Molecular brightness determined from a generalized form of Mandel's Q-parameter

Mandel's Q-parameter, which is determined from the first two photon count moments, provides an alternative to PCH analysis for determining the brightness of fluorophores. Here, the definition of the Q-parameter is generalized to include correlations between photon counts that are separated by a time tau. We develop and experimentally verify a theory that takes the effects of dead time, afterpulsing, and the finite sampling time on the generalized parameter Q(tau) into account. Q(0), which corresponds to the original Q-parameter, is severely affected by dead time and afterpulsing. Q(tau) for tau>0, on the other hand, is quite robust with respect to nonideal detector effects. Thus, analysis of Q(tau) provides a robust method for determining the brightness of fluorophores. We extend the theory to a mixture of species, which is characterized by an apparent brightness. The brightness of EGFP in CV-1 cells is measured as a function of protein concentration to demonstrate the feasibility of Q(tau) analysis in cells. In addition, we monitor protein association of the ligand-binding domain of retinoid X receptor in the presence and absence of 9-cis-retinoic acid by Q(tau) analysis.