## 3 Results and Discussion
### Evaluation of the Mobility of DNA-GNP Associates by Agarose Gel Electrophoresis  
Determination of surface capacity of GNPs for DNA characterizes the average occupancy of the nanoparticles by oligonucleotides in a given sample. The gel electrophoresis method enables researchers (i) to separate DNA/GNP associates by their charge and size and (ii) to estimate the proportion of associates having different levels of oligonucleotide occupancy in one sample. It has been previously reported that the mobility of associates of GNPs with unstructured ssDNA is determined only by the charge of these associates [4]. In general, the higher the capacity of a GNP for ssDNA, the greater the negative charge on the surface of GNPs (owing to negatively charged internucleotide phosphate groups  
Figure 5: The dependence of the capacity of GNPs for a mixture of DNAs on the temperature of incubation of the DNAs with GNPs. (**A**) DNAs of the L series in a mixture with complementary R, (**B**) DNAs of the T series in a mixture with complementary R, (**C**) complementary R mixed with DNA of the L series, (**D**) complementary R mixed with DNA of the T series, (**E**) competitive T20 mixed with DNA of the L series, and (**F**) competitive T20 mixed with DNA of the T series. * denotes radioactively labeled DNA. in DNA) and the higher the electrophoretic mobility of ssDNA/GNP associates and the proportion of maximally mobile GNPs in the sample [4,49]. Analyzing scans and autoradiographs of the same agarose gel containing GNPs with radioactively labeled ssDNA, we found that the mobility of the associates indeed directly depends on the number of adsorbed molecules of ssDNA (Figure 6). On the contrary, images of associates consisting of GNPs and a pair of complementary ssDNA did not correlate with the surface capacity of GNPs for dsDNA (Figure 7). We hypothesized that for associates of GNPs and a pair of complementary ssDNA, the relation between the capacity and mobility in the gel differs from this relation for associates of GNPs with one ssDNA. Therefore, to analyze the mobility of DNA-/GNP associates, in each lane of the gel image, we identified two parts having the same geometric area (marked with a blue dotted line in Figure 6: the upper part contained \"slow\" associates, and the lower one contained \"fast\" ones). We calculated the proportion \"slow\" and \"fast\" associates relative to the total staining intensity of the entire lane for each associate formation temperature (25, 37, and 45 \({}^{\circ}\)C). Let us first examine the electrophoresis of ssDNA/GNP associates using FL/GNP associates as an example (Figure 7A). At 25 \({}^{\circ}\)C and at a concentration of ssDNA from 30 to 50 nM, the capacity in FL-GNP associates increases from 47 to 54 molecules of FL per GNP (Figure 7A, rows [DNA] and FL*/GNP). These seven FL molecules correspond to an addition of 175 internucleotide phosphate groups (Figure 7A, row \"charge\"). In the meantime, the increase in the lower fraction (\"fast\" associates) in the gel was 14% (Figure 7A, row \"% bottom\"). For the 50 nM concentration of FL, while changing the temperature from 25 to 37 and to 45 \({}^{\circ}\)C, we observed an increase in FL/GNP capacity by 21 and 23 FL molecules, that is, by 525 and 575 phosphate groups. The proportion of \"fast\" associates grew to 86% and 93%, respectively. Furthermore, it is visible that the increase in the FL concentration and in incubation temperature (with the increase in capacity and charge up to 2450 phosphate groups) did not raise the highest mobility of the associates under electrophoresis conditions. This outcome is due to the highest occupancy of the binding sites on the surface of GNPs by ssDNA molecules [4,14]. Thus, for high-affinity unstructured ssDNA FL, the expected picture was observed: with increasing capacity, the charge increased, and the proportion of \"fast\" associates grew.