372 8.5  Advanced In Silico Analysis Tools

The challenge is often to estimate an accurate value for ID. For purely in vitro assays, indi­

vidual dye molecule can be chemically immobilized onto glass microscope coverslip surfaces

to quantify their mean brightness from a population. However, inside living cells, the physical

and chemical environment can often affect the brightness significantly. For example, laser

excitation light can be scattered inside a cellular structure, but also the pH and the presence

of ions such as chloride Cl⁻, in particular, can affect the brightness of fluorescent proteins in

particular (see Chapter 3).

Thus, it is important for in vivo fluorescence imaging to determine ID in the same native

cellular context. One way to achieve this is to extract the characteristic periodicity in inten­

sity of each track, since steplike events occur in the intensity traces of tracks due to integer

multiples of dye molecule photobleaching within a single sampling time window. Fourier

spectral methods are ideal for extracting the underlying periodicity of these step events and

thus estimating ID (Figure 8.8).

Often molecular complexes will exhibit an underlying distribution of stoichiometry

values. Traditional histogram methods of rendering this distribution for subsequent analysis

are prone to subjectivity errors since they depend on the precise position of histogram bin

edges and of the number of bins used to pool the stoichiometry data. A more objective and

robust method involves kernel density estimation (KDE). This is a 1D convolution of the stoi­

chiometry data using a Gaussian kernel whose integrated area is exactly 1 (i.e., representing

a single point), and the width is a measure of the experimental error of the data measure­

ment. This avoids the risks in particular of using too many histogram bins that suggest

more multimodality in a distribution than really exists or too few bins that may suggest no

multimodality when, in fact, there may well be some (Figure 8.9).

KEY POINT 8.10

KDE can be generally applied to all experimental datasets. If there are significant

difficulties in estimating the experimental error in a given measurement, then you

should probably not be doing that experiment. You may never need to use a histo­

gram again!

Sometimes there will be periodicity in the observed experimental stoichiometry distributions

of molecular complexes across a population, for example, due to modality of whole molecular

complexes themselves in tracked spots. Such periodicity can again be determined using basic

Fourier spectral methods.

FIGURE 8.8  Measuring stoichiometry using stepwise photobleaching of fluorophores.

(a) Example of a photobleach trace for a protein component of a bacterial flagellar motor called

FliM labeled with the yellow fluorescent protein YPet, raw data (dots), and filtered data (line)

shown, initial intensity indicated (arrow), with (b) a zoom-​in of trace and (c) power spectrum of

the pairwise difference distribution of these photobleaching data, indicating a brightness of a

single YPet molecule of ~1.3 kcounts on the camera detector used on the microscope.