Photon counting histogram analysis for two-dimensional systems.

Area of Science:

• Confocal microscopy
• Fluorescence spectroscopy
• Physical chemistry

Background:

• Photon counting statistics in 3D PCH analysis depend on molecular brightness and number within the confocal volume.
• Standard PCH theory assumes molecules are equally probable anywhere in the excitation volume.
• Geometric constraints in samples, like surfaces or membranes, violate this assumption.

Purpose of the Study:

• To extend PCH theory for analyzing systems with molecules confined to two-dimensional structures.
• To develop a method for quantifying fluorescent particles per unit area and their molecular brightness in 2D.
• To enable PCH analysis in systems where molecular distribution is geometrically constrained.

Main Methods:

• Developed a modified theoretical framework called two-dimensional photon counting histogram (2D PCH).
• Approximated the excitation-detection volume as a 3D Gaussian function within PCH equations.
• Validated the 2D PCH method using computer simulations and experimental confocal microscopy data.

Main Results:

• The 2D PCH method successfully recovers the number of fluorescent particles per unit area.
• Molecular brightness of fluorescent particles in 2D systems can be accurately determined.
• The modified framework was tested with simulated and experimental 2D PCH data.

Conclusions:

• 2D PCH provides a robust tool for analyzing molecular behavior in effectively two-dimensional systems.
• This method allows extraction of data revealing aggregation states, surface photophysics, and reactivity.
• The extension of PCH theory broadens its applicability to geometrically constrained molecular systems.