly transferred ('channelled') from an enzyme that catalyses its production to another that uses it as substrate, there is no change in its free concentration compared with a system with the same net flux in which there is no direct transfer. Thus the widespread idea that channelling provides a mechanism for decreasing metabolite concentrations at constant flux is false. Results from computer simulation that suggest otherwise [Mendes, P., Kell, D. B. & Westerhoff, H. V. (1992) Eur. J. Biochem. 204, 257-266] are artefacts either of variations in flux or of alterations in opposite directions of the activities of the relevant enzymes.