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

1Fahy et al. J. Lipid. Res. 46: 839 (2005).

Complex biomolecules • Contain a fatty acid chains and head group

Classified into 8 categories1

Modified(Fig. 1)1

Fatty acyls

Glycerolphospholipids

Sterol Lipids

Saccharolipids

Glycerolipids

Sphingolipids

Phenol lipids

Polyketides

Glycerophospholipids

1Fahy et al. J. Lipid. Res. 46: 839 (2005).

Some Common Subclasses of GP lipids1

(Modified Fig. 4)1

Phosphocholines Phosphonocholines

Phosphoethanolamines Phosphonoethanolamines

Phosphoserines Phosphoglycerols

Phosphoglycerophosphates Phosphoinsitols

Phosphoinsitolmonophosphates Phosphates

Lipid/Cholesterol Bilayer

Membrane Proteins

Periplasm

Cytoplasmic Membrane

Cytoplasm

Channel Proteins

Membranes in Single Cell Organisms

• Plasma membrane1 contains many constituents

E. coli

1Fig. 1b from Engelman, D.M. Nature. 438: 578 (2005).2Fig. 1a from McMahon, H.T. et al. Nature. 438: 590 (2005).

Cell Membranes2

• Membranes are located throughout the cell interior

Diversity of Lipid Types in Organisms Yeast (Saccharomyces cerevisiae)1

• Mixture of fully saturated and unsaturated chains

1Daum G. et al. Yeast. 15: 601 (1999). 2Wylie, J.L. et al. J. Bact. 179: 7233 (1997).3Shokri, 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)

Membrane Composition within Cell Distribution of phospholipids (PL) vs. sterols1

1van 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

Force Fields Biomolecular Force Field (CHARMM)

· Many terms to describe intra- and intermolecular interactions

• CHARMM Family: CHARMM27r and CHARMM36 (C27r1 and C362)

jipairsnonbonded ijD

ji

jipairsnonbonded ij

ij

ij

ijij

dihedrals jjjj

improperim

crossUB

anglesbondsb

rqq

rR

rR

nK

KrrKKbbKRV

,,

6

min,

12

min,,

UB

203,13,1

20

20

cos(1

2cos1)ˆ(

All-atom Lipid Force Fields

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).

• AMBER Family: GAFFlipid3 and Lipid144

• Stockholm Lipids (Amber-compatible): Slipid5

AMBER Lipids Summary of Lipid14 FF1 Results (NPT Ensemble)

· Generally good agreement with experiment (slight tendency to underestimate)

1Dickson 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

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

Surface Area/lipid [Å2]

Deuterium Order Parameters

(Fig. 71)

· 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

Stockholm Lipids (Slipids) Summary of Slipids1-3 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 lipids3

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


Deuterium Order Parameters

(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

1Jämbeck & Lyubartsev. JPCB. 116: 3164 (2012). 2Jämbeck & Lyubartsev. J. Chem. Theory Comput. 8: 2938 (2012).3Jämbeck & Lyubartsev. J. Chem. Theory Comput. 9: 774 (2013).

(Fig. 22)

Biomolecular Force Field (CHARMM)

· Many terms to describe intra- and intermolecular interactions


ji

jipairsnonbonded ij

ij

ij

ijij

dihedrals jjjj

improperim

crossUB

anglesbondsb

rqq

rR

rR

nK

KrrKKbbKRV

,,

6

min,

12

min,,

UB

203,13,1

20

20

cos(1

2cos1)ˆ(

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). 2Lee, Tran, Allsopp, Lim, Henin & Klauda. JPCB 118: 547 (2014).4Berger, O. et al. BJ. 72: 2002 (1997). 4Marrink et al. JPCB. 111: 7812 (2007). 5Shinoda, DeVane, & Klein. JPCB. 114: 6836 (2010).

Force Fields Continued

1Klauda, J.B. et al. BJ. 90: 2796 (2006).2Klauda, J.B. et al. JPCB. 111: 4393 (2007).

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

Issues with the CHARMM27r FF

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 -- ~0-5

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

1Vorobyov, 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

Dipole QM C27r C36

X/Y Ratio 1.48 -7.83 1.52

Total 1.65 2.40 1.52

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

Modification of CHARMM Charges

Small Molecule Models of DPPC

Dihedral Modifications


ji

jipairsnonbonded ij

ij

ij

ijij

dihedrals jjjj

anglesbondsb

rqq

rR

rR

nKKbbKRV

,,

6

min,

12

min,

,2

02

0 cos(1)ˆ(

QM of bilayers (Alex MacKerell)

Fits to QM of small molecules

1Klauda et al. JPCB. 114: 7830 (2010).

Glycerol FF Adjustments• Adjust the g1 torsion

Dihedral Modifications: CHARMM364

g1b1

2

• Issues fitting the 4 and b1 torsions

MP2/6-31g(d): 648 Energy Points

kcal/mol

1Klauda et al. JPCB. 114: 7830 (2010).

DPPC SCD Targets• MD simulations of the DPPC bilayer with an intermediate FF were used to empirically

fit 2, 4, and b1 torsions.

Empirical Fits of Torsions (C36)

• Populations of trans and gauche conformations of these torsions were optimized

G+ T G-

2 18% 36% 45%

4 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).

Torsional surface scans from 20 ns MD simulations

Empirical Fits of Torsions (C36)

1Klauda et al. JPCB. 114: 7830 (2010).

Deuterium Order Parameters (SCD): NPAT/NPT1 vs. Experiment2

DPPC Bilayer and C36

NPATA=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).

5.0cos5.1 CH2

CD S

Density Profiles & Form Factors Compared to Experiment1

DPPC Bilayer

1Kučerka, N. et al. BJ. 95: 2356 (2008).

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

CHARMM36 Lipids Initial Parameterization with PC & PE lipids

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).

• Lipids with polyunsaturated chains2

• Branched and cyclic-containing chains (important for certain bacteria)3,4

• Sterols (cholesterol, oxysterols, ergosterol)5

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


Additional Lipids

a323Kb303Kc310K

DAPC

• Other lipid parameters on the way: PI, PIP, SM, and CER

• Various published parameters: PS, PG, PA and Cardiolipin

CHARMM-GUI

1Jo, Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) .2Jo, Lim, Klauda & Im. Biophys. J. 97: 50 (2009).

CHARMM-GUI.org – Membrane Builder1,2

• 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)

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)

CHARMM-GUI


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

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!

Simulation Snapshot

ERG, YOPS, DYPC and water

Multilayer System/Periodic Boundary Conditions

ST-Analyzer Web-based Interface for Simulation Trajectory Analysis1

• Allows for easy collection of data on membranes and proteins

1Jeong 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

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 50-300 ns (or

longer) for complex mixtures (General rules of thumb without phase transitions)· Current run suggest longer times (beyond 20ns) are needed

Thermal Equilibration NPT-Production

Membrane Area per Lipid: Examples

DPPC at 200 ns (303K)

z

• 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

Lipid Bilayer Structure: Simulation Molecular Dynamics

• Simulations can easily obtain density profiles

Dz=0.1ÅCount number electrons/binand average

SM=Structural Model

Headgroup

Hydrophobic/Chain

Bulk Water


Lipid Bilayer Structure: Experiment

1Kučerka, 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)EDP, A

Only Total EDP & Fourier Wiggles

Structural Models

Fourier Reconstruction

HB Fit to Exp. F(q) for the DMPC Bilayer1

Development of H2 Structural Model Density Profile

• Component electron density used to guide model development

BC=water+choline CG=carbonyl-glycerolchol = choline

New Hybrid Model (H2)1

• Consists of five physical components

BCCHCGMPH2

2zzzzzz

MMCHCHHCCHCH ,0,98,,3222

zGrDzpCz C

1Klauda, J.B. et al. Biophys. J. 90: 2796 (2006).

Black & Blue: SimulationRed: H2 fit to density

Asim=60.7 Å2

Comparing to X-ray/Neutron Scattering Model Free Comparison

• Form Factors (symmetric bilayers, where D-repeat spacing)

1Kučerka et al. J. Membr. Biol. 235: 43 (2010).

• Method to use and program

2/

2/sincos

D

D zzWzz dzzqizqznqfqFa

aa

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)

W: scattering density of water (solvent)

· 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)

Examples for C36

1Zhuang, Makover, Im & Klauda. BBA-Biomemb. Submitted (2014).

0 0.2 0.4 0.6 0.80

0.5

1

1.5

2

2.5

q [1/Å]

|F(q

)| [

e/Å

2 ]

20°Ca XRaySIM

0 0.2 0.4 0.6 0.80

0.5

1

1.5

2

2.5

q [1/Å]

|F(q

)| [

e/Å

2 ]

30°Cb XRayULV

XRayORI

SIM

0 0.2 0.4 0.6 0.80

0.5

1

1.5

2

2.5

q [1/Å]

|F(q

)| [

e/Å

2 ]

40°Cc XRaySIM

0 0.2 0.4 0.6 0.80

0.5

1

1.5

2

2.5

q [1/Å]

|F(q

)| [

e/Å

2 ]

50°Cd XRaySIM

0 0.2 0.4 0.6 0.80

0.5

1

1.5

2

2.5

q [1/Å]

|F(q

)| [

e/Å

2 ]

60°Ce XRaySIM

POPC Form Factors & Density Profiles1

0 5 10 15 20 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

z [Å]ED

[e/Å

3 ]

d POPCTotalWaterCholinePhosphateGlycerolCarbonylCH2CHCH3

· Excellent agreement between experiment and MD simulation for form factors.

· Can easily obtain density profiles of groups within the bilayer

Overview of Lipid Dynamics and Internal Structure Range of Lipid Motions

Internal Structure• Orientation of bonds

0

1ps

1ns

10ns

1ms

Bond Vibrations

Hydrogen Bonds

Internal Isomerization (C-H, P-H, etc.)and Wobbling3

Lipid Axial Rotation3

Lateral Diffusion2

Vesicle Rotation

Wobbling in a Cone Model1Isomerization

Axial Rotation

Wobbling

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).

• Angle of bond vectors with respect to bilayer normal

Methods to obtain these Quantities• NMR• Molecular dynamics

Nuclear Magnetic Resonance (NMR)NMR Background

)()( 111 CSARdipolarRR

• Magnetic nuclei (13C/31P) respond to an oscillating magnetic field

• Spin-lattice relaxation rates (R1)

• Dipolar term: nuclear spin interaction between neighbors

)(6)(3)(14

1.0)(2

3

2

01 PHPPH

HP

HP JJJr

dipolarR mgg

0 2 )cos()()( dtttCJ

C2 t P2 ˆ m(0)ˆ m(t)

Spectral Density

Reorientational Correlation Function

2nd Order Legendre Polynomial

Unit vector between P and its neighboring H

Nuclear Magnetic Resonance (NMR)NMR Background

)()( 111 CSARdipolarRR

• Magnetic nuclei (13C/31P) respond to an oscillating magnetic field

• Spin-lattice relaxation rates (R1)

• Chemical Shift Anisotropy: on nucleus

3/1)()( 222152

1 PCSAP JCSAR

· Based on sold-state measurements on lipids1

1Herzfel, J. et al. Biochem. 17: 2711 (1978).

· Major principal axis1 (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

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

Deuterium NMR: Examples

2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

Carbon Number

S CD

POPC sn-2

a

2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

Carbon NumberS CD

POPC sn-1

b

10°C20°C30°C40°C50°C60°C

2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

Carbon Number

S CD

POPC sn-2

c SIM 30°CNMR 27°C

2 4 6 8 10 120

0.05

0.1

0.15

0.2

Carbon Number

S CD

DLPC sn-2

a

2 4 6 8 10 120

0.05

0.1

0.15

0.2

Carbon Number

S CD

DLPC sn-1

b

20°C30°C40°C50°C60°C

2 4 6 8 10 120

0.05

0.1

0.15

0.2

Carbon Number

S CD

DLPC sn-2

c

SIM 20°CNMR 20°CSIM 40°CNMR 40°C

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).

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

lipid bilayer simulations: force fields, simulation and analysis

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