Chapter 8 – Theoretical Biophysics  373

8.5.3  COLOCALIZATION ANALYSIS FOR DETERMINING

MOLECULAR INTERACTIONS IN IMAGES

Experiments to monitor molecular interactions have been revolutionized by multicolor fluor­

escence microscopy techniques (see Chapter 3). These enable one to monitor two or more

different molecular components in a live biological sample labeled with different color dye

that can be detected via separate color channels. The question then is to determine whether

or not two such components really are interacting, in which case they will be colocalized in

space at the same time. However, the situation is complicated by the optical resolution limit

being several hundred nanometers, which is two orders of magnitude larger than the length

scale over which molecular interactions occur.

The extent of colocalization of two given spots in separate color channels can best be

determined computationally by constructing an overlap integral based on the fit outputs

from the localization tracking microscopy. Each candidate spot is first fitted using a 2D

Gaussian as before, and these functions are then normalized to give two Gaussian probability

distribution functions g1 and g2, centered around (x1, y1) with width σ1 and around (x2, y2) with

width σ2, respectively, and defined as

FIGURE 8.9  Using kernel density estimation to objectify stoichiometry distributions. Too few

histogram bins can mask underlying multimodality in a distribution, whereas too many can

give the impression of more multimodality than really exists. A kernel density estimation (here

of width w =​ 0.7 molecules, equivalent to the measurement error in this case) generates an

objective distribution.