Static and dynamic rough energy landscapes can lead to identical diffusivity

Area of Science:

• Statistical mechanics
• Biophysics
• Computational modeling

Background:

• Molecules in biological cells face forces fluctuating in time and space.
• Existing models like Lifson-Jackson-Zwanzig capture spatial fluctuations but lack temporal dynamics.
• A unified view of time- and space-fluctuating environments is needed.

Purpose of the Study:

• Introduce a discrete-state model for landscapes fluctuating in both time and space.
• Incorporate reciprocal interactions between diffusing particles and the landscape.
• Reevaluate experimental protein dynamics studies with the new model.

Main Methods:

• Developed a discrete-state model for time- and space-fluctuating landscapes.
• Included particle-landscape reciprocal interactions influencing landscape dynamics.
• Applied the model to analyze existing experimental data on protein dynamics.

Main Results:

• Observable molecular dynamics are often independent of temporal fluctuation timescales.
• Static energy landscape models (diffusion in a rough potential) capture key dynamics.
• The new model allows for more accurate bounds on energetic roughness scales.

Conclusions:

• Temporal landscape dynamics may not significantly alter observable molecular motion in dense environments.
• Simplified models assuming static landscapes can effectively describe many dynamic features.
• The study provides improved methods for analyzing protein dynamics and landscape roughness.