Testing for renewal and detailed balance violations in single-molecule blinking processes

Area of Science:

• * Computational Chemistry
• * Statistical Physics
• * Biophysics

Background:

• * Histograms are fundamental in analyzing experimental data, particularly in fields like statistical physics and computational chemistry.
• * Understanding kinetic features such as renewal properties and detailed balance is essential for accurate model building.
• * Current methods may lack the statistical rigor for definitive feature identification.

Purpose of the Study:

• * To develop and present straightforward statistical tests for evaluating one- and two-dimensional histograms.
• * To rigorously assess key kinetic features within data, including renewal properties and detailed balance.
• * To establish a method for determining the minimum number of measurements required for kinetic model differentiation.

Main Methods:

• * Application of statistical tests to one- and two-dimensional histograms.
• * Analysis of histogram properties related to renewal processes.
• * Examination of detailed balance violations in kinetic systems.
• * Assessment of dependencies on experimental conditions.

Main Results:

• * Developed simple yet statistically rigorous tests for histogram analysis.
• * Demonstrated the capability of these tests to identify specific kinetic features.
• * Established a framework for determining the lower bound on necessary measurements for model discrimination.

Conclusions:

• * The presented statistical tests offer a robust approach to analyzing histogram data.
• * These methods facilitate the rigorous identification of kinetic features.
• * The study provides a quantitative basis for designing experiments to differentiate kinetic models.