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.