2D lattice model of a lipid bilayer: Microscopic derivation and thermodynamic exploration

Abstract

Based on all-atom Molecular Dynamics (MD) simulations of a lipid bilayer we present a systematic mapping on a 2D lattice model. Keeping the lipid type and the chain order parameter as key variables we derive a free energy functional, containing the enthalpic interaction of adjacent lipids as well as the tail entropy. The functional form of both functions is explicitly determined for saturated and polyunsaturated lipids. By studying the lattice model via Monte Carlo simulations it is possible to reproduce the temperature dependence of the distribution of order parameters of the pure lipids, including the prediction of the gel transition. Furthermore, application to a mixture of saturated and polyunsaturated lipids yields the correct phase separation behavior at lower temperatures with a simulation time reduced by approximately 7 orders of magnitude as compared to the corresponding MD simulations. Even the time-dependence of the de-mixing is reproduced on a semi-quantitative level. Due to the generality of the approach we envisage a large number of further applications, ranging from modeling larger sets of lipids, sterols, and solvent proteins to predicting nucleation barriers for the melting of lipids. Particularly, from the properties of the 2D lattice model one can directly read off the enthalpy and entropy change of the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine gel-to-liquid transition in excellent agreement with experimental and MD results.

Understanding Conformational Dynamics of Complex Lipid Mixtures Relevant to Biology

“…A comparison of the MD and MC simulations revealed a qualitative agreement with respect to the unmixing process (upper and middle frames). Such an agreement was even found on a quantitative level (Hakobyan and Heuer 2017 ). Importantly, the MC simulations were eight orders of magnitude faster than the MD simulations.…”

“…Later on, it could be shown that with time-consuming MD simulations the onset of the domain formation could also be obtained from united atom modelling, which required simulation times of more than 10 μs (Hakobyan and Heuer 2013 ). A recently introduced 2D-lattice-based approach was used to exceed the previous limitations in timescale and length scale by orders of magnitude (Hakobyan and Heuer 2017 ). At the same time, it allowed the extraction of the underlying information about the thermodynamic origin of domain formation.…”

“…The lattice can represent either pure lipid membranes or lipid mixtures. So far, pure DPPC and DLiPC membranes as well as DPPC/DLiPC mixtures have been systematically explored (Hakobyan and Heuer 2017 ). Several key aspects of model design can be addressed based on an analysis of MD simulations.…”

Chain ordering of phospholipids in membranes containing cholesterol: What matters?

“…Due to the lack of significant dependence on cholesterol concentration, the impact of the PL-interaction with water and the opposite leaflet can be directly taken into account by the use of an effective entropy function, as used, e.g., in. 41 This model may help to better rationalize the impact of local interaction properties on the mesoscopic phase behavior of lipid mixtures. Figure S4: Interleaflet interaction as a function of both, the lipids overlap and its chain order parameter in respective bilayer DPPC/CHOL and DLiPC/CHOL mixtures from 0% to 30% CHOL.…”

“…The importance of nearest neighbor interactions to describe the lateral range of influence has been discussed in various simplistic models of lipid bilayers, strongly supporting the notion that lipids in a bilayer are only influenced by their nearest neighbors. [41][42][43] The question arises whether this influence or lack thereof can effectively be observed in the interaction functions and how this observation deviates between the examined lipid types.…”