Spatiotemporal Fluctuation Analysis: A Powerful Tool for the Future Nanoscopy of Molecular Processes

Abstract

The enormous wealth of information available today from optical microscopy measurements on living samples is often underexploited. We argue that spatiotemporal analysis of fluorescence fluctuations using multiple detection channels can enhance the performance of current nanoscopy methods and provide further insight into dynamic molecular processes of high biological relevance.

Figure 1

Comparison between the static resolution of superresolution approaches and the temporal scale of molecular motion. (A) In SML methods, the relationship between spatial and temporal resolution is set by the brightness of the chromophore (dark blue-to-cyan solid lines; see Supporting Materials and Methods for further details). In fact, the brighter the chromophore, the shorter is the minimum time required to localize the single molecule. On the other side, the space explored by molecular motion increases in time according to the law of motion of the molecule (which is simplified here as a Brownian motion). The characteristic spatial scale of molecular displacement is identified as the square root of the expected MSD. Three representative diffusivities spanning from 0.1 to 100 μm²/s are pictured as yellow-to-red lines. Please note that 0.1 μm²/s well represents the slow diffusivity of membrane proteins, and 100 μm²/s represents the fast diffusivity of soluble proteins. The maximum dynamic resolution of each selected label in describing a dynamic system is represented by the intercept between the corresponding brightness and rate-of-motion curves. (B) In a typical fluorescence-based SIM experiment, the sample is illuminated with a defined light pattern and the image is collected for each illumination structure. The illumination pattern defines where the sample is illuminated, and the image thus formed provides spatial information about the sample emission. This information provides a gain in resolution by a factor of ∼2. On the other hand, the temporal resolution is set solely by the acquisition protocol that is applied. (C) In STED microscopy, the spatial resolution is set by the efficiency of the depletion of peripheral chromophores and, in the simplest case, it depends only on the power of the depletion beam. Also in this case, the temporal resolution is set by the acquisition protocol that is applied.

Figure 2

Precision in measuring the molecular MSD by correlation spectroscopy. (A) ${\mathit{\sigma }}_{\mathit{iMSD}}$, as defined in Supporting Materials and Methods, is quantified for a defined range of molecular brightness (N_ph, number of photons per molecule per frame) and molecular density (N_mol, number of molecules per PSF) values. In detail, the measured ${\mathit{\sigma }}_{\mathit{iMSD}}$ is plotted against N_ph for the two selected brightness values of 0.1 and 10 molecules per PSF (open and solid dots, respectively). The red lines underline the dependence of ${\mathit{\sigma }}_{\mathit{iMSD}}$ on the square root of N_ph. In the inset, a surface plot for all tested conditions is shown. (B) The same plot as in Fig. 1A shows the contribution of spatiotemporal fluctuation analysis to the calculation of ${\mathit{\sigma }}_{\mathit{iMSD}}$ as obtained from simulated experiments for three representative molecular brightness levels of 10, 100, and 1000 kPhs/s (dark blue to cyan solid lines).

Figure 3

Spatiotemporal fluctuation analysis can superresolve single-molecule dynamics: a simulated experiment. A three-dimensional moving spherical object (in this case, a vesicle) with a diameter corresponding to the nominal measurement resolution (PSF) is filled with fluorescent molecules (see drawing in the inset). Both the vesicle and the molecules are free to diffuse, but the latter are 10 times faster than the vesicle and cannot cross the imposed spherical boundary. By applying spatiotemporal analysis of fluorescence fluctuations, one can measure the motion of the molecules within the vesicle (red dashed line) and the motion of the vesicle (blue dashed line) concomitantly, even if both are significantly smaller than the nominal imaging resolution. Further details about the simulations and data analysis are reported in Supporting Materials and Methods.