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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
16:12 Lipid Bilayer Simulations: Force fields, Simulation and Analysis Jeffery B. Klauda Model Yeast Membrane Chemical Structure of Lipids

2 Lipids Complex biomolecules Classified into 8 categories1
16:12 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
16:12 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 Membranes in Single Cell Organisms
16:12 Membranes in Single Cell Organisms Lipid/Cholesterol Bilayer Membrane Proteins Periplasm Cytoplasmic Membrane Cytoplasm Channel Proteins 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
16:12 Diversity of Lipid Types in Organisms Yeast (Saccharomyces cerevisiae)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 (chlamydia trachomatis)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) Wylie, J.L. et al. J. Bact. 179: 7233 (1997). 3Shokri, A. & G. Larsson. Microbial Cell Factories. 3: 9 (2004) .

6 Membrane Composition within Cell
16:12 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)
16:12 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)
16:12 AMBER Lipids Summary of Lipid14 FF1 Results (NPT Ensemble) Surface Area/lipid [Å2] DPPC DMPC DLPC DOPC POPC POPE MD 62.0±0.3 59.7±0.7 63.0±0.2 69.0±0.3 65.6±0.5 55.5±0.2 Exp 63.0±1.0 60.6±0.5 63.2±0.5 67.4±1.0 68.3±1.5 ~60 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)
16:12 Stockholm Lipids (Slipids) Summary of Slipids1-3 Results (NPT Ensemble) Surface Area/lipid [Å2] DPPC DMPC DLPC DOPC POPC POPE MD 62.6±0.5 60.8±0.5 62.4±0.4 68.0±0.5 64.6±0.4 56.3±0.4 Exp 63.0±1.0 60.6±0.5 63.2±0.5 67.4±1.0 68.3±1.5 ~60 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) Jämbeck & Lyubartsev. J. Chem. Theory Comput. 8: 2938 (2012). 3Jämbeck & Lyubartsev. J. Chem. Theory Comput. 9: 774 (2013).

10 Force Fields Continued
16:12 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: MARTINI4 and Shinoda/DeVane/Klein5 1Henin, Shinoda & Klein. JPCB. 112: 7008 (2008) Lee, Tran, Allsopp, Lim, Henin & Klauda. JPCB 118: 547 (2014). 4Berger, O. et al. BJ. 72: 2002 (1997) Marrink et al. JPCB. 111: 7812 (2007). 5Shinoda, DeVane, & Klein. JPCB. 114: 6836 (2010).

11 Issues with the CHARMM27r FF
16:12 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 LR LJ No LR-LJ Exp. Estimate DPPC bilayer (64 Å2/lipid, 323K) 19.7 16.8 ~0-5 DMPC bilayer (60.7 Å2/lipid, 303K) 19.8 -- 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
16:12 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) Dipole QM C27r C36 X/Y Ratio 1.48 -7.83 1.52 Total 1.65 2.40 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
16:12 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 MP2/6-31g(d): 648 Energy Points
16:12 Dihedral Modifications: CHARMM36 Glycerol FF Adjustments q4 g1 b1 q2 Adjust the g1 torsion MP2/6-31g(d): 648 Energy Points kcal/mol Issues fitting the q4 and b1 torsions 1Klauda et al. JPCB. 114: 7830 (2010).

15 Empirical Fits of Torsions (C36)
16:12 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 G+ T G- q2 18% 36% 45% q4 66% 3% 31% b1 56% 43% 1% 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)
16:12 Empirical Fits of Torsions (C36) Torsional surface scans from 20 ns MD simulations 1Klauda et al. JPCB. 114: 7830 (2010).

17 16:12 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
16:12 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
16:12 CHARMM36 Lipids Initial Parameterization with PC & PE lipids Surface Area/lipid [Å2] DPPCa DMPCb DLPCb DOPCb POPCb POPEc MD 62.9±0.3 60.8±0.2 64.4±0.3 69.0±0.3 64.7±0.2 59.2±0.3 Exp 63.0±1.0 60.6±0.5 63.2±0.5 67.4±1.0 68.3±1.5 ~60 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
16:12 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
16:12 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
16:12 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
16:12 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 16:12 Simulation Snapshot ERG, YOPS, DYPC and water

25 Multilayer System/Periodic Boundary Conditions
16:12 Multilayer System/Periodic Boundary Conditions

26 ST-Analyzer Web-based Interface for Simulation Trajectory Analysis1
16:12 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
16:12 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 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
16:12 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
16:12 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 HB Fit to Exp. F(q) for the DMPC Bilayer1
16:12 Lipid Bilayer Structure: Experiment Form Factors F(q) F(q) is transformed into real space to get structural properties F(q) EDP, A Only Total EDP & Fourier Wiggles Structural Models Fourier Reconstruction 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
16:12 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
16:12 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
16:12 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 Wobbling in a Cone Model1
16:12 Overview of Lipid Dynamics and Internal Structure Range of Lipid Motions Isomerization Wobbling in a Cone Model1 1ps 1ns 10ns 1ms Bond Vibrations Hydrogen Bonds Internal Isomerization (C-H, P-H, etc.) and Wobbling3 Lipid Axial Rotation3 Lateral Diffusion2 Vesicle Rotation 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: (2006). 3Klauda et al. Biophys. J. 94: 3074 (2008).

35 NMR Background Nuclear Magnetic Resonance (NMR)
16:12 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 2nd Order Legendre Polynomial Unit vector between P and its neighboring H

36 NMR Background Nuclear Magnetic Resonance (NMR)
16:12 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
16:12 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
16:12 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 16:12 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 Lipids from 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 (SCD and density profiles) and dynamical properties (diffusion and relaxation rates) can easily be obtained with proper analysis of MD simulations


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