Complexation of DNA with Cationic Surfactant

Transfection of an anionic polynucleotide through a negatively charged membrane is an important problem in genetic engineering. The direct association of cationic surfactant to DNA decreases the effective negative charge of the nucleic acid, allowing the DNA-surfactant complex to approach a negatively charged membrane. The paper develops a theory for solutions composed of polyelectrolyte, salt, and ionic surfactant. The theoretical predictions are compared with the experimental measurements. PACS.05.70.Ce Thermodynamic functions and equations of state PACS.61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc. PACS.61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling Corresponding author; e-mail: [email protected] 1 Gene therapy has increasingly captured public attention after the first gene transfer study in humans was completed in 1995 [1–3]. The procedure delivers a functional polynucleotide sequence into the cells of an organism affected by a genetic disorder. The gene delivery system that has been adopted in over 90% of the clinical trials to date is in the form of genetically engineered non-replicating retroviral or adenoviral vectors [2]. Unfortunately, the adverse response of the immune system has hindered application of virus based gene therapy. New strategies are now being explored [4–19]. One of the approaches, pioneered by Felgner and Ringold [5], relies on association between the anionic nucleic acid and cationic lipid liposomes. The process of association neutralizes the excess negative charge of a polynucleotide, allowing the DNA-lipid complex to approach a negatively charged phospholipid membrane. Unfortunately, the cationic lipids and surfactants are toxic to an organism. A question that we will try to answer in this letter is: What is the minimum amount of cationic surfactant or lipid that is necessary to form a complex and how does this amount depends on various properties of a system? We study a solution consisting of DNA segments of density ρDNA, surfactants of density ρsurf , and salt molecules of density ρsalt [21]. The solvent is idealized as a uniform medium of dielectric constant D. Since the DNA molecule has a large intrinsic rigidity, we model it as a cylinder of fixed length and diameter. When in solution, the Z phosphate groups of the DNA strand become ionized, resulting in a net molecular charge, −Zq. An equivalent number of counterions of density ZρDNA are released into solution preserving the overall charge neutrality. Similarly, the cationic surfactant molecule in aqueous solution becomes ionized, producing a free negative ion and a flexible chain consisting of one positively charged hydrophilic head group and a neutral hydrophobic tail. The ions of salt, the counterions, and the negative ions dissociated from the surfactant are modeled as hard spheres with point charge located at the center. For simplicity, we shall call the negative ions, “coions”, and the positive ions, “counterions” — independent of the species from which they are derived (see Figure 1). The strong electrostatic attraction between the counterions, cationic surfactant, and the 2 DNA favors formation of clusters consisting of one DNA molecule and ncount associated counterions, and nsurf associated surfactants. The process of association neutralizes nsurf + ncount phosphate groups of a DNA molecule, decreasing the net charge of a complex to, qcomplex = −(Z − nsurf − ncount)q (Figure 1). Our task is to determine the values of ncount and nsurf which are thermodynamically favored, i.e. which minimize the overall Helmholtz free energy of solution. For a dilute suspension, the main contributions to the free energy can be subdivided into three parts: the energy that it takes to construct an isolated complex, Fassociation; an energy that it takes to solvate this complex in the ionic sea, Fsolvation; and the entropic energy of mixing, Fmixing. To calculate the free energy of an isolated cluster, we use the following simplified model of a complex. Each monomer of a polyion is treated as free or occupied by a counterion or a surfactant (Figure 2). We associate with each monomer i two occupation variables σ(i) and τ(i), such that σ(t) = 1 if the site is occupied by a condensed counterion, and σ(i) = 0 otherwise. The occupation number for surfactants, τ(i), behaves in a similar way. The free energy can now be calculated as a logarithm of the Boltzmann sum over all possible configurations of condensed counterions and surfactants along the polyion, βFassociation = − ln ∑ ν eν . (1) The energy of a given configuration ν can be subdivided into two parts, Eν = E1 + E2, where the electrostatic contribution is, E1 = q 2 ∑ i6=j [−1 + σ(i) + τ(i)][−1 + σ(j) + τ(j)] D|r(i)− r(j)| . (2) The energy E2 arises from hydrophobicity of surfactant molecules. Clearly, when two adjacent sites are occupied by surfactants, the net exposure of hydrocarbon tails to water is reduced. We capture this effect by introducing an additional contribution to the overall energy of interaction, E2, given by E2 = − χ 2 ∑ τ(i)τ(j) , (3)