Cumulant analysis in fluorescence fluctuation spectroscopy.

Area of Science:

• Biophysics
• Analytical Chemistry
• Spectroscopy

Background:

• Fluorescence fluctuation spectroscopy (FFS) is a powerful technique for analyzing molecular dynamics and interactions.
• Existing methods like photon-counting histogram (PCH) analysis have limitations regarding data sampling times.
• Resolving complex heterogeneous samples requires advanced analytical approaches.

Purpose of the Study:

• Introduce a novel technique, fluorescence cumulant analysis (FCA), for analyzing fluorescence fluctuation experiments.
• Develop theoretical frameworks for rigorous error analysis of FCA.
• Extend FCA capabilities to handle arbitrary sampling times, overcoming limitations of existing methods.

Main Methods:

• Exploiting factorial cumulants of photon counts to resolve heterogeneous samples.
• Developing analytical models connecting photon count cumulants to molecular brightness and number.
• Deriving expressions for the variance of factorial cumulants for error analysis.
• Comparing FCA with photon-counting histogram (PCH) analysis using experimental data.

Main Results:

• FCA successfully resolves heterogeneous samples based on differences in molecular brightness.
• Analytical models accurately describe the relationship between cumulants, brightness, and molecular counts.
• FCA and PCH analysis yield identical results within experimental uncertainty for short sampling times.
• Extended FCA theory successfully models fluorescence fluctuation data for arbitrary sampling times.

Conclusions:

• Fluorescence cumulant analysis (FCA) offers a robust method for analyzing fluorescence fluctuation data.
• FCA provides a powerful tool for characterizing heterogeneous fluorescent samples.
• The extended FCA theory broadens the applicability of fluorescence fluctuation spectroscopy to longer timescales.