Heterogeneity in Dynamics of Dioctadecyldimethylammonium

Subscriber access provided by Kaohsiung Medical University

C: Surfaces, Interfaces, Porous Materials, and Catalysis

Heterogeneity in Dynamics of Dioctadecyldimethylammonium Bromide Bilayers: Molecular Dynamics Simulation and Neutron Scattering Study Harish Srinivasan, Veerendra Kumar Sharma, Subhankur Mitra, and Ramaprosad Mukhopadhyay J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06216 • Publication Date (Web): 13 Aug 2018 Downloaded from http://pubs.acs.org on August 15, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Heterogeneity in Dynamics of Dioctadecyldimethylammonium Bromide Bilayers: Molecular Dynamics Simulation and Neutron Scattering Study H. Srinivasan, V.K. Sharma, S. Mitra# and R. Mukhopadhyay#* Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 40085, India #

Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India

* Corresponding author: [email protected] Tel:+91-22-25594667; Fax:+91-22-25505151

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 40

ABSTRACT: Molecular dynamics (MD) simulations have been carried out to investigate the structural and dynamical aspects of dioctadecyldimethylammonium bromide (DODAB) bilayer which exists in various phases. MD simulation at 300 K, shows that the bilayer system is found to form an asymmetric ripple phase with highly ordered and tightly packed alkyl chains. While at 350 K, the system is found to be in the fluid phase, marked by a significant increase in fluidity and presence of significant gauche defects. Alkyl chain order parameter suggests that ordering is highest near the headgroup region in both the phases. The mean squared displacement (MSD) corresponding to the lateral motion of DODAB lipid, scales as tα, with α ~0.5 at 300 K and ~0.62 at 350 K, indicating subdiffusive motion, which is modelled in the framework of generalized Langevin equation (GLE). It is also found that the lateral motion of the lipid is spatially homogenous; hence the origin of subdiffusive process is temporal heterogeneity which is captured by the memory function obtained from GLE. High energy resolution neutron scattering data recorded on the same system are analyzed by comparing the incoherent intermediate scattering function (IISF) calculated from simulation. IISF are analyzed assuming three independent dynamical processes – lateral, segmental and torsional motion of the lipids. Here too, the lateral motion is found to be well described by a spatially homogenous subdiffusive motion. The segmental dynamics of the alkyl chain is delineated successfully using the localized translational diffusion model, where the variation of dynamicity along the alkyl chain is in compliance with the internal dynamics observed in the MD simulation. The torsional motion is described by 2-fold rotation. This work describes the complex dynamical behavior of DODAB lipid bilayer using MD simulation and neutron scattering studies consistently. The understanding of dynamics of DODAB bilayer would be useful in various applications including DNA/gene transfection and drug transport.


Page 3 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. INTRODUCTION Cationic liposomes have been of immense interest from the aspect of both fundamental and applied sciences. Their membrane mimicking properties enable them as excellent models to explore and understand the biophysics of cell membranes. It has also been found to have tremendous applicability in pharmaceutical industries for gene/ DNA transfection, drug delivery, antimicrobial and antifungal activity, etc.1-8 Dioctadecyldimethylammonium bromide (DODAB) is a synthetic cationic lipid found to self-aggregate under suitable conditions in aqueous media.9 Since its discovery, it has been studied quite extensively1,6-7,10-19 to understand its applicability and phase behavior. As a model membrane system, it has been observed that the unilamellar DODAX (X = Br-, Cl-) vesicles are able to model the process of endocytosis and vesicular traffic.12,17 Carmona and co-workers2,5,20 have explored the possibility of its application in drug/vaccine delivery and antimicrobial activity. They have found DODAB in the form of bilayer fragments/disks show great drug encapsulation ability for hydrophobic drugs.2 Further it has been observed that DODAB itself shows biocidal action against various bacteria and fungi.20 Unlike its single-chain counterparts, CnTAB surfactants, the cell killing by DODAB is effected by charge inversion rather than cell lysis.1 It is notable that DODAB is effective in killing bacterial and fungal cells at micromolar concentration but is non-toxic to mammalian cells up to ~ 1 mM.2 Positively charged cationic liposomes and negatively charged DNA form a complex due to their electrostatic interaction. The formation of cationic lipid-DNA complex due to electrostatic interactions results in DNA condensation on the surface of the liposome. Since liposomes as vectors are non-immunogenic, non-oncogenic and easy to produce, they have a special advantage over viral vectors in gene/DNA transfection.4,7-8 It has been shown that DODAB bilayer coated gold nanoparticles 3 ACS Paragon Plus Environment


Page 4 of 40

could deliver DNA to human embryonic kidney cells in the presence of serum.4 A very recent study8 has also revealed that DODAB modified CeO2 nanoparticles to be an efficient non-viral vector for in-vivo gene/DNA transfection to mammalian cells. Aqueous dispersions of DODAX have been studied over the last few decades to understand the various aspects of its rich phase behavior.13-16,18-19 The main transition temperature of chain melting from the ordered (gel, subgel and coagel) to fluid phase is found to be highly dependent on the method of preparation and the counterion.15 Differential scanning

Fig. 1 Phase diagram of DODAB dispersion (heating cycle), based on DSC, FTIR and NMR studies from Refs13-14,18-19. calorimetry (DSC) studies reveal that there are primarily four polymorphic phases14,18 in the DODAB aqueous dispersions – coagel, subgel, gel and fluid. At sufficiently low concentrations (< 0.5 wt %) the system is found to be in the subgel phase that transforms to the fluid phase through an intermediate gel phase. But as the concentration is increased the system tends to form a mixture of coagel and subgel or coagel and gel phases below the main transition temperature.18 4 ACS Paragon Plus Environment

Page 5 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


However, at concentrations above 7 wt% the dispersion is found to be purely in the coagel phase that directly transforms into the fluid phase. Interestingly though, in the cooling cycle the fluid phase transforms to coagel phase via an intermediate gel phase due to non-synchronous change in the head and tail of the DODAB molecule.19 FTIR measurements18-19 on these dispersions suggest that subgel and coagel phases have a high degree of alkyl chain ordering, with an almost all-trans configuration, closely followed by the gel phase. However, beyond the main transition temperature, the alkyl chain melts and significant chain disorder is introduced in the fluid phase. It is found from the FTIR measurements that there is an increase in number of gauche conformers18-19 in fluid phase. Moreover, the broadening of the CH2 stretching mode18 in the FTIR spectra indicates increased mobility of alkyl chains in the fluid phase. This observation is also supported by NMR measurements13, where the frozen dynamical degrees of freedom in subgel/gel phases are found to be activated in the fluid phase. The lamellar spacing, as observed from SAXS measurements,14,19 is found to be the highest in fluid phase and least in the coagel phase, where the latter is found to form a crystalline-like multilamellar packing with highly dehydrated headgroup and almost no interlamellar water. However, in the low concentration regime, the subgel and gel phases are found to be predominantly made of large and faceted unilamellar vesicles.14,18 In spite of such extensive studies in DODAB vesicles, the dynamics of the bilayer system from the viewpoint of its phase behavior is not yet fully understood. Molecular dynamics (MD) simulations stand out as a technique complementary to experiments due to its accessibility to molecular level details that are difficult to attain with experiments. A detailed investigation of the molecular structure of DODAB using MD simulation carried out at 300 K by Jamróz et al 21 showed that the bilayer spontaneously arranges itself into an asymmetric ripple phase with alkyl chains packed in almost all trans configuration.



Page 6 of 40

This phase is observed to be reminiscent of ordered phase before the chain melting transition in lipid bilayer systems.21 Quasielastic neutron scattering (QENS) is a very suitable technique to study molecular motions in the timescale of nanosecond to picosecond and has been used widely to describe dynamics in lipid bilayers22-24. Here we report the structural and dynamical aspects of DODAB lipid bilayer in the ordered (300 K) and fluid (350 K) phases using MD simulation. QENS experiments are also carried out in DODAB bilayer and the results are compared with dynamical description obtained from MD simulations.

2. METHODS AND PARAMETERS 2.1 Molecular Dynamics Simulation. Dioctadecyldimethylammonium ion (DODA+) molecule was constructed using Avogadro25 in all-trans form. Packmol26 was used to arrange two monolayers of DODA+ ions with 64 monomers in each monolayer, such that the tails of DODA+ ions were facing each other. The resultant bilayer had a dimension of (64×64×50) Å and it was solvated by adding 3600 water molecules and 128 bromide ions above and below the bilayer. Potential parameters for DODA+ molecules were obtained from CHARMM force field 27 using the DL_FIELD package

28

. Solvent water was considered explicitly with TIP3P model.

The parameters for Bromide ion were obtained from a recent work by Joung and Cheatham

29

.

DL_POLY-4 30 was used to simulate the bilayer system. Long range interactions for the periodic system were treated using particle mesh Ewald sum with a real space cut-off of 10 Å and the short range interaction cut-off were set to 12 Å. An integration timestep of 2 fs was chosen post structural minimization. MD simulations were carried out at two different temperatures, 300 K and 350 K corresponding to ordered and fluid phases respectively, with a pressure of 1 atm. The temperature and pressure of the system was maintained using Langevin thermostat and barostat 6 ACS Paragon Plus Environment

Page 7 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


giving rise to a simulation in NPT ensemble. An equilibration of 20 ns was followed by a production run of 5 ns for further structural and dynamical analysis. The trajectories were recorded at an interval of 4 ps. In order to obtain the short time trajectories, separate run of 20 ps was also carried out with trajectory being recorded for every 0.02 ps.

Fig. 2 Snapshots of the bilayer system in the ordered and fluid phases. The snapshot is a projection on the xz plane (marked in the image), y-axis is pointing out of the paper. Two monomers in each phase are also highlighted to show the conformation of the DODAB molecules in each of these phases. A DODAB molecule in all-trans configuration is also shown beside the snapshots. 2.2 Neutron Scattering Experiment. DODAB (C18H37)2 N(CH3)2Br powder (purity > 98%) and D2O (99.9% atom D purity) were obtained from Tokyo Chemical Industries Co. LTD. 7 ACS Paragon Plus Environment


Page 8 of 40

and Aldrich, respectively. The DODAB vesicles were prepared by mixing DODAB and D2O, which was kept under magnetic stirring at a temperature of ~340 K until a clear solution was formed. The DODAB vesicles were prepared at concentration of 70 mM (4.4% by weight) in D2O solvent. D2O was used as a solvent in the QENS experiments to minimize scattering contribution of the solvent. Neutron scattering experiments on DODAB vesicles and D2O were carried out at 345 K using IRIS spectrometer31 at the ISIS pulsed Neutron and Muon source at the Rutherford Appleton Laboratory, UK. IRIS spectrometer was used with PG(002) analyzer in the offset mode providing energy transfer range from -0.3 to 1.0 meV with a resolution of ~17 µeV. Samples were placed in annular aluminium sample cans with 0.5 mm internal spacing such that the sample scattering was no more than 10%, thereby minimizing multiple scattering effects.

3. RESULTS AND DISCUSSION DODAB bilayer system was simulated in the presence of water at 300 K and 350 K corresponding to the ordered and fluid phases respectively. In the ordered phase, the bilayer system spontaneously formed into asymmetric ripple phase, where some regions of the chain were interdigitated. This is in concurrence with the earlier MD simulation of the DODAB bilayer by Jamroz et al.21 However, in the fluid phase no interdigitation was observed but a significant increase in alkyl chain disorder was found to be present. Fig. 2 shows the snapshot of the DODAB bilayer in both the phases, two individual monomers in each of these phases are highlighted to indicate the alkyl chain ordering. The normal and interdigitated regions can be clearly observed in the ordered phase. The system equilibration was concluded effectively from the stability of area per lipid (APL) with time. The APL for ordered phase converged to ~ 60 Å2, while in the fluid phase it was ~ 64 Å2. 8 ACS Paragon Plus Environment

Page 9 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.1 Dihedral Angle Distribution and Chain Melting. Dihedral angle is the angle between two intersecting planes, where each plane is defined by three atoms.32 The ith dihedral angle in DODAB alkyl chain is calculated as the angle between the planes formed by atoms (i, i+1, i+2) and (i+1, i+2, i+3). Distribution of dihedral angles can be used to characterize the conformational changes taking place across the phase transition. In the gel and coagel phases, it is experimentally observed that the alkyl chains are well-ordered and stay in almost all-trans configuration.18-19 As the bilayer transforms into the fluid phase, melting of alkyl chains occur that lead to a rise in gauche defects in the chain. Figure 3a shows the distribution of dihedral angles of the alkyl chain in the ordered and fluid phases obtained from MD simulation trajectories. From Figure 3a, it is apparent that the number of trans dihedrals decrease significantly as the bilayer transforms to the fluid phase. The fraction of gauche defects is found to increase by 70% upon transformation from the ordered to the fluid phase. This suggests that the observed ordered phase is reminiscent of the gel phase observed in experiments.18-19 The first dihedral angle, associated with the carbon atoms C1-C4, in the alkyl chain is found to possess a significant amount of gauche defect with a preferred orientation even in the ordered phase, as seen from Figure 3b. This preferred orientation might be due to the strong repulsive interaction between the first CH2 units in both the alkyl chains connected to the ammonium headgroup. Upon transformation to the fluid phase, although the gauche defect does not decrease, the preferred orientation is lost. It might happen due to the increased gauche defects further along the alkyl chain.



Page 10 of 40

3.2 Order Parameter and Isomerization Dynamics. The time-correlation function of C-H bond vectors can be calculated from the MD simulation trajectories for each carbon atom along the alkyl chain, C i (t ) =

1 Nl

Nl

∑ P (µ 2

ik

(t ). µik (0) )

(1)

k =1

Here, µi(t) is the unit-vector of CH bond of the ith carbon atom in the alkyl chain numbered beginning from the headgroup of the kth lipid, and P2 is the second rank Legendre polynomial, Nl is number of lipids and the angular brackets indicate time-origin average.

Fig. 3 Distribution of (a) dihedral angles of the alkyl chain and (b) first dihedral angle along the alkyl chain of the DODAB monomer are shown at both the phases. We have calculated time correlation functions of CH vectors associated with all the carbon atoms along the alkyl chain. A typical time-correlation function, C5(t), corresponding to the 5th carbon atom is shown in Fig. 4. It is observed that C5(t) decays very quickly to a value of ~0.6 in ~ 2 ps. The initial decay till ~0.1 ps has been ascribed 33-34 to the fast librational motions. Subsequent decay up to ~2 ps is related to the coupled relaxation of isomerization and librational 10 ACS Paragon Plus Environment

Page 11 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


motions in the alkyl chain.34 The decay of C5(t) between 2-100 ps is found to be associated to the trans-gauche isomerization dynamics.33-36 The slowest decay in the curve has been shown in Refs 35-36 to be associated to the reorientations/wobbles of the long axis of the lipids. Finally the asymptotic non-zero value of C5(t) is an indicator of residual correlation in the system. This nonzero value of correlation at large times characterizes the degree of ordering in the lipid bilayer system. It is observed that, the following equation with a sum of four exponentials and a constant was able to fit Ci(t) for all the carbon atoms in the chain for both the phases,35

Ci (t ) = a libi e

−t / τ ilib

+ a ili e

−t / τ ili

+ a isoi e

−t / τ iiso

+ a is e

− t / τ is

( )

i + S CH

2

(2)

where alib, ali, aiso & as are the weight factors and τlib, τli, τiso & τs are the relaxation timescales corresponding to librational, libration-isomerization coupling, isomerization and slow relaxation

Fig. 4 The time correlation function correspond to the 5th carbon atom, C5(t), in the fluid phase along the alkyl chain. The least squares fit according to eq. (2) along with all the four components are also shown. 11 ACS Paragon Plus Environment


Page 12 of 40

processes, respectively. The constant SCH is the alkyl chain order parameter which is the indicator of ordering in the lipid bilayer system.21,35. While the first two terms of the equation correspond to the fast librational motions and the coupling between libration and isomerization; the third term gives the timescale associated to the isomerization dynamics, τiso. The fourth term is related


Page 13 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 5 Ci(t) (i=3, 10, 17) of the CH bond vector along the alkyl chain of the DODAB lipid. The sites are labelled beginning from head to tail region of the alkyl chain. to the rates of reorientation of the lipid axis and is the slowest relaxation processes among the four. From Fig. 4 it is seen that the fit of C5(t) according to eq. (2) is quite good. Individual components of relaxation are also shown separately in the figure. Typical fits of Ci(t) at three different carbon sites in the alkyl chain (i=3,10,17) for the fluid and ordered phases are shown in Fig. 5. First, it is observed that irrespective of carbon site along the alkyl chain, Ci(t) decays faster in the fluid phase compared to the ordered phase. Second, the asymptotic values of the Ci(t) are significantly different for the two phases suggesting a marked difference in SCH. Last, it is found that the decay of Ci(t) is faster as one moves towards the tail of the alkyl chain in both the phases. All these observations can be succinctly captured by plotting, alkyl chain order parameter, SiCH , and the relaxation time related to trans-gauche isomerization, τiiso , with respect to carbon sites, i, along the alkyl chain (Fig. 6a). It is evident that SCH is lower in the fluid phase compared to the ordered phase. In the fluid phase, the DODAB molecule is more ordered near the headgroup region and subsequently decreases as we reach the tail region. This is in contrast to the earlier reports

21,11

, where it was observed that the carbon atoms near the headgroup were

highly disordered. This may be because the order parameter in their case was calculated using time-averaged orientations of CH bonds. As discussed earlier the gauche defects of the first dihedral introduced due to the preferred orientation of the CH2 units near the headgroup, might have reflected as higher disorder in this region, in the time-averaged picture.



Page 14 of 40

Fig. 6 (a) Alkyl chain order parameter (SCH) and (b) Relaxation time, τiso, related to trans-gauche isomerization with respect to the carbon sites, i, along the alkyl chain Relaxation times related to trans-gauche isomerization in the alkyl chain in the ordered and the fluid phases are shown in Fig. 6b. In the fluid phase, in addition to the observed increase in gauche defects, it is found that the trans-gauche transition rates are also significantly higher. The increase in transition rate by more than a factor of two for the carbon atoms near the headgroup is in support of the results in the previous section, that the preferred orientation of the first dihedral is lost in the fluid phase. The variation of τiso suggests that the disordered tail region, i.e. beyond 8th carbon atom in the chain, has a notably high transition rate in both the phases. 3.3 Internal Motion. The discussion on isomerization dynamics gives us a hint of mobility of lipid alkyl chains in the different phases. However, it is expedient to calculate the diffusivity corresponding to carbon atoms in the alkyl chain to obtain a rather complete picture of the geometry of alkyl chain motion. The motion of the centre of mass (COM) of lipids was subtracted from the motion of the carbon atoms to obtain the internal motion corresponding to the carbon 14 ACS Paragon Plus Environment

Page 15 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 7 MSD corresponding to the internal motion of the alkyl chain for different carbon atoms in DODAB lipid. It may be noted that the scale in y-axis (MSD) is about factor of four larger for the fluid phase compared to the ordered phase. atoms in the chain. The trajectory of the internal motion was then used to calculate the meansquared displacement (MSD) of the carbon atoms. Fig. 7 shows the MSD corresponding to the internal motion of the different carbon atoms along the alkyl chain. Clearly, the saturating trend of the MSD in both the phases for almost all the carbon atoms along the alkyl chain is an indication of the localized nature of the motion. It is found that the internal dynamics of alkyl chain is enhanced by about an order of magnitude in the ordered to fluid phase transition. In both phases, it is observed that the motion of carbon atoms near the headgroup is much more restricted compared to the tail region. The increase of the mobility from head to tail region is very much pronounced in the fluid phase and it corroborates well with the fact that isomerization rates are faster near the tail of alkyl chain. In fact, in the fluid phase, the MSD of the 17th carbon atom at ~1ns is about an order of magnitude higher compared to the 1st carbon atom, while, in the ordered phase, it is higher by only a factor of ~3.



Page 16 of 40

3.4 Lateral Motion. Chain-melting transition in lipid bilayer systems leads to a sharp increase in the lateral diffusivity of lipid molecules.11,37 Trajectory of the COM of the lipid from MD simulation was used to calculate MSD, 〈 ( )〉, for the lateral motion of the lipids in

bilayer plane (xy plane, see Fig. 2). The lateral MSD is calculated using the (x,y) coordinates of the lipid COM and is shown in Fig 8a. It is found that the variation of MSD is found to be proportional to t2 (ballistic regime) up to ~0.1 ps and is followed by a subdiffusive regime with a dependence of tα. α can be explicitly calculated by getting the logarithmic time derivative of logarithm of MSD,

δrlat2 (t ) = Atα

⇒

α (t ) =

d (lnδrlat2 (t )) d (ln t )

(3)

Variation of 〈 ( )〉 and α(t) are shown in Figs. 8a and 8b, respectively. Clearly, it indicates

that the lateral motion of the lipid molecules is subdiffusive with α ~ 0.62 in the fluid phase and ~ 0.5 in the ordered phase. The subdiffusive motion and subdiffusive exponent, α(t), has been associated to the crowding of the lipid molecules in the bilayer.38 It is known that the crowding of lipids in the system leads to some memory effects that give rise to a non-Markovian diffusion process38-39. This diffusion mechanism can be described using a generalized Langevin equation (GLE) for the velocity of the lipid COM. For a system in equilibrium without any external force, the GLE for the velocity of the particle is given by,40 t

dv + M (t − t ' )v (t ' )dt ' = ζ (t ) dt ∫0

(4)

where M(t) is the memory function characterising the intrinsic memory of the system and ζ(t) is the internal stochastic noise that obeys fluctuation-dissipation theorem given by,40


Page 17 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ζ (t )ζ (t ' ) =

k BT M (t − t ' ) m

(5)

Fig. 8 (a) MSD correspond to the lateral motion, 〈 ( )〉, and (b) Variation of the exponent,

α(t) (Eq. 3) for the DODAB lipid COM in the ordered and fluid phases, the dotted line at α=1 is indicative of the exponent for normal Brownian motion. where T is the temperature of the system, kB is the Boltzmann’s constant, m is the mass of the particle and the angular brackets denote ensemble average. It can be easily deduced that the velocity autocorrelation (VACF), Cv(t), in such systems follow the integro-differential equation41, t

dCv (t ) = − ∫ dt ' M (t − t ' )Cv (t ' ) dt 0

(6)

This equation can be evaluated numerically to extract the memory function from the VACF. VACFs, Cv(t), for both the phases are calculated from the velocity of lipid COM obtained from simulation trajectories and are shown in Fig 9a. The memory functions calculated from their 17 ACS Paragon Plus Environment


Page 18 of 40

respective VACFs for both the fluid and ordered phases are shown in Fig. 9 b. For t >~ 1 ps, the asymptotic limit of the memory function is reached and it decays as a power law. The long time tails for the VACF and memory function can be explicitly derived for the particular GLE (Eq.(4)) that describes the subdiffusion processes and can be given by the following asymptotic limits 41,

Cv (t ) t → Aα (α − 1)t →∞

α −2

v 2 sin(πα ) −α M (t ) t → t →∞ A πα

(7)

The corresponding theoretical curves for the asymptotic limits (t > 1 ps) using above equation is also indicated in Fig. 9a and 9b. These curves were obtained from fitting the VACF and memory function (for t > 1 ps) based on the above equations where α was kept fixed at the values obtained from Eq. (3). It is observed that there is a reasonable agreement between the theoretical curves and calculated values (Fig. 9a and 9b) suggesting that lateral motion of lipid is well described in the framework of GLE. The values of A in the ordered and fluid phases were found


Page 19 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 9 (a) VACF, Cv(t) obtained from MD simulations, (b) Memory function, M(t), calculated numerically from Cv(t) based on eq. (6). Solid lines indicate the theoretical curves for the asymptotic limits based on GLE, as given in eq. (7). Insets are for the ordered phase. to be ~0.36 Å2/psα (α=0.5) and ~0.41 Å2/psα (α=0.62) respectively. From Fig. 9b, it is clear that M(t) decays slower in the ordered phase compared to the fluid phase. This indicates that the memory effects are more pronounced in the ordered phase compared to the fluid phase. The interdigitation of alkyl chains in the ordered phase might give rise to longer memory in the system. Dynamic self-correlation, Gs(r,t;t0), is defined as the probability of finding a particle at some position r at a time t, given the particle was at the origin at time t0. The incoherent intermediate scattering function (IISF) is the time Fourier transform of Gs(r,t;t0) and can be calculated directly from the trajectory of lipid COM using the equation,

I COM (Q, t ) =

1 Nl

N

∑e

−iQ. Ri ( t0 ) iQ.Ri ( t +t0 )

e

(8)

i =1

where, Q is the scattering vector, Ri(t) is the position of the COM of ith lipid molecule in the x-y plane, t0 is an arbitrary time-origin and Nl is the total number of DODAB lipids. While the angular brackets denote average over time-origins, the bar denotes average over all Qorientations. IISFs corresponding to lateral motion of DODAB, (, ) have been calculated at different Q values (0.5-1.8 Å-1) in both ordered and fluid phases and typical IISFs are shown in Fig. 10.



Page 20 of 40

IISF captures all the higher moments of displacement in a concise manner. Although, in the Gaussian approximation42, IISF of lateral motion of lipid can be written in terms of just the MSD of lipid COM, 〈 ( )〉. Using eq. (3), IISF in Gaussian approximation can be written as,

I

COM

 δrlat2 (t ) 2  (Q, t ) ≈ exp − Q  4 

  = exp − A Q 2 t α    4  

(9)

The lines in Fig. 10 correspond to the fit assuming the above equation. It is clear from the figure, that the Eq. (9) is able to describe the IISF for lateral motion of lipid COM quite well in both the phases at all the Q-values. The value of A obtained from eq. (9) is found to be ~0.35 Å2/psα (α = 0.5) and ~0.39 Å2/psα (α = 0.62) for ordered and fluid phases respectively, which is in agreement


Page 21 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 10 Variation of ICOM(Q,t) with respect to time at typical Q-values in the ordered (300 K) and fluid (350 K) phases. Fits based on Gaussian approximation given in eq. (9) are shown by solid lines.

with those obtained using the GLE description. This suggests that the lateral motion of lipid is spatially homogenous in nature and the subdiffusive behavior in 〈 ( )〉 is from the temporal

heterogeneity in the system which is well explained by GLE as mentioned earlier.



Page 22 of 40

3.5 Comparison with Neutron Scattering Data. Quasielastic neutron scattering (QENS) is a useful technique to study the stochastic dynamics of molecules. It has been used extensively to study the molecular dynamics of micelles43-44, lipid bilayers11,22-23,37 etc. Neutron scattering spectra of hydrogenous materials (eg. alkanes, lipids, surfactants) is dominated by incoherent scattering due to the high incoherent cross-section of hydrogen in comparison to other elements. The incoherent part of the neutron spectra, Sinc (Q , ω ) , is the space-time Fourier transform of the self-part of van-Hove correlation function, Gs(r,t;t0). Therefore, neutron spectra from a hydrogenous system provide a spatio-temporal profile of hydrogen mobility in the sample. The incoherent intermediate scattering function (IISF), I(Q,t), is written as, ∞

I QENS (Q , t ) =

∫S

inc

(Q , ω ) e itω dω

(9)

−∞

IISF of all hydrogen atoms in the system can also be calculated from MD simulations using the trajectories, thereby providing a bridge between QENS experiments and MD simulation. The calculation of IISF from simulation trajectories is carried out using time-origin average,

I MD (Q , t ) =

1 N

N

∑

e −iQ .ri ( t0 ) e iQ .ri ( t +t0 )

(10)

i =1

where, ri(t) is the position of the ith hydrogen atom and N is the total number of hydrogen atoms. Similar to eq. (8), the angular brackets indicate average over time-origins, the bar denotes average over all Q-orientations. QENS experiments have been carried out on DODAB dispersion in D2O to minimize the scattering contribution from solvent. Although MD simulations have been carried out with H2O as solvent, it has been shown45-46 that the solvent isotope effect doesn’t significantly alter the dynamics of lipids in the bilayer. Hence the QENS results can be directly compared with MD


Page 23 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


simulation. In order to estimate the solvent contribution, QENS spectra of D2O were separately recorded at 345 K. The measurement of both D2O and DODAB vesicles were carried out using the same sample cell to minimize systematic errors. The scattering law of DODAB bilayer, Sbilayer(Q,E) is obtained using eq. S1 (Supporting information). Typical observed QENS spectra of DODAB dispersion, pure D2O and subtracted data of DODAB bilayer at a Q value of 1.0 Å-1 are shown in Fig. S1 (Supporting information). The resultant scattering law, Sbilayer(Q,E) of the DODAB bilayer at 345 K (in the fluid phase) can be compared with IISF of hydrogen atoms calculated from MD simulation of DODAB bilayer at 350 K (fluid phase). The motion of hydrogen atoms is a superposition of various dynamical components inclusive of the internal motion of the alkyl chain and lateral motion of the lipids. The internal dynamics in the alkyl chain can be described using a combination of segmental motion of the alkyl chain and torsional motion of the CH2 units along the chain. The effective IISF

(a)

(b)

Fig. 11 Incoherent intermediate scattering function, I(Q,t) from (a) MD simulation (b) QENS experiment are shown at a typical Q = 1.2 Å-1. The fits and its components are indicated by lines. 23 ACS Paragon Plus Environment


Page 24 of 40

for describing the motion of all hydrogen atoms in the system can be given as, I MD (Q, t ) = I lat (Q, t ) I seg (Q, t ) I tor (Q, t )

[ (

)][

]

= exp − Γlat t α a0 + (1 − a0 )exp(− Γseg t ) [b0 + (1 − b0 )exp(− Γtor t )]

(11)

where, the first term corresponds to the lateral motion, considering the subdiffusive nature of the motion with the exponent α. The second and third terms describe the segmental and torsional dynamics in the system respectively, where the weight factors a0(Q) and b0(Q) are called as the elastic incoherent structure factors (EISF), corresponding to segmental and torsional motion respectively. EISF holds information about the geometric nature of the motions. The coefficients in the exponents, Γlat, Γseg and Γtor characterize the timescales of the lateral, segmental and torsional processes respectively. The IISFs calculated from MD simulation (from eq. 10) is described using the model function given above (eq. 11) and is shown at a typical Q-value (1.2 Å-1) in Fig. 11a. The fit and its three components are also indicated in the same Figure. It is found that the timescale of the torsional motion is ~ 1 ps, which is the fastest relaxation process among the three, and falls outside the energy-transfer range of the IRIS spectrometer used to obtain the QENS data. It is observed that the QENS spectra of DODAB bilayer are well described considering only lateral and segmental dynamics (using eq. S2) along with a flat background. Typical fitted QENS spectra are shown in the Fig. S2 (Supporting information). Therefore, we proceed to calculate the experimental IISF using the inverse Fourier transform of the scattering law using eq. 9 and modelled it using only the lateral and segmental components,

(

I QENS (Q , t ) = exp − Γlat t α

) [a + (1 − a )exp (− Γ t )] 0

0

seg

(12)

The IISFs as obtained from QENS experiment is shown in Fig. 11 (b) at a typical Q-value of 1.2 Å-1. It also indicates the fit and its two components described in the model function in eq. (12). 24 ACS Paragon Plus Environment

Page 25 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The variations of α with respect to Q, obtained from fitting the model function given in eq. (11) and eq. (12) for MD simulation and QENS experiment respectively are shown in Fig. 12 (a). It is found that the lateral motion of DODAB lipids is subdiffusive in nature with an exponent ~ 0.61, which matches with the exponent obtained from the analysis of COM motion of DODAB lipids in section 3.4. Variation of Γlat with respect to Q is shown in Fig 12b. The least squares fit using quadratic dependence

, assuming spatially homogenous nature of the

motion as indicated by motion of COM of the lipids from MD simulation, is also shown in Fig 12b. The

(b)

(a)

Fig. 12 Variation of the (a) the exponent, α, and (b) Γlat with respect Q as obtained from fitting to IISF obtained from MD simulation and QENS data. Solid line in (a) indicates the value obtained from the MSD of lipid COM motion (eq. (9)). The continuous (MD) and dashed (QENS) lines in

(b) correspond to the respective quadratic fits using .

obtained value of the coefficient A is found to 0.42 Å2/psα (α = 0.61) for the MD simulation and 0.34 Å2/psα (α = 0.61) for QENS data. This is not very different in comparison to the value ~0.39 Å2/psα (α = 0.62) as obtained from the IISF of the COM of the lipid that was obtained in the previous section. 25 ACS Paragon Plus Environment


Page 26 of 40

In order to formulate a description for the segmental dynamics of the alkyl chain; we first observe from MSD corresponding to internal motion of carbon atoms in the fluid phase that the segmental mobility is not uniform along the alkyl chain. Therefore, we consider a model where the segmental dynamics of the ith carbon atom along the alkyl chain diffuse inside a sphere of radius Ri with a diffusivity Di. This is known as the localized translational diffusion (LTD) model. The IISF for segmental dynamics of the system based on LTD model is given by43-44,47,

  x l  2  1 18  0 l I seg (Q, t ) = ∑  A0 (QRi ) + ∑ (2l + 1)An (QRi ) exp− 2 n  Di t  18 i =1  l , n ≠{0 , 0}   Ri   

(13)

where the first summation indicates sum over all 18 carbon atoms in the alkyl chain. The first term A00 inside the summation is the elastic structure factor and is given by 47,

 3 j (QRi )  A (QRi ) =  1   QRi 

2

0 0

(13a)

where, j1(x) is first order spherical Bessel function of the first kind. The second term corresponds to the quasielastic component which is a series of exponentials and the coefficients, Aln are the quasielastic structure factors, given by47, for l ≠ 0, n ≠ 0,

A ( z) = l n

(x )

( )

l 2 n

2

 zjl +1 ( z ) − ljl ( z )    2 − l (l + 1)  z 2 − xnl 

6 xnl

( )

(13b)

The numbers xln are mentioned in the detailed work by Volino and Dianoux47. It is evident from Fig 7 that the segmental mobility is significant only beyond the 10th carbon atom from the headgroup. Hence, we considered variation of radius, Ri, and diffusivity, Di, to follow a Lorentzian distribution along the alkyl chain,


Page 27 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


( σ R )2 Ri = (Rmax − Rmin ) +R (σ R )2 − (i − 18)2 min

( σ D )2 Di = (Dmax − Dmin ) +D (σ D )2 − (i − 18 )2 min

(14)

where, Rmax, Rmin are the maximum and minimum radii and Dmax, Dmin are likewise the maximum and minimum diffusivities. σR and σD are the full-width at half-maxima of the Lorentzians; they characterize the spread of the radii and diffusivities along the chain. It is clear from the distribution (eq. 14) that the maximum value of radius (Rmax) and diffusivity (Dmax) is for 18th carbon atom in the alkyl chain and minimum values (Rmin & Dmin) are for the 1st carbon atom near the headgroup. In order validate this model, the EISF of segmental motion, a0, obtained from MD simulation and QENS experiment are fitted with the theoretical EISF from eq. (13 (a)),

 3 j (QRi )  a0 (Q) = ∑  1 QRi  i =1  18

2

(15)

with Rmin, Rmax and σR as the fitting parameters. The calculated a0(Q) for MD simulation and QENS spectra along with the theoretical fits based on the above equation are shown in Fig 13a.

Table 1. Dynamical Parameters as Obtained from the Model (eq. 13) Describing Segmental Motion of the Alkyl Chain in DODAB Bilayer Dmin Dmax Rmin (Å) Rmax (Å) σR σD (× 10-6 cm2/s) (× 10-6 cm2/s) MD simulation

0.50

4.62

3.61

3.55

19.95

3.66

QENS

0.57

4.61

3.41

1.05

15.48

2.82



(a)

Page 28 of 40

(b)

Fig. 13 Variation of (a) EISF of segmental motion, a0(Q), and (b) Γseg with respect to Q obtained from fitting IISF obtained from MD simulation and QENS data. Fits for a0(Q) based on eq. (15) is indicated in (a) by continuous and dashed lines for MD and QENS respectively. Similarly fits for Γseg based on the model for segmental dynamics described by eq. (13) are shown in (b). The EISF, a0, obtained from MD simulation and QENS experiment match very well with each other as well with the theoretical fit indicating that the geometry of the motion is well described by the LTD model. The obtained values of Rmin and Rmax from the fitting are shown in Table 1. Fig. 13b shows the variation of Γseg along with theoretical fits based on model described by eq. (13) for both MD simulation trajectories and QENS spectra. The maximum and minimum diffusivities, Dmin and Dmax obtained from fitting are also given in Table 1. Fig. 14 shows the variation of the radii of the spheres along the alkyl chain of the DODAB lipid. A schematic of the DODAB lipid with the variation of radii along one of the alkyl chains is also shown in Fig. 14. The other alkyl chain too has the same variation but is not indicated in the schematic for the sake of brevity. The distribution of radii and diffusivities suggest that the segmental dynamics quite pronounced beyond the 10th carbon atom in the alkyl chain. This is congruous with the observation in isomerization dynamics and internal motion in the earlier sections. The order


Page 29 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


parameter which indicates higher degree of ordering near the headgroup region is reflected in the lesser mobility of first few carbon atoms near the headgroup region. It is found that the segmental dynamics of the chain is successfully described using LTD model with a Lorentzian distribution of radii and diffusivities. As noted earlier, the torsional motion of the CH2 units is not observable in the QENS spectra due to the limited energy-transfer window of the IRIS spectrometer. The torsional dynamics of the CH2 units in the alkyl chain observed from MD simulation is described by a two-fold reorientation process. The IISF for two-fold reorientation is given by48,

Fig 14. Variation of (a) radii based on Lorentzian distribution obtained in the description of the LTD model for segmental dynamics using MD simulation trajectories and QENS experimental data. The schematic of a DODAB molecule is shown alongside that shows the variation of radii along one of the alkyl chains, the other chain also has exactly the same distribution but is not shown here.



I tor (Q, t ) =

  1 (1 + j0 (Qd )) + 1 (1 − j0 (Qd )) exp− 2t  2 2  τ tor 

Page 30 of 40

(16)

where, d is the distance between the two jump sites and τtor is the average residence time; j0(x) is the zeroth-order spherical Bessel function of the first kind. The first term is elastic and the second term the quasielastic component. Therefore, we verify the model for torsional motion by fitting the EISF, b0, obtained from eq. (11) with the model described in the above equation,

b0 (Q) =

1 (1 + j0 (Qd )) 2

(17)

The EISF, b0, obtained from eq. (11) along with the fit based on above equation is shown in Fig. 15a. In the above description of torsional motion, distance between the jump sites, d ~ 1.4 ± 0.3 Å. The average residence time is τtor ~ 1.4 ± 0.4 ps.

Fig. 15. Variation of (a) EISF correspond to the torsional motion, b0(Q) and (b) τtor as obtained from the fitting of eq. (11) to IISF obtained from MD simulation. The solid line in (a) represents the fit as per 2-fold motion (Eq. 17).


Page 31 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The simultaneous analysis of the data obtained from MD simulation and QENS experiments gives us a comprehensive description of dynamics in the DODAB lipid bilayer. The lateral subdiffusion of lipids indicated by the results of MD simulation is found to be consistent with the QENS data. Moreover, the geometric description of segmental dynamics which is related to internal motion of the alkyl chain shows an excellent match between simulation and experiment. It may be noted that the torsional motion of the alkyl chain is not observable in the present QENS spectra.

4. CONCLUSION Systematic study of structure and dynamics of the DODAB lipid bilayer in the ordered and fluid phases is carried out using fully atomistic MD simulation. The results are compared with the neutron scattering experiments and found to be very consistent. MD simulation showed that there is an increase in gauche defects in the fluid phase at 350 K in comparison to the ordered phase at 300 K. This is also indicated by the order parameter that is found to be quite low in the case of the fluid phase. The isomerization dynamics is slower near the headgroup in both the phases, which indicates that the region near the head group is more ordered. It becomes faster as we move towards the tail end, while the isomerization rate reaches a plateau beyond 9th carbon atom along the chain. The results of MSD corresponding to the internal motion also support the nature of dynamics as found in the isomerization dynamics. This is well supported by experimental evidence obtained from QENS experiment on the DODAB bilayer in the fluid phase, where the segmental dynamics of the alkyl chain was very well described using localized translational diffusion (LTD) model. In this model, it is considered that the ith CH2 unit in the alkyl chain 31 ACS Paragon Plus Environment


Page 32 of 40

diffuses inside a sphere of radius Ri with a diffusivity Di. In our work we found that the variation of the radii and diffusivities follows a Lorentzian distribution with the peak at the tail end of the alkyl chain. The distributions also show that the increase in dynamics is significant only beyond the ~10th carbon atom in the alkyl chain. The lateral motion of the DODAB lipids is also explicitly studied by considering the motion of the centre of mass (COM) of the lipids. It is observed that the nature of lateral motion is strongly subdiffusive in both the ordered and fluid phases. The motion of the COM of lipids is described successfully using the scheme of generalized Langevin equation (GLE). The memory function associated with the motion of COM, explicitly calculated from velocity auto-correlation is found to be well described by a power law in the asymptotic limit, which is in agreement with the framework of GLE. Moreover, by observing the incoherent intermediate scattering function of lipid COM, it is clear that the motion of lipids is spatially homogenous. Therefore, the subdiffusive behavior of the COM is due to temporal heterogeneity in the system, which is well captured by the memory function in the GLE description. Detailed analysis of QENS spectra of DODAB bilayer in the fluid phase considering lateral motion explicitly supports the subdiffusive nature of the lateral motion of lipids. Here we have successfully demonstrated that use of MD simulation and neutron scattering experiment could describe the dynamical features in DODAB lipid bilayer. The results obtained from the MD simulation were used to analyse the neutron scattering data and found to be consistent. The detailed description of lipid dynamics in this study can be of use in applications of DODAB lipids like DNA/gene transfection, drug transport, etc. The absorption of gene/DNA or drug to bilayer could effectively alter the crowding of the lipids. Therefore, it will


Page 33 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


be interesting to probe the changes in dynamics of DODAB bilayer in the presence of these additives. This study will be of use to establish the nature of dynamics in DODAB bilayer itself.

Supporting Information Details of solvent (D2O) subtraction and QENS data fitting are given in supporting information

Acknowledgements R. Mukhopadhyay would like to thank the Department of Atomic Energy, India, for the award of Raja Ramanna Fellowship. Authors would like to thank Dr. V. G. Sakai from ISIS facility for fruitful discussions. Beam time provided by ISIS Pulsed Neutron and Muon source is duly acknowledged. We would like to record our sincere thanks to the reviewers for their useful suggestions.



Page 34 of 40

REFERENCES 1.

Vieira, D. B.; Carmona-Ribeiro, A. M. Cationic lipids and surfactants as antifungal

agents: mode of action. J. Antimicrob. Chemother. 2006, 58, 760-767. 2.

Carmona-Ribeiro, A. M. Biomimetic Particles in Drug and Vaccine Delivery. J.

Liposome Res. 2007, 17, 165-172. 3.

Zaru, M.; Mourtas, S.; Klepetsanis, P.; Fadda, A. M.; Antimisiaris, S. G. Liposomes for

drug delivery to the lungs by nebulization. Eur. J. Pharm. Biopharm. 2007, 67. 4.

Li, P.; Li, D.; Zhang, L.; Li, G.; Wang, E. Cationic lipid bilayer coated gold

nanoparticles-mediated transfection of mammalian cells. Biomaterials 2008, 29, 3617-3624. 5.

Carmona-Ribeiro, A. M. Biomimetic nanoparticles: preparation, characterization and

biomedical applications. Int. J. Nanomed. 2010, 5. 6.

Barbassa, L.; Mamizuka, E. M.; Carmona-Ribeiro, A. M. Supramolecular assemblies of

rifampicin and cationic bilayers: preparation, characterization and micobactericidal activity. BMC Biotechnol. 2011, 11, 40. 7.

Silva, J. P. N.; Oliveira, A. C. N.; Casal, M. P. P. A.; Gomes, A. C.; Coutinho, P. J. G.;

Coutinho, O. P.; Oliveira, M. E. C. D. R. DODAB:monoolein-based lipoplexes as non-viral vectors for transfection of mammalian cells. Biochim. Biophys. Acta, Biomembr. 2011, 1808, 2440-2449. 8.

Das, J.; Han, J. W.; Choi, Y.-J.; Song, H.; Cho, S.-G.; Park, C.; Seo, H. G.; Kim, J.-H.

Cationic lipid-nanoceria hybrids, a novel nonviral vector-mediated gene delivery into mammalian cells: investigation of the cellular uptake mechanism. Sci. Rep. 2016, 6, 29197. 9.

Kunitake, T.; Okahata, Y. A totally synthetic bilayer membrane. J. Am. Chem. Soc. 1977,

99, 3860-3861. 34 ACS Paragon Plus Environment

Page 35 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10.

Sobral, C. N. C.; Soto, M. A.; Carmona-Ribeiro, A. M. Characterization of

DODAB/DPPC vesicles. Chem. Phys. Lipids 2008, 152. 11.

Dubey, P. S.; Srinivasan, H.; Sharma, V. K.; Mitra, S.; Sakai, V. G.; Mukhopadhyay, R.

Dynamical Transitions and Diffusion Mechanism in DODAB Bilayer. Sci. Rep. 2018, 8, 1862. 12.

Hubert, D. H. W.; Jung, M.; Frederik, P. M.; Bomans, P. H. H.; Meuldijk, J.; German, A.

L. Morphology Transformations of DODAB Vesicles Reminiscent of Endocytosis and Vesicular Traffic. Langmuir 2000, 16, 8973-8979. 13.

Saveyn, P.; Van der Meeren, P.; Zackrisson, M.; Narayanan, T.; Olsson, U. Subgel

transition in diluted vesicular DODAB dispersions. Soft Matter 2009, 5, 1735-1742. 14.

Feitosa, E.; Adati, R. D.; Hansson, P.; Malmsten, M. Thermal and Structural Behavior of

Dioctadecyldimethylammonium Bromide Dispersions Studied by Differential Scanning Calorimetry and X-Ray Scattering. PLOS ONE 2012, 7, e44702. 15.

Feitosa, E.; Alves, F. R.; Niemiec, A.; Real Oliveira, M. E. C. D.; Castanheira, E. M. S.;

Baptista, A. L. F. Cationic Liposomes in Mixed Didodecyldimethylammonium Bromide and Dioctadecyldimethylammonium Bromide Aqueous Dispersions Studied by Differential Scanning Calorimetry, Nile Red Fluorescence, and Turbidity. Langmuir 2006, 22, 3579-3585. 16.

Feitosa,

E.;

Barreleiro,

P.

C.

A.;

Olofsson,

G.

Phase

transition

in

dioctadecyldimethylammonium bromide and chloride vesicles prepared by different methods. Chem. Phys. Lipids 2000, 105, 201-213. 17.

Saveyn, P.; Bomans, P.; Frederik, P.; De Cuyper, M.; Van der Meeren, P. Osmotically

Induced Morphological Changes of Extruded Dioctadecyldimethylammonium Chloride (DODAC) Dispersions. Langmuir 2007, 23, 4775-4781.



18.

Page 36 of 40

Wu, F.-G.; Yu, Z.-W.; Ji, G. Formation and Transformation of the Subgel Phase in

Dioctadecyldimethylammonium Bromide Aqueous Dispersions. Langmuir 2011, 27, 2349-2356. 19.

Wu, F.-G.; Wang, N.-N.; Yu, Z.-W. Nonsynchronous Change in the Head and Tail of

Dioctadecyldimethylammonium Bromide Molecules during the Liquid Crystalline to Coagel Phase Transformation Process. Langmuir 2009, 25, 13394-13401. 20.

Carmona-Ribeiro, A. M. Bilayer-forming synthetic lipids: drugs or carriers? Curr. Med.

Chem. 2003, 10. 21.

Jamróz, D.; Kepczynski, M.; Nowakowska, M. Molecular Structure of the

Dioctadecyldimethylammonium Bromide (DODAB) Bilayer. Langmuir 2010, 26, 15076-15079. 22.

Sharma, V. K.; Mamontov, E.; Anunciado, D. B.; O'Neill, H.; Urban, V. S. Effect of

antimicrobial peptide on the dynamics of phosphocholine membrane: role of cholesterol and physical state of bilayer. Soft Matter 2015, 11, 6755-6767. 23.

Toppozini, L.; Armstrong, C. L.; Barrett, M. A.; Zheng, S.; Luo, L.; Nanda, H.; Sakai, V.

G.; Rheinstadter, M. C. Partitioning of ethanol into lipid membranes and its effect on fluidity and permeability as seen by X-ray and neutron scattering. Soft Matter 2012, 8, 11839-11849. 24.

Armstrong, C. L.; Trapp, M.; Peters, J.; Seydel, T.; Rheinstadter, M. C. Short range

ballistic motion in fluid lipid bilayers studied by quasi-elastic neutron scattering. Soft Matter

2011, 7, 8358-8362. 25.

Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G.

R. Avogadro: an advanced semantic chemical editor, visualization, and analysis platform. J. Cheminf. 2012, 4, 17.


Page 37 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


26.

Martínez, L.; Andrade, R.; Birgin, E. G.; Martínez, J. M. PACKMOL: A package for

building initial configurations for molecular dynamics simulations. J. Comput. Chem. 2009, 30, 2157-2164. 27.

Best, R. B.; Zhu, X.; Shim, J.; Lopes, P. E. M.; Mittal, J.; Feig, M.; MacKerell, A. D.

Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone ϕ, ψ and Side-Chain χ1 and χ2 Dihedral Angles. J. Chem. Theory Comput. 2012, 8, 3257-3273. 28.

Yong, C. W. Descriptions and Implementations of DL_F Notation: A Natural Chemical

Expression System of Atom Types for Molecular Simulations. J. Chem. Inf. Model. 2016, 56, 1405-1409. 29.

Joung, I. S.; Cheatham, T. E. Determination of Alkali and Halide Monovalent Ion

Parameters for Use in Explicitly Solvated Biomolecular Simulations. J. Phys. Chem. B 2008, 112, 9020-9041. 30.

Smith, W.; Yong, C. W.; Rodger, P. M. DL_POLY: Application to molecular simulation.

Mol. Sim. 2002, 28, 385-471. 31.

Carlile, C. J.; Adams, M. A. The design of the IRIS inelastic neutron spectrometer and

improvements to its analysers. Phys. B 1992, 182, 431-440. 32.

Allen, M. P.; Tildesley, D. J. Computer simulation of liquids. Clarendon Press: 1989; p

385. 33.

Wymore, T.; Gao, X. F.; Wong, T. C. Molecular dynamics simulation of the structure and

dynamics of a dodecylphosphocholine micelle in aqueous solution. J. Mol. Struct. 1999, 485486, 195-210.



34.

Page 38 of 40

Zhang, Y.; Venable, R. M.; Pastor, R. W. Molecular Dynamics Simulations of Neat

Alkanes: The Viscosity Dependence of Rotational Relaxation. J. Phys. Chem. 1996, 100, 26522660. 35.

Venable, R. M.; Zhang, Y.; Hardy, B. J.; Pastor, R. W. Molecular dynamics simulations

of a lipid bilayer and of hexadecane: an investigation of membrane fluidity. Science 1993, 262, 223. 36.

Soederman, O.; Walderhaug, H.; Henriksson, U.; Stilbs, P. NMR relaxation in isotropic

surfactant systems. A deuterium, carbon-13, and nitrogen-14 NMR study of the micellar (L1) and cubic (I1) phases in the dodecyltrimethylammonium chloride water system. J. Phys. Chem.

1985, 89, 3693-3701. 37.

Sharma, V. K.; Mamontov, E.; Anunciado, D. B.; O’Neill, H.; Urban, V. Nanoscopic

Dynamics of Phospholipid in Unilamellar Vesicles: Effect of Gel to Fluid Phase Transition. J. Phys. Chem. B 2015, 119, 4460-4470. 38.

Metzler, R.; Jeon, J. H.; Cherstvy, A. G. Non-Brownian diffusion in lipid membranes:

Experiments and simulations. Biochim. Biophys. Acta, Biomembr. 2016, 1858, 2451-2467. 39.

Jeon, J.-H.; Monne, H. M.-S.; Javanainen, M.; Metzler, R. Anomalous Diffusion of

Phospholipids and Cholesterols in a Lipid Bilayer and its Origins. Phys. Rev. Lett. 2012, 109, 188103. 40.

Wang, K. G.; Tokuyama, M. Nonequilibrium statistical description of anomalous

diffusion. Phys. A 1999, 265, 341-351. 41.

Kneller, G. R. Generalized Kubo relations and conditions for anomalous diffusion:

Physical insights from a mathematical theorem. J. Chem. Phys. 2011, 134, 224106.


Page 39 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


42.

Flenner, E.; Das, J.; Rheinstädter, M. C.; Kosztin, I. Subdiffusion and lateral diffusion

coefficient of lipid atoms and molecules in phospholipid bilayers. Phys. Rev. E 2009, 79, 011907. 43.

Sharma, V. K.; Mitra, S.; Garcia Sakai, V.; Hassan, P. A.; Peter Embs, J.;

Mukhopadhyay, R. The dynamical landscape in CTAB micelles. Soft Matter 2012, 8, 7151-7160. 44.

Sharma, V. K.; Mitra, S.; Verma, G.; Hassan, P. A.; Garcia Sakai, V.; Mukhopadhyay, R.

Internal Dynamics in SDS Micelles: Neutron Scattering Study. J. Phys. Chem. B 2010, 114, 17049-17056. 45.

Beranová, L.; Humpolíčková, J.; Sýkora, J.; Benda, A.; Cwiklik, L.; Jurkiewicz, P.;

Gröbner, G.; Hof, M. Effect of heavy water on phospholipid membranes: experimental confirmation of molecular dynamics simulations. Phys. Chem. Chem. Phys. 2012, 14, 1451614522. 46.

Róg, T.; Murzyn, K.; Milhaud, J.; Karttunen, M.; Pasenkiewicz-Gierula, M. Water

Isotope Effect on the Phosphatidylcholine Bilayer Properties: A Molecular Dynamics Simulation Study. J. Phys. Chem. B 2009, 113, 2378-2387. 47.

Volino, F.; Dianoux, A. J. Neutron incoherent scattering law for diffusion in a potential

of spherical symmetry: general formalism and application to diffusion inside a sphere. Mol. Phys. 1980, 41, 271-279. 48.

Bée, M. Quasielastic neutron scattering : principles and applications in solid state

chemistry, biology and materials science. A. Hilger: Bristol; Philadelphia, 1988.



Page 40 of 40

TOC:


Heterogeneity in Dynamics of Dioctadecyldimethylammonium

Recommend Documents