correlation (Fig.1c). In the presence of diffusion only, the correla-
tion function can be interpolated by a Gaussian function (Fig.1d),
whose variance provides a measurement of the average molecular
displacement, directly from imaging (hereafter,iMSD). Thanks to
theiMSD vs time plot, protein diffusion modes can be directly
identified with no need for an interpretative model or assumptions
about the spatial organization of the membrane (Fig.1e). The
method is put to test in live cells with two benchmark molecules
diffusing on the plasma membrane: a GFP-tagged variant of the
trans-membrane transferrin receptor (TfR), a well-known bench-
mark of confined diffusion [21, 22] and a GFP-tagged variant of
glycosylphosphatidyl inositol (GPI), a benchmark of dynamic par-
titioning into cholesterol-enriched membrane compartments, also
known as “lipid rafts.” It will be shown how characteristic diffusion
constants, confinement areas, and partitioning coefficients can be
quantitatively extracted over many microns in the sample. From a
theoretical point of view, as previously shown, the spatio-temporal
auto-correlation function of the acquired image series criticallyFig. 1(a) Image acquisition can be performed in wide-field excitation. In particular, a convenient wide-field
strategy takes advantage of the total internal reflection (TIR) of the excitation light at the interface between the
glass and the sample, limiting the excitation to the close proximity of the interface. In this case, fluorescence
light produced in the sample is measured concomitantly in all the positions in space using an array of photo-
detectors such as an EMCCD. (b) The spatiotemporal fluctuation analysis proposed here converts a stack of
fluorescence intensity imagesI(x,y,t), into (c) a stack of images representing the spatiotemporal evolution of
correlationG(ξ,χ,τ) (Eq.1). (d) If the dynamic behavior of molecules is governed exclusively by diffusion the
peak of correlation will remain fixed in the origin of the Cartesian axes. If the correlation function is
interpolated by a Gaussian function (Eq.3), the variance of the Gaussian will provide a measurement of the
average molecular displacement (iMSD). (e) TheiMSD plot can be used to distinguish among the different
diffusion modes, such as free and confined diffusion
Fluctuation-Based Diffusion Laws 279