Enzyme Kinetics for Complex System Enables Accurate Determination of Specificity Constants of Numerous Substrates in a Mixture by Proteomics Platform

Many important experiments in proteomics including protein digestion, enzyme substrate screening, enzymatic labeling, etc., involve the enzymatic reactions in a complex system where numerous substrates coexists with an enzyme. However, the enzyme kinetics in such a system remains unexplored and poorly understood. Herein, we derived and validated the kinetics equations for the enzymatic reactions in complex system. We developed an iteration approach to depict the enzymatic reactions in complex system. It was validated by 630 time-course points from 24 enzymatic reaction experiments and was demonstrated to be a powerful tool to simulate the reactions in the complex system. By applying this approach, we found that the ratio of substrate depletion is independent of other coexisted substrates under specific condition. This observation was then validated by experiments. Based on this striking observation, a simplified model was developed to determine the catalytic efficiencies of numerous competing substrates presented in the complex enzyme reaction system. When coupled with high-throughput quantitative proteomics technique, this simplified model enabled the accurate determination of catalytic efficiencies for 2369 peptide substrates of a protease by using only one enzymatic reaction experiment. Thus, this study provided, in the first time, a validated model for the large scale determination of specificity constants which could enable the enzyme substrate screening approach turned from a qualitative method of identifying substrates to a quantitative method of identifying and prioritizing substrates. Data are available via ProteomeXchange with identifier PXD004665.     

Kinetic analysis of the mechanism of Escherichia coli dihydrofolate reductase

A kinetic mechanism is presented for Escherichia coli dihydrofolate reductase which describes the full time course of the enzymatic reaction over a wide range of substrate and enzyme concentrations at pH 7.2 and 20 degrees C. Specific rate constants were estimated by computer simulation of the full time course of single turnover, burst, and steady-state experiments using both nondeuterated and deuterated NADPH. The mechanism involves the random addition of substrates, but the substrates and enzyme are not at equilibrium prior to the chemical transformation step. The rate-limiting step follows the chemical transformation, and the maximum velocity of the reaction is limited by the release of the product tetrahydrofolate. The full time course of the reaction is markedly affected by the formation of the enzyme-NADPH-tetrahydrofolate abortive complex, but not by the enzyme-NADP-dihydrofolate abortive complex.     

Statistical kinetics of macromolecular dynamics

Fluctuations in biochemical processes can provide insights into the underlying kinetics beyond what can be gleaned from studies of average rates alone. Historically, analysis of fluctuating transmembrane currents supplied information about ion channel conductance states and lifetimes before single-channel recording techniques emerged. More recently, fluctuation analysis has helped to define mechanochemical pathways and coupling ratios for the motor protein kinesin as well as to probe the contributions of static and dynamic disorder to the kinetics of single enzymes. As growing numbers of assays are developed for enzymatic or folding behaviors of single macromolecules, the range of applications for fluctuation analysis increases. To evaluate specific biochemical models against experimental data, one needs to predict analytically the distribution of times required for completion of each reaction pathway. Unfortunately, using traditional methods, such calculations can be challenging for pathways of even modest complexity. Here, we derive an exact expression for the distribution of completion times for an arbitrary pathway with a finite number of states, using a recursive method to solve algebraically for the appropriate moment-generating function. To facilitate comparisons with experiments on processive motor proteins, we develop a theoretical formalism for the randomness parameter, a dimensionless measure of the variance in motor output. We derive the randomness for motors that take steps of variable sizes or that move on heterogeneous substrates, and then discuss possible applications to enzymes such as RNA polymerase, which transcribes varying DNA sequences, and to myosin V and cytoplasmic dynein, which may advance by variable increments.     

Modeling intrinsic kinetics of enzymatic cellulose hydrolysis

A multistep approach was taken to investigate the intrinsic kinetics of the cellulase enzyme complex as observed with hydrolysis of noncrystalline cellulose (NCC). In the first stage, published initial rate mechanistic models were built and critically evaluated for their performance in predicting time-course kinetics, using the data obtained from enzymatic hydrolysis experiments performed on two substrates: NCC and alpha-cellulose. In the second stage, assessment of the effect of reaction intermediates and products on intrinsic kinetics of enzymatic hydrolysis was performed using NCC hydrolysis experiments, isolating external factors such as mass transfer effects, physical properties of substrate, etc. In the final stage, a comprehensive intrinsic kinetics mechanism was proposed. From batch experiments using NCC, the time-course data on cellulose, cello-oligosaccharides (COS), cellobiose, and glucose were taken and used to estimate the parameters in the kinetic model. The model predictions of NCC, COS, cellobiose, and glucose profiles show a good agreement with experimental data generated from hydrolysis of different initial compositions of substrate (NCC supplemented with COS, cellobiose, and glucose). Finally, sensitivity analysis was performed on each model parameter; this analysis provides some insights into the yield of glucose in the enzymatic hydrolysis. The proposed intrinsic kinetic model parametrized for dilute cellulose systems forms a basis for modeling the complex enzymatic kinetics of cellulose hydrolysis in the presence of limiting factors offered by substrate and enzyme characteristics.     

Self-organizing molecular networks.

Strong diffusional mixing and short delivery times typical for micrometer and sub-micrometer reaction volumes lead to a special situation where the turnover times of individual enzyme molecules become the largest characteristic time scale of the chemical kinetics. Under these conditions, populations of cross-regulating allosteric enzymes form molecular networks that exhibit various kinds of self-organized coherent collective dynamics.     

Free energy differences between enzyme bound states

A theory is presented that describes the free energy difference between the enzyme-substrate (ES) and enzyme-product (EP) complexes that is expected in enzymes optimized for catalytic efficiency. In such enzymes, the free energy drop between ES and EP complexes reflects a portion of the chemical potential difference between substrates and products outside the active site under physiological conditions. Qualitative and quantitative predictions of the model are discussed and compared with experimental data. The controversy over the kinetically optimal free energy profile for an enzymatic reaction operating under constraints set forward by Albery & Knowles (1976) is resolved.     

Elucidation of the chemical nature of the steady-state intermediates in the mechanism of carboxypeptidase A

Cryospectrokinetic studies of zinc and cobalt carboxypeptidase A disclosed two intermediates in the hydrolysis of both peptides and depsipeptides and furnished all the rate and equilibrium constants for the reaction scheme E + S in equilibrium ES1 in equilibrium ES2---E + P [Auld, D. S., Galdes, A., Geoghegan, K. F., Holmquist, B., Martinelli, R. A., & Vallee, B. L. (1984) Proc. Natl. Acad. Sci. U.S.A. 81, 5041-5045]. Since the ES2 intermediate is the predominate enzyme species present at steady state, its chemical nature is deducible from subzero chemical quench studies done after steady state is established. Extrapolation of the product concentration to zero time, [P0], measures the concentration of the enzyme species in which bond cleavage has occurred. For peptides, the [P0]values are zero, indicating that no product is generated prior to turnover and therefore the ES2 intermediate involves a complex between enzyme and intact peptide substrate. For depsipeptides, [P0] values are 1 mol of produce per mole of enzyme over the entire temperature range -20 to -50 degrees C, indicating cleavage of the ester bond occurs prior to the rate-limiting step so that ES2 is more properly denoted by EP1P2, where P1 and P2 are the substrates for the reverse reaction. The rate-limiting step for depsipeptides thus involves release of the products which may occur directly or through a mandatory conformational change followed by rapid product release.     

A century of enzyme kinetic analysis, 1913 to 2013

This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis–Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function.     

A ribonucleotide Origin for Life – Fluctuation and Near-ideal Reactions

Oligoribonucleotides are potentially capable of Darwinian evolution – they may replicate and can express an independent chemical phenotype, as embodied in modern enzymatic cofactors. Using quantitative chemical kinetics on a sporadically fed ribonucleotide pool, unreliable supplies of unstable activated ribonucleotides A and B at low concentrations recurrently yield a replicating AB polymer with a potential chemical phenotype. Self-complementary replication in the pool occurs during a minority (here ≈ 35 %) of synthetic episodes that exploit coincidental overlaps between 4, 5 or 6 spikes of arbitrarily arriving substrates. Such uniquely productive synthetic episodes, in which near-ideal reaction sequences recur at random, account for most AB oligonucleotide synthesis, and therefore underlie the emergence of net replication under realistic primordial conditions. Because overlapping substrate spikes are unexpectedly frequent, and in addition, complex spike sequences appear disproportionately, a sporadically fed pool can host unexpectedly complex syntheses. Thus, primordial substrate fluctuations are not necessarily a barrier to Darwinism, but instead can facilitate early evolution.     

Yeast orotidine-5'-phosphate decarboxylase: steady-state and pre-steady-state analysis of the kinetic mechanism of substrate decarboxylation

The catalytically active form of monofunctional yeast orotidine-5'-phosphate decarboxylase was a dimer (E(2)). The dimer equilibrium dissociation constant was 0.25 microM in 0.01 M MOPS Na(+) at pH 7.2. The bimolecular rate constant for dimer formation was 1.56 microM(-1) s(-1). The dimeric form of the enzyme was stabilized by NaCl such that the enzyme was E(2) in 100 mM NaCl at all concentrations of enzyme tested. The kinetics of binding of OMP to E(2) was governed by two ionizations (pK(1) = 6.1 and pK(2) = 7.7). From studies with substrate analogues, the higher pK was assigned to a group on the enzyme that interacted with the pyrimidinyl moiety. The value of the lower pK was dependent on the substrate analogue, which suggested that it was not exclusively the result of ionization of the phosphoryl moiety. During the decarboxylation of OMP, the fluorescence of E(2) was quenched over 20%. The enzymatic species with reduced fluorescence was a catalytically competent intermediate that had kinetic properties consistent with it being the initial enzyme-substrate complex. The stoichiometry for binding of OMP to E(2) was one OMP per enzyme monomer. The value of the first-order rate constant for conversion of the enzyme-substrate complex to free enzyme (36 s(-1)) calculated from a single turnover experiment ([E] > [S]) was slightly greater than the value of k(cat), 20 s(-1) (corrected for stoichiometry), calculated from steady-state data. In the single turnover experiments, the enzyme was E(2)*S, whereas in the steady-state turnover the experiment enzyme was E(2)*S(2). The similarity of these values suggested that the subunits were catalytically independent such that E(2)*S(2) could be treated as E*S and that conversion of the enzyme-substrate complex to E was k(cat). Kinetic data for the approach to the steady-state with OMP and E(2) yield a bimolecular association rate complex of 62 microM(-1) s(-1)and a dissociation rate constant for E*S of 60 s(-1). The commitment to catalysis was 0.25. By monitoring the effect of carbonic anhydrase on [H(+)] changes during a single turnover experiment, the initial product of the decarboxylation reaction was shown to be CO(2) not HCO(3-). UMP was released from the enzyme concomitantly with CO(2) during the conversion of E*S to E. Furthermore, the enzyme removed an enzyme equivalent of H(+) from solvent during this step of the reaction. The bimolecular rate constants for association of 6-AzaUMP and 8-AzaXMP, substrate analogues with markedly different nucleobases, had association rate constants of 112 and 130 microM(-1) s(-1), respectively. These results suggested that the nucleobase did not contribute significantly to the success of formation of the initial enzyme-substrate complex.     

Presteady state kinetic analysis of riboflavin synthase

Riboflavin synthase catalyzes a mechanistically complex dismutation affording riboflavin and 5-amino-6-ribitylamino-2,4(1H,3H)-pyrimidinedione from 6,7-dimethyl-8-ribityllumazine. The kinetics of the enzyme from Escherichia coli were studied under single turnover conditions. Stopped flow as well as quenched flow experiments documented the transient formation of a pentacyclic reaction intermediate. No other transient species were sufficiently populated to allow detection. The data are best described by a sequence of one second order and one first order reaction.     

DNA-(N4-cytosine)-methyltransferase from Bacillus amyloliquefaciens: kinetic and substrate binding properties

Interaction of DNA-(N4-cytosine)-methyltransferase from the Bacillus amyloliquefaciens (BamHI MTase, 49 kDa) with a 20-mer oligonucleotide duplex containing the palindrome recognition site GGATCC was studied by methods of steady-state and presteady-state kinetics of the methyl group transfer, gel retardation, and crosslinking of the enzyme subunits with glutaric aldehyde. In steady-state conditions, BamHI MTase displays a simple kinetic behavior toward a 20-mer oligonucleotide substrate. A linear dependence was observed for the reaction rate on the enzyme concentration and a Michaelis dependence of the reaction rate on the concentration of both substrates: S-adenosyl-L-methionine (SAM), the methyl group donor, and DNA, the methyl group acceptor. In independent experiments, the concentration of the 20-mer duplex or SAM was changed, the enzyme concentration being substantially lower then the concentrations of substrates. The kcat values determined in these conditions are in good agreement with one another and approximately equal to 0.05 s-1. The Km values for the duplex and SAM are 0.35 and 1.6 microM, respectively. An analysis of single turnover kinetics (at limiting concentration of the 20-mer oligonucleotide duplex) revealed the following characteristics of the BamHI MTase-dependent methylation of DNA. The value of rate constant of the DNA methylation step at the enzyme saturating concentration is on average 0.085 s-1, which is only 1.6 times higher than the value determined in steady-state conditions. Only one of two target cytidine residues was methylated in the course of the enzyme single turnover, which coincides with the earlier data on EcoRI MTase. Regardless of the order of the enzyme preincubation with SAM and DNA, both curves for the single turnover methylation are comparable. These results are consistent with the model of the random order of the productive ternary enzyme-substrate complex formation. In contrast to the relatively simple kinetic behavior of BamHI MTase in the steady-state reaction are the data on the enzyme binding of DNA. In gel retardation experiments, there was no stoichiometrically simple complexes with the oligonucleotide duplex even at low enzyme concentrations. The molecular mass of the complexes was so high that they did not enter 12% PAG. In experiments on crosslinking of the BamHI MTase subunits, it was shown that the enzyme in a free state exists as a dimer. Introduction of substoichiometric amounts of DNA into the reaction mixture results in pronounced multimerization of the enzyme. However, addition of SAM in saturating concentration at an excess of the oligonucleotide duplex over BamHI MTase converts most of the enzyme into a monomeric state.     

A new mechanism and kinetic model for the enzymatic synthesis of short-chain fructooligosaccharides from sucrose

A kinetic model based on a ping-pong mechanism was developed under the steady-state hypothesis to account for the short-chain fructooligosaccharides (sc-FOS) synthesis using the commercial cellulolytic enzyme preparation, Rohapect CM. This new mechanism takes into account the interactions between the enzyme species and potential substrates (sucrose and sc-FOS) as a single complex reaction, allowing a better understanding of the reaction kinetics.The initial reaction rate laws appropriately describe the kinetic profiles of the examined substrates. Whereas sucrose exhibited Michaelis–Menten behavior with substrate inhibition, 1-kestose and nystose followed Michaelis–Menten and sigmoid enzyme kinetics. In addition, the enzyme was competitively inhibited by glucose and exhibited significant hydrolytic activity in the presence of nystose.The overall model was simultaneously fitted to experimental data from three initial sucrose concentrations (0.5, 1.5 and 2.1 M) using a multi-response regression with kinetic parameters that have biochemical relevance and are independent of the enzyme concentration. According to the model, sucrose acts almost exclusively as a fructosyl donor substrate. The mathematical development described herein is expected to be suitable for modeling similar enzymatic reaction systems.     

Kinetics of Inhibition of Green Crab (Scylla serrata) Alkaline Phosphatase by L-Cysteine

The inhibition of alkaline phosphatase from green crab (Scylla serrata) by L-cysteine has been studied. The results show that L-cysteine gives a mixed-type inhibition. The progress-of-substrate-reaction method previously described by Tsou [(1988), Adv. Enzymol. Related Areas Mol. Biol. 61, 391–436] was used to study the inactivation kinetics of the enzyme by L-cysteine. The microscopic rate constants were determined for reaction of the inhibitor with the free enzyme and the enzyme–substrate complex (ES) The results show that inactivation of the enzyme by L-cysteine is a slow, reversible reaction. Comparison of the inactivation rate constants of free enzyme and ES suggests that the presence of the substrate offers marked protection of this enzyme against inactivation by L-cysteine.     

DNA-(N4-Cytosine)-Methyltransferase from Bacillus amyloliquefaciens: Kinetic and Substrate-binding Properties

Interaction of DNA-(N4-cytosine)-methyltransferase from the Bacillus amyloliquefaciens (BamHI MTase, 49 kDa) with a 20-mer duplex containing a palindromic recognition site GGATCC was studied by methods of steady-state and pre-steady-state kinetics of the methyl group transfer, gel retardation, and crosslinking of the enzyme subunits with glutaraldehyde. In steady-state conditions, BamHI MTase displays a simple kinetic behavior toward the 20-mer substrate. A linear dependence was observed for the reaction rate on the enzyme concentration and a Michaelis dependence of the reaction rate on the concentration of both substrates: S-adenosyl-L-methionine (SAM), the methyl group donor, and DNA, the methyl group acceptor. In independent experiments, the concentration of the 20-mer duplex or SAM was changed, the enzyme concentration being substantially lower than the concentrations of substrates. The k _cat values determined in these conditions are in good agreement with one another and approximately equal to 0.05 s^–1. The K _M values for the duplex and SAM are 0.35 and 1.6 M, respectively. An analysis of single turnover kinetics (at limiting concentration of the 20-mer duplex) revealed the following characteristics of the BamHI MTase-dependent methylation of DNA. The value of rate constant of the DNA methylation step at the enzyme saturating concentration is on average 0.085 s^–1, which is only 1.6 times higher than the value determined in steady-state conditions. Only one of two target cytidine residues was methylated in a single turnover of the enzyme, which coincides with the earlier data on EcoRI MTase. Regardless of the order of enzyme preincubation with SAM and DNA, both curves for the single turnover methylation are comparable. These results are consistent with the model of the random order of the productive ternary enzyme–substrate complex formation. In contrast to the relatively simple kinetic behavior of BamHI MTase in the steady-state reaction are the data on the enzyme binding with DNA. In gel retardation experiments, there was no stoichiometrically simple complex with the oligonucleotide duplex even at low enzyme concentrations. The molecular mass of the complexes was so high that they did not enter 12% PAG. In experiments on crosslinking of the BamHI MTase subunits, it was shown that the enzyme in a free state exists as a dimer. Introduction of substoichiometric amounts of DNA into the reaction mixture results in pronounced multimerization of the enzyme. However, addition of SAM in saturating concentration at an excess of the oligonucleotide duplex over BamHI MTase converts most of the enzyme into a monomeric state.     

Kinetics of Inhibition of Green Crab (Scylla serrata) Alkaline Phosphatase by L-Cysteine

The inhibition of alkaline phosphatase from green crab (Scylla serrata) by L-cysteine has been studied. The results show that L-cysteine gives a mixed-type inhibition. The progress-of-substrate-reaction method previously described by Tsou [(1988), Adv. Enzymol. Related Areas Mol. Biol. 61, 391–436] was used to study the inactivation kinetics of the enzyme by L-cysteine. The microscopic rate constants were determined for reaction of the inhibitor with the free enzyme and the enzyme–substrate complex (ES) The results show that inactivation of the enzyme by L-cysteine is a slow, reversible reaction. Comparison of the inactivation rate constants of free enzyme and ES suggests that the presence of the substrate offers marked protection of this enzyme against inactivation by L-cysteine.     

Coordinating the initial steps of base excision repair. Apurinic/apyrimidinic endonuclease 1 actively stimulates thymine DNA glycosylase by disrupting the product complex

DNA glycosylases initiate base excision repair by removing damaged or mismatched bases, producing apurinic/apyrimidinic (AP) DNA. For many glycosylases, the AP-DNA remains tightly bound, impeding enzymatic turnover. A prominent example is thymine DNA glycosylase (TDG), which removes T from G.T mispairs and recognizes other lesions, with specificity for damage at CpG dinucleotides. TDG turnover is very slow; its activity appears to reach a plateau as the [product]/[enzyme] ratio approaches unity. The follow-on base excision repair enzyme, AP endonuclease 1 (APE1), stimulates the turnover of TDG and other glycosylases, involving a mechanism that remains largely unknown. We examined the catalytic activity of human TDG (hTDG), alone and with human APE1 (hAPE1), using pre-steady-state kinetics and a coupled-enzyme (hTDG-hAPE1) fluorescence assay. hTDG turnover is exceedingly slow for G.T (k(cat)=0.00034 min(-1)) and G.U (k(cat)=0.005 min(-1)) substrates, much slower than k(max) from single turnover experiments, confirming that AP-DNA release is rate-limiting. We find unexpectedly large differences in k(cat) for G.T, G.U, and G.FU substrates, indicating the excised base remains trapped in the product complex by AP-DNA. hAPE1 increases hTDG turnover by 42- and 26-fold for G.T and G.U substrates, the first quantitative measure of the effect of hAPE1. hAPE1 stimulates hTDG by disrupting the product complex rather than merely depleting (endonucleolytically) the AP-DNA. The enhancement is greater for hTDG catalytic core (residues 111-308 of 410), indicating the N- and C-terminal domains are dispensable for stimulatory interactions with hAPE1. Potential mechanisms for hAPE1 disruption of the of hTDG product complex are discussed.     

A study of heat of formation of acetyl-alpha-chymotrypsin intermediate by stopped flow calorimetry

The catalytic hydrolysis of p-nitrophenyl acetate by alpha-chymotrypsin was studied by stopped-flow calorimetry and spectrophotometry at pH 8.0 and 25 degrees C. The initial burst and subsequent steady state of the reaction were observed by rapid calorimetry and spectrophotometry. Based on the three-step mechanism established for the enzymatic reaction, E + S in equilibrium ES leads to acetyl-E + P1 (p-nitrophenol) leads to E + P1 + acetic acid, the enthalpy change of formation of the acetyl enzyme from ES complex was estimated to be -29 kJ . mol-1.     

Improving the catalytic activity of a thermophilic enzyme at low temperatures

Enzymes from thermophilic organisms often are barely active at low temperatures. To obtain a better understanding of this sluggishness, we used DNA shuffling to mutagenize the trpC gene, which encodes indoleglycerol phosphate synthase, from the hyperthermophile Sulfolobus solfataricus. Mutants producing more active protein variants were selected by genetic complementation of an Escherichia coli mutant bearing a trpC deletion. Single amino acid changes and combinations of these changes improved growth appreciably. Five singly and doubly altered protein variants with changes at the N- and C-termini, or at the phosphate binding site, were purified and characterized with regard to their kinetics of enzymatic catalysis, product binding, cleavage by trypsin, and inactivation by heat. Turnover numbers of the purified variant proteins correlated with the corresponding growth rates, showing that the turnover number was the selected trait. Although the affinities for both the substrate and the product decreased appreciably in most protein variants, these defects were offset by the accumulation of high levels of the enzyme's substrate. Rapid mixing of the product indoleglycerol phosphate with the parental enzyme revealed that the enzyme's turnover number at low temperatures is limited by the dissociation of the enzyme-product complex. In contrast, representative protein variants bind and release the product far more rapidly, shifting the bottleneck to the preceding chemical step. The turnover number of the parental enzyme increases with temperature, suggesting that its structural rigidity is responsible for its poor catalytic activity at low temperatures. In support of this interpretation, the rate of trypsinolysis or of thermal denaturation is accelerated significantly in the activated protein variants.