Behavior of chemical reaction catalyzed by allosteric enzyme: threshold phenomena and discontinuous transition to oscillatory state

A theoretical study is made on a chemical reaction system catalyzed by an allosteric protein, especially on its behavior in far-from-equilibrium situations. The reaction system, which was introduced in a previous paper, consists of two chemical species, S and P, and an allosteric enzyme, E, which catalyzes the reaction of interconversion between them. This system is kept far-from-equilibrium by an interaction with its environment. This interaction is characterized by four parameters. For certain values of the parameters, the system was previously shown to have multiple steady states. In the present paper it is shown that a sustained oscillation takes place in a certain region of the control-parameter space. On one part of the boundary of this region, the system undergoes a discontinuous transition from a steady state to a state oscillating with finite amplitude, while on the other part of the boundary the amplitude of oscillation is vanishingly small right after the transition. It is also shown that this system exhibits a threshold phenomenon. A few possible mechanisms are discussed by which the assumed interaction of the system with its environment can be realized.     

Distinct conformational dynamics and allosteric networks in alpha tryptophan synthase during active catalysis

Experimental observations of enzymes under active turnover conditions have brought new insight into the role of protein motions and allosteric networks in catalysis. Many of these studies characterize enzymes under dynamic chemical equilibrium conditions, in which the enzyme is actively catalyzing both the forward and reverse reactions during data acquisition. We have previously analyzed conformational dynamics and allosteric networks of the alpha subunit of tryptophan synthase under such conditions using NMR. We have proposed that this working state represents a four to one ratio of the enzyme bound with the indole‐3‐glycerol phosphate substrate (E:IGP) to the enzyme bound with the products indole and glyceraldehyde‐3‐phosphate (E:indole:G3P). Here, we analyze the inactive D60N variant to deconvolute the contributions of the substrate‐ and products‐bound states to the working state. While the D60N substitution itself induces small structural and dynamic changes, the D60N E:IGP and E:indole:G3P states cannot entirely account for the conformational dynamics and allosteric networks present in the working state. The act of chemical bond breakage and/or formation, or possibly the generation of an intermediate, may alter the structure and dynamics present in the working state. As the enzyme transitions from the substrate‐bound to the products‐bound state, millisecond conformational exchange processes are quenched and new allosteric connections are made between the alpha active site and the surface which interfaces with the beta subunit. The structural ordering of the enzyme and these new allosteric connections may be important in coordinating the channeling of the indole product into the beta subunit.     

Some equilibrium and nonequilibrium properties of the allosteric interactions in enzymes. II. Allosteric effect in the absence of a rapid quilibrium between substrate and enzyme

The existence of allosteric interactions in enzymes was determined even in the absence of a rapid equilibrium between enzyme and substrate. The ratio between the rate constants was found at which the K allosteric effect was possible. Rate equations were formulated in which the two-stage substrate binding was taken into account. The conditions for the existence of allosteric interactions were verified by means of theoretical curves. The calculations were made with the help of rate equations taking into account the two stages in substrate binding.     

Reciprocal allostery arising from a bienzyme assembly controls aromatic amino acid biosynthesis in Prevotella nigrescens

Modular protein assembly has been widely reported as a mechanism for constructing allosteric machinery. Recently, a distinctive allosteric system has been identified in a bienzyme assembly comprising a 3-deoxy-d-arabino heptulosonate-7-phosphate synthase (DAH7PS) and chorismate mutase (CM). These enzymes catalyze the first and branch point reactions of aromatic amino acid biosynthesis in the bacterium Prevotella nigrescens (PniDAH7PS), respectively. The interactions between these two distinct catalytic domains support functional interreliance within this bifunctional enzyme. The binding of prephenate, the product of CM-catalyzed reaction, to the CM domain is associated with a striking rearrangement of overall protein conformation that alters the interdomain interactions and allosterically inhibits the DAH7PS activity. Here, we have further investigated the complex allosteric communication demonstrated by this bifunctional enzyme. We observed allosteric activation of CM activity in the presence of all DAH7PS substrates. Using small-angle X-ray scattering (SAXS) experiments, we show that changes in overall protein conformations and dynamics are associated with the presence of different DAH7PS substrates and the allosteric inhibitor prephenate. Furthermore, we have identified an extended interhelix loop located in CM domain, loop_C320-F333, as a crucial segment for the interdomain structural and catalytic communications. Our results suggest that the dual-function enzyme PniDAH7PS contains a reciprocal allosteric system between the two enzymatic moieties as a result of this bidirectional interdomain communication. This arrangement allows for a complex feedback and feedforward system for control of pathway flux by connecting the initiation and branch point of aromatic amino acid biosynthesis.     

Canine erythrocyte pyruvate kinase. II. Properties of the abnormal enzyme associated with hemolytic anemia in the basenji dog

We have compared the solubility, kinetic, immunological, and electrophoretic properties of erythrocyte pyruvate kinase from normal dogs and Basenji dogs with congenital hemolytic anemia due to pyruvate kinase deficiency. Differences can be detected between the two enzymes by all methods. The enzyme from the affected animals has a greater solubility in ammonium sulfate. It has a lower K _m for phosphoenolpyruvate, while the K _m for ADP is increased. This enzyme is not inhibited by ATP or activated by fructose 1,6-diphosphate. The enzyme from the affected animals has none of the allosteric properties characteristic of the normal canine enzyme. No difference can be detected by enzyme inactivation with rabbit antiserum against the human erythrocyte enzyme, but a slight spur is observed on comparison of the two enzymes by Ouchterlony immunodiffusion. The enzymes also differ in their electrophoretic mobilities on starch gel electrophoresis.     

On the detection of homotropic effects in enzymes of low co-operativity. Application to modified aspartate transcarbamoylase

In contrast with the ease of observing heterotropic effects in allosteric enzymes of low co-operativity, the detection of homotropic effects is often difficult. As a consequence, erroneous conclusions about the uncoupling of homotropic and heterotropic effects can result unless sensitive techniques are used for analyzing the kinetic data. Simulations of experiments as well as actual measurements on the allosteric enzyme, aspartate transcarbamoylase, of Escherichia coli and some of its modified forms, were performed in attempts to develop stringent diagnostic procedures for the detection of homotropic effects in enzymes of low co-operativity. The analyses show that direct saturation plots (velocity versus substrate concentration), double reciprocal plots, and Hill plots yield misleading results in that the co-operativity known to be present is not observed. In contrast, Eadie plots (velocity/substrate concentration versus velocity) are much more sensitive in revealing homotropic effects. Since the observed co-operativity depends on both the allosteric equilibrium constant, L, and the number of active sites, n, simulations were performed on the effect of those parameters. The maxima in the Eadie plots increased as L was lowered and conversely the maxima decreased as n was reduced. These changes were confirmed with a mutant aspartate transcarbamoylase which had the same specific activity as the wild-type enzyme and a lower value of L, and also with a hybrid enzyme containing fewer active sites and the same L value. Analogous experiments on nitrated aspartate transcarbamoylase derivatives of decreasing activity showed that Eadie plots were of value in distinguishing between the changes in L and n values resulting from the inactivation. Data from the literature were analyzed in the form of Eadie plots and in all cases homotropic effects were readily detectable for aspartate transcarbamoylase derivatives previously claimed to be devoid of co-operativity.     

Finite fluctuations and multiple steady states far from equilibrium

The role of finite fluctuations in transitions between nonequilibrium steady states in nonlinear systems is investigated. Attention is focused on a model biochemical system for which the usual deterministic chemical kinetics predicts a far-from-equilibrium region of multiple steady states. A stochastic approach to chemical kinetics is adopted to study explicitly the effect of fluctuations around the coexisting stable states on a predicted hysteresis in the transition between those states. A numerical solution of the stochastic master equation for the system yields results which differ qualitatively from predictions of the purely macroscopic theory. Possible implications of these results are considered, and several important aspects of the computational scheme are discussed in some detail.     

Space-filling effects of inert solutes as probes for the detection and study of substrate-mediated conformational changes by enzyme kinetics: theoretical considerations

From expressions derived for the space-filling effects of small inert solutes on kinetic parameters for univalent enzymes undergoing isomerizations that are substrate-induced and pre-existing, it is concluded that experimental observation of an enhanced maximal velocity in the presence of inert solute can only reflect the existence of the former type of conformational change; and that the isomerization must be governed by a relatively small equilibrium constant. Similar conclusions apply to multivalent enzymes exhibiting Michaelis-Menten kinetics. Extension of the theory to provide quantitative expressions for multivalent enzymes has made possible the numerical simulation of thermodynamic non-ideality effects on systems conforming with the Monod and Koshland models of allostery. In that regard the simulated Scatchard plots for the two models differ sufficiently in form to suggest that detailed examination of the space-filling effects of small solutes on the kinetics of an allosteric enzyme may, under favourable circumstances, allow identification of the appropriate allosteric mechanism. Finally, these considerations of thermodynamic non-ideality in relation to the kinetics of allosteric enzymes have revealed formal similarities between the consequences of space-filling by inert solutes and the specific effects of allosteric activators or inhibitors. Attention is drawn to the possible implications of this observation in relation to the functioning of allosteric enzymes in vivo, where catalytic performance may be modified by factors no more specific than the ability of unrelated solutes to occupy space in the highly concentrated cellular environment.     

Apparent co-operativity for highly concentrated Michaelian and allosteric enzymes

The effect of high enzyme concentration on velocity curves is analysed quantitatively for both Michaelian and simple allosteric enzymes. The general principles and practical approaches developed here are applicable to other models and may provide information on enzyme function in vivo. At physiological enzyme concentrations, Michaelian enzymes display amplification properties of the same magnitude as those observed for allosteric enzymes. In terms of apparent co-operativity, this corresponds to Hill coefficients that are locally much larger than the number of interacting or non-interacting binding sites. However, compared to the Michaelian case, allosteric interactions are needed to provide a combination of both positive and negative apparent co-operativities. These effects are important for understanding the biological significance of intersubunit co-operation in oligomeric enzymes.     

Using enzyme cascades in biocatalysis: Highlight on transaminases and carboxylic acid reductases

Biocatalysis, the use of enzymes in chemical transformations, is an important green chemistry tool. Cascade reactions combine different enzyme activities in a sequential set of reactions. Cascades can occur within a living (usually bacterial) cell; in vitro in ‘one pot’ systems where the desired enzymes are mixed together to carry out the multi-enzyme reaction; or using microfluidic systems. Microfluidics offers particular advantages when the product of the reaction inhibits the enzyme(s). In vitro systems allow variation of different enzyme concentrations to optimise the metabolic ‘flux’, and the addition of enzyme cofactors as required. Cascades including cofactor recycling systems and modelling approaches are being developed to optimise cascades for wider industrial scale use. Two industrially important enzymes, transaminases and carboxylic acid reductases are used as examples regarding their applications in cascade reactions with other enzyme classes to obtain important synthons of pharmaceutical interest.     

Effect of internal diffusion in heterogeneous enzyme systems: Evaluation of true kinetic parameters and substrate diffusivity

The effect of internal diffusion on the overall reaction rate in spherical particles and membranes containing immobilized enzymes has been investigated theoretically. Since they represent open systems, the MichaelisMenten kinetics is obeyed in the absence of diffusional effects at steady state even at high enzyme concentrations. When internal diffusion perturbs the reaction, the system can not be described any more by K_M and V_max? alone, but is conveniently characterized by the modulus. Assuming that only internal diffusion interferes with the enzyme reaction, the effect of the modulus on the overall rate of reaction is illustrated by the results of computer calculations. Plots of the overall reaction rate against the substrate concentration are hyperbolas at various moduli for both membranes and spherical particles and no sigmoidal curves are obtained with immobilized enzyme systems. Since the conventional plots of enzyme kinetics do not yield straight lines under such conditions, a graphical method is proposed to determine K_M and V_max? as well as the substrate diffusivity in the enzymic medium.     

Complex Formation between Two Biosynthetic Enzymes Modifies the Allosteric Regulatory Properties of Both: AN EXAMPLE OF MOLECULAR SYMBIOSIS*

Allostery, where remote ligand binding alters protein function, is essential for the control of metabolism. Here, we have identified a highly sophisticated allosteric response that allows complex control of the pathway for aromatic amino acid biosynthesis in the pathogen Mycobacterium tuberculosis. This response is mediated by an enzyme complex formed by two pathway enzymes: chorismate mutase (CM) and 3-deoxy-d-arabino-heptulosonate 7-phosphate synthase (DAH7PS). Whereas both enzymes are active in isolation, the catalytic activity of both enzymes is enhanced, and in particular that of the much smaller CM is greatly enhanced (by 120-fold), by formation of a hetero-octameric complex between CM and DAH7PS. Moreover, on complex formation M. tuberculosis CM, which has no allosteric response on its own, acquires allosteric behavior to facilitate its own regulatory needs by directly appropriating and partly reconfiguring the allosteric machinery that provides a synergistic allosteric response in DAH7PS. Kinetic and analytical ultracentrifugation experiments demonstrate that allosteric binding of phenylalanine specifically promotes hetero-octameric complex dissociation, with concomitant reduction of CM activity. Together, DAH7PS and CM from M. tuberculosis provide exquisite control of aromatic amino acid biosynthesis, not only controlling flux into the start of the pathway, but also directing the pathway intermediate chorismate into either Phe/Tyr or Trp biosynthesis.     

The theoretical analysis of kinetic behaviour of “hysteretic” allosteric enzymes. II. The dissociating and associating enzymic systems in which the rate of installation of equilibrium between the oligomeric forms is small in comparison with that of enzymatic reaction

The present paper is concerned with the specificities of kinetic behaviour of dissociating enzyme systems where the equilibrium between oligomeric forms installs rather slowly in comparison with the rate of enzymatic reaction. In the slowly dissociating enzyme systems of the type Np ? P (P is enzyme oligomer and p is a subunit; N ? 2) in which the forms P and p exhibit different allosteric interactions between active and allosteric sites the initial rate of enzymatic reaction (v) versus the substrate concentration (S) or the effector concentration (F) were shown to be of rather complex pattern. In similar systems the v versus [S]₀ plots may show an intermediate plateau, maximum and minimum simultaneously, an intermediate plateau and its preceding S-shape, etc., as well as v versus [F]₀ may show an intermediate plateau.     

Biological processes in organised media

Embedding a simple Michaelis-Menten enzyme in a gel slice may allow the catalysis of not only scalar processes but also vectorial ones, including uphill transport of a substrate between two compartments, and may make it seem as if two enzymes or transporters are present or as if an allosterically controlled enzyme/transporter is operating. The values of kinetic parameters of an enzyme in a partially hydrophobic environment are usually different from those actually measured in a homogeneous aqueous solution. This implies that fitting kinetic data (expressed in reciprocal co-ordinates) from in vivo studies of enzymes or transporters to two straight lines or a sigmoidal curve does not prove the existence of two different membrane mechanisms or allosteric control. In the artificial transport systems described here, a functional asymmetry was sufficient to induce uphill transport, therefore, although the active transport systems characterised so far correspond to proteins asymmetrically anchored in a membrane, the past or present existence of structurally symmetrical systems of transport in vivo cannot be excluded. The fact that oscillations can be induced in studies of the maintenance of the electrical potential of frog skin by addition of lithium allowed evaluation of several parameters fundamental to the functioning of the system in vivo (e.g., relative volumes of internal compartments, characteristic times of ionic exchanges between compartments). Hence, under conditions that approach real biological complexity, increasing the complexity of the behaviour of the system may provide information that cannot be obtained by a conventional, reductionist approach.     

The role of adenosine monophosphate nucleosidase in the regulation of adenine nucleotide levels in Azotobacter vinelandii during aerobic-anaerobic transitions

When cultures of Azotobacter vinelandii are made anaerobic the adenylate pool size remains constant or increases slightly while the adenylate energy charge decreases. Under these conditions, cell growth stops but the cells remain viable for at least 5 h with the decreased energy charge. The changes in the adenylate pool during the aerobic-anaerobic transition include: the formation of adenylates as a result of RNA degradation; the degradation of a portion of the excess AMP to form hypoxanthine by the sequential actions of AMP nucleosidase and adenine deaminase; an increase in the total adenylate pool which is stabilized at approximately 1.5 times the level in growing cells; and stabilization of the adenylate energy charge at a value near 0.3. The degradation of AMP is regulated by AMP nucleosidase, an allosteric enzyme which is activated by MgATP^2? and inhibited by P_i. The in vivo activity of AMP nucleosidase was estimated by measuring the rate of hypoxanthine formation in the culture or by measuring the activity of purified enzyme at the concentrations of AMP, ATP, and P_i found in the cells. The maximum estimated in vivo rate of AMP degradation was less than 3% of the catalytic capacity of AMP nucleosidase. Thus ample activity is present for rapid adjustments of the AMP levels in these cells. Expression of AMP nucleosidase catalytic activity is tightly controlled since high constant concentrations of intracellular AMP can be maintained for extended time periods at low adenylate energy charge values. Under these conditions controlled degradation of AMP can occur to maintain a constant AMP concentration.     

Biosynthesis of bacterial glycogen: Kinetic studies of a glucose-1-P adenylyltransferase (EC 2.7.7.27) from a glycogen-excess mutant of Escherichia coli B

An Escherichia coli B mutant, CL1136 accumulates glycogen at 3.4 to 4 times the rate observed for the parent E. coli B strain. The glycogen accumulated in the mutant is similar to the glycogen isolated from the parent strain with respect to α- and β-amylolysis, chain length determination and I₂-complex absorption spectra. The CL1136 mutant contains normal glycogen synthase and branching enzyme activity but has an ADPglucose pyrophosphorylase with altered kinetic and allosteric properties. The mutant enzyme has been partially purified and in contrast to the present strain enzyme studied previously, is highly active in the absence of the allosteric activator. The response of the CL1136 enzyme to energy charge has been determined and this enzyme shows appreciable activity at low energy charge values where the E. coli B enzyme is inactive. The response to energy charge for the CL1136 and E. coli B enzymes are correlated with the rates of glycogen accumulation observed in the microorganisms. The regulation of glycogen synthesis in E. coli is to a great extent at the level of ADPglucose pyrophosphorylase; varying concentrations of fructose-P₂ and energy charge determine the rate of ADPglucose and glycogen synthesis. Both the allosteric regulation of ADPglucose pyrophosphorylase as well as the genetic regulations of the synthesis of glycogen biosynthetic enzymes (glycogen synthase and ADPglucose pyrophosphorylase) are involved in the regulation of glycogen accumulation in E. coli B.     

Allosteric interactions and bifunctionality make the response of glutamine synthetase cascade system of Escherichia coli robust and ultrasensitive

Glutamine synthetase (GS) regulation in Escherichia coli by reversible covalent modification cycles is a prototype of signal transduction by enzyme cascades. Such enzyme cascades are known to exhibit ultrasensitive response to primary stimuli and act as signal integration systems. Here, we have quantified GS bicyclic cascade based on steady state analysis by evaluating Hill coefficient. We demonstrate that adenylylation of GS with glutamine as input is insensitive to total enzyme concentrations of GS, uridylyltransferase/uridylyl-removing enzyme, regulatory protein PII, and adenylyltransferase/adenylyl-removing enzyme. This robust response of GS adenylylation is also observed for change in system parameters. From numerical analyses, we show that the robust ultrasensitive response of bicyclic cascade is because of allosteric interactions of glutamine and 2-ketoglutarate, bifunctionality of converter enzymes, and closed loop bicyclic cascade structure. By system level quantification of the GS bicyclic cascade, we conclude that such a robust response may help the cell in adapting to different carbon and nitrogen status.     

Technical aspects of separation using aqueous two-phase systems in enzyme isolation processes.

Technical aspects of the separation of aqueous two-phase systems in a commercial separator were studied in detail. For the Gyrotester B, the smallest available separator, a flow rate of 200 ml/min and a length of the regulating screw in the outlet port of 13.5 mm were found as optimal operation parameters for the separation of a poly(ethylene glycol) (PEG)/dextran two-phase system. In the presence of cells and cell debris the characteristics of the carrier two-phase systems are changed, most notably the phase ratio. Nevertheless good separation and high throughput can be maintained up to 30% wet cell material in the complete system. Using this method the enzyme pullulanase was extracted from 6.65 kg Klebsiella pneumoniae in 88% yield in a single step in less than 2 hr. A yield of 90% was predicted for this step based upon laboratory data, indicating that the performance of the extraction and separation can be calculated with the necessary accuracy and the further scale-up of the process should be accomplished quite easily. The hydrophilic polymers Constituting the phase system will often stabilize the enzymes, So that the separation can be carried out at room temperature without extensive cooling. The method of enzyme solubilization or cell disruption is not decisive for the successful extraction of the enzymes, the only limitation being the necessity to find a suitable two-phase system where the desired product and the cells or cell debris will partition in opposite phases. This is shown for α-glucosidase from Saccharomyces carlsbergensis and three aminoacyl-tRNA-synthetases from Escherichia coli. The results obtained demonstrate that aqueous two-phase systems can be separated in commercially available separators with high capacity and efficiency. It can be expected that the advanced separation technology available from chemical engineering studies can also be used for the development of large-scale isolation processes for enzymes involving liquid–liquid partitions.     

In vitro control analysis of an enzyme system: Experimental and analytical developments

In this paper we describe a flow-through system for reconstituting parts of metabolism from purified enzymes. This involves pumping continuously into a reaction chamber, fresh enzymes and reagents so that metabolic reactions occur in the chamber. The waste products leave the chamber via the outflow so that a steady state can be setup. The system we chose consisted of a single enzyme, lactate dehydrogenase. This enzyme was chosen because it consumes NADH in the chamber which could be monitored spectrophotometrically. The aim of the work was to investigate whether a steady state could be achieved in the flow system and whether a metabolic control analysis could be done. We measured two control coefficients, C_LDH and C_pump for the enzyme flux and NADH concentration and confirmed that the summation theorem applied to this system. The advantage of a flow-through system is that the titrations necessary to estimate the control coefficients can be easily and precisely controlled; this means that accurate estimates for the control coefficients can be obtained. In the paper, we discuss some statistical aspects of the data analysis and some possible applications of the technique, including a method to determine the presence of metabolic channelling between two different enzymes.