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

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Presentation on theme: "Lipid Bilayer Simulations: Force fields, Simulation and Analysis Jeffery B. Klauda Model Yeast Membrane Chemical Structure of Lipids."— Presentation transcript:

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

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

3 Glycerophospholipids 1 Fahy et al. J. Lipid. Res. 46: 839 (2005).  Some Common Subclasses of GP lipids 1 (Modified Fig. 4) 1 PhosphocholinesPhosphonocholines PhosphoethanolaminesPhosphonoethanolamines PhosphoserinesPhosphoglycerols PhosphoglycerophosphatesPhosphoinsitols PhosphoinsitolmonophosphatesPhosphates

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

5 Diversity of Lipid Types in Organisms  Yeast (Saccharomyces cerevisiae) 1 Mixture of fully saturated and unsaturated chains 1 Daum G. et al. Yeast. 15: 601 (1999). 2 Wylie, J.L. et al. J. Bact. 179: 7233 (1997). 3 Shokri, A. & G. Larsson. Microbial Cell Factories. 3: 9 (2004). Mixture of charged and zwitterionic head groups and typically 10-20% sterols  Chlamydia (chlamydia trachomatis) 2 Compositions depend on strain of yeast 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  E. coli (Escherichia coli) 3 Mixture of fully saturated and unsaturated chains Zwitterionic (~80% PE) and anionic (~20 %PG) head groups 20-30% sterols Limited to no sterols Fatty acid chains can contain cyclic moieties (cyclopropane)

6 Membrane Composition within Cell  Distribution of phospholipids (PL) vs. sterols 1 1 van Meer, G. et al. Nature Rev. Mol. Cell. Bio. 9: 112 (2008). · 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

7 Force Fields  Biomolecular Force Field (CHARMM) · Many terms to describe intra- and intermolecular interactions CHARMM Family: CHARMM27r and CHARMM36 (C27r 1 and C36 2 )  All-atom Lipid Force Fields 1 Klauda, J. B. et al. JPCB. 109: 5300 (2005). 2 Klauda, J.B. et al. JPCB. 114: 7830 (2010). 3 Dickson et al. Soft Matter. 8: 9617 (2012). 4 Dickson et al. J. Chem. Theory Comput. 10: 865 (2014). 5 Jämbeck & Lyubartsev. JPCB. 116: 3164 (2012). AMBER Family: GAFFlipid 3 and Lipid14 4 Stockholm Lipids (Amber-compatible): Slipid 5

8 AMBER Lipids  Summary of Lipid14 FF 1 Results (NPT Ensemble) · Generally good agreement with experiment (slight tendency to underestimate) 1 Dickson et al. J. Chem. Theory Comput. 10: 865 (2014). Procedure follows typical rules for AMBER FF optimization (RESP charges in gas phase) Should only be used with the AMBER family of FF DPPCDMPCDLPCDOPCPOPCPOPE MD62.0± ± ± ± ± ±0.2 Exp63.0± ± ± ± ±1.5~60 Surface Area/lipid [Å 2 ] Deuterium Order Parameters (Fig. 7 1 ) · Overall excellent agreement with NMR S CD s · POPE S CD s 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

9 Stockholm Lipids (Slipids)  Summary of Slipids 1-3 Results (NPT Ensemble) · Generally good agreement with experiment (slight tendency to underestimate) Procedure similar to AMBER FF optimization (RESP charges in gas phase) Extensions to PS, PG and SM lipids 3 DPPCDMPCDLPCDOPCPOPCPOPE MD62.6± ± ± ± ± ±0.4 Exp63.0± ± ± ± ±1.5~60 Surface Area/lipid [Å 2 ] Deuterium Order Parameters (Fig. 5 1 ) · Overall excellent agreement with NMR S CD s · Better POPE S CD s compared to Lipid14 · Decent splitting for the C2 position · Unclear if the head group order parameters are in agreement with experiment 1 Jämbeck & Lyubartsev. JPCB. 116: 3164 (2012). 2 Jämbeck & Lyubartsev. J. Chem. Theory Comput. 8: 2938 (2012). 3 Jämbeck & Lyubartsev. J. Chem. Theory Comput. 9: 774 (2013). (Fig. 2 2 )

10  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-UA 2 and GROMOS 3 Coarse-grained: MARTINI 4 and Shinoda/DeVane/Klein 5 1 Henin, Shinoda & Klein. JPCB. 112: 7008 (2008). 2 Lee, Tran, Allsopp, Lim, Henin & Klauda. JPCB 118: 547 (2014). 4 Berger, O. et al. BJ. 72: 2002 (1997). 4 Marrink et al. JPCB. 111: 7812 (2007). 5 Shinoda, DeVane, & Klein. JPCB. 114: 6836 (2010). Force Fields Continued

11 1 Klauda, J.B. et al. BJ. 90: 2796 (2006). 2 Klauda, J.B. et al. JPCB. 111: 4393 (2007).  Surface Tension To maintain good agreement with density profiles and S CD, 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 high 2 Issues with the CHARMM27r FF LR LJNo LR-LJExp. Estimate DPPC bilayer (64 Å 2 /lipid, 323K) ~0-5 DMPC bilayer (60.7 Å 2 /lipid, 303K)19.8--~0-5 Surface Tension in dyn/cm  Freezing or Phase Change with NPT · Freezing of aliphatic chains at T > T b · Issue with lipids that have 1-2 fully saturated chains · Problematic when surface areas are not available for lipids and their mixtures

12 1 Vorobyov, I, et al. J. Chem. Theory and Comp. 3: 1120 (2007). · Increase in polarization occurred going from the gas phase to realistic bilayer  Charge/LJ Modification Looked at small molecules and DPPC bilayer charges using semi-empirical AM1 · Therefore, increasing the lipid charges in the glycerol region is justified Adjusted charges/LJ DipoleQMC27rC36 X/Y Ratio Total 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 optimizations 1 Modification of CHARMM Charges

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

14  Glycerol FF Adjustments Adjust the  1 torsion Dihedral Modifications: CHARMM36 44 11 11 22 Issues fitting the  4 and  1 torsions MP2/6-31g(d): 648 Energy Points kcal/mol 1 Klauda et al. JPCB. 114: 7830 (2010).

15  DPPC S CD Targets MD simulations of the DPPC bilayer with an intermediate FF were used to empirically fit  2,  4, and  1 torsions. Empirical Fits of Torsions (C36) Populations of trans and gauche conformations of these torsions were optimized G+G+ TG-G- 22 18%36%45% 44 66%3%31% 11 56%43%1% · The torsional potential was adjusted to bound the PMFs based on these fits and the optimal set was chosen. 1 Klauda et al. JPCB. 114: 7830 (2010).

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

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

18  Density Profiles & Form Factors Compared to Experiment 1 DPPC Bilayer 1 Kučerka, N. et al. BJ. 95: 2356 (2008). A exp =63±1Å 2 · Good agreement with the experimental form factors, F(q) · The methyl & methylene density is improved · NPT captures the overall and component densities correctly

19 CHARMM36 Lipids  Initial Parameterization with PC & PE lipids 1 Klauda et al. JPCB. 114: 7830 (2010). 2 Klauda et al. JPCB. 116: 9424 (2012). 3 Lim & Klauda. BBA: Biomemb. 1808: 323 (2011). 4 Pandit & Klauda. BBA: Biomemb. 1818: 1818 (2012). 5 Lim et al. JPCB. 116: 203 (2012). Lipids with polyunsaturated chains 2 Branched and cyclic-containing chains (important for certain bacteria) 3,4 Sterols (cholesterol, oxysterols, ergosterol) 5 DPPC a DMPC b DLPC b DOPC b POPC b POPE c MD62.9± ± ± ± ± ±0.3 Exp63.0± ± ± ± ±1.5~60 Surface Area/lipid [Å 2 ]  Additional Lipids a 323K b 303K c 310K DAPC Other lipid parameters on the way: PI, PIP, SM, and CER Various published parameters: PS, PG, PA and Cardiolipin

20 CHARMM-GUI 1 Jo, Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008). 2 Jo, Lim, Klauda & Im. Biophys. J. 97: 50 (2009).  CHARMM-GUI.org – Membrane Builder 1,2 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 Dr. Im (KU)

21 CHARMM-GUI 1 Jo, Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008). 2 Jo, Lim, Klauda & Im. Biophys. J. 97: 50 (2009).  CHARMM-GUI.org – Membrane Builder 1,2 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)

22 CHARMM-GUI 1 Jo, Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008). 2 Jo, Lim, Klauda & Im. Biophys. J. 97: 50 (2009).  Output Initial Structure of Bilayer 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)  Restraints During Equilibration 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

23  Caveats of CHARMM-GUI with membranes Membrane surface area/volume Membrane equilibration · 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 · 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 MD Simulations of Membranes · 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 · 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 Analysis 1 Allows for easy collection of data on membranes and proteins 1 Jeong et al. J. Comput. Chem. 35: 957 (2014). Dr. Im (KU) Can be setup to on a workstation or a cluster environment with batch submission of analysis

27 Membrane Area per Lipid  Equilibrated? 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 Thermal EquilibrationNPT-Production

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

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

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

31 Development of H2 Structural Model  Density Profile Component electron density used to guide model development BC=water+choline CG=carbonyl-glycerol chol = choline  New Hybrid Model (H2) 1 Consists of five physical components 1 Klauda, J.B. et al. Biophys. J. 90: 2796 (2006). Black & Blue: Simulation Red: H2 fit to density A sim =60.7 Å 2

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

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

34 Overview of Lipid Dynamics and Internal Structure  Range of Lipid Motions  Internal Structure Orientation of bonds 0 1ps 1ns 10ns 1s1s Bond Vibrations Hydrogen Bonds Internal Isomerization (C-H, P-H, etc.) and Wobbling 3 Lipid Axial Rotation 3 Lateral Diffusion 2 Vesicle Rotation Wobbling in a Cone Model 1 Isomerization Axial Rotation Wobbling 1 Pastor, R.W. et al. Accounts. Chem. Res. 35: 438 (2002). 2 Klauda et al. J. Chem. Phys. 125: (2006). 3 Klauda et al. Biophys. J. 94: 3074 (2008). Angle of bond vectors with respect to bilayer normal  Methods to obtain these Quantities NMR Molecular dynamics

35  Nuclear Magnetic Resonance (NMR) NMR Background Magnetic nuclei ( 13 C/ 31 P) respond to an oscillating magnetic field Spin-lattice relaxation rates (R 1 ) Dipolar term: nuclear spin interaction between neighbors Spectral Density Reorientational Correlation Function 2 nd Order Legendre Polynomial Unit vector between P and its neighboring H

36  Nuclear Magnetic Resonance (NMR) NMR Background Magnetic nuclei ( 13 C/ 31 P) respond to an oscillating magnetic field Spin-lattice relaxation rates (R 1 ) Chemical Shift Anisotropy: on nucleus · Based on sold-state measurements on lipids 1 1 Herzfel, J. et al. Biochem. 17: 2711 (1978). · Major principal axis 1 (  33 ) is used to obtain the spectral density · The asymmetry in principal axis is accounted for by  Field dependence · Dipolar contribution is important at low field · CSA is important at high field

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

38 Deuterium NMR: Examples S CD ’s for POPC and DLPC 1 · Higher values indicate more order (lower disorder) · Double bond adds a kink to the chain and more disorder · S CD s depend on temperature and agree fairly well with experimental data 1 Zhuang, 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 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 (S CD and density profiles) and dynamical properties (diffusion and relaxation rates) can easily be obtained with proper analysis of MD simulations


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