Prediction by Statistical Overlap Theory of Fraction of Baseline Occupied by Chromatographic Peaks

Abstract The average minimum resolution required for separating adjacent single-component peaks (SCPs) in one-dimensional chromatograms is an important metric in statistical overlap theory (SOT). However, its value changes with changing chromatographic conditions in non-intuitive ways, when SOT predicts the average number of peaks (maxima). A more stable and easily understood value of resolution is obtained on making a different prediction. A general equation is derived for the sum of all separated and superposed widths of SCPs in a chromatogram. The equation is a function of the saturation α, a metric of chromatographic crowdedness, and is expressed in dimensionless form by dividing by the duration of the chromatogram. This dimensionless function, f(α), is also the cumulative distribution function of the probability of separating adjacent SCPs. Simulations based on the clustering of line segments representing SCPs verify expressions for f(α) calculated from five functions for the distribution of intervals between adjacent SCPs. Synthetic chromatograms are computed with different saturations, distributions of intervals, and distribution of SCP amplitudes. The chromatograms are analyzed by calculating the sum of the widths of peaks at different relative responses, dividing the sum by the duration of the chromatograms, and graphing the reduced sum against relative response. For small values of relative response, the reduced sum approaches the fraction of baseline that is occupied by chromatographic peaks. This fraction can be identified with f(α), if the saturation α is defined with the average minimum resolution equaling 1.5. The identification is general and is independent of the saturation, the interval distribution, or the amplitude distribution. This constant value of resolution corresponds to baseline resolution, which simplifies the interpretation of SOT.