Diffusive searches in high-dimensional spaces and apparent 'two-state' behaviour in protein folding

Area of Science:

• Biophysics
• Computational Biology
• Chemical Physics

Background:

• Protein folding is crucial for biological function.
• Observed folding kinetics often appear as simple 'two-state' processes.
• The underlying conformational landscape can be complex with intermediate states.

Purpose of the Study:

• To investigate the relationship between complex folding landscapes and observed kinetics.
• To model protein folding as a diffusive search in high dimensions.
• To determine if simple exponential kinetics can arise from complex folding pathways.

Main Methods:

• Developed a simplified model for protein folding.
• Treated folding as a diffusive search process.
• Solved a steady-state diffusion equation on a hypersphere with an absorbing 'native state'.

Main Results:

• Demonstrated that diffusive searches on a hypersphere naturally yield nearly single-exponential kinetics.
• Showed that complex folding pathways with intermediate structures can result in simple observed kinetics.
• Identified a general property of diffusive searches relevant to folding dynamics.

Conclusions:

• Single-exponential folding kinetics do not necessarily imply a simple two-state folding mechanism.
• The observed simplicity in folding kinetics can mask underlying complexity.
• This model provides a theoretical basis for understanding apparent two-state folding behavior.