Journey Into Hyperspace III: Biplot Revisited
Francis L. Battye
The Walter & Eliza Hall Institute
Hand in hand, the inexorable increase in sophistication of flow cytometry applications and the expanding capability of the flow cytometers themselves continues. However, the methods of displaying multiparameter flow cytometry data for analysis have not really changed substantially in the last two decades. 3-dimensional display styles have not been widely accepted so that, in most cases, combinations of 2-dimensional contour or scatter plot displays are used. For cell sorting, hardware limitations have enforced the 2-dimensional limit for constructing sort regions. But now the increased speed of today's computing and digital signal processing hardware tempts us to reconsider one intriguing data display idea that, from the point of view of flow cytometry, has long lain dormant.
The biplot is a technique quite commonly used in the social sciences for the plotting of multidimensional data in a 2-dimensional plane. The methods of linear algebra are used to operate on the data which is treated as an m X n matrix whose m rows correspond in our case to the m analysed cells and whose n columns correspond to the n measured parameters. Firstly, the data is transformed into a space spanned by linearly independent vectors derived from its own variance and covariance. Both this transformed data and the transformed axes identified with the flow cytometry parameters are then projected onto the 2-dimensional display plane.
In the work reported here, three example analyses have been chosen to investigate the value of the biplot technique. The first is an analysis of a peripheral blood stained with FITC.CD8, PE.CD4 and Tricolor.CD32. This is a simple analysis in which three subsets are expected to be singly-fluorescence-positive. Eight parameters were measured in the second example [see the figure] on mouse lymph node cells; FSC, SSC, FSC pulse width, FITC.CD3, PE.B220, Texas Red.Thy-1, APC.CD8 and PI. In this case subsets may be singly, doubly or triply fluorescent and of different FSC and SSC. The third example comes from experiments on mouse spleen cells stained for B220, IgG1, a cocktail of irrelevant cell markers and a fluorochrome-conjugated specific antigen. A separate cluster analysis of this data revealed a number of subpopulations but was unsuccessful in identifying the 0.2% of the cells which were specific antigen binding, germinal centre, B-Lymphocytes. The search for this tiny subpopulation in a biplot of the sample was expected to be a most demanding test of the technique.
An exciting aspect of the biplot's potential utility is that the selection of a subset of cells for sorting may be made by drawing a single amorphous region on a single 2-dimensional display, but this selection is then inherently based on all of the measured parameters.