Generic Schemes for Single-Molecule Kinetics. 3: Self-Consistent Pathway Solutions for Nonrenewal Processes.

Area of Science:

• Biophysics
• Chemical Kinetics
• Single-Molecule Biophysics

Background:

• Existing kinetic models often assume renewal processes (memoryless events).
• Describing non-renewal processes with event correlations requires more sophisticated frameworks.
• Previous work established a pathway analysis for renewal kinetics using generic structures.

Purpose of the Study:

• To extend the pathway analysis framework to non-renewal processes.
• To develop a general method for calculating waiting time probability distribution functions (PDFs) for complex kinetic networks.
• To analyze enzyme turnover kinetics beyond the Poissonian assumption.

Main Methods:

• Decomposition of kinetic schemes into generic structures.
• Self-consistent pathway solutions to derive waiting time distribution functions.
• Extension of the framework to incorporate correlations in non-renewal processes.
• Application to single-enzyme turnover models with conformational changes.

Main Results:

• Developed a general framework for calculating waiting time PDFs for non-renewal processes.
• Demonstrated the method's applicability to enzyme kinetics, including mean first-passage time analysis.
• Showed that the Michaelis-Menten form emerges under conformational detailed balance, confirming generality.
• The framework avoids Poissonian assumptions, offering a broader kinetic description.

Conclusions:

• The extended pathway analysis framework provides a general and intuitive approach for evaluating measurable waiting time PDFs and their moments.
• This method is a valuable kinetic tool for diverse single-molecule processes, especially those with non-renewal characteristics.
• The framework reconciles complex kinetics with established models like Michaelis-Menten, enhancing our understanding of enzyme mechanisms.