The Daily Dongle

Three Rules for Compensation Controls

First and foremost, there must be a single stained control for every parameter in the experiment!

In addition, there are three rules for “good” compensation controls:

1) Controls need to be at least as bright or brighter than any sample the          compensation will be applied to

2) Background fluorescence should be the same for the positive and negative control

3) Compensation controls MUST match the exact experimental fluorochrome

 

1) Controls need to be at least as bright or brighter than any sample the compensation will be applied to

An important consideration is to select the sample with the brightest fluorescence of the experiment. “Dimness” is relatively irrelevant. Only brightest matters, and that is so that low spillovers can be accurately estimated. For example, if a spillover is so low that a MFI of 10,000 doesn't cause enough spillover to be above autofluorescence, then the system assumes no compensation is necessary. At a MFI of 100,000, the spillover becomes apparent and then compensation value can be accurately assessed. Compensation is only about estimating the slope. The bottom line is that because the compensation coefficients are computed based on the RATIO of the DIFFERENCE in MFI's (of the spillover channel and the primary channel), so small absolute errors in the position of the negative control become irrelevant as the positive controls become brighter. The error in the compensation coefficient is the sum of the absolute errors in the MFI's of both the negative and the positive control; the latter has an inherently much larger absolute error than the former.

2) Background fluorescence should be the same for the positive and negative control

Any carrier for binding fluorochromes can be used for single stain compensation controls, such as cells or particles. However, the positive and negative carrier of a parameter must have the same autofluorescence. This is because compensation is a subtraction algorithm. It is imperative to NOT include autofluorescence in the compensation calculation, so if the positive and negative have the same autofluorescence, then the autofluorescence contribution to the compensation spillover calculation will be zero. If this is met, one can apply the compensation matrix to any population. For example, one can compensate on particles and apply that to cells.

3) Compensation control fluorochromes MUST match the exact experimental fluorochrome

Each flurochrome has a unique emission profile.  Therefore, the amount of spillover will be different, even for fluorochromes that emit light at about the same wavelength (e.g. FITC and Alexa Fluor 488) 

This rule is even more restrictive when applied to tandem dyes.  Each lot of tandem dye (PE-TR, PE-Cy5, PerCP-Cy5.5, APC-Cy7, etc.) should be considered unique and require its own single stain control. If a user is using two different lots of PE-Cy7 in an experiment, then they need to have two PE-Cy7 compensation single stain controls, one from each lot. Different lots will have different conjugation ratios, i.e. more Cy7 conjugates to PE or less.

One final note

Finally, compensation controls must be treated in the same manner as experimental samples. This is because exposure to light and treatments like fixation/permeabilization may alter the fluorochrome, particularly the tandem conjugation ratio, i.e. lose some Cy7 on each PE molecule.

Compensation particles versus cells for single stain controls

There is no difference in the accuracy of the two approaches for compensation. However, compensation particles do have numerous benefits over using cells. First and foremost, precious sample does not need to be wasted on single stain controls. All the cells can then be used for the experimental samples. In addition, compensation particles typically provide the brightest signal possible for any given parameter. Compensation particles are also more precise. The reason that particles are more precise for compensation is fairly straightforward. Cells have a large variance in background fluorescence (a high CV), higher than particles. This means that the spillover computation has significant error for compensation coefficients where the measurement of spillover fluorescence on cells is dominated by the error in the autofluorescence measurement. On the other hand, the particles have a much smaller error in the distribution of background fluorescence, meaning that the spillover computation is far more precise.

Of course, particles have some limitations.   

1) Compensation particles cannot be used for dyes like PI, DAPI, or EMA -- but they can be used them with amine-reactive viability dyes.  (Also, some manufacturers are now providing specific dyes preloaded into particles to use as single stain compensation controls).

2)  Particles do not bind all antibody reagents and in some cases they simply are not bright enough.

3) For some experimental conditions using tandems (e.g. permeabilization/fixation), one must ensure that the fluorescence spectrum of the experiment does not alter the emission spectrum of the tandems attached to particles in a different manner than it would the tandems attached to cells.

So, in fact, in many experiments, a user may have one or two cell-based compensation controls for some parameters used together with bead based compensation controls for the other parameters.

- Question of comments can be sent to nick@treestar.com

 

Why do My Platform Stats Differ from my Workspace Stats?

Users of the Proliferation and Cell Cycle Platforms have undoubtedly noticed that the statistics the model produces do not transfer exactly to the workspace when Gates are created from the model. 

For example, the figure below shows a Watson-Pragmatic cell cycle model for one of our demo files.  The associated statistics are noted on the model.  The stats pertinent to this discussion are the G₀/G₁, S, G₂/M frequencies which in the model are roughly 57% / 24% / 18%.

If you were to press the Create Gates button at the top of the model window, and accept the “Stage” prefix you would get the workspace shown below the figure. Notice that the frequencies are roughly 64% / 14% / 21%.  Why have 7% of the cells “shifted” from the S phase into the G₀/G₁ and another 3% shifted from S into the G₂/M?

The statistics are actually calculated in two different ways.  When using the models the frequencies are calculated using probabilities of membership, based on the model fit.  For cells with intensity measured within a given range, the model can be used to determine the prob

ability of the cell belonging to each of the identified populations plus sub-G₀/G₁ and super G₂/M.  The probabilities of all cells are then added up to computethe phase probabilities for the entire sample.  The summation of these probabilities will be another probability.  To create fractions that add up to ~100% a normalization step is required.  To preserve the relative relationship between phases we do not simply normalize to 100% but rather map the probabilities to those that sum to 100%.  This process can sometimes lead to small negative numbers, particularly in the sub-G0/G1 or super G2/M populations.  In these cases it is reasonable to think of a population with a negative frequency as simply a very small number of cells. 

When you press the Create Gates button FlowJo places hard line gates on the model at the points where it becomes less probable that a cell belongs to one population and more probable that it belongs to another.  Cells that are in the gate are treated as having a probability of membership of 100% for the “winning” phase and 0% for all other. 

You’ll notice in the above example that the difference in the statistics is that the gated frequencies do not take into account that there are probably a decent number of S phase cells that spill into the other two distributions, so if you have the opportunity to use the model statistics, do so.  The stochastic approach models the data better.  However, if you use the model created subpopulations, continue to add layers of gates, and in the end need to come up with fractions that add up to 100%, you will need to use the gate frequencies. 

- Bad Mo'Flow

Send comments and questions to john@treestar.com

 

 

how to check your fluorescence spillover matrices ?

So here's a comp matrix as seen in FlowJo. It has some numbers. How do you check those numbers are right? 

 

Here's one idea:

make a plot for each comp control, showing the control parameter vs. it's biggest spill value- so for the PE-A control (top row), I plot it vs. PE-Cy5, etc. 

Then I overlay the plot with itself - except comped, dressed up with some math. Here's what that looks like, just for the PE control tube: 

 

To get the above figure, make the two separate figs first (PE vs PeCy5 and comp-PE vs comp-PeCy5, in this example). Set both figs background "N" (transparent). Then select both and tap T (top align) and L (left align). 

To get the formulas to evaluate in your textboxes, simply wrap them in {{}} brackets around the expression. You can mix FJML with regular math operations. For example, the formula for the median % error was: 

{{abs(1-<fjml for uncomped median> / <fjml for comped median>) * 100 }}

and for the vertical spread error, 

{{abs (1- (<fjml for SD1> + <fjml for CV1>)/(<fjml for SD2> + <fjml for CV2> ))*100 }}

These stat calculations are the interesting bit which needs some more formulation. The easy check is to line up the medians of the data before and after compensation (shown in the top textbox.)

The harder bit is to check that the vertical spread hasn't changed. In the plot above, the red and black populations should have the same footprint on the Y scale. I tried to quantitate this using SD/CV math but I get much bigger errors.. has anyone done this sort of thing systematically, I'd love to get some feedback!

interesting world map projections

http://www.worldmapper.org/

Many of us have already experienced the double-take when we saw the usual (Mercator's) world map vs. Peter's projection - all of the sudden, North Hemisphere countries appear compressed on  log scale, and Africa becomes huge.

The link above has several other takes. Like science research funding:

or poverty:

so check out the link and "see the world as you've never seen it".

awesome - motion magnification

A research group at MIT presented a cool technique called motion magnification back at siggraph05. I just got the memo ;) if this is new to you as well, see webpage here - http://people.csail.mit.edu/celiu/motionmag/motionmag.html

I wonder if there is a way to apply this in bioimaging - this technique would be not unlike biexponential scaling - in that it helps to visualize the data better.

Anyway, if you really wanna be blown away by what these guys are doing, watch the demo movie [link] especially the parts towards the end.

Mean, Median, Mode.

Many novice users call and ask us about 'mfi' of their data. Since the acronym is ambiguous, we ask the scientist to specify if they are asking about median, mean, or geometric mean fluorescence intensity.

Mean and Geometric mean are easiest to understand - here are their formulae (from wikipedia):

Mean (aka arithmetic average) is defined as the sum of N things divided by N:

If your data is scaled in Log, you might want to use the log-friendly version of Mean, the Geometric Mean. This expression takes the Nth root of the product of N things:

Median is the number which divides the first half of your data from the second half, if sorted by some variable. Suppose you had 1 event with fluorescence of "262144" and 19 events with fluorescence of "1". The "mean" fluorescence would be (262144+19)/20 = 13108.

The Median fluorescence is 1 - if we sort the events by fluorescence and divide them in two parts, half of the events will have intensity no less than 1, the other half, no more than  1.

Depending on how you look at your data, Median usually gives the representation of a "typical" event. In the example above, no single event had fluorescence of "13108" which is what Mean would have us believe!

Also here is an interesting figure demonstrating the relationship of mode/median/mean in some types of distributions.

Courtesy of Jerrold H. Zar from Biostatistical Analysis, fourth edition, Simon & Schuester 1999

Negative Fluorescence

I saw an interesting post by Dr. Roederer on Purdue list archives discussing the topic of negative fluorescence. This question came up in my email as well just last week, so it's nice to get a real scientist's (as opposed to us flow-jocks) perspective:

Recently, I was queried by a user who complained about the new data 
transformations (Biexponential, Logicle, Hyperlog, etc.), which show 
negative values.  The user complained that negative fluorescence is 
not biologically meaningful.

Indeed, the user is correct.  There is no meaning to negative 
fluorescence; there is no such thing.  However, what we are 
displaying on the graphs is no longer fluorescence, it is a corrected 
measurement derived from fluorescence.    The corrected measurement has 
been manipulated by both the instrument firmware, and possibly   
software (in the case of compensation), before it is displayed.

When the fluorescence is detected off the PMT, the voltage 
measurement has "baseline" subtracted from it.    Baseline is measured 
during the time between pulses.  However, there is an error in the 
measurement of both the fluorescence as well as the baseline.  So, 
for "negative" cells (cells with little or no fluorescence), there's 
a chance that the measurement for the cell will be less than the 
measurement for the baseline, because of the errors involved.  After 
subtraction, the measurement is less than zero.

Likewise, for compensation, additional measurement errors from all of 
the compensation channels are aggregated into the final computed 
value; thus, frequently this value is less than zero.

Look at it another way:  there is a distribution of measurements 
around the true value; that distribution is dictated by the error in 
the measurement (i.e., the SD).  If the true fluorescence is nearly 
zero, and the error is fairly large, then of course we expect the 
distribution to rise to the positive values -- with 95% of the values 
being within a few SD of the "true" value.  But measurement errors 
are always symmetrically distributed--so the distribution has to 
reach into the negative values just as far.  It would be incorrect to 
set these negative values to zero, because they you would 
systematically increase the mean of the distribution (you are always 
increasing negative values, but you are not decreasing any other 
values).

But the bottom line is that we are not displaying measured 
fluorescence values -- those of course are always positive.  We are 
displaying corrected measurements.  Notably, the corrected 
measurements are still linearly related to the fluorescence of the 
original event.

*update 5/13/08* There was another question posted about this on the list, and Dr. Roederer added..

negative values are not a consequence of the biexponential scaling --  
that's only a visualization too.  Rather, negative values are a  
consequence of two different operations: (1) baseline restore -- a  
subtraction process that instruments do on a event-by-event basis  
before reporting the data to the computer; on the DiVa, this can  
result in a value less than zero for events that have essentially no  
fluorescence, because the error in the estimation of the background  
can exceed the absolute magnitude of the background itself; and (2)  
compensation, which subtracts values from the fluorescence signal  
based on the fluorescence in other channels -- and once again, the  
error in the estimation of the amount to subtract can exceed by a  
large amount the absolute magnitude of the value after subtraction.   
With both of these operations, you will end up with a distribution of  
events near zero, but with a standard deviation such that the tails of  
the distributions go negative or positive.

If you've over-compensated, or if you've gated on events to select  
primarily events that are below zero, then any estimate of the central  
tendency of this population (median, mean, geometric mean) will be  
negative.  If the value is substantially less than zero, then you have  
overcompensation problems.  If the value is near zero, then it's  
probably just random luck that it wasn't above zero...        In the former  
case, I would be cautious about any MFI values to begin with, since  
with improper compensation settings you cannot rely on the MFI.  In  
the latter case, whether you use the actual value or you use "zero"  
probably won't change your answer, so it becomes academic.

Finally, a purist may note that the geometric mean fluorescence should  
never be less than zero (because of how geometric mean is  
computationally defined).  Strictly speaking, this is correct -- a  
geometric mean can never be negative.  The software, however, is  
attempting to compute a central tendency that is weighted similarly to  
the geometric mean for these distributions, where negative values can  
exist.        Thus, it uses the same biexponential transformation to aid in  
defining a statistic that gives you this value -- the "geometric" mean  
has the same functionality in terms of providing an estimate of the  
center of the population as it is drawn in your graphs (after all,  
this is origin of the term "geometric") -- and thus, a population that  
is centered below zero would have an "undefined" geometric mean by the  
original algorithm, but a meaningful and applicable geometric mean in  
biexponential geometry.

mr

(Note: here's a trivial example of why the "standard" geometric mean  
is not a good estimate of central tendency when you have values near  
zero.  If you have a single cell with zero fluorescence, and a million  
cells with fluorescence of 10^5, then the geometric mean of this  
population of 1,000,001 cells is.... zero!  Not a very good estimate.   
However, software that uses the biexponential geometry to calculate  
the gMFI will give the much better value of 10^5, as it would for the  
mean and the median...)

another logicle (biexponential, hyperlog..) PDF...

found this on google:

A New ‘‘Logicle’’ Display Method Avoids Deceptive Effects of Logarithmic Scaling for Low Signals and Compensated Data

practical flow cytometry online

This is old news, but I can never find the link - free online access to Howard Shapiro's Practical Flow Cytometry:

http://probes.invitrogen.com/products/flowcytometry/practicalflowcytometry.html

 

Dr. Howard Shapiro's P.F.C. is probably the most comprehensive, freely and publicly available compillation of Flow knowledge found in the universe.

Speaking of Comprehensive, there is a rather extensive list of Flow-links here.

how to convert log data to linear

This post from the Cytometry Mailing list answers a question I got earlier today:

Scale (linear) Value = f * 10^ [(C * n) / R]

where

C = channel number
n = number of decades for the full range (~4 on BD & Cytomation machines,
~3 on many Coulters)
R = range (maximum number of channels; typically 1024)
f = log offset (typically 1 or 0.1)

The FCS keyword $PxE (x = parameter number) has the values for f and n
(e.g., <$P4E = 4,0.1>  means that parameter 4 has a 4 decade range with the
linear scale value of channel 0 equal to 0.1); $PxR has the value for R.
Note that for most BD-generated FCS files, the offset for all log
parameters is incorrectly stored in the FCS keyword list as 0 (zero); it
should be 1.0.