SUPPLEMENTARY INFORMATION
Hydration strongly affects the molecular and electronic structure of
membrane phospholipids
Alireza Mashaghi1,†, P. Partovi-Azar2, Tayebeh Jadidi2, Nasser Nafari2, Philipp Maass2, M. Reza Rahimi
Tabar2, Mischa Bonn3 and Huib J. Bakker1
1FOM
Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands
Physik, Universitat Osnabruck, Barbarastrasse 7, 49076 Osnabruck, Germany
3Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
†mashaghi@amolf.nl
2Fachbereich
Supplementary figures
Fig S1. Electronic Density of States of pure and hydrated DPPC and DPPE lipids. The energy gaps are
tabulated in the supplementary information (Table S4). We observed a reduction in the energy gap
(HOMO-LUMO gap) upon hydration in agreement with experimental observations [1-3].
Fig S2. The calculated surface potential for Dipalmitoyl phosphatidyl ethanolamine (DPPE) with 50
water molecules. For this system, we find a similar molecular shape as that of hydrated DPPC. The
electric dipole moment of the system is 8.52 D.
Supplementary tables
Table S1. Structural parameters of DPPC and hydrated DPPC
DPPC
DPPC, (H2O)50
linear extension
(Å)
28.8
28.2
Ellipsoid radii of the head (Å)
ax
az
4.27
7.63
7.45
6.26
Ellipsoid radii of the tails (Å)
ax
az
4.17
6.90
7.83
4.16
Table S2. Angle between the normal of the specified planes with the normal of the tail plane
DPPC
DPPC, (H2O)50
Glycerol
124.71
154.23
sp2 of sn-1 carbonyl
161.92
103.27
sp2 of sn-2 carbonyl
103.47
114.04
Table S3. Electric Quadrupole tensor (ea02) with respect to center of mass
Pure DPPC
Q=
-33.6962048444739, -200.878815412606, -87.0458920451317
-200.878815412608, -58.1695319219012, -55.2874701895716
-87.0458920451328, -55.2874701895716, 91.8657367729295
Trace= 6.554429887728475E-009
Eigen Vectors & Eigen Values:
A1
A2
A3
----------- ---------- ------------0.6723 -0.7224 0.1620
-0.6916 0.5348 -0.4855
-0.2641 0.4384 0.8591
a1 = -274.5428
a2 = 167.8477
a3 = 106.6951
DPPC, (H2O)50
Q=
144.75824904866917, -10.025454080146032, 32.999471401474665
-10.025454080145712, -252.05823852511330, 13.793085476215943
32.999471401474551, 13.793085476215548, 107.29998947679509
Trace= 3.50965478901343886E-010
Eigen Vectors & Eigen Values:
A1
A2
A3
----------- ---------- -----------0.8646 -0.5016 0.0286
-0.0042 0.0497 0.9988
0.5024 0.8637 -0.0409
a1 = 163.9803
a2 = 88.9290
a3 = -252.9093
Table S4. Energy band gap estimates for DPPC and DPPE
Phospholipid
DPPC
DPPC with 50 water molecules
DPPC with 75 water molecules
DPPE with 50 water molecules
Energy band gap (eV)
4.2
3.4
3.35
3.5
Supplementary methods
Method SM1. Technical details of the simulation
To calculate the ground state structure of a DPPC monomer, we first built the molecule by putting
atoms together while treating the bonds of each of them properly (considering the number of
valence electrons of each of the atoms and their hybridizations). In order to avoid any local minima in
the energy landscape, we set the maximum displacement of the atoms to a large value of 0.5 Bohr in
each conjugate gradient step. The molecule was relaxed until the maximum force on the atoms fell
bellow 0.005 eV/Å. Since, we were considering a single molecule, the length of the unit cell vectors
were set to a much longer value than the size of the molecule. As such, we only considered the
Gamma point in the reciprocal space for energy integration in this calculation.
To find the ground state of the hydrated lipids, we first obtained the relaxed structure of a single
water molecule with the same simulation parameters. Then, we placed the replicas of the water
molecules around the relaxed structure of a DPPC monomer in the vacuum in such a way that the
water molecules thoroughly covered the hydrophilic head group of DPPC. The full system was
relaxed again with the same procedure explained above. The sample was also considered as a single
molecule, a cluster.
To obtain the ground state structure of the hydrated 2DPPC monolayer (a membrane), we placed
two relaxed DPPCs parallel to each other, with opposite dipole moment vectors. Having in mind the
experimental value for area per lipid in a lipid membrane, we set the unit cell vectors in such a way
that the dimer with water molecules made a periodic structure, and started another relaxation with
periodic boundary conditions, this time letting the unit cell be relaxed as well. Then, since we were
dealing with a "crystal" in this case, we used a 3x3x1 grid in the reciprocal lattice for k-grid sampling.
In the final relaxation step, the lipids were tilted and the final configuration (Fig 3a) was reached. The
maximum force was again less than 0.005 eV/Å, and the maximum stress tensor element was less
than 0.25 GPa. The target pressure was set to 0.0 GPa.
The van der Waals (vdW) interactions are generally necessary between the two parallel DPPC within
a unit cell and the neighboring unit cells, and even among the tails of a single DPPC. There are some
experimental implementations of the vdW exchange-correlation functional based on [4], in a selfconsistent scheme, like the one developed in [5]. In the results reported in the article, only Local
Density Approximation (LDA) for exchange-correlation functional was used.
We also performed the simulation with vdW functional, based on the Refs [4] and [5], for the
hydrated DPPC and hydrated 2DPPC, to compare the results with ones reported in Fig. 1(a) and 1(b).
Apart from small local differences, the structures were basically the same.
For example, the difference between the angle joining the tilted tails of the lipid (Fig 1(a)) in vdW
calculation (155 deg.) and the reported LDA calculation (156 deg.) was less than %0.7. The difference
between the length of the lipid in vdW calculation (28.30 Å) and the reported LDA calculation (28.24
Å) was less than %0.3.
In the case of the hydrated 2DPPC, the total energy of the system was about 1.2% lower when the
vdW functional was used. The structure of hydrated 2DPPC system showed little changes while the
electric dipole was found to be very close to the LDA value, ~0.48 D.
Method SM2. Hydration energy estimation
The hydration energy is calculated by:
1
𝑪𝑷
𝑬 = − 𝑛 [𝐄(DPPC. (H2O)n) – 𝑬𝑪𝑷
𝑩𝑺𝑺𝑬 (DPPC) – 𝑬𝑩𝑺𝑺𝑬 ((H2O)n)],
where n is the number of water and E denotes the total energy. The Basis Set Superposition Error
(BSSE) was dealt with using the Counterpoise method (CP) using ghost atoms, i.e. removing the
atoms but keeping the basis functions of them. For example, in the case of 𝑬𝑪𝑷
𝑩𝑺𝑺𝑬 (DPPC), we
removed the water molecules, but kept their basis functions, and carried out the total energy
calculation for the lipid.
To estimate the contribution of two water bridges to the stability of the hydrated 2DPPC, we
calculate the stabilization energy by:
1
𝑪𝑷
∗
𝑬 = − 2 [𝐄(2DPPC. (H2O)n-2(H2 O∗ )2 ) – 𝑬𝑪𝑷
𝑩𝑺𝑺𝑬 (2DPPC. (H2 O)n−2 ) – 𝑬𝑩𝑺𝑺𝑬 ((H2 O )2)],
where the star superscripts denote the water bridges. The values reported in the article are
corrected for the BSSE with the same CP method.
References:
[1] Rosenberg B. and Jendrasiak G.L., Chem Phys Lipids 2, 47-54 (1968).
[2] Rosenberg B and Pant H.C., Chem. Phys. Lipids 4, 203-207 (1970).
[3] Rosenberg B., Postow E., Annals of the New York Academy of Sciences 158, 161–190 (1969).
[4] Dion M., Rydberg H., Schröder E., Langreth D.C., and Lundqvist B.I., Phys. Rev. Lett. 92, 246401
(2004).
[5] Román-Pérez G. and Soler J.M., Phys. Rev. Lett. 103, 096102 (2009).