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.