Origin of Rate Dispersion in Translational Diffusion: Distinguishing Heterogeneous from Homogeneous Using 2D Correlation Analysis

Rate dispersion is commonly observed when measuring relaxation in complex media such as solution of a protein. Its origin is often associated to molecular heterogeneity in the system. However, interpretation of rate dispersion is not straightforward, and it can be exhibited by both heterogeneous (all molecules are different) and homogeneous (all molecules are identical) systems. Here, we report two-dimensional (2D) correlation analysis of intensity fluctuations originating from translational diffusion-lead fluctuations in number of particles simulated in an observation volume resembling fluorescence correlation spectroscopy experiment. Translational diffusion of particles representing a protein having two different conformations are simulated. Homogeneous and heterogeneous systems are simulated to have similar one-dimensional (1D) autocorrelation curves with comparable extent of rate dispersion, α ∼ 0.8. Time slices of 2D autocorrelation curves and rate-rate spectra obtained from them clearly demonstrate that similar extent of rate dispersion observed in 1D autocorrelation can originate from both heterogeneous and homogeneous systems. We establish that one-dimensional analysis only reports on the extent of rate dispersion. Two-dimensional analysis reports on the origin of rate dispersion and distinguishes heterogeneous from homogeneous.