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Lipid Bilayer Simulations: Force fields, Simulation and Analysis

Lipid Bilayer Simulations: Force fields, Simulation and Analysis. Jeffery B. Klauda. Model Yeast Membrane. Chemical Structure of Lipids. Lipids. Complex biomolecules. Contain a fatty acid chains and head group. Classified into 8 categories 1. Fatty acyls. Glycerolipids.

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Lipid Bilayer Simulations: Force fields, Simulation and Analysis

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  1. Lipid Bilayer Simulations: Force fields, Simulation and Analysis Jeffery B. Klauda Model Yeast Membrane Chemical Structure of Lipids

  2. Lipids • Complex biomolecules • Contain a fatty acid chains and head group • Classified into 8 categories1 Fatty acyls Glycerolipids Glycerolphospholipids Sphingolipids Phenol lipids Sterol Lipids Modified (Fig. 1)1 Saccharolipids Polyketides 1Fahy et al. J. Lipid. Res.46: 839 (2005).

  3. Glycerophospholipids • Some Common Subclasses of GP lipids1 Phosphocholines Phosphonocholines Phosphoethanolamines Phosphonoethanolamines Phosphoserines Phosphoglycerols Phosphoglycerophosphates Phosphoinsitols (Modified Fig. 4)1 Phosphoinsitolmonophosphates Phosphates 1Fahy et al. J. Lipid. Res.46: 839 (2005).

  4. Periplasm Channel Proteins Cytoplasmic Membrane Lipid/Cholesterol Bilayer Membrane Proteins Cytoplasm Membranes in Single Cell Organisms E. coli • Plasma membrane1 contains many constituents • Membranes are located throughout the cell interior Cell Membranes2 1Fig. 1b from Engelman, D.M. Nature.438: 578 (2005). 2Fig. 1a from McMahon, H.T. et al. Nature.438: 590 (2005).

  5. Diversity of Lipid Types in Organisms • Yeast (Saccharomycescerevisiae)1 • Mixture of fully saturated and unsaturated chains • Mixture of charged and zwitterionic head groups and typically 10-20% sterols • Compositions depend on strain of yeast • Chlamydia (chlamydiatrachomatis)2 • Exists in two forms reticulate body (metabolically active) and elementary body (infectious) • Bacterial membranes contain various chain types including branched chains (10-20%) • Primarily zwitterionic and phosphatidylinositol head groups • 20-30% sterols • E. coli (Escherichia coli)3 • Mixture of fully saturated and unsaturated chains • Fatty acid chains can contain cyclic moieties (cyclopropane) • Zwitterionic (~80% PE) and anionic (~20 %PG) head groups • Limited to no sterols 1Daum G. et al. Yeast. 15: 601 (1999). 2Wylie, J.L. et al. J. Bact.179: 7233 (1997). 3Shokri, A. & G. Larsson. MicrobialCellFactories. 3: 9 (2004) .

  6. Membrane Composition within Cell • Distribution of phospholipids (PL) vs. sterols1 • Mammals in dark blue and yeast in light blue • Plasma membrane (PM) contains a significant amount of sterol (largest of all organelles) • Mammalian PM contain more sterol than yeast • Endoplasmic reticulum (ER) manufactures sterol, but levels are low • Large diversity of phospholipids between mammals and yeast and within a cell 1van Meer, G. et al. Nature Rev. Mol. Cell. Bio. 9: 112 (2008).

  7. Force Fields • Biomolecular Force Field (CHARMM) • Many terms to describe intra- and intermolecular interactions • All-atom Lipid Force Fields • CHARMM Family: CHARMM27r and CHARMM36 (C27r1 and C362) • AMBER Family: GAFFlipid3 and Lipid144 • Stockholm Lipids (Amber-compatible): Slipid5 1Klauda, J. B. et al. JPCB.109: 5300 (2005). 2Klauda, J.B. et al. JPCB.114: 7830 (2010). 3Dickson et al. Soft Matter.8: 9617 (2012). 4Dickson et al. J. Chem. Theory Comput.10: 865 (2014). 5Jämbeck & Lyubartsev. JPCB. 116: 3164 (2012).

  8. AMBER Lipids • Summary of Lipid14 FF1 Results (NPT Ensemble) Surface Area/lipid [Å2] • Generally good agreement with experiment (slight tendency to underestimate) Deuterium Order Parameters • Overall excellent agreement with NMR SCDs • POPE SCDs of the saturated chain are somewhat high, which may indicate that the SA/lipid is too low • Decent splitting for the C2 position • Unclear if the head group order parameters are in agreement with experiment (Fig. 71) • Procedure follows typical rules for AMBER FF optimization (RESP charges in gas phase) • Should only be used with the AMBER family of FF 1Dickson et al. J. Chem. Theory Comput.10: 865 (2014).

  9. Stockholm Lipids (Slipids) • Summary of Slipids1-3 Results (NPT Ensemble) Surface Area/lipid [Å2] • Generally good agreement with experiment (slight tendency to underestimate) Deuterium Order Parameters (Fig. 22) (Fig. 51) • Overall excellent agreement with NMR SCDs • Better POPE SCDs compared to Lipid14 • Decent splitting for the C2 position • Unclear if the head group order parameters are in agreement with experiment • Procedure similar to AMBER FF optimization (RESP charges in gas phase) • Extensions to PS, PG and SM lipids3 1Jämbeck & Lyubartsev. JPCB. 116: 3164 (2012).2Jämbeck & Lyubartsev. J. Chem. Theory Comput. 8: 2938 (2012). 3Jämbeck & Lyubartsev. J. Chem. Theory Comput. 9: 774 (2013).

  10. Force Fields Continued • Biomolecular Force Field (CHARMM) • Many terms to describe intra- and intermolecular interactions • United Atom/Coarse-grained Lipid Force Fields • United atom: C27-UA(acyl)1, C36-UA2 and GROMOS3 • Coarse-grained: MARTINI4and Shinoda/DeVane/Klein5 1Henin, Shinoda & Klein. JPCB. 112: 7008 (2008). 2Lee, Tran, Allsopp, Lim, Henin & Klauda. JPCB118: 547 (2014). 4Berger, O. et al. BJ. 72: 2002 (1997). 4Marrink et al. JPCB. 111: 7812 (2007). 5Shinoda, DeVane, & Klein. JPCB. 114: 6836 (2010).

  11. Issues with the CHARMM27r FF • Surface Tension • To maintain good agreement with density profiles and SCD, NPAT simulations at the experimental area are needed for MD simulations with C27r • Finite size effects may result in a non-zero surface tension,1 but C27r values are too high2 Surface Tension in dyn/cm • Freezing or Phase Change with NPT • Freezing of aliphatic chains at T > Tb • Issue with lipids that have 1-2 fully saturated chains • Problematic when surface areas are not available for lipids and their mixtures 1Klauda, J.B. et al. BJ. 90: 2796 (2006). 2Klauda, J.B. et al. JPCB. 111: 4393 (2007).

  12. Modification of CHARMM Charges • Charge/LJ Modification • Looked at small molecules and DPPC bilayer charges using semi-empirical AM1 • Increase in polarization occurred going from the gas phase to realistic bilayer • Therefore, increasing the lipid charges in the glycerol region is justified • Adjusted charges/LJ Dipole moment of methylacetate (debye) • Adjustments are supported by AM1 on the bilayer, small molecule dipoles and water-molecule interactions. • Small adjustments on the carbonyl carbon LJ parameters with the ester oxygen taken from previous optimizations1 1Vorobyov, I, et al. J. Chem. Theory and Comp.3: 1120 (2007).

  13. Dihedral Modifications Fits to QM of small molecules QM of bilayers (Alex MacKerell) • Small Molecule Models of DPPC 1Klauda et al. JPCB.114: 7830 (2010).

  14. Dihedral Modifications: CHARMM36 • Glycerol FF Adjustments q4 q2 • Adjust the g1 torsion g1 b1 MP2/6-31g(d): 648 Energy Points • Issues fitting the q4 and b1 torsions kcal/mol 1Klauda et al. JPCB.114: 7830 (2010).

  15. Empirical Fits of Torsions (C36) • DPPC SCD Targets • MD simulations of the DPPC bilayer with an intermediate FF were used to empirically fit q2, q4, and b1 torsions. • Populations of trans and gauche conformations of these torsions were optimized • The torsional potential was adjusted to bound the PMFs based on these fits and the optimal set was chosen. 1Klauda et al. JPCB.114: 7830 (2010).

  16. Empirical Fits of Torsions (C36) • Torsional surface scans from 20 ns MD simulations 1Klauda et al. JPCB.114: 7830 (2010).

  17. DPPC Bilayer and C36 • Deuterium Order Parameters (SCD): NPAT/NPT1 vs. Experiment2 NPAT A=64Å2 NPT • Excellent agreement with experiment and fairly independent of the ensemble. 1Klauda, J. B. et al. JPCB.114: 7830 (2010). 2Seelig, A. & J. Seelig. Biochem.13: 4839 (1974).

  18. DPPC Bilayer • Density Profiles & Form Factors Compared to Experiment1 Aexp=63±1Å2 • Good agreement with the experimental form factors, F(q) • The methyl & methylene density is improved • NPT captures the overall and component densities correctly 1Kučerka, N. et al. BJ.95: 2356 (2008).

  19. CHARMM36 Lipids • Initial Parameterization with PC & PE lipids Surface Area/lipid [Å2] a323K b303K c310K • Additional Lipids • Lipids with polyunsaturated chains2 DAPC • Branched and cyclic-containing chains (important for certain bacteria)3,4 • Sterols (cholesterol, oxysterols, ergosterol)5 • Various published parameters: PS, PG, PA and Cardiolipin • Other lipid parameters on the way: PI, PIP, SM, and CER 1Klauda et al. JPCB.114: 7830 (2010).2Klauda et al. JPCB. 116: 9424 (2012). 3Lim & Klauda. BBA: Biomemb.1808: 323 (2011). 4Pandit & Klauda. BBA: Biomemb.1818: 1818 (2012). 5Lim et al. JPCB. 116: 203 (2012).

  20. CHARMM-GUI • CHARMM-GUI.org – Membrane Builder1,2 Dr. Im (KU) • Allows for easy building of lipid membranes • Select from 140+ lipids and any mixture from these lipids • Builds membranes and provides rigorously tested equilibration inputs for CHARMM and NAMD simulations • Membrane proteins can be easily incorporated into the bilayer • Freely available to any researcher 1Jo, Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) . 2Jo, Lim, Klauda & Im. Biophys. J.97: 50 (2009).

  21. CHARMM-GUI • CHARMM-GUI.org – Membrane Builder1,2 • Can easily build heterogeneous bilayers • Specify water hydration in three ways (defaults are safe for fully hydrated bilayers) • Can choose ratio or number of lipids for each leaflet • Reported surface area per lipid is based on simulations with a pure membrane • Further steps ask for ion concentration, ring penetration checks, ensemble and temperature • At the end (or during the process) you can download the files in .tgz format (all files needed to simulate bilayer) 1Jo, Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) . 2Jo, Lim, Klauda & Im. Biophys. J.97: 50 (2009).

  22. CHARMM-GUI • Output Initial Structure of Bilayer • Water is initially away from bilayer (will quickly fill in the vacuum space). • Lipid head groups are aligned to a specific z-position based on prefered location in the bilayer • Chains can tangle and careful equilibration is required • Restraints During Equilibration • Water away from hydrophobic core • Head group and tails to appropriate regions • Double bonds in their respective cis or trans conformation • Ring conformations (chair & upright for PI lipids) 1Jo, Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) . 2Jo, Lim, Klauda & Im. Biophys. J.97: 50 (2009).

  23. MD Simulations of Membranes • Caveats of CHARMM-GUI with membranes • Membrane surface area/volume • Primarily based on SA from pure lipid bilayers with C36 force field at 303K • Some lipids have high gel transition temperatures >303K and values are based on higher temps • This can result in poor initial guess for mixed lipid systems, especially with sterols • If the SA is known or can be estimated a priori then this is preferred • Membrane equilibration • Although we have tested this extensively there might be some issues • Pay careful attention to your bilayer lipids • Make sure all bonds are maintained after equilibration, otherwise results will be off • Building the membrane may cause chain overlap • Internal checks for ring penetration by chain (chain through cholesterol or amino acid rings) • If these exist, then you need to rebuild the system!

  24. Simulation Snapshot ERG, YOPS, DYPC and water

  25. Multilayer System/Periodic Boundary Conditions

  26. ST-Analyzer • Web-based Interface for Simulation Trajectory Analysis1 Dr. Im (KU) • Allows for easy collection of data on membranes and proteins • Can be setup to on a workstation or a cluster environment with batch submission of analysis 1Jeong et al. J. Comput. Chem. 35: 957 (2014) .

  27. Membrane Area per Lipid • Equilibrated? Thermal Equilibration NPT-Production • Things to consider with membrane equilibration • Possible transient stability in volume/surface area • Must run for long periods of time: 10-30ns for simple single lipids and 50-300 ns (or longer) for complex mixtures (General rules of thumb without phase transitions) • Current run suggest longer times (beyond 20ns) are needed

  28. Membrane Area per Lipid: Examples • Equilibration is slower during changes in phase (La to gel-like phase) • 100ns or greater can be required to obtain a fully equilibrated bilayer even for single lipids DPPC at 200 ns (303K) z

  29. Lipid Bilayer Structure: Simulation • Molecular Dynamics • Simulations can easily obtain density profiles Bulk Water Headgroup Dz=0.1Å Count number electrons/bin and average Hydrophobic/Chain 1Jo, Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) . 2Jo, Lim, Klauda & Im. Biophys. J.97: 50 (2009). SM=Structural Model

  30. Structural Models EDP, A F(q) Fourier Reconstruction Only Total EDP & Fourier Wiggles Lipid Bilayer Structure: Experiment • Form Factors F(q) • F(q) is transformed into real space to get structural properties HB Fit to Exp. F(q) for the DMPC Bilayer1 1Kučerka, N. et al. Biophys. J.88: 2626 (2005).

  31. Development of H2 Structural Model • Density Profile • Component electron density used to guide model development Asim=60.7 Å2 Black & Blue: Simulation Red: H2 fit to density • New Hybrid Model (H2)1 • Consists of five physical components 1Klauda, J.B. et al. Biophys. J.90: 2796 (2006). BC=water+choline CG=carbonyl-glycerol chol = choline

  32. Comparing to X-ray/Neutron Scattering • Model Free Comparison • Form Factors (symmetric bilayers, where D-repeat spacing) fa(q): atomic form factors (depend on q for X-ray (not neutron data)) na(z): atomic number distribution (density of atoms of each type) rW: scattering density of water (solvent) • Method to use and program • Calculate atomic densities (na(z)) (in CHARMM or ST-Analyzer) and use SIMtoEXP program1 • Load in atomic density to SIMtoEXP program to get F(q) 1Kučerka et al. J. Membr. Biol.235: 43 (2010).

  33. Examples for C36 POPC Form Factors & Density Profiles1 • Excellent agreement between experiment and MD simulation for form factors. • Can easily obtain density profiles of groups within the bilayer 1Zhuang, Makover, Im & Klauda. BBA-Biomemb.Submitted (2014).

  34. 0 Bond Vibrations 1ps Hydrogen Bonds Internal Isomerization (C-H, P-H, etc.) and Wobbling3 1ns 10ns Lipid Axial Rotation3 Lateral Diffusion2 1ms Vesicle Rotation Overview of Lipid Dynamics and Internal Structure • Range of Lipid Motions Isomerization Wobbling in a Cone Model1 Axial Rotation Wobbling • Internal Structure • Orientation of bonds • Angle of bond vectors with respect to bilayer normal • Methods to obtain these Quantities • NMR • Molecular dynamics 1Pastor, R.W. et al. Accounts. Chem. Res.35: 438 (2002). 2Klauda et al. J. Chem. Phys.125: 144710 (2006). 3Klauda et al. Biophys. J. 94: 3074 (2008).

  35. NMR Background • Nuclear Magnetic Resonance (NMR) • Magnetic nuclei (13C/31P) respond to an oscillating magnetic field • Spin-lattice relaxation rates (R1) • Dipolar term: nuclear spin interaction between neighbors Spectral Density Reorientational Correlation Function Unit vector between P and its neighboring H 2nd Order Legendre Polynomial

  36. NMR Background • Nuclear Magnetic Resonance (NMR) • Magnetic nuclei (13C/31P) respond to an oscillating magnetic field • Spin-lattice relaxation rates (R1) • Chemical Shift Anisotropy: on nucleus • Based on sold-state measurements on lipids1 • Major principal axis1 (s33) is used to obtain the spectral density • The asymmetry in principal axis is accounted for by h • Field dependence • Dipolar contribution is important at low field • CSA is important at high field 1Herzfel, J. et al. Biochem.17: 2711 (1978).

  37. Deuterium NMR • Deuterium NMR • Order parameters • qi is the angle of a C-D vector with the bilayer normal (usually the z axis) • Internal structure of lipids • How obtain this via MD Simulations • Calculate the C-H angle (MD simulations without deuterium) • Do this for every carbon • Simple trig calculation

  38. Deuterium NMR: Examples SCD’s for POPC and DLPC1 • Higher values indicate more order (lower disorder) • Double bond adds a kink to the chain and more disorder • SCDs depend on temperature and agree fairly well with experimental data 1Zhuang, Makover, Im & Klauda. BBA-Biomemb.Submitted (2014).

  39. Summary • There are many lipid types that can exist in biology and each has it own function to the cell • Lipid diversity in biology can vary between different head groups to chain types • Lipidsfrom in vivo membranes are diverse between organisms and organelles with a single organism • There are several options for lipid force fields to run MD simulations (all-atom, united-atom and coarse-grained) • CHARMM36 lipid force field has been parameterized and agrees well with a multitude of experiments (dynamical and structural) for all regions of the lipid • CHARMM-GUI allows for easy building of simple and complex membranes with/without proteins • ST-Analyzer allows for easy access and analysis of simulation trajectories from many different simulation program platforms • A key test for bilayer equilibration is the surface area per lipid • Structural (SCDand density profiles) and dynamical properties (diffusion and relaxation rates) can easily be obtained with proper analysis of MD simulations

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