Background: The recently proposed Taylor-Aris dispersion-assisted mass spectrometry (TADA-MS) enables the direct injection mass spectrometric analysis of samples where the analyte is a large molecule present in a matrix that would generally cause serious interferences. Numerous parameters can affect the outcome of these measurements such as mobilizing pressures, capillary geometry, sample volume, analyte and matrix concentrations and characteristics. The aim of this work was to develop a mathematical model that can describe TADA-MS measurements enabling the in-silico investigation into the effects of operating conditions.

Results: Although Taylor dispersion has been described before mathematically for sample volumes negligible compared to the capillary volume, in this work a formula is proposed describing the peak shape for finite (non-negligible) injection volume, which is crucial for obtaining the highest sensitivity for TADA-MS. The validity of the introduced formula was corroborated by UV measurements at different injection times, mobilizing pressures and capillary geometries. Incorporating electrospray ionization specific phenomena into the model, the TADA-MS measurements of rituximab agreed well with the prediction of the model. This model was used to evaluate the effects of both operating conditions and analyte properties - such as capillary inner diameter, length, mobilizing pressure, injected sample volume, protein diffusion coefficient and the signal suppressing effects of the matrix. It was found that increasing the sample volume the sensitivity only increases up to a certain point. Similarly to previously described for negligible sample volumes, the operating conditions do not affect the degree of separation at larger, optimal injection volumes. Rather, the extent of separation is attributed to the relative diffusion coefficients of the analyte and the matrix - with larger proteins (lower diffusivity) leading to better separation from low-molecular-weight matrix components.

Significance: The Taylor dispersion in case of non-negligible sample volumes was first described mathematically. A model describing TADA-MS measurements was proposed considering the electrospray ionization specific phenomena as well. The effects of operating conditions were evaluated, and a formula was presented for the suggested sample volume for the highest sensitivity.

Keywords: Direct injection; Mass spectrometry; Mathematical modeling; Protein analysis; Taylor–Aris dispersion.

Copyright © 2025 The Authors. Published by Elsevier B.V. All rights reserved.

背景： 最近提出的泰勒-阿里斯色散辅助质谱法（TADA-MS）能够直接对样品进行质谱分析，其中分析物是大分子物质，并且该物质通常存在于会导致严重干扰的基质中。许多参数会影响这些测量结果，如移动压力、毛细管几何形状、样品体积、分析物和基质浓度及特性等。本研究旨在开发一个数学模型来描述TADA-MS测量，以便对操作条件的影响进行计算机仿真调查。

结果： 尽管以前已经用数学方法描述过泰勒扩散现象（对于相对于毛细管体积可忽略的样品量而言），但在本研究中提出了一种公式来描述有限（不可忽略）注入体积下的峰形，这对于获得最高灵敏度至关重要。通过在不同注射时间、移动压力和毛细管几何形状下进行UV测量验证了所引入公式的有效性。将电喷雾离子化特有的现象纳入模型后，TADA-MS对利妥昔单抗的测量结果与预测吻合良好。该模型用于评估操作条件和分析物特性（如毛细管内径、长度、移动压力、注入样品体积、蛋白质扩散系数以及基质抑制信号的效果）的影响。发现随着样品量增加，灵敏度仅在达到某个点之前会有所提升。类似地，在可忽略样本量的情况下，正如先前所述，操作条件不会影响大体积（最优注射量）下的分离程度。相反，分离范围归因于分析物和基质的相对扩散系数——较大的蛋白质（较低的扩散性）会使低分子量基质成分与之更好地分离。

意义： 首次通过数学方法描述了非可忽略样品体积情况下的泰勒扩散。提出了一个考虑电喷雾离子化特有的现象来描述TADA-MS测量的模型，并评估了操作条件的影响，同时提供了一个建议的最大灵敏度所需样本量的公式。

关键词： 直接进样；质谱法；数学建模；蛋白质分析；泰勒—阿里斯扩散。