Understand the relationship
The reasoning behind the result
Each daughter generation is traced back to precursor equivalents
P(i) = N(i)/2^i
Under binary doubling, one reconstructed precursor represented in generation i corresponds to 2^i final-generation descendants. Dividing the entered generation amount by 2^i places every generation on a common starting-precursor basis.
This is an arithmetic reconstruction from entered generation assignments or fitted amounts. It does not locate peaks, prove that fluorescence halved cleanly or correct generation-dependent loss.
Proliferation index uses only reconstructed responders
PI = ΣiP(i) / Σᵢ≥1P(i)
The numerator weights every responding precursor equivalent by its entered division number. The denominator excludes generation 0 and therefore represents only reconstructed precursors with descendants in a divided generation.
When all entered amount is in generation 0, that responder denominator is zero. The workbench reports PI as undefined rather than zero.
Division index includes responders and nonresponders
DI = ΣiP(i) / Σᵢ≥0P(i)
Division index uses the same weighted division total but divides by all reconstructed starting precursor equivalents, including generation 0.
For a record with responders, DI/PI equals the reconstructed responding-precursor fraction. The result ledger exposes that reconciliation rather than treating PI and DI as synonyms.
Starting-basis and final-basis percentages are different
% divided = 100R/S; fraction diluted = 100Q/F
Percent divided, also called precursor frequency in this convention, uses reconstructed responding precursors R over all reconstructed starting precursors S.
Final fraction diluted uses final entered amount in divided generations Q over total final entered amount F. Later generations contain more descendants per precursor, so these percentages need not agree.
Expansion and replication indices use cell-number ratios
EI = F/S; RI = Q/R
Expansion index compares all final entered amount with reconstructed starting precursor equivalents. Replication index compares final divided-generation amount with responding precursor equivalents.
These ratios describe the entered reconstruction. Differential death, sampling loss, recovery, peak overlap and culture history can change their experimental interpretation.
Metric names depend on software convention
Published software packages have used the same names for different proliferation quantities. In particular, proliferation index may mean responder-average division number in one package and a cell-expansion ratio in another.
This workbench therefore identifies its definitions as FlowJo-style and prints every component needed to verify the denominator independently.
Follow the numbers
Separate responder-only and all-precursor averages
- Enter 800 events in each of generations 0, 1, 2 and 3.
- Reconstruct precursor equivalents as 800, 400, 200 and 100, for a starting total of 1,500 and a responding total of 700.
- Calculate the precursor-weighted division total: 0×800 + 1×400 + 2×200 + 3×100 = 1,100.
- Divide 1,100 by 700 responding precursors to obtain PI = 1.57142857; divide by all 1,500 precursors to obtain DI = 0.73333333.
- Calculate percent divided as 700/1,500 = 46.6667%, while the final fraction diluted is 2,400/3,200 = 75%.
The two averages and two percentages differ because they answer different questions with different denominators.
Quick guide
How to use this calculator
- Enter generation 0 and every modeled or gated daughter generation through the last generation, including explicit zeros for empty intermediate generations.
- Declare whether the amounts are whole assigned events or model-fitted estimates; decimal values are accepted only for the fitted basis.
- Review the precursor-equivalent ledger before using the named metrics, especially the different denominators for proliferation index, division index, precursor frequency and final fraction diluted.
- Retain the FlowJo-style naming label, generation model, gate definitions, dye, culture time, controls and acquisition context with any exported result.
Calculation method
Calculation and interpretation
Audit generation-count proliferation arithmetic without fitting peaks, identifying responders or turning software-specific metric names into universal biology.
For generation i with entered amount N(i), precursor equivalent P(i)=N(i)/2^i. FlowJo-style PI=ΣiP(i)/Σᵢ≥1P(i); DI=ΣiP(i)/Σᵢ≥0P(i); % divided=100Σᵢ≥1P(i)/Σᵢ≥0P(i); EI=ΣN(i)/ΣP(i); RI=Σᵢ≥1N(i)/Σᵢ≥1P(i).
Worked example
Separate responder-only and all-precursor averages
The two averages and two percentages differ because they answer different questions with different denominators.
For generation i with entered amount N(i), precursor equivalent P(i)=N(i)/2^i. FlowJo-style PI=ΣiP(i)/Σᵢ≥1P(i); DI=ΣiP(i)/Σᵢ≥0P(i); % divided=100Σᵢ≥1P(i)/Σᵢ≥0P(i); EI=ΣN(i)/ΣP(i); RI=Σᵢ≥1N(i)/Σᵢ≥1P(i).
Supported inputs
Precision and limits
Entered generation summaries only
The workbench does not read FCS files, transform fluorescence, locate peaks, fit distributions, assign generations, gate cells or identify responding populations.
One declared software convention
Named outputs follow the displayed FlowJo-style division-number definitions. They must not be compared with same-named metrics from another package without verifying its equations.
Binary-doubling reconstruction
Dividing N(i) by 2^i assumes the entered generation number represents successive binary divisions. It does not model asymmetric division, dye transfer, unresolved peaks or non-division dye loss.
No death or recovery correction
Differential death, sample loss, acquisition fraction and generation-dependent recovery can alter surviving counts; no unobserved cells are reconstructed beyond the stated 2^i relationship.
No automatic comparability
Dyes, labeling, culture duration, gates, model settings, controls, event counts, compensation and acquisition configuration remain external evidence for every record.
No response threshold
PI, DI, precursor frequency, expansion, replication and diluted fraction receive no pass/fail, activation, potency, inhibition or significance label.
No uncertainty model
The outputs are deterministic point calculations from entered amounts and include no confidence interval, replicate model, goodness-of-fit measure or sampling inference.
No clinical interpretation
The metrics do not diagnose a specimen, establish immune function, determine treatment response or support a patient-specific decision.
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