The inflow of the substrate can regulate the persistence of memory of enzymes having the properties of hysteresis: theoretical analysis

A simple kinetic model of hysteretic enzymes with the influx of substrate or ion (transported by the enzyme) is considered. Two alternative steady activity levels are shown to arise in the system with a hysteretic enzyme. The transition between these levels can proceed in an oscillatory manner. The duration of the initial steady activity level is shown to be determined by the initial substrate (or ion) level, and the oscillatory transition between the activity levels is the property of hysteretic enzymes. It was shown for plasma membrane Ca2+-ATPase as an example that the level of the signal can be encoded into the time interval in which the enzyme retains the memory about this signal.     

The reduced nicotinamide adenine dinucleotide-activated phosphoenolpyruvate carboxylase from Pseudomonas MA. Correlation of allosteric properties with changes in the sedimentation behavior.

Phosphoenolpyruvate carboxylase from Pseudomonas MA, grown on methylamine as a sole carbon source, has been studied with respect to some of its regulatory properties. The enzyme shows both negative and positive cooperativity with respect to the substrate phosphoenolpyruvate (Hill coefficients of 0.5 and 1.75). The enzyme requires a divalent cation for activity. Either magnesium or manganous ion is effective. While magnesium shows normal kinetics, manganous ion shows positive cooperativity with a Hill coefficient of 1.4. The enzyme is activated 50-fold by 0.2 mM NADH at 1 mM phosphoenolpyruvate. This activation is hysteretic, showing a lag of 2 to 3 min. Both NADH and Mn2+ induce a change in the sedimentation coefficient of the enzyme from 12.4 to 8.5 as measured by sucrose density gradient centrifugation. High concentrations of phosphate or sulfate are capable of producing this effect on sedimentation, but neither will activate more than 3-fold. Thus, if NADH is an indicator of the total energy level of the cell, the enzyme appears to be susceptible to control by factors which reflect this total energy level. The importance of this control with respect to hypothetical pathways of carbon utilization in the organism is discussed.     

Time-dependent kinetic complexities in cholinesterase-catalyzed reactions

Cholinesterases (ChEs) display a hysteretic behavior with certain substrates and inhibitors. Kinetic cooperativity in hysteresis of ChE-catalyzed reactions is characterized by a lag or burst phase in the approach to steady state. With some substrates damped oscillations are shown to superimpose on hysteretic lags. These time dependent peculiarities are observed for both butyrylcholinesterase and acetylcholinesterase from different sources. Hysteresis in ChE-catalyzed reactions can be interpreted in terms of slow transitions between two enzyme conformers E and E′. Substrate can bind to E and/or E′, both Michaelian complexes ES and E’s can be catalytically competent, or only one of them can make products. The formal reaction pathway depends on both the chemical structure of the substrate and the type of enzyme. In particular, damped oscillations develop when substrate exists in different, slowly interconvertible, conformational, and/or micellar forms, of which only the minor form is capable of binding and reacting with the enzyme. Biphasic pseudo-first-order progressive inhibition of ChEs by certain carbamates and organophosphates also fits with a slow equilibrium between two reactive enzyme forms. Hysteresis can be modulated by medium parameters (pH, chaotropic and kosmotropic salts, organic solvents, temperature, osmotic pressure, and hydrostatic pressure). These studies showed that water structure plays a role in hysteretic behavior of ChEs. Attempts to provide a molecular mechanism for ChE hysteresis from mutagenesis studies or crystallographic studies failed so far. In fact, several lines of evidence suggest that hysteresis is controlled by the conformation of His438, a key residue in the catalytic triad of cholinesterases. Induction time may depend on the probability of His438 to adopt the operative conformation in the catalytic triad. The functional significance of ChE hysteresis is puzzling. However, the accepted view that proteins are in equilibrium between preexisting functional and non-functional conformers, and that binding of a ligand to the functional form shifts equilibrium towards the functional conformation, suggests that slow equilibrium between two conformational states of these enzymes may have a regulatory function in damping out the response to certain ligands and irreversible inhibitors. This is particularly true for immobilized (membrane bound) enzymes where the local substrate and/or inhibitor concentrations depend on influx in crowded organellar systems, e.g. cholinergic synaptic clefts. Therefore, physiological or toxicological relevance of the hysteretic behavior and damped oscillations in ChE-catalyzed reactions and inhibition cannot be ruled out.     

Role of protein conformational dynamics in the catalysis by 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase

Enzymatic catalysis has conflicting structural requirements of the enzyme. In order for the enzyme to form a Michaelis complex, the enzyme must be in an open conformation so that the substrate can get into its active center. On the other hand, in order to maximize the stabilization of the transition state of the enzymatic reaction, the enzyme must be in a closed conformation to maximize its interactions with the transition state. The conflicting structural requirements can be resolved by a flexible active center that can sample both open and closed conformational states. For a bisubstrate enzyme, the Michaelis complex consists of two substrates in addition to the enzyme. The enzyme must remain flexible upon the binding of the first substrate so that the second substrate can get into the active center. The active center is fully assembled and stabilized only when both substrates bind to the enzyme. However, the side-chain positions of the catalytic residues in the Michaelis complex are still not optimally aligned for the stabilization of the transition state, which lasts only approximately 10(-13) s. The instantaneous and optimal alignment of catalytic groups for the transition state stabilization requires a dynamic enzyme, not an enzyme which undergoes a large scale of movements but an enzyme which permits at least a small scale of adjustment of catalytic group positions. This review will summarize the structure, catalytic mechanism, and dynamic properties of 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase and examine the role of protein conformational dynamics in the catalysis of a bisubstrate enzymatic reaction.     

Kinetic studies of the lipid-activated pyruvate oxidase flavoprotein of Escherichia coli

Pyruvate oxidase is a flavoprotein dehydrogenase isolated from Escherichia coli which catalyzes the oxidative decarboxylation of pyruvate to acetate and CO2. In vivo, the enzyme can bind to the bacterial membrane and reduce ubiquinone-8, feeding electrons into the respiratory chain. The purified enzyme has been shown previously to bind to phospholipids and detergents and, upon doing so, is activated. The turnover with ferricyanide as an electron acceptor increases 20- to 30-fold upon lipid binding. In this work, initial velocity and stop-flow kinetics are used to investigate the activation of this enzyme. It is shown that the unactivated form of the enzyme is markedly hysteretic. Progress curves at low substrate concentrations show an initial acceleration in enzyme turnover. This is consistent with the results of stop-flow experiments. Rates obtained for either the reduction of the unactivated flavoprotein by pyruvate or its reoxidation by ferricyanide in single turnover experiments are much slower than the rates predicted by observed turnover in initial velocity studies, in some cases by more than 2 orders of magnitude. The data are best explained by the slow interconversion between two forms of the enzyme, one with low turnover and one which rapidly turns over. As isolated, the enzyme is highly unreactive, as revealed by the stop-flow experiments. During turnover, even in the absence of lipid activators, some of the enzyme converts to the rapid-turnover form. This slow interconversion is shown by kinetic simulation to preclude a steady state from being established. Lipid activators appear to shift the equilibrium to favor the rapid-turnover form of the enzyme. Once the enzyme is "locked" into an activated conformation, the hysteresis is no longer observed, and the stop-flow results are in agreement with data obtained from initial velocity experiments. Activation appears to result in both increased rates of electron transfer into and out of the flavin.     

Hysteretic behaviour of glucose-6-phosphate dehydrogenase of pea chloroplasts

Glucose-6-phosphate dehydrogenase (G6PDH) from pea chloroplasts has at least two interconvertible kinetic states which differ from one another in their catalytic activities (‘hyperactive’ and ‘hypoactive’ forms). Preincubation of chloroplast extracts with 10 mM glucose-6-phosphate (G6P) led to the accumulation of a ‘hyperactive’ G6PDH form which exhibited a burst of activity at the start of the assay; steady state was reached after a period of several minutes. Preincubation of the pea chloroplast extracts in the absence of G6P resulted in the formation of a ‘hypoactive’ enzyme from which exhibited a lag during the assay. Steady state was reached after several minutes. The enzyme activity in the steady state was the same for both forms. The length of the lag (τ) was inversely related to the concentration of G6DH and substrate concentration. These results show that the G6PDH of pea chloroplasts, like the enzyme of cyanobacteria, behaves as a hysteretic enzyme.     

Regulatory role of polyamine in the acid phosphatase from potato tubers.

Effects of polyamine and metal ions on the new type of acid phosphatase purified from potato (Solanum tuberosum L. Irish Cobbler) tubers were analyzed. The enzyme belongs to nonspecific acid phosphatase family (EC 3.1.3.2), which hydrolyzes various phosphorylated substrates. The enzyme hydrolyzed inorganic pyrophosphate as a preferred substrate, and exhibited the hyperbolic kinetics with respect to the substrate, inorganic pyrophosphate in the absence of metal cations. Polyamine activated the enzyme effectively by lowering the K(m) value without appreciable changes in the maximal velocity. The most effective polyamines as activators were spermine and spermidine. Mg(2+) ion increased the K(m) value without affecting the maximal velocity of the enzyme, but Ca(2+) ion decreased both the K(m) and V(max) values. Increasing concentrations of spermine also decreased the K(m) value irrespective of Mg(2+) ion included, but gave a constant K(m) and V(max) values in the absence and presence of Ca(2+) ion. Action of spermine and metal ions can be explained by the complex formation with the substrate pyrophosphate. The acid phosphatase from potato can utilize the pyrophosphate-spermine or pyrophosphate-Ca(2+) complex as the preferred substrates. However, the enzyme can use the pyrophosphate-Mg complex with a weak affinity for the active site. Polyamine activates acid phosphatase in the absence and presence of metal cations, and activation by polyamine of the enzyme may contribute to the stimulation of starch biosynthesis and the control of glycolysis/gluconeogenesis by regulating PPi levels in growing potato tubers.     

The role and specificity of the catalytic and regulatory cation-binding sites of the Na+-pumping NADH:quinone oxidoreductase from Vibrio cholerae

The Na(+)-translocating NADH:quinone oxidoreductase is the entry site for electrons into the respiratory chain and the main sodium pump in Vibrio cholerae and many other pathogenic bacteria. In this work, we have employed steady-state and transient kinetics, together with equilibrium binding measurements to define the number of cation-binding sites and characterize their roles in the enzyme. Our results show that sodium and lithium ions stimulate enzyme activity, and that Na(+)-NQR enables pumping of Li(+), as well as Na(+) across the membrane. We also confirm that the enzyme is not able to translocate other monovalent cations, such as potassium or rubidium. Although potassium is not used as a substrate, Na(+)-NQR contains a regulatory site for this ion, which acts as a nonessential activator, increasing the activity and affinity for sodium. Rubidium can bind to the same site as potassium, but instead of being activated, enzyme turnover is inhibited. Activity measurements in the presence of both sodium and lithium indicate that the enzyme contains at least two functional sodium-binding sites. We also show that the binding sites are not exclusively responsible for ion selectivity, and other steps downstream in the mechanism also play a role. Finally, equilibrium-binding measurements with (22)Na(+) show that, in both its oxidized and reduced states, Na(+)-NQR binds three sodium ions, and that the affinity for sodium is the same for both of these states.     

Structural basis for the 3''-5'' exonuclease activity of Escherichia coli DNA polymerase I: a two metal ion mechanism.

The refined crystal structures of the large proteolytic fragment (Klenow fragment) of Escherichia coli DNA polymerase I and its complexes with a deoxynucleoside monophosphate product and a single-stranded DNA substrate offer a detailed picture of an editing 3'-5' exonuclease active site. The structures of these complexes have been refined to R-factors of 0.18 and 0.19 at 2.6 and 3.1 A resolution respectively. The complex with a thymidine tetranucleotide complex shows numerous hydrophobic and hydrogen-bonding interactions between the protein and an extended tetranucleotide that account for the ability of this enzyme to denature four nucleotides at the 3' end of duplex DNA. The structures of these complexes provide details that support and extend a proposed two metal ion mechanism for the 3'-5' editing exonuclease reaction that may be general for a large family of phosphoryltransfer enzymes. A nucleophilic attack on the phosphorous atom of the terminal nucleotide is postulated to be carried out by a hydroxide ion that is activated by one divalent metal, while the expected pentacoordinate transition state and the leaving oxyanion are stabilized by a second divalent metal ion that is 3.9 A from the first. Virtually all aspects of the pretransition state substrate complex are directly seen in the structures, and only very small changes in the positions of phosphate atoms are required to form the transition state.     

Dynamic flaps in HIV-1 protease adopt unique ordering at different stages in the catalytic cycle

The flexibility of HIV-1 protease flaps is known to be essential for the enzymatic activity. Here we attempt to capture a multitude of conformations of the free and substrate-bound HIV-1 protease that differ drastically in their flap arrangements. The substrate binding process suggests the opening of active site gate in conjunction with a reversal of flap tip ordering, from the native semiopen state. The reversed-flap, open-gated enzyme readily transforms to a closed conformation after proper placement of the substrate into the binding cleft. After substrate processing, the closed state protease which possessed opposite flap ordering relative to the semiopen state, encounters another flap reversal via a second open conformation that facilitates the evolution of native semiopen state of correct flap ordering. The complicated transitional pathway, comprising of many high and low energy states, is explored by combining standard and activated molecular dynamics (MD) simulation techniques. The study not only complements the existing findings from X-ray, NMR, EPR, and MD studies but also provides a wealth of detailed information that could help the structure-based drug design process.     

Substrate ground state binding energy concentration is realized as transition state stabilization in physiological enzyme catalysis

Previously published kinetic data on the interactions of seventeen different enzymes with their physiological substrates are re-examined in order to understand the connection between ground state binding energy and transition state stabilization of the enzyme-catalyzed reactions. When the substrate ground state binding energies are normalized by the substrate molar volumes, binding of the substrate to the enzyme active site may be thought of as an energy concentration interaction; that is, binding of the substrate ground state brings in a certain concentration of energy. When kinetic data of the enzyme/substrate interactions are analyzed from this point of view, the following relationships are discovered: 1) smaller substrates possess more binding energy concentrations than do larger substrates with the effect dropping off exponentially, 2) larger enzymes (relative to substrate size) bind both the ground and transition states more tightly than smaller enzymes, and 3) high substrate ground state binding energy concentration is associated with greater reaction transition state stabilization. It is proposed that these observations are inconsistent with the conventional (Haldane) view of enzyme catalysis and are better reconciled with the shifting specificity model for enzyme catalysis.     

Bistability in the isocitrate dehydrogenase reaction: an experimentally based theoretical study.

The enzyme isocitrate dehydrogenase (IDH, EC 1.1.1.42) can exhibit activation by one of its products, NADPH. This activation is competitively inhibited by the substrate NADP+, whereas NADPH competes with NADP+ for the catalytic site. Experimental observations briefly presented here have shown that if IDH is coupled to another enzyme, diaphorase (EC 1.8.1.4), which transforms NADPH into NADP+, the system can attain either one of two stable states, corresponding to a low and a high NADPH concentration. The evolution toward either one of these stable states depends on the time of addition of diaphorase to the medium containing IDH and its substrate NADP+. We present a theoretical and numerical analysis of a model for the IDH-diaphorase bienzymatic system, based on the regulatory properties of IDH. The results confirm the occurrence of bistability for parameter values derived from the experiments. Depending on the total concentration of NADP+ plus NADPH and the concentration of IDH, the system can either admit a single steady state or display bistability. We obtain an expression for the critical time t*, before which diaphorase addition leads to the lower steady state and after which addition of the enzyme leads to the upper steady state of NADPH. The analysis is extended to the case where the second substrate of IDH, isocitrate, is consumed in the course of the reaction without being regenerated. Bistability occurs only as a transient phenomenon in these conditions.     

蛇肌果糖1，6－二磷酸酯酶的R态和T态的构象

几种高活性形式的蛇肌果糖１,６－二磷酸酯酸的紫外差光谱与酶在尿素或盐酸胍中差光谱相似,它们的酶学性质及巯基暴露的程度各不相同,提示这些高活性形式的酶的构象呈稳定的松驰状态（Ｂ态）,构象松驰的程度也各不相同。受果糖２,６－二磷酸、ＡＭＰ和过量底物抑制的酶处于三种不同的低活性状态,它们的构象特征与Ｒ态相反,提示此三种低活性酶构象处于较紧凑状态（Ｔ态）。这几种Ｔ态酶流基暴露的程度,受蛋白水解酶限制性酶解的速度不同,说明这些Ｔ态酶的构象的紧凑程度是有差异的。蛇肌酶的不同的活化状态所具有不同的稳定的构象状态,在能量上可能相差很小,便于受到多种因子的调节。这可能是别构酶所普遍具有的现象。     

Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

We demonstrate strong experimental support for the cybernetic model based on maximizing carbon uptake rate in describing the microorganism's regulatory behavior by verifying exacting predictions of steady state multiplicity in a chemostat. Experiments with a feed mixture of glucose and pyruvate show multiple steady state behavior as predicted by the cybernetic model. When multiplicity occurs at a dilution (growth) rate, it results in hysteretic behavior following switches in dilution rate from above and below. This phenomenon is caused by transient paths leading to different steady states through dynamic maximization of the carbon uptake rate. Thus steady state multiplicity is a manifestation of the nonlinearity arising from cybernetic mechanisms rather than of the nonlinear kinetics. The predicted metabolic multiplicity would extend to intracellular states such as enzyme levels and fluxes to be verified in future experiments. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Role of phosphate on the ADP-induced hysteretic inhibition of mitochondrial adenosine 5'-triphosphatase. Effects of the natural protein inhibitor

Preincubation of F1-ATPase with ADP and Mg2+ leads to ADP binding at regulatory site inducing a hysteretic inhibition of ATP hydrolysis, i.e., an inhibition that slowly develops after Mg-ATP addition (Di Pietro, A., Penin, F., Godinot, C. and Gautheron, D.C. (1980) Biochemistry 19, 5671-5678). It is shown here that inorganic phosphate (Pi) together with ADP during preincubation abolishes the time-dependence of the inhibition after the addition of the substrate Mg-ATP. This preincubation in the presence of both Pi and ADP slowly leads to a conformation of the enzyme immediately inhibited after the addition of the substrate Mg-ATP. The Pi effect is half-maximal at 35 microM and pH 6.6, whereas a limited effect is induced at pH 8.0. The preincubation of F1-ATPase with Pi and ADP must last long enough (t1/2 = 5 min). The effects can be correlated to the amount of Pi bound to the enzyme, 1 mol Pi per mol (apparent KD of 33 microM) at saturation. Pi neither modifies the ADP binding nor the final level of the concomitant inhibition. When Pi is not present in the preincubation, the final stable rate of ADP-induced hysteretic inhibition is always reached when a near-constant amount of Pi has been generated during Mg-ATP hydrolysis. Kinetic experiments indicate that preincubation with ADP and Pi decreases both Vmax and Km which would favor a conformational change of the enzyme. Taking into account the Pi effects, a more precise model of hysteretic inhibition is proposed. The natural protein inhibitor IF1 efficiently prevents the binding of Pi produced by ATP hydrolysis indicating that the hysteretic inhibition and the IF1-dependent inhibition obey different mechanisms.     

Purification and state of activation of rat kidney phenylalanine hydroxylase

Phenylalanine hydroxylase, the enzyme that catalyzes the irreversible hydroxylation of phenylalanine to tyrosine, was purified from rat kidney with the use of phenyl-Sepharose, DEAE-Sephacel, and gel permeation high pressure liquid chromatography. Our most highly purified fractions had a specific activity in the presence of 6-methyltetrahydropterin, of 1.5 mumol of tyrosine formed/min/mg of protein, which is higher than has been reported hitherto. For the rat kidney enzyme, the ratio of specific activity in the presence of 6-methyltetrahydropterin to the specific activity in the presence of tetrahydrobiopterin (BH4) is 5. By contrast, this ratio for the unactivated rat liver hydroxylase is 80. These results indicate that the kidney enzyme is in a highly activated state. The rat kidney hydroxylase could not be further activated by any of the methods that stimulate the BH4-dependent activity of the rat liver enzyme. In addition, the kidney enzyme binds to phenyl-Sepharose without prior activation with phenylalanine. The phenylalanine saturation pattern with BH4 as a cofactor is hyperbolic with substrate inhibition at greater than 0.5 mM phenylalanine, a pattern that is characteristic of the activated liver hydroxylase. The molecular weight of the rat kidney enzyme as determined by gel permeation chromatography is 110,000, suggesting that the enzyme might be an activated dimer. We conclude, therefore, that phenylalanine hydroxylases from rat kidney and liver are in different states of activation and may be regulated in different ways.     

Analysis of the quasi-steady-state approximation for an enzymatic one-substrate reaction

The validity of the quasi-steady state approximation for the calculation of the rate function of an isolated enzyme reaction is analysed by a detailed consideration of the time dependent process. For the characterization of the deviations of the real motion from the quasi-stationary state three kinds of error functions are used, the relaxation deficit, the relative relaxation time and the relaxation error. An improved approximation procedure is developed to calculate the transient states of the system. The maximum distance of the original motion from the quasi-stationary states is estimated by a general method. By consideration of different enzyme and substrate concentrations as well as different kinetic constants those parameter regions have been determined, where the errors of the quasi-steady state approximation do not exceed tolerated values. It is suggested how the methods can be applied to metabolic pathways.     

The dimeric form of phosphoenolpyruvate carboxylase isolated from maize: physical and kinetic properties

Phosphoenolpyruvate carboxylase purified from maize was a homodimer of molecular weight 200 kDa and was readily converted to a tetrameric form in the presence of Mg2+ plus PEP or Mg2+ alone. During the assay, the enzyme activity increased with time, reaching a steady state after a discernible lag, suggesting its hysteretic nature. The hystereses was not due to oligomerization of the enzyme as the lag time tau was independent of the enzyme concentration and the lag was not abolished on preincubation with 25 mM Mg2+, the condition under which the enzyme existed in tetrameric form. Nevertheless, the lag could be abolished on preincubating the enzyme with PEP plus Mg2+, indicating that the hystereses is due to a PEP plus Mg2(+)-induced slow transition of the enzyme to an activated state during the catalysis. During steady state, the enzyme showed cooperative kinetics for PEP and Mg2+ at pH 7. It had two binding sites with nearly 10-fold difference in affinities for PEP and Mg2+.     

Activation of residual acidic α-mannosidase activity in mannosidosis tissues by metal ions

The residual acidic α-mannosidase activity from mannosidosis tissues, representing between 1 and 8 % of the activity found in normal tissues, was significantly activated by Zn²⁺ and Co²⁺, whereas these metal ions respectively activated or inhibited the acidic enzyme activity from normal tissues. The defective enzyme from mannosidosis liver bound most effectively to the synthetic substrate in the presence of Co²⁺. This metal ion also improved the hydrolysis of a natural substrate by the acidic enzyme from mannosidosis liver. The results indicate that the defective enzyme in the disease has an altered capacity to bind metal ions. The demonstration that this defective enzyme can be activated may have an important bearing on the therapy of the disease.