Hybrid lipids as a biological surface-active component

Abstract

Cell membranes contain small domains (on the order of nanometers in size, sometimes called rafts) of lipids whose hydrocarbon chains are more ordered than those of the surrounding bulk-phase lipids. Whether these domains are fluctuations, metastable, or thermodynamically stable, is still unclear. Here, we show theoretically how a lipid with one saturated hydrocarbon chain that prefers the ordered environment and one partially unsaturated chain that prefers the less ordered phase, can act as a line-active component. We present a unified model that treats the lipids in both the bulk and at the interface and show how they lower the line tension between domains, eventually driving it to zero at sufficiently large interaction strengths or at sufficiently low temperatures. In this limit, finite-sized domains stabilized by the packing of these hybrid lipids can form as equilibrium structures.

Figure 1

Schematic picture of (a) high and (b) low temperature (or, respectively, small/large interaction strengths, J_T) for the lattice populated with s and u molecules with some bonds occupied by the h component in various configurations. In panel a, the molecule labeled h₁ has the same type of neighbor on both sides and so its orientation does not matter. The two possible orientations in the presence of a concentration gradient are shown with h₂ and h₃, where h₂ is in the higher energy state, represented by orientational order parameter σ = −1. The lower energy configuration of molecule h₃ is noted by σ = 1. In the low temperature limit (b), entropy becomes irrelevant and the equilibrium configuration is that of lowest interaction energy where the h molecule populates the interface in the σ = 1 state.

Figure 2

Concentration profile of the interface between the two bulk phases. The red dashed line represents the numerical solution for the continuum, mean-field expansion near T_c for the interfacial concentration that varies as ϕ ∼ tanh [z/ξ] and the black line is the linear approximation for the interfacial concentration profile ϕ ∼ z/λ with $\lambda =\sqrt{3/4}\xi$ close to the critical temperature.

Figure 3

(a) Normalized tension versus interaction strength, J_T/T, near the critical point and for strong interaction strengths (or low temperatures) with J_T/T ≫ 1, for which the interface thickness is a molecular length and the bulk phases are ψ = 0 and 1 with corrections proportional to exp(−J_T/T). The black solid line shows the normalized tension γ/(aJ_T) for ${\overline{\psi }}_{\mathrm{h}}=0.01$ and the red dashed line shows the tension for ${\overline{\psi }}_{\mathrm{h}}=0.05$. The thin dotted lines, intermediate between the critical temperature and the low temperature (strong interaction) regime, are continuations of these solutions into the region between the two extreme regimes. The colored points, which coincide with the plots of γ for low temperatures (or strong interactions), are plots of Eq. 13, where terms proportional to exp(−J_T/T) are ignored. The presence of the h component at the interface drives the line tension to zero, as can be seen in the inset, which shows the interfacial concentration of h, ψ^int_h, for ${\overline{\psi }}_{\mathrm{h}}=0.01$ (black solid line) and ${\overline{\psi }}_{\mathrm{h}}=0.05$ (red dashed line). (b) Line tension versus average h concentration for a fixed interaction strength J_T/T = 10 (black solid), 12 (red dashed), and 16 (blue dot-dashed). The colored points are, again, from Eq. 13. The tension is driven to zero as ${\overline{\psi }}_{\mathrm{h}}$, an experimentally controlled parameter, is increased. For the interaction strengths chosen, the tension reaches zero for very small concentrations of ${\overline{\psi }}_{\mathrm{h}}$. Values of J_T include the number of nearest neighbors and the number of chains per lipid. For a linear interface, a value of J_T/T = 16 implies an interaction strength of ∼4 kT per chain.