Cooperativity in enzyme function: equilibrium and kinetic aspects

The bacterial magnesium transporter MgtA reveals highly selective interaction with specific cardiolipin species

The bacterial magnesium transporter A (MgtA) is a specialized P-type ATPase important for Mg2+ import into the cytoplasm; disrupted magnesium homeostasis is linked to intrinsic ribosome instability and antibacterial resistance in Salmonella strains. Here, we show that MgtA has functional specificity for cardiolipin 18:1. Still, it reaches maximum activity only in combination with cardiolipin 16:0, equivalent to the major components of native cardiolipin found in E. coli membranes. Native mass spectrometry indicates the presence of two binding sites for cardiolipin, agreeing with the kinetic studies revealing that a cooperative relationship likely exists between the two cardiolipin variants. This is the first experimental evidence of cooperative effects between lipids of the same class, with only minor variations in their acyl chain composition, acting on a membrane protein. In summary, our results reveal that MgtA exhibits a highly complex interaction with one cardiolipin 18:1 and one cardiolipin 16:0, affecting protein activity and stability, contributing to our understanding of the particular interactions between lipid environment and membrane proteins. Further, a better understanding of Mg2+ homeostasis in bacteria, due to its role as a virulence regulator, will provide further insights into the regulation and mechanism of bacterial infections.

Product inhibition of mammalian thiamine pyrophosphokinase is an important mechanism for maintaining thiamine diphosphate homeostasis

BACKGROUND

Thiamine diphosphate (ThDP), an indispensable cofactor for oxidative energy metabolism, is synthesized through the reaction thiamine + ATP ⇆ ThDP + AMP, catalyzed by thiamine pyrophosphokinase 1 (TPK1), a cytosolic dimeric enzyme. It was claimed that the equilibrium of the reaction is in favor of the formation of thiamine and ATP, at odds with thermodynamic calculations. Here we show that this discrepancy is due to feedback inhibition by the product ThDP.

METHODS

We used a purified recombinant mouse TPK1 to study reaction kinetics in the forward (physiological) and for the first time also in the reverse direction.

RESULTS

Keq values reported previously are strongly underestimated, due to the fact the reaction in the forward direction rapidly slows down and reaches a pseudo-equilibrium as ThDP accumulates. We found that ThDP is a potent non-competitive inhibitor (Ki ≈ 0.4 μM) of the forward reaction. In the reverse direction, a true equilibrium is reached with a Keq of about 2 × 10-5, strongly in favor of ThDP formation. In the reverse direction, we found a very low Km for ThDP (0.05 μM), in agreement with a tight binding of ThDP to the enzyme.

GENERAL SIGNIFICANCE

Inhibition of TPK1 by ThDP explains why intracellular ThDP levels remain low after administration of even very high doses of thiamine. Understanding the consequences of this feedback inhibition is essential for developing reliable methods for measuring TPK activity in tissue extracts and for optimizing the therapeutic use of thiamine and its prodrugs with higher bioavailability under pathological conditions.

Explicit Treatment of Non-Michaelis-Menten and Atypical Kinetics in Early Drug Discovery*

Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential to sustain life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were mostly tested and implemented for cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more-complex systems (for instance, multiprotein complexes, oligomeric assemblies, membrane proteins and post-translationally modified proteins), the initial axioms defined by Michaelis-Menten (MM) kinetics are rendered inadequate, and the development of a new kind of kinetic analysis to study these systems is required. This review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents initial ideas on the design and analysis of experiments in early drug-discovery for such systems, to enable effective screening and characterisation of small-molecule inhibitors with desirable physiological outcomes.

Eukaryotic transcription factors: paradigms of protein intrinsic disorder

Gene-specific transcription factors (TFs) are key regulatory components of signaling pathways, controlling, for example, cell growth, development, and stress responses. Their biological functions are determined by their molecular structures, as exemplified by their structured DNA-binding domains targeting specific cis-acting elements in genes, and by the significant lack of fixed tertiary structure in their extensive intrinsically disordered regions. Recent research in protein intrinsic disorder (ID) has changed our understanding of transcriptional activation domains from ‘negative noodles’ to ID regions with function-related, short sequence motifs and molecular recognition features with structural propensities. This review focuses on molecular aspects of TFs, which represent paradigms of ID-related features. Through specific examples, we review how the ID-associated flexibility of TFs enables them to participate in large interactomes, how they use only a few hydrophobic residues, short sequence motifs, prestructured motifs, and coupled folding and binding for their interactions with co-activators, and how their accessibility to post-translational modification affects their interactions. It is furthermore emphasized how classic biochemical concepts like allostery, conformational selection, induced fit, and feedback regulation are undergoing a revival with the appreciation of ID. The review also describes the most recent advances based on computational simulations of ID-based interaction mechanisms and structural analysis of ID in the context of full-length TFs and suggests future directions for research in TF ID.

Anaerobic Heme Degradation: ChuY Is an Anaerobilin Reductase That Exhibits Kinetic Cooperativity

Heme catabolism is an important biochemical process that many bacterial pathogens utilize to acquire iron. However, tetrapyrrole catabolites can be reactive and often require further processing for transport out of the cell or conversion to another useful cofactor. In previous work, we presented in vitro evidence of an anaerobic heme degradation pathway in Escherichia coli O157:H7. Consistent with reactions that have been reported for other radical S-adenosyl-l-methionine methyltransferases, ChuW transfers a methyl group to heme by a radical-mediated mechanism and catalyzes the β-scission of the porphyrin macrocycle. This facilitates iron release and the production of a new linear tetrapyrrole termed "anaerobilin". In this work, we describe the structure and function of ChuY, an enzyme expressed downstream from chuW within the same heme utilization operon. ChuY is structurally similar to biliverdin reductase and forms a dimeric complex in solution that reduces anaerobilin to the product we have termed anaerorubin. Steady state analysis of ChuY exhibits kinetic cooperativity that is best explained by a random addition mechanism with a kinetically preferred path for initial reduced nicotinamide adenine dinucleotide phosphate binding.

Investigating the Reaction Mechanism of F420-Dependent Glucose-6-phosphate Dehydrogenase from Mycobacterium tuberculosis: Kinetic Analysis of the Wild-Type and Mutant Enzymes

F₄₂₀-dependent glucose-6-phosphate dehydrogenase (FGD) catalyzes the conversion of glucose-6-phosphate (G6P) to 6-phosphogluconolactone, using F₄₂₀ cofactor as the hydride transfer acceptor, within mycobacteria. A previous crystal structure of wild-type FGD led to a proposed mechanism suggesting that the active site residues His40, Trp44, and Glu109 could be involved in catalysis. We have characterized the wild-type FGD and five FGD variants (H40A, W44F, W44Y, W44A, and E109Q) by fluorescence binding assays and steady-state and pre-steady-state kinetic experiments. Compared to wild-type FGD, all the variants had lower binding affinities for F₄₂₀, thus suggesting that Trp44, His40, and Glu109 aid in F₄₂₀ binding. While all the variants had decreased catalytic efficiencies, FGD H40A and W44A were the least efficient, having lost ∼1000- and ∼2000-fold activity, respectively. This confirms a crucial catalytic role for His40 in the FGD reaction and suggests that aromaticity at residue 44 aids catalysis. To investigate the proposed roles of Glu109 and His40 in acid-base catalysis, the pH dependence of kinetic parameters has been determined for the E109Q and H40A mutants and compared to those of the wild-type enzyme. The log k_cat-pH profile of wild-type FGD and E109Q revealed two ionizable residues in the enzyme-substrate complex, while H40A displayed only one ionization event. The FGD E109Q variant displayed pH-dependent kinetic cooperativity with respect to the F₄₂₀ cofactor. The multiple-turnover pre-steady-state kinetics were biphasic for wild-type FGD, W44F, W44Y, and E109Q, while the H40A and W44A variants displayed only a single phase because of their reduced catalytic efficiency.

Evidence of Negative Cooperativity and Half-Site Reactivity within an F420-Dependent Enzyme: Kinetic Analysis of F420H2:NADP(+) Oxidoreductase

Here, we report the very first example of half-site reactivity and negative cooperativity involving an important F420 cofactor-dependent enzyme. F420H2:NADP(+) oxidoreductase (Fno) is an F420 cofactor-dependent enzyme that catalyzes the reversible reduction of NADP(+) through the transfer of a hydride from the reduced F420 cofactor. These catalytic processes are of major significance in numerous biochemical processes. While the steady-state kinetic analysis showed classic Michaelis-Menten kinetics with varying concentrations of the F420 redox moiety, FO, such plots revealed non-Michaelis-Menten kinetic behavior when NADPH was varied. The double reciprocal plot of the varying concentrations of NADPH displays a downward concave shape, suggesting that negative cooperativity occurs between the two identical monomers. The transient state kinetic data show a burst prior to entering steady-state turnover. The burst suggests that product release is rate-limiting, and the amplitude of the burst phase corresponds to production of product in only one of the active sites of the functional dimer. These results suggest either half-site reactivity or an alternate sites model wherein the reduction of the cofactor, FO occurs at one active site at a time followed by reduction at the second active site. Thus, the data imply that Fno may be a functional regulatory enzyme.

Evidence of Kinetic Cooperativity in Dimeric Ketopantoate Reductase from Staphylococcus aureus

Ketopantoate reductase (KPR) catalyzes the NADPH-dependent production of pantoate, an essential precursor in the biosynthesis of coenzyme A. Previous structural studies have been limited to Escherichia coli KPR, a monomeric enzyme that follows a sequential ordered mechanism. Here we report the crystal structure of the Staphylococcus aureus enzyme at 1.8 Å resolution, the first description of a dimeric KPR. Using sedimentation velocity analysis, we show that the S. aureus KPR dimer is stable in solution. In fact, our structural analysis shows that the dimeric assembly we identify is present in the majority of KPR crystal structures. Steady state analysis of S. aureus KPR reveals strong positive cooperativity with respect to NADPH (Hill coefficient of 2.5). In contrast, high concentrations of the substrate ketopantoate (KP) inhibit the activity of the enzyme. These observations are consistent with a random addition mechanism in which the initial binding of NADPH is the kinetically preferred path. In fact, Förster resonance energy transfer studies of the equilibrium binding of NADPH show only a small degree of cooperativity between subunits (Hill coefficient of 1.3). Thus, the apparently strong cooperativity observed in substrate saturation curves is due to a kinetic process that favors NADPH binding first. This interpretation is consistent with our analysis of the A181L substitution, which increases the Km of ketopantoate 844-fold, without affecting kcat. The crystal structure of KPRA181L shows that the substitution displaces Ser239, which is known to be important for the binding affinity of KP. The decrease in KP affinity would enhance the already kinetically preferred NADPH binding path, making the random mechanism appear to be sequentially ordered and reducing the kinetic cooperativity. Consistent with this interpretation, the NADPH saturation curve for KPRA181L is hyperbolic.

Unraveling subunit cooperativity in homotetrameric HCN2 channels

In a multimeric receptor protein, the binding of a ligand can modulate the binding of a succeeding ligand. This phenomenon, called cooperativity, is caused by the interaction of the receptor subunits. By using a complex Markovian model and a set of parameters determined previously, we analyzed how the successive binding of four ligands leads to a complex cooperative interaction of the subunits in homotetrameric HCN2 pacemaker channels. The individual steps in the model were characterized by Gibbs free energies for the equilibria and activation energies, specifying the affinity of the binding sites and the transition rates, respectively. Moreover, cooperative free energies were calculated for each binding step in both the closed and the open channel. We show that the cooperativity sequence positive-negative-positive determined for the binding affinity is generated by the combined effect of very different cooperativity sequences determined for the binding and unbinding rates, which are negative-negative-positive and no-negative-no, respectively. It is concluded that in the ligand-induced activation of HCN2 channels, the sequence of cooperativity based on the binding affinity is caused by two even qualitatively different sequences of cooperativity that are based on the rates of ligand binding and unbinding.

Biochemical characterization and homology modeling of methylbutenol synthase and implications for understanding hemiterpene synthase evolution in plants

2-Methyl-3-buten-2-ol (MBO) is a five-carbon alcohol produced and emitted in large quantities by many species of pine native to western North America. MBO is structurally and biosynthetically related to isoprene and can have an important impact on regional atmospheric chemistry. The gene for MBO synthase was identified from Pinus sabiniana, and the protein encoded was functionally characterized. MBO synthase is a bifunctional enzyme that produces both MBO and isoprene in a ratio of ~90:1. Divalent cations are required for activity, whereas monovalent cations are not. MBO production is enhanced by K(+), whereas isoprene production is inhibited by K(+) such that, at physiologically relevant [K(+)], little or no isoprene emission should be detected from MBO-emitting trees. The K(m) of MBO synthase for dimethylallyl diphosphate (20 mm) is comparable with that observed for angiosperm isoprene synthases and 3 orders of magnitude higher than that observed for monoterpene and sesquiterpene synthases. Phylogenetic analysis showed that MBO synthase falls into the TPS-d1 group (gymnosperm monoterpene synthases) and is most closely related to linalool synthase from Picea abies. Structural modeling showed that up to three phenylalanine residues restrict the size of the active site and may be responsible for making this a hemiterpene synthase rather than a monoterpene synthase. One of these residues is homologous to a Phe residue found in the active site of isoprene synthases. The remaining two Phe residues do not have homologs in isoprene synthases but occupy the same space as a second Phe residue that closes off the isoprene synthase active site.

Equilibrium unfolding studies of monellin: the double-chain variant appears to be more stable than the single-chain variant

To improve our understanding of the contributions of different stabilizing interactions to protein stability, including that of residual structure in the unfolded state, the small sweet protein monellin has been studied in both its two variant forms, the naturally occurring double-chain variant (dcMN) and the artificially created single-chain variant (scMN). Equilibrium guanidine hydrochloride-induced unfolding studies at pH 7 show that the standard free energy of unfolding, ΔG°(U), of dcMN to unfolded chains A and B and its dependence on guanidine hydrochloride (GdnHCl) concentration are both independent of protein concentration, while the midpoint of unfolding has an exponential dependence on protein concentration. Hence, the unfolding of dcMN like that of scMN can be described as two-state unfolding. The free energy of dissociation, ΔG°(d), of the two free chains, A and B, from dcMN, as measured by equilibrium binding studies, is significantly lower than ΔG°(U), apparently because of the presence of residual structure in free chain B. The value of ΔG°(U), at the standard concentration of 1 M, is found to be ∼5.5 kcal mol(-1) higher for dcMN than for scMN in the range from pH 4 to 9, over which unfolding appears to be two-state. Hence, dcMN appears to be more stable than scMN. It seems that unfolded scMN is stabilized by residual structure that is absent in unfolded dcMN and/or that native scMN is destabilized by strain that is relieved in native dcMN. The value of ΔG°(U) for both protein variants decreases with an increase in pH from 4 to 9, apparently because of the thermodynamic coupling of unfolding to the protonation of a buried carboxylate side chain whose pK(a) shifts from 4.5 in the unfolded state to 9 in the native state. Finally, it is shown that although the thermodynamic stabilities of dcMN and scMN are very different, their kinetic stabilities with respect to unfolding in GdnHCl are very similar.

Kinetic parameters of efflux of penicillins by the multidrug efflux transporter AcrAB-TolC of Escherichia coli

The multidrug efflux transporter AcrAB-TolC is known to pump out a diverse range of antibiotics, including beta-lactams. However, the kinetic constants of the efflux process, needed for the quantitative understanding of resistance, were not available until those accompanying the efflux of some cephalosporins were recently determined by combining efflux with the hydrolysis of drugs by the periplasmic beta-lactamase. In the present study we extended this approach to the study of a wide range of penicillins, from ampicillin and penicillin V to ureidopenicillins and isoxazolylpenicillins, by combining efflux with hydrolysis with the OXA-7 penicillinase. We found that the penicillins had a much stronger apparent affinity to AcrB and higher maximum rates of efflux than the cephalosporins. All penicillins showed strong positive cooperativity kinetics for export. The kinetic constants obtained were validated, as the MICs theoretically predicted on the basis of efflux and hydrolysis kinetics were remarkably similar to the observed MICs (except for the isoxazolylpenicillins). Surprisingly, however, the efflux kinetics of cloxacillin, for example, whose MIC decreased 512-fold in Escherichia coli upon the genetic deletion of the acrB gene, were quite similar to those of ampicillin, whose MIC decreased only 2-fold with the same treatment. Analysis of this phenomenon showed that the extensive decrease in the MIC for the acrB mutant is primarily due to the low permeation of the drug and that comparison of the MICs between the parent and the acrB strains is a very poor measure of the ability of AcrB to pump a drug out.

Stomach lysozymes of the three-toed sloth (Bradypus variegatus), an arboreal folivore from the Neotropics

Lysozymes are antimicrobial defences that act as digestive enzymes when expressed in the stomach of herbivores with pre-gastric fermentation. We studied this enzyme in the complex stomach of the three-toed sloth (Bradypus variegatus), a folivore with pre-gastric fermentation. Lysozymes were identified by SDS-PAGE and immunoblotting in all portions: diverticulum, pouch, glandular and muscular prepyloric area with 14.3 kDa of molecular mass. Purified lysozymes from all areas but the diverticulum were characterized by MALDI-TOF, optimal pH, optimal ionic strength, and specific activity. The differences observed suggested at least three isoforms. The optimal pHs were similar to the pH of the stomach portion where the enzymes were isolated. The lysozyme from the pouch (fermentation chamber) exhibited higher specific activity and concentration than the others. The specific activity of the enzyme from the acid muscular prepyloric portion was comparable to that reported in the cow abomasums; however, its concentration was lower than that observed in cow. This distinctive pattern of secretion/specific activity and overall low concentration suggests different roles for the lysozymes in this herbivore compared to Artiodactyla. We postulate that sloth stomach lysozymes may still be antimicrobial defences by protecting the microbial flora of the fermentation chamber against foreign bacteria.

Single-molecule kinetics reveals signatures of half-sites reactivity in dihydroorotate dehydrogenase A catalysis

Subunit activity and cooperativity of a homodimeric flavoenzyme, dihydroorotate dehydrogenase A (DHODA) from Lactococcus lactis, were characterized by employing single-molecule spectroscopy to follow the turnover kinetics of individual DHODA molecules, eliminating ensemble averaging. Because the enzyme-bound FMN is fluorescent in its oxidized state but not when reduced, a single DHODA molecule exhibits stepwise fluorescence changes during turnover, providing a signal to determine reaction kinetics and study cooperativity. Our results showed significant heterogeneity in the catalytic behaviors of individual dimer molecules, with only 40% interconverting between the three possible redox states: the fully fluorescent (both subunits oxidized), the half-fluorescent (one subunit oxidized and the other reduced), and the nonfluorescent (both subunits reduced). Forty percent of the single dimer traces showed turnovers between only the fully fluorescent and half-fluorescent states. The remaining 20% of the molecules interconverted only between the half-fluorescent state and the nonfluorescent state. Kinetic analysis revealed very similar reaction rates in both the reductive and oxidative half-reactions for different DHODA dimers. Our single-molecule data provide strong evidence for half-sites reactivity, in which only one subunit reacts at a time. The present study presents an effective way to explore the subunit catalytic activity and cooperativity of oligomeric enzymes by virtue of single-molecule fluorescence.

Interaction and electron transfer between the high molecular weight cytochrome and cytochrome c3 from Desulfovibrio vulgaris Hildenborough: Kinetic, microcalorimetric, EPR and electrochemical studies

The complex formation between the tetraheme cytochrome c3 and hexadecaheme high molecular weight cytochrome c (Hmc), the structure of which has recently been resolved, has been characterized by cross-linking experiments, EPR, electrochemistry and kinetic analysis, and some key parameters of the interaction were determined. The analysis of electron transfer between [Fe] hydrogenase, cytochrome c3 and Hmc demonstrates a redox-shuttling role of cytochrome c3 in the pathway from hydrogenase to Hmc, and shows an effect of redox state on the interaction between the two cytochromes. The role of polyheme cytochromes in electron transfer from periplasmic hydrogenase to membrane redox proteins is assessed. A model with cytochrome c3 as an intermediate between hydrogenase and various polyheme cytochromes is proposed and its physiological consequences are discussed.

Catalytic cooperativity among subunits of Escherichia coli transcription termination factor Rho. Kinetics and substrate structural requirements

Escherichia coli transcription termination factor Rho shows a 30-fold faster rate of ATP hydrolysis when all three catalytic sites are filled with ATP than when only a single site is filled (Stitt, B. L. and Xu, Y. (1998) J. Biol. Chem. 273, 26477-26486). To study the structural requirements of the substrate for this catalytic cooperativity, rapid mix/chemical quench experiments using various ATP analogs were performed. The results indicate that it is the configuration of the beta- and gamma-phosphoryl groups of ATP that is of primary importance for the rate enhancement. Our results also show that there are kinetically slow branches of the enzyme mechanism that are not seen when the chemistry step of the catalytic cycle is fast. These branches become prominent, however, when two of the three Rho active sites are empty or bear non-hydrolyzable compounds. A first-order step that is slow compared with V(max) catalysis enables a single ATP molecule bound in any one of the three Rho active sites to be hydrolyzed and defines the kinetically slow branches. This first-order step could be a protein conformation change or a rearrangement of bound RNA. The results reinforce the importance of catalytic cooperativity in normal Rho function and suggest that several protein conformations exist along the catalytic pathway.

Positive cooperativity in substrate binding of human prostatic acid phosphatase entrapped in AOT–isooctane–water reverse micelles

The kinetics of 1-naphthyl phosphate and phenyl phosphate hydrolysis, catalyzed by human prostatic acid phosphatase (PAP) entrapped in AOT-isooctane-water reverse micelles, has been studied over surfactant hydration degree (w0) range 5 to 35. Continuous spectrophotometric acid phosphatase assays, previously prepared, were employed. PAP was catalytically active over the whole w0 studied range. In order to determine steady-state reaction constants the experimental data were fitted to Hill rate equation. Positive cooperativity in substrate binding was observed, as it was earlier found in aqueous solutions. The extent of cooperativity (expressed as the value of the Hill cooperation coefficient h) increased from 1 to 4, when the micellar water-pool size was growing, at fixed enzyme concentration. In the plots of catalytic activity (kcat) versus w0, the maxima have been found at w0=10 (pH 5.6) and 23 (pH 3.8). It is suggested that catalytically active monomeric and dimeric PAP forms are entrapped in reverse micelles of w0=10 and 23, respectively.

Interaction of 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/FBPase-2) with glucokinase activates glucose phosphorylation and glucose metabolism in insulin-producing cells

The bifunctional enzyme 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/FBPase-2) was recently identified as a new intracellular binding partner for glucokinase (GK). Therefore, we studied the importance of this interaction for the activity status of GK and glucose metabolism in insulin-producing cells by overexpression of the rat liver and pancreatic islet isoforms of PFK-2/FBPase-2. PFK-2/FBPase-2 overexpression in RINm5F-GK cells significantly increased the GK activity by 78% in cells expressing the islet isoform, by 130% in cells expressing the liver isoform, and by 116% in cells expressing a cAMP-insensitive liver S32A/H258A double mutant isoform. Only in cells overexpressing the wild-type liver PFK-2/FBPase-2 isoform was the increase of GK activity abolished by forskolin, apparently due to the regulatory site for phosphorylation by a cAMP-dependent protein kinase. In cells overexpressing any isoform of the PFK-2/FBPase-2, the increase of the GK enzyme activity was antagonized by treatment with anti-FBPase-2 antibody. Increasing the glucose concentration from 2 to 10 mmol/l had a significant stimulatory effect on the GK activity in RINm5F-GK cells overexpressing any isoform of PFK-2/FBPase-2. The interaction of GK with PFK-2/FBPase-2 takes place at glucose concentrations that are physiologically relevant for the activation of GK and the regulation of glucose-induced insulin secretion. This new mechanism of posttranslational GK regulation may also represent a new site for pharmacotherapeutic intervention in type 2 diabetes treatment.

The metabolic role of human ADH3 functioning as ethanol dehydrogenase

Human class III alcohol dehydrogenase (ADH3), also known as glutathione-dependent formaldehyde dehydrogenase, exhibited non-hyperbolic kinetics with ethanol at a near physiological pH 7.5. The S(0.5) and k(cat) were determined to be 3.4+/-0.3 M and 33+/-3 min(-1), and the Hill coefficient (h) 2.21+/-0.09, indicating positive cooperativity. Strikingly, the S(0.5) for ethanol was found to be 5.4 x 10(6)-fold higher than the K(m) for S-(hydroxymethyl)glutathione, a classic substrate for the enzyme, whereas the k(cat) for the former was 41% lower than that for the latter. Isotope effects on enzyme activity suggest that hydride transfer may be rate-limiting in the oxidation of ethanol. Kinetic simulations using the experimentally determined Hill constant suggest that gastric ADH3 may highly effectively contribute to the first-pass metabolism at 0.5-3 M ethanol, an attainable range in the gastric lumen during alcohol consumption. The positive cooperativity mainly accounts for this metabolic role of ADH3.

Allosteric interactions within subsites of a monomeric enzyme: kinetics of fluorogenic substrates of PI-specific phospholipase C

Two novel water-soluble fluorescein myo-inositol phosphate (FLIP) substrates, butyl-FLIP and methyl-FLIP, were used to examine the kinetics and subsite interactions of Bacillus cereus phosphatidylinositol-specific phospholipase C. Butyl-FLIP exhibited sigmoidal kinetics when initial rates are plotted versus substrate concentration. The data fit a Hill coefficient of 1.2-1.5, suggesting an allosteric interaction between two sites. Two substrate molecules bind to this enzyme, one at the active site and one at a subsite, causing an increase in activity. The kinetic behavior is mathematically similar to that of well-known cooperative multimeric enzymes even though this phosphatidylinositol-specific phospholipase C is a small, monomeric enzyme. The less hydrophobic substrate, methyl-FLIP, binds only to the active site and not the activator site, and thus exhibits standard hyperbolic kinetics. An analytical expression is presented that accounts for the kinetics of both substrates in the absence and presence of a nonsubstrate short-chain phospholipid, dihexanoylphosphatidylcholine. The fluorogenic substrates detect activation at much lower concentrations of dihexanoylphosphatidylcholine than previously reported.

A sigmoidal transcriptional response: cooperativity, synergy and dosage effects

A sigmoidal transcriptional response (STR) is thought to act as a molecular switch to control gene expression. This nonlinear behaviour arises as a result of the cooperative recognition of a promoter/enhancer by transcription factors (TFs) and/or their synergy to attract the basal transcriptional machinery (BTM). Although this cooperation between TFs is additive in terms of energy, it leads to an exponential increase in affinity between the BTM and the pre-initiation complexes. This exponential increase in the strength of interactions is the principle that governs synergistic systems. Here, I propose a minimalist quasi-equilibrium model to explore qualitatively the STR taking into account cooperative recognition of the promoter/enhancer and synergy. Although the focus is on the effect of activators, a similar treatment can be applied to inhibitors. One of the main insights obtained from the model is that generation of a sigmoidal threshold is possible even in the absence of cooperative DNA binding provided the TFs synergistically interact with the BTM. On the contrary, when there is cooperative binding, the impact of synergy diminishes. It will also be shown that a sigmoidal response to a morphogenetic gradient can be used to generate a nested gradient of another morphogen. Previously, I had proposed that halving the amounts of TFs involved in sigmoidal transcriptional switches could account for the abnormal dominant phenotypes associated with some of these genes. This phenomenon, called haploinsufficiency (HI), has been recognised as the basis of many human diseases. Although a formal proof linking HI and a sigmoidal response is lacking, it is tempting to explore the model from the perspective of dosage effects.

Nested MWC model describes hydrolysis of GroEL without assuming negative cooperativity in binding

Folding assistance and ATPase activity of GroEL are based on the existence of different conformations. In order to characterise these conformations, published data on steady state ATPase activity in the absence of GroES were reanalysed simultaneously in terms of the Nested MWC model. This model is a hierarchical extension of the symmetry-model of Monod et al. [J. Mol. Biol. 12 (1965) 88]. An unique set of GroEL specific parameters was obtained. This set was supported by comparison of predictions arising from this set of values with experimental data for hydrolysis of ATP in the presence of ADP and ATPgammaS, binding of ATPgammaS and ADP to GroEL in the absence of ATP, and binding of ATP as monitored by fluorescence labelling. Thus, for the first time, multiple data sets for the interaction of nucleotides with GroEL are described quantitatively by an allosteric model. A noteworthy feature of our model is that no negative cooperativity in ATP binding occurs in accordance to experimental observations. Furthermore, the model also includes the existence of a conformation with very high ATPase activity. Such a conformation might be of importance at a certain stage in the folding cycle.

HNF-1alpha G319S, a transactivation-deficient mutant, is associated with altered dynamics of diabetes onset in an Oji-Cree community

The prevalence of type 2 diabetes mellitus in the Oji-Cree of northwestern Ontario is the third highest in the world. A private mutation, G319S, in HNF1A, which encodes hepatic nuclear factor-1alpha (HNF-1alpha), was associated with Oji-Cree type 2 diabetes and was found in approximately 40% of affected subjects. The G319S mutation reduced the in vitro ability of HNF-1alpha to activate transcription by approximately 50%, with no effect on DNA binding or protein stability. There was no evidence of a dominant negative effect of the mutant protein. The impact of the G319S mutation at the population level was assessed by classifying subjects with type 2 diabetes according to HNF1A genotype and plotting the cumulative age of onset of diabetes. Disease onset was modeled satisfactorily by two-parameter sigmoidal functions for all diabetic subjects and all three HNF1A genotypes. Pairwise statistical comparisons showed significant between-genotype differences in t50 (all P < 0.00001), corresponding to the age at which half the subjects had become diabetic. Each dose of G319S accelerated median disease onset by approximately 7 years. Thus, the transactivation-deficient HNF1A G319S mutation affects the dynamics of disease onset. The demonstration of a functional consequence for HNF1A G319S provides a mechanistic basis for its strong association with Oji-Cree type 2 diabetes and its unparalleled specificity for diabetes prediction in these people, in whom diabetes presents a significant public health dilemma. The findings also show that HNF1A mutations can be associated with typical adult-onset insulin-resistant obesity-related diabetes in addition to maturity-onset diabetes of the young.

Coupling between substrate binding and allosteric regulation in ribozyme catalysis

The contribution of substrate binding to allosteric regulation in the ribozyme catalysis has been investigated using allosteric ribozymes consisting of the hammerhead ribozyme and a flavin mononucleotide (FMN) aptamer. Kinetic parameters were measured for various lengths of the substrates with a wide range of binding energy. The maximum cleavage rate of each ribozyme was retained with the long substrates. However, the cleavage rates largely decreased by the truncation of the substrates according to loss in the free energy of substrate binding. The high sensitivity to the substrate lengths is attributed to the increase in the energetic requirement for the catalytic core folding, which is caused by the incorporation of the aptamer region. One role of FMN binding is assisting the promotion of the core folding through the stabilization of the aptamer domain. The allosteric effect is significantly expressed only when the substrate binding energy is insufficient for the core folding of the ribozyme-substrate complex. This type of allosteric interaction dominates the substrate dependency of another type of regulation. These results demonstrate that an adequate correlation between the type of regulation and the substrate binding is responsible for the effective allosteric interaction in the kinetic process.

Cooperative kinetics of human prostatic acid phosphatase

The steady-state kinetics of hydrolysis reaction catalysed by human prostatic acid phosphatase (PAP) by using 1-naphthyl phosphate, phenyl phosphate and phosphotyrosine as substrates has been studied at pH 5.5. The substrate binding curves were sigmoidal and Hill cooperation coefficient h was higher than 1 for each of the examined compounds. Thus, human prostatic acid phosphatase kinetics exhibits positive cooperativity towards the studied substrates. The extent of cooperativity was found to depend on the substrate used and on enzyme concentration. The highest cooperativity of PAP was observed for 1-naphthyl phosphate and the lowest for phosphotyrosine. When prostatic phosphatase concentration increased, Hill cooperation coefficient (h) and half saturation constant (K(0.5)) both grew, but the catalytic constant (k(cat)) remained constant, for each of the substrates studied. Ligand-induced association-dissociation equilibrium of the active oligomeric species (monomer-dimer-tetramer-oligomers) is suggested.

Genomics, complexity and drug discovery: insights from Boolean network models of cellular regulation

The completion of the first draft of the human genome sequence has revived the old notion that there is no one-to-one mapping between genotype and phenotype. It is now becoming clear that to elucidate the fundamental principles that govern how genomic information translates into organismal complexity, we must overcome the current habit of ad hoc explanations and instead embrace novel, formal concepts that will involve computer modelling. Most modelling approaches aim at recreating a living system via computer simulation, by including as much details as possible. In contrast, the Boolean network model reviewed here represents an abstraction and a coarse-graining, such that it can serve as a simple, efficient tool for the extraction of the very basic design principles of molecular regulatory networks, without having to deal with all the biochemical details. We demonstrate here that such a discrete network model can help to examine how genome-wide molecular interactions generate the coherent, rule-like behaviour of a cell - the first level of integration in the multi-scale complexity of the living organism. Hereby the various cell fates, such as differentiation, proliferation and apoptosis, are treated as attractor states of the network. This modelling language allows us to integrate qualitative gene and protein interaction data to explain a series of hitherto non-intuitive cell behaviours. As the human genome project starts to reveal the limits of the current simplistic 'one gene - one function - one target' paradigm, the development of conceptual tools to increase our understanding of how the intricate interplay of genes gives rise to a global 'biological observable' will open a new perspective for post-genomic drug target discovery.

Kinetic cooperativity of human liver alcohol dehydrogenase gamma(2)

Previous studies showed that natural human liver alcohol dehydrogenase gamma exhibits negative cooperativity (substrate activation) with ethanol. Studies with the recombinant gamma(2) isoenzyme now confirm that observation and show that the saturation kinetics with other alcohols are also nonhyperbolic, whereas the kinetics for reactions with NAD(+), NADH, and acetaldehyde are hyperbolic. The substrate activation with ethanol and 1-butanol are explained by an ordered mechanism with an abortive enzyme-NADH-alcohol complex that releases NADH more rapidly than does the enzyme-NADH complex. In contrast, high concentrations of cyclohexanol produce noncompetitive substrate inhibition against varied concentrations of NAD(+) and decrease the maximum velocity to 25% of the value that is observed at optimal concentrations of cyclohexanol. Transient kinetics experiments show that cyclohexanol inhibition is due to a slower rate of dissociation of NADH from the abortive enzyme-NADH-cyclohexanol complex than from the enzyme-NADH complex. Fluorescence quenching experiments confirm that the alcohols bind to the enzyme-NADH complex. The nonhyperbolic saturation kinetics for oxidation of ethanol, cyclohexanol, and 1-butanol are quantitatively explained with the abortive complex mechanism. Physiologically relevant concentrations of ethanol would be oxidized predominantly by the abortive complex pathway.

Tyrosine hydroxylase binds tetrahydrobiopterin cofactor with negative cooperativity, as shown by kinetic analyses and surface plasmon resonance detection

Kinetic studies of tetrameric recombinant human tyrosine hydroxylase isoform 1 (hTH1) have revealed properties so far not reported for this enzyme. Firstly, with the natural cofactor (6R)-Lerythro-5,6,7, 8-tetrahydrobiopterin (H4biopterin) a time-dependent change (burst) in enzyme activity was observed, with a half-time of about 20 s for the kinetic transient. Secondly, nonhyperbolic saturation behaviour was found for H4biopterin with a pronounced negative cooperativity (0.39 < h < 0.58; [S]0.5 = 24 +/- 4 microM). On phosphorylation of Ser40 by protein kinase A, the affinity for H4biopterin increased ([S]0.5 = 11 +/- 2 microM) and the negative cooperativity was amplified (h = 0.27 +/- 0.03). The dimeric C-terminal deletion mutant (Delta473-528) of hTH1 also showed negative cooperativity of H4biopterin binding (h = 0.4). Cooperativity was not observed with the cofactor analogues 6-methyl-5,6,7,8-tetrahydropterin (h = 0.9 +/- 0.1; Km = 62.7 +/- 5.7 microM) and 3-methyl-5,6,7, 8-tetrahydropterin (H43-methyl-pterin)(h = 1.0 +/- 0.1; Km = 687 +/- 50 microM). In the presence of 1 mM H43-methyl-pterin, used as a competitive cofactor analogue to BH4, hyperbolic saturation curves were also found for H4biopterin (h = 1.0), thus confirming the genuine nature of the kinetic negative cooperativity. This cooperativity was confirmed by real-time biospecific interaction analysis by surface plasmon resonance detection. The equilibrium binding of H4biopterin to the immobilized iron-free apoenzyme results in a saturable positive resonance unit (DeltaRU) response with negative cooperativity (h = 0.52-0.56). Infrared spectroscopic studies revealed a reduced thermal stability both of the apo-and the holo-hTH1 on binding of H4biopterin and Lerythro-dihydrobiopterin (H2biopterin). Moreover, the ligand-bound forms of the enzyme also showed a decreased resistance to limited tryptic proteolysis. These findings indicate that the binding of H4biopterin at the active site induces a destabilizing conformational change in the enzyme which could be related to the observed negative cooperativity. Thus, our studies provide new insight into the regulation of TH by the concentration of H4biopterin which may have significant implications for the physiological regulation of catecholamine biosynthesis in neuroendocrine cells.

Conformational changes affect binding and catalysis by ester-hydrolysing antibodies

D2.3, D2.4 and D2.5 are ester-hydrolysing antibodies raised against a phosphonate transition state analogue (TSA). All three antibody-TSA binding kinetics, as monitored by fluorescence quenching, indicate an "induced-fit" mechanism: fast bimolecular association followed by a unimolecular isomerisation (k=1-7 s-1). Isomerisation leads to a 30-170-fold increase in affinity towards the TSA and, consequently, to higher catalytic rates. Antibody D2.3 exhibits a complex three-step binding mechanism, in which the last step is a "very slow" isomerisation (k<0.02 s-1). This very slow isomerisation is limiting the rate of catalysis by D2.3, as indicated by the kinetics of product release which show characteristics of enzyme "conformational memory" or "hysteresis". The results support a mechanism consisting of pre-equilibrium between "nether-active" (low affinity) and "active" (high affinity) antibody conformers (prior to ligand addition) as well as induced-fit, i.e. isomerisation of the nether-active ligand-antibody complex to give the active complex. Crystal structures of these antibodies, free and complexed, have previously indicated that their conformation does not change upon binding. Here, we show that the buffer used to crystallise the antibodies, and in particular its polyethylene glycol component, alters the pre-equilibrium in favour of the active conformer, leading to its crystallisation both in the presence and in the absence of the TSA.

Information transfer in multienzyme complexes--1. Thermodynamics of conformational constraints and memory effects in the bienzyme glyceraldehyde-3-phosphate-dehydrogenase-phosphoribulokinase complex of Chlamydomonas reinhardtii chloroplasts

Oxidized phosphoribulokinase is almost inactive in its isolated state but becomes active when associated with glyceraldehyde-3-phosphate dehydrogenase. There is therefore an information transfer that takes place between these two enzymes. However, when the complex dissociates, free oxidized phosphoribulokinase is even more active than when it is associated with glyceraldehyde-3-phosphate dehydrogenase. This means that glyceraldehyde-3-phosphate dehydrogenase exerts an imprinting effect upon phosphoribulokinase which persists for a while after the parting of the two proteins. Various methods derived from statistical thermodynamics can be used to estimate the fraction of energy transferred from glyceraldehyde-3-phosphate dehydrogenase to phosphoribulokinase and which alters the kinetic parameters of the latter enzyme. In the complex, the decrease of the free energy associated with the binding of ribulose 5-phosphate is larger than that of ATP. This implies that the mutual association of the two enzymes facilitates the binding of the former substrate but is without effect on that of the latter. The main effect exerted by the association of the two enzymes is to decrease by about 10 kJ/mol the height of the energy barrier of the catalytic process. Phosphoribulokinase keeps an imprinting effect exerted by glyceraldehyde-3-phosphate dehydrogenase after the parting of the two enzymes. Part of the energy transferred from one protein to the other is used to decrease slightly the apparent binding free energy of the two substrates of phosphoribulokinase by about 1.5 kJ/mol. Whereas the previous association of the two enzymes does not significantly alter substrate binding to phosphoribulokinase, it greatly affects catalysis and decreases by about 16 kJ/mol the height of the energy barrier pertaining to this step. Therefore, within multienzyme complexes, information and energy can be transferred between proteins. Statistical thermodynamics offers the possibility of estimating how this energy is used to alter the various kinetic parameters of the reaction.

Allosteric gating of a large conductance Ca-activated K+ channel

Large-conductance Ca-activated potassium channels (BK channels) are uniquely sensitive to both membrane potential and intracellular Ca2+. Recent work has demonstrated that in the gating of these channels there are voltage-sensitive steps that are separate from Ca2+ binding steps. Based on this result and the macroscopic steady state and kinetic properties of the cloned BK channel mslo, we have recently proposed a general kinetic scheme to describe the interaction between voltage and Ca2+ in the gating of the mslo channel (Cui, J., D.H. Cox, and R.W. Aldrich. 1997. J. Gen. Physiol. In press.). This scheme supposes that the channel exists in two main conformations, closed and open. The conformational change between closed and open is voltage dependent. Ca2+ binds to both the closed and open conformations, but on average binds more tightly to the open conformation and thereby promotes channel opening. Here we describe the basic properties of models of this form and test their ability to mimic mslo macroscopic steady state and kinetic behavior. The simplest form of this scheme corresponds to a voltage-dependent version of the Monod-Wyman-Changeux (MWC) model of allosteric proteins. The success of voltage-dependent MWC models in describing many aspects of mslo gating suggests that these channels may share a common molecular mechanism with other allosteric proteins whose behaviors have been modeled using the MWC formalism. We also demonstrate how this scheme can arise as a simplification of a more complex scheme that is based on the premise that the channel is a homotetramer with a single Ca2+ binding site and a single voltage sensor in each subunit. Aspects of the mslo data not well fitted by the simplified scheme will likely be better accounted for by this more general scheme. The kinetic schemes discussed in this paper may be useful in interpreting the effects of BK channel modifications or mutations.

The replisome organizer (G38P) of Bacillus subtilis bacteriophage SPP1 forms specialized nucleoprotein complexes with two discrete distant regions of the SPP1 genome

Initiation of Bacillus subtilis bacteriophage SPP1 DNA replication requires the products of genes 38, 39 and 40 (G38P, G39P and G40P). G38P specifically binds two discrete regions, which are 32.1 kb apart in a linear map of the SPP1 genome. One of these target sites, which maps at the left end of the phage genome, within gene 38, was shown to function as an origin of replication and was therefore termed left origin (oriL). The other site, which lies within a non-coding segment in the late transcribed region on the right end of the genome, was termed oriR. Both sites contain two types of repeated elements (termed Box AB and A + T-rich region). The K(app) for the G38P-oriL DNA and G38P-oriR DNA complexes was estimated to be 1 nM and 4 nM, respectively. G38P binds to the distant oriL and oriR sites cooperatively. DNase I footprinting experiments showed protection by G38P in Box AB, but not in the A + T-rich region. Electron microscopy analysis showed that G38P forms a higher-order nucleoprotein structure with the SPP1 oriL and oriR sites through protein-protein interaction. G38P binding at its cognate sites does not seem to modify the length of the DNA, but to bend it. These results suggest that G38P forms a nucleoprotein complex on the regions where the SPP1 replication origins were previously predicted.

Domain motions in dihydrofolate reductase: a molecular dynamics study

Molecular dynamics simulations have been carried out on the enzyme dihydrofolate reductase from Lactobacillus casei complexed with methotrexate, NADPH and 264 crystallographic water molecules. Analysis of correlations in atomic fluctuations reveal the presence of highly correlated motion (correlation coefficient > 0.6) in the region between residues 30 to 35 and 85 to 90 leading to the identification of two domains, an "adenosine-binding domain" and a "large domain", which rotate by 3 to 4 degrees with respect to each other. The strongest correlation (> 0.6) within the large domain involves a coupling between the motions of the "teen-loop", and the spatially contiguous loops linking beta 6-beta 7 and beta 7-beta 8. Moreover, there is a significant correlation (approximately 0.5) between the adenosine fragment of NADPH and the pteridine and p-aminobenzoyl fragments of methotrexate, which are separated by approximately 17 A, and is lost on removal of "rigid-body" motion from the original trajectory. This provides support for the idea that the relative motion of the two domains is a means by which the occupation of the binding site for the adenosine end of the coenzyme can affect methotrexate binding and vice versa. Quasiharmonic vibrational analysis of the trajectory reveals that the overall dynamics of the system are governed by domain motions whose contributions are dominant at low frequencies. In addition, different low-frequency modes are responsible for separately coupling the adenosine-binding site and parts of methotrexate.

Modulation of human glucokinase intrinsic activity by SH reagents mirrors post-translational regulation of enzyme activity

The low-affinity glucose phosphorylating enzyme glucokinase plays a key role in the process of glucose recognition in pancreatic B-cells. To evaluate mechanisms of intrinsic regulation of enzyme activity human pancreatic B-cell and liver glucokinase and for comparison rat liver glucokinase were expressed in E. coli bacteria. A one-step purification procedure through metal chelate affinity chromatography revealed 58 kDa proteins with high specific activities in the range of 50 U/mg protein and K(m) values around 8 mM for the substrate D-glucose with a preference for the alpha-anomer. There were no tissue specific differences, no species differences in the electrophoretic mobility, and no differences of the kinetic properties of these well conserved enzymes. The deletion of the 15 tissue-specific NH2-terminal amino acids of the human glucokinase resulted in a catalytically active enzyme whose kinetic properties were not significantly different from those of the wild-type enzymes. The human and rat glucokinase isoforms were non-competitively inhibited by the sulfhydryl group reagents alloxan and ninhydrin with Ki values in the range of 1 microM. The inhibition of glucokinase enzyme activity was reversed by dithiothreitol with an EC50 value of 9 microM for alloxan and of 50 microM for ninhydrin. D-Glucose provided protection against alloxan-induced inhibition of human and rat glucokinase isoenzymes with half-maximal effective concentrations between 11 and 16 mM. The enzyme inhibition by alloxan was accompanied by a change in the electrophoretic mobility with a second lower molecular 49 kDa glucokinase band which can be interpreted as a compact glucokinase molecule locked by disulfide bonds. Quantification of free sulfhydryl groups revealed an average number of 3.6 free sulfhydryl groups per enzyme molecule for the native human glucokinase isoforms. Alloxan decreased the average number of free sulfhydryl groups to 1.9 per enzyme molecule indicating that more than one SH side group is oxidized by this compound. The extraordinary sensitivity of the SH side groups of the glucokinase may be a possible mechanism of enzyme regulation by interconversion of stable (active) and unstable (inactive) conformations of the enzyme. In pancreatic B-cells the glucose-dependent increase of reduced pyridine nucleotides may stabilize the enzyme in the 58 kDa form and provide optimal conditions for glucose recognition and glucose-induced insulin secretion.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

The origin of kinetic cooperativity in prebiotic catalysts

A polyallylamine carrying long hydrophobic dodecyl groups and adenine residues as side chains (PALAD C12) may be able to catalyze the hydrolysis of N-carbobenzoxy-l-alanine p-nitrophenyl ester (N-Cbz-Ala) as well as p-nitrophenyl acetate (pNPA). The progress curve of hydrolysis of the former displays a long lag and apparently no steady state. After this transient the rate falls off due to the accumulation of the products. Conversely, the hydrolysis of p-nitrophenyl acetate displays classical burst kinetics followed by a slow decline of the reaction rate.Theoretical considerations show that a steady state may be expected to occur only if the concentration of the free catalyst is very small during the reaction. This condition is sufficient to allow the rate of disappearance of the substrate to be equal to the rate of appearance of the products, which is precisely a condition for the existence of a steady state. If the catalyst is poorly active and has a loose affinity for its substrate and product, the measurement of a significant reaction rate will require a much larger concentration of the catalyst. Therefore, under these conditions, one cannot expect a steady state to occur. The mathematical expression of the error made in the steady-state assumption has been derived. This error increases with the catalyst concentration and decreases if the affinity of the substrate for the catalyst is high. Therefore the lack of steady state is associated with the affinity (or the dissociation) of the substrate and the product for the catalyst. When this affinity is low, the free concentration of the catalyst during the reaction is high and one cannot expect a steady state to occur. This is precisely what takes place with N-Cbz-Ala.A mathematical expression of the rate of hydrolysis of N-Cbz-Ala and of any reactant that displays this type of kinetics may be derived at the end of the transient when the rate is close to its maximum value. Under these conditions the rate cannot follow classical Michaelis-Menten kinetics and displays positive cooperativity. It may therefore be speculated that primordial template-like catalysts that were displaying a poor affinity for their substrates and products were already exhibiting apparent positive cooperativity in the kinetic reactions they were able to catalyze.

Model for magnetic field effects on radical pair recombination in enzyme kinetics

A prototypical model for describing magnetic field effects on the reaction kinetics of enzymes that exhibit radical pair recombination steps in their reaction cycle is presented. The model is an extended Michaelis-Menten reaction scheme including an intermediate enzyme-substrate complex where a spin-correlated radical pair state exists. The simple structure of the scheme makes it possible to calculate the enzyme reaction rate explicitly by combining chemical kinetics with magnetic field-dependent spin kinetics (radical pair mechanism). Recombination probability is determined by using the exponential model. Simulations show that the size of the magnetic field effect depends on relations between different rate constants, such as 1) the ratio between radical pair-lifetime and the magnetic field-sensitive intersystem crossing induced by the hyperfine interaction and the delta g mechanisms and 2) the chemical rate constants of the enzyme reaction cycle. An amplification factor that is derived from the specific relations between the rate constants is defined. It accounts for the fact that although the magnetic field-induced change in radical pair recombination probability is very small, the effect on the enzyme reaction rate is considerably larger, for example, by a factor of 1 to 100. Model simulations enable a qualitative comparison with recent experimental studies reporting magnetic field effects on coenzyme B12-dependent ethanolamine ammonia lyase in vitro activity that revealed a reduction in Vmax/KM at low flux densities and a return to the zero-field rate or an increase at high flux densities.