The responses of rat hepatocytes to glucagon and adrenaline. Application of quantified elasticity analysis.

The internal control of hepatocyte metabolism has been previously analysed using metabolic control analysis. The aim of this paper is to extend this analysis to include the responses of the cells to hormonal stimulus. Hepatocyte metabolism was divided into nine reaction blocks: glycogen breakdown, glucose release, glycolysis, lactate production, NADH oxidation, pyruvate oxidation, proton leak, mitochondrial phosphorylation and ATP consumption, linked by five intermediates: mitochondrial membrane potential, cytoplasmic NADH/NAD and total cellular ATP, glucose 6-phosphate and pyruvate. The kinetic responses of the reaction blocks to the intermediates were determined previously in the absence of added hormones. In this study, the changes in flux and intermediate levels that occurred upon addition of either glucagon or adrenaline were measured. From comparison of the fractional changes in fluxes and intermediate levels with the known kinetics of the system, it was possible to determine the primary sites of action of the hormones. The results show that the majority of processes in the cell are responsive to the hormones. The notable exception to this is the failure of adrenaline to have a direct effect on glycolysis. The activity change of each metabolic block observed in the presence of either hormone was quantified and compared to the indirect effects on each block caused by changes in metabolite levels. The second stage of the analysis was to use the calculated activity changes and the known control pattern of the system to give a semiquantitative analysis of the regulatory pathways employed by the hormones to achieve the changes in fluxes and metabolite levels. This was instructive in analysing, for example, how glucagon caused a decrease in flux through glycolysis and an increase in oxidative phosphorylation without large changes in metabolite levels (homeostasis). Conversely, it could be seen that the failure of adrenaline to maintain a constant glucose 6-phosphate concentration was due to the stimulation of glycogen breakdown and inhibition of glucose release.     

Internal regulation of ATP turnover, glycolysis and oxidative phosphorylation in rat hepatocytes.

Previously [Ainscow, E.K. & Brand, M.D. (1999) Eur. J. Biochem. 263, 671-685], top-down control analysis was used to describe the control pattern of energy metabolism in rat hepatocytes. The system was divided into nine reaction blocks (glycogen breakdown, glucose release, glycolysis, lactate production, NADH oxidation, pyruvate oxidation, mitochondrial proton leak, mitochondrial phosphorylation and ATP consumption) linked by five intermediates (intracellular glucose 6-phosphate, pyruvate and ATP levels, cytoplasmic NADH/NAD ratio and mitochondrial membrane potential). The kinetic responses (elasticities) of reaction blocks to intermediates were determined and used to calculate control coefficients. In the present paper, these elasticities and control coefficients are used to quantify the internal regulatory pathways within the cell. Flux control coefficients were partitioned to give partial flux control coefficients. These describe how strongly one block of reactions controls the flux through another via its effects on the concentration of a particular intermediate. Most flux control coefficients were the sum of positive and negative partial effects acting through different intermediates; these partial effects could be large compared to the final control strength. An important result was the breakdown of the way ATP consumption controlled respiration: changes in ATP level were more important than changes in mitochondrial membrane potential in stimulating oxygen consumption when ATP consumption increased. The partial internal response coefficients to changes in each intermediate were also calculated; they describe how steady state concentrations of intermediates are maintained. Increases in mitochondrial membrane potential were opposed mostly by decreased supply, whereas increases in glucose-6-phosphate, NADH/NAD and pyruvate were opposed mostly by increased consumption. Increases in ATP were opposed significantly by both decreased supply and increased consumption.     

Quantifying elasticity analysis: how external effectors cause changes to metabolic systems

The sites of action of external effectors, such as inhibitors or hormones, on metabolic systems can be described qualitatively by elasticity analysis, or quantitatively by regulation analysis. The use of the latter approach has been limited, due to its practical complexity. In this study, we report mathematical relationships that relate the finite changes in system variables (fluxes and metabolite concentrations) to changes in activity of metabolic processes brought about by a single step addition of an effector. The activation or inhibition of a process by an effector is measured from changes in flux and intermediate levels. The changes in activity of each process can be used to describe, semi-quantitatively, which activations or inhibitions of the system processes are important in bringing about the observed levels of system variables.     

Metabolic regulation: A control analytic perspective

A possible basis for a quantitative theory of metabolic regulation is outlined. Regulation is defined here as the alteration of reaction properties to augment or counteract the mass-action trend in a network reactions. In living systems the enzymes that catalyze these reactions are the handles through which such alteration is effected. It is shown how the elasticity coefficients of an enzyme-catalyzed reaction with respect to substrates and products are the sum of a massaction term and a regulatory kinetic term; these coefficients therefore distinguish between massaction effects and regulatory effects and are recognized as the key to quantifying regulation. As elasticity coefficients are also basic ingredients of metabolic control analysis, it is possible to relate regulation to such concepts as control, signalling, stability, and homeostasis. The need for care in the choice of relative or absolute changes when considering questions of metabolic regulation is stressed. Although the concepts are illustrated in terms of a simple coupled reaction system, they apply equally to more complex systems. When such systems are divided into reaction blocks, co-response coefficients can be used to measure the elasticities of these blocks.I dedicate this paper to Henrik Kacser, co-founder of and guiding light in the field of metabolic control analysis. His recent death leaves us bereft of a fount of wisdom and kindness, but his work remains as a monument along the path of our search for an understanding of metabolic behavior.     

Characterization of a quaternary-structured folding intermediate of an antibody Fab-fragment.

Antibody folding is a complex process comprising folding and association reactions. Although it is usually difficult to characterize kinetic folding intermediates, in the case of the antibody Fab fragment, domain-domain interactions lead to a rate-limiting step of folding, thus accumulating folding intermediates at a late step of folding. Here, we analyzed a late folding intermediate of the Fab fragment of the monoclonal antibody MAK 33 from mouse (kappa/IgG1). As a strategy for accumulation of this intermediate we used partial denaturation of the native Fab by guanidinium chloride. This denaturation intermediate, which can be populated to about 90%, is indistinguishable from a late-folding intermediate with respect to denaturation and renaturation kinetics. The spectroscopic analysis reveals a native-like secondary structure of this intermediate with aromatic side chains only slightly more solvent exposed than in the native state. The respective partner domains are weekly associated. From these data we conclude that the intramolecular association of the two chains during folding, with all domains in a native-like structure, follows a two-step mechanism. In this mechanism, presumably hydrophobic interactions are followed by rearrangements leading to the exact complementarity of the contact sites of the respective domains.     

The control of source to sink carbon flux during tuber development in potato

We have used top-down metabolic control analysis to investigate the control of carbon flux through potato (Solanum tuberosum) plants during tuberisation. The metabolism of the potato plant was divided into two blocks of reactions (the source and sink blocks) that communicate through the leaf apoplastic sucrose pool. Flux was measured as the transfer of ¹⁴C from CO₂ to the tuber. Flux and apoplastic sucrose concentration were varied either by changing the light intensity or using transgenic manipulations that specifically affect the source or sink blocks, and elasticity coefficients were measured. We have provided evidence in support of our assumption that apoplastic sucrose is the only communicating metabolite between the source and sink blocks. The elasticity coefficients were used to calculate the flux control coefficients of the source and sink blocks, which were 0.8 and 0.2, respectively. This work suggests that the best strategy for the manipulation of tuber yield in potato will involve increases in photosynthetic capacity, rather than sink metabolism.     

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric,thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.     

Metabolic control analysis of developing oilseed rape (Brassica napus cv Westar) embryos shows that lipid assembly exerts significant control over oil accumulation

? Metabolic control analysis allows the study of metabolic regulation. We applied both single- and double-manipulation top-down control analysis to examine the control of lipid accumulation in developing oilseed rape (Brassica napus) embryos. ? The biosynthetic pathway was conceptually divided into two blocks of reactions (fatty acid biosynthesis (Block A), lipid assembly (Block B)) connected by a single system intermediate, the acyl-coenzyme A (acyl-CoA) pool. Single manipulation used exogenous oleate. Triclosan was used to inhibit specifically Block A, whereas diazepam selectively manipulated flux through Block B. ? Exogenous oleate inhibited the radiolabelling of fatty acids from [1-(14) C]acetate, but stimulated that from [U-(14) C]glycerol into acyl lipids. The calculation of group flux control coefficients showed that c. 70% of the metabolic control was in the lipid assembly block of reactions. Monte Carlo simulations gave an estimation of the error of the resulting group flux control coefficients as 0.27?±?0.06 for Block A and 0.73?±?0.06 for Block B. ? The two methods of control analysis gave very similar results and showed that Block B reactions were more important under our conditions. This contrasts notably with data from oil palm or olive fruit cultures and is important for efforts to increase oilseed rape lipid yields.     

Development of a kinetic metabolic model: application to Catharanthus roseus hairy root

A kinetic metabolic model describing Catharanthus roseus hairy root growth and nutrition was developed. The metabolic network includes glycolysis, pentose-phosphate pathway, TCA cycle and the catabolic reactions leading to cell building blocks such as amino acids, organic acids, organic phosphates, lipids and structural hexoses. The central primary metabolic network was taken at pseudo-steady state and metabolic flux analysis technique allowed reducing from 31 metabolic fluxes to 20 independent pathways. Hairy root specific growth rate was described as a function of intracellular concentration in cell building blocks. Intracellular transport and accumulation kinetics for major nutrients were included. The model uses intracellular nutrients as well as energy shuttles to describe metabolic regulation. Model calibration was performed using experimental data obtained from batch and medium exchange liquid cultures of C. roseus hairy root using a minimal medium in Petri dish. The model is efficient in estimating the growth rate.     

Kinetic competence of enzymic intermediates: fact or fiction?

A number of enzymatic reactions involve intermediates that are not normally released during the reaction. Whether such an intermediate when added to the enzyme reacts as fast or faster than the normal substrates, and thus is "kinetically competent", depends on the degree to which the equilibrium constant for forming the intermediate from the substrates is different on the enzyme surface and in solution, as well as on the relative affinities of the enzyme for substrate and intermediate. Similar values for these equilibrium constants require that the intermediate react slowly, while a far more favorable value for intermediate formation on the enzyme allows the intermediate to react at up to the diffusion-limiting rate. When one intermediate is formed from two substrates, it may react much more rapidly than when two intermediates are formed from two substrates, or one from one. Comparison of the kinetics of the putative intermediate(s) and the substrate(s) can reveal a great deal about the mechanism of the catalytic reaction and the kinetic barrier that normally keeps the intermediate(s) on the enzyme.     

Characterization of kinetic folding intermediates of recombinant canine milk lysozyme by stopped-flow circular dichroism

The intermediate in the equilibrium unfolding of canine milk lysozyme induced by a denaturant is known to be very stable with characteristics of the molten globule state. Furthermore, there are at least two kinetic intermediates during refolding of this protein: a burst-phase (first) intermediate formed within the dead time of stopped-flow measurements and a second intermediate that accumulates with a rate constant of 22 s(-)(1). To clarify the relationships of these intermediates with the equilibrium intermediate, and also to characterize the structural changes of the protein during refolding, here we studied the kinetic refolding reactions using stopped-flow circular dichroism at 10 different wavelengths and obtained the circular dichroism spectra of the intermediates. Comparison of the circular dichroism spectra of the intermediates, as well as the absence of observed kinetics in the refolding from the fully unfolded state to the equilibrium intermediate, has demonstrated that the burst-phase intermediate is equivalent to the equilibrium intermediate. The difference circular dichroism spectrum that represented changes from the kinetic intermediate to the native state had characteristics of an exciton coupling band, indicating that specific packing of tryptophan residues in this protein occurred in this phase. From these findings, we propose a schematic model of the refolding of canine milk lysozyme that is consistent with the hierarchical mechanism of protein folding.     

Kinetic analysis of the mechanism for subtilisin in essentially anhydrous organic solvents

Steady-state kinetic analysis has been used to confirm the catalytic mechanism of lyophilized subtilisin suspended in a variety of organic solvents. Specifically, this article demonstrates that partial reactions can occur between subtilisin and ester substrates in organic solvents. Partitioning of common intermediates between competing acceptors at a constant ratio of products has also been described. The decomposition of a common intermediate formed from different substrates at the same rate is also further evidence of an acyl-enzyme mechanism for subtilisin suspended in anhydrous solvents. Partitioning of a common intermediate to give two products at a constant total rate, and saturation kinetics at varying substrate concentrations, complete a kinetic investigation of the enzyme mechanism. All the data generated support the formation of a stable acyl enzyme during the transesterification reaction catalzyed by subtilisin in the solvents used.     

A reaction landscape identifies the intermediates critical for self-assembly of virus capsids and other polyhedral structures

The capsids of spherical viruses may contain from tens to hundreds of copies of the capsid protein(s). Despite their complexity, these particles assemble rapidly and with high fidelity. Subunit and capsid represent unique end states. However, the number of intermediate states in these reactions can be enormous-a situation analogous to the protein folding problem. Approaches to accurately model capsid assembly are still in their infancy. In this paper, we describe a sail-shaped reaction landscape, defined by the number of subunits in each species, the predicted prevalence of each species, and species stability. Prevalence can be calculated from the probability of synthesis of a given intermediate and correlates well with the appearance of intermediates in kinetics simulations. In these landscapes, we find that only those intermediates along the leading edge make a significant contribution to assembly. Although the total number of intermediates grows exponentially with capsid size, the number of leading-edge intermediates grows at a much slower rate. This result suggests that only a minute fraction of intermediates needs to be considered when describing capsid assembly.     

Measurements of cysteine reactivity during protein unfolding suggest the presence of competing pathways

Evidence that proteins may unfold utilizing complex competing pathways comes from a new pulse-labeling protocol in which the change in reactivity of a single cysteine residue in a protein during unfolding is measured, making use of its easily monitored reaction with the Ellman reagent, dithionitrobenzoic acid. The kinetics of unfolding of two single cysteine-containing mutant forms of the small protein barstar, C82A, which contains only Cys40, and C40A, which contains only Cys82, have been studied. The data suggest that unfolding occurs via two parallel pathways, each forming competing intermediates. In one of these early intermediates, Cys40 and Cys82 are already as reactive as they are in the fully unfolded protein, while in the other intermediate, the Cys thiol groups are unreactive. One more long-lived intermediate also needs to be included on the pathway defined by the early intermediate with unreactive Cys thiol groups to account for the difference in the rates of fluorescence change and of change in Cys40 reactivity. The demonstration of multiple intermediates and pathways for unfolding indicates that protein unfolding reactions can be as complex as protein folding reactions.     

Control of molecular transformations in polyenzyme systems: quantitative theory of the regulation of metabolism

An attempt of a comprehensive treatment of the theory of metabolic control is presented. The introductory section giving an outline of the early development of the theory, is followed by definitions quantifying the control in the metabolic system. By means of the perturbation method the complete system of equations is obtained which allows one to express all the enzyme control coefficients ("global" coefficients) through the elasticity coefficients characterizing kinetic properties of individual enzymes ("local" coefficients) and through the steady-state values of metabolic fluxes and concentrations. It is shown how connectivity relations between global and local coefficients should be modified when conserved sums of intermediates are present in the system. A new theorem is derived, it allows one to express the global response of the system to any change in the external parameter (such as external effector concentration, or temperature, pH, ionic strength, ets.) through the control coefficients and local responses of individual reaction steps. Explicit formulas are derived for response coefficients of the fluxes and concentrations to changes in the conserved sums of intermediates, which express the values of these global coefficients through the control and elasticity coefficients of enzymes and steady-state pools. The results obtained comprise as a special case all the results published so far in the literature.     

Diffusion-collision model study of misfolding in a four-helix bundle protein.

Proteins with complex folding kinetics will be susceptible to misfolding at some stage in the folding process. We simulate this problem by using the diffusion-collision model to study non-native kinetic intermediate misfolding in a four-helix bundle protein. We find a limit on the size of the pairwise hydrophobic area loss in non-native intermediates, such that burying above this limit creates long-lasting non-native kinetic intermediates that would disrupt folding and prevent formation of the native state. Our study of misfolding suggests a method for limiting the production of misfolded kinetic intermediates for helical proteins and could, perhaps, lead to more efficient production of proteins in bulk.     

How reproducible are flow cytometry data from paraffin-embedded blocks?

The purpose of this technical report is to determine the reproducibility of flow cytometry data for ploidy and cell cycle kinetics using paraffin-embedded blocks of breast cancer tissue. One block from each of 39 tumors was studied in this report with each block having multiple sections analyzed independently. All of these sections gave ploidy analyses, while only 34 gave cell kinetic values. The standard deviation for the DNA index value in the multiple analysis study was less than 0.1 in all but three cases. The cell kinetic values gave larger variability, and the actual values were dependent on the method of analysis. Comparison of the variability for each method of analysis could not predict which procedure was superior. These results would indicate that ploidy is a reproducible value, while cell kinetic parameters should only be used as an indicator of proliferative activity that has been normalized to the mean or median of a large set of observations processed and analyzed by the same procedure.