Conventional molecular dynamics (MD) simulations are seriously limited by the slow rate of diffusive mixing in their ability to predict lateral distributions of different lipid types within mixed-lipid bilayers using atomistic models. A method to overcome this limitation, using configuration-bias Monte Carlo (MC) "mutation" moves to transform lipids from one type to another in dynamic equilibrium, is demonstrated in binary fluid-phase mixtures of lipids whose tails differ in length by four carbons. The hybrid MC-MD method operates within a semigrand canonical ensemble, so that an equilibrium composition of the mixture is determined by a constant difference in chemical potential (Delta(mu)) chosen for the components. Within several nanoseconds, bilayer structures initiated as pure dipalmitoyl phosphatidylcholine (DPPC) or pure dilauroyl phosphatidylcholine (DLPC) converge to a common composition and structure in independent simulations conducted at the same Delta(mu). Trends in bilayer thickness, area per lipid, density distributions across the bilayer, and order parameters have been investigated at three mixture compositions and compared with results from the pure bilayers at 323 K. The mixtures showed a moderate increase in DPPC acyl tail sites crossing the bilayer midplane relative to pure DPPC. Correlations between lateral positions of the two lipid types within or across the bilayer were found to be weak or absent. While the lateral distribution is consistent with nearly ideal mixing, the dependence of composition on Delta(mu) indicates a positive excess free energy of mixing.
Mixed MD/MC simulation at fixed difference in chemical potential (Δμ) between two lipid types provides a computational indicator of the relative affinities of the two lipids for different environments. Applying this technique to ternary DPPC/DOPC/cholesterol bilayers yields a DPPC/DOPC ratio that increases with increasing cholesterol content at fixed Δμ, consistent with the known enrichment of DPPC and cholesterol-rich in liquid-ordered phase domains in the fluid-fluid coexistence region of the ternary phase diagram. Comparison of the cholesterol-dependence of PC compositions at constant Δμ with experimentally measured coexistence tie line end point compositions affords a direct test of the faithfulness of the atomistic model to experimental phase behavior. DPPC/DOPC ratios show little or no dependence on cholesterol content at or below 16% cholesterol in the DOPC-rich region of the composition diagram, indicating cooperativity in the favorable interaction between DPPC and cholesterol. The relative affinity of DPPC and DOPC for high cholesterol bilayer environments in simulations is explicitly shown to depend on the degree of cholesterol alignment with the bilayer normal, suggesting that a source of the cooperativity is the composition dependence of cholesterol tilt angle distributions.
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