Search

Coarse-grained simulations of model membranes containing mixtures of phospholipid and cholesterol molecules at different concentrations and temperatures have been performed. A random mixing without tendencies for segregation or formation of domains was observed on spatial scales corresponding to a few thousand lipids and timescales up to several microseconds. The gel-to-liquid crystalline phase transition is successively weakened with increasing amounts of cholesterol without disappearing completely even at a concentration of cholesterol as high as 60%. The phase transition temperature increases slightly depending on the cholesterol concentration. The gel phase system undergoes a transition with increasing amounts of cholesterol from a solid-ordered phase into a liquid-ordered one. In the solid phase, the amplitude of the oscillations in the radial distribution function decays algebraically with a prefactor that goes to zero at the solid-liquid transition.

It is here shown that there is a considerable system size-dependence in the area compressibility calculated from area fluctuations in lipid bilayers. This is caused by the contributions to the area fluctuations from undulations. This is also the case in experiments. At present, such a contribution, in most cases, is subtracted from the experimental values to obtain a true area compressibility. This should also be done with the simulation values. Here, this is done by extrapolating area compressibility versus system size, down to very small (zero) system size, where undulations no longer exist. The area compressibility moduli obtained from such simulations do not agree with experimental true area compressibility moduli as well as the uncorrected ones from contemporary or earlier simulations, but tend, instead, to be approximately 50% too large. As a byproduct, the bending modulus can be calculated from the slope of the compressibility modulus versus system-size. The values obtained in this way for the bending modulus are then in good agreement with experiment.

Molecular dynamics simulations of atomistic models show the ordering and condensing effect of the cholesterol on phospholipid bilayers. Such simulations are, however, too time consuming to permit monitoring of the gel/liquid crystalline phase transition. We used therefore the simplified coarse grained MARTINI model to study the phase transition in dipalmitoylphosphatidylcholine (DPPC) cholesterol mixtures. A recent study by Marrink shows that this model is able to describe the main phase transition of pure phospholipid systems reasonably.The area per molecule was calculated separately for the phospholipids and cholesterol as a partial specific area (Edholm & Nagle). The condensation effect of cholesterol is obtained with the atomistic model as a negative partial specific area for cholesterol. The coarse grained model reproduce the condensation effect and gives a negative partial specific area of cholesterol molecule at low cholesterol concentration and low temperatures above the main phase transition. The main phase transition occurs already at about 295K for the coarse grained model. There is, however, another (second order) phase transition at 304K, where partial specific area suddenly becomes positive for all cholesterol concentrations. Such a transition was, however, not observed with the atomistic model. A similar transition was observed in the order parameter versus temperature at low cholesterol concentration, but this vanishes at high concentration. These results were used to test different suggested relations between area per lipid and the order parameter.Below, the main transition, the radial distribution functions and chain order parameters were used to monitor the difference between long range positional order and chain order as well as to search for inhomogeneities in the lipid distribution.

Coarse grained simulations of membranes containing mixtures of phospholipids and cholesterol at different concentrations and temperatures (below and above the main transition) have been performed. Random mixing without formation of domains was observed. On the contrary, we observed that phase separated fluid systems with different cholesterol concentrations mix into uniform systems in less than 200 nsec. For the gel phase the results are less conclusive due to the two orders of magnitude slower dynamics. The gel to liquid crystalline phase transition is successively weakened by cholesterol while the phase transition temperature increases slightly.The gel phase system undergoes a transition with increasing amounts of cholesterol from a solid ordered phase into a liquid ordered one. In the solid phase, the amplitude of the oscillations in the radial distribution functions decays algebraically with a pre-factor that goes to zero at the two-dimensional solid-liquid transition. The liquid ordered phase is characterized by liquid-like pair correlation functions that decay exponentially to one and have just one detectable peak. Angular correlation functions that measure how the orientation of the lattice vectors in the membrane plane decorrelates with distance were also calculated. They show an algebraic decay with exponent 0.15-0.25 in large regions of the solid ordered phase. This indicates that the liquid ordered phase has more structure than a two-dimensional liquid and may be a hexatic phase.To explore further whether phase segregation into cholesterol-rich and cholesterol-poor domains is favorable from a free energy point of view, the chemical potential for cholesterol insertion into lipid bilayers at different cholesterol concentrations was calculated from simulations. This shows a small bulk free energy of about 0.3kT per lipid that favors phase separation while a small line tension (a few pN) between cholesterol-rich and -poor regions favors mixing.

Experimental data for many important properties of lipid bilayers are scarce and uncertain. This includes for instance area per lipid, area and volume compressibilities, area expansion coefficients and heat capacity.Present simulation techniques can often give such properties more easily and sometimes with better accuracy than experiments. Simulation results depend, however, upon potential parameters that yet are not enough tested and validated. Still, the time is getting ripe for systematic calculation of membrane properties using simulation techniques. This is useful both since it will provide better values for a number of membranes properties but also since a more serious test of the membrane force field parameters will push the refinement and development on this side.Initially, the study has concentrated on area per lipid, area compressibility and bending modulus. We have shown that the inverse apparent area compressibility modulus obtained from the area fluctuations of the system shows a linear variation with system size. From this, the the true area compressibility modulus can be obtained by extrapolating to small areas. From the term that varies linearly with system size and is due to undulations, the bending modulus of the bilayer can easily be calculated. The method has been applied to several lipids including DPPC and DMPC.