From in silico to in spectro kinetics of respiratory complex I

An enzyme's activity is the consequence of its structure. The stochastic approach we developed to study the functioning of the respiratory complexes is based upon their 3D structure and their physical and chemical properties. Consequently it should predict their kinetic properties. In this paper we compare the predictions of our stochastic model derived for the complex I with a number of experiments performed with a large range of complex I substrates and products. A good fit was found between the experiments and the prediction of our stochastic approach. We show that, due to the spatial separation of the two half redox reactions (NADH/NAD and Q/QH(2)), the kinetics cannot necessarily obey a simple mechanism (ordered or ping-pong for instance). A plateau in the kinetics is observed at high substrates concentrations, well evidenced in the double reciprocal plots, which is explained by the limiting rate of quinone reduction as compared with the oxidation of NADH at the other end of complex I. Moreover, we show that the set of the seven redox reactions in between the two half redox reactions (NADH/NAD and Q/QH(2)) acts as an electron buffer. An inhibition of complex I activity by quinone is observed at high concentration of this molecule, which cannot be explained by a simple stochastic model based on the known structure. We hypothesize that the distance between the catalytic site close to N2 (iron/sulfur redox center that transfers electrons to quinone) and the membrane forces the quinone/quinol to take several positions in between these sites. We represent these possible positions by an extra site necessarily occupied by the quinone/quinol molecules on their way to the redox site. With this hypothesis, we are able to fit the kinetic experiments over a large range of substrates and products concentrations. The slow rate constants derived for the transition between the two sites could be an indication of a conformational change of the enzyme during the quinone/quinol movement. This article is part of a Special Issue entitled: 17th European Bioenergetics Conference (EBEC 2012).     

Dynamics of granzyme B-induced apoptosis: mathematical modeling

Apoptosis is mediated by an intracellular biochemical system that mainly includes proteins (procaspases, caspases, inhibitors, Bcl-2 protein family as well as substances released from mitochondrial intermembrane space). The dynamics of caspase activation and target cleavage in apoptosis induced by granzyme B in a single K562 cell was studied using a mathematical model of the dynamics of granzyme B-induced apoptosis developed in this work. Also the first application of optimization approach to determination of unknown kinetic constants of biochemical apoptotic reactions was presented. The optimization approach involves solving of two problems: direct and inverse. Solving the direct optimization problem, we obtain the initial (baseline) concentrations of procaspases for known kinetic constants through conditional minimization of a cost function based on the principle of minimum protein consumption by the apoptosis system. The inverse optimization problem is aimed at determination of unknown kinetic constants of apoptotic biochemical reactions proceeding from the condition that the optimal concentrations of procaspases resulting from the solution of the direct optimization problem coincide with the observed ones, that is, those determined by biochemical methods. The Multidimensional Index Method was used to perform numerical solution of the inverse optimization problem.     

The regulation of the interaction between F-actin and muscle fructose 1,6-bisphosphatase

Interaction between rabbit muscle fructose 1,6-bisphosphatase (FBPase) and rabbit muscle F-actin results in heterologous complex formation [A. Gizak, D. Rakus, A. Dzugaj, Histol. Histopathol. 18 (2003) 135]. Calculated on the basis of co-sedimentation-binding experiments and ELISA assay-binding constant (Ka) revealed that FBPase binds to F-actin with Ka equal to 7.4 x 10(4) M(-1). The binding is down-regulated by ligands interacting with the FBPase active site (fructose 6-phosphate, fructose 1,6-bisphosphate, fructose 2,6-bisphosphate) and with the FBPase allosteric inhibitory site (AMP). The binding and the kinetic data suggests that FBPase may bind F-actin using a bipartite motif which includes the amino acids residues involved in the binding of the substrate as well as of the allosteric inhibitor of the enzyme. The in situ co-localization experiment, in which FBPase was diffused into skinned muscle fibres pre-incubated with phalloidin (polymeric actin-interacting toxin), has shown that FBPase binds predominantly to the region of the Z-line.     

Über Automatenmodelle in der statistischen Lerntheorie

Summary Following up Feichtinger (1968b), an automaton-theoretic interpretation of the N-element stimulus sampling model with two response classes is given. Finite stochastic automata are used and in particular investigated relative to the limit behavior. Moreover the conception of abstract automata as generators for stochastic processes is suggested. This approach is suitable to supply exact and formal models for different empirical fields of knowledges.     

Binding features of chloroplast fructose-1,6-bisphosphatase-thioredoxin interaction

It has been proposed that a hydrophobic groove surrounded by positively charged amino acids on thioredoxin (Trx) serves as the recognition and docking site for the interaction of Trx with target proteins. This model for Trx-protein interactions fits well with the Trx-mediated fructose-1,6-bisphosphatase (FBPase) activation, where a protruding negatively charged loop of FBPase would bind to this Trx groove, in a process involving both electrostatic and hydrophobic interactions. This model facilitates the prediction of Trx amino acid residues likely to be involved in enzyme binding. Site-directed mutagenesis of some of these amino acids, in conjunction with measurements of the FBPase activation capacity of the wild type and mutated Trxs, was used to check the model and provided evidence that lysine-70 and arginine-74 of pea Trx m play an essential role in FBPase binding. The binding parameters for the interaction between chloroplast FBPase and the wild type pea Trxs f and m, as well as mutated pea Trx m, determined by equilibrium dialysis in accordance with the Koshland-Nemethy-Filmer model of saturation kinetics, provided additional support for the role of these basic Trx residues in the interaction with FBPase. These data, in conjunction with the midpoint redox potential (E(m)) determinations of Trxs, support the hydrophobic groove model for the interaction between chloroplast FBPase and Trx. This model predicts that differences in the FBPase activation capacity of Trxs arise from their different binding abilities.     

Use of peptide antibodies to probe for the mitoxantrone resistance-associated protein MXR/BCRP/ABCP/ABCG2

Previous kinetic characterization of Escherichia coli fructose 1,6-bisphosphatase (FBPase) was performed on enzyme with an estimated purity of only 50%. Contradictory kinetic properties of the partially purified E. coli FBPase have been reported in regard to AMP cooperativity and inactivation by fructose-2,6-bisphosphate. In this investigation, a new purification for E. coli FBPase has been devised yielding enzyme with purity levels as high as 98%. This highly purified E. coli FBPase was characterized and the data compared to that for the pig kidney enzyme. Also, a homology model was created based upon the known three-dimensional structure of the pig kidney enzyme. The kcat of the E. coli FBPase was 14.6 s(-1) as compared to 21 s(-1) for the pig kidney enzyme, while the K(m) of the E. coli enzyme was approximately 10-fold higher than that of the pig kidney enzyme. The concentration of Mg2+ required to bring E. coli FBPase to half maximal activity was estimated to be 0.62 mM Mg2+, which is twice that required for the pig kidney enzyme. Unlike the pig kidney enzyme, the Mg2+ activation of the E. coli FBPase is not cooperative. AMP inhibition of mammalian FBPases is cooperative with a Hill coefficient of 2; however, the E. coli FBPase displays no cooperativity. Although cooperativity is not observed, the E. coli and pig kidney enzymes show similar AMP affinity. The quaternary structure of the E. coli enzyme is tetrameric, although higher molecular mass aggregates were also observed. The homology model of the E. coli enzyme indicated slight variations in the ligand-binding pockets compared to the pig kidney enzyme. The homology model of the E. coli enzyme also identified significant changes in the interfaces between the subunits, indicating possible changes in the path of communication of the allosteric signal.     

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary reaction functions are derived by applying the quasi-steady-state approximation (QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems. In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA, developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation. To facilitate the framework, we provide a user-friendly open-source computational package, ASSISTER, that automatically performs the present framework.     

Amino acid sequence of spinach chloroplast fructose-1,6-bisphosphatase

The amino acid sequence of the spinach chloroplast fructose-1,6-bisphosphatase (FBPase) subunit has been determined. Placement of the 358 residues in the polypeptide chain was based on automated Edman degradation of the intact protein and of peptides obtained by enzymatic or chemical cleavage. The sequence of spinach chloroplast FBPase shows clear homology (ca. 40%) to gluconeogenic (mammalian, yeast, and Escherichia coli) fructose-1,6-bisphosphatases and 80% homology with the wheat chloroplast enzyme. The two chloroplast enzymes show near the middle of the structure a unique sequence insert probably involved in light-dependent regulation of the chloroplast FBPase enzyme activity. This sequence insert contains two cysteines separated by only 4 amino acid residues, a characteristic feature of some enzymes containing redox-active cysteines. The recent X-ray crystallographic resolution of pig kidney FBPase (H. Ke, C. M. Thorpe, B. A. Seaton, F. Marcus, and W. N. Lipscomb, 1989, Proc. Natl. Acad. Sci. USA 86, 1475-1479) has allowed the discussion of the amino acid sequence of spinach chloroplast FBPase in structural terms. It is to be noted that most of pig kidney FBPase residues shown to be either at (or close to) the sugar bisphosphate binding site or located at the negatively charged metal binding pocket are conserved in the chloroplast enzyme. The unique chloroplast FBPase insert presumably involved in light-dependent activation of the enzyme via a thioredoxin-linked mechanism can be accommodated in the surface of the FBPase molecule.     

Magnetic field perturbations as a tool for controlling enzyme-regulated and oscillatory biochemical reactions

The feasibility of magnetic field perturbations as a tool for controlling enzyme-regulated and oscillatory biochemical reactions is studied. Our approach is based on recent experimental results that revealed magnetic field effects on the in vitro activity of enzyme systems in accordance with the radical pair mechanism. A minimum model consisting of two coupled enzyme-regulated reactions is discussed that combines, in a self-consistent manner, magnetic field-sensitive enzyme kinetics with non-linear dynamical principles. Furthermore, a simple detector mechanism is described that is capable of responding to an oscillatory input. Results reveal that moderate-strength magnetic fields (B=1-100 mT) may effectively alter the dynamics of the system. In particular, a response behavior is observed that depends on: (1) the combination of static and time-varying magnetic fields; (2) the field amplitude; and (3) the field frequency in a non-linear fashion. The specific response behavior is critically determined by the biochemical boundary conditions as defined by the kinetic properties of the system. We propose an experimental implementation of the results based on the oscillatory peroxidase-oxidase reaction controlled by the enzyme horseradish peroxidase.     

Affinity labeling of the allosteric site of fructose 1,6-bisphosphatase with an AMP analog

D-Fructose 1,6-bisphosphatase [EC 3.1.3.11, FBPase] is one of the key enzymes in glyconeogenesis and its activity is controlled by various effectors such as substrate, AMP and ATP. To analyze this complex regulation system, we tried an affinity labeling of FBPase with an AMP derivative, since AMP is a potent allosteric inhibitor of this enzyme. The results obtained are as follows. 1. To determine the functional groups which are essential for AMP as an inhibitor, inhibitory activities of some AMP derivatives were examined. These derivatives modified at the purine ring or phosphate group lost the activity while one modified at the ribose ring retained the ability to inhibit FBPase. This shows that an affinity labeling reagent should be an AMP derivative in which the ribose ring is modified. 2. 2',3'-Dialdehyde AMP (dial-AMP) was prepared by periodate oxidation of AMP and was reacted with FBPase. Under appropriate conditions, 1 mol of the reagent was incorporated per mol of enzyme subunit with a concomitant loss of enzyme activity. The reaction was prevented by the presence of AMP but not of ATP. The heat-stability, the kinetic parameters and the UV-absorption spectrum of the modified enzyme were all the same as those of native FBPase in the presence of AMP. Thus it was concluded that the allosteric AMP site in FBPase was modified specifically.     

Binding site on pea chloroplast fructose-1,6-bisphosphatase involved in the interaction with thioredoxin

When we compare the primary structures of the six chloroplast fructose-1,6-bisphosphatases (FBPase) so far sequenced, the existence of a poorly conserved fragment in the region just preceding the redox regulatory cysteines cluster can be observed. This region is a good candidate for binding of FBPase to its physiological modulator thioredoxin (Td), as this association shows clear differences between species. Using a cDNA clone for pea chloroplast FBPase as template, we have amplified by PCR a DNA insert coding for a 19 amino acid fragment (¹⁴⁹Pro-¹⁶⁷Gly), which was expressed in pGEMEX-1 as a fusion protein. This protein strongly interacts with pea Td m, as shown by ELISA and Superose 12 gel filtration, depending on pH of the medium. Preliminary assays have shown inhibition of FBPase activity in the presence of specific IgG against the 19 amino acid insert. Surprisingly the fusion protein enhances the FBPase activation in competitive inhibition experiments carried out with FBPase and Td. These results show the fundamental role played by this domain in FBPase-Td binding, not only as docking point for Td, but also by inducing some structural modification in the Td molecule. Taking as model the structural data recently published for spinach photosynthetic FBPase [29], this sequence from a tertiary and quaternary structural point of view appears available for rearrangement.     

Dynamical properties of Discrete Reaction Networks

Reaction networks are commonly used to model the dynamics of populations subject to transformations that follow an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs). DRNs can be seen as modeling the underlying discrete nondeterministic transitions of stochastic models of reaction networks. In that sense, a proof of non-reachability in a given DRN has immediate implications for any concrete stochastic model based on that DRN, independent of the choice of kinetic laws and constants. Moreover, if we assume that stochastic kinetic rates are given by the mass-action law (or any other kinetic law that gives non-vanishing probability to each reaction if the required number of interacting substrates is present), then reachability properties are equivalent in the two settings. The analysis of two types of global dynamical properties of DRNs is addressed: irreducibility, i.e., the ability to reach any discrete state from any other state; and recurrence, i.e., the ability to return to any initial state. Our results consider both the verification of such properties when species are present in a large copy number, and in the general case. The necessary and sufficient conditions obtained involve algebraic conditions on the network reactions which in most cases can be verified using linear programming. Finally, the relationship of DRN irreducibility and recurrence with dynamical properties of stochastic and continuous models of reaction networks is discussed.     

C3 photosynthesis in silico

A computer model comprising light reactions, electron–proton transport, enzymatic reactions, and regulatory functions of C₃ photosynthesis has been developed as a system of differential budget equations for intermediate compounds. The emphasis is on electron transport through PSII and PSI and on the modeling of Chl fluorescence and 810 nm absorptance signals. Non-photochemical quenching of PSII excitation is controlled by lumenal pH. Alternative electron transport is modeled as the Mehler type O₂ reduction plus the malate-oxaloacetate shuttle based on the chloroplast malate dehydrogenase. Carbon reduction enzymes are redox-controlled by the ferredoxin–thioredoxin system, sucrose synthesis is controlled by the fructose 2,6-bisphosphate inhibition of cytosolic FBPase, and starch synthesis is controlled by ADP-glucose pyrophosphorylase. Photorespiratory glycolate pathway is included in an integrated way, sufficient to reproduce steady-state rates of photorespiration. Rate-equations are designed on principles of multisubstrate-multiproduct enzyme kinetics. The parameters of the model were adopted from literature or were estimated from fitting the photosynthetic rate and pool sizes to experimental data. The model provided good simulations for steady-state photosynthesis, Chl fluorescence, and 810 nm transmittance signals under varying light, CO₂ and O₂ concentrations, as well as for the transients of post-illumination CO₂ uptake, Chl fluorescence induction and the 810 nm signal. The modeling shows that the present understanding of photosynthesis incorporated in the model is basically correct, but still insufficient to reproduce the dark-light induction of photosynthesis, the time kinetics of non-photochemical quenching, ‘photosynthetic control’ of plastoquinone oxidation, cyclic electron flow around PSI, oscillations in photosynthesis. The model may find application for predicting the results of gene transformations, the analysis of kinetic experimental data, the training of students.     

Increased glucose production in mice overexpressing human fructose-1,6-bisphosphatase in the liver

Increased endogenous glucose production (EGP) predominantly from the liver is a characteristic feature of type 2 diabetes, which positively correlates with fasting hyperglycemia. Gluconeogenesis is the biochemical pathway shown to significantly contribute to increased EGP in diabetes. Fructose-1,6-bisphosphatase (FBPase) is a regulated enzyme in gluconeogenesis that is increased in animal models of obesity and insulin resistance. However, whether a specific increase in liver FBPase can result in increased EGP has not been shown. The objective of this study was to determine the role of upregulated liver FBPase in glucose homeostasis. To achieve this goal, we generated human liver FBPase transgenic mice under the control of the transthyretin promoter, using insulator sequences to flank the transgene and protect it from site-of-integration effects. This resulted in a liver-specific model, as transgene expression was not detected in other tissues. Mice were studied under the following conditions: 1) at two ages (24 wk and 1 yr old), 2) after a 60% high-fat diet, and 3) when bred to homozygosity. Hemizygous transgenic mice had an approximately threefold increase in total liver FBPase mRNA with concomitant increases in FBPase protein and enzyme activity levels. After high-fat feeding, hemizygous transgenics were glucose intolerant compared with negative littermates (P < 0.02). Furthermore, when bred to homozygosity, chow-fed transgenic mice showed a 5.5-fold increase in liver FBPase levels and were glucose intolerant compared with negative littermates, with a significantly higher rate of EGP (P < 0.006). This is the first study to show that FBPase regulates EGP and whole body glucose homeostasis in a liver-specific transgenic model. Our homozygous transgenic model may be useful for testing human FBPase inhibitor compounds with the potential to treat patients with type 2 diabetes.     

Binding of AMP to two of the four subunits of pig kidney fructose-1,6-bisphosphatase induces the allosteric transition.

To study the allosteric transition in pig kidney fructose 1,6-bisphosphatase (FBPase), we constructed hybrids in which subunits have either their active or regulatory sites rendered nonfunctional by specific mutations. This was accomplished by the coexpression of the enzyme from a plasmid that contained two slightly different copies of the cDNA. To resolve and purify each of the hybrid enzymes, six aspartic acid codons were added before the termination codon of one of the cDNAs. The addition of these Asp residues to the protein did not alter the kinetic or allosteric properties of the resulting FBPase. Expression of the enzyme from a dual-gene plasmid resulted in the production of a set of five different enzymes (two homotetramers and three hybrid tetramers) that could be purified by a combination of affinity and anion-exchange chromatography because of the differential charge on each of these species. The hybrid with one subunit that only had a functional regulatory site (R) and three subunits that only had a functional active site (A) exhibited biphasic AMP inhibition. Analysis of these data suggest that the binding of AMP to the R subunit is able to globally alter the activity of the other three A subunits. The hybrid composed of two R and two A subunits is completely inhibited at an AMP concentration of approximately 0.5 mM, 100-fold less than the concentration required to fully inhibit the A(4) enzyme. The monophasic nature of this cooperative inhibition suggests that the AMP binding to the two R subunits is sufficient to completely inhibit the enzyme and suggests that the binding of AMP to only two of the four subunits of the enzyme induces the global allosteric transition from the R to the T state.     

Physico-chemical study of the heterogeneous population of opioid receptors

A physico-chemical analysis of the heterogenous population of opioid receptors was carried out. A new difference approach to the analysis of heterogenous receptor systems was developed. This procedure permits to estimate even in high stringency conditions of parameters of three or more types of receptors from the binding isotherms or competitive replacement curves as well as to determine the total receptor concentration in the system. A DELTA computer program based on this difference approach has been developed. The experimental results obtained through the use of the difference technique led to a kinetic model of interaction between morphine and D-Ala2, D-Leu5-enkephalin with rat brain receptors. This model based on the interaction of each ligand with three types of specific binding sites can be used for the determination of kinetic and thermodynamic parameters.     

The form II fructose 1,6-bisphosphatase and phosphoribulokinase genes form part of a large operon in Rhodobacter sphaeroides: primary structure and insertional mutagenesis analysis

Fructose 1,6-bisphosphatase (FBPase) and phosphoribulokinase (PRK) are two key enzymes of the reductive pentose phosphate pathway or Calvin cycle of photosynthetic carbon dioxide assimilation. Early studies had indicated that the properties of enzymes isolated from photosynthetic bacteria were clearly distinct from those of enzymes obtained from the chloroplasts of higher plants [for a review, see Tabita (1988)]. The eucaryotic enzymes, which are light activated by the thioredoxin/ferredoxin system (Buchanan, 1980), were each shown to contain a putative regulatory amino acid sequence (Marcus et al., 1988; Porter et al., 1988). The enzymes from photosynthetic bacteria are not controlled by the thioredoxin/ferredoxin system but exhibit complex kinetic properties and, in the case of PRK, there is an absolute requirement of NADH for activity. In the photosynthetic bacterium Rhodobacter sphaeroides, the structural genes of the Calvin cycle, including the genes that encode FBPase (fbp) and PRK (prk), are found in two distinct clusters, and the fbp and prk genes are closely associated in each cluster. In the present investigation, we have determined the nucleotide sequence of the fbpB and prkB genes of the form II cluster and have compared the deduced amino acid sequences to previously determined sequences of light-activated enzymes from higher plants and from other eucaryotic and procaryotic sources. In the case of FBPase, there are several regions that are conserved in the R. sphaeroides enzymes, including a protease-sensitive area located in a region equivalent to residues 51-71 of mammalian FBPase.(ABSTRACT TRUNCATED AT 250 WORDS)