Computational and analytical modeling of cationic lipid-DNA complexes

Abstract

We present a theoretical study of the physical properties of cationic lipid-DNA (CL-DNA) complexes--a promising synthetically based nonviral carrier of DNA for gene therapy. The study is based on a coarse-grained molecular model, which is used in Monte Carlo simulations of mesoscopically large systems over timescales long enough to address experimental reality. In the present work, we focus on the statistical-mechanical behavior of lamellar complexes, which in Monte Carlo simulations self-assemble spontaneously from a disordered random initial state. We measure the DNA-interaxial spacing, d(DNA), and the local cationic area charge density, sigma(M), for a wide range of values of the parameter (c) representing the fraction of cationic lipids. For weakly charged complexes (low values of (c)), we find that d(DNA) has a linear dependence on (c)(-1), which is in excellent agreement with x-ray diffraction experimental data. We also observe, in qualitative agreement with previous Poisson-Boltzmann calculations of the system, large fluctuations in the local area charge density with a pronounced minimum of sigma(M) halfway between adjacent DNA molecules. For highly-charged complexes (large (c)), we find moderate charge density fluctuations and observe deviations from linear dependence of d(DNA) on (c)(-1). This last result, together with other findings such as the decrease in the effective stretching modulus of the complex and the increased rate at which pores are formed in the complex membranes, are indicative of the gradual loss of mechanical stability of the complex, which occurs when (c) becomes large. We suggest that this may be the origin of the recently observed enhanced transfection efficiency of lamellar CL-DNA complexes at high charge densities, because the completion of the transfection process requires the disassembly of the complex and the release of the DNA into the cytoplasm. Some of the structural properties of the system are also predicted by a continuum free energy minimization. The analysis, which semiquantitatively agrees with the computational results, shows that that mesoscale physical behavior of CL-DNA complexes is governed by interplay among electrostatic, elastic, and mixing free energies.

FIGURE 1

Equilibrium configuration of a complex consisting of two bilayer membranes, each with 390 lipids and five DNA strands. The lipids are modeled as trimers with hydrophilic (black) and hydrophobic (gray) particles. The DNA (red) are modeled as rigid rods with a uniform negative axial charge density. The complex is isoelectric, i.e., the negative charge of the DNA is neutralized by the charge of the cationic lipids with no added salt. Thus, each bilayer in the shown complex includes 150 monovalent lipids, all of which reside in the inner layers facing the DNA array. Each DNA rod carries a total charge of −60 e.

FIGURE 2

Average DNA spacing, d_DNA, as a function of the inverse of the fraction of charged lipids 1/φ_c. Markers, numerical results (uncertainties are smaller than symbols); solid line, fit to Eq. 5 with a_lipid = 69 Ų.

FIGURE 3

The average area per lipid, a_lipid, as a function of the fraction of charged lipids φ_c.

FIGURE 4

Equilibrium configuration of a complex with φ_c ∼ 0.9 whose membranes develop pores.

FIGURE 5

The effective stretching modulus, of the complex as a function of φ_c.

FIGURE 6

Local fraction of charged lipids φ_c as a function of x, the position within a unit cell of the complex. Curves, from bottom to top, correspond to mean fraction of 0.3, 0.4, 0.5, 0.6, 0.68, 0.77, and 0.81.

FIGURE 7

Local charge density of the membranes σ_M as a function of x. Curves, from bottom to top, correspond to φ_c = 0.3, 0.4, 0.5, 0.6, 0.68, 0.77, and 0.81. Dashed horizontal line corresponds to the effective charge density of the DNA σ_DNA ∼ 9.4 × 10⁻³ e/Ų.

FIGURE 8

Total area density of the lipids ρ as a function of x for different values of φ_c. The expression ρ₀ = ()⁻¹ = 1/69 Å⁻² is the area density of uncharged membranes. Lines are guide to the eyes.

FIGURE 9

Schematic picture of the complex consisting of an array of equally spaced DNA rods with nearest-neighbor spacing d_DNA and two surfaces separated a distance D from the midplane of the DNA array. The DNA rods are uniformly charged with charge density λ < 0 per unit length. Surfaces have a mean charge density σ_M > 0 per unit area and local charge density σ_M + δσ(x). Their local height above/below the DNA midplane is denoted by D − h(x). Lower surface is drawn in the reference state, where δσ = 0 and h = 0.