Association free energy of dipalmitoylphosphatidylserines in a mixed dipalmitoylphosphatidylcholine membrane

Abstract

Blood coagulation is strongly dependent on the binding of vitamin K-dependent proteins to cell membranes containing phosphatidylserine (PS) via gamma-carboxyglutamic acid (Gla) domains. The process depends on calcium, which can induce nonideal behavior in membranes through domain formation. Such domain separation mediated by Ca(2+) ions or proteins can have an important contribution to the thermodynamics of the interaction between charged peripheral proteins and oppositely charged membranes. To characterize the properties of lipid-lipid interactions, molecular dynamics, and free energy simulations in a mixed bilayer membrane containing dipalmitoylphosphatidylcholine and dipalmitoylphosphatidylserine were carried out. The free energy of association between dipalmitoylphosphatidylserines in the environment of dipalmitoylphosphatidylcholines has been calculated by using a novel approach to the dual topology technique of the PS-PC hybrid. Two different methods, free energy perturbation and thermodynamic integration, were used to calculate the free energy difference. In thermodynamic integration runs three schemes were applied to evaluate the integral at the limits of lambda --> 0 or lambda --> 1. Our studies show that the association of two PSs in the environment of PCs is repulsive in the absence of Ca(2+) and becomes favorable in their presence. We also show that the mixed component membrane should exhibit nonideal behavior that will lead to PS clustering.

SCHEME I

Interconversion between DPPS and DPPC form the PS/PC/PS to a PS/PS/PC configuration in the environment of PC. The most probable distance, obtained from the radial distribution function of the phosphorous atoms of DPPC, is ∼6 Å.

FIGURE 1

Local dual topology of the PS-PC hybrid residue. The conformation shown is the starting geometry used in the dynamics. The atoms of the choline headgroup (N, C₁₂, C₁₁, blue) are superimposed on the corresponding atoms in the serine headgroup (N, C_A, C₄, green). The atoms were slightly shifted to make them visible.

FIGURE 2

Density profile of the main components for the lipid membrane without calcium ions along the z axis. The distribution of waters (red), hydrocarbon chains (green), P (yellow), N (pink) atoms of PC, and P (cyan), N (orange), and carboxyl group (gray) of PS are shown. In panel B the distribution of the components of the PC and PS headgroups represented in panel A are magnified.

FIGURE 3

TI integrand for the transition PS/PC/PS → PS/PS/PC. Five-point Gaussian quadrature fit polynomials were used to calculate the free energy differences in a lipid membrane without calcium ions. The values at the end points were obtained by extrapolation (see text). Run 1 (♦, lower layer) and run 2 (•, upper layer).

FIGURE 4

Density profile of the main components for the lipid membrane with calcium ions along the z axis. The distribution of the waters (red), hydrocarbon chains (green), P (yellow), N (pink) atoms of PC, and P (cyan), N (orange), and carboxyl group atoms of PS (gray), and Ca²⁺ (dark blue) are shown. In panel B the distribution of the components of the PC and PS headgroups represented in panel A are magnified.

FIGURE 5

TI integrand, as a function of simulation time (ps) for all λ-values, run 1.

FIGURE 6

(A) TI integrand for the transition PS/PC/PS → PS/PS/PC. Five points (λ = 0.1, 0.3, 0.5, 0.7, 0.9) were used to calculate the free energy differences in a lipid membrane with calcium ions. Diamonds, circles, and triangles correspond to run 1 (lower layer), 2 (upper layer), and 3 (lower layer with different initial conditions), respectively. (B) Free energy differences showing the similarity on the final values (see Table 2).

FIGURE 7

Radial distribution function for the P atoms of the PC headgroup lipids and the number of neighbors (PC) as a function of the phosphorous atom distance (P–P distance).