Image correlation spectroscopy of randomly distributed disks

Image correlation spectroscopy (ICS) has been widely used to quantify spatiotemporal distributions of fluorescently labelled cell membrane proteins and receptors. When the membrane proteins are randomly distributed, ICS may be used to estimate protein densities, provided the proteins behave as point-like objects. At high protein area fraction, however, even randomly placed proteins cannot obey Poisson statistics, because of excluded area. The difficulty can arise if the protein effective area is quite large, or if proteins form large complexes or aggregate into clusters. In these cases, there is a need to determine the correct form of the intensity correlation function for hard disks in two dimensions, including the excluded area effects. We present an approximate but highly accurate algorithm for the computation of this correlation function. The correlation function was verified using test images of randomly distributed hard disks of uniform intensity convolved with the microscope point spread function. This algorithm can be readily modified to compute exact intensity correlation functions for any probe geometry, interaction potential, and fluorophore distribution; we show how to apply it to describe a random distribution of large proteins labeled with a single fluorophore.