Introduction

Nucleic acid-based drugs (NABD) represent a novel group of molecules with the potential to treat several different human diseases (^{Grassi et al 2004}; ^{Heidenreich 2004}). Because all are constituted by either RNA, such as small interfering RNAs (^{Hannon and Rossi 2004}) or DNA, such as DNA enzymes (^{Breaker 1997}), NABD are rapidly destroyed in physiological fluids. Additionally, their hydrophilic nature makes cellular internalization a problematic step. Thus, to be effective in vivo, they need to be protected against degradation and the crossing of cellular membrane improved. A strategy to accomplish these requirements deals with the incorporation of NABD in microparticles made up of synthetic polymers (^{Jong et al 1997}; ^{Luo et al 1999}; ^{Wang et al 1999}) or in polymeric nanoparticles (^{Hirosue et al 2001}). The use of micro- and nanodevices is dictated by the fact that the smaller the particle diameter, the easier is the NABD cellular uptake (^{Luo and Saltzman 2000}).

The mechanisms of NABD release from micro- or nanoparticles can be predicted to play a relevant role in the effectiveness of the delivery system. Thus, an investigation conducted both from the theoretical and experimental point of view in this sense is of potential relevance. Among others, a hydrodynamic condition corresponding to a virtual zero shear condition can be of interest for different applications such as trans-dermal delivery and the in situ delivery to organ parenchyma. The zero shear condition is realized when a particle suspension is put in contact with the surface of interest and no mixing is imposed on the suspension. For this purpose, we have used an experimental apparatus made up of a donor chamber separated from the receiver chamber by a synthetic membrane. The donor chamber hosts an unstirred particle suspension while the receiver chamber hosts a pure fluid undergoing proper mixing. A mathematical model based on the hypothesis that NABD release from particles is due to particle erosion is used to interpret experimental data. This experimental set up enables the predominant mechanism governing the delivery under our conditions to be determined. In particular, in this work we focused on the study, in conditions of virtual zero shear, of the delivery kinetics of single-stranded DNA oligonucleotide, chosen as a prototype for NABD, from poly(DL-lactide-co-glycolide) (PLGA) microparticles and stearic acid (SA) nanoparticles. Additionally, for just PLGA microparticles, we explored the possible toxic effects of PLGA on cultured humans cells, evaluated by studying the effects on cell proliferation.

DNA-based molecules instead of RNA-based molecule (such as siRNAs and ribozymes) were chosed because of their better stability and lower cost.

Materials and methods

Modeling

In the light of the programmed experimental tests, 2 mathematical models need to be examined. The first refers to single-stranded DNA oligonucleotide permeation across the synthetic membrane assuming that the donor chamber contains a single-stranded DNA oligonucleotide PBS solution of known initial concentration. The second refers to the simultaneous single-stranded DNA oligonucleotide release from particles and permeation across the synthetic membrane.

Assuming that the synthetic membrane thickness is very small, it follows that a linear concentration profile of the single-stranded DNA oligonucleotide always holds inside the membrane (^{Grassi and Colombo 1999}). In addition, we assume that no interactions between single-stranded DNA oligonucleotide and synthetic membrane occur (^{Coviello et al 2005}; ^{Grassi and Grassi 2005}). Thus, the single-stranded DNA oligonucleotide concentration in the receiver chamber C_r can be evaluated according to the following equations:

where C_r, V_r, and C_d, V_d are, respectively, single-stranded DNA oligonucleotide concentration and volume of the receiver and donor chamber, t is time, S and L_M are, respectively, membrane surface and thickness, k_d and k_r are, respectively, single-stranded DNA oligonucleotide partition coefficients on the donor and receiver chamber side, C_d0 is the initial single-stranded DNA oligonucleotide concentration in the donor chamber, X is the abscissa, and D is the single-stranded DNA oligonucleotide diffusion coefficient in the membrane. Eq.(1) is a kinetic equation stating that the time variation of the single-stranded DNA oligonucleotide mass (V_rC_r) in the receiver solution depends on the concentration gradient ((k_dC_dk_rC_r)/L_M), the diffusion coefficient (D), and the membrane area (S) available for permeation. Eq.(2), instead, is a mass balance stating that, at any time t, the sum of the single-stranded DNA oligonucleotide mass present in the donor chamber (V_dC_d), in the membrane (S??0LMCM?(X)?dX) and in the receiver chamber (V_rC_r) must be equal to the initial (t = 0) single-stranded DNA oligonucleotide mass present in the donor chamber when both the membrane and the receiver chamber are empty of single-stranded DNA oligonucleotide. Assuming that the initial single-stranded DNA oligonucleotide concentration in the donor chamber is C_d0, that a linear single-stranded DNA oligonucleotide concentration profile in the membrane holds, and expressing C_d as a function of C_r by m s of eq.(2), eq.(1), the model solution is: Eq.(3) represents the analytical expression of the first model.

Although the real physical situation can be more complicated by the fact that single-stranded DNA oligonucleotide molecules can be in part inside the particles and, in part, adsorbed on to particle surfaces (particularly true for nanoparticles), the main hypotheses of the second model rely on the assumption that all particles are characterized by the same initial mean radius R₀ and that single-stranded DNA oligonucleotide release from particles occurs according to a pure particle erosion mechanism. In particular, we assume that particle radius R declines according to a linear law:

where b is the erosion velocity. Accordingly, if the hypotheses of model 1 are always true (thin membrane and no single-stranded DNA oligonucleotide interaction with the membrane), the second model differential equations are: where C_p0 is single-stranded DNA oligonucleotide concentration in the particles and V_p is the eroded volume of the N_p particles present in the donor chamber. Eq.(5) is a kinetics equation stating that the time variation of single-stranded DNA oligonucleotide mass in the donor chamber (V_dC_d) is determined by the single-stranded DNA oligonucleotide income due to particle erosion (Cp0dVpdt) less the amount diffusing through the membrane (SDLM(kdCd?krCr)). Eq.(6), another kinetics equation, models the increase of the eroded volume and it states that it depends on the square of particles radius and, consequently (see also eq.(4)), on the square of time. Finally, eq.(7) is the new expression of the single-stranded DNA oligonucleotide mass balance that differs from the previous one (eq.(2)) only for the presence of particles. Indeed, an additional term (Np43?Cp0R3(t)) related to the amount of single-stranded DNA oligonucleotide still present inside the particles at time t, appears in eq.(7), left hand side. Finally, the total amount of single-stranded DNA oligonucleotide must be always equal to the amount initially present inside the particles (Np43?Cp0R03?(t)). Eqs.(5)?(7) solution, assuming that C_r = C_d = 0 at the beginning (t = 0), yields the following analytical solution: where Z₁, Z₂, Z₃, Z₄, Z₅, ?, ?, and ? are time-independent parameters depending on system geometry, initial conditions erosion kinetics parameter, and single-stranded DNA oligonucleotide diffusion coefficient in the membrane (see Appendix for a detailed expression of these parameters). Obviously, this second model expression holds until particles are not completely eroded (R(t) ? 0). Indeed just after particle disappearance (it occurs when R = 0; t^* = R₀/b), the second model expression becomes: Indeed, for t > t^*, the second model identifies with the first model as the erosion phenomenon disappears. Eqs.(10)?(11) solution, assuming that for t = t^*C_r (t^*) = ? ? ?C_d(t) ? ? (R₀ ? bt^*)³ = C^* (see eq.(9)), reads: where, again, ?₁ ?₁ ?₁ are time-independent parameters depending on system geometry, initial conditions, erosion kinetics parameter, and single-stranded DNA oligonucleotide diffusion coefficient in the membrane (see Appendix for a detailed expression of these parameters).

Results and discussion

Figure 2a reveals that PLGA microparticles are characterized by a perfect spherical shape and that diameter ranges between 12 ?m and 2 ?m (mean 7?8 ?m), confirmed by photon correlation spectroscopy (PCS). On the contrary, Figure 2b reveals that SA nanoparticles show an ellipsoidal shape, the smaller diameter (?300 nm) being approximately half the longer one (?600 nm). PCS measurements gave a mean nanoparticle spherical diameter of 280 nm. Notably, the nanoparticle size distribution is much narrow than that for microparticles.

Before studying the release properties of the micro- and nanoparticle preparation loaded with single-stranded DNA oligonucleotides, we wanted to make sure that the polymers used do not significantly affect human cell viability. For this purpose, the effects on cell proliferation, a sensible marker of cell viability, were explored. Whereas studies dealing with SA effect on cell biology have been already reported (^{Lima et al 2002}), the effect of the combination of chemicals we used to prepare the PLGA microparticles is less clear. For this reason, we limited the analysis to the effect on cell proliferation of PLGA microparticles. As target cells we used human CSMC, known to be implicated in vascular pathologies (^{Grassi et al 2005}), which can benefit from the release of NABD by means of micro- and nanoparticles loaded with therapeutic molecules (^{Labhasetwar et al 1997}). The double staining technique used (^{Dolbeare et al 1983}; ^{Grassi et al 2005}) allows detection of cells in the different phases of the cell cycle as reported in the representative experiment of Figure 3 and summarized in Figure 4. It is evident that there are no significant differences in cell cycle phase distribution in cells treated by PLGA nanoparticles compared with controls cells represented by cells treated by a liposome commonly used to transfect CSMC and non-treated cells. We thus concluded that, limited to this fundamental biological parameter, PLGA microparticles do not substantially affect cell viability. It should be also added that light microscopy inspection of the cells in the different treatments did not reveal any significant difference in morphology, further strengthening the concept of the compatibility of PLGA microparticles we prepared with CSMC biology (data not shown).

We then moved to the evaluation of the release properties of the micro- and nanoparticle preparations loaded with the single-stranded DNA oligonucleotide, chosen as a prototype of NABD. Figure 5, referring to single-stranded DNA oligonucleotide permeation, shows the very good agreement between experimental data (symbols) and first model (eq.(3)) best fit (solid line). This evidence is also statistically proved by the huge value assumed by the F value (^{Draper and Smith 1966}) (F = 53293 >> F_TABULATED (?₁ = 1, ?₂ = 87, 0.01) = 6.9). This means that first model hypotheses (thin membrane and no plasmid DNA/membrane interactions) are reasonable. Model fitting, performed assuming unitary values for both the partition coefficients k_d and k_r, yields the following value for the single stranded DNA oligonucleotide diffusion coefficient in the membrane: D = (7.5 ? 0.1)*10^?8 cm²/s. Figure 6 reports the second model (eqs.(9) and (12)) best fit (solid line) on experimental data (symbols) referring to single-stranded DNA oligonucleotide release from PLGA microparticles and subsequent permeation through the membrane. Also in this case the data fitting is good, as also proved by the huge F value (F = 10555 >> F_TABULATED (?₁ = 1, ?₂ = 69, 0.01) = 6.9). In order to get a more reliable evaluation of the model fitting parameters (D and b), initial D value is assumed equal to that previously determined in the single-stranded DNA oligonucleotide permeation experiment ((7.5 ? 0.1)*10^?8 cm²/s) as, in our hypotheses, D should not be influenced by the erosion phenomenon taking place in the donor chamber. Additionally, the initial b value is deduced on the basis of the data shown in Figure 7. This figure shows the reduction in mean PLGA microparticle diameter in PBS, 37?C, in zero shear conditions (evaluated by PCS). Although the reduction is not exactly linear, rough b estimation can be performed by calculating the ratio between radius reduction and time needed for this decrease. This leads to b = 2*10^?9 cm/s. On the basis of these values, model data fitting yields D = (1.0 ? 0.05)*10^?7 cm²/s and b = (3.6 ? 0.3) 10^?8 cm/s. Although statistically different, this value for the single-stranded DNA oligonucleotide diffusion coefficient is close to that previously determined, as the difference is below 30%. On the contrary, a one order of magnitude difference exists between b value evaluated according to second model best fit and that estimated on the basis of PLGA microparticle erosion (see Figure 7). Nevertheless, due to the difficulty of exactly recreating the same hydrodynamic conditions in both cases, we can accept this discrepancy. It is worth mentioning that, according to this data fitting, complete particle erosion takes 10555 s (= t^*) and this corresponds to single-stranded DNA oligonucleotide concentration in the receiver environment equal to approximately 0.22 ?g/cm³. This means that up to 10555 s, eq.(9) holds, then eq.(12) holds. Qualitative experimental observations verified that after around 10000 s, particle volume was greatly reduced although complete particle disappearance did not occur. This discrepancy with model prediction can be explained by remembering that our model assumes all particles were equal (same diameter) and perfectly spherical. If microparticles are really spherical, they do not constitute a perfect mono-disperse particles ensemble as shown in Figure 2a. Bigger particles require a more time for complete dissolution.

In fitting single-stranded DNA oligonucleotide release from SA nanoparticles and subsequent permeation, initial D value was fixed to (7.5 ? 0.1)*10^?8 cm²/s and initial b value was assumed to be 2*10^?9 cm/s, as we did in the PLGA microparticles case. Indeed, theoretically, D should be the same in all the release tests performed. Unfortunately, as nanoparticle dimensions prevented a reliable experimental b determination, unlike microparticles, we decided to assume the value for microparticle erosion. Figure 8 clearly shows that in this case data fitting is more than satisfactory and this assumption is statistically supported by the huge F value (F = 31647 >> F_TABULATED (?₁ = 1, ?₂ = 87, 0.01) = 6.9). Fitting parameters gave D = (1.5 ? 0.1)*10^?7 cm²/s and b = (2.8 ? 0.2)?10^?9 cm/s. Also, in this case the single-stranded DNA oligonucleotide diffusion coefficient is bigger (two fold) than that evaluated in the permeation experiment and that evaluated in the microparticle erosion/permeation experiment (exceeded by 50%). This evidence let us conclude that the single-stranded DNA oligonucleotide diffusion coefficient in our synthetic membrane is around 10^?7 cm²/s. In addition, data fitting reveals that the SA nanoparticle erosion is one order of magnitude smaller than that found for PLGA microparticles. Thus, theoretically, SA nanoparticles disappear after 5360 s (= t^*) and, consequently, eq.(9) holds at up to 5360 s, and then eq.(12) holds. Also in this case, qualitative experimental observations verified that after around 5000 s, particle volume was greatly reduced although a complete particle disappearance did not occur. This discrepancy with model prediction can be explained by remembering that our nanoparticles are not perfectly spherical (see Figure 2b), as required by the model.

The fact that nanoparticle erosion is smaller than that of microparticle erosion could be relevant in the optimization of NABD delivery from micro- and nanoparticles. Indeed, in relation to a particular pathology, the desired NABD release rate can be reached by properly selecting particle dimensions (size distribution) and composition.

Conclusions

In this paper we developed an experimental and theoretical approach to clarify how NABD can be released from PLGA microparticles and SA nanoparticles in zero shear conditions. This situation can be experienced in some delivery situations such as those found in trans-dermal release and the in situ release to organ parenchyma. Attention was focused on the evaluation of the possible toxic effects on cell biology for only PLGA microparticles, as investigations already exist for the effects of SA on cell biology (^{Lima et al 2002}). For NABD release from PLGA microparticles and SA nanoparticles, experimental evidence and the theoretical interpretation of the data lead to the conclusion that NABD release from PLGA microparticles and SA nanoparticles in zero shear conditions is perfectly compatible with a pure particle erosion mechanism. In addition, the release kinetics strongly depend on the material constituting the particles. We also found that PLGA microparticle erosion is, approximately, one order of magnitude higher than that for SA nanoparticles. These data suggest that a proper balance between small and big particles, eventually of different materials, can be used to obtain the delivery kinetics suitable for the specific application. Finally, to evaluating the possible toxic effects of PLGA microparticles on cell biology, we could not show any detectable negative effects, at least on cell proliferation and cell morphology, two pivotal biological parameters.

In conclusion, we believe that the reported observations can can help optimize delivery systems aimed at release of NABD from micro- and nanoparticles, which have applications in many in situ delivery conditions.

This work was supported in part by the Dr. Karl-Kuhn-award 2003, by the Fondazione Cassa di Risparmio of Trieste, by Fondazione Sostegno delle Strutture Cardiovascolari, by the Fondazione Casali of Trieste and by Fondo Trieste 2006. G Grassi is supported by the program Rientro cervelli art. 1 DM n.13, MIUR (Ministero dell?Istruzione, dell?Universit? e della Ricerca Scientifica).

Appendix

Assuming that a linear concentration profile instantaneously develops inside the membrane, the integral appearing in eq.(7) becomes:

Accordingly, eq.(7) can be used to express C_r in function of R(t) and C_d(t):

where:

Inserting eq.(14) into eq.(5) gives the following differential equation:

where:

Imposing that C_d = 0 for t = 0, eq.(16) solution reads:

where:

C_rtemporal evolution is then given by eq.(9) or (14).

For t ? t^* (= R₀/b), eq.(8) and (14) do not longer hold and model solution is given by solving eq.(10) and (11):

Inserting eq.(13) into eq.(10), it is possible to express C_d as a function of C_r:

Inserting eq.(20) into eq.(10) leads to:

where:

Imposing that, for t = t*, Cr=Cr*=???Cd(t*), eq.(21) solution is given by eq.(12):