Mathematical modeling of Taylor-Aris dispersion-assisted mass spectrometry for the study of operating conditions

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.

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.

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.