Testing for the heterogeneity of complex fluid samples in nanobiophysics

Improvements in light microscopy, fluorescence techniques, nanoparticle synthesis and high-speed video have ushered in a flurry of experimental activity [1]. Single particle tracking has become a common tool in many scientific areas, such as colloid physics [2], the study of nanobiophysical systems, both in vivo and in vitro [7], and the microrheology of complex fluids [3–6]. In particular, the latter is the application that motivates the research in this dissertation. Of primary concern in the analysis of particle path data is the mean squared displacement (MSD) ⟨X(t)⟩, whereX is the tracer particle’s position. A basic dynamic characterization of the latter is given by the relation