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 categories1
Modified
(Fig. 1)1
1Fahy
Fatty acyls
Glycerolipids
Glycerolphospholipids
Sphingolipids
Sterol Lipids
Phenol lipids
Saccharolipids
Polyketides
et al. J. Lipid. Res. 46: 839 (2005).
Glycerophospholipids
 Some Common Subclasses of GP lipids1
Phosphocholines
Phosphonocholines
Phosphoethanolamines
Phosphonoethanolamines
Phosphoserines
Phosphoglycerols
Phosphoglycerophosphates
Phosphoinsitols
(Modified Fig. 4)1
Phosphoinsitolmonophosphates
1Fahy
et al. J. Lipid. Res. 46: 839 (2005).
Phosphates
Membranes in Single Cell Organisms
Periplasm
Cytoplasmic
Membrane
Channel Proteins
Lipid/Cholesterol Bilayer
Membrane Proteins
Cytoplasm
E. coli
• Plasma membrane1 contains many constituents
• Membranes are located throughout the cell interior
Cell Membranes2
1Fig.
2Fig.
1b from Engelman, D.M. Nature. 438: 578 (2005).
1a from McMahon, H.T. et al. Nature. 438: 590 (2005).
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
2Wylie, J.L. et al. J. Bact. 179: 7233 (1997).
G. et al. Yeast. 15: 601 (1999).
& G. Larsson. Microbial Cell Factories. 3: 9 (2004) .
3Shokri, A.
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).
Force Fields
 Biomolecular Force Field (CHARMM)
V ( Rˆ ) 
 K b  b 
2
b
bonds
0

 K    
2
0
angles

 K r
UB

2
0

1, 3  r1, 3
cross UB
 K 1  cos2 
im
improper
12
6
 R

 Rmin,ij  
qi q j


min,ij
 
  
   K , j 1  cos(n j   j     ij 
 r   nonbonded  r
 rij 
dihedrals  j
 nonbonded
 ij   pairs i , j D ij

pairs i , j
· 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,
2Klauda,
3Dickson
4Dickson
J. B. et al. JPCB. 109: 5300 (2005).
et al. Soft Matter. 8: 9617 (2012).
5Jämbeck & Lyubartsev. JPCB. 116: 3164 (2012).
J.B. et al. JPCB. 114: 7830 (2010).
et al. J. Chem. Theory Comput. 10: 865 (2014).
AMBER Lipids
 Summary of Lipid14 FF1 Results (NPT Ensemble)
Surface Area/lipid [Å2]
MD
DPPC
DMPC
DLPC
DOPC
62.0±0.3
59.7±0.7
63.0±0.2 69.0±0.3
POPC
POPE
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
(Fig. 71)
· Unclear if the head group order parameters are in
agreement with experiment
• 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).
Stockholm Lipids (Slipids)
 Summary of Slipids1-3 Results (NPT Ensemble)
Surface Area/lipid [Å2]
MD
DPPC
DMPC
DLPC
DOPC
62.6±0.5
60.8±0.5
62.4±0.4 68.0±0.5
POPC
POPE
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. 51)
(Fig. 22)
· 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
3Jämbeck
& Lyubartsev. JPCB. 116: 3164 (2012). 2Jämbeck & Lyubartsev. J. Chem. Theory Comput. 8: 2938 (2012).
& Lyubartsev. J. Chem. Theory Comput. 9: 774 (2013).
Force Fields Continued
 Biomolecular Force Field (CHARMM)
V ( Rˆ ) 
 K b  b 
2
b
0

bonds
 K    
2
0
angles
 K r

UB

2
0

1, 3  r1, 3
cross UB
 K 1  cos2 
im
improper
12
6
 R

 Rmin,ij  
qi q j


min,ij
 
  
   K , j 1  cos(n j   j     ij 
 r   nonbonded  r
 rij 
dihedrals  j
 nonbonded
 ij   pairs i , j D ij

pairs i , j
· 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).
4Berger O. et al. BJ. 72: 2002 (1997).
,
5Shinoda, DeVane, & Klein. JPCB. 114:
2Lee,
Tran, Allsopp, Lim, Henin & Klauda. JPCB 118: 547 (2014).
et al. JPCB. 111: 7812 (2007).
4Marrink
6836 (2010).
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
--
~0-5
 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,
2Klauda,
J.B. et al. BJ. 90: 2796 (2006).
J.B. et al. JPCB. 111: 4393 (2007).
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
1.52
· Adjustments are supported by AM1 on the bilayer, small molecule dipoles and watermolecule 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).
Dihedral Modifications
V ( Rˆ ) 
 K b b  b0  
2
bonds
 K    0  
2
angles




K
1

cos(
n



   , j
j
j 
dihedrals  j

12
6
 R




R
qi q j
min,ij
min,ij
 
  
   ij 
 r   nonbonded  r
 rij 
nonbonded
 ij   pairs i , j D ij

pairs i , j
 Small Molecule Models of DPPC
1Klauda
et al. JPCB. 114: 7830 (2010).
Fits to QM of small molecules
QM of bilayers
(Alex MacKerell)
Dihedral Modifications: CHARMM36
 Glycerol FF Adjustments
• Adjust the g1 torsion
2
4
b 1 g1
MP2/6-31g(d): 648 Energy Points
• Issues fitting the 4 and b1 torsions
kcal/mol
1Klauda
et al. JPCB. 114: 7830 (2010).
Empirical Fits of Torsions (C36)
 DPPC SCD Targets
• MD simulations of the DPPC bilayer with an intermediate FF were used to empirically
fit 2, 4, and b1 torsions.
• 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).
Empirical Fits of Torsions (C36)
 Torsional surface scans from 20 ns MD simulations
1Klauda
et al. JPCB. 114: 7830 (2010).
DPPC Bilayer and C36
 Deuterium Order Parameters (SCD): NPAT/NPT1 vs. Experiment2
NPAT
A=64Å2
NPT
S CD  1.5 cos 2  CH  0.5
· 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).
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).
CHARMM36 Lipids
 Initial Parameterization with PC & PE lipids
Surface Area/lipid [Å2]
DPPCa
DMPCb
DLPCb
MD
62.9±0.3
60.8±0.2
Exp
63.0±1.0
60.6±0.5
DOPCb
POPCb
POPEc
64.4±0.3 69.0±0.3
64.7±0.2
59.2±0.3
63.2±0.5 67.4±1.0
68.3±1.5
~60
 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
2Klauda
3Lim
4Pandit
et al. JPCB. 114: 7830 (2010).
& Klauda. BBA: Biomemb. 1808: 323 (2011).
5Lim et al. JPCB. 116: 203 (2012).
et al. JPCB. 116: 9424 (2012).
& Klauda. BBA: Biomemb. 1818: 1818 (2012).
a323K
b303K
c310K
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,
2Jo,
Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) .
Lim, Klauda & Im. Biophys. J. 97: 50 (2009).
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,
2Jo,
Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) .
Lim, Klauda & Im. Biophys. J. 97: 50 (2009).
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,
2Jo,
Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) .
Lim, Klauda & Im. Biophys. J. 97: 50 (2009).
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!
Simulation Snapshot
ERG, YOPS, DYPC and water
Multilayer System/Periodic Boundary Conditions
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) .
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
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
Lipid Bilayer Structure: Simulation
 Molecular Dynamics
• Simulations can easily obtain density profiles
Bulk Water
Headgroup
Dz=0.1Å
Count number
electrons/bin
and average
1Jo,
2Jo,
Kim, Iyer & Im. J. Comput. Chem. 29: 1859 (2008) .
Lim, Klauda & Im. Biophys. J. 97: 50 (2009).
SM=Structural Model
Hydrophobic/Chain
Lipid Bilayer Structure: Experiment
 Form Factors F(q)
• F(q) is transformed into real space to get structural
properties
Structural Models
EDP, A
Fourier Reconstruction
Only Total EDP & Fourier Wiggles
F(q)
HB Fit to Exp. F(q) for the DMPC Bilayer1
1Kučerka,
N. et al. Biophys. J. 88: 2626 (2005).
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
 H2 z   P z   M z   CG z   CH z   BC z 
2
CH z   CCH pHC z, DC , CH   8rCH 9GM z,0, M 
2
1Klauda,
2
J.B. et al. Biophys. J. 90: 2796 (2006).
2
3
BC=water+choline CG=carbonyl-glycerol
chol = choline
Comparing to X-ray/Neutron Scattering
 Model Free Comparison
• Form Factors (symmetric bilayers, where D-repeat spacing)
F qz  






f
q
n
z



a
z
a
W cos zq z   i sin  zq z dz
D / 2  
a

D/2
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)
• 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).
Examples for C36
POPC Form Factors & Density Profiles1
0.5
2.5
2
0.2
d
0.4
0.6
q [1/Å]
50°C
1.5
1
0.5
0
0
0.2
0.4
0.6
q [1/Å]
0.8
30°C
SIM
1
0.5
2.5
2
0.2
e
0.4
0.6
q [1/Å]
60°C
1
0.5
0
0
0.5
XRay
SIM
0.45
0.4
0.35
1
0.5
0.2
0.4
0.6
q [1/Å]
0.8
· Can easily obtain density profiles of groups
within the bilayer
Makover, Im & Klauda. BBA-Biomemb. Submitted (2014).
XRay
SIM
40°C
1.5
1.5
0
0
c
2
0.8
· Excellent agreement between experiment and MD
simulation for form factors.
1Zhuang,
2.5
XRayULV
XRayORI
1.5
0
0
0.8
XRay
SIM
2
b
|F(q)| [e/Å2]
1
2.5
ED [e/Å3]
XRay
SIM
1.5
0
0
|F(q)| [e/Å2]
20°C
|F(q)| [e/Å2]
2
a
|F(q)| [e/Å2]
|F(q)| [e/Å2]
2.5
0.3
0.2
0.4
0.6
q [1/Å]
Total
Water
Choline
Phosphate
Glycerol
Carbonyl
CH2
CH
CH3
0.8
d
POPC
0.25
0.2
0.15
0.1
0.05
0
0
5
10
15
z [Å]
20
25
Overview of Lipid Dynamics and Internal Structure
 Range of Lipid Motions
0
Wobbling in a Cone Model1
Bond Vibrations
1ps
Hydrogen Bonds
1ns
Internal Isomerization (C-H, P-H, etc.)
and Wobbling3
10ns
Isomerization
Axial
Rotation
Lipid Axial Rotation3
Lateral Diffusion2
1ms
Vesicle 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,
3Klauda
R.W. et al. Accounts. Chem. Res. 35: 438 (2002).
et al. Biophys. J. 94: 3074 (2008).
2Klauda
et al. J. Chem. Phys. 125: 144710 (2006).
NMR Background
 Nuclear Magnetic Resonance (NMR)
• Magnetic nuclei (13C/31P) respond to an oscillating magnetic field
• Spin-lattice relaxation rates (R1)
R1  R1 (dipolar)  R1 (CSA)
• Dipolar term: nuclear spin interaction between neighbors
2
2
 g Pg H m 0 
1

J (H  P )  3J (P )  6 J (H  P )
R1 (dipolar)  0.1
3
 4
 rP  H

J ()   C2 (t ) cos(t )dt
0
ˆ (0)  m
ˆ (t)
C2 t  P2 m

2nd Order Legendre
Polynomial
Spectral Density
Reorientational
Correlation Function
Unit vector between P and its
neighboring H
NMR Background
 Nuclear Magnetic Resonance (NMR)
• Magnetic nuclei (13C/31P) respond to an oscillating magnetic field
• Spin-lattice relaxation rates (R1)
R1  R1 (dipolar)  R1 (CSA)
• Chemical Shift Anisotropy: on nucleus
R1(CSA) 
   J
2
15
2
P
2


2
(

)
1


/3
CSA
P
· Based on sold-state measurements on lipids1
· 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
1Herzfel,
J. et al. Biochem. 17: 2711 (1978).
Deuterium NMR
 Deuterium NMR
• Order parameters
· i 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
Deuterium NMR: Examples
SCD’s for POPC and DLPC1
0.1
0.05
DLPC
sn-2
0.1
0.1
0.05
0.15
0.1
0.05
4
6
8
10
Carbon Number
12
0
2
b
POPC
sn-2
0.15
0.1
DLPC
sn-1
20°C
30°C
40°C
50°C
60°C
4
6
8
10
Carbon Number
0
2 4 6 8 10 12 14 16 18
Carbon Number
0.2
DLPC
sn-2
0.15
0.1
0.05
12
c
0
2
SIM 20°C
NMR 20°C
SIM 40°C
NMR 40°C
4
6
8
10
Carbon Number
· 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).
SIM 30°C
NMR 27°C
0.05
0
2 4 6 8 10 12 14 16 18
Carbon Number
0.2
SCD
SCD
a
0.15
0
2
10°C
20°C
30°C
40°C
50°C
60°C
0.05
0
2 4 6 8 10 12 14 16 18
Carbon Number
0.2
0.15
0.2
SCD
0.15
c
POPC
sn-1
0.2
SCD
SCD
0.2
b
POPC
sn-2
SCD
a
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