Background

Phospholipids are central building blocks of biological membranes (Figure 1). As amphipathic molecules, each contains a hydrophobic region consisting of acyl chains and a hydrophilic region consisting of a polar headgroup (Figure 1A). Some phospholipid headgroups are zwitterionic, containing both positively and negatively charged functional groups at physiological pH (Figure 1B), whereas others are acidic, bearing an overall formal negative charge (Figure 1C). Lipids within biomembranes exist stably as a lamellar assembly, forming bilayers in which the acyl chains of two leaflets interact to form a hydrophobic core and two interfacial regions consisting of the polar headgroups (Figure 1D). Most naturally occurring biomembranes contain a certain percentage of acidic phospholipids; therefore, their lipid composition imparts a net negative charge to the interfacial region (Gennis, 1989; Marsh, 2013). Bilayer surface charge is a key factor in many membrane-level processes including interactions with proteins and solution ions as well as membrane morphology, fusion and phase changes. Because the formal charge of lipid headgroups is a primary determinant of this surface charge, it is critical to have accurate measurements of the proton dissociation behavior (quantified as pK_a values) of the constituent functional groups.


Figure 1. Phospholipid structure and the lamellar lipid bilayer. A. General structure of a glycerophospholipid. A common phospholipid is based on a scaffold of a central glycerol molecule (thickened line), with the constituent carbons designated by stereospecific numbering (sn-1, sn-2 and sn-3, as indicated). The hydrophobic domain consists of hydrocarbon tails esterified at the sn-1 and sn-2 positions. The polar headgroup contains a negatively charged phosphate group attached to the sn-3 position, which may be modified by an R group to render specific headgroup identity. B. Structure of phosphatidylcholine (R = choline) with a saturated 16 carbon aliphatic tail at the sn-1 position and an unsaturated 18 carbon tail at the sn-2 position. The zwitterionic nature of the headgroup is shown as the negative phosphate and the positive tertiary amine. C. Structure of phosphatidylglycerol (R = glycerol) with acyl chains identical to those shown above. The anionic nature of the headgroup is shown by the uncompensated negative charge on the phosphate. D. The lamellar lipid bilayer, showing the hydrocarbon core composed of the aliphatic lipid tails and the solvent-exposed interfacial regions.

The electric field that is established by charged headgroups results in a complex profile of electric potential in the aqueous region (Figure 2) (McLaughlin, 1977). Models for the electric potential profile are based on the physical chemistry of phase boundary interfaces, here representing a solid surface in contact with an aqueous phase (Oshima, 2010). Membrane surface electrostatics can be quantitatively modeled using Gouy-Chapman-Stern theory, which relates the density of charges on the membrane surface (σ, C m^-2) and the electric potential (ψ, V), as described in the data analysis section. In a simplified model, the surface charge is comprised of charges that are fixed to the solid body as well as solution ions that are adsorbed tightly to the surface by chemical interactions. For lipid bilayers, the fixed charges can be considered to be the titratable acidic (phosphate) and basic (primary anime) functional groups of lipid headgroups, whereas the adsorbed ions are solution electrolytes that specifically bind headgroup sites with nonzero association constants (Tocanne and Teissie, 1990). This layer of charges is collectively defined as the Stern layer, but may be subdivided into other layers with increasing complexity. Adjacent to this region is a layer in which solvated solution ions are more diffusely distributed. In this region, termed the Gouy-Chapman layer, the distribution of counterions (those with charges opposite to the dominant surface charge) and coions (those with charges identical to the surface charge) arises from electrostatic attraction (counterions) or repulsion (coions) balanced with the entropic tendency of ions to diffuse away from the surface. Because counterions are highly enriched in this region due to electrostatic attraction to the surface, they act to screen the surface charge, thereby attenuating the electric field. Taken as a whole, this distribution of charges sets up the ‘diffuse electrical double layer’ of biomembranes.

Here we describe a methodology to determine the pK_a of lipid headgroups using measurements of the electrostatic potentials of model membranes. This approach is based on the electrophoresis of lipid bilayer vesicles (liposomes), which we used in a recent publication to measure the proton dissociation behavior of the dimeric phospholipid cardiolipin (Sathappa and Alder, 2016). In the presence of an applied electric field, charged colloidal particles will migrate relative to the suspending liquid toward the electrode of opposing charge (Delgado et al., 2007). As the charged particle surface flows tangentially along the bulk fluid, there exists a thin layer of solution, termed the hydrodynamically stagnant layer, which moves with the particle. This layer extends into the diffuse region to a so-called slipping plane or shear plane. The electric potential at this layer that separates the hydrodynamically immobile layer from the bulk is termed the zeta potential (ζ) (Figure 2). The speed of migration depends on the electrophoretic mobility (μ, m² V^-1 s^-1) of the particle, defined by the Helmholtz-Smoluchowski equation as the particle velocity per unit electric field:

Where, ε_r is the relative permittivity, ε₀ is the permittivity of free space, and η is the viscosity of the solution (Aveyard and Haydon, 1973). As Eq. 1 shows, the mobility of charged particles in an external electric field is directly related to the magnitude of ζ. Hence, in an electrolyte solution of a given pH, liposomes with greater surface charge will have a higher ζ and therefore move with higher velocity in a given electric field.

Whereas optical electrophoresis measurements provide an unambiguous measure of electrokinetic mobility and zeta potential, translating these measurements into information on proton dissociation characteristics of titratable groups requires more detailed evaluation. This protocol explains the preparation of suitable model membranes, measurements of zeta potential using optical electrophoresis, and data analysis using Gouy-Chapman-Stern formalism to obtain lipid pK_a values.


Figure 2. The electrostatic profile of the diffuse double layer. A liposome is a model membrane that consists of a vesicular lipid bilayer (left), whose surface and interfacial region in the aqueous phase can be modeled as an electrical double layer (right). In this model, a bilayer surface containing anionic phospholipids is modeled as a planar surface (gray) with uniformly distributed negative charges, from which an electric field originates (red shading). The distribution of solution electrolytes is shown for counterions (in this case, cations shown in blue) and coions (in this case, anions shown in red). Within the Stern layer, counterions are firmly bound to the bilayer surface. Within the Gouy-Chapman layer, solution ions are more disperse, reflecting a balance between Coulombic attraction (cations) or repulsion (anions) and thermal motion. The titratable charged lipid headgroups and adsorbed counterions together define the surface charge density (σ). The electric potential (ψ) assumes a maximum magnitude at the interface surface (ψ₀) and attenuates toward the bulk solution (ψ_bulk) in a manner that is dependent on the ionic characteristics of the bathing solution. The electric potential at the slip plane, termed the zeta potential (ζ) is the measured parameter in this protocol.