Analysis of fluorescence-fluctuation spectroscopy combining autocorrelation and time-integrated cumulants in confocal microscopy
Phys. Rev. Applied 26, 024022 – Published 10 August, 2026
DOI: https://doi.org/10.1103/pngm-pry7
Abstract
Quantification in fluorescence correlation spectroscopy relies on diffusion models where the confocal volume is approximated usually by a three-dimensional Gaussian (3DG) function. Although this assumption is essential for estimating the fluorophore diffusion parameters (such as the number of molecules, their brightness, and their diffusion coefficient), it is rarely verified experimentally due to the difficulty of performing it in three dimensions. In this work, we propose a method based on the concomitant analysis of fluorescence fluctuation time traces using both autocorrelation and time-integrated cumulants. This approach enables us to confirm the shape of the focal volume. We also show that this confocal volume is not necessarily a 3DG. For some experimental parameters (objective filling factor and confocal pinhole diameter), we demonstrate that it can be more accurately approximated by a two-dimensional Gaussian function in the lateral direction and a Lorentzian function in the axial direction (2DG-L). We report the analytical expressions of both autocorrelation and time-integrated cumulants for free Brownian motion through a 2DG-L volume. By analyzing fluorescence fluctuation time traces with our method, we can unambiguously retrieve the true shape of the observation volume and, consequently, all molecular diffusion parameters. We apply our method to both Monte Carlo simulations and experimental data acquired using a confocal microscope. We find that the number of molecules in the observation volume is overestimated and that their brightness is underestimated by more than 30% if the adequate observation volume is not used. We therefore believe that the proposed method has the potential to significantly improve the quantitative analysis of fluorescence fluctuations.
