The effect of time resolution on the observed first passage times in diffusive dynamics

Area of Science:

• * Biophysics
• * Physical Chemistry
• * Statistical Mechanics

Background:

• * Single-molecule and single-particle tracking (SMT/SPT) experiments provide insights into molecular dynamics.
• * Thermal motion at short timescales is continuous, posing challenges for trajectory analysis.
• * Current methods struggle to resolve fine details of motion due to finite sampling intervals.

Purpose of the Study:

• * To quantify errors in first passage time (FPT) measurements due to finite sampling in diffusive trajectories.
• * To investigate the impact of unobserved trajectory segments on FPT calculations.
• * To develop a method for recovering accurate FPTs and other trajectory properties.

Main Methods:

• * Analysis of diffusive trajectories sampled at finite time intervals (δt).
• * Theoretical quantification of systematic errors in FPT calculations.
• * Development and application of a stochastic algorithm to correct for unobserved events.

Main Results:

• * Finite sampling can lead to FPT measurement errors exceeding the time resolution by over an order of magnitude.
• * Unobserved entry and exit events significantly lengthen apparent FPTs.
• * The proposed stochastic algorithm successfully recovers accurate FPTs and splitting probabilities.

Conclusions:

• * Systematic errors in FPT measurements are inherent to finite sampling in SMT/SPT.
• * These errors are particularly critical for studying barrier crossing dynamics.
• * The developed stochastic algorithm offers a robust solution for accurate trajectory analysis in SMT/SPT.