  Cells rely on focal adhesions (FAs) to carry out a variety of important
tasks, including motion, environmental sensing, and adhesion to the
extracellular matrix. Although attaining a fundamental characterization of FAs
is a compelling goal, their extensive complexity and small size, which can be
below the diffraction limit, have hindered a full understanding. In this study
we have used single-molecule localization microscopy (SMLM) to investigate
integrin $\beta$3 and paxillin in rat embryonic fibroblasts growing on two
different extracellular matrix-representing substrates (i.e. fibronectin-coated
substrates and specifically bio-functionalized nano-patterned substrates). To
quantify the substructure of FAs, we developed a method based on expectation
maximization of a Gaussian mixture that accounts for localization uncertainty
and background. Analysis of our SMLM data indicates that the structures within
FAs, characterized as a Gaussian mixture, typically have areas between 0.01 and
1 $\mu$m$^2$, contain 10 to 100 localizations, and can exhibit substantial
eccentricity. Our approach based on SMLM opens new avenues for studying
structural and functional biology of molecular assemblies that display
substantial varieties in size, shape, and density.
