Spherical-Shape Assumption for Protein–Aptamer Complexes Facilitates Prediction of Their Electrophoretic Mobility

DNA aptamers are single-strand DNA (ssDNA) capable of selectively and tightly binding a target molecule. Capillary electrophoresis-based selection of aptamers for protein targets requires the knowledge of electrophoretic mobilities of protein–aptamer complexes, while measuring these mobilities requires having the aptamers. Here, we report on breaking this vicious circle. We introduce a mathematical model that allows prediction of protein–aptamer complex mobility, while requiring only three easy-to-determine input parameters: the number N of nucleotides in the aptamer, electrophoretic mobility of N-nucleotide-long ssDNA, and a sum molecular weight of the protein–aptamer complex. The model was derived upon simplifying assumptions of a spherical shape of the protein–aptamer complex. According to this model, the protein–aptamer complex mobility is a linear function of a combination of the three input parameters with empirically determined line’s intercept and slope. The intercept and slope were determined using experimental data for seven complexes. The model was then cross-validated with the leave-one-out approach revealing only 2% residual standard deviations for both the slope and the intercept. Such a precise determination of these constants allowed accurate mobility prediction for the excluded complexes with only a 3% maximum deviation from the experimentally determined mobilities. The model was tested by applying it to three protein–aptamer complexes that were not a part of the training/cross-validation set; deviations of the predicted mobilities from the experimentally determined ones were within 5% of the latter. To complete this study, the model was fine-tuned using the 10 complexes. Our results strongly suggest the validity of the spherical-shape assumption for the protein–aptamer complexes when considering complex mobility. The developed model will make it possible to rationally design capillary electrophoresis-based selection of DNA aptamers for protein targets.