Dye Finder
A brief explanation
Dye Finder summarizes several functions which have all the same target: remove crosstalk.
Crosstalk is a common phenomenon in multiparameter fluorescence. It describes the
appearance of signal from a fluorescenct dye in more than one channel. Ideally, each dye
causes signal only in one channel. But in most cases, you will find some signal from each dye
in all channels. This crosstalk (also called “bleed through”) is of course most significant in
spectrally adjacent channels.
As an example, see below the emission characteristics of two (hypothetic) dyes (Fig 01). As
you can see, there is overlap of the emissions, and some signal from the green dye spills into
the red channel, and some red signal spills into the green channel.
Fig. 01
We can visualize this spill over very nicely, when we draw the emission curves for the dyes
separately:
Fig. 02
Fig. 03
The goal is, to separate the signals, so that each image channel contains only signal from one
dye. In general, two approaches have been introduced in LCS Software:
1. Dye Separation based on linear algebra. Equivalent terms: linear unmixing
In this category we can find the functions
2. Manual Dye Separation
3. Channel Dye Separation
4. Spectral Dye Separation
2. Dye Separation based on intensity correlation in channels
Here we have
2. Adaptive Dye Separation (weak)
3. Adaptive Dye Separation (strong)
4. Dimensionality Reduction
Manual Dye Separation (applicable to multichannel data):
As one can see from Fig. 02 and 03, the green channel composes of ca. 95% green dye and
5% red dye. This red contribution is spill over. Thus, by removing 0,05*RedChannel from the
green channel, this incorrect crosstalk can be removed. In manual dye separation, this
coefficients have to be estimated (if not measured separately) and applied to the multichannel
image. Similarly, one can clean the red channel. Result is a bleed-through free image.
Channel Dye Separation (applicable to multichannel data):
In this method, one has to know the distribution coefficients of all dyes into all channels. The
difference to manual dye separation is, that the coefficients are calculated by the system
instead guessing by the operator. Therefore, it is necessary, to find the pure dyes in the
specimen. The coefficients will be measured, and the sample can be analyzed. The “sample”
here is an object with unknown distribution of dyes in the pixels. Consequently, the signal
contribution of one dye into all channels can be reconstructed and a new dye image can be
calculated. This is done for all dyes in the sample. As a result, one will have a multilayer
image, whose layers are not “emission-channel” information (i.e. the signal which falls
between the edges of a bandpass filter or a spectrometer-slit) but “dye-information”, because
each layer contains the redistributed signals from all channels which make up that dye.
This method is just application of linear algebra to the pixelated image. It represents the task
to solve a set of linear equations, where the unknowns have to be resolved. In the most
common case for two dyes, one would select 2 channels and can solve the 2 equations with
the unkowns “dye 1” and “dye 2”, which in turn will result in a dye-image (Fig 04).
Here is an example, which may help to understand, what happens during “linear unmixing”. If
you have to prepare cakes for a birthday of your kids, you will need to make not just one type
of cake. Let us assume, you have two favourites, which you need to bake. One is the very
most favourite, and therefore you need to prepare many of them. The other one is more to
satisfy those, who are always hungry, also if the nice ones have gone. And therefore, you will
not need too much of those.
The shopping list will include all ingredients for both cakes, and of course, typically some
ingredients will be needed for both type of cakes. For example, most probably you will need
buttter, sugar and flour in all cakes.
The task of linear unmixing is, to recalculate from the composite shopping list, how many
cakes type 1 and how many cakes type 2 are planned. That’s all the mystery of unmixing.
Fig. 04
Spectral Dye Separation (applicable to lambda-stacks):
This method is similar to the above one. The difference is, that it is the mechanism, which
solves the problem for lambda stacks. Mathematically, it is the same. As a matter of fact, the
spectral dye separation employs more equations than unknowns, (this phenomenon is called
overdetermination). To separate two dyes, just two channels are sufficient. There is no need
to record data with many spectral bands, as some might suggest. In contrary, two channel
recording with tunable gain and tunable bands are preferable to improve in signal to noise.
Spectral dye separation is included to allow treatment of lambda stacks.
The set of coefficients for a dye in spectral dye separation is called the “spectrum”. It
compares to the recipe in the bakery. Thus, the two spectra of the two dyes are the recipes
for the two cakes. And the list of the measured signal strengths in all channels is the shopping
list. But there is again no difference to a two-channel image, where the spectral information is
in the coefficient matrix. If you need to separate n different dyes, it is sufficient to collect n
different channels. No “spectrum” must be recorded!
Adaptive Dye Separation (weak) (applicable to multichannel data):
The approach of adaptive dye separation is completely different from “solving sets of linear
equations” as described in the unmix-methods above. The adaptive dye separation analyses
the correlation statistics of the channels recorded. The graphical representation of such
correlations is called “scatter diagram”, “correlation diagram” or, in confocal fluorescence
literature “cytofluorogram”. For detailed information see the literature. These diagrams are
used to e.g. show colocalisation. The diagram is a two-dimensional histogram, where the two
axes represent the grayvalues of the red resp. green channel. The image is analyzed, and the
count, how many pixels are found where green has greyvalue g and red has greyvalue r is
written in the coordinate g,r. The areas of the image, which are red only, will create a cloud
parallel to the green axis, at very low green levels, as there is no green other than noise.
Same is true for the green-only areas.
If bleed through occurs, the cloud will be tilted towards the diagonal, as there is also a green
contribution in the pixels from crosstalk (Fig. 05)
Fig. 05
Fig. 06
The concept of dye separation is, to move the cloud back to the origin and thus get rid of the
crosstalk. (Fig. 06).
The weak modus of adaptive dye separation will move the clouds only until they just touch the
axes.
Adaptive Dye Separation (strong) (applicable to multichannel data):
The strong modus of adaptive dye separation will do exactly as in weak, but move the clouds
to coincide with the axes. (The clouds can be fitted by straight lines, comparable to a least
squares fit to any simple measurement. In the strong mode, these lines will be made to
overlay with the axes of the coordinate system).
Both adaptive dye separation modes will not need any additional spectral information but are
just based on the statistical information in the pixels and how the intensities of the channels
correlate. On the other hand, this would imply, that the system is not able to separate the
“clouds” if there are no areas of pure dyes, but only colocalisation! (compare Fig. 08)
Dimensionality Reduction (applicable to lambda stacks):
This is not an unmixing method, but a method to reduce the number of dimensions, as the
title suggests. In the literature, it is called “principal component analysis”. Here, what it does:
Two channels will give a 2-dimensional cytofluorogram (Fig. 07):
Fig 07
Three channels will give a 3-dimensional cytofluorogram:
Fig
08
(Fig. 08 is a stereopair of a 3D cytofluorogram calculated from a 3-color bead. For unaided
fusion freaks: you can see the cloud sticking into the front!)
A lambda stack with 200 layers will give a 200-dimensional cytofluorogram. I’m not going to
try to visualize that. If the sample contains only two dyes, it is possible to shrink this 200dimension thing into a 2-dimensional cytofluorogram. This is done by dimensionality
reduction. It requires to insert the number of dyes in the sample and will then perform the
requested reduction. Consequently, adaptive dye separation (weak or strong) is applicable.
Summary:
1. Spectral Dye Separation and Channel Dye separation represent linear spectral
unmixing, which is just solving sets of linear equations.
2. If n dyes are in your sample, you need to record only n channels. A “spectrum”
is not needed to record.
3. Additional to the linear unmixing approach, we offer a statistical approach
which allows to solve crosstalk problems without having any additional spectral
information. (It will fail, if there is no pure dye anywhere in the sample.)