PolyVariate Display

The Polyvariate Display function shows more than 2 parameters on a 2D graph. This allows the user to define complex populations of cells using one gate. Multiparameter populations have until now required complex boolean gates or multiple, hierarchical gates.

The gates created using this tool work as any other gates in FlowJo. You can drag/drop them just the same and the contents can be interrogated in Graph Windows or the Layout Editor.

You can launch the GUI from a Graph Window. Open a Graph Window, click Graph menu, and choose PolyVariate Plot. The Polyvariate Plot tool changes the appearance of the original graph. As you make changes in the tool, observe the corresponding changes in the graph.

There are 5 controls in this GUI. They are explained below.

1. Add/Remove Parameters menu.
2. X/Y Axis Range.
3. Vector Controls.
4. Pivot Range.
5. Histogram Pivots.

The Vector Controls and Pivot Range are part of the PolyVariate circle. The PV circle is a representation of the graph space. The standard 2D plot has two axes at a 90 degree angle with the 0 point in the lower left corner. The PV plot has the 0 point in the center. The vector angle determines which direction away from the 0 point the parameter will be scaled. The vector length from center controls the scaling of the parameter, where the 0 point is the minimum value and the rounded end is the max value. The pivot range circle corresponds to the pivot points on the accompanying histograms, explained below.

1. Add/Remove Parameter pulldown menu. To add one, select it from the pulldown list. To remove it, click it again from the same list. Each parameter you select will add a colored vector control line to the tool and a histogram of that parameter with the same color as the vector line. Forward and side scatter appear by default.
2. X/Y axis range. This is the equivalent of zoom control. The short blue lines
   accompanying the X and Y axes can be dragged to control the display
   scaling. Consider the next two screenshots as examples:
   
   

In the graph above, the X and Y axis zoom controls are at their default extended positions. The resulting plot is small and does not take up the whole graph space. To zoom in on it, I've adjusted all 4 of the controls to yield the plot below. Please pay attention to the positions of the blue range sliders before and after the change. Notice that they need not be moved to symmetrical positions.

3. Vector Controls. These are the colorful lines across the PV circle. You can drag the rounded end of the line to change the vector direction and magnitude.
4. Pivot Range – this is the light-gray inner-circle in the illustration above. It corresponds to the gray vertical lines on the histograms on the right side of the tool. The events below the grey threshold line on the histogram plot are drawn from zero (the center) to the gray circle on the PolyVariate plot; the events above the gray histogram threshold line are drawn from the gray circle outward--in other words, the position of the line on the histogram plot is mapped to the position of the gray circle along the vector. You can drag this circle to change its size.
   Consider the next few screenshots as examples:

In the graphic above, we're looking at a cluster of CD3+ lymphocytes (lower left) with default pivots and adjusted X/Y axis ranges.

Above, we've adjusted the CD3 histogram pivot to accent only the brightest cells. The cluster becomes bigger after adjusting the ranges, because the bright CD3 peak is stretched into the "outer" circle.

In the screenshot above, the gray pivot range circle was dragged outward to make the CD3 cluster tighter.

5. Histogram Pivots. This control ties in with #4 to warp the parameter with the help of the Pivot Range circle. The default value is 0.25 (first quarter of your scale - imagine the length of your parameter in pixels rather than lin/log scaling, and take ¼ of that value... that's how it works)

Example 1 - A 3 Parameter exercise (FSC, SSC, CD3)

First, open a graph window for a sample stained with CD3. Select Graph > PolyVariate Plot from the main menu , and add CD3 from the pulldown in the PV tool:

The resulting graph has Forward Scatter increasing from 0 point (ZP) to vertically up, Side Scatter from ZP to horizontally right and CD3 from ZP to diagonally right-and-up.

We know that CD3 is mostly expressed by cells with lower FSC and SSC values, so I'm inclined to point the CD3 diagonally left-and-down from the ZP. After adjusting the X/Y ranges and the histogram pivot points, the plot looks like the one below. The Forward and Side scatter pivot points were adjusted to approximately the upper value of the Lymphocyte cells (most of lymphocytes will be found to the LEFT of the FSC/SSC pivots. Most CD3 bright cells will be found to the RIGHT of the CD3 pivot):

Now let's draw some gates and find out what we have:

Draw two rectangular gates, one on the area controlled by the CD3 vector (CD3+), one on the Forward/Side scatter area. Since the center is zero, this is also the CD3 negative area.

Drag the ungated population from the Workspace window into the Layout Editor. Drag in a second copy and change the X axis to CD3. The Y axes on these graphs are OrthSc. Drag the CD3+ gated population onto each graph. The top two graphs above are the result. Drag two more copies of the ungated population into the Layout and adjust the X axis again on the second one.. Drop the CD3+ gated population onto each.

The CD3+ gate, which also includes FSC/SSC parameters, is faster to make than two separate gates on FSC/SSC then CD3. The purity and recovery is within 3% of the standard gates.

Example 2 – A 5 parameter exercise (FSC, SSC, CD3, CD4, CD8)

Please note, I've already adjusted pivots/vectors above. The FSC/SSC axes are both pointing up vertically - in my tests including both of them and combining them works better than using either/or.

Let's inspect the gates as before, the ungated population in red, the subsets in blue:

The phenotypes are as clean as they can be - you can use conventional gating to compare purity/recovery.

Example 3 - A 5 parameter exercise 2 (CD3 vs. CD4 AND CD8)

What if we wanted to create a single gate that encompasses the phenotype CD3+(CD4+ AND CD8+)? Set it up like this:

...and the gate contains...

To revert to the graph with which you began, you can click the Clear button at the bottom of the window, or, if you have closed the PolyVariate Plot GUI, you can use this button in the Graph Window to revert to the two parameter graph type.