Presentation on theme: "Lipid Bilayer Simulations: Force fields, Simulation and Analysis"— Presentation transcript:
1 Lipid Bilayer Simulations: Force fields, Simulation and Analysis 16:12Lipid Bilayer Simulations: Force fields, Simulation and AnalysisJeffery B. KlaudaModel Yeast MembraneChemical Structure of Lipids
2 Lipids Complex biomolecules Classified into 8 categories1 16:12LipidsComplex biomoleculesContain a fatty acid chains and head groupClassified into 8 categories1Fatty acylsGlycerolipidsGlycerolphospholipidsSphingolipidsPhenol lipidsSterol LipidsModified(Fig. 1)1SaccharolipidsPolyketides1Fahy et al. J. Lipid. Res. 46: 839 (2005).
3 Glycerophospholipids 16:12GlycerophospholipidsSome Common Subclasses of GP lipids1PhosphocholinesPhosphonocholinesPhosphoethanolaminesPhosphonoethanolaminesPhosphoserinesPhosphoglycerolsPhosphoglycerophosphatesPhosphoinsitols(Modified Fig. 4)1PhosphoinsitolmonophosphatesPhosphates1Fahy et al. J. Lipid. Res. 46: 839 (2005).
4 Membranes in Single Cell Organisms 16:12Membranes in Single Cell OrganismsLipid/Cholesterol BilayerMembrane ProteinsPeriplasmCytoplasmicMembraneCytoplasmChannel ProteinsE. coliPlasma membrane1 contains many constituentsMembranes are located throughout the cell interiorCell Membranes21Fig. 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 16:12Diversity of Lipid Types in OrganismsYeast (Saccharomyces cerevisiae)1Mixture of fully saturated and unsaturated chainsMixture of charged and zwitterionic head groups and typically 10-20% sterolsCompositions depend on strain of yeastChlamydia (chlamydia trachomatis)2Exists 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 groups20-30% sterolsE. coli (Escherichia coli)3Mixture of fully saturated and unsaturated chainsFatty acid chains can contain cyclic moieties (cyclopropane)Zwitterionic (~80% PE) and anionic (~20 %PG) head groupsLimited to no sterols1Daum 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 16:12Membrane Composition within CellDistribution of phospholipids (PL) vs. sterols1Mammals in dark blue and yeast in light bluePlasma membrane (PM) contains a significant amount of sterol (largest of all organelles)Mammalian PM contain more sterol than yeastEndoplasmic reticulum (ER) manufactures sterol, but levels are lowLarge diversity of phospholipids between mammals and yeast and within a cell1van Meer, G. et al. Nature Rev. Mol. Cell. Bio. 9: 112 (2008).
7 Force Fields Biomolecular Force Field (CHARMM) 16:12Force FieldsBiomolecular Force Field (CHARMM)Many terms to describe intra- and intermolecular interactionsAll-atom Lipid Force FieldsCHARMM Family: CHARMM27r and CHARMM36 (C27r1 and C362)AMBER Family: GAFFlipid3 and Lipid144Stockholm Lipids (Amber-compatible): Slipid51Klauda, 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) 16:12AMBER LipidsSummary of Lipid14 FF1 Results (NPT Ensemble)Surface Area/lipid [Å2]DPPCDMPCDLPCDOPCPOPCPOPEMD62.0±0.359.7±0.763.0±0.269.0±0.365.6±0.555.5±0.2Exp63.0±1.060.6±0.563.2±0.567.4±1.068.3±1.5~60Generally good agreement with experiment (slight tendency to underestimate)Deuterium Order ParametersOverall excellent agreement with NMR SCDsPOPE SCDs of the saturated chain are somewhat high, which may indicate that the SA/lipid is too lowDecent splitting for the C2 positionUnclear 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 FF1Dickson et al. J. Chem. Theory Comput. 10: 865 (2014).
9 Stockholm Lipids (Slipids) 16:12Stockholm Lipids (Slipids)Summary of Slipids1-3 Results (NPT Ensemble)Surface Area/lipid [Å2]DPPCDMPCDLPCDOPCPOPCPOPEMD62.6±0.560.8±0.562.4±0.468.0±0.564.6±0.456.3±0.4Exp63.0±1.060.6±0.563.2±0.567.4±1.068.3±1.5~60Generally good agreement with experiment (slight tendency to underestimate)Deuterium Order Parameters(Fig. 22)(Fig. 51)Overall excellent agreement with NMR SCDsBetter POPE SCDs compared to Lipid14Decent splitting for the C2 positionUnclear if the head group order parameters are in agreement with experimentProcedure similar to AMBER FF optimization (RESP charges in gas phase)Extensions to PS, PG and SM lipids31Jämbeck & 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 16:12Force Fields ContinuedBiomolecular Force Field (CHARMM)Many terms to describe intra- and intermolecular interactionsUnited Atom/Coarse-grained Lipid Force FieldsUnited atom: C27-UA(acyl)1, C36-UA2 and GROMOS3Coarse-grained: MARTINI4 and Shinoda/DeVane/Klein51Henin, 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 16:12Issues with the CHARMM27r FFSurface TensionTo maintain good agreement with density profiles and SCD, NPAT simulations at the experimental area are needed for MD simulations with C27rFinite size effects may result in a non-zero surface tension,1 but C27r values are too high2Surface Tension in dyn/cmLR LJNo LR-LJExp. EstimateDPPC bilayer (64 Å2/lipid, 323K)19.716.8~0-5DMPC bilayer (60.7 Å2/lipid, 303K)19.8--Freezing or Phase Change with NPTFreezing of aliphatic chains at T > TbIssue with lipids that have 1-2 fully saturated chainsProblematic when surface areas are not available for lipids and their mixtures1Klauda, J.B. et al. BJ. 90: 2796 (2006).2Klauda, J.B. et al. JPCB. 111: 4393 (2007).
12 Modification of CHARMM Charges 16:12Modification of CHARMM ChargesCharge/LJ ModificationLooked at small molecules and DPPC bilayer charges using semi-empirical AM1Increase in polarization occurred going from the gas phase to realistic bilayerTherefore, increasing the lipid charges in the glycerol region is justifiedAdjusted charges/LJDipole moment of methylacetate (debye)DipoleQMC27rC36X/Y Ratio1.48-7.831.52Total1.652.40Adjustments 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 optimizations11Vorobyov, I, et al. J. Chem. Theory and Comp. 3: 1120 (2007).
13 Dihedral Modifications 16:12Dihedral ModificationsFits to QM of small moleculesQM of bilayers(Alex MacKerell)Small Molecule Models of DPPC1Klauda et al. JPCB. 114: 7830 (2010).
14 MP2/6-31g(d): 648 Energy Points 16:12Dihedral Modifications: CHARMM36Glycerol FF Adjustmentsq4g1b1q2Adjust the g1 torsionMP2/6-31g(d): 648 Energy Pointskcal/molIssues fitting the q4 and b1 torsions1Klauda et al. JPCB. 114: 7830 (2010).
15 Empirical Fits of Torsions (C36) 16:12Empirical Fits of Torsions (C36)DPPC SCD TargetsMD 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 optimizedG+TG-q218%36%45%q466%3%31%b156%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) 16:12Empirical Fits of Torsions (C36)Torsional surface scans from 20 ns MD simulations1Klauda et al. JPCB. 114: 7830 (2010).
17 16:12DPPC Bilayer and C36Deuterium Order Parameters (SCD): NPAT/NPT1 vs. Experiment2NPATA=64Å2NPTExcellent 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 16:12DPPC BilayerDensity Profiles & Form Factors Compared to Experiment1Aexp=63±1Å2Good agreement with the experimental form factors, F(q)The methyl & methylene density is improvedNPT captures the overall and component densities correctly1Kučerka, N. et al. BJ. 95: 2356 (2008).
19 CHARMM36 Lipids Initial Parameterization with PC & PE lipids 16:12CHARMM36 LipidsInitial Parameterization with PC & PE lipidsSurface Area/lipid [Å2]DPPCaDMPCbDLPCbDOPCbPOPCbPOPEcMD62.9±0.360.8±0.264.4±0.369.0±0.364.7±0.259.2±0.3Exp63.0±1.060.6±0.563.2±0.567.4±1.068.3±1.5~60a323Kb303Kc310KAdditional LipidsLipids with polyunsaturated chains2DAPCBranched and cyclic-containing chains (important for certain bacteria)3,4Sterols (cholesterol, oxysterols, ergosterol)5Various published parameters: PS, PG, PA and CardiolipinOther lipid parameters on the way: PI, PIP, SM, and CER1Klauda 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 16:12CHARMM-GUICHARMM-GUI.org – Membrane Builder1,2Dr. Im (KU)Allows for easy building of lipid membranesSelect from 140+ lipids and any mixture from these lipidsBuilds membranes and provides rigorously tested equilibration inputs for CHARMM and NAMD simulationsMembrane proteins can be easily incorporated into the bilayerFreely available to any researcher1Jo, 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 16:12CHARMM-GUICHARMM-GUI.org – Membrane Builder1,2Can easily build heterogeneous bilayersSpecify water hydration in three ways (defaults are safe for fully hydrated bilayers)Can choose ratio or number of lipids for each leafletReported surface area per lipid is based on simulations with a pure membraneFurther steps ask for ion concentration, ring penetration checks, ensemble and temperatureAt 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 16:12CHARMM-GUIOutput Initial Structure of BilayerWater 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 bilayerChains can tangle and careful equilibration is requiredRestraints During EquilibrationWater away from hydrophobic coreHead group and tails to appropriate regionsDouble bonds in their respective cis or trans conformationRing 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 16:12MD Simulations of MembranesCaveats of CHARMM-GUI with membranesMembrane surface area/volumePrimarily based on SA from pure lipid bilayers with C36 force field at 303KSome lipids have high gel transition temperatures >303K and values are based on higher tempsThis can result in poor initial guess for mixed lipid systems, especially with sterolsIf the SA is known or can be estimated a priori then this is preferredMembrane equilibrationAlthough we have tested this extensively there might be some issuesPay careful attention to your bilayer lipidsMake sure all bonds are maintained after equilibration, otherwise results will be offBuilding the membrane may cause chain overlapInternal checks for ring penetration by chain (chain through cholesterol or amino acid rings)If these exist, then you need to rebuild the system!
24 16:12Simulation SnapshotERG, YOPS, DYPC and water
26 ST-Analyzer Web-based Interface for Simulation Trajectory Analysis1 16:12ST-AnalyzerWeb-based Interface for Simulation Trajectory Analysis1Dr. Im (KU)Allows for easy collection of data on membranes and proteinsCan be setup to on a workstation or a cluster environment with batch submission of analysis1Jeong et al. J. Comput. Chem. 35: 957 (2014) .
27 Membrane Area per Lipid 16:12Membrane Area per LipidEquilibrated?Thermal EquilibrationNPT-ProductionThings to consider with membrane equilibrationPossible transient stability in volume/surface areaMust 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 16:12Membrane Area per Lipid: ExamplesEquilibration 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 lipidsDPPC at 200 ns (303K)z
29 Lipid Bilayer Structure: Simulation 16:12Lipid Bilayer Structure: SimulationMolecular DynamicsSimulations can easily obtain density profilesBulk WaterHeadgroupDz=0.1ÅCount numberelectrons/binand averageHydrophobic/Chain1Jo, 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 16:12Lipid Bilayer Structure: ExperimentForm Factors F(q)F(q) is transformed into real space to get structural propertiesF(q)EDP, AOnly Total EDP & Fourier WigglesStructural ModelsFourier ReconstructionHB Fit to Exp. F(q) for the DMPC Bilayer11Kučerka, N. et al. Biophys. J. 88: 2626 (2005).
31 Development of H2 Structural Model 16:12Development of H2 Structural ModelDensity ProfileComponent electron density used to guide model developmentAsim=60.7 Å2Black & Blue: SimulationRed: H2 fit to densityNew Hybrid Model (H2)1Consists of five physical components1Klauda, J.B. et al. Biophys. J. 90: 2796 (2006).BC=water+choline CG=carbonyl-glycerolchol = choline
32 Comparing to X-ray/Neutron Scattering 16:12Comparing to X-ray/Neutron ScatteringModel Free ComparisonForm 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 programCalculate atomic densities (na(z)) (in CHARMM or ST-Analyzer) and use SIMtoEXP program1Load 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 16:12Examples for C36POPC Form Factors & Density Profiles1Excellent agreement between experiment and MD simulation for form factors.Can easily obtain density profiles of groups within the bilayer1Zhuang, Makover, Im & Klauda. BBA-Biomemb. Submitted (2014).
34 Wobbling in a Cone Model1 16:12Overview of Lipid Dynamics and Internal StructureRange of Lipid MotionsIsomerizationWobbling in a Cone Model11ps1ns10ns1msBond VibrationsHydrogen BondsInternal Isomerization (C-H, P-H, etc.)and Wobbling3Lipid Axial Rotation3Lateral Diffusion2Vesicle RotationAxialRotationWobblingInternal StructureOrientation of bondsAngle of bond vectors with respect to bilayer normalMethods to obtain these QuantitiesNMRMolecular dynamics1Pastor, 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) 16:12NMR BackgroundNuclear Magnetic Resonance (NMR)Magnetic nuclei (13C/31P) respond to an oscillating magnetic fieldSpin-lattice relaxation rates (R1)Dipolar term: nuclear spin interaction between neighborsSpectral DensityReorientationalCorrelation Function2nd Order LegendrePolynomialUnit vector between P and itsneighboring H
36 NMR Background Nuclear Magnetic Resonance (NMR) 16:12NMR BackgroundNuclear Magnetic Resonance (NMR)Magnetic nuclei (13C/31P) respond to an oscillating magnetic fieldSpin-lattice relaxation rates (R1)Chemical Shift Anisotropy: on nucleusBased on sold-state measurements on lipids1Major principal axis1 (s33) is used to obtain the spectral densityThe asymmetry in principal axis is accounted for by hField dependenceDipolar contribution is important at low fieldCSA is important at high field1Herzfel, J. et al. Biochem. 17: 2711 (1978).
37 Deuterium NMR Deuterium NMR Order parameters 16:12Deuterium NMRDeuterium NMROrder parametersqi is the angle of a C-D vector with the bilayer normal (usually the z axis)Internal structure of lipidsHow obtain this via MD SimulationsCalculate the C-H angle (MD simulations without deuterium)Do this for every carbonSimple trig calculation
38 Deuterium NMR: Examples 16:12Deuterium NMR: ExamplesSCD’s for POPC and DLPC1Higher values indicate more order (lower disorder)Double bond adds a kink to the chain and more disorderSCDs depend on temperature and agree fairly well with experimental data1Zhuang, Makover, Im & Klauda. BBA-Biomemb. Submitted (2014).
39 16:12SummaryThere are many lipid types that can exist in biology and each has it own function to the cellLipid diversity in biology can vary between different head groups to chain typesLipids from in vivo membranes are diverse between organisms and organelles with a single organismThere 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 lipidCHARMM-GUI allows for easy building of simple and complex membranes with/without proteinsST-Analyzer allows for easy access and analysis of simulation trajectories from many different simulation program platformsA key test for bilayer equilibration is the surface area per lipidStructural (SCD and density profiles) and dynamical properties (diffusion and relaxation rates) can easily be obtained with proper analysis of MD simulations