These variables are calculated in terms of the fraction of each mode that corresponds to the size range designated by the number in the variable names. For example,
PM1AT refers to the fraction of the Aitken mode that corresponds to PM1 (or particles with diameter less than 1 micrometer)
whereas PM25AT is the fraction of the Aitken mode that is in the PM2.5 range.
Therefore, it is not expected that these fractions will sum to 1. To use these variables, you may multiply bulk variables like ASO4I by PM1AT to get the mass of SO4 from the aitken mode that is in the PM1 range. To get the total sulfate in the PM1 range you would sum the following:
PM1SO4 = (ASO4I * PM1AT) + (ASO4J * PM1AC) + (ASO4K * PM1CO)
The AMS suffix means Aerosol Mass Spectrometer. This device is commonly used in field and lab experiments to characterize aerosol composition. The instrument design focuses on particles in the PM1 range but there is a size dependence for its collection. At small sizes and large sizes, it gets less good at transmitting particles for analysis. This dependence was parameterized in Appendix B of Ensberg et al. (2013: doi:10.1029/2012JD018136).