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Understanding the orientation of water moleculesaround the phosphate and attached functional groupsin a phospholipid molecule: a DFT-based studyDeepti Mishra a , Susanta Das a , Sailaja Krishnamurthy b & Sourav Pal aa Physical Chemistry Division, CSIR-National Chemical Laboratory, Dr Homi Bhabha Road,Pune, 411008, Indiab Functional Materials Division, CSIR-Central Electrochemical Research Institute, Karaikudi,630006, IndiaVersion of record first published: 11 Apr 2013.

To cite this article: Deepti Mishra , Susanta Das , Sailaja Krishnamurthy & Sourav Pal (2013): Understanding the orientationof water molecules around the phosphate and attached functional groups in a phospholipid molecule: a DFT-based study,Molecular Simulation, DOI:10.1080/08927022.2013.783701

To link to this article: http://dx.doi.org/10.1080/08927022.2013.783701

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Understanding the orientation of water molecules around the phosphate and attached functionalgroups in a phospholipid molecule: a DFT-based study

Deepti Mishraa, Susanta Dasa, Sailaja Krishnamurthyb and Sourav Pala*aPhysical Chemistry Division, CSIR-National Chemical Laboratory, Dr Homi Bhabha Road, Pune 411008, India; bFunctional MaterialsDivision, CSIR-Central Electrochemical Research Institute, Karaikudi 630006, India

(Received 1 December 2012; final version received 28 February 2013)

The adsorption of water molecules around a polar region (in particular around the phosphate moiety) in the phospholipidmolecules is studied in this work. Phospholipid molecules with different functional groups are known to respond differentlyto the water molecules. Hence, we attempt to study the adsorption of water molecules around the phosphate group as aconsequence of the change of functional group attached to the phosphate group, viz. phosphatidyl ethanolamine (PE),phosphatidyl choline (PC) and phosphatidyl glycerol (PG). As the latter is anionic in nature, the charge is compensated byNaþ counterion. Up to seven water molecules are adsorbed around the phosphate groups in model systems mimickingphospholipid molecule. The corresponding changes in the structural and electronic aspects are analysed. The significantdifference between the PE and PC model systems is the formation of clathrate-like structure in the latter. It is noticed that asthe number of water molecules increases to seven, both the hydrogen atoms in the water molecule participate in hydrogenbonding. However, in the PG model system, the charge-compensating counterion prevents the water molecule to formclathrate-like structures. The adsorption sites for water molecules are validated by density functional theory-based reactivitydescriptors, viz. Fukui functions in the PE model system.

Keywords: DMPC; DMPE; DMPG; hydration; cHelpG; Fukui functions

1. Introduction

Phospholipid molecules are the building blocks of any

biological membrane. The two principal regions of a

phospholipid molecule are the polar group (we refer to this

as the head), which is hydrophilic in nature, and the non-

polar group, hydrophobic alkyl chains (which we refer as

to tails). The basic conformation of the phospholipid

molecule is governed by torsion angles between the atoms

within it. The conformational orientation in turn affects the

chemical properties and also the interatomic molecular

packing. However, the most critical factors controlling the

chemical properties and the molecular packing are

functional groups attached to the phosphate group. The

functional groups also play a role in determining the

essential physical properties of a lipid molecule such as its

surface charge density. Importantly, the presence of

different functional groups modifies the overall charge of a

phospholipid molecule, making it zwitterionic, anionic or

cationic in nature. The overall charge on the molecule

modulates its molecular interactions with the components

present in the aqueous phase resulting in different

membrane responses towards the incoming ion, protein,

drug molecule, etc. Hence, depending on the functional

group in the molecule, its application is seen to vary, viz.

drug delivery, protein–lipid interaction, solvation and so

on [1]. In other words, the chemical and physical responses

of any biological membrane are controlled by the chemical

structure of the constituting phospholipid molecules.

One of the first factors to be affected by the chemical

structure of a lipid molecule is the orientation of water

molecules around it. The binding capacity or specifically

‘hydration force’ [2–4] arises due to the association of

water molecules with the polar region of the phospholipid.

The behaviour of the water molecules at the polar site of

phospholipids depends on the structure and type of the

functional group attached to the phosphate moiety. In

addition to the functional groups, the presence of

counterion compensates the charges on the phospholipids

also modifies the hydration behaviour. The presence of

different functional groups at the polar region changes

entirely the electrostatic interaction involved and hence

the hydration behaviour too.

X-ray and other experimental studies show that for an

individual phospholipid molecule in the gas phase, the

functional groups tend to orient towards the phosphate

group due to electrostatic interactions [5]. However, the

molecule adopts an extended form in the presence of water

and a neighbouring phospholipid molecule [6]. The strong

dipole of the head region of phospholipid is responsible for

its interaction with water molecules present in the vicinity

of interaction. Water molecules are present in spaces

between the two phospholipid head regions, resulting in

q 2013 Taylor & Francis

*Corresponding author. Email: s.pal@ncl.res.in

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the formation of intramolecular and intermolecular H-

bond bridges.

Various experimental and computational studies have

been carried out on phospholipid molecules in recent

decades [7–13]. Experimental studies also direct the

characteristics of single phospholipid molecular structure

in various assemblies. Emphasis has been laid on the

structure and dynamics of the phospholipid monomer

within an assembly in order to understand the bilayer

functional role in biological membranes [14–19]. Internal

monomer properties are better preserved in a single crystal

structure, because the intermolecular forces are less

dominant than the intramolecular forces [13,14]. The

single crystal atomic positions are therefore used for the

fluid phase simulation. However, this may not be true in

the case of crystalline state because strong intermolecular

electrostatics is involved [13].

It is difficult to study the bilayer structure using

quantum mechanics due to its large size. Therefore, model

systems such as methyl phosphate ion and methylpho-

sphocholine have been studied well using Hartree Fock

and density functional theory (DFT), respectively [20–

25]. The effect of continuum solvation model has been

studied on PE and PC model systems using Hartree Fock

[23]. However, the study of hydration of different

functional groups attached to the phosphate group with

explicit water molecules using more accurate methods is

still eluding. Semi-empirical PM3 method has also been

used to study the interaction of dipyridamole with

dimyristoyl phosphatidyl choline (DMPC) [26]. In

addition to the head group, the tail region has also been

taken into account in the more extended form of the model

system to study the various conformations and their

energetic profile as a result of intramolecular interactions

involved in the phospholipid system [27,28]. However, in

such cases, more extensively classical molecular dynamics

methods have been used to study biological membrane

properties. The force fields used in these classical

molecular dynamics simulations to reproduce the exper-

imental properties are parameterised using quantum

mechanics calculations on small model molecules [29–

33]. Molecular dynamics (MD) studies have been devoted

to a large number of structural properties and has explored,

till date, dihedral angle values [26–29], head group

flexibility [34,35], tail orientation [32], phase changes

[36,37], hydration effect [38–40], interaction with ions

[33] and molecules [41,42] and evaluation of local order

parameter [43,44]. In addition to this, recently, Parthasar-

athi et al. [45] have studied the significant interaction of

mannose sugar with two different phospholipids using

DFT. Parthsarathi et al. have shown the importance of the

influence of tail on phospholipid interaction with other

molecules.

To evaluate the role of water in modifying the

structural and electronic properties of lipid molecules as a

function of functional group, we have chosen three model

systems, viz. DMPC, dimyristoyl phosphatidyl ethanola-

mine (DMPE) and dimyristoyl phosphatidyl glycerol

(DMPG). The background for choosing these molecules is

as follows: the main constituents of a lipid bilayer in the

animal cells are DMPC and DMPE. In case of the latter,

the choline group in DMPC (N(CH3)3) is replaced by the

amine group, NH3, leading to differences in the physical

properties of both, more importantly, in their hydration

behaviour by which lamellar phases of PE are less strongly

hydrated than those of PC in the bilayer system [46]. The

main structural difference is that the sheer volume of PC is

greater than that of PE, and also the non-hydrogen atom of

PC is arranged in branched fashion and heavy atoms of PE

are arranged in a linear manner, which together makes a lot

of difference in the physicochemical properties. Therefore,

we attempt here to study the hydration of both PC and PE

model head group systems with various number of water

molecules. In addition to these two neutral systems, we

have one charged model system, viz. model system of

DMPG for studying hydration and the effect of counterion

on hydration.

The more preferable sites of hydration in head groups

are phosphate, carbonyl and carboxyl which determine the

hydrophilicity of the head group by directly forming the

H-bonds with the water molecules. The hydration of

hydrocarbon chains is quite weak due to its non-polar

nature; therefore, we are restricting our study to only the

shortened model system of the head group region. Hence,

we attempt to study the structure, hydration energy and

electrostatics involved during the interaction of water

molecules with three different model systems.

We also attempt to predict the site of hydration of the

model system of the PE head group using Fukui functions

(FFs) [47,48]. Finite difference approximation has been

used to calculate these reactivity descriptors. From the

values of FFs, we can predict which site of the molecule is

more reactive than the other for hydration. Therefore, the

concept of local reactivity descriptors (LRDs) can give the

information beforehand without forming the complex of

lipid head group model system and water molecules.

The paper is organised as follows. In Section 2, we

give the brief overview of the LRDs. Section 3 presents the

methodology and computational details. Section 4 presents

the Results and Discussion of this study, and Section 5

presents the Conclusions.

2. Local reactivity descriptors

Density-based response functions, called LRDs and global

reactivity descriptors, are derived from DFT [49]. Within

the framework of DFT, Parr and co-workers have

introduced several important chemical tools [50]. DFT

has provided the theoretical basis for the concepts such as

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electronic chemical potential, electro negativity and

hardness, collectively known as global chemical reactivity

descriptor [51–55]. FF [46] can be interpreted either as the

change of electron density rðrÞ at each point r when the

total number of electrons is changed or as the sensitivity of

chemical potential of a system to an external perturbation

at a particular point r.

Therefore, the expression of FF can be written as:

f ðrÞ ¼›rðrÞ

›N

� �vðrÞ

¼›m

›vðrÞ

� �N

ð1Þ

Equation (1) involves the N-discontinuity problem [56,57]

leading to the introduction of both right- and left-hand

derivatives.

f þðrÞ ¼›rðrÞ

›N

� �þ

vðrÞ

ð2Þ

for a nucleophilic attack and

f 2ðrÞ ¼›rðrÞ

›N

� �2

vðrÞ

ð3Þ

for an electrophilic attack.

The finite difference method, using the electron

densities of N0, N0þ1, N0-1, defines

f þðrÞ < rN0þ1ðrÞ2 rN0

ðrÞ ð4aÞ

f 2ðrÞ < rN0ðrÞ2 rN021

ðrÞ ð4bÞ

f 0ðrÞ <1

2rN0þ1

ðrÞ2 rN021ðrÞ

� �ð4cÞ

In order to describe the site reactivity or site

selectivity, Yang et al. [47,48] proposed atom-condensed

FF, based on the idea of electronic population around an

atom in a molecule, similar to the procedure followed in a

population analysis technique. The condensed FF for an

atom k undergoing nucleophilic, electrophilic or radical

attack can be defined, respectively, as

f k < qN0þ1

k 2 qN0

k ð5aÞ

f k < qN0

k 2 qN021

k ð5bÞ

f 0k <1

2qN0þ1

k 2 qN021

k

� �ð5cÞ

where qk is the electronic population of the kth atom of a

particular species.

The first and second partial derivatives of E[r ] with

respect to the number of electrons N under the constant

external potential v(r) are defined as the chemical potential

m and the global hardness h of the system, respectively

[51–55].

m ¼›E

›N

� �vðrÞ

h ¼1

2

›2E

›N 2

� �vðrÞ

ð6Þ

The inverse of the hardness is expressed as the global

softness,

S ¼1

2hð7Þ

The global descriptor of hardness has been an indicator of

overall stability of the system. When the two molecules

interact, specific reactive sites of both the molecules are

involved in bond formation. So reaction between two

reactants is always local. That is why the site selectivity of

a chemical system cannot be studied using the global

descriptors of reactivity. For this, appropriate local

descriptors need to be defined. An appropriate definition

of local softness s(r) is given by [47,48],

sðrÞ ¼›rðrÞ

›m

� �vðrÞ

ð8Þ

such that

ðsðrÞdr ¼ S ð9Þ

Rewriting Equation (8) and the definition of global

softness, we can write

sðrÞ ¼›rðrÞ

›N

� �vðrÞ

›N

›m

� �vðrÞ

ð10Þ

¼ f ðrÞS ð11Þ

The condensed local softness, sþk and s2k , are defined

accordingly for nucleophilic and electrophilic attack,

respectively. This can determine the behaviour of different

reactive sites with respect to the hard and soft reagents.

Subsequently, Gazquez and Mendez proposed a local

version of the hard and soft acid bases (HSAB) principle,

which generally states that the interaction between any two

chemical species will not necessarily occur through their

softest centres, but rather through those whose FFs are

nearly equal [58–60].

3. Methods and computational details

The standard nomenclature of the head group torsion

angles has been shown in Figure 1. The model system as

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shown in Figure 1 is the model system of consideration in

this study with varying functional groups attached to the

phosphate moiety. The systematic change in a torsion

angle produces many conformers (nearly 50 confor-

mations) which are low in energy (DE varies from 0 to

7 kcal/mol). We note that the various bond lengths (such as

PvO, PZO, CZH and so on) and bond angles (such as

OZPZO, OvPvO and so on) were not varied during the

process of generating various conformations. The bond

lengths and bond angles have limited flexibility within the

tetrahedral symmetry, and it is the variation in the torsion

angles that leads to a wide range of conformations. All the

model systems having different conformations were

optimised using the deMon2k program [61]. The

calculations were carried out using a generalised gradient

approximation of Perdew–Burke–Ernzerhof exchange

functional [62] and Lee, Yang and Parr (LYP) correlation

functional [63].

All the atoms were described using double zeta plus

valence polarisation basis sets [64]. A2 auxiliary function

was used for fitting the density. The exchange correlation

functional was numerically integrated on an adaptive grid

with an accuracy of 1025 [65]. The Coulomb energy was

calculated by the variational fitting procedure proposed by

Dunlap, Connolly and Sabin [66,67]. A quasi-Newton

method in internal redundant coordinates with analytical

energy gradients was used for optimising the systems [68].

The structure was considered to be optimised once the

Cartesian gradient and displacement vectors reached a

threshold of 1024 and 1023, respectively.

We have then taken one of the low-lying (in terms of

energy) conformers to see the hydration effect on the PC

model system. Similarly, we obtained the various

conformations for the PE and PG model systems. The

lowest energy conformer for all the model systems is then

used to study the hydration. The models, which we have

studied in this paper, are head groups of DMPE, DMPC

and DMPG. Two of them are neutral models (viz. DMPC

and DMPE) and the other is a charged model (viz.

DMPG). Therefore, we have taken into account both the

neutral and charged head groups to study the hydration.

The systematic addition of one to seven water molecules to

each of the model systems is used for calculating the

hydration energy and also the electrostatics involved

during hydration.

The lowest energy conformer with various number of

water molecules is then optimised using Gaussian09

software [69]. The optimisation was carried out using 6-

311G**þþ basis set and B3LYP exchange and

correlation functional [70] for all the model systems.

Hirshfeld population has been calculated for the

prediction of the hydration site using FFs. The reason for

using the Hirshfeld population is that it leads non-negative

FF and thus avoids the difficulty of obtaining the rank

ordering of reactivity in a molecule. Roy et al. [71]

analysed the procedure of giving non-negative Fukui

indices using Hirshfeld electronic population. Hirshfeld

population analysis is defined relative to the ‘deformation

density’ using stockholders’ partitioning technique [72].

4. Results and discussion

In our previous study, we have obtained various low-lying

conformations that are lower in energy than the

experimentally found conformers [28]. Therefore, there

can be many other conformations possible which are lower

in energy than what we know presently from the

experimental results. To obtain many such conformations,

we have systematically varied a torsional angle (see

Figure 1 for details) for the PC, PE and PG head group

model system. Experimentally it is proposed that the

conformations of the molecule depend mainly on

intramolecular interactions, and to stabilise these confor-

mations, intermolecular interactions are required [73].

Therefore, to study intramolecular electrostatic inter-

actions that are involved dominantly in the polar region of

phospholipids, we attempt to study model systems with

different functional groups in gas phase and in the

presence of various number of water molecules. The

model systems of DMPE, DMPC and DMPG have been

tailored up to the glycerol C1 atom as shown in Figure 1 of

the PE model system.

Using deMon2k, we have optimised several confor-

mations and studied in detail the lowest 47 conformers of

the PC head group model system. The optimised

conformers are analysed to understand their electronic

and structural properties in each of the conformers. The

energetic profile and structural parameters of these 47

α2

α4

α3

α5

O2

O3

O4

O5

Figure 1. (Colour online) The gas phase optimised PE headgroup model system.

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Tab

le1

.T

he

stru

ctu

ral

par

amet

ers

of

the

gen

erat

edco

nfo

rmer

so

fP

Ch

ead

gro

up

mo

del

syst

em.

Confo

rmer

sa

2a

3a

4a

5PZ

N(A

)H

18Z

O3(P

O4)(

A)

H19Z

O2(P

O4)

(A)

OZ

PZ

Ofr

eeOZ

PZ

Obound

DE

(kca

l/m

ol)

174

112

110

265

3.8

51.9

82.0

7123

100

22

74.3

2112

2110

65

3.8

51.9

82.0

7123

100

32

74.3

2112

2110

65

3.8

51.9

82.0

8123

101

0.0

474.3

112

110

265

3.8

51.9

82.0

7123

100

52

74.3

2112

2110

65

3.8

51.9

82.0

8123

100

676

2163

249

266

3.8

24.1

52.0

5122

97

72

76

163

49

66

3.8

24.1

52.0

5122

97

0.1

88

77

2169

2119

65

3.9

92.0

43.5

2123

96

92

78

169

119

265

3.9

92.0

43.5

4123

96

0.7

510

278

170

120

265

4.0

02.0

43.5

6123

96

11

77

2165

2118

65

3.9

83.4

12.0

3123

96

12

74

92

71

47

3.8

92.3

74.4

6124

100

1.0

613

274

292

271

247

3.8

92.3

64.4

9124

100

14

164

118

108

267

3.8

32.0

02.0

3120

96

1.1

915

74

154

47

66

3.8

02.0

43.9

5122

98

1.3

816

274

2154

247

266

3.8

12.0

33.9

7122

98

17

2177

272

2117

71

3.9

92.0

03.1

2122

96

2.0

818

280

2138

120

267

4.0

32.7

94.4

0126

95

19

280

2138

120

267

4.0

32.7

94.4

0126

95

2.0

720

80

138

2120

67

4.0

32.7

84.4

0126

95

21

2150

2141

120

268

4.0

22.6

84.4

0123

92

2.3

222

150

141

2120

68

4.0

22.7

24.4

0123

92

23

2175

2100

269

247

3.8

53.8

33.0

0122

96

2.6

924

75

2170

270

122

3.9

03.5

33.0

0121

97

25

275

170

70

2122

3.9

03.1

74.2

5121

97

26

75

2170

270

122

3.9

13.0

12.2

7121

97

3.3

227

275

170

70

2122

3.9

03.1

74.2

4121

97

28

150

141

2120

69

4.0

24.4

12.6

6123

92

29

74

167

70

2122

3.9

13.1

54.2

3121

98

3.7

630

274

2167

270

122

3.9

13.0

13.5

6121

98

31

75

2170

270

122

3.9

03.0

03.5

5121

97

4.1

432

275

170

70

2122

3.9

03.1

64.2

3121

97

33

277

257

267

125

4.0

51.9

95.6

3125

99

34

77

57

67

2125

4.0

61.9

95.6

4125

99

4.3

235

77

57

67

2125

4.0

61.9

95.6

4125

99

36

77

57

68

2126

4.0

61.9

95.6

4125

99

37

277

257

268

126

4.0

61.9

95.6

4125

99

5.1

438

77

57

68

2126

4.0

61.9

95.6

4125

99

39

277

257

268

126

4.0

61.9

95.6

4125

99

40

166

167

71

2123

3.9

03.0

03.5

8119

94

5.3

341

2162

2167

271

123

3.9

03.0

33.6

4121

96

42

2162

296

60

70

4.0

64.0

73.9

7123

96

6.0

243

163

96

260

270

4.0

84.2

83.9

5121

99

6.0

844

164

89

283

123

4.1

25.8

33.3

2122

99

6.9

045

2159

259

266

123

4.0

41.9

95.6

0121

96

7.3

446

159

59

66

2123

4.0

41.9

95.6

0121

97

47

76

89

267

143

4.2

33.9

94.1

0121

99

7.7

1

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Table 2(a). Structural parameters of PE head group in gas phase and with varying number of water molecules.

Torsional angles Bond distances

Structures a2 a3 a4 a5 PvO2 PZO3 PZO4 PZO5 PZNH2

Gas phase 95 42 92 272 1.48 1.58 1.62 1.63 3.47

82 91 89 260 1.50 1.59 1.62 1.65 3.28

80 74 92 271 1.49 1.52 1.62 1.66 3.41

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conformers are given in Table 1. The energetic profile of

these conformers varies from 0 to 7 kcal/mol. We have

found many conformers that are degenerate in energy. The

degenerate conformers are mirror image of each other. In a

previous work of Krishnamurthy et al. [27], it was

observed that despite the differences in combinations of

torsion angles, all the conformers share a common

geometric profile, which includes a balance of attractive,

repulsive and steric forces between and within specific

groups of atoms of the DMPC molecule. Similarly, we

note a balance of attractive and repulsive forces in the 12

nearly degenerate conformers with the DE value within the

range of 1 kcal/mol. The attraction between the phosphate

group and the choline group decreases in higher energy

conformers. This is due to the increase in interatomic

distance between P and N atoms. The interatomic distance

(P–N) increases from 3.85 to 4.23 A. The effect of

different functional groups on the phosphate group reflects

the role of intramolecular interactions involved in different

conformers of the head group model system and also in

full phospholipid molecule. We have also obtained the

lowest energy conformer for the PE and PG head group

model systems using a similar approach of systematically

varying torsional angles. The head group model systems in

this study have been categorised into two different groups

of neutral and charged category.

4.1 Hydration behaviour of neutral head groups

In order to understand the structural and conformational

behaviour of the PE and PC model systems, the torsion

angles have been measured in the presence and absence of

explicit water molecules. As shown in Table 2(a), the

torsion angle a3 undergoes a noticeable change with the

addition of a water molecule. It changes from 42o to 91o

with the addition of one water molecule; however, this

change gets stabilised with respect to the successive

addition of water molecules. The change in a3 torsion

Table 2(a) – continued

Torsional angles Bond distances

Structures a2 a3 a4 a5 PvO2 PZO3 PZO4 PZO5 PZNH2

77 82 89 274 1.50 1.51 1.62 1.66 3.43

80 66 100 258 1.49 1.51 1.62 1.69 3.42

Molecular Simulation 7

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angle is due to the phosphate group which interacts with

the neighbouring water molecules. Thus, a critical number

of water molecules are required for stabilising the torsion

angles near the phosphate group. We also noticed a proton

transfer from NHþ3 to the PO2

4 functional group in the gas

phase and with one water molecule in the PE head group

model system. Interestingly, the proton transfer does not

depend on the distance between the two groups, e.g.

distance is the same in the case of gas phase (i.e. no water

molecule around the phosphate group) and the model with

seven water molecules. Therefore, it is worth noting that

the proton transfer depends on the number of water

molecules in the first hydration shell of the PE head

group. However, the change in the a3 torsion angle makes

the PO4 group to move parallel to the bilayer plane away

from the NH3 group, but the distance between these

groups does not change much due to the electrostatic

interaction between the two charged groups of the head

region of PE.

The partial CHeplG charges of the various functional

groups of the PE model system have been calculated to

support the electrostatic interactions. The partitioning

scheme of the CHelpG point charges is very well

explained in the literature and describes electrostatics

quite accurately [74,75]. The CHelpG charges are

considerably less dependent upon molecular orientation.

Although Clark et al. showed that VESPA charges are less

sensitive to molecular orientation [76,77], CHelpG

charges work well while predicting the electrostatics for

our model systems of the phospholipid molecule. CHeplG

charges and other electrostatic properties are given in

Table 2(b). The charge on NH3 is quite low in the gas

phase and with one water molecule as compared with more

number of water molecules. The partial charge on NH3

increases to 0.622 from 0.284 as going from the one-water

molecule to the three-water molecule system. The reason

for this is the proton transfer from NH3 to the PO4

group. The atomic distance between P and N atoms also

decreases from 3.47 to 3.28 A from gas phase to one water-

solvated state. The change in the atomic distance is due to

the H-bond formation of water molecule which involves

both the functional groups. This decrease in atomic

distance reflects back when we calculate the dipole

moment of the system. Dipole moment of a system can

quantitatively explain the charge separation. The PE head

group dipole moment in the gas phase is 7.70 D, which

changes to 3.14 D in the one water-molecule solvated state

as given in Table 2(b). It has also been observed that the

charge on the N atom of the NHþ3 functional group

increases which implies that the electro-positivity of N

increases with the addition of water molecules because the

hydrogen atoms in NH3þ are involved in the hydrogen bond

formation.

From earlier studies, it is very well understood that the

phosphate moiety of the phospholipids is the active region Tab

le2

(b).

Par

tial

char

ges

of

ato

ms/

gro

up

and

hy

dra

tio

nen

erg

yca

lcu

lati

on

of

the

mo

del

syst

emo

fP

Eh

ead

gro

up

. Hy

dra

tio

nst

ates

Par

tial

char

ges

on

ato

m/m

ole

cule

Gas

ph

ase

1w

ater

2w

ater

3w

ater

4w

ater

5w

ater

6w

ater

7w

ater

PO

42

1.0

27

20

.92

32

1.0

30

21

.18

72

1.1

99

21

.17

02

1.1

68

21

.09

6N

H3

0.3

33

0.2

84

0.3

86

0.6

22

0.6

31

0.6

21

0.6

35

0.6

17

CH

30

.24

30

.23

90

.22

70

.21

60

.21

50

.21

90

.21

00

.21

4(C

H2) 2

0.4

50

0.4

79

0.4

36

0.3

31

0.3

81

0.3

45

0.3

08

0.3

02

Dip

ole

mo

men

t(D

)7

.70

3.1

44

.16

6.3

05

.02

7.6

27

.51

6.4

3H

yd

rati

on

ener

gy

(DH

)(k

cal/

mo

l)at

0K

–2

12

.11

21

2.2

92

11

.76

21

2.1

72

11

.24

21

1.1

32

11

.05

Hy

dra

tio

nen

erg

y(D

H)

(kca

l/m

ol)

at2

98

K–

21

0.4

02

10

.72

21

0.1

32

10

.21

29

.44

29

.34

29

.17

DG

(kca

l/m

ol)

at2

98

K–

20

.27

20

.84

20

.22

0.3

52

0.1

72

0.2

22

0.2

1C

ou

nte

rpo

ise

corr

ecte

d(k

cal/

mo

l)at

0K

–2

10

.92

21

1.5

12

11

.15

21

1.4

02

10

.76

21

0.7

22

10

.62

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Table 3(a). Structural parameters of PC head group in gas phase and with varying number of water molecules.

Torsional angles Bond distances

Structures a2 a3 a4 a5 PvO2 PZO3 PZO4 PZO5 PZN(CH3)

Gas phase 74 112 110 265 1.51 1.52 1.65 1.74 3.85

74 84 114 272 1.52 1.52 1.65 1.72 3.97

71 74 118 272 1.52 1.51 1.65 1.70 4.03

Molecular Simulation 9

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of hydration [22]. It is also observed that there are many

possibilities of water molecules in the first, intermediate

and second hydration shell. Up to six water molecules may

be accommodated in the first hydration shell. Intermediate

hydration shell has two to five water molecules. It has been

reported that the average energy for water attachment is

approximately 223 kcal/mole for n ¼ 2 and 3 and

decreases when n increases further, down to 217.3 for

n ¼ 6 [59]. Therefore, we started with the phosphate group

and kept on adding water molecules systematically up to

seven. The hydration energy calculation showed that the

PE model system solvated with two explicit water

molecules has the highest counterpoise-corrected

hydration energy per water molecule. The hydration

energy for the two-water molecular system is211.51 kcal/

mol. One of the water molecules is hydrogen bonded with

O of the phosphate group, and the other water molecule

has bridged structure with both its hydrogen atoms

involved in the hydrogen bonding with free oxygen atoms

of the phosphate group. The model system with seven

water molecule has hydration energy ,1 kcal/mol less

than that of two water molecule system. The hydrogen

atoms of NH3 group are all involved in H-bond formation,

i.e. two with water molecules and one with PO4 group in

seven water molecule model system (Figure shown in

Table 2(a)). There is a formation of clathrate-like structure

of water molecules around the polar groups of head group

model system.

Similar to the DMPE shortened model system, DMPC

has also been shortened to study the structural and

electronic properties in the presence and absence of

varying number of water molecules. We notice the increase

in P–N distance with the addition of water molecules in PC

head group model system which shows the straightening of

Table 3(a) – continued

Torsional angles Bond distances

Structures a2 a3 a4 a5 PvO2 PZO3 PZO4 PZO5 PZN(CH3)

70 80 116 276 1.52 1.51 1.64 1.72 4.07

67 81 123 271 1.54 1.52 1.64 1.67 4.09

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the head group. We also noticed a significant change in a3

torsion angle in PC head group model as in case of PE. The

bond distance oxygen with the phosphorus in PO4- shows a

minor change from gas phase to hydrated phase as shown in

Table 3(a). Unlike in the case of PE, there is no proton

transfer due to the presence of bulkier choline group

N(CH3)3 in the PC. In an earlier study, it was shown

experimentally that DMPC is more favourable for

hydration than DMPE [46]. Also, in the previous

experimental studies, it has been shown that although the

CH3 groups would not be expected to bind strongly to

water, it would appear that entropic considerations may be

of major significance in the binding process. In agreement

with the experimental studies, we also observed a

significant contribution of entropy in both PC and PE

hydrated model systems as shown in Tables 2(b) and 3(b).

We also notice that trend ofDG is different fromDH in both

PE and PC. However, the change of trend is remarkably

different in case of PE hydrated systems. Therefore, the

entropy has a significant role while calculating the

hydration energy for both the model systems. The change

of trend of DG is more clearly shown in Figures 2 and 3 for

PE and PC water complexes, respectively. It has also been

concluded that the hydration of lipids with phosphatidyl-

choline head groups is more favourable than phosphatidy-

lethanolamine as can be seen by comparing DG values of

PC and PE hydrated model systems. This shows that the

contribution of entropy is significant in PC model system.

The change of partial charge on N is not significant

unlike in the case of PE model system. We attribute this to

the presence of bulkier CH3 groups attached to it.

Therefore, the effect of water on N atom is almost

negligible in terms of partial charge. With the addition of

water molecules, there is a gradual change in the electro

positivity of choline group and electro-negativity of

phosphate group which changes from 0.676 to 0.909 and

21.234 to 21.154, respectively. The prominent positive

and negative groups in the PC model system are well

separated which is responsible for its higher dipole

moment as shown in Table 3(b). However, the dipole

moment gradually decreases with the addition of water

molecule. The reason for the same can be explained by the

orientation of the water molecules in the model systems

which reduce the overall charge separation.

4.2 Hydration behaviour of charged head groups

The PG head group model system has one negative charge

which is compensated by putting Naþ as the counter ion.

As observed in the case of neutral head group model

system, charged phospholipid model system also under-

goes a change in only a3 torsion angle and the

straightening of the head group model system observed

while hydration. The atomic distance between phosphate

group P and C of CH2OH depicts this straightening uponTab

le3

(b).

Par

tial

char

ges

of

ato

m/g

rou

pan

dh

yd

rati

on

ener

gy

calc

ula

tio

no

fth

em

od

elsy

stem

of

DM

PC

.

Hy

dra

tio

nst

ates

Par

tial

char

ges

on

ato

m/m

ole

cule

Gas

ph

ase

1w

ater

2w

ater

3w

ater

4w

ater

5w

ater

6w

ater

7w

ater

PO

42

1.2

34

21

.24

42

1.1

87

21

.17

72

1.1

85

21

.05

02

1.1

71

21

.15

4N

(CH

3) 3

0.6

76

0.7

82

0.7

41

0.8

25

0.8

51

0.7

75

0.9

11

0.9

09

CH

30

.21

30

.21

00

.21

40

.20

90

.21

80

.20

20

.21

20

.23

5(C

H2) 2

0.3

44

0.3

41

0.2

96

0.2

40

0.2

16

0.2

57

0.2

02

0.2

69

Dip

ole

mo

men

t(D

)1

2.5

41

1.2

11

0.2

69

.04

7.7

17

.05

5.4

04

.78

Hy

dra

tio

nen

erg

y(k

cal/

mo

l)–

21

3.8

52

13

.32

21

3.2

72

13

.42

21

2.6

52

12

.67

21

2.9

4H

yd

rati

on

ener

gy

at2

98

K–

21

2.1

42

11

.51

21

1.5

22

11

.62

21

0.8

02

10

.89

21

1.0

6D

G(k

cal/

mo

l)at

29

8K

–2

3.5

82

2.5

62

2.1

52

2.1

32

1.1

62

1.7

12

1.3

0C

ou

nte

rpo

ise

corr

ecte

d(k

cal/

mo

l)at

0K

–2

12

.73

21

2.1

52

12

.61

21

2.6

72

12

.10

21

2.2

12

12

.38

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addition of water molecules. It has changed from 3.84

(gas phase) to 5.29 (seven water molecules) as shown in

Table 4(a). As concluded in our previous study [28], the

DMPG molecular structure stabilises as a function of

number of Na-O bonds. Therefore, we also measured the

number of Na-O bonds both ionic (,2.34 A) and

coordinate (.2.34 A). In this case, Na þ is surrounded

by both the phosphate group oxygen atoms as well as the

oxygen atoms in the water molecules (typically called as

hydration of the counter ion). The number of NaZO bonds

increases upon hydration in the model system. The partial

charge on Na atom changes upon hydration and oscillates

2

0

–2

–4

–6

–8

–10

–12

–14

1 2 3 4 5 6 7

DMPE-water complexes

The

rmoc

hem

istr

y (k

cal/m

ol)

∆H at 298K∆G at 298K∆H at 0KBSSE corrected ∆H at 0K

Figure 2. Thermo chemistry explained of DMPE model system with increasing number of water molecules. *Each point on x-axisdenotes the PE-nH2O where n ¼ 1 to 7.

0

–2

–4

–6

–8

–10

–12

–14

–16

1 2 3 4 5 6 7

DMPC-water complexes

∆H at 0K∆H at 298K∆G at 298KBSSE corrected ∆H at 0K

The

rmoc

hem

istr

y (k

cal/m

ol)

Figure 3. Thermochemistry explained of DMPC model system with varying number of water molecules. *Each point on x-axis denotesthe PC-nH2O where n ¼ 1 to 7.

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Table 4(a). Structural parameters of DMPG in gas phase and with varying number of water molecules.

Torsional angles Bond distances

Structures a2 a3 a4 a5 PvO2 PZO3 PZO4 PZO5NaZObonds PZCH2OH

Gas phase 272 2133 269 255 1.51 1.50 1.67 1.60 3 (ionic) 3.84

1 water 267 2132 271 256 1.52 1.50 1.66 1.61 3 (ionic) 1(coordinate)

3.87

3 water 265 2115 283 267 1.52 1.50 1.66 1.61 3 (ionic) 1(coordinate)

4.20

Molecular Simulation 13

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with respect to the number of oxygen atoms of water.

Therefore, the charge on the Naþ is getting distributed to

the oxygen atoms of water in addition to the oxygen atoms

of head group. The hydration energy in the case of PG is

higher with respect to the PE and PC model systems. This

is due to the presence of counter ion which is hydrated in

addition to the other polar groups in the model system. The

trend of DH with and without counterpoise basis set

superposition error (BSSE) corrections follows the same

path; however, the difference is noticed quantitatively in

the values as it is well known that without counterpoise

correction, the hydration energy value is little higher than

that shown in Figure 4. We also note that the formation of

clathrate-like structure of the water molecules is not seen

around the counter ion.

Therefore, for hydrating counter ion, clathrate-like

structure of water molecules is not favourable. The

negative charge on the dipoles of the hydroxyl group of PG

head group might have been expected to significantly

perturb the dipole moment, but the counter ion present to

compensate the charge makes the glycerol group bends

towards the phosphate group. Therefore, both the groups

bend towards the counter ion thereby making that region

more polar. As a result, we noticed lower dipole moment

in the PG than in case of PE and PC head group model

system. However, like in the PC and PE head group, the

dipole moment in PG head group also decreases with the

addition of more number of water molecules as shown in

Table 4(b).

The surface charge and the molecular structures of the

above systems are very different, and therefore, one should

expect the orientation of water molecules to be different in

all these cases. Our present study is in agreement with the

previous experimental studies of surface sum frequency

generation spectroscopy which proves that the interfacial

water near the different head groups of phospholipid

Table 4(a) – continued

Torsional angles Bond distances

Structures a2 a3 a4 a5 PvO2 PZO3 PZO4 PZO5NaZObonds PZCH2OH

5 water 272 2111 285 269 1.51 1.51 1.64 1.61 3 (ionic) 2(coordinate)

4.43

7 water 270 286 292 259 1.51 1.52 1.64 1.61 2 (ionic) 3(coordinate)

5.29

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(either charged or neutral) behaves similarly in terms of

orientation of the OH bond of water molecules towards the

bulk water [78]. We have also observed the same

orientation of water in each of the different head group

model systems (PE, PC and PG), i.e. OZH group pointing

towards the bulk water. The strength of H-bond increases

in the order of PE , PC , PG.

4.3 Prediction of hydration sites using LRDs

LRDs predict the site of interaction of nucleophile and

electrophile attack. These descriptors have been used

widely to predict the organic reactions and substituent

effects [79]. We have calculated the FFs for the PE head

group in the gas phase, one and two water molecule model

system to predict the site of water molecule interaction. As

shown in Table 5(a) for the gas phase and Table 5(b) for

the one water molecule system, the FF values have been

validated and also studied geometrically for validation. As

shown in Table 5(a), the FF value for H7 atom (hydrogen

attached to the N) is having the highest value, and it is the

best H-bond donor atom having N attached to it. In

addition to the H7, O2 is the atom which is having next

higher FF value. Therefore, both H7 and O2 make the H-

bond with water molecule where H7 act as an H-bond

donor atom having N attached to it while O2 is an H-bond

acceptor. We also note that the higher value of fþk of H7

predicts that it will react with a nucleophile. In the

complex of one water molecule, the H7 was making H-

bond with the water oxygen. We also looked upon the

Hirshfeld population of the added water molecule. The

population shows that water molecule has 10.036 electrons

–12

–13

–14

–15

–16

–17

–180 1 2 3 4 5 6 7 8

DMPG-water complexes

The

rmoc

hem

istr

y (k

cal/m

ol)

∆H at 0KBSSE corrected ∆ at 0K

Figure 4. Thermochemistry explained of DMPG model system with varying number of water molecules. *Each point on x-axis denotesthe PG-nH2O where n ¼ 1 to 7.

Table 4(b). Partial charges of atom/group and hydration energy calculation of the model system of PG head group.

Hydration states

Partial charges on atom/molecule Gas phase 1 water 2 water 3 water 4 water 5 water 6 water 7 water

PO4 21.183 21.108 21.175 21.220 21.159 20.713 21.268 21.293Na 0.850 0.824 0.795 0.866 0.842 0.840 0.933 0.951Glycerol 0.014 0.026 0.041 0.037 0.019 0.018 0.006 0.006CH3 0.222 0.212 0.208 0.228 0.240 0.244 0.233 0.242Dipole (D) 7.149 5.372 5.427 5.291 6.332 4.339 2.008 2.637Hydration energy

(kcal/mol) at 0 K– 217.16 215.58 214.82 214.66 213.77 214.42 213.29

Counterpoise corrected(kcal/mol) at 0 K

– 216.23 214.41 214.19 213.21 212.95 213.51 214.34

Molecular Simulation 15

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and hence gains electrons from the system. The H7 and O2

have higher fþk and f2k value, respectively, where at one

site O2 will donate electrons and H7 will accept electrons

from the oxygen atom of the added water molecule. The

electron density of the H7 of PE head group model system

in gas phase is 0.8739 which later on increased to 0.9027

while interacting with a water molecule. Therefore, H has

higher fþk value and O2 of the phosphate group on the

other hand has higher f2k value where its electron density

decreases from 8.4095 to 8.3898 during complex

formation.

Therefore, the site of hydration can be predicted

beforehand by calculating the LRDs. Likewise, we can

predict the site of hydration for the second water molecule

when the model system is already interacting with one

water molecule. According to the values of FF as shown

in Table 5(b), the next site of hydration is H8 of NH3

showing the highest fþk value. Therefore, we validate in

these calculations the ability of FFs to predict the site of

interaction in biological molecules.

In addition to the gas phase and one water PE head

group model system, we continued to calculate the FF

values of two water PE head group model system to

predict the site of interaction of third water molecule. It is

well known that the water molecules very close to the head

group form a cage-like structure and form the innermost

hydration shell around it. Therefore, the third water

molecule surely makes H-bond with the water molecules

and forms the cage-like structure. Table 5(c) shows the

considerably high value of H8 which predicts the site of

next water molecule. Recently, analytical FF was

implemented in deMon2k program [80]; however using

the approximate FF also, we have got the satisfactory

results for predicting the hydration sites.

5. Conclusions

In the present study, the hydration behaviours of different

head group system, viz. PE, PC and PG have been explored.

Our study reveals substantial changes in the hydration

properties of different head groups. A clathrate-like

structure was seen to form in PE model system during

hydration. This structure is missing when the hydrogen

atoms are replaced by methyl groups (PC model system) in

the functional group. In PE hydrated model system, all three

hydrogen atoms of 2NHþ3 are involved in H-bond with

water molecules. However, similar behaviour is not

Table 5(a). LRDs for PE head group gas phase. The values inbold are the preferable site of hydration.

PE gas phase model system Atoms Fukui functions

P1 0.0853O2 0.1979O3 0.0761O4 0.0369O5 0.0811N6 0.1018H7 0.2153H8 0.1883H9 0.0167

Table 5(c). LRDs for PE head group with two water molecules.The values in bold are the preferable site of hydration.

PE 2 water model system Atoms Fukui functions

P1 0.0445O2 0.0782O3 0.0670O4 0.0657O5 0.0660N6 0.0985H7 0.0242H8 0.1529H9 0.0110

O10 0.0698H11 0.0500H12 0.0101O13 0.0327H14H15

0.10470.0183

Table 5(b). LRDs for PE head group with one water molecule.The values in bold are the preferable site of hydration.

PE 1 water model system Atoms Fukui functions

P1 0.0466O2 0.0888O3 0.0571O4 0.0813O5 0.0796N6 0.1073H7 0.0298H8 0.2010H9 0.0160

O10 0.0470H11H12

0.08400.0154

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observed in PC model system due to the presence of bulkier

choline group. In agreement with the experimental studies,

we also observed the significant contribution of entropy in

both PC and PE hydrated model systems. However,

hydration phosphatidylcholine head group model system is

more favourable than phosphatidyl ethanolamine as can be

seen by comparingDG values of PC and PE hydrated model

systems. Thus, the contribution of entropy is significant in

hydrated PC model systems. The presence of counter ion in

PG head group model system makes water to behave

differently and prevent the water molecules to form

clathrate-like clusters. The hydration of PG model system is

even favourable than PC model system due to the presence

of counter ion which also needs to be hydrated apart from

the functional groups present in the PG head group. The

functional group attached to the phosphate group is

involved mainly in both intramolecular and intermolecular

interactions and hence makes the phospholipid behave

differently in the presence of water, ligand or any other

molecules.

In addition to this, the condensed FF value of each atom

is used to predict the active site of hydration. Therefore to

prevent the large complex geometry optimisation, we can

have the information on the site of hydration of the next

water molecule before without doing quantum chemical

optimisation. The results of FF also show that the phosphate

moiety is the preferable site of hydration as proved by many

experimental studies also.

Acknowledgements

DM and SD acknowledge Council of Scientific and IndustrialResearch (CSIR) for providing financial assistance. The authorsacknowledge Center of Excellence in Scientific Computing atCSIR-NCL and CSIR-CECRI for providing computationalfacility. DM also acknowledges Ms. Pallabi Chatterji for doingsome of the initial calculations. SP acknowledges the J. C. Boseand SSB grant for the financial support.

References

[1] Kinnunen PKJ. On the principles of functional ordering inbiological membranes. Chem. Phys. Lipids. 1991;57:375–399.

[2] Fitter J, Lechner RE. Interaction of hydration water and biologicalmembranes studied by neutron scattering. J. Phys. Chem. B.1999;103:8036–8050.

[3] Leikin S, Parsegian VA, Rau DC. Hydration forces. Annu. Rev.Phys. Chem. 1993;44:369–395.

[4] Katsaras J, Jeffrey KK. Evidence of the hydration force in gel phaselipid multiblayers. Europhys. Lett. 1997;38:43–48.

[5] Pascher I, Lundmark M, Nyholm PG, Sundell S. Crystal structure ofmembrane lipids. Biochim. Biophys. Acta. 1992;113:339–373.

[6] Pullman B, Berthod H, Gresh N. Quantum mechanical studies on theconformation of phospholipids. The effect of water on confor-mational properties of polar head. FEBS Lett. 1975;53:199–204.

[7] Berger O, Edholm O, Jahnig F. Molecular dynamics simulation of afluid bilayer of DMPC at full hydration, constant pressure andconstant temperature. Biophys. J. 1997;72:2002–2013.

[8] Landin J, Pascher I, Cremer D. Ab initio and semiempirical confor-mation potentials for phospholipid head group. J. Phys. Chem.1995;99:4471–4485.

[9] Leonenko ZV, Finot E, Ma H, Dahms TES, Cramb DT.Investigation of temperature-induced phase transitions in DOPCand DPPC phospholipid bilayers using temperature-controlledscanning force microscopy. Biophys. J. 2004;86:3783–3793.

[10] Li W, Lagowski JB. Ab initio study of phospholipid headgroups:GPE and GPC. Chem. Phys. Lipids. 1999;103:137–160.

[11] Marrink SJ, Berger O, Tieleman P, Jahnig F. Adhesion forces oflipids in phospholipid membrane studied by molecular dynamicssimulation. Biophys. J. 1998;74:931–943.

[12] Meyer HW, Semmler K, Rettig W, Pohle WA, Ulrich S, Grage S,Selle C, Quinn PJ. Hydration of DMPC and DPPC at 48C produces anovel sub gel phase with convex-concave bilayer curvature. Chem.Phys. Lipids. 2000;105:149–166.

[13] Bhide SY, Berkowitz ML. The behaviour of reorientationcorrelation functions of water at the water-lipid bilayer interface.J. Chem. Phys. 2006;125:94713–94719.

[14] Hauser H, Pascher I, Pearson RH, Sundell S. Preferred conformationand molecular packing of phosphatidylethanolamine and phospha-tidylcholine. Biochim. Biophys. Acta. 1981;650:21–51.

[15] Hauser H, Guyer W, Pascher I, Skrabal P, Sundell S. Polar groupconformation of phosphatidyl chloline: effect of solvent andaggregation. Biochemistry. 1980;19:366–373.

[16] Hauser H, Pascher I, Sundell S. Preferred conformation anddynamics of the glycerol backbone in phospholipids. An NMR andX-ray single-crystal analysis. Biochemistry. 1988;27:9166–9174.

[17] Hong M, Schmidt-Rohr ZH, Zimmermann H. Conformationalconstraint on the headgroup and sn-2 chain of bilayer DMPC fromNMR dipolar coupling. Biochemistry. 1996;35:8335–8341.

[18] Bruzik KS, Harwood S. Conformational study of phospholipids incrystalline state and hydrated bilayers by 13C and 31P CP-MASNMR. J. Am. Chem. Soc. 1997;119:6629–6637.

[19] Aussenac F, Laguerre M, Schmitter JM, Dufourc EJ. Detailedstructure and dynamics of bicelle phospholipids using selectivelydeuterated and perdeuterated labels. 2H NMR and molecularmechanics study. Langmuir. 2003;19:10468–10479.

[20] Florian J, Baumruk V, Strajbl M, Bednarova L, Stepanek J. IR andNMR spectra conformational flexibility, and scaled quantummechanical force fields of sodium dimethyl phosphate and dimethylphosphate anion. J. Phys. Chem. 1996;100:1559–1568.

[21] Liang C, Ewig CS, Stouch TR, Hagler AT. Ab initio studies of lipidmodel species. 1. dimethyl phosphate and methyl propyl phosphateanions. J. Am. Chem. Soc. 1993;115:1537–1545.

[22] Pullman B, Pullman A, Berthod H, Gresh N. Quantum-mechanicalstudies of environmental effects on biomolecules vi. Ab initiostudies on the hydration scheme of the phosphate group. Theor.Chem. Acc. 1975;40:93–111.

[23] Landin J, Pascher I, Cremer D. Effect of a polar environment onthe conformation of phospholipid head groups analyzed with theonsager continuum solvation model. J. Phys. Chem. A.1997;101:2996–3004.

[24] Pohle W, Gauger DR, Bohl M, Mrazkova E, Hobza P. Lipidhydration: headgroup CH moieties are involved in water binding.Biopolymers. 2004;74:27–31.

[25] Mrazkova E, Hobza P, Bohl M, Gauger DR, Pohle W. Hydration-induced changes of structure and vibrational frequencies ofmethylphosphocholine studied as a model of biomembrane lipids.J. Phys. Chem. B. 2005;109:15126–15134.

[26] Thirumoorthy K, Nandi N, Vollhardt D, Oliveira ON. Semiempi-rical quantum mechanical calculations of dipolar interactionbetween dipyridamole and dipalmitoyl phosphatidyl choline inLangmuir monolayers. Langmuir. 2006;22:5398–5402.

[27] Krishnamurty S, Stefanov M, Mineva T, Begu S, Devoisselle JM,Goursot A, Zhu R, Salahub DR. DFT based conformational analysisof a Phospholipid molecule (DMPC). J. Phys. Chem. B.2008;112:13433–13442.

[28] Mishra D, Pal S, Krishnamurthy S. Understanding the molecularconformations of Na-dimyristoylphosphatidylglycerol (DMPG)using DFT based method. Mol. Simul. 2011;37:953–963.

[29] Weiner SJ, Kollman PA, Nguyen DT, Case DA. An all atom forcefield for simulation of proteins and nucleic acids. J. Comput. Chem.1986;7:230–252.

[30] Duan Y, Wu C, Chowdhury S, Lee MC, Xiong GM, Zhang W, YangR, Cieplak P, Luo R, Lee T, Caldwell J, Wang JM, Kollman P. A

Molecular Simulation 17

Dow

nloa

ded

by [

Indi

ana

Uni

vers

ities

] at

22:

45 1

5 A

pril

2013

point-charge force field for molecular mechanics simulations ofproteins based on condensed-phase quantum mechanical calcu-lations. J. Comput. Chem. 2003;24:1999–2012.

[31] Kaminski GA, Friesner RA, Tirado-Rives J, Jorgensen WL.Evaluation and reparametrization of the OPLS-AA force field forproteins via comparison with accurate quantum chemicalcalculations on peptides. J. Phys. Chem. B. 2001;105:6474–6487.

[32] Feller S, MacKerell AD Jr. An improved empirical potential energyfunctions for molecular simulations of Phospholipids. J. Phys.Chem. B. 2000;104:7510–7515.

[33] Akutsu H, Nagamori T. Conformational analysis of the polar headgroup in phosphatidylcholine bilayers: a structural change inducedby cations. Biochemistry. 1991;30:4510–4516.

[34] Vanderkooi G. Multibilayer structure of dimyristoylphosphatidylcholine dehydrates as determined by energy minimization.Biochemistry. 1991;90:10760–10768.

[35] Stauch TR. Lipid membrane structure and dynamics studied by allatom molecular dynamics simulations of hydrated phospholipidbilayer. Mol. Simul. 1993;10:335–362.

[36] Egberts E, Marrink SJ, Berendsen HJC. Molecular dynamicssimulation of phospholipid membrane. Eur. Biophys. J. 1994;22:423–436.

[37] Marrink SJ, Mark AE. Molecular view of hexagonal phaseformation in phospholipid membranes. Biophys. J. 2004;87:3894–3900.

[38] Murzyn K, Zhao W, Karttunen M, Kurziel M, Rog T. Dynamics ofwater at membrane surfaces: effect of head group structures.Biointerphases. 2006;1:98–105.

[39] Rog T, Murzyn K, Pasenkiewicz-Gierula M. The dynamics of waterat the phospholipid bilayer surface. A molecular dynamicssimulation study. Chem. Phys. Lett. 2002;352:323–327.

[40] Pandey PR, Roy S. Headgroup mediated water insertion into theDPPC bilayer. A molecular dynamics study. J. Phys. Chem. B.2011;115:3155–3163.

[41] Vanderkoi G. Computation of mixed phosphatidylcholine-choles-terol bilayer structures by energy minimization. Biophys. J. 1994;66:1457–1468.

[42] Chanda J, Bandyopadhyay S. Perturbation of phospholipid bilayerproperties by ethanol at a high concentration. Langmuir.2006;22:3775–3781.

[43] Hogberg CJ, Lyubartsev A. A molecular dynamics investigation ofthe influence of hydration and temperature on structural anddynamical properties of a dimyristoylphosphatidylcholine bilayer.J. Phys. Chem. B. 2006;110:14326–14336.

[44] Thaning J, Hogberg CJ, Stevensson B, Lyubartsev A, Maliniak A.Molecular conformations in a phospholipid bilayer extracted fromdipolar couplings: a computer simulation study. J. Phys. Chem. B.2007;111:13638–13644.

[45] Pathasarathi R, Jianhui T, Redondo A, Gnankaran S. Quantumchemical study of Carbohydrate-Phospholipid interactions. J. Phys.Chem. A. 2011;115:12826–128240.

[46] Lis LJ, McAlister M, Fuller N, Rand RP, Parsegian VA.Measurement of the lateral compressibility of several phospholipidbilayers. Biophys. J. 1982;37:667–672.

[47] Yang Y, Parr RG. Hardness, softness, and the fukui function in theelectronic theory of metals and catalysis. Proc. Natl. Acad. Sci.USA. 1985;82:6723–6726.

[48] Yang W, Mortier WJ. The use of global and local molecularparameters for the analysis of the gas-phase basicity of amines.J. Am. Chem. Soc. 1986;108:5708–5711.

[49] Parr RG, Yang W. Density-functional theory of atoms andmolecules. New York: Oxford University Press; 1989.

[50] Parr RG, Yang W. Density functional approach to the frontier-electron theory of chemical reactivity. J. Am. Chem. Soc. 1984;106:4049–4050.

[51] Pearson RG. Hard and soft acids and bases. J. Am. Chem. Soc.1963;85:3533–3539.

[52] Sen KD. Chemical hardness Structure and bonding. Berlin:Springer-Verlag; 1993. p. 80.

[53] Parr RG, Pearson RG. Absolute hardness: companion parameterto absolute electronegativity. J. Am. Chem. Soc. 1983;105:7512–7516.

[54] Parr RG, Donnelley RA, Levy M, Palke WE. Electronegativity: thedensity functional viewpoint. J. Chem. Phys. 1978;68:3801–3808.

[55] Pearson R. Absolute electronegativity and absolute hardness ofLewis acids and bases. J. Am. Chem. Soc. 1985;107:6801–6806.

[56] Perdew JP, Parr RG, Levy M, Balduz JL. Density-functional theoryfor fractional particle number: derivative discontinuities of theenergy. Phys. Rev. Lett. 1982;49:1691–1694.

[57] Zhang Y, Yang W. Perspective on “Density-functional theory forfractional particle number: derivative discontinuities of the energy”.Theor. Chem. Acc. 2000;103:346–351.

[58] Gazquez JL, Mendez F. The hard and soft acids and bases principle:an atoms in molecules viewpoint. J. Phys. Chem. 1994;98:4591–4593.

[59] Mendez F, Gazquez JL. Chemical reactivity of enolate ions: thelocal hard and soft acids and bases principle viewpoint. J. Am.Chem. Soc. 1994;116:9298–9301.

[60] Gazquez JL, Martinez A, Mendez F. Relationship between energyand hardness differences. J. Phys. Chem. 1993;97:4059–4063.

[61] Koster AM, Calaminici P, Casida ME, Flores MR, Geudtner G,Goursot A, Heine T, Ipatov A, Janetzko F, Martin del Campo J,Patchkovskii S, Reveles JU, Salahub DR, Vela A. The deMondevelopers. Mexico City: Cinvestav; 2006.

[62] Zhang Y, Yang W. Comment on “Generalized gradient approxi-mation made simple. Phys. Rev. Lett. 1998;80:890–890.

[63] Lee C, Yang W, Parr RG. Development of the Colle-Salvetticorrelation-energy formula into a functional of the electron density.Phys. Rev. B: Condens. Matter Phys. 1988;37:785–789.

[64] Godbout N, Salahub DR, Andzelm J, Wimmer E. Optimization ofGaussian-type basis sets for local spin density functionalcalculations. Part I. Boron through neon, optimization techniqueand validation. Can. J. Chem. 1992;70:560–571.

[65] Koster AM, Flores-Moreno R, Reveles JU. Efficient and reliablenumerical integration of exchange-correlation energies andpotentials. J. Chem. Phys. 2004;121:681–691.

[66] Dunlap BI, Connolly JWD, Sabin JR. On first-row diatomicmolecules and local density models. J. Chem. Phys. 1979;71:4993–5000.

[67] Mintmire W, Dunlap BI. Fitting the Coulomb potential variationallyin linear-combination-of-atomic-orbitals density-functional calcu-lations. Phys. Rev. A. 1982;25:88–95.

[68] Reveles JU, Koster AM. Geometry optimization in densityfunctional methods. J. Comput. Chem. 2004;25:1109–1116.

[69] Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA,Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA,Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, BloinoJ, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R,Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H,Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M,Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R,Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS,Tomasi J, Cossi M, Rega N, Millam NJ, Klene M, Knox JE, CrossJB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE,Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, MartinRL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P,Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB,Ortiz JV, Cioslowski J, Fox DJ. Gaussian 09 Revision. A.1 Inc.Wallingford CT; 2009.

[70] Becke AD. Density-functional thermochemistry. III. The role ofexact exchange. J. Chem. Phys. 1993;98:5648–5653.

[71] Roy RK, Pal S, Hirao K. On non-negativity of Fukui functionindices. J. Chem. Phys. 1999;110:8236–8246.

[72] Hirshfeld FL. Bonded-atom fragments for describing molecularcharge densities. Theor. Chim. Acta. 1977;44:129–138.

[73] Frischleder H, Lochmann R. Quantum-chemical and semiclassicalcalculations of intermolecular interactions of phospholipids. Int.J. Quant. Chem. 1979;16:203–213.

[74] Breneman MC, Wiberg KB. Determining atom-centered monopolesfrom molecular electrostatic potentials. The need for high samplingdensity in formamide conformational analysis. J. Comput. Chem.1990;11:361–373.

[75] Thanikaivelan P, Padmanabhan J, Subramanian V, Ramasami T.Chemical reactivity and selectivity using Fukui functions: basis set

D. Mishra et al.18

Dow

nloa

ded

by [

Indi

ana

Uni

vers

ities

] at

22:

45 1

5 A

pril

2013

and population scheme dependence in the framework of B3LYPtheory. Theor. Chem. Acta. 2004;107:326–335.

[76] Beck B, Clark T, Glen RC. A detailed study of VESPA electrostaticpotential-derived atomic charges. J. Mol. Mod. 1995;1:176–187.

[77] Beck B, Clark T, Glen RC. VESPA: a new, fast approach toelectrostatic potential-derived atomic charges from semiempiricalmethods. J. Comput. Chem. 1997;18:744–750.

[78] Sovago M, Vartiainen E, Bonn M. Observation of buried watermolecules in phospholipid membranes by surface sum-frequency

generation spectroscopy. J. Chem. Phys. 2009;131:161107–

161111.

[79] Vleeschouwer FD, Jaque P, Geerlings P, Toro-Labbe A, De Proft F.

Regioselectivity of radical additions to substituted alkenes: insight

from conceptual density functional theory. J. Org. Chem.

2010;75:4964–4974.

[80] Moreno RF. Symmetry conservation in Fukui functions. J. Chem.

Theor. Com. 2010;6:48–54.

Molecular Simulation 19

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nloa

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by [

Indi

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Uni

vers

ities

] at

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