FCS Express: Hybrid Scalings

Data is traditionally displayed on either a linear or logarithmic scale, and the appropriate scaling is stored in the header of the data file. Although FCS Express has supported displaying linear data on a logarithmic scale, the data has traditionally been displayed on the same scale as it was acquired.

The logarithmic scale has the major disadvantage that it cannot display values below zero. This is a severe limitation when performing software compensation when it is common that a significant proportion of the data goes below zero. When displayed on a log scale, the negative values are placed on the axis, and it is very easy to be mislead and overcompensate your data.

To overcome this limitation, several additional scalings have been performed. These scalings share the general characteristic that they behave linearly close to zero, and behave logarithmically farther away from zero. These scalings also are defined to be able to graph data below zero. Scalings that are a combination of linear and log scalings are called hybrid scalings.

FCS Express supports several different hybrid scaling and you can choose whichever you want from the Axis Formatting screen.

The different axis scalings are:
  • Linear - standard linear scaling. (can display values below zero)
  • Biexponential -The biexponential display was popularized by the BD FACSDiva software. As a result of our close collaboration with BD, FCS Express now supports all of the options that FACSDiva does in terms of displaying biexponential data. In fact, we have implemented FACSDiva's proprietary algorithm for calculating the reflection point, so the results from FCS Express will look identical to the results from the FACSDiva software.
  • Log - standard log scaling
  • Hyperlog™ - a hybrid scaling described in: Bagwell, CB. (2005). Hyperlog-a flexible log-like transform for negative, zero, and positive valued data. Cytometry. 64: 34-42.
  • Log With Negative - a modified log scale that can display negative values. An artificial symmetry is created at zero and negative values are displayed to the "negative" side of the axis.
  • Lin/Log - a hybrid scaling that is perfectly linear below a user defined transition point, and purely logarithmic above it.
  • ArcSinh - an inverse hyperbolic function most widely used with .fcs files generated by CyTOF Mass Cytometry, that helps display and visualize values at or near zero with a "spread" that we normally expect when visualizing with standard flow cytometry data.

The axis scale can be modified on a plot by plot basis. Some examples of the different scalings are shown below:


Rest assured that in FCS Express, gates drawn in any scale are displayed appropriately in any other scale. Notice how the straight lines of the polygon gate in linear space become curved when displayed on a non-native scale such as log space. The reflects the non-intuitive mapping of the linear to logarithmic coordinates.

A detailed description of the hyperlog and biexponential transformations can be found here.