Update for the logicle data scale including operational code implementations

Since its introduction in the early 2000s, the logicle data scale (1,2) has been widely adopted by the cytometry community. The characteristics of logicle displays and their use to facilitate interpretation of flow cytometry data have been discussed in several papers (3,4). FlowJo software (Tree Star, Ashland, OR) offers the option of setting logicle transformation as the default for some data types. Diva software (BD Biosciences, San Jose, CA) offers logicle displays with scaling customized to the distribution of the data in each plot (called “Biexponential” but using the logicle constraints on the biexponential and logicle methods for selecting display parameters). In our experience with data from many different biological applications and a variety of instruments, logicle transformation provides good representation of all cytometry data for which direct linear presentation is not the most appropriate choice and has shown no tendency to generate artifactual features in displays. On this basis, we now recommend logicle as the appropriate default method for nonlinear transformation of cytometric data. In support of this recommendation, this communication provides (1) minor updates to the logicle specification, (2) a rigorously defined parameterization that should clarify questions that have come from people who were implementing logicle transformations in software, (3) technical details that were not considered suitable for the original publication but have become important for the standardization and consistent application of the method, (4) reference implementation code for both high-precision and routine calculations, and (5) a more detailed mathematical exposition on Biexponential Functions (Supporting Information). We expect that the formulas presented here will be the normative definition for the logicle transformation included in the ISAC Standards Committee’s recommendation in Gating-ML (Analytical Cytometry Standard (ACS)—Gating-ML Component, http://flowcyt.sourceforge.net/gating/). Implementations of the logicle scale in the Java, C++, and C programming languages are provided in the Supporting Information and are released under the Revised Berkeley Software Distribution open source license for free use in cytometry software. A module for integrating the logicle scale into the R statistical programming environment is available in the Bio-conductor repository (http://www.bioconductor.org/). Several algorithms and computational methods used in this work were adopted or modified from Ref. 5 (NR3, www.cambridge.org/numericalrecipes and www.nr.com).