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Enzyme kinetics. Systematic generation of valid King-Altman patterns.

C F Lam, D G Priest

Biophysical Journal

|March 1, 1972

Summary

This study introduces a novel graph theory method to efficiently generate valid patterns for complex enzyme reaction mechanisms, improving upon the King and Altman algorithm. This approach streamlines the derivation of steady-state rate equations, making it computer-adaptable.

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Area of Science:

Biochemistry
Chemical Kinetics
Computational Biology

Background:

The King and Altman algorithm is widely used for deriving steady-state rate equations in enzyme kinetics.
Existing modifications often involve generating and filtering numerous invalid patterns, which is inefficient.
A systematic and computationally efficient method is needed for pattern generation in enzyme reaction mechanisms.

Purpose of the Study:

To present a novel method for systematically generating only valid patterns for enzyme reaction mechanisms.
To adapt this method for digital computer implementation.
To develop an independent method for calculating the number of valid patterns to ensure accuracy.

Main Methods:

Employs the topological theory of linear graphs to systematically generate valid patterns.

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Develops an independent combinatorial method for calculating the number of valid patterns.

Demonstrates the methods with examples of specific enzyme mechanisms.

Main Results:

Successfully generates only valid patterns for enzyme reaction mechanisms, avoiding invalid ones.
Provides a method for calculating the number of valid patterns, useful for verifying accuracy.
Both pattern generation and counting methods are adaptable for computerization.

Conclusions:

The presented graph theory method offers a systematic and efficient approach to generating valid patterns for enzyme kinetics.
The independent calculation of pattern numbers serves as a validation tool.
These computational methods enhance the derivation of steady-state rate equations for complex enzyme systems.