Protein Oligomerization Equilibria and Kinetics Investigated by Fluorescence Correlation Spectroscopy: A Mathematical Treatment

Fluorescence
correlation spectroscopy (FCS) is a technique that is increasingly
being used to investigate protein oligomerization equilibria and dynamics.
Each individual FCS decay is characterized by its amplitude and a
characteristic diffusion time, both of which are sensitive to the
degree of dissociation of the protein. Here, we provide a mathematical
treatment that relates these observables with the parameters of interest:
the equilibrium constants of the different protein dissociation steps
and their corresponding dissociation and association kinetic rate
constants. We focused on the two most common types of protein homooligomers
(dimers and tetramers) and on the experimental variables relevant
for the design of the experiment (protein concentration, fractional
concentration of labeled protein). The analysis of the theoretical
expectations for proteins with different dissociation constants is
a key aspect of experiment design and data analysis and cannot be
performed without a physically accurate treatment of the system. In
particular, we show that the analysis of FCS data using some commonly
used empirical models may result in a serious misinterpretation of
the experimental results.