The non-linear effects of the number of stochastic single-molecule adsorption events on ensemble elution profiles

The stochastic model of chromatography mathematically represents the molecular mass transfer that occurs during a separation. Single-molecule microscopy allows for direct visualization of molecular analytes adsorbing within column materials. Experimental single-molecule data and the stochastic model can predict elution profiles using the adjustable variable r̄_m, the average number of adsorptions per molecule. Previously, only a single r̄_m value was used to match either peak location or shape, while the effects of adjusting n_p, the number of modeling points, have not been studied. Here, we systematically explore a wide range of these two variables in the stochastic model to determine if it is possible to optimize agreement between modeled single-molecule and high-performance liquid chromatography (HPLC) chromatograms. A metric to quantify chromatogram agreement is introduced by taking the weighted difference in the elution time and shape of the chromatograms. We determine the non-linear effects of r̄_m and n_p on peak height, width, and asymmetry and link the observations to the molecular behavior. Applying our approach to experiments with variable flow rate shows that increased sampling of rare, long time adsorption events affects agreement between simulated and HPLC elution profiles. Finally, we make quantitative recommendations that the single-molecule experiments should sample available binding sites following an exponential association model and that n_p must be > 1.5 × r̄_m to achieve accurate results. Overall, we verify that the current form of the stochastic model based solely on mass transfer is unable to simultaneously match both peak location and shape and make recommendations for future improvements to the model by separation scientists.