Chapter 4 – Making Light Work Harder in Biology  117

cell that will satisfy this condition. This depends upon the spatial dimensionality of the local­

ization of the biomolecule. For example, it might be 3D in the cell cytoplasm, 2D confined to

the cell membrane, or even 1D delimited to a filamentous molecular track. Also, it depends

upon the mobility of the molecule in question.

The distribution of nearest-​neighbor distances can be modeled precisely mathematically

(see Chapter 8); however, to obtain a rough idea of the limiting concentration Clim, we can use

the simple arguments previously in this chapter indicating that in the cytoplasm, the mean

fluorophore concentration in a typical bacterial cell such as Escherichia coli used is equiva­

lent to ~50–​350 molecules per cell, depending on whether they are free to diffuse (low end of

the range) or immobile but randomly distributed (high end of the range). In practice, much of

a cell contains excluded volumes (such as due to the presence of DNA genetic material), and/​

or biomolecules may group together in a nonrandom way, so in reality, there may be non­

trivial differences from cell to cell and molecule to molecule (see Worked Case Example 4.1).

There are several different types of biomolecules that are expressed in low copy numbers

in the cell, some of which, such as transcription factors, regulate the on/​off switching of

genes, down to only 1–​10 per cell in E. coli at any one time, which therefore satisfy the mean

nearest-​neighbor distance condition to be distinctly detected. However, there are similarly

other types of molecules that are expressed at effective mean concentration levels per cell of

four or more orders of magnitude beyond this (see Chapter 1), whose concentration therefore

results in typical nearest-​neighbor separations that are less than the optical resolution limit.

In practice, what often happens is that single fluorescently tagged molecules, often FPs,

integrate into molecular machines in living cells. These often have characteristic modular

molecular architecture, meaning that a given molecule may be present in multiple copies

in a given molecular complex in the machine. These machines have a characteristic length

scale of ~5–​50 nm, much less than the optical resolution limit, and since the image is a con­

volution of the PSF for a single fluorophore with the spatial probability function for all such

fluorophores in the machine, this results in a very similar albeit marginally wider PSF as a

single fluorophore but with an amplitude greater by a factor equal to the number of copies of

that fluorophore in the machine.

4.2.6  SUBSTOICHIOMETRIC LABELING AND DELIMITED PHOTOBLEACHING

There are several techniques to overcome the nearest-​neighbor problem. One of the simplest

is to substoichiometrically label the molecular population of interest, for example, adjusting

the concentration of fluorescent dyes relative to the biomolecule of interest and reducing

the incubation time. This involves labeling just a subpopulation of molecules of a specific

type such that the cellular concentration of fluorophore is below Clim. Irreversibly, photo­

bleaching a proportion of fluorophores in a cell with excitation light for a given duration prior

to normal localization microscopy analysis can also reduce the concentration of photoactive

fluorophore in cell to below Clim (Figure 4.1b).

This method is superior to substoichiometric labeling in that there are not significant

numbers of unlabeled molecules of interest in the cell, which would potentially have different

physical properties to the tagged molecule such as mobility and rates of insertion into a com­

plex so forth, and also has the advantage of being applicable to cases of genomic FP-​fusion

labeling. This method has been used to monitor the diffusion of fluorescently labeled proteins

in the cell membrane of bacteria using a high-​intensity focused laser bleach at one end of the

cell to locally bleach a ~1 μm diameter region and then observe fluorescence subsequently at

a lower laser intensity. The main issue with both of these approaches is that they produce a

dark population of the particular biomolecule that is under investigation, which may well be

affecting the experimental measurements but which we cannot detect.

Dynamic biological processes may also be studied using substoichiometric labeling in

combination with fluorescent speckle microscopy (see Waterman-​Storer et al., 1998). Here,

a cellular substructure is substoichiometrically labeled with fluorescent dye (i.e., meaning

that not all of the molecules of a particular type being investigated are fluorescently

labeled). This results in a speckled appearance in conventional fluorescence imaging, and