Effect of finite trajectory length on the correlation function analysis of single molecule data

Area of Science:

• Single-molecule biophysics
• Chemical physics
• Statistical mechanics

Background:

• Single molecule rotational correlation functions are crucial for understanding molecular dynamics.
• Finite trajectory length can introduce artifacts in correlation function analysis.
• Previous studies have not fully quantified the impact of trajectory length on rotational dynamics.

Purpose of the Study:

• To investigate the influence of finite trajectory length on single molecule rotational correlation functions.
• To develop methods for mitigating trajectory length effects in dynamical analysis.
• To assess the accuracy of rotational diffusion models under limited trajectory lengths.

Main Methods:

• Numerical simulations of single molecule trajectories.
• Time series analysis of rotational dynamics.
• Fitting trajectories to stretched exponential models to extract time constants and stretching exponents.
• Analysis using higher-order spherical harmonics.

Main Results:

• Correlation functions deviate significantly when trajectory length is less than 100 times the correlation time constant.
• Distributions of fitted time constants and stretching exponents broaden and become asymmetric with shorter trajectories.
• Mean values of these parameters deviate from theoretical predictions for pure rotational diffusion.
• Higher-order spherical harmonics show promise in reducing trajectory length dependency.

Conclusions:

• Finite trajectory length is a critical factor affecting the accuracy of single molecule rotational correlation functions.
• Shorter trajectories lead to biased estimations of molecular dynamics parameters.
• Analysis employing higher-order spherical harmonics offers a more robust approach for studying molecular rotation.
• The findings are applicable to various dynamical processes exhibiting exponential correlation functions.