A study of the precision and accuracy of peak quantification in comprehensive two-dimensional liquid chromatography in time

Abstract

Simulated chromatographic data were used to determine the precision and accuracy in the estimation of peak volumes (i.e., peak sizes) in comprehensive two-dimensional liquid chromatography in time (LCxLC). Peak volumes were determined both by summing the areas in the second dimension chromatograms and by fitting the second dimension areas to a Gaussian peak. The Gaussian method is better at predicting the peak volume than the moments method provided there are at least three second dimension injections above the limit of detection (LOD). However, when only two of the second dimension signals are substantially above baseline, the accuracy and precision of the Gaussian fit method become quite poor because the results from the fitting algorithm become indeterminate. Based on simulations in which the modulation ratio (M(R)=4(1)sigma/t(s)) and sampling phase (phi) were varied, we conclude for well-resolved peaks that the optimum precision in peak volumes in 2D separations will be obtained when the M(R) is between two and five, such that there are typically four to ten second dimension peaks recorded over the eight sigma width of the first dimension peak. This sampling rate is similar to that suggested by the Murphy-Schure-Foley criterion. This provides an RSD of approximately 2% for the signal-to-noise ratio used in the present simulations. The precision of the peak volume of experimental data was also assessed, and RSD values were in the range of 4-5%. We conclude that the poorer precision found in the LCxLC experimental data as compared to LC may be due to experimental imprecision in sampling the effluent from the first dimension column.

Fig. 1

(A) Simulated sequential second dimension chromatograms for a single component. The vertical lines in this figure denote the point of injection from the first dimension column onto the second dimension column; (B) A contour plot of this same simulated data; (C) Demonstration of how to sum the second dimension chromatogram areas to generate the volume of a LC×LC peak and of the fitting the second dimension peak areas to the Gaussian model to reconstruct the first dimension chromatogram and subsequently to obtain the volume of the two-dimensional peak. The numbers 1–6 in the mesh plot correspond to the sequential ‘slices’ or second dimension chromatograms. This figure corresponds to the ¹σ = 0.20 min (M_R = 2.29), t_R = 1.05 min case shown in Table 2.

Fig. 2

A contour plot of the LC×LC chromatogram provided by Stoll et al. [9]. Peaks 1 through 6 are the standards identified in the text. The colorbar units are in milliabsorbance units (mAU) measured at a wavelength of 220 nm.

Fig. 3

The effect of first dimension sampling phase on the series of second dimension peak areas. Sampling period is set at 0.35 min for peaks with a first dimension retention times and sampling phases of (a) 1.050 min (φ = 0), (b) 1.100 min (φ = −0.286π), (c) 1.175 min (φ = −0.714π), and (d) 1.225 min (φ = −π). ¹σ = 0.20 min (M_R = 2.29). The vertical lines indicate the start and stop of the accumulation intervals. The bar graphs to the right show the relative amount of analyte injected onto the second dimension column upon sample collection at the indicated vertical lines.

Fig. 4

The effect of sampling phase (φ) and M_R on peak metrics as a function of sampling phase variations. Results of the moments and Gaussian fit method are given as filled (●) and open circles (○), respectively: (a) and (b) % RSD in peak volume; (c) and (d) % error in peak volume; (e) and (f) % RSD in ¹σ; (g) and (h) % difference in ¹σ relative to that calculated by eq. 4.

Fig. 5

Effect of peak width on sampling the first dimension peak at fixed sampling interval and phase. Conditions: sampling interval 0.35 min, ¹t_R = 1.15 min (φ = −0.572π) for a peak with ¹σ values of (a) 0.15 min (M_R = 1.7), (b) 0.25 min (M_R = 2.9), (c) 0.35 min (M_R = 4.0), and (d) 0.45 min (M_R = 5.1).

Fig. 6

The effect of M_R on peak metrics. Results of the moments and Gaussian fit method are given as filled (●) and open circles (○), respectively: (a) % RSD in peak volume; (b) % error in peak volume; (c) % RSD in ¹σ; (d) % difference in ¹σ relative to that calculated by eq. 4.

Fig. 7

The effect of sampling phase (φ) and modulation ratio (M_R) on the precision and accuracy of peak volume determination.. The circles (●) and triangles (▲) represent the values previously shown in Figs. 4 and 6. (A) %RSD of peak volume using the Gaussian method; (B) %RSD of peak volume using the moments method; (C) % error of peak volume using the Gaussian method; (D) % error of peak volume using the moments method.

Fig. 8

The effect of sampling phase (φ) and modulation ratio (M_R) on the precision and accuracy of peak retention times.. The circles (●) and triangles (▲) represent the values previously shown in Figs. 4 and 6. (A) %RSD of retention time using the Gaussian method; (B) %RSD of retention time using the moments method; (C) % error of retention time using the Gaussian method; (D) % error of retention time using the moments method.

Fig. 9

The effect of sampling phase (φ) and modulation ratio (M_R) on the precision and accuracy of peak width determination.. The circles (●) and triangles (▲) represent the values previously shown in Figs. 4 and 6. (A) %RSD of peak volume using the Gaussian method; (B) %RSD of peak volume using the moments method; (C) % error of peak volume using the Gaussian method; (D) % error of peak volume using the moments method.

Fig. 10

Comparison of Experimental and Simulated Estimates of Peak Volume. The bars represent the % RSD in peak volume for the evaluation of peaks 1–6 in the work of Stoll [9]. Results from the moments method and the Gaussian method are given in the top and bottom panes respectively. The blue bar represents %RSD of quantification of the results of three replicate LCxLC chromatograms from Stoll et al. The cyan bar gives %RSD of quantification of the results from simulated Gaussian peaks in which a single replicate (represented by the six blue profiles shown in Fig. 11) added to three replicate real LC×LC blank chromatograms. The yellow bar represents the %RSD of quantification of simulated Gaussian peaks from the three replicates of shown in Fig. 11 (blue, green and red, respectively) to three LC×LC blank chromatograms. The dark red bar represents the %RSD of quantification for 50 replicate simulated Gaussian peaks positioned at randomly generated first dimension retention times with a standard deviation in peak position of ±0.35 min (±2π), (¹σ_avg = 0.21 min, t_s = 0.35 min), added to the same blank LC×LC chromatogram.

Fig. 11

First dimension chromatographic profiles derived from the second dimension peak areas for peaks 1–6. The blue profile is the first replicate, the green profile is the second replicate, and the red profile is the third replicate.