An algebraic model for the kinetics of covalent enzyme inhibition at low substrate concentrations

This article describes an integrated rate equation for the time course of covalent enzyme inhibition under the conditions where the substrate concentration is significantly lower than the corresponding Michaelis constant, for example, in the Omnia assays of epidermal growth factor receptor (EGFR) kinase. The newly described method is applicable to experimental conditions where the enzyme concentration is significantly lower than the dissociation constant of the initially formed reversible enzyme–inhibitor complex (no “tight binding”). A detailed comparison with the traditionally used rate equation for covalent inhibition is presented. The two methods produce approximately identical values of the first-order inactivation rate constant (k_inact). However, the inhibition constant (K_i), and therefore also the second-order inactivation rate constant k_inact/K_i, is underestimated by the traditional method by up to an order of magnitude.     

OptZyme: Computational Enzyme Redesign Using Transition State Analogues

OptZyme is a new computational procedure for designing improved enzymatic activity (i.e., k_cat or k_cat/K_M) with a novel substrate. The key concept is to use transition state analogue compounds, which are known for many reactions, as proxies for the typically unknown transition state structures. Mutations that minimize the interaction energy of the enzyme with its transition state analogue, rather than with its substrate, are identified that lower the transition state formation energy barrier. Using Escherichia coli β-glucuronidase as a benchmark system, we confirm that K_M correlates (R² = 0.960) with the computed interaction energy between the enzyme and the para-nitrophenyl- β, D-glucuronide substrate, k_cat/K_M correlates (R² = 0.864) with the interaction energy of the transition state analogue, 1,5-glucarolactone, and k_cat correlates (R² = 0.854) with a weighted combination of interaction energies with the substrate and transition state analogue. OptZyme is subsequently used to identify mutants with improved K_M, k_cat, and k_cat/K_M for a new substrate, para-nitrophenyl- β, D-galactoside. Differences between the three libraries reveal structural differences that underpin improving K_M, k_cat, or k_cat/K_M. Mutants predicted to enhance the activity for para-nitrophenyl- β, D-galactoside directly or indirectly create hydrogen bonds with the altered sugar ring conformation or its substituents, namely H162S, L361G, W549R, and N550S.     

On the optimality of the enzyme–substrate relationship in bacteria

Much recent progress has been made to understand the impact of proteome allocation on bacterial growth; much less is known about the relationship between the abundances of the enzymes and their substrates, which jointly determine metabolic fluxes. Here, we report a correlation between the concentrations of enzymes and their substrates in Escherichia coli. We suggest this relationship to be a consequence of optimal resource allocation, subject to an overall constraint on the biomass density: For a cellular reaction network composed of effectively irreversible reactions, maximal reaction flux is achieved when the dry mass allocated to each substrate is equal to the dry mass of the unsaturated (or “free”) enzymes waiting to consume it. Calculations based on this optimality principle successfully predict the quantitative relationship between the observed enzyme and metabolite abundances, parameterized only by molecular masses and enzyme–substrate dissociation constants (K_m). The corresponding organizing principle provides a fundamental rationale for cellular investment into different types of molecules, which may aid in the design of more efficient synthetic cellular systems.

This study shows that in E. coli, the cellular mass of each metabolite approximately equals the combined mass of the free enzymes waiting to consume it; this simple relationship arises from the optimal utilization of cellular dry mass, and quantitatively describes available experimental data.     

Purification and properties of adenosine triphosphate–creatine phosphotransferase from muscle of the dogfish Scylliorhinus canicula

1. Creatine kinase occurs in high concentration in the soluble proteins of dogfish muscle. A fourfold purification gives essentially pure enzyme but with a low specific activity. This appears to be a property of the native enzyme and not a result of the isolation procedures used. 2. The amino acid composition is similar to that of other phosphagen kinases, but the enzyme differs from mammalian creatine kinases in having four thiol groups readily reactive towards 5,5′-dithiobis-(2-nitrobenzoic acid). Titration of two thiol groups is accompanied by almost complete loss of activity. The remaining two thiol groups react at different rates, suggesting that modifying the third thiol group affects the reactivity of the fourth thiol group. 3. The enzyme is markedly protected against inactivation by iodoacetamide by MgATP or MgADP. Addition of creatine to MgADP decreases protection, but the further addition of Cl⁻ restores protection to the original value. The quaternary MgADP–creatine–enzyme–nitrate complex protects very strongly as is found for the rabbit enzyme. The involvement of the conformational state of the enzyme in such effects is discussed. 4. Creatine kinase from both dogfish and rabbit is equally sensitive to urea denaturation. Urea protects the dogfish enzyme by about 9% against inhibition by iodoacetamide. 5. The formation of a hybrid between the dogfish and rabbit enzymes in vitro has been demonstrated. 6. At high substrate concentrations the dogfish enzyme shows apparent ordered kinetics. The effect of temperature on V_max. and the Michaelis constants for MgATP and creatine were determined. These and changes in the apparent activation energy suggest that limited adaptation has occurred commensurate with physiological need.     

Dimensionless parameter predicts bacterial prodrug success

Understanding mechanisms of antibiotic failure is foundational to combating the growing threat of multidrug‐resistant bacteria. Prodrugs—which are converted into a pharmacologically active compound after administration—represent a growing class of therapeutics for treating bacterial infections but are understudied in the context of antibiotic failure. We hypothesize that strategies that rely on pathogen‐specific pathways for prodrug conversion are susceptible to competing rates of prodrug activation and bacterial replication, which could lead to treatment escape and failure. Here, we construct a mathematical model of prodrug kinetics to predict rate‐dependent conditions under which bacteria escape prodrug treatment. From this model, we derive a dimensionless parameter we call the Bacterial Advantage Heuristic (BAH) that predicts the transition between prodrug escape and successful treatment across a range of time scales (1–10⁴ h), bacterial carrying capacities (5 × 10⁴–10⁵ CFU/µl), and Michaelis constants (K_M  = 0.747–7.47 mM). To verify these predictions in vitro, we use two models of bacteria‐prodrug competition: (i) an antimicrobial peptide hairpin that is enzymatically activated by bacterial surface proteases and (ii) a thiomaltose‐conjugated trimethoprim that is internalized by bacterial maltodextrin transporters and hydrolyzed by free thiols. We observe that prodrug failure occurs at BAH values above the same critical threshold predicted by the model. Furthermore, we demonstrate two examples of how failing prodrugs can be rescued by decreasing the BAH below the critical threshold via (i) substrate design and (ii) nutrient control. We envision such dimensionless parameters serving as supportive pharmacokinetic quantities that guide the design and administration of prodrug therapeutics.     

A heat-stable nicotinamide–adenine dinucleotide glycohydrolase from Pseudomonas putida KB1. Partial purification and some properties of the enzyme and an inhibitory protein

A thermostable NAD(P)⁺ glycohydrolase (EC 3.2.2.6) detected in cell-free extracts of Pseudomonas putida KB1 was purified to a single component on polyacrylamide-gel electrophoresis. A heat-labile inhibitor of the enzyme was also partially purified. Enzyme free of inhibitor is present in culture supernatants. After an ultrasonic treatment enzyme–inhibitor complex and excess of inhibitor are present in both the cell-debris and soluble fractions. The general properties of the enzyme and inhibitor are described. The molecular weights of enzyme, inhibitor and enzyme–inhibitor complex, determined by gel filtration are about 23500, 15000 and 35000 respectively. The binding of inhibitor and enzyme is inhibited by the presence of substrate.     

Nucleoside diphosphate kinase from Mycobacterium tuberculosis cleaves single strand DNA within the human c-myc promoter in an enzyme-catalyzed reaction

The reason for secretion of nucleoside diphosphate kinase (NdK), an enzyme involved in maintaining the cellular pool of nucleoside triphosphates in both prokaryotes and eukaryotes, by Mycobacterium tuberculosis is intriguing. We recently observed that NdK from M.tuberculosis (mNdK) localizes within nuclei of HeLa and COS-1 cells and also nicks chromosomal DNA in situ (A. K. Saini, K. Maithal, P. Chand, S. Chowdhury, R. Vohra, A. Goyal, G. P. Dubey, P. Chopra, R. Chandra, A. K. Tyagi, Y. Singh and V. Tandon (2004) J. Biol. Chem., 279, 50142–50149). In the current study, using a molecular beacon approach, we demonstrate that the mNdK catalyzes the cleavage of single strand DNA. It displays Michaelis–Menten kinetics with a k_cat/K_M of 9.65 (±0.88) × 10⁶ M⁻¹ s⁻¹. High affinity (K_d ≈ K_M of ~66 nM) and sequence-specific binding to the sense strand of the nuclease hypersensitive region in the c-myc promoter was observed. This is the first study demonstrating that the cleavage reaction is also enzyme-catalyzed in addition to the enzymatic kinase activity of multifunctional NdK. Using our approach, we demonstrate that GDP competitively inhibits the nuclease activity with a K_I of ~1.9 mM. Recent evidence implicates mNdK as a potent virulence factor in tuberculosis owing to its DNase-like activity. In this context, our results demonstrate a molecular mechanism that could be the basis for assessing in situ DNA damage by secretory mNdK.     

Conformational change in the Bacillus subtilis RNase P holoenzyme–pre-tRNA complex enhances substrate affinity and limits cleavage rate

Ribonuclease P (RNase P) is a ribonucleoprotein complex that catalyzes the 5′ maturation of precursor tRNAs. To investigate the mechanism of substrate recognition in this enzyme, we characterize the thermodynamics and kinetics of Bacillus subtilis pre-tRNA^Asp binding to B. subtilis RNase P holoenzyme using fluorescence techniques. Time courses for fluorescein-labeled pre-tRNA binding to RNase P are biphasic in the presence of both Ca(II) and Mg(II), requiring a minimal two-step association mechanism. In the first step, the apparent bimolecular rate constant for pre-tRNA associating with RNase P has a value that is near the diffusion limit and is independent of the length of the pre-tRNA leader. Following formation of the initial enzyme–substrate complex, a unimolecular step enhances the overall affinity of pre-tRNA by eight- to 300-fold as the length of the leader sequence increases from 2 to 5 nucleotides. This increase in affinity is due to a decrease in the reverse rate constant for the conformational change that correlates with the formation of an optimal leader–protein interaction in the RNase P holoenzyme–pre-tRNA complex. Furthermore, the forward rate constant for the conformational change becomes rate limiting for cleavage under single-turnover conditions at high pH, explaining the origin of the observed apparent pK_a in the RNase P-catalyzed cleavage reaction. These data suggest that a conformational change in the RNase P•pre-tRNA complex is coupled to the interactions between the 5′ leader and P protein and aligns essential functional groups at the cleavage active site to enhance efficient cleavage of pre-tRNA.     

A steady state model of sequential irreversible enzyme reactions

Summary One of the questions which arises in the study of certain inborn errors of metabolism as well as in the field of enzyme kinetics is: what are the quantitative relationships between parameters of enzyme activity and substrate pool sizes in a metabolic pathway? A steady state model has been devised to answer this question for a homogeneous system of non-branched sequential irreversible enzyme reactions which follow Michaelis-Menten kinetics. The concentration of a substrate in such a pathway, [S_i], is a function of 5 variables: (a) the K_M of the enzyme which forms the substrate (K_{M (i–1)}), (b) the K_M of the enzyme which utilizes the substrate (K_{M i}), (c) the V_max of the enzyme which forms the substrate (V_{m (i–1)}), (d) the V_max of the enzyme which utilizes the substrate (V_{m i}) and (e) the immediate precursor concentration [S_(i–1)] where [S_i] = K_{M i} V_{m (i–1)} [S_(i–1)]/[S_(i–1)] (V_mi -V_{m (i–1)}) + K_{M (i–1)}) V_mi The model introduces and defines the concept of and conditions for amplification. An input in the form of a steady state concentration of precursor [S_(i–1)] may be amplified as an output in the form of an increased steady state concentration of product [S_i]. The model also defines the values of the above 5 parameters which do not allow attainment of a steady state for the type of pathway considered.From the Metabolism Branch, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20014.     

Purification of quinolinic acid phosphoribosyltransferase from rat liver and brain

Quinolinic acid phosphoribosyltransferase (EC 2.4.2.19) was purified 3600-fold from rat liver and 280-fold from rat brain. Kinetic analyses (K_m = 12 μM for the substrate quinolinic acid and K_m 23 μM for the cosubstrate phosphoribosylpyrophosphate), physicochemical properties of the purified enzymes, inhibition by phthalic acid (K_i = 1.4 μM) and molecular weight determination (M_r 160 000 for the holoenzyme, consisting of five identical 32 kDa subunits) indicated the structural identity of quinolinic acid phosphoribosyltransferase from the two rat tissues. This was further confirmed immunologically, using antibodies raised against purified rat liver quinolinic acid phosphoribosyltransferase. Rat quinolinic acid phosphoribosyltransferase differs in several aspects from quinolinic acid phosphoribosyltransferase isolated from other organisms. The purified enzyme will prove a useful tool in the examination of a possible role of quinolinic acid in cellular function and/or dysfunction.     

Nutrient Uptake by Microorganisms according to Kinetic Parameters from Theory as Related to Cytoarchitecture

The abilities of organisms to sequester substrate are described by the two kinetic constants specific affinity, a°, and maximal velocity V_max. Specific affinity is derived from the frequency of substrate-molecule collisions with permease sites on the cell surface at subsaturating concentrations of substrates. V_max is derived from the number of permeases and the effective residence time, τ, of the transported molecule on the permease. The results may be analyzed with affinity plots (v/S versus v, where v is the rate of substrate uptake), which extrapolate to the specific affinity and are usually concave up. A third derived parameter, the affinity constant K_A, is similar to K_M but is compared to the specific affinity rather than V_max and is defined as the concentration of substrate necessary to reduce the specific affinity by half. It can be determined in the absence of a maximal velocity measurement and is equal to the Michaelis constant for a system with hyperbolic kinetics. Both are taken as a measure of τ, with departure of K_M from K_A being affected by permease/enzyme ratios. Compilation of kinetic data indicates a 10⁸-fold range in specific affinities and a smaller (10³-fold) range in V_max values. Data suggest that both specific affinities and maximal velocities can be underestimated by protocols which interrupt nutrient flow prior to kinetic analysis. A previously reported inverse relationship between specific affinity and saturation constants was confirmed. Comparisons of affinities with ambient concentrations of substrates indicated that only the largest a°_S values are compatible with growth in natural systems.     

Thymine DNA glycosylase exhibits negligible affinity for nucleobases that it removes from DNA

Thymine DNA Glycosylase (TDG) performs essential functions in maintaining genetic integrity and epigenetic regulation. Initiating base excision repair, TDG removes thymine from mutagenic G·T mispairs caused by 5-methylcytosine (mC) deamination and other lesions including uracil (U) and 5-hydroxymethyluracil (hmU). In DNA demethylation, TDG excises 5-formylcytosine (fC) and 5-carboxylcytosine (caC), which are generated from mC by Tet (ten–eleven translocation) enzymes. Using improved crystallization conditions, we solved high-resolution (up to 1.45 Å) structures of TDG enzyme–product complexes generated from substrates including G·U, G·T, G·hmU, G·fC and G·caC. The structures reveal many new features, including key water-mediated enzyme–substrate interactions. Together with nuclear magnetic resonance experiments, the structures demonstrate that TDG releases the excised base from its tight product complex with abasic DNA, contrary to previous reports. Moreover, DNA-free TDG exhibits no significant binding to free nucleobases (U, T, hmU), indicating a K_d >> 10 mM. The structures reveal a solvent-filled channel to the active site, which might facilitate dissociation of the excised base and enable caC excision, which involves solvent-mediated acid catalysis. Dissociation of the excised base allows TDG to bind the beta rather than the alpha anomer of the abasic sugar, which might stabilize the enzyme–product complex.     

Enzyme kinetics and distinct modulation of the protein kinase N family of kinases by lipid activators and small molecule inhibitors

The PKN (protein kinase N) family of Ser/Thr protein kinases regulates a diverse set of cellular functions, such as cell migration and cytoskeletal organization. Inhibition of tumour PKN activity has been explored as an oncology therapeutic approach, with a PKN3-targeted RNAi (RNA interference)-derived therapeutic agent in Phase I clinical trials. To better understand this important family of kinases, we performed detailed enzymatic characterization, determining the kinetic mechanism and lipid sensitivity of each PKN isoform using full-length enzymes and synthetic peptide substrate. Steady-state kinetic analysis revealed that PKN1–3 follows a sequential ordered Bi–Bi kinetic mechanism, where peptide substrate binding is preceded by ATP binding. This kinetic mechanism was confirmed by additional kinetic studies for product inhibition and affinity of small molecule inhibitors. The known lipid effector, arachidonic acid, increased the catalytic efficiency of each isoform, mainly through an increase in k_cat for PKN1 and PKN2, and a decrease in peptide K_M for PKN3. In addition, a number of PKN inhibitors with various degrees of isoform selectivity, including potent (K_i<10 nM) and selective PKN3 inhibitors, were identified by testing commercial libraries of small molecule kinase inhibitors. This study provides a kinetic framework and useful chemical probes for understanding PKN biology and the discovery of isoform-selective PKN-targeted inhibitors.     

The kinetics of carboxymethylcellulose--ficin in packed beds

1. The kinetics of the hydrolysis of benzoylarginine ethyl ester in packed columns of CM-cellulose-70–ficin and CM-cellulose-90–ficin were studied. 2. The apparent Michaelis constant, K′_m, of these preparations was calculated and shown to be dependent on the flow rate at low rates of perfusion through the columns. 3. The values for k₃ of these preparations were calculated and shown to be nearly independent of flow rate. 4. A modified form of the integrated Michaelis rate equation was used to describe the action of these materials and its limitations are discussed. 5. The hydrolysis of solutions of casein by these columns was studied.     

Estimating Kinetic Parameters when the Amount of Enzyme Added to an Assay Is Not a Controlled Variable: NITROGENASE ACTIVITY OF INTACT LEGUMES

Reliable estimates of Michaelis constants (K_m) and inhibitor constants may be obtained, in the absence of control over the amount of enzyme being added to any assay system, provided the following constraints are met. Michaelis-Menten kinetics are obeyed. Two rate measurements must be made with the same sample of enzyme: at low and high substrate concentration for determining K_m or minus and plus an inhibitor for determining inhibitor constants. The Michaelis constant may be calculated from the equation [Formula: see text] Inhibitor constants are derived graphically from Lineweaver-Burk or Dixon plots, once the K_m has been calculated. The above technique has been applied to study of the acetylene-reducing ability of intact legume plants. The apparent K_m for acetylene reduction by nitrogenase in legume nodules is ~1/100 atmosphere in the absence of nitrogen and ~1/40 atmosphere in its presence.     

Pyruvate kinase variants of the Alaskan king-crab. Evidence for a temperature-dependent interconversion between two forms having distinct and adaptive kinetic properties

1. Pyruvate kinase of Alaskan king-crab leg muscle exists in two kinetically distinct forms, each of which displays a different temperature-dependence in the K_m for phosphoenolpyruvate. 2. A `cold' variant of the enzyme has hyperbolic kinetics and exhibits a minimal K<sub>m</sub> for substrate at 5°. At physiological concentrations of phosphoenolpyruvate the `cold' enzyme is active only below 10°. A `warm' pyruvate kinase has a minimal K<sub>m</sub> for substrate at about 12°. This enzyme displays sigmoidal kinetics and is likely to be inactive, at physiological substrate concentrations, at temperatures below 9°. 3. The combined activities of these two pyruvate kinases yield highly temperature-independent rates of catalysis, at physiological substrate concentrations, over the range of habitat temperatures encountered by the organism, namely 4–12°. 4. The two variants of pyruvate kinase do not appear to be isoenzymes in the conventional sense. Electrophoretic and electrofocus analyses revealed only single peaks of activity. 5. The results suggest that the `warm' pyruvate kinase and the `cold' pyruvate kinase are formed by a temperature-dependent interconversion of one protein species. This interconversion has major adaptive significance: as the temperature is lowered the `warm' enzyme is converted into the `cold' enzyme; the opposite situation obtains when the temperature is raised. Temperature changes thus mimic the effects noted for fructose 1,6-diphosphate on certain mammalian pyruvate kinases.     

Purification and properties of glutamine synthetase from the plant cytosol fraction of lupin nodules

Glutamine synthetase from the plant cytosol fraction of lupin nodules was purified 89-fold to apparent homogeneity. The enzyme molecule is composed of eight subunits of M_r 44,700 ± 10%. Kinetic analysis indicates that the reaction mechanism is sequential and there is some evidence that Mg-ATP is the first substrate to bind to the enzyme. Michaelis constants for each substrate using the ammonium-dependent biosynthetic reaction are as follows: ATP, 0.24 mm; l-glutamate, 4.0–4.2 mm; ammonium, 0.16 mm. Using an hydroxamate-forming biosynthetic reaction the K_m ATP is 1.1 mm but the K_m for l-glutamate is not altered. The effect of pH on the K_m for ammonium indicates that NH₃ rather than NH₄⁺ may be the true substrate. At 10 mm Mg²⁺, the pH optimum of the enzyme is between 7.5 and 8, but increasing Mg²⁺ concentrations produce progressively more acidic optima while lower Mg²⁺ concentrations raise the pH optimum. The rate-response curve for Mg²⁺ is sigmoidal becoming bell-shaped in alkaline conditions. The enzyme is inhibited by l-Asp (K_i, 1.4 mm) and less markedly by l-Gln and l-Asn. Inhibition by ADP and AMP is strong, both nucleotides exhibiting K_i values around 0.3 mM. Investigations of the probable physiological conditions within the nodule plant cytosol indicate that in situ glutamine synthetase has an activity greater than that required to support the efflux of amino acid nitrogen from the nodule. A possible role for glutamine synthetase in the control of nodule ammonium assimilation is suggested.     

Directed evolution of an orthogonal nucleoside analog kinase via fluorescence-activated cell sorting

Nucleoside analogs (NAs) represent an important category of prodrugs for the treatment of viral infections and cancer, yet the biological potency of many analogs is compromised by their inefficient activation through cellular 2′-deoxyribonucleoside kinases (dNKs). We herein report the directed evolution and characterization of an orthogonal NA kinase for 3′-deoxythymidine (ddT), using a new FACS-based screening protocol in combination with a fluorescent analog of ddT. Four rounds of random mutagenesis and DNA shuffling of Drosophila melanogaster 2′-deoxynucleoside kinase, followed by FACS analysis, yielded an orthogonal ddT kinase with a 6-fold higher activity for the NA and a 20-fold k_cat/K_M preference for ddT over thymidine, an overall 10 000-fold change in substrate specificity. The contributions of individual amino acid substitutions in the ddT kinase were evaluated by reverse engineering, enabling a detailed structure–function analysis to rationalize the observed changes in performance. Based on our results, kinase engineering with fluorescent NAs and FACS should prove a highly versatile method for evolving selective kinase:NA pairs and for studying fundamental aspects of the structure–function relationship in dNKs.     

Inhibition of renin by conformationally restricted analogues of angiotensinogen

[Cys⁵,Cys¹⁰]Angiotensinogen-(5–14)-peptide analogues and homologues were synthesized, in which a disulphide bond between residues 5 and 10 stabilized a 9→6 β-turn proposed for the substrate. These compounds were competitive inhibitors of human and pig renins with K_i values of the order of 10⁻⁶–10⁻⁵m, indicating that the conformation proposed for the substrate is important for the interaction with the enzyme.     

Spinach leaf acetyl-coenzyme a synthetase: purification and characterization

Acetyl-coenzyme A (CoA) synthetase was purified 364-fold from leaves of spinach (Spinacia oleracea L.) using ammonium sulfate fractionation followed by ion exchange, dye-ligand, and gel permeation chromatography. The final specific activity was 2.77 units per milligram protein. The average M_r value of the native enzyme was about 73,000. The Michaelis constants determined for Mg-ATP, acetate, and coenzyme A were 150, 57, and 5 micromolar, respectively. The purified enzyme was sensitive to substrate inhibition by CoA with an apparent K_i for CoA of 700 micromolar. The enzyme was specific for acetate; other short and long chain fatty acids were ineffective as substrates. Several intermediates and end products of fatty acid synthesis were examined as potential inhibitors of acetyl-CoA synthetase activity, but none of the compounds tested significantly inhibited acetyl-CoA synthetase activity in vitro. The properties of the purified enzyme support the postulated role of acetyl-CoA synthetase as a primary source of chloroplast acetyl-CoA.