Rapid numerical integration algorithm for finding the equilibrium state of a system of coupled binding reactions

Area of Science:

• Biochemistry
• Computational Chemistry
• Chemical Kinetics

Background:

• Predicting molecular interactions is crucial in biochemistry.
• Understanding reversible association reactions, like protein binding, is key to biological processes.
• Existing numerical methods for equilibrium prediction can be computationally intensive.

Purpose of the Study:

• To develop and validate a novel, efficient numerical integration method for predicting equilibrium states in reversible association reactions.
• To apply this method to populations of protein molecules in aqueous solution.
• To compare the performance of the new method against conventional numerical techniques.

Main Methods:

• Adaptation of Euler integration with an adaptive step size.
• Time increment adjustment based on component concentration changes and rates.
• Empirical optimization of algorithm parameters using model binding equilibria (dissociation constants 10^-5 M to 10^-9 M).

Main Results:

• The adaptive method predicts equilibrium states of reversible association more rapidly than standard initial value methods (Euler, Runge-Kutta variants).
• Achieved comparable accuracy to conventional methods while significantly reducing computation time.
• A computer code in standard C implementing the method is provided.

Conclusions:

• The developed adaptive numerical integration method offers a faster and accurate solution for predicting binding equilibria.
• This approach is particularly beneficial for studying protein-protein interactions and other molecular associations in solution.
• The provided C code facilitates the implementation of this efficient computational tool.