A major challenge of present (and future) biophysics is to quantitatively study how molecular subensembles dynamically interact to fulfill their physiological roles in living cells and organisms. This is the classic research target of molecular cell biology and quantitative fluorescence microscopy: individual molecular components (proteins, lipids, etc.) are cloned/purified/synthesized, tagged, and analyzed. In this context, high-speed single-particle tracking (SPT) techniques play a crucial role and yield information at the nano-meso-scale on the dynamics and interactions of several molecular cellular components. Based on SPT, for instance, Kusumi and coworkers thoroughly investigated the compartmentalization of the fluid plasma membrane into submicron domains throughout the cell membrane and the hop diffusion of many relevant molecules (for a review see Kusumi et al. 2005a, 2005b; 2010). Widespread exploitation of the SPT approach is hindered, however, by at least four characteristics that, at present, appear unavoidable: (1) the experiment relies on production, purification, and labeling of a single molecule with a suitable marker particle (e.g., a gold colloidal particle or quantum dot); (2) the usable labels are rather large on the molecular scale and can induce cross-linking of target molecules or steric hindrance effects, thus affecting the biological function under study; (3) the size (colloidal gold particles typically used have diameters of 20-40 nm)

and chemical nature of the label typically prevents the application of SPT measurements to intracellular molecules; (4) a large number of single-molecule trajectories must be recorded to fit statistical criteria, thus dramatically increasing the time required to gather and analyze SPT data. In regard to these SPT drawbacks, fluorescence correlation spectroscopy (FCS) is a very attractive alternative approach. In fact, thanks to its intrinsic single-molecule sensitivity even in the presence of many molecules, it can easily afford the required statistics in a reasonable amount of time. FCS can be performed well with genetically encoded FPs and, in general, with fluorophores not particularly bright. The basic principle of fluctuation analysis is to decrease the detection volume so that small numbers of fluorescent molecules are excited at the same time. Molecules stochastically cross the open detection volume defined by the laser beam, leading to a fluctuating occupancy that follows Poisson statistics (which in turn obeys the relation that the variance is proportional to the average number of observed molecules). The underlying molecular dynamics are extracted as characteristic decay times through fluctuation correlation analysis. In its classic view, FCS is used as a “local” measurement of the concentration and residency time of molecules present in the diffraction-limited focal area defined by the laser beam. Many efforts targeted the extension of the FCS principle to the spatial scale. For instance, the focal area was duplicated (Ries and Schwille 2006), moved in space in laser “scanning” microscopes (Berland et  al. 1996; Ruan et al. 2004; Heinemann et al. 2012; Cardarelli et al. 2012a, 2012b; Di Rienzo et al. 2014b), or combined with fast cameras (Kannan et al. 2006; Unruh and Gratton 2008; Di Rienzo et al. 2013b, 2014a). Using these “spatiotemporal” correlation approaches, diffusion constant, concentration, and partitioning coefficient of several membrane components were measured on both model membranes and actual biological ones (Schwille et al. 1999; Weiss et al. 2003). An alternative way to sample both time and space is based on the size change of the focal area. For instance, it was demonstrated that molecular FCS-based diffusion laws can be recovered by performing fluctuation analysis at various spatial scales larger than the laser focal area (Wawrezinieck et al. 2005; Lenne et al. 2006). Based on these data, inferences were drawn about the dynamical organization of cell membrane components by extrapolation below the diffraction limit. Along this reasoning, similar studies can be performed by downsizing the focal area: recent reports successfully exploited the ~30  nm focal area attained by stimulated emission depletion (STED) (Hell and Wichmann 1994) to directly probe the nanoscale dynamics of membrane components in a living cell by fluctuation analysis (Eggeling et al. 2009; Mueller et al. 2011; Sezgin et al. 2012). In all the FCS experiments described, however, the size of the focal spot represents a limit in spatial resolution that cannot be overcome. In addition, the information collected always requires assumptions and models that describe the molecular dynamics under study. These models must then be translated into equations to be fitted to FCS measurements. In an effort to overcome these limitations an approach based on spatiotemporal image correlation spectroscopy (Hebert et al. 2005) method will be discussed here, that is suitable for the study of the dynamics of fluorescently tagged molecules in live cells with high temporal (up to 10−4 s for images and 10−6 for line scans) and spatial (well below the diffraction limit) resolution (schematic representation in Figure 2.1).