Southern Illinois University at Carbondale, Department of Chemistry and Biochemistry, 1245 Lincoln Drive, Carbondale, IL 62901-4409, USA.
J Chromatogr A. 2011 Aug 26;1218(34):5819-28. doi: 10.1016/j.chroma.2011.06.086. Epub 2011 Jun 30.
The average value of the multivariate selectivity (SEL) of randomly positioned peaks in a multi-component separation is shown to equal the average fraction of peaks that are singlets, as predicted by statistical-overlap theory (SOT). This equality is the basis for proposing a useful metric, specifically the average minimum resolution of nearest-neighbor peaks, for the performance of comprehensive two-dimensional (2D) separations. Furthermore this metric was computed both without ancillary spectroscopic information and with the assistance of such help, specifically multi-wavelength UV-vis spectra, acquired during the separation. Separations are simulated with randomly positioned peaks over wide ranges of total number of peaks, first- and second-dimension peak capacity, dimensionless first-dimension sampling time, and spectral diversity. The specific version of the general multivariate selectivity concept that is used here--identified as SEL--gives the relative precision of quantification when using the PARAFAC (parallel factor analysis) method, a popular curve resolution algorithm. The SEL values of all peaks were calculated, averaged, and compared to the predictions of SOT. In the absence of auxiliary spectral data, the SEL-based average minimum resolution required to separate two peaks in a 2D separation is 0.256, compared to resolution of 0.5 if no chemometric assistance is available. This was found to be valid over a wide range of conditions and is essentially independent of peak crowding. With the assistance of the spectral data, the requisite minimum resolution substantially improves, that is, it decreases, especially when peak crowding is severe. The requisite minimum resolution decreases even further, up to a limit, as the spectral diversity is increased. In contrast, the SEL-based average under-sampling correction factor is virtually independent of the presence of the additional spectral data, and additionally is about the same as calculated with SOT from the average number of maxima in closely analogous simulations. The use of selectivity greatly increases the fraction of peaks that are singlets, relative to the number of singlet maxima, especially when spectral assistance is added. The insensitivity of the under-sampling correction factor to either the use of selectivity or added spectral data simplifies optimization of the corrected peak capacity in on-line comprehensive 2D separations.
随机放置的多组分分离中多元选择性（SEL）的平均值被证明等于统计重叠理论（SOT）预测的单峰分数。这种相等性是提出有用度量标准的基础，特别是最近邻峰的平均最小分辨率，用于评估全面二维（2D）分离的性能。此外，该度量标准是在没有辅助光谱信息和利用辅助信息（例如，在分离过程中获得的多波长紫外可见光谱）的情况下计算的。通过在总峰数、一维和二维峰容量、无维一维采样时间和光谱多样性的宽范围内随机放置峰来模拟分离。使用这里标识为 SEL 的一般多元选择性概念的特定版本-用于使用 PARAFAC（平行因子分析）方法进行定量时，给出相对精度，这是一种流行的曲线分辨率算法。计算所有峰的 SEL 值，取平均值，并与 SOT 的预测进行比较。在没有辅助光谱数据的情况下，在二维分离中分离两个峰所需的基于 SEL 的平均最小分辨率为 0.256，而如果没有化学计量学辅助，则分辨率为 0.5。这在广泛的条件下都是有效的，并且基本上与峰拥挤无关。在光谱数据的辅助下，所需的最小分辨率大大提高，即，特别是在峰拥挤严重时，它会降低。随着光谱多样性的增加，所需的最小分辨率进一步降低，直到达到极限。相反，基于选择性的平均欠采样校正因子几乎与存在额外光谱数据无关，并且与从紧密类似的模拟中的平均最大数量计算的 SOT 几乎相同。选择性的使用大大增加了单峰的分数，相对于单峰最大值的数量，特别是在添加光谱辅助时。欠采样校正因子对选择性或附加光谱数据的使用都不敏感，这简化了在线全面 2D 分离中校正后的峰容量的优化。
