Exponential model for a two-ligand, regulatory enzyme. Part 3: Performance tests of INDEXP computer programs for determination of model constants from initial velocity data. 2. Experimental data

Exponential model for a regulatory enzyme. Computer program for the determination of the model constants from initial velocity data

The paper describes a program (DESCENT) which evaluates the constants of the exponential model for a regulatory enzyme with up to four substrates or up to three substrates and one effector. The program operates by repetitive adjustment of the model constants so as to secure a better fit between the observed and calculated initial velocities of reaction. At each adjustment, all the constants are incremented simultaneously by amounts determined by a steepest descent criterion. The program is tested by artificial data with and without added error and it is shown that good estimates of the constants can be recovered.

The exponential model for a regulatory enzyme. An interpretation of the linear free-energy relationship

A physical mechanism is suggested to explain the linear free-energy relationship employed in the exponential model for a regulatory enzyme [Ainsworth (1977) J. Theor. Biol. 68, 391-413]. The interpretation depends on the assumption that the structure of the enzyme changes in proportion to its saturation by substrate but at a rate that is low compared with the rates of the association-dissociation reactions of the enzyme-substrate system.

Location of critical points in the reaction velocity/concentration relationships predicted by the exponential model for a two substrate regulatory enzyme

The two substrate exponential model for a regulatory enzyme (Ainsworth and Gregory, J. Theor. Biol., 75 (1978) 97-114) can be employed to describe non-hyperbolic relationships between the initial velocity of the catalysed reaction and the concentration of one substrate when the concentration of the second substrate is kept constant, v = f(A)B. The model equation for v = f(A)B predicts the possibility of a maximum, catastrophe and inflections but, because the equation is transcendental, it is not possible to locate the critical points by algebraic analysis. The paper describes an iterative computer program that has been devised to solve this problem.

The regulatory properties of rabbit muscle pyruvate kinase. The influence of substrate concentrations

The kinetics of rabbit muscle pyruvate kinase were studied in assays at pH 7.4, where the relationships between the initial velocities of the catalysed reaction and the concentrations of substrates ADP, phosphoenolpyruvate and Mg2+ are non-hyperbolic. The data were used to test the applicability of the exponential model for a regulatory enzyme, which has been here extended to describe the behaviour of a three-substrate enzyme. It appears that the data can be represented by the model and as a result permit the conclusion that the substrates influence one another's binding by the same type of charge interactions that are evident in the Michaelis-Menten kinetics of the enzyme observed at pH 6.2. Evidence is also presented indicating that MgADP acts as a dead-end inhibitor of the enzyme at pH 7.4.

Exponential model for a two-ligand, regulatory enzyme. Part 2: Performance tests of the 'INDEXP' computer program for the determination of model constants from initial velocity data. I. Artificial data

The exponential model for a regulatory enzyme describes the relationship between the initial velocity of the catalysed reaction and the concentration of two ligands. A program, entitled 'INDEXP' has been designed to analyse rate data in terms of the model (Kinderlerer et at., 1981) and, in this report, its performance is examined when presented with artificial data generated from known constants and random, normally distributed error. It is shown that 'INDEXP' is able to recover good estimates of the constants.

Exponential model for a two-ligand, regulatory enzyme. Part 1: computer programs for the determination of the model constants from initial velocity data

The exponential model for a regulatory enzyme with two ligands (either two substrates or one substrate and an effector) provides an expression for the initial velocity of the catalysed reaction in terms of the fractional saturation of the enzyme by each ligand. This paper describes a program which determines the constants of the model from velocity data, measured with respect to the concentrations of the two ligands, when the corresponding fractional saturations are unknown. Listings of the essential routines, written in BASIC, are provided.