Correlated measurements in single-particle-tracking dynamics

Area of Science:

• Physics
• Biophysics
• Statistical Mechanics

Background:

• Single-particle tracking (SPT) is crucial for understanding molecular dynamics.
• The generalized Langevin equation (GLE) framework models complex dynamics.
• Displacement and velocity correlations are key observables in SPT.

Purpose of the Study:

• To reformulate SPT analysis within the GLE framework using velocity correlations.
• To identify scaling laws for displacement correlation functions in nonstationary and aging systems.
• To investigate ergodic properties and introduce a metric for effective friction.

Main Methods:

• Reformulation of the generalized Langevin equation in terms of the velocity correlation function.
• Derivation of scaling laws for the normalized displacement correlation function.
• Analysis of ergodic properties and introduction of a kinetic energy-based effective friction metric.

Main Results:

• Identified universal scaling laws for normalized displacement correlation functions.
• Demonstrated that correlation decays faster with lag time in aging dynamics compared to nonaging, nonstationary processes.
• Showcased that effective friction increases with shorter decay time components in multiexponential memory kernels.

Conclusions:

• The study provides a unified framework for analyzing SPT data across different dynamic regimes.
• The findings offer insights into the relationship between correlation decay, aging, and effective friction.
• Application to protein folding models highlights the practical utility of the developed metric.