Complex ligand-protein systems: a globally convergent iterative method for the n x m case

Area of Science:

• Biochemistry
• Computational Chemistry
• Systems Biology

Background:

• Determining equilibrium in ligand-protein binding is crucial for understanding biological processes.
• Existing methods for solving the resulting non-linear systems can be computationally intensive or lack guaranteed convergence.

Purpose of the Study:

• To develop and validate a robust iterative method for solving non-linear equations in ligand-protein binding equilibrium.
• To demonstrate the guaranteed convergence and uniqueness of the solution provided by the proposed method.

Main Methods:

• Formulation of the problem as a non-linear system of n equations.
• Development of a novel iterative algorithm to solve the system.
• Mathematical proof of convergence for the iterative sequence, irrespective of the initial conditions.

Main Results:

• The iterative method successfully solves the non-linear system of equations governing ligand-protein binding.
• The convergence of the proposed iterative sequence is proven for all initial values.
• The method yields a unique solution for the system composition at equilibrium.

Conclusions:

• The presented iterative method offers an efficient and reliable approach to determine equilibrium compositions in complex ligand-protein binding systems.
• This work provides a valuable computational tool for researchers in biochemistry and pharmacology.
• The guaranteed convergence ensures the robustness of the method for diverse biological scenarios.