Checkerboard synergistic data analysis using a Hill function-based approach

This study presents a checkerboard data analysis approach using a Hill function (y = 1/(1+(x/K)ⁿ) to fit each column and row of checkerboard assay data. Column fits give a K (MIC) value in units of row concentration for each column antibiotic concentration (MIC_row vs [Col]), and row fits give an MIC_col value for each row antibiotic (MIC_row vs [Row]). Since the corresponding row and column concentrations are themselves MICs, this provides two sets of MIC vs MIC data pairs which can be plotted together as an isobologram. These MIC_A vs MIC_B values can be subjected to a second round of Hill function fitting, separately in x-y and y-x directions. Finally, a fit based on overlapping Hill functions is developed that allows x-y and y-x dimension fits to be performed simultaneously. Formula for fractional inhibitory concentrations (FICIs) as a function of fit parameters, and other features of these curves, are derived. This analysis also provides "n" (steepness) values from column and row fits, which are themselves dependent on the other antibiotic concentration and can be exceptionally, as in the case of ceftobiprole alone (n>10). This synergistic checkerboard analysis approach is implemented in MATLAB, which performs the fits and provides statistics variable values and alternative models significance.