## 3 Results and Discussion
### Plasmid Release Analysis  
In vitro release studies of pVAX1-NH36 from pDNA-NPs were performed with three different TDL used in preparations and are presented in Figure 5. During the first days of the study, initial burst rate was proportionally related to DL of pVAX1-NH36. Amounts of pVAX1-NH36 released in these initial burst stages were around 0.44, 1.88 and 10.39 \(\upmu\)g, corresponding to 13%, 22% and 55% for TDL of 0.2%, 0.5% and 0.8% respectively. Since pVAX1-NH36 is hydrophilic in nature, we hypothesize that most of the plasmid was encapsulated close to the surface of nanoparticles, which could explain the initial high rate of release by rapid dissolution of pVAX1-NH36 in release media. After the initial burst stage, a slow release was observed for three TDL evaluated until a plateau was reached, indicating that all pVAX1-NH36 was released from pDNA-NPs. This retardation in release after initial burst could be explained by physical entrapment of pVAX1-NH36 and low rate of water penetration into nanoparticle. Plasmid is then slowly released by degradation-relaxation of NPs. In addition, PLGA NPs hydrolysis promotes water permeation and transport of plasmid into media. Similar results have been presented by [PERSON] et al. with an initial burst of 40% within the first four hours of the study, followed by a slower release rate period of seven days with a cumulative release of 60% after day 1 and 70% after day 3 [61]. The difference in release times could be attributed to porosity of particles. Likewise, [PERSON] et al. observed the same profile behavior with release of a drug from PLGA-PEG-FA nanoparticles with an initial burst release of 20% in the first two hours, followed by a cumulative release of 40% by the next 12 h, and then a slow linear release until it reached 80% at day 7 [13]. Figure 5: In vitro pVAX1-NH36 release profiles from pDNA-NP for theoretical pVAX1-NH36 loadings (TDL) of 0.2% (\(\,\)), 0.5% (\(\,\)m) and 0.8% (\(\,\)a). Data represent mean (\(n=3\)). Experimental pVAX1-NH36 release data was analyzed by a coupled model that incorporates initial burst as well as NPs degradation-relaxation (Equation (3)). In general, an excellent fit of the proposed model with experimental profiles was obtained. Figure 5A-C shows the release profiles of pVAX1-NH36 for TDL of 0.2%, 0.5% and 0.8%, where experimental data is represented by diamonds, squares and triangles in figures, respectively. For all cases, fitting of the model to experimental release was denoted by a solid line. Model parameters obtained by fitting are presented in Table 2. Burst constant decreases from 4.4513 to 3.6538 days\({}^{-1}\) when TDL increases from 0.2% to 0.5% and is maintained in the same range even though TDL increases up to 0.8%. Fraction of burst release increases proportionally with TDL, from \(1.0587\times 10^{-8}\) to 0.1914 and finally to 0.4977 for TDL of 0.2%, 0.5% and 0.8% respectively. Degradation-relaxation constant increases from 0.2060 to 0.2792 days\({}^{-1}\) for 0.2% and 0.5% TDL, followed by a decrease to 0.2439 days\({}^{-1}\) for 0.8% TDL. The time to achieve 50% of release was maintained in the range of 12 to 15 days for all cases. As expected, fraction of NPs relaxation release behaves in the opposite way to fraction of burst release, decreasing from 0.9999 to 0.8086 to 0.5023 for TDL of 0.2%, 0.5% and 0.8% respectively. The proposed model of release, presented in Equation (3), simultaneously considers the stages of initial burst and NPs degradation-relaxation. Therefore, depending on experimental data, the fraction values of burst (\(\theta_{b}\)) or NP relaxation (\(\theta_{r}\)) reflected contributions of each mechanism over the complete release profile. Values obtained with the model are within the same range as others reported in literature for release of small molecules (ketoprofen, indomethacin, and coumarin-6) and macromolecules (human serum albumin, ovalbumin) [40].