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Atomistic Monte Carlo simulation of lipid membranes.

Wüstner D, Sklenar H - Int J Mol Sci (2014)

Bottom Line: In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches.We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements.We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

View Article: PubMed Central - PubMed

Affiliation: Department of Biochemistry and Molecular Biology, University of Southern Denmark, Odense M DK-5230, Denmark. wuestner@bmb.sdu.dk.

ABSTRACT
Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

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Simulation snapshot and system energy of a DPPC bilayer. The membrane simulation started from a crystalline bilayer consisting of 32 DPPC molecules with straight fatty acyl chains in each leaflet. Each molecule was rotated by a random rotation angle around the molecular long axis in the start configuration ((A), “N = 0”); (B–D) show snapshots after N = 10,000 (B); N = 20,000 (C); and N = 40,000 (D) MC steps, respectively. United atoms of methyl and methylen as well as carbon atoms are shown in grey, oxygen in red, nitrogen in blue, and phosphorus in yellow. Fatty acyl chains become increasingly disordered in course of the simulation; (E) the enthalpy of the bilayer in the implicit solvent was calculated after a given number of MC steps of the simulation performed in the constant NPT-ensemble. The temperature of the simulation was 323 K (i.e., 50 °C); (F) a histogram of the conformational energy of the last 40,000 MC steps (grey bars) overlaid with a fit to a Gaussian function of the form  provides the mean energy at equilibrium, E, and the standard deviation, σ, as a measure of fluctuations around the mean value (light grey line). See text for further explanation.
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f5-ijms-15-01767: Simulation snapshot and system energy of a DPPC bilayer. The membrane simulation started from a crystalline bilayer consisting of 32 DPPC molecules with straight fatty acyl chains in each leaflet. Each molecule was rotated by a random rotation angle around the molecular long axis in the start configuration ((A), “N = 0”); (B–D) show snapshots after N = 10,000 (B); N = 20,000 (C); and N = 40,000 (D) MC steps, respectively. United atoms of methyl and methylen as well as carbon atoms are shown in grey, oxygen in red, nitrogen in blue, and phosphorus in yellow. Fatty acyl chains become increasingly disordered in course of the simulation; (E) the enthalpy of the bilayer in the implicit solvent was calculated after a given number of MC steps of the simulation performed in the constant NPT-ensemble. The temperature of the simulation was 323 K (i.e., 50 °C); (F) a histogram of the conformational energy of the last 40,000 MC steps (grey bars) overlaid with a fit to a Gaussian function of the form provides the mean energy at equilibrium, E, and the standard deviation, σ, as a measure of fluctuations around the mean value (light grey line). See text for further explanation.

Mentions: A DPPC molecule was built using in-house modeling software. Values for bond angles, torsion angles, and bond lengths were taken from their equilibrium values defined in [99]. These values yielded straight fatty acyl chains of DPPC and a molecular conformation close to but not identical to the crystal structure previously defined for the closely related DMPC (PDB ID XP4; Figure 1) [103]. For one-lipid simulations, one MC cycle comprised changing all 88 DOF. Efficiency of energy calculations was guaranteed by calculating energy differences for each moved fragment with respect to all other atoms in the same lipid prior and after the local MC move. For the bilayer, the energy calculation included additionally the non-bonded interactions to other lipids (see below). The DPPC bilayer is approximately described by a two-dimensional periodic model with a cubic elementary cell, and the simulations were done under the condition of constant pressure of 1 atmosphere. This means that, in addition to structural moves, random variations of the volume have to be included, and the energetic contribution of the volume change adds to the structural intra- and intermolecular energy. The resulting enthalpy decides on the acceptance of the move by the Metropolis algorithm. We started with the crystalline-like conformation for 64 DPPC molecules (compare Figure 2A, “start” and Figure 5A). Cut-offs used in calculation of pair-wise (atom-atom) energies were defined by the minimum image convention [44]. For 6–12-Lennard Jones and electrostatic interactions a cut-off of 10 Å and a shell with a non-bonded list of 10 Å was generated. This list was updated every 10 cycles. That is, interaction of groups at a distance between 0 and 10 Å were calculated every cycle, while those of groups at a distance between 10 and 20 Å were stored in the pair list, similar as described previously [44,101]. Volume moves were attempted in every MC cycle for the bilayer by isotropic adjustment of the box length. For that purpose, the center-of-mass distance between all DPPC molecules was adjusted in each MC cycle. To account for effects of the solvent, an implicit description of dielectric properties of the water phase close to the bilayer/solvent interface was chosen. Thus, electrostatics was treated by employing a sigmoidal damping function for the dielectric constant ɛ(r) in the Coulomb term of the AMBER 4.1. force field function [104]. This is based on a function originally proposed by Hingerty et al. [105], and refitted by Lavery et al. [106], for large distances from the interface:


Atomistic Monte Carlo simulation of lipid membranes.

Wüstner D, Sklenar H - Int J Mol Sci (2014)

Simulation snapshot and system energy of a DPPC bilayer. The membrane simulation started from a crystalline bilayer consisting of 32 DPPC molecules with straight fatty acyl chains in each leaflet. Each molecule was rotated by a random rotation angle around the molecular long axis in the start configuration ((A), “N = 0”); (B–D) show snapshots after N = 10,000 (B); N = 20,000 (C); and N = 40,000 (D) MC steps, respectively. United atoms of methyl and methylen as well as carbon atoms are shown in grey, oxygen in red, nitrogen in blue, and phosphorus in yellow. Fatty acyl chains become increasingly disordered in course of the simulation; (E) the enthalpy of the bilayer in the implicit solvent was calculated after a given number of MC steps of the simulation performed in the constant NPT-ensemble. The temperature of the simulation was 323 K (i.e., 50 °C); (F) a histogram of the conformational energy of the last 40,000 MC steps (grey bars) overlaid with a fit to a Gaussian function of the form  provides the mean energy at equilibrium, E, and the standard deviation, σ, as a measure of fluctuations around the mean value (light grey line). See text for further explanation.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3958820&req=5

f5-ijms-15-01767: Simulation snapshot and system energy of a DPPC bilayer. The membrane simulation started from a crystalline bilayer consisting of 32 DPPC molecules with straight fatty acyl chains in each leaflet. Each molecule was rotated by a random rotation angle around the molecular long axis in the start configuration ((A), “N = 0”); (B–D) show snapshots after N = 10,000 (B); N = 20,000 (C); and N = 40,000 (D) MC steps, respectively. United atoms of methyl and methylen as well as carbon atoms are shown in grey, oxygen in red, nitrogen in blue, and phosphorus in yellow. Fatty acyl chains become increasingly disordered in course of the simulation; (E) the enthalpy of the bilayer in the implicit solvent was calculated after a given number of MC steps of the simulation performed in the constant NPT-ensemble. The temperature of the simulation was 323 K (i.e., 50 °C); (F) a histogram of the conformational energy of the last 40,000 MC steps (grey bars) overlaid with a fit to a Gaussian function of the form provides the mean energy at equilibrium, E, and the standard deviation, σ, as a measure of fluctuations around the mean value (light grey line). See text for further explanation.
Mentions: A DPPC molecule was built using in-house modeling software. Values for bond angles, torsion angles, and bond lengths were taken from their equilibrium values defined in [99]. These values yielded straight fatty acyl chains of DPPC and a molecular conformation close to but not identical to the crystal structure previously defined for the closely related DMPC (PDB ID XP4; Figure 1) [103]. For one-lipid simulations, one MC cycle comprised changing all 88 DOF. Efficiency of energy calculations was guaranteed by calculating energy differences for each moved fragment with respect to all other atoms in the same lipid prior and after the local MC move. For the bilayer, the energy calculation included additionally the non-bonded interactions to other lipids (see below). The DPPC bilayer is approximately described by a two-dimensional periodic model with a cubic elementary cell, and the simulations were done under the condition of constant pressure of 1 atmosphere. This means that, in addition to structural moves, random variations of the volume have to be included, and the energetic contribution of the volume change adds to the structural intra- and intermolecular energy. The resulting enthalpy decides on the acceptance of the move by the Metropolis algorithm. We started with the crystalline-like conformation for 64 DPPC molecules (compare Figure 2A, “start” and Figure 5A). Cut-offs used in calculation of pair-wise (atom-atom) energies were defined by the minimum image convention [44]. For 6–12-Lennard Jones and electrostatic interactions a cut-off of 10 Å and a shell with a non-bonded list of 10 Å was generated. This list was updated every 10 cycles. That is, interaction of groups at a distance between 0 and 10 Å were calculated every cycle, while those of groups at a distance between 10 and 20 Å were stored in the pair list, similar as described previously [44,101]. Volume moves were attempted in every MC cycle for the bilayer by isotropic adjustment of the box length. For that purpose, the center-of-mass distance between all DPPC molecules was adjusted in each MC cycle. To account for effects of the solvent, an implicit description of dielectric properties of the water phase close to the bilayer/solvent interface was chosen. Thus, electrostatics was treated by employing a sigmoidal damping function for the dielectric constant ɛ(r) in the Coulomb term of the AMBER 4.1. force field function [104]. This is based on a function originally proposed by Hingerty et al. [105], and refitted by Lavery et al. [106], for large distances from the interface:

Bottom Line: In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches.We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements.We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

View Article: PubMed Central - PubMed

Affiliation: Department of Biochemistry and Molecular Biology, University of Southern Denmark, Odense M DK-5230, Denmark. wuestner@bmb.sdu.dk.

ABSTRACT
Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

Show MeSH
Related in: MedlinePlus