Interactions of a charged nanoparticle with a lipid membrane: implications for gene delivery

Abstract

We employ self-consistent field theory to study the thermodynamics of membrane-particle interactions in the context of gene delivery systems, with the aim to guide the design of dendrimers that can overcome the endosomal escape barrier by inserting into membranes and creating pores. We consider the interaction between a model polyamidoamine dendrimer and a membrane under controlled tension as a function of the separation between the dendrimer and the membrane. In all the cases we have studied, the lowest free energy state corresponds to the membrane partially wrapping the dendrimer. However, with moderate tension, we find that a G5 (or larger) generation dendrimer, through thermal fluctuation, can induce the formation of metastable pores. These metastable pores are subsequently shown to significantly lower the critical tension necessary for membrane rupture, thus possibly enhancing the release of the trapped genetic material from the endosome.

Figure 1

A double-tailed lipid model consisting of head (blue) and tail (red) monomers. The values q_I and q_I^∗, where I = H, T, are the chain propagator and complementary chain propagator, respectively, used for calculating the single chain statistics (see Appendix).

Figure 2

(a) Volume fractions and (b) ion number concentrations (nm⁻³) across the axis perpendicular to the membrane.

Figure 3

Membrane tension (k_BT/nm²) as a function of the area per lipid (nm²). The limit of metastability occurs where ∂γ/∂σ = 0.

Figure 4

Free energy profile (k_BT) for the tensionless membrane. ΔF is relative to a noninteracting membrane-particle system, where z_F → ∞. The particle is a G5 dendrimer with radius R_F = 2.7 nm and charge density c_F = 1.55 nm⁻³ (all 128 surface amines are protonated). For comparison, we have also plotted the results for a hypothetical G5 dendrimer with c_F = 5.00 nm⁻³. Open symbols correspond to method 1; +and × correspond to method 2 (see text for description).

Figure 5

ϕ_H in cylindrical coordinates for a tensionless membrane and a fully protonated G5 dendrimer with c_F = 1.55 nm⁻³. (a–c) Solutions to both methods 1 and 2. (d–f) Solutions to method 2 only.

Figure 6

Free energy profile (k_BT) for a membrane with γ = 0.74 k_BT/nm², shown together with the tensionless membrane from Fig. 4. The particle is once again a fully protonated G5 dendrimer. Open symbols correspond to method 1; +and × correspond to method 2 (see text for description). Note that we are well below the limit of metastability for a homogeneous membrane, where rupture occurs at γ_c ∼ 4.5 k_BT/nm².

Figure 7

Free energy profile (k_BT) for a membrane with γ = 0.74 k_BT/nm² interacting with G3 (R_F = 1.8 nm, c_F = 1.30 nm⁻³), G5 (R_F = 2.7 nm, c_F = 1.55 nm⁻³), and G7 (R_F = 4.0 nm, c_F = 2.0 nm⁻³) dendrimers. Open symbols correspond to method 1; +, × and ▴ correspond to method 2 (see text for description).

Figure 8

Rupture tension (k_BT/nm²) for a membrane containing a pore, plotted as a function of the charge density (nm⁻³) of the G5 dendrimer stabilizing the pore.