Modulation of Elasticity and Interactions in Charged Lipid Multibilayers: Monovalent Salt Solutions

Abstract

We have studied the electrostatic screening effect of NaCl solutions on the interactions between anionic lipid bilayers in the fluid lamellar phase using a Poisson-Boltzmann-based mean-field approach with constant charge and constant potential limiting charge regulation boundary conditions. The full DLVO potential, including the electrostatic, hydration and van der Waals interactions, was coupled to thermal bending fluctuations of the membranes via a variational Gaussian Ansatz. This allowed us to analyze the coupling between the osmotic pressure and the fluctuation amplitudes and compare them both simultaneously with their measured dependence on the bilayer separation, determined by the small-angle X-ray scattering experiments. High-structural resolution analysis of the scattering data revealed no significant changes of membrane structure as a function of salt concentration. Parsimonious description of our results is consistent with the constant charge limit of the general charge regulation phenomenology, with fully dissociated lipid charge groups, together with a 6-fold reduction of the membranes' bending rigidity upon increasing NaCl concentration.

Figure 1

Global analysis of SAXS data in terms of the SDP model. (A) Scattering patterns of unstressed DPPG multibilayers at 50 °C as a function of NaCl concentration. Numbers right to the patterns give salt concentration in mM. For clarity of display data have been offset by a constant. Solid lines correspond to the best fits from the SDP-GAP model. The resulting electron density profile at 700 mM NaCl is shown in the inset. (B) Applied parsing scheme for DPPG and (C) the corresponding volume probability distributions (right-hand side) and electron densities (left-hand side).

Figure 2

Screening of electrostatic interactions between fluid DPPG bilayers in the presence of NaCl. (A) Osmotic pressure isotherms and (B) the corresponding membrane fluctuation amplitudes as a function of the equilibrium spacing ⟨l₀⟩. A constant of δ = 10^–3 atm was added to the P_osm data to include zero osmotic pressure data on the log-scale. Numbers adjacent to data denote the given salt concentration in mM. Solid lines represent the best fits obtained from CC-BCs. The dashed lines correspond to the solutions obtained using CP-BCs. Resulting fit parameters for CC-BCs are displayed in Table 1 and Figure 4.

Figure 3

Behavior of the Hessian ≡ ∂²f_var/∂l₀² as a function of membrane equilibrium spacing ⟨l₀⟩ and salt concentrations for CC (solid lines) and CP (dashed lines) boundary conditions. Colors represent different salt concentrations, given in units of mM by numbers next to the data. All the CC curves show a non-negative Hessian, and the Gaussian theory on which they are based is stable. The CP curves show a more complicated behavior, often exhibiting negative values of the Hessian, signaling a breakdown of the Gaussian theory.

Figure 4

(A) Bending rigidity and (B) projected membrane surface area as a function of salt concentration. The bending rigidity clearly attests to the softening of the bilayer elasticity due to solution ion screening, leading consistently also to a diminished projected membrane surface area.