Question 1:

I have a CFSE plot where the majority of the cells are in the peak corresponding to four rounds of division. Yet- the proliferation index is only 2.14.  Although I understand that this is the relevant number and is what people use in the literature, I can’t explain why the proliferation index number is so low compared to what our eyes tell us is the median division number.  I would like to understand for my own self as well as so I can explain it to people in my lab. Can you help?

Your question illustrates why it is so important to rely on the computer – and not your eye!  Remember, every time a cell divides, it makes 2 progeny.  Thus, for every 4 cells in the second peak, only 1 cell was responsible… for every 16 cells in the fourth peak, only 1 original cell was responsible.  Thus, when you see a big 4-division peak, remember to mentally divide it by 16 (!) in order to estimate how many cells in the original population were responsible for that peak.

The proliferation index does not refer to how many cells are dividing at the time of analysis–it refers to how many cells out of the original population underwent division.  If exactly half of the original population of cells divided exactly 3 times, and the other half did not, then you would have two peaks: one at 1/8th fluorescence that is 8 times as big as the undivided peak.  By eye, it would look like a vast majority of cells had divided… but: only half had divided, and then only 3 times.  Hence, the proliferation index (the average number of divisions for the dividing population) is 3; the division index (the average number of divisions for all cells in the original population) is 1.5 (half divided 3 times, and half did not).

In the example from the web site, the proliferation index is 2 — meaning that the average original cell divided twice.  Since peaks #1 and #2 are about the same height, that means that twice as many cells only divided once as those that divided twice…  and, roughly speaking, peaks #3-5 are also the same height, but only represent 1/2, 1/4, and 1/8th as many cells as those in peak #2, out of the original population.

The bottom line:  Because growth is exponential, the number of cells in each subsequent division peak represent twice as many original cells as from the previous peak–and thus the mathematical weighting assigned to each subsequent peak must be halved.

Question 2:

Is it possible, to see the actual mathematics FlowJo is performing to get the Division and Proliferation Index and the % of divided cells? Because based on the cell counts that FlowJo is showing for the different generations I always generate different numbers if I calculate e.g. the Precursor Frequency myself.

If sample “A” has twice as many responding cells as sample “B”, but the number of divisions that responding cells actually did was the same, then the proliferation index of sample “A” is twice as large as that for sample “B”, but the division indices are the same.

Note that the statistic “% Divided” that the platform provides is the same as the Precursor frequency.

Division Index = sum ( i * N(i) / 2^i ) / sum ( N(i) / 2^i )

where i = division number (undivided = 0)

N(i) = number of events in division i

This equation gives you the average number of divisions that a cell in the original population underwent. (If you start the sum with i = 1, then you get the “proliferation index”, which is the average number of divisions that all “responding” cells underwent. By definition, this has to be >1). Note that the ratio of the proliferation index to the division index is the precursor frequency. So FlowJo reports division statistics in terms of number of divisions rather than number of cells; I feel that the number of divisions is more meaningful, biologically, since the number of cells grows exponentially with divisions and therefore does not lend itself well to averaging.

Division Index is the same, but you sum from i = 0 to nPeaks (i.e., include the undivided).

%Divided = Division Index / Proliferation Index