Slow-equilibration approximation in macroscopic approach to studying kinetics at equilibrium

Area of Science:

• Chemical kinetics
• Biophysical chemistry
• Physical chemistry

Background:

• The Macroscopic Approach to Studying Kinetics at Equilibrium (MASKE) measures affinity complex formation (k(+)) and dissociation (k(-)) rate constants.
• MASKE typically requires fitting experimental data to simulated patterns, a complex process.
• Existing MASKE methods rely on creating informational nonequilibrium via nonuniform reactant labeling.

Purpose of the Study:

• To develop a simplified, fitting-free method for determining rate constants (k(+) and k(-)) using MASKE.
• To enable accurate kinetic measurements under conditions of slow equilibration.
• To validate a new mathematical approach for kinetic analysis.

Main Methods:

• Developed a fitting-free mathematical approach by solving differential equations of mass transfer under the assumption of slow equilibration.
• Defined slow equilibration as a state where characteristic equilibration time (t(eq)) significantly exceeds separation time (t(sep)).
• Tested the approach by comparing its results to label-propagation patterns generated by an exact mass-transfer solution.

Main Results:

• The fitting-free approach accurately determines rate constants (k(+) and k(-)) under slow equilibration conditions.
• The method achieves a relative error of less than 20% when the separation time is less than 0.6 times the equilibration time (t(sep) < 0.6t(eq)).
• The accuracy of the approximate solution was validated against exact solutions, confirming its correctness.

Conclusions:

• A novel, fitting-free method simplifies the determination of kinetic rate constants in affinity complex formation and dissociation.
• This approach is practical for systems exhibiting slow equilibration, offering a significant advancement in kinetic analysis.
• The study discusses the practical limitations of the slow-equilibration approximation for broader applicability.