Temperature Dependence of theMolecular Conformations of DilauroylPhosphatidylcholine: A DensityFunctional Study

TZONKA MINEVA,1 SAILAJA KRISHNAMURTY,1,2

DENNIS R. SALAHUB,3 ANNICK GOURSOT1

1Institut Charles Gerhardt Montpellier, UMR 5253 CNRS/ENSCM/UM2/UM1, 8 rue de l’EcoleNormale, 34296 Montpellier Cedex 5, France2Functional Materials Division, Central Electrochemical Research Institute, Karaikudi 630006,Tamil Nadu, India3Department of Chemistry and Institute for Biocomplexity and Informatics, University of Calgary,2500 University Drive NW, Calgary, AB, Canada T2N 1N4

Received 30 September 2011; Revised 18 November 2011; accepted 2 December 2011Published online in Wiley Online Library (wileyonlinelibrary.com).DOI 10.1002/qua.24015

ABSTRACT: Born–Oppenheimer molecular dynamics (BOMD) in combination withdensity functional theory, augmented with a damped empirical dispersion term, has beenused to study the behavior of dilauroyl phosphatidylcholine (DLPC) isomers with tempera-ture. In contrast to dimyristoyl phosphatidylcholine (DMPC), the BOMD results show thepresence of various conformations at different temperatures. The molecular order–disorderprocess, quantified by the distance-fluctuation criterion as a function of temperature, is char-acterized by two transitions. This is in line with the known two-phase transitions of DLPCbilayers, involving trans to gauche conformational changes in the alkane chains. The differ-ent temperature dependence of the DLPC and DMPCmolecules suggests that the experi-mentally observed unusual dynamics of DLPC bilayers compared to that of longer chainlipids is governed to a large extent by the intramolecular dynamics. A first-principles meth-odology applied at the molecular level can thus be an appropriate tool for microscopic anal-ysis of the order–disorder transitions, which are related to the molecular structuraltransformations within large assemblies.VC 2012 Wiley Periodicals, Inc.

Key words: dilauroyl phosphatidylcholine; Born–Oppenheimer molecular dynamics;conformations; DFT-D

Correspondence to: T. Mineva; e-mail: tzonka.mineva@enscm.fr

International Journal of Quantum Chemistry, Vol. 000, 000–000 (2012)VC 2012 Wiley Periodicals, Inc.

1. Introduction

I n view of the importance of lipid phase transi-tions in biological membranes, the dynamics

of synthetic phosphatidylcholine (PC) lipidbilayers, whose major component consists of PClipids with saturated 14–24 carbon (C) acyl chains,have been studied extensively. Most of the struc-tural transformations of the PC lipid bilayers withrespect to environmental conditions such as tem-perature, pressure, and pH are associated withisomerization of the constituent lipid molecules.For instance, the transition on heating from thevery ordered gel (Lc) to the fluid liquid crystalline(La) phase, called the main phase transition, hasbeen related to the ‘‘melting’’ of the hydrocarbonchains: in the gel phase, phospholipids with alltrans alkyl chains are present, whereas in the dis-ordered liquid crystalline phase, the most popu-lated conformational states correspond to gaucheforms in the alkyl chains.

Among the PC lipids, the dynamics of dimyris-toyl phosphatidylcholine (DMPC; dimyristoyl,14C and DPPC; dipalmytoyl, 16 C) have been themost studied. Phase transitions of bilayers ofshorter carbon chain, that is, dilauroyl phosphati-dylcholine (DLPC; dilauroyl, 12C) bilayers, werealso examined and compared with the dynamicsof longer chain bilayers. The thermograms ofDMPC and longer chain lipid bilayers show asmall peak at temperatures well below that of thesharp peak of the main phase transition. The gen-eral interpretation is that, when the bilayers arefully hydrated and sufficiently incubated at lowtemperature, this small endothermic peak (about1 kcal/mol) is related to a pretransition betweenan Lc gel state and a rippled gel state (Pb0), bothcharacterized by all-trans chain conformers. Thispretransition state is thus not related to molecularstructural changes but to a different packingarrangement of the molecules in the gel. The pre-transition peak is followed by the main phasetransition to a liquid crystalline La state with pre-dominantly gauche chain conformers of the con-stituent lipid molecules.

In contrast, the phase pattern of the DLPC ther-mograms, characterized by one sharp peak fol-lowed by a broad band spreading over about 10 K[1–11], is more complex. Note that this complexityis enhanced by the overlapping of the lipid andwater solid–liquid phase transition. Various inter-pretations of the unusual DLPC thermograms

have been proposed. In the earliest experiments [1,3], the observed two closely spaced peaks (onesharp peak at 271 K and a broad peak at around278 K) were interpreted as a bimodal phase transi-tion of a direct ‘‘multistage’’ transformation fromthe Lc to the La phase. Two phase transitions wereassigned to the two peaks observed in more recentexperiments, using various techniques such as dif-ferential scanning calorimetry (DSC) [4, 5], X-raydiffraction [6, 9], neutron diffraction [10], Raman[2], and NMR [4, 7] spectroscopies. All these stud-ies agreed also in reporting a strong dependenceof the position of the first peak on the temperatureand the heating rate. Some of the published ther-modynamic properties from DSC experiments aresummarized in Table I.

Note that the positions of the peaks are slightlydifferent in different works. Moreover, threepeaks were reported in the most recent experi-ments [11], where a mixture of water and ethyl-ene glycol solvent was used to avoid water freez-ing at the temperature close to the first peak.

In parallel with experimental studies on thetemperature dependence of the lipid bilayer struc-tural transformations, molecular mechanics simu-lations based on classical force-field (FF)approaches have also reported sound informationabout the dihedral angle values [12, 13], tail orien-tations [14], and phase changes [15, 16] in PClipid bilayers. It has been recognized that the reli-ability of the FF-based molecular dynamicsstrongly depends on the accuracy of describingthe torsional potential energies of alkanes [17].This understanding has prompted the improve-ment of some of the most widely applied FFs forbiomolecules [17], using recent ab initio computa-tions of torsional potentials in various trans/gauche n-alkanes (up to n-decane) [18]. Our previ-ous theoretical works [19, 20] on the PC lipid con-formations (DLPC, DMPC, and DPPC) based ondensity functional theory (DFT) augmented witha damped empirical dispersion term (DFT-D)demonstrated the existence of several conformers(at T ¼ 0 K and in the gas phase) with relativeenergies in an interval of 2 kcal/mol, independentof the chain length. The dynamics of the individ-ual DMPC molecule studied for a series of tem-peratures, ranging from 200 to 350 K, using Born–Oppenheimer molecular dynamics (BOMD)coupled with DFT-D, shows only one discontinu-ity (at 300 K) of the interatomic distance-fluctua-tion as a function of temperature [21]. This valueis close to the experimentally known main phase

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transition temperature obtained for a fullyhydrated bilayer of DMPC lipids, that is, 295 �1.5 K [22–24].

To gain more insight into the influence of themolecular degrees of freedom on the bilayerproperties, we focus, in this article, on the micro-scopic structural changes of DLPC isomers at dif-ferent temperatures. Our BOMD results showindeed a different dynamical evolution from thatobtained for DMPC [14]. The main difference liesin the presence of two peaks in the interatomicdistance fluctuations at temperatures differing byonly 10–15 K from those reported for the twophase transitions of the DLPC bilayer. The pres-ent results confirm that lipid phase transitionsrelated to intramolecular structural changes canbe predicted using molecular models and first-principles methods.

2. Methods and Computational Details

The calculations were performed within theframework of DFT, using a linear-combination-of-Gaussian-orbitals approach, as implemented inthe deMon2k program [25]. All calculations werecarried out with the revised Perdew, Burke andErnzerhof (PBE) exchange [26] and the Lee, Yangand Parr (LYP) [27] correlation functional, aug-mented by a damped empirical correction for dis-persion-like interactions [28, 29].

The DLPC dynamics were studied by carryingout BOMD simulations on two lowest energy

isomers. All momenta are conserved during thedynamics. The total equilibrated simulation timeamounts to 184 ps with a minimum of 9 ps for thefirst conformer and 16 ps for the second one ateach temperature. The simulations were carriedout at 230, 250, 261, 273, 285, 290, and 300 K,starting from the optimized structures of the twoisomers. The temperature of the system was main-tained using the Berendsen thermostat (s ¼ 0.5 ps)in the NVT ensemble, where N is the number ofparticles, V is the volume and T is the temperature.The nuclear positions were updated with the veloc-ity Verlet algorithm with a time step of 1 fs. At allthe simulation temperatures, the equilibration waseffective after a time period of 3–4 ps.

DFT-optimized double zeta plus valence polar-ization (DZVP) basis sets [30] were used for allatoms, associated with automatically generatedfunctions up to l ¼ 2 for fitting the density [31].The exchange-correlation potential was numeri-cally integrated on an adaptive grid [32]. The gridaccuracy was set to 10�5 in all calculations.

The accuracy of the presently used DFT-Dmethod has been validated for the energetics andgeometries of all-trans n-alkane dimmers [28].Evaluation of the relative stabilities of DLPC,DMPC, and DPPC with one kink (single gauchestate with either 60 or �60) at various positions inthe chains with respect to all-trans structuresshowed that the gauche conformations are notdegenerate in contrast to n-tetradecane studied atthe same level of theory [19]. In addition, theDFT-D/DZVP relative energy of single gaucheand all-trans tetradecane states [19] of 0.46 kcal/

TABLE IThermodynamic properties from DSC studies of DLPC bilayer dynamics.

SolventAssignedtransition

Transitiontemperature (K)

Enthalpy change(kcal/mol)

Entropy change(cal/K mol)

Watera Pb0 ! La 271.2 1.8 6.7Waterb Pb0 ! La 271.1 1.8

Lc ! Lac 280.2 13.4

Waterd Pb0! La 270.9 1.8 6.7Water/ethyleneglycol (50 wt%)d

Pb0 ! La or Lx 272.8 2.2 8.1Lc ! Lx 274.9 7.9 28.7Lx ! La 277.7 0.4 1.2

Lc, Pb0, Lx, and La denote, respectively, the stable gel, metastable (ripple) gel, intermediate liquid crystalline, and liquid crystallinephases.a From Ref. [1].b From Ref. [3].c Probably through intermediate phases.d From Ref. [11].

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mol compares very well with the value of 0.54kcal/mol for octane to decane, computed with thecoupled-cluster singles and doubles with pertur-bative triples (CCSD(T)) method for the MP2 opti-mized geometries. We performed additionalbenchmark calculations of four pentane conform-ers, for example, structures with all trans (tt),with a single gauche (tgþ), and with two adjacentgauche states, respectively, with (60�, 60�) and(60�, �60�), noted as gþgþ and gþg�. Our DFT-D/DZVP calculations yielded relative energies of,respectively, 0.65, 1.42, and 2.91 eV for the tgþ,gþgþ, and gþg� states with respect to the all-transconformer. These results compare reasonably wellwith the CCSD(T)/cc-pVTZ (geometries opti-mized at CCSD/cc-pVDZ level) values of 0.59(tgþ), 0.95 (gþgþ), and 2.79 (gþg�) in Ref. [18].

To quantify the structural deformations occur-ring along the molecular dynamics, we used thedistance-fluctuation criterion initially introducedby Berry et al. [33]. The Berry parameter DB isexpressed for a system of N atoms and rij intera-tomic distances between atoms i and j as

DB ¼ 2NðN�1Þ

Pi\j

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDr2

ij

D E� rijh i2

r

rijh i . The critical value of

DB for the solid to liquid transition of finite systemshas been suggested to be close to 0.1 [33–36].

3. Results and Discussion

3.1. CONFORMATIONAL CHANGES ASA FUNCTION OF TEMPERATURE

Several isomer interchanges were observedalong the BOMD trajectories of DLPC at differenttemperatures. A diacyl phosphatydilcholine lipidmolecule consists of a head group or a chain andtwo glycerolipid b and c chains as illustrated inFigure 1. Low-energy conformers have been ana-lyzed in previous works [19, 20]. We chose tostart the BOMD simulations using the initial mini-mum energy isomer structure, labeled 1a in Fig-ure 1, whose dynamical behavior has alreadybeen studied in detail for the DMPC molecule[21]. The structure of the DLPC conformer 1b,also shown in Figure 1, was obtained along thedynamics at 240 and 250 K and subsequentlyoptimized at T ¼ 0 K (isomer 1b is more stablethan 1a by 1 kcal/mol). The optimized a, b, and cdihedral angles for both minima 1a and 1b aregiven in Table II.

These two isomers differ by their b3 and c4dihedrals. Figure 2 illustrates the concomitantchanges of b3 and c4 dihedral angles along the 1adynamics at T ¼ 240 K, which occurred at around3 ps after the equilibration.

BOMD calculations were carried out with theinitial 1b isomer as well. For this starting

FIGURE 1. Nomenclature of a PC lipid molecule. (a)Notations of torsional angles, (b) DLPC conformerfound from the BOMD simulations. In both structuresthe red, yellow, green, pink, and light gray balls repre-sent oxygen, carbon, nitrogen, phosphorous, andhydrogen atoms, respectively. Optimized geometries of1a and 1b isomers were used as initial structures in theBOMD dynamics at various temperatures. [Color figurecan be viewed in the online issue, which is available atwileyonlinelibrary.com.]

TABLE IITorsion angles in degrees for selected DLPC ground-state conformers, optimized at T 5 0 K, used as initialstructures in the BOMD simulations.

Conformer a5 a4 a3 a2 a1 y1/y2 y3/y4 c1 c2 c3 c4 b1 b2 b3 b4

1a �71.1 120.4 71.9 78.8 �97.9 172.5/�70.0 176.0/65.6 �114.2 170.5 �143.0 173.8 128.6 176.0 �100.9 169.51b �71.0 120.7 71.8 78.9 �98.1 175.5/�69.9 174.8/66.9 �117.0 179.0 �159.1 70.9 125.9 179.1 62.8 177.7

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geometry, no conformational transformationswere observed during 16 ps trajectories at 230,240, 250 K. The first structural changes are foundat 261 K, when a kink (gauche conformer)appears in one alkane tail. For both 1a and 1b iso-mers, gauche alkane chain conformations occur atT � 261 K. Interestingly, comparison of the 261,273, and 285 K dynamics reveals that much largera, b, and c chain fluctuations occur at 261 K, thanat 273 and 285 K, despite the occurrence of a glyc-erol conformational change in 1b and 1a, at 273and 285 K, respectively (illustrated in Fig. 3). At

higher temperatures (290 and 300 K), severalgauche forms are formed in the alkyl chains ofboth systems.

Analysis of these BOMD trajectories, startingfrom slightly different isomers, shows that confor-mational changes associated with the ester groupsand the glycerol may appear at various tempera-tures. This result is at variance with the DMPCdynamical behavior, which only showed kink for-mation in the alkyl chains, after a first appearanceat 297 K [21].

The different dynamical behaviors of DLPCand DMPC are also observed experimentally, withthe very specific property of DLPC that it under-goes a first phase transition at temperatures vary-ing with the thermal history of the sample [2–11].

3.2. MOLECULAR ORDER–DISORDERTRANSITION

We will discuss below how the sampling ofdiverse vibrational energy states as obtained fromBOMD can be related to the molecular order–dis-order process. The Berry parameter values, shownin Figure 4 as a function of temperature, com-puted from the fluctuations in intramolecularatomic distances during the dynamics of 1a and1b isomers, have been weighted by the popula-tions of the two isomers (assuming a Boltzmandistribution) at the studied temperatures. The DB

values vary between 0.060 and 0.063 for the struc-tures with all-trans tail conformers preserved dur-ing the simulations at T � 250 K and jumps to0.097 at T ¼ 261 K, the temperature at which atrans to gauche transformation occurs in the alkylchains. Increasing the temperature to T ¼ 273 and285 K, we obtained unexpectedly a reduction ofDB. Despite the fact that the alkyl chains keep one

FIGURE 2. Dihedral angle values of f (red line), c4(black line), b4 (pink line), and b3 (cyanide line) as afunction of time, obtained from the BOMD simulation at240 K starting from the 1a structure. [Color figure canbe viewed in the online issue, which is available atwileyonlinelibrary.com.]

FIGURE 3. Dihedral angle values of y1 and y2 as afunction of time, obtained from the BOMD simulation at273 K starting from the 1b structure. [Color figure canbe viewed in the online issue, which is available atwileyonlinelibrary.com.]

FIGURE 4. The distance-fluctuation criterion DB as afunction of temperature. [Color figure can be viewed inthe online issue, which is available atwileyonlinelibrary.com.]

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gauche form as is the case at T ¼ 261 K, itappears that the fluctuations of the intramolecularatomic distances decrease. This peculiar behaviorof an isolated DLPC molecule corresponds to theconclusions drawn from both DSC [11] and neu-tron diffraction measurements [10] attributing thebroad area between 272.6 and 281 K to an un-usual transition from a gel state to an ‘‘intermedi-ate’’ liquid state (Lx), which shows ‘‘a substantialslowing of molecular motions’’ [7] with respect tothe first transition.

For the dynamics at T ¼ 290 and 300 K oneobserves in Figure 4 a second increase of DB to0.117 and 0.121, respectively. At these tempera-tures, a much larger conformational space issampled as concluded from the appearance of sev-eral gauche conformers in the b and c alkyl chains.The a chain bends toward either the b or the c chaindepending on the initial structure. As a conse-quence, DB increases above 0.11. This picture corre-sponds indeed to a fully disordered state.

Using the critical DB value of about 0.1, as sug-gested for finite system order–disorder phasetransitions, the value of 261 K can be consideredas a DLPC intramolecular melting temperature.The second intramolecular transition to a moredisordered state occurs at T ¼ 290 K as followsfrom the DB evolution. It is interesting to relatethese two peaks of the Berry parameter to thethermograms of the DLPC bilayers, which displaytwo-phase transitions also. The calculated temper-ature of 261 K is about 10 K lower than the exper-imental temperatures, indicated for the first gel toliquid (Pb0 ! La or Lx) phase transition (Table I).The second peak of the DB function is shiftedupward by about 10–15 K when compared to theexperimental temperatures of 275–280 K [1, 3, 11].Despite the shifts between calculated and experi-mental melting temperatures, we observe that thedynamical behavior of the individual DLPC mole-cules is largely preserved in the ensemble dynam-ical properties that are not attributed to changesof the ensemble topology.

It is also worth noting that for the DMPC mole-cule, the distance-fluctuation criterion shows onlyone abrupt increase at T between 297 and 301 K[21], related to the main phase transition at T ¼295 � 1.5 K [22–24]. This confirms that C12 andC14 PC lipids have different dynamics at a molec-ular level. It is thus most likely that one may at-tribute the origins for the ‘‘intrinsically different’’[7, 10] gel-to-liquid phase transitions of PCbilayers with chains shorter than C13 to the sub-

stantially different dynamical behavior of the con-stituent lipid molecules.

4. Conclusion

The dynamical behavior of DLPC, studied withBOMD and DFT-D methods, reveals several sub-stantial differences from that of DMPC [21].Before the DLPC tail trans-to-gauche isomeriza-tion (240 and 250 K), the initial 1a structure trans-forms into another conformer, differing by its b3and c4 dihedral angles, keeping all-trans alkylchains. Such an isomer interchange was notobserved in the dynamics of DMPC.

In contrast to the DMPC molecular dynamics,the DLPC DB as a function of temperature showstwo sharp discontinuities. The latter characteristicis in line with the peculiar thermograms, reportedfor DLPC bilayers, which are interpreted as twogel-to-liquid crystalline (fully or medium disor-dered) states, eventually completed with a transi-tion from a medium disordered liquid to a fullydisordered liquid state. These results lead to theconclusion that the substantially different dynami-cal behavior observed experimentally for theDLPC and DMPC bilayers originates in the differ-ent intramolecular dynamical behavior of the C12and C14 PC lipid molecules. Moreover, they allowone to propose that BOMD/DFT studies of com-plex molecule can help in the understanding ofsome dynamical properties of their ensembles.

ACKNOWLEDGMENT

This work was granted access to the HPCresources of CCRT under the allocationst2011036031 and t2011085018 made by GENCI(Grand Equipement National de Calcul Intensif).D.R.S. is grateful to NSERC for continued support.Compute Canada/WestGrid is acknowledged forthe provision of computational resources. S.K.thanks high performance computational centre,Central Electrochemical Research Institute, Karai-kudi, India, for partial computational support.

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