An analysis of non-linear Eadie-Hofstee-Scatchard representations of ligand-binding and initial-rate data for allosteric and other complex enzyme mechanisms

1. The eight methods for plotting enzyme kinetic data are classified and analysed, and it is shown how, in each case, it is only possible to obtain quantitative data on the coefficients of the lowest- and highest-degree terms in the rate equation. 2. The combinations of coefficients that are accessible experimentally from limiting slopes and intercepts at both low and high substrate concentration are stated for all the graphical methods and the precise effects of these on curve shape in different spaces is discussed. 3. Ambiguities arising in the analysis of complex curves and certain special features are also investigated. 4. Four special ordering functions are defined and investigated and it is shown how knowledge of these allows a complete description of all possible complex curve shapes.

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STUDIES ON THE FORMATION OF HEXAMINE

Canadian Journal of Chemistry ◽

10.1139/v52-081 ◽

1952 ◽

Vol 30 (9) ◽

pp. 687-693 ◽

Cited By ~ 1

Author(s):

T. R. Ingraham ◽

C. A. Winkler

Keyword(s):

Activation Energy ◽

Acetic Acid ◽

Acid Solution ◽

Induction Period ◽

Ammonium Nitrate ◽

Sodium Acetate ◽

Glacial Acetic Acid ◽

Initial Rate ◽

Acetic Acid Solution ◽

Rate Data

Rate curves have been determined for the reaction of ammonium nitrate with formaldehyde in glacial acetic acid solution at 25 °C., 35 °C., 45 °C., and 55 °C. over a range of Initial mole ratios (formaldehyde: ammonia) of 0.75:1 to 9.0:1. Data obtained at 25 °C. show a definite induction period in the formation of hexamine. The length of the induction period is not changed by increasing ammonium nitrate concentrations above the theoretical (1.5:1), but may be appreciably shortened by initial additions of excess formaldehyde or of sodium acetate. From 35 °C. upward, the induction period is not apparent. The order of the reaction with respect to formaldehyde has been determined from initial rate data, and an activation energy calculated. The reactions in general appear analogous to those found in slightly acid aqueous systems.

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Correspondence. Batch and Continuous Thickening. Prediction of Batch Settling Behavior from Initial Rate Data with Results for Rigid Spheres

Industrial & Engineering Chemistry Fundamentals ◽

10.1021/i160015a026 ◽

1965 ◽

Vol 4 (3) ◽

pp. 366-368 ◽

Cited By ~ 1

Author(s):

J. E. Buchanan ◽

P. T. Shannon ◽

E. M. Tory

Keyword(s):

Initial Rate ◽

Rate Data ◽

Rigid Spheres ◽

Settling Behavior

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The Reaction of Ozone with SBR Rubbers

Rubber Chemistry and Technology ◽

10.5254/1.3542467 ◽

1959 ◽

Vol 32 (4) ◽

pp. 1062-1079 ◽

Cited By ~ 12

Author(s):

E. R. Erickson ◽

R. A. Berntsen ◽

E. L. Hill ◽

Paul Kusy

Keyword(s):

Initial Rate ◽

Protective Action ◽

Rate Data ◽

High Solubility ◽

Initial Concentration ◽

Degree Of Protection ◽

Effective Barrier ◽

Gaseous Ozone ◽

Low Concentrations ◽

Oxidized Products

Abstract All SBR vulcanizates, when tested in a relaxed state, reacted with ozone of low concentrations to form a film of oxidized products which provided an effective barrier against further attack by gaseous ozone. SBR vulcanizates that were under stress, but which contained no effective antiozonant in their formulation, were readily attacked by ozone. The absorption of ozone appeared to begin with an initial rate of zero which was followed by rapidly increasing rates until a maximum had been reached, when ozone cracks were visible on the surface of the rubber. SBR vulcanizates that were under stress, but which contained an antiozonant, were protected from an attack by ozone to a degree that ranged from poor to excellent. The degree of protection depended (a) on the differential in the rates of reaction of the antiozonant and the rubber hydrocarbon with ozone, (b) on the initial concentration of the antiozonant on the surface of the vulcanizate which reacted with ozone to form a barrier of oxidized residues, and (c) on the rate of effusion of fresh antiozonant from within the rubber to the outer surface of the barrier. SBR vulcanizates containing a naphthenic processing oil as an extender were not so resistant to ozone as standard SBR vulcanizates. It is probable that the effectiveness of the antiozonants tested in these vulcanizates was reduced by their high solubility in the oil phase. SBR vulcanizates containing trioctyl phosphate as a plasticizer were vigorously attacked by ozone. It is possible that the gaseous ozone dissolved to some extent into the plasticizer phase, increasing the concentration of ozone in the area causing a more severe oxidation of the rubber. SBR vulcanizates that had been coated with an antiozonant by dipping the specimen several times into a solution of the antiozonant in a solvent were found to contain a higher concentration of the antioxonant directly on the surface of the vulcanizate than in the case where three parts of the antiozonant were added during vulcanization. A mechanism for the ozonization of SBR vulcanizates has been proposed which includes a possible mechanism for the protective action of antiozonants. A rate equation has been derived from this mechanism which was consistent with the experimental rate data.

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Initial-rate studies of a thermophilic glucokinase from Bacillus stearothermophilus

Biochemical Journal ◽

10.1042/bj2480013 ◽

1987 ◽

Vol 248 (1) ◽

pp. 13-20 ◽

Cited By ~ 17

Author(s):

H Ishikawa ◽

T Maeda ◽

H Hikita

Keyword(s):

Thermal Stability ◽

Ternary Complex ◽

Bacillus Stearothermophilus ◽

Initial Rate ◽

Rate Equations ◽

Rate Data ◽

Michaelis Constant ◽

Wide Range ◽

State Assumption ◽

Reaction Schemes

The initial rates of phosphorylation of glucose catalysed by glucokinase from Bacillus stearothermophilus were measured over a wide range of glucose, MgATP2-, MgADP- and glucose 6-phosphate concentrations. The results of the effects of the inhibitors on the initial rates suggest that the reaction mechanism is essentially the ordered Bi Bi, in which glucose adds to the enzyme before MgATP2- and glucose 6-phosphate is released from the enzyme after the dissociation of MgADP-, and also suggest that the final step in which glucose 6-phosphate is released is irreversible. For many reaction schemes, the rate equations were derived on the basis of the pseudo-steady-state assumption and were used to correlate the experimental rate data. From this result, we concluded that the reaction obeys the ordered mechanism accompanied by the formation of a non-productive ternary complex, glucose-MgADP--enzyme. By using the experimental Dalziel coefficients phi i, some kinetic parameters were evaluated. The enzyme was characterized by the thermal stability and the low Michaelis constant, the values of which were 54 microM for glucose and 32 microM for MgATP2-.

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Sigmoid curves, non-linear double-reciprocal plots and allosterism

Biochemical Journal ◽

10.1042/bj1490313 ◽

1975 ◽

Vol 149 (2) ◽

pp. 313-328 ◽

Cited By ~ 81

Author(s):

W G Bardsley ◽

R E Childs

Keyword(s):

Steady State ◽

Kinetic Data ◽

Initial Rate ◽

Plane Curves ◽

British Library ◽

Mathematical Significance ◽

Steady State Kinetic ◽

Non Linear ◽

State Kinetic ◽

Maximum Utilization

1. The theory of plane curves was applied to the graphical methods used in enzyme kinetics and a mathematical analysis of the possible graph shapes is given. 2. The belief that allosterism can be inferred from steady-state data alone is subjected to criticism and the mathematical significance of sigmoid curves and non-linear double-reciprocal plots is explored. 3. It is suggested that the usual methods of interpreting steady-state kinetic data are often based on over-restrictive assumptions which prevent maximum utilization of the available data. 4. Methods for obtaining the degree of the rate equation from graph shapes obtained directly from initial-rate measurements and from replots of asymptotic behaviour as x → 0 and x → ∞ are discussed. 5. Detailed proofs of the theorems given in the text have been deposited as Supplementary Publication SUP 50049 (10 pages) at the British Library (Lending Division), Boston Spa, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1975), 145, 5.

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