## 3 Results and Discussion
### Evaluation of the Mobility of DNA-GNP Associates by Agarose Gel Electrophoresis
FL/GNP associates are compact, their movement is not hindered by the size of the gel pores, and their velocity is  
Figure 6: Mobility and charge analysis (agarose gel electrophoresis) of DNA–GNP associates obtained at 25 \({}^{\circ}\)C. A scanned image of an agarose gel (**left**) and its autoradiograph (**right**) for FT-GNP associates differing in the capacity of one GNP for ssDNA. The black frames indicate the distribution of the upper (top) and lower (bottom) fractions of FT–GNP associates on a gel lane. The boundary between them is indicated by a blue dotted line. The arrow shows the direction of the electric current. determined only by the electric field parameters used. For the second ssDNA, R, which is complementary to FL, a similar pattern was registered (Figure S4). The associates obtained by incubation of GNPs with a mixture of FL and R at 25 \({}^{\circ}\)C in the concentration range of 30-50 nM ssDNA (Figure 7) had the same capacity for ssDNA FL (40 molecules on average, row FL*-R/GNP in the figure) and for ssDNA R (11 molecules on average, row FL-R*/GNP in the figure), corresponding to 1134-1303 internucleotide phosphate groups (Figure 7B, row \"charge\"). Nonetheless, 72-81% of FL-R/GNP associates were \"slow\" rather than \"fast,\" as might be expected from their high negative charge (Figure 7B). According to the FL-R melting point (Table S2), the ssDNA should be in a duplex at 25 \({}^{\circ}\)C [48]. Although occupancy levels of GNPs by FL and R molecules are not equal, it is expected that some of the adsorbed DNAs formed a duplex because we see a decrease in the mobility of the FL-R/GNP associate, probably owing to an increase in the size of the associate itself. Raising the temperature of incubation of GNPs with mixture FL-R up to 37 \({}^{\circ}\)C enlarged the capacity of GNPs (on average) by 16 molecules of FL and by 10 molecules of R (an increase of 690 phosphate groups in row \"charge\" in Figure 7). At this temperature, the DNA  
Figure 7: Scans of agarose gels and analysis (in GelAnalyzer 19.1 software, \(\kappa\)www.gelanalyzer.com\(\kappa\) (accessed on 20 February 2022), created by [PERSON], Ph.D., and [PERSON], Ph.D., CSc, March 2022) of the distribution of FL/GNP associates (**A**) and of FL–R-GNP associates. T: associate incubation temperature, [DNA]: concentration of ssDNA, Charge: the number of internucleotide phosphate groups. Rows FL*/GNP, R*/GNP, FL*–R/GNP, and FL–R*/GNP: capacity of GNPs for respective associates; % (top) and % (bottom): the proportion of the upper and lower fractions of associates of GNPs with DNA. The arrow indicates the highest electrophoretic mobility of DNA/GNP associates (**B**). in the incubation solution can be of single- and double-stranded form (Tables S1 and S2). Consequently, some oligonucleotides could be adsorbed in a single-stranded state, thereby forming compact \"fast\" associates. Moreover, with increasing temperature, the greater increase in capacity was due to FL. This effect widened the imbalance between the amounts of adsorbed FL and R even more and increased the proportion of associates of GNPs with ssDNA. Overall, for FL-R/GNP associates, these changes elevated the proportion of \"fast\" associates (from 28% at 30 nM to 56% at 50 nM, Figure 7B, for 37 \({}^{\circ}\)C, row \"% bottom\"). At 45 \({}^{\circ}\)C, the DNA should be in a single-stranded state (Tables S1 and S2). Accordingly, we predicted the formation of mostly \"fast\" associates at all DNA concentrations. Nevertheless, the proportion of \"fast\" associates was only 36% at a DNA concentration of 30 nM and a large total charge of associates: 1952 phosphate groups (Figure 7B, for 45 \({}^{\circ}\)C, row \"Charge\"). Considering the high capacity of GNPs for oligonucleotides, especially FL, at 45 \({}^{\circ}\)C, FL/GNP associates are most likely formed via DNA adsorption through the \"anchor\" and a vertical arrangement of the \"main\" part (F) of the FL oligonucleotide with respect to the GNP surface.