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.

Effect of the potential-energy surface on the diatom dissociation rate constant for F 2 in Ar at 3000 K

1987 ◽  
Vol 414 (1847) ◽  
pp. 297-314
Keyword(s):  
Steady State ◽  
Rate Constant ◽  
Rate Constants ◽  
Reaction Rate ◽  
Energy Surface ◽  
Rate Coefficient ◽  
Classical Mechanics ◽  
Rate Coefficients ◽  
Steady State Rate ◽  
State Rate

Gas-phase dissociation of fluorine ( 1 Ʃ + g ) molecules in an agron bath at 3000 K was studied by using the 3D Monte Carlo classical trajectory (3DMCCT) method. To assess the importance of the potential energy surface (PES) in such calculations, three surfaces, with a fixed, experimentally determined F 2 dissociation energy, were constructed. These surfaces span the existing experimental uncertainties in the shape of the F 2 potential. The first potential was the widest and softest; in the second potential the anharmonicity was minimized. The intermediate potential was constructed to ‘localize’ anharmonicity in the energy range in which the collisions are most reactive. The remaining parameters for each PES were estimated from the best available data on interatomic potentials. By using the single uniform ensemble (SUE) method (Kutz, H. D. & Burns, G. J. chem. Phys . 72, 3652-3657 (1980)), large ensembles of trajectories (LET) were generated for the PES. Two such ensembles consisted of 30000 trajectories each and the third of 26200. It was found that the computed one-way-flux equilibrium rate coefficients (Widom, B. Science 148, 1555-1560 (1965)) depend in a systematic way upon the anharmonicity of the potential, with the most anharmonic potential yielding the largest rate coefficient. Steady-state reaction-rate constants, which correspond to experimentally observable rate constants, were calculated by the SUE method. It was determined that this method yields (for a given trajectory ensemble, PES and translational temperature) a unique steady-state rate constant, independent of the initial, arbitrarily chosen, state (Tolman, R. C. The principles of statistical mechanics , p. 17. Oxford University Press (1938)) of the LET, and consequently independent of the corresponding initial value of the reaction rate coefficient. For each initial state of the LET, the development of the steady-state rate constant from the equilibrium rate coefficient was smooth, monotonic, and consistent with the detailed properties of the PES. It was found that, although the increased anharmonicity of the F 2 potential enhanced the equilibrium rate coefficients, it also enhanced the non-equilibrium effects. As a result, the steady-state rate constants were found to be insensitive to the variation of the PES. Thus, the differences among the steady-state rate constants for the three potentials were of the order of their standard errors, which was about 15% or less. On the other hand, the calculated rate constants exceeded the experimental rate constant by a factor of five to six. Because within the limitations of classical mechanics the calculations were ab initio , it was tentatively concluded that the discrepancy of five to six is due to the use of classical mechanics rather than details of the PES structure.

scholarly journals The computerized derivation of steady-state rate equations for enzyme kinetics

1984 ◽  
Vol 223 (2) ◽  
pp. 551-553 ◽  
Author(s):  
D G Herries
Keyword(s):  
Steady State ◽  
Enzyme Kinetics ◽  
Rate Constants ◽  
Rate Equations ◽  
British Library ◽  
Steady State Rate ◽  
State Rate ◽  
Basic Version ◽  
Fortran 77

A FORTRAN 77 program is described for the derivation of steady-state rate equations for enzyme kinetics. Input is very simple and consists of the two enzyme forms and the two rate constants for each step in the mechanism. The program may be run interactively or off-line. The results are produced after collecting together the algebraic coefficients of like concentration terms, taking account of sign. A fully interactive BASIC version running on a BBC Microcomputer is also available. Details of the programs have been deposited as Supplementary Publication SUP 50126 (45 pages) with the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies may be obtained as indicated in Biochem. J. (1984) 217, 5.

A New Method for Determining Individual Rate Constants for Specific Non-chromophoric Substrates of Proteolytic Enzymes

1975 ◽  
Vol 53 (4) ◽  
pp. 564-571
Author(s):  
Lewis J. Brubacher
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Proteolytic Enzymes ◽  
Enzyme Mechanism ◽  
Steady State Kinetics ◽  
Steady State Rate ◽  
State Rate ◽  
Individual Rate ◽  
Kinetics Of ◽  
Hydrolysis Of

Equations are developed for the pre-steady state kinetics of the proteolytic enzyme-catalyzed hydrolysis of a substrate A in the presence of a monitoring substrate (or covalent inhibitor) S of known properties. A two-intermediate acyl–enzyme mechanism is assumed in which the first intermediate is in instantaneous equilibrium with enzyme and substrate. The appearance of the first product of substrate S is characterized by two relaxation rate constants. From these constants it is possible to determine the dissociation constant and the acylation and deacylation rate constants of substrate A. Criteria are also developed for using the steady state rate parameters of A to establish conditions for which the slower relaxation process is equivalent to the deacylation rate constant of A. The technique of premixing enzyme with substrate A has certain advantages in this approach.

scholarly journals Methods of determining rate constants in single-substrate–single-product enzyme reactions. Use of induced transport: limitations of product inhibition

1973 ◽  
Vol 133 (2) ◽  
pp. 255-261 ◽  
Author(s):  
H. G. Britton
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Enzyme Reaction ◽  
Product Inhibition ◽  
Single Product ◽  
Single Substrate ◽  
Product Term ◽  
Steady State Kinetics ◽  
Steady State Rate ◽  
State Rate

1. The calculation of the rate constants from steady-state kinetics of a single-substrate–single-product enzyme reaction in which there is an isomerization of the enzyme is described. 2. It is shown that even with the use of isotopically labelled substrates a set of solutions for the constants is obtained rather than a unique solution. However, limits are derived within which they must lie. 3. The most appropriate observations to determine the rate constants are measurements of Vmax. and Km for both substrate and product, and measurement of the degree of countertransport in an induced-transport test. 4. Experimental procedures for induced-transport tests and the quantitative interpretation of the results obtained are discussed. 5. Product inhibition is shown to be an ambiguous and imprecise means of determining the rate constants. Further, the absence of a [substrate]×[product] term in the denominator of the steady-state rate equation does not necessarily mean that the isomerization of the enzyme is rapid, since the term also disappears when the isomerization is very slow. 6. Similar considerations apply to carrier mechanisms.

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.

scholarly journals Algebraic methods for deriving steady-state rate equations. Practical difficulties with mechanisms that contain repeated rate constants

1976 ◽  
Vol 159 (1) ◽  
pp. 167-167 ◽  
Author(s):  
A Cornish-Bowden
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Algebraic Methods ◽  
Rate Equations ◽  
Steady State Rate ◽  
State Rate

Methods of deriving rate equations that rely on repetition of terms for identification of redundant or invalid terms give incorrect results if used with mechanisms in which some rate constants appear more than once.

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.

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.

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