scholarly journals The kinetics of the reaction of nitrophenyl phosphates with alkaline phosphatase from Escherichia coli

1968 ◽  
Vol 106 (2) ◽  
pp. 455-460 ◽  
Author(s):  
D. R. Trentham ◽  
H. Gutfreund
Keyword(s):  
Escherichia Coli ◽  
Steady State ◽  
Ph Dependence ◽  
Substrate Complex ◽  
Enzyme Substrate ◽  
Nitrophenyl Phosphate ◽  
Steady State Rate ◽  
State Rate ◽  
Rate Of Hydrolysis ◽  
Ph Range

1. The steady-state rate of hydrolysis of 2,4-dinitrophenyl phosphate catalysed by Escherichia coli phosphatase is identical with that of 4-nitrophenyl phosphate over the pH range 5·5–8·5. 2. The increase in the rate of the enzyme-catalysed decomposition of nitrophenyl phosphates in the presence of tris at pH8·1 and 5·9 is consistent with the hypothesis that tris increases the rate of decomposition of a phosphoryl-enzyme intermediate. At pH8·1 the rate of decomposition of the phosphoryl-enzyme is approximately twice as fast as the rate of its formation, whereas at pH5·9 the rate of formation of the phosphoryl-enzyme is considerably faster than its decomposition. 3. Pre-steady-state measurements of the initial transient of the liberation of 2,4-dinitrophenol during the reaction of the enzyme with 2,4-dinitrophenyl phosphate confirmed the above pH-dependence of the ratio of the rates of phosphorylation and dephosphorylation of the enzyme. At optimum pH (above pH8), when the phosphorylation of the enzyme by the substrate is rate-determining, this step must be controlled by a rearrangement of the enzyme or enzyme–substrate complex.

The influence of pH and inhibitors on the kinetics of enzyme reactions involving two intermediates

1967 ◽  
Vol 45 (5) ◽  
pp. 539-546 ◽  
Author(s):  
Harvey Kaplan ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Ph Dependence ◽  
Free Enzyme ◽  
State Equations ◽  
Enzyme Reactions ◽  
Substrate Complex ◽  
Rate Determining Step ◽  
Enzyme Substrate ◽  
Special Cases ◽  
Influence Of Ph

General steady-state equations are worked out for enzyme reactions which occur according to the scheme [Formula: see text]Equations showing the pH dependence of the kinetic parameters are developed in a form which distinguishes between essential and nonessential ionizing groups. The pK dependence of [Formula: see text], the second-order constant extrapolated to zero substrate constant, gives pK values for groups which ionize on the free enzyme, but reveals such a pK only if the corresponding group is also involved in the breakdown of the Michaelis complex. General steady-state equations are also developed for the case in which an inhibitor can combine with the free enzyme, the enzyme–substrate complex, and also a second intermediate (e.g. an acyl enzyme). The equations are given in a form that is convenient for analyzing the experimental results, and a number of special cases are considered. It is shown how the type of inhibition depends not only on the nature of the inhibitor but also on that of the substrate, an important factor being the rate-determining step of the reaction. Examples of the various kinds of behavior are given.

THEORY OF THE TRANSIENT PHASE IN KINETICS, WITH SPECIAL REFERENCE TO ENZYME SYSTEMS: II. THE CASE OF TWO ENZYME–SUBSTRATE COMPLEXES

1956 ◽  
Vol 34 (2) ◽  
pp. 146-150 ◽  
Author(s):  
Ludovic Ouellet ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Substrate Concentration ◽  
Kinetic Scheme ◽  
Rate Equations ◽  
Theoretical Treatment ◽  
Transient Phase ◽  
Enzyme Substrate ◽  
Enzyme Systems ◽  
Steady State Rate ◽  
State Rate

A theoretical treatment is worked out for the kinetic scheme[Formula: see text]in which two enzyme–substrate complexes are formed consecutively. The steady-state rate equations are obtained, and equations are given for the transient phase subject to the condition that the substrate concentration is greatly in excess of that of the enzyme. Some kinetic consequences of the resulting equations are discussed.

scholarly journals The kinetics of ox kidney biliverdin reductase in the pre-steady state. Evidence that the dissociation of bilirubin is the rate-determining step

1989 ◽  
Vol 259 (3) ◽  
pp. 709-713 ◽  
Author(s):  
E Rigney ◽  
T J Mantle ◽  
F M Dickinson
Keyword(s):  
Steady State ◽  
Rate Constant ◽  
Ph Dependence ◽  
Order Rate Constant ◽  
Protein Fluorescence ◽  
Biliverdin Reductase ◽  
Rate Determining Step ◽  
Steady State Rate ◽  
State Rate ◽  
Kinetics Of

When the production of bilirubin by biliverdin reductase was monitored at 460 nm by stopped-flow spectrophotometry a ‘burst’ was observed with a first-order rate constant at pH 8 of 20 s-1. The steady-state rate was established on completion of the ‘burst’. When the reaction was monitored at 401 nm there was no observed steady-state rate, but a diminished pre-steady-state ‘burst’ reaction was still seen with a rate constant of 22 s-1. We argue that the rate-limiting reaction is the dissociation of bilirubin from an enzyme.NADP+.bilirubin complex. With NADPH as the cofactor the hydride-transfer step was shown to exhibit pH-dependence associated with an ionizing group with a pK of 7.2. The kinetics of NADPH binding to the enzyme at pH 7.0 were measured by monitoring the quenching of protein fluorescence on binding the coenzyme.

pH-dependence of the fast step of maltose hydrolysis catalysed by glucoamylase G1 from Aspergillus niger

2000 ◽  
Vol 349 (2) ◽  
pp. 623-628 ◽  
Author(s):  
Ulla CHRISTENSEN
Keyword(s):  
Aspergillus Niger ◽  
Ph Dependence ◽  
Acid Group ◽  
Reaction Scheme ◽  
Free Enzyme ◽  
Pka Values ◽  
Substrate Complex ◽  
Enzyme Substrate ◽  
Ph Range ◽  
State Kinetic

The presteady-state kinetic parameters of the interaction of wild-type glucoamylase from Aspergillus niger (EC 3.2.1.3) with maltose were obtained and analysed in the pH range 3-7 with intervals of 0.25 pH units. In all cases the following three-step reaction scheme was found to apply. E+S ES1 ES2 E+P The general result of the analysis of the presteady-state kinetics is that glucoamylase G1 is affected by the protonation states of three groups, with pKa values of 2.7, 4.5 and 5.7 in the free enzyme and of 2.7, 4.75 and 6.5 in the first enzyme-substrate complex. The protonation of the group in the enzyme-substrate complex with a pKa 6.5 had no effect on k2 (1640 s-1) or k-2 (20±4 s-1), but resulted in a stronger enzyme-substrate interaction, due to a decrease of K1 from 40 to 6.3 mM. In other words, when the substrate is bound, the pKa of the acid group changes to increase the fraction of reactive enzyme. Since this pKa parallels that of the Michaelis complex, known from the pH-dependence of kcat, the group in question is most probably the catalytic acid Glu-179. Protonation of Glu-179 thus is of no importance in the second step, clearly indicating that this step represents a conformational change and not the actual hydrolysis step of the reaction. Protonation of the pKa = 4.75 group leads to a small decrease in k2 to 1090 s-1, and also to minor changes in K1. The group with pKa = 2.7 leads to a major decrease of k2, of which the limit may be zero, but shows no effect on K1. Thus no difference is seen between the pKa values of the free enzyme and of the first enzyme-substrate complex at low pH.

Transient-phase studies of a trypsin-catalyzed reaction

1970 ◽  
Vol 48 (12) ◽  
pp. 1793-1802 ◽  
Author(s):  
H. P. Kasserra ◽  
K. J. Laidler
Keyword(s):  
Steady State ◽  
Ph Dependence ◽  
Enzyme Concentration ◽  
Alcohol Concentration ◽  
Substrate Complex ◽  
Enzyme Substrate ◽  
Steady State Kinetics ◽  
Kinetics Of ◽  
Hydrolysis Of ◽  
Nitrophenyl Ester

The stopped-flow technique has been used to study the pre-steady-state kinetics of the hydrolysis of N-carbobenzoxy-L-alanine-p-nitrophenyl ester catalyzed by trypsin. By working under conditions such that the enzyme concentration is much greater than that of the substrate, it has been possible to measure [Formula: see text] the rate constant for the conversion of the enzyme-substrate complex into the acyl enzyme. The pH dependence of [Formula: see text] reveals a pKb′ value of 6.9 for the conversion of complex into acyl enzyme, in agreement with deductions from steady-state investigations. The pH dependence of [Formula: see text] (equal to k−1 + k2)/k1) has also been determined. The results provide direct evidence for the existence of an enzyme-substrate complex for this reaction.The work has been done in various mixtures of water and isopropyl alcohol. The logarithms of the rate constants [Formula: see text] and [Formula: see text] vary linearly with 1/D, showing a decrease with increasing alcohol concentration; [Formula: see text] increases with alcohol concentration. The solvent results suggest that addition of alcohol affects the hydrophobic bonding in the protein and leads to unfolding of the enzyme.

scholarly journals PH-dependence of the steady-state rate of a two-step enzymic reaction

1976 ◽  
Vol 155 (1) ◽  
pp. 61-70 ◽  
Author(s):  
K Brocklehurst ◽  
H B F Dixon
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Total Concentration ◽  
Ph Dependence ◽  
Ionization Constants ◽  
Ph Profile ◽  
Irreversible Reaction ◽  
Steady State Rate ◽  
State Rate ◽  
Molecular Ionization

1. The pH-dependence is considered of a reaction between E and S that proceeds through an intermediate ES under “Briggs-Haldane” conditions, i.e. there is a steady state in ES and [S]o greater than [E]T, where [S]o is the initial concentration of S and [E]T is the total concentration of all forms of E. Reactants and intermediates are assumed to interconvert in three protonic states (E equilibrium ES; EH equilibrium EHS; EH2 equilibrium EH2S), but only EHS provides products by an irreversible reaction whose rate constant is kcat. Protonations are assumed to be so fast that they are all at equilibrium. 2. The rate equation for this model is shown to be v = d[P]/dt = (kcat.[E]T[S]o/A)/[(KmBC/DA) + [S]o], where Km is the usual assembly of rate constants around EHS and A-D are functions of the form (1 + [H]/K1 + K2/[H]), in which K1 and K2 are: in A, the molecular ionization constants of ES; in B, the analogous constants of E; in C and D, apparent ionization constants composed of molecular ionization constants (of E or ES) and assemblies of rate constants. 3. As in earlier treatments of this type of reaction which involve either the assumption that the reactants and intermediate are in equilibrium or the assumption of Peller & Alberty [(1959) J. Am. Chem. Soc. 81, 5907-5914] that only EH and EHS interconvert directly, the pH-dependence of kcat. is determined only by A. 4. The pH-dependence of Km is determined in general by B-C/A-D, but when reactants and intermediate are in equilibrium, C identical to D and this expression simplifies to B/A. 5. The pH-dependence of kcat./Km, i.e. of the rate when [S]o less than Km, is not necessarily a simple bell-shaped curve characterized only by the ionization constants of B, but is a complex curve characterized by D/B-C. 6. Various situations are discussed in which the pH-dependence of kcat./Km is determined by assemblies simpler than D/B-C. The special situation in which a kcat./Km-pH profile provides the molecular pKa values of the intermediate ES complex is delineated.

scholarly journals Spontaneous Cleavages of a Heterologous Protein, the CenA Endoglucanase of Cellulomonas fimi, in Escherichia coli

2021 ◽  
Vol 14 ◽  
pp. 117863612110246
Author(s):  
Cheuk Yin Lai ◽  
Ka Lun Ng ◽  
Hao Wang ◽  
Chui Chi Lam ◽  
Wan Keung Raymond Wong
Keyword(s):  
Escherichia Coli ◽  
Cellulolytic Bacterium ◽  
Systematic Screening ◽  
Cellulomonas Fimi ◽  
E Coli ◽  
Substrate Complex ◽  
Enzyme Substrate ◽  
Glycosylation Sites ◽  
Endogenous Proteins ◽  
Cellulose Binding

CenA is an endoglucanase secreted by the Gram-positive cellulolytic bacterium, Cellulomonas fimi, to the environment as a glycosylated protein. The role of glycosylation in CenA is unclear. However, it seems not crucial for functional activity and secretion since the unglycosylated counterpart, recombinant CenA (rCenA), is both bioactive and secretable in Escherichia coli. Using a systematic screening approach, we have demonstrated that rCenA is subjected to spontaneous cleavages (SC) in both the cytoplasm and culture medium of E. coli, under the influence of different environmental factors. The cleavages were found to occur in both the cellulose-binding (CellBD) and catalytic domains, with a notably higher occurring rate detected in the former than the latter. In CellBD, the cleavages were shown to occur close to potential N-linked glycosylation sites, suggesting that these sites might serve as ‘attributive tags’ for differentiating rCenA from endogenous proteins and the points of initiation of SC. It is hypothesized that glycosylation plays a crucial role in protecting CenA from SC when interacting with cellulose in the environment. Subsequent to hydrolysis, SC would ensure the dissociation of CenA from the enzyme-substrate complex. Thus, our findings may help elucidate the mechanisms of protein turnover and enzymatic cellulolysis.

Corticosterone secretion in rats as a function of ACTH input and adrenal blood flow

1965 ◽  
Vol 209 (4) ◽  
pp. 811-814 ◽  
Author(s):  
John C. Porter ◽  
M. S. Klaiber
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Steady Increase ◽  
Constant Input ◽  
Corticosterone Secretion ◽  
Steady State Rate ◽  
State Rate

The rate of secretion of corticosterone from the left adrenal of rats receiving a constant input of ACTH was determined for different flows of blood through the adrenal during the 2- to 3-hr interval following hypophysectomy. Two hours after hypophysectomy the secretion of corticosterone was low in all groups regardless of flow. An input of 0.26 mU ACTH/min caused a steady increase in secretion for 30–40 min before a steady-state rate was attained. The average steady-state rate of secretion was 1.1, 2.4, 3.5, 6.2, 7.2, 6.2, and 6.2 µg/5 min for flows of 0.005, 0.012, 0.023, 0.034, 0.039, 0.051, and 0.058 ml/min, respectively. Under the conditions of these experiments where the input of ACTH was 0.26 mU/min the secretion of corticosterone increased significantly with time of input of ACTH and with flow of blood through the adrenal.

scholarly journals The Natural Rate of Interest and the Optimal Rate of Interest in the Steady State

2021 ◽  
pp. 17-41
Author(s):  
Carl Christian von Weizsäcker ◽  
Hagen M. Krämer
Keyword(s):  
Steady State ◽  
Public Debt ◽  
Fundamental Equation ◽  
Optimal Rate ◽  
Natural Rate ◽  
Real Rate ◽  
Capital Theory ◽  
Steady State Rate ◽  
Natural Rate Of Interest ◽  
State Rate

AbstractThe “natural rate of interest” is the hypothetical, risk-free real rate of interest that would obtain in a closed economy, if net public debt were zero. It is considerably less than the optimal steady-state rate of interest, which is equal to the system’s growth rate. This holds for a very general “meta-model.” The fundamental equation of capital theory holds on the optimal steady-state path: T = Z − D, where T is the overall economic period of production, Z is the representative private “waiting period” of consumers and D is the public debt ratio. Prosperity is at least 30% lower at the natural rate of interest than at the optimal rate.

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