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Journal of Biomolecular Structure and Dynamics

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Artificial biomembrane morphology: a dissipativeparticle dynamics study

Matthew Becton, Rodney Averett & Xianqiao Wang

To cite this article: Matthew Becton, Rodney Averett & Xianqiao Wang (2017): Artificialbiomembrane morphology: a dissipative particle dynamics study, Journal of Biomolecular Structureand Dynamics, DOI: 10.1080/07391102.2017.1373705

To link to this article: https://doi.org/10.1080/07391102.2017.1373705

Accepted author version posted online: 30Aug 2017.Published online: 18 Sep 2017.

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Artificial biomembrane morphology: a dissipative particle dynamics study

Matthew Becton, Rodney Averett and Xianqiao Wang*

College of Engineering, University of Georgia, Athens, GA, USA

Communicated by Ramaswamy H. Sarma

(Received 19 June 2017; accepted 21 August 2017)

Artificial membranes mimicking biological structures are rapidly breaking new ground in the areas of medicine and soft-matter physics. In this endeavor, we use dissipative particle dynamics simulation to investigate the morphology andbehavior of lipid-based biomembranes under conditions of varied lipid density and self-interaction. Our results show thata less-than-normal initial lipid density does not create the traditional membrane; but instead results in the formation of a‘net’, or at very low densities, a series of disparate ‘clumps’ similar to the micelles formed by lipids in nature. When theinitial lipid density is high, a membrane forms, but due to the large number of lipids, the naturally formed membranewould be larger than the simulation box, leading to ‘rippling’ behavior as the excess repulsive force of the membraneinterior overcomes the bending energy of the membrane. Once the density reaches a certain point however, ‘bubbles’appear inside the membrane, reducing the rippling behavior and eventually generating a relatively flat, but thick, struc-ture with micelles of water inside the membrane itself. Our simulations also demonstrate that the interaction parameterbetween individual lipids plays a significant role in the formation and behavior of lipid membrane assemblies, creatingsimilar structures as the initial lipid density distribution. This work provides a comprehensive approach to the intricaciesof lipid membranes, and offers a guideline to design biological or polymeric membranes through self-assembly processesas well as develop novel cellular manipulation and destruction techniques.

Keywords: biomembrane; lipid; dissipative particle dynamics; self-assembly

1. Introduction

Current techniques for the prediction and modeling ofnot only inorganics but also more complex biologicalmaterials have made possible the study of technologi-cally relevant soft materials, such as recently developedartificial lipid-based biomembranes (Mashaghi, Jadidi,Koenderink, & Mashaghi, 2013; Whitesides & Lipomi,2009). These structures are worth studying via simulationin order to build knowledge relevant to medical technol-ogy and industry while simultaneously lessening theneed for expensive, uncontrollable, or dangerous physicalexperiments. The morphology of a lipid membrane isstrongly dependent on the density of lipids and the inter-actions between the lipids, and thus these conditions arewhat we will be focusing on for this work. To beginwith, the lipid membrane is a ubiquitous construction inthe natural world, forming the structural support for liv-ing cells and able to keep the cellular structures insidewhile regulating the passage of molecules. The utility ofthe lipid membrane is the foundation of complex organ-isms and has received a large amount of attention andresearch, both for its chemical and mechanical properties(Essmann, Perera, & Berkowitz, 1995; Grunze, Fedya-nin, & Pertsin, 2009; Israelachvili & Wennerstrom, 1992;Kranenburg & Smit, 2005; Long, Zhang, & Qian, 2006;

Lyubartsev, 2005; Mao, Chen, Liang, Guo, & Yan, 2016;McIntosh & Simon, 1996; Peng et al., 2013; Pertsin,Platonov, & Grunze, 2007; Rangamani et al., 2014; Smit,Kranenburg, Sperotto, & Venturoli, 2006; Venturoli,Sperotto, Kranenburg, & Smit, 2006). Due to their use-fulness and relative simplicity, designed nanoscopicassemblies of lipids in the form of membranes andmicelles are used in various fields, from soft matter phy-sics to actual synthetic biology, where lipids are used togenerate systems mimicking biological structures(Mashaghi et al., 2013). Artificial membranes are a bur-geoning technology allowing for an explosion ofresearch into synthetic biology and medicine (Dankerset al., 2011; Lee et al., 2008; Malinova, Belegrinou,Ouboter, & Meier, 2010; Zhao et al., 2010). Designedmembranes are able to accomplish sensitive tasksunsuited to natural structures, such as binding selectedsurfaces, serving as catalytic nanoreactors for controlledchemical reactions, dispersing CNTs into solution, andthe carrying and delivering drugs or other payloads intocell interiors (Adeli, Kalantari, Parsamanesh, Sadeghi, &Mahmoudi, 2011; Angius, Murgia, Berti, Baglioni, &Monduzzi, 2006; Anraku, Kishimura, Oba, Yamasaki, &Kataoka, 2010; Baca et al., 2011; Beales & Vanderlick,2009; Bombelli et al., 2009; Lee, Lee, Kim, Suh, &

*Corresponding author. Email: xqwang@uga.edu

© 2017 Informa UK Limited, trading as Taylor & Francis Group

Journal of Biomolecular Structure and Dynamics, 2017https://doi.org/10.1080/07391102.2017.1373705

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Kawai, 2009; Mashaghi et al., 2013; Mayer, 2005;Schoonen & van Hest, 2016; Wang, Michielssens,Moors, & Ceulemans, 2009).

In accordance with this wide range of applications,in order to further the progression of science and tech-nology focused on biomimetic structures it is imperativeto not only to understand the structure of the normallyseen lipid bilayer, but also investigate the properties andbehaviors of lipid membrane behavior beyond the stan-dard. Previous studies into the behaviors of lipid-basedstructures have dealt with the dynamics between lipidtype, concentration, and structure, but have focused onvesicles or otherwise have not gone in-depth into thefiner characteristics and limits of specifically membraneformation and morphology (Arai, Yasuoka, & Zeng,2013; de Meyer, Benjamini, Rodgers, Misteli, & Smit,2010; Kranenburg, Vlaar, & Smit, 2004; Lin, Li, Sheng,Wu, & Tsao, 2012; Murtola, Falck, Patra, Karttunen, &Vattulainen, 2004; Rozycki & Lipowsky, 2015; Tan,Shen, Li, Elson, & Ma, 2008; van Hoof, Markvoort, vanSanten, & Hilbers, 2014; Yamamoto, Maruyama, &Hyodo, 2002). There are many conditions wherein cellsdisplay unusual or non-flat membranes, such as whenexposed to chemoattractant, (Mckay, Kusel, & Wilkin-son, 1991) irregularities during culture growth, (Power,Neylan, & Collum, 1993) exposure to magnetic fields,(Chionna et al., 2005; Dini & Abbro, 2005) and cellshape change (Kapustina et al., 2016). These experimen-tal results show that the addition of chemoattractant andexposure to magnetic fields can create rippled or bubbledlamellar membranes, while growth irregularities and themovement of a cell can cause protrusions and bulging ofthe cell membrane. It is rare to see works which tacklethese specific cases, and so there is a need to explore thetendencies of cell membrane morphology under the influ-ence of these effects.

In order to accomplish the necessary tasks utilizingthis cutting-edge soft material technology, it is valuableto understand more completely the variability exhibitedby such biomembranes under different conditions. Weaim to build on previous literature in order to come upwith a more comprehensive set of common membranemodes, and to examine and explore the conditions andformation dynamics of these modalities. This workseeks to employ dissipative particle dynamics simulationin order to determine the effect of varying lipid densityand interaction on the stability and morphology of amodeled biomembrane, in order to mimic the effects ofirregularly formed biomembranes. First, we describe thedetails of the simulation methodologies. Next, wepresent and analyze the results obtained by varying theinitial parameters of the lipid density and interactionparameter. Conclusions are drawn and discussed inSection 4.

2. Computational model and methodology

In what follows, molecular dynamics simulations basedon the open source code LAMMPS [version 13 August2016] (Plimpton, 1995) developed by Sandia NationalLaboratories are employed to perform the simulationbased on dissipative particle dynamics (DPD), a meso-scopic coarse-grained simulation method suitable for softmatter and biomembrane systems (Espanol & Warren,1995; Groot & Rabone, 2001; Groot & Warren, 1997;Hoogerbrugge & Koelman, 1992; Moeendarbary, Ng, &Zangeneh, 2010). In these coarse-grained simulations, agroup of atoms is treated to be a single bead located atthe center of mass of the group, with beads on the samemolecule interacting via a harmonic bond potential; thisis the classic bead-spring model for coarse-grained lipids(Venturoli et al., 2006). Beads i and j interact with eachother via a pairwise force consisting of a conservativeforce FC

ij representing excluded volume effect, a dissipa-tive force FD

ij representing viscous drag between movingbeads and a random force FR

ij representing stochasticimpulse. Both FD

ij and FRij act together as a thermostat

for the beads. Similar to molecular dynamics simulation,time evolution is also governed by the Newton’s equa-tion of motion. The total force on bead i can beexpressed as

Fi ¼Xi 6¼j

FCij þ FD

ij þ FRij

� �

¼Xi 6¼j

aijx rij� �

r̂ij � cx2 rij� �

r̂ij � vij� �

r̂ij�

þ rx rij� �

fijDt�1=2r̂ij

�

where aij is the maximum repulsive force, rij the dis-tance, r̂ij the unit vector and vij the relative velocitybetween beads i and j; ζij denotes a random number withzero mean and unit variance, and

xðrijÞ ¼ 1� rijrc; rij\rc

0; rij [ rc

�

is a normalized distribution function, rc being the cut-offradius; γ and σ are parameters related to each other asσ2 = 2γkBT, kBT being the unit of energy. The standardvalues σ = 3.0 and γ = 4.5 are used in our study (Zhang,Becton, & Wang, 2015; Zhang & Wang, 2015a, 2015b).The mass, length, and time scales are all normalized inthe DPD simulations, with the unit of length taken to bethe cut-off radius rc, the unit of mass to be that of thesolvent beads, and the unit of energy to be kBT . Allother quantities are expressed in terms of these basicunits. The reduced DPD units can be converted to SIunits by examining the membrane thickness and the lipiddiffusion coefficient. The simulated value of bilayerthickness is 10rc and the effective time scale of

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simulation can be determined from the simulated lateraldiffusion constants of lipid bilayer (Zhang et al., 2015).The typical phospholipid bilayer has a thickness of about4 nm with a diffusion coefficient around 5 μm2s−1, (Mur-zyn, Rog, & Pasenkiewicz-Gierula, 2005; Shillcock &Lipowsky, 2005) by comparison with typical experimen-tal values, it can be shown that one DPD length unit cor-responds to approximately 0.8 nm in physical units andthe time unit to τ = 24.32 ps. The time step is taken asΔt = 0.01τ. All simulations are performed usingLAMMPS.

The phospholipid phosphatidylcholine (PC) is chosenas the base for this DPD model, as it is a common com-ponent of biological membranes. To simulate the mole-cule here, three types of beads are used: hydrophobic,hydrophilic, and water-like. The lipid model is con-structed by connecting hydrophilic ‘head’ beads withhydrophobic ‘tail’ beads via harmonic springs, with bondangle constraints controlling the chain bending stiffness.The dimensions of the periodic simulation box are120rc � 120rc � 100rc, with the lipids being insertedinto a 120rc � 120rc � 10rc sized volume before the sys-tem is equilibrated. Water is inserted into the volumeoutside the lipid bilayer such that the system is main-tained at a particle density of approximately 3 particlesper unit volume (hereafter, density is taken to be unit-less) (Nielsen, Ensing, Ortiz, Moore, & Klein, 2005).The initial simulation system consists of the biomem-brane made of lipid molecules and solvent particles. Sol-vent beads are not shown for clarity. The lipid moleculeis represented by the coarse-grained model proposed byGroot and Rabone (2001) as shown in Figure 1(a); itconsists of 3 lipid hydrophilic head beads and 10 lipidhydrophobic tail beads (in two tail chains of 5 beadseach). The repulsive interaction parameters between lipid

beads of the same type are typically taken as aii ¼ 25,and those for beads of different types are set asaij ¼ 100. Hydrophobic bead interactions with water areset as aij ¼ 100, while hydrophilic bead-water interac-tions have the parameter aij ¼ 25 (Y. F. Li, X. J. Li, Z.H. Li, & H. J. Gao, 2012). Within a lipid molecule, anelastic harmonic force,

FSij ¼ ks 1� rij

rs

� �r̂ij

is used to connect two consecutive beads, where ks andrs are the spring constant and equilibrium bond length,respectively. Here we use ks = 100.0 and rs = 0.7rc forlipid molecules (Venturoli, Smit, & Sperotto, 2005). Thebending resistance of the lipid chain is represented as anadditional force due to a harmonic constraint on twoconsecutive bonds

Fh ¼ �rVbend ¼ �r khðh� h0Þ2h i

where kh, θ and θ0 are the bending constant, inclinationangle and equilibrium angle, respectively. As shown inFigure 1(a), for three consecutive lipid tail beads or threeconsecutive lipid head beads in a lipid molecule, we takek1 = 6 and h ¼ 180

�; for the last head-bead and the top

tail-beads k2 = 3 and h ¼ 120�; for the bottom two con-

secutive head beads and the first bead in each tailk3 = 4.5 and h ¼ 120

�(Y. Li, X. Li, Z. Li, & H. Gao,

2012). A sample structure of lipids congregated into abiomembrane is shown in Figure 1(b) and (c). Wherementioned, a biomembrane’s amplitude refers to thetime-averaged equilibrium value of the distance betweenthe lowest and highest (along the z-axis) lipid bead inthe membrane or structure; however, it is assigned a neg-ative value when the membrane incompletely separatesthe simulation box (incomplete or perforated membrane).All simulations are treated as NVE and run for1,000,000 time steps to ensure that a representative struc-ture is taken, with time-averaged equilibrium data takenfrom time steps 500,000 – 1,000,000 (~122 – 243 ns) asall structures reach their final state before 300,000 timesteps (~73 ns). We now turn our focus on characterizingthe biomembrane itself.

3. Results and discussion

3.1. Classification of biomembrane morphology

To characterize the various types of biomembrane mor-phology, we turn to the physical behaviors of lipidbiomembranes. It has been shown that the lipid bilayerstructure exhibits a number of suitable characteristics forits ubiquity in biological structures, including flexibilityand adaptivity. Here, we observe that at the density andparameters described in the Methods section, the typical

180°

180°

0.7 rc

(a)(b)

(c)

Figure 1. (a) A representative structure of the DPD model fora lipid molecule. Blue is the hydrophilic head; red is thehydrophobic tail. (b) Top and (c) side views of the lipids form-ing a bilayer membrane; the water beads are not displayed forclarity.

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behavior of the lipid bilayer membrane is to form a flatsheet with minimal ‘ripples’ or ‘waves’. Figure 2 givesthe typical lipid agglomeration modes that form duringour runs with different initial conditions. Here the modesare labeled and described. Figure 2(a) shows the forma-tion of ‘clumps’, which happens when the lipids do notform a singular contiguous membrane but rather congre-gate into small micelle structures. Figure 2(b) illustrates‘net’-like behavior wherein the membrane is stretchedtoo tight to form a solid membrane, or has sustainedirreparable damage. Figure 2(c) is the typically seen ‘flatsheet’ bilayer, and what is typically referenced as thetextbook membrane. Figure 2(d) is a ‘wavy’ or ‘rippled’membrane, which occurs when the membrane is not intension but rather experiences compressive forces. Fig-ure 2(e) conveys what happens when the compressiveforce on the membrane becomes large enough that themembrane ripples self-adhere and fuse together, forminginner ‘pockets’ or ‘bubbles’; this phenomenon can beconsidered a smaller scaled, incomplete version of the

bilayer-vesicle transition observed previously (Wu &Guo, 2008). Finally, Figure 2(f) displays the outcome offurther formation of bubbles beyond a single membranelayer, labeled here as ‘stacked’. These are the major mor-phologies noted in this work; both the ‘clumps’ and the‘stacked’ modes extend to their respective ends: withfewer lipids the ‘clumps’ become smaller until they aresingular lipids in water, and at the other end of the spec-trum the ‘stacked’ formation becomes larger and largeruntil it fills the system. Due to these reasons, we con-sider these six modes to be the major ones that we willexplore.

3.2. Effect of lipid density

There is a certain range of lipid density wherein the mem-brane model most accurately depicts typical membranestructures. However, it is important to examine casesnear this specific density to investigate the behaviorand mechanical properties of membranes that may have a

(a) (b)

(c)(d)

(e) (f)

Figure 2. A differentiation of the different membrane modes observed in this work. In order of increasing lipid density, the observedmodes are (a) clumping, (b) forming nets, (c) the flat membrane, (d) the rippled membrane, (e) the bubbled membrane, (f) thestacked membrane.

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deficit or overabundance of lipids in them, such as whena cell changes shape and ends up with an excess or lackof membrane for the cell volume (Kapustina et al., 2016).Here, we will explore the cell membrane morphology forcases where the membrane lipid density is above or belowthat which is normally observed in cellular biomem-branes. To study this, we create the membrane as men-tioned in the Methods Section, putting the lipids into aplane of 120rc � 120rc � 10rc sized volume. The originaldensity of 3 beads per unit volume is then varied to insertmore or fewer lipids into this volume, and the system isthen allowed to evolve to equilibrium. The morphologicalchanges that the membrane undergoes as the lipid densityis increased from 0.78 to 45 are shown in Figure 3, assnapshots along with the evolution of the measured ampli-tude of the bilayer membrane, with ‘incomplete’ mem-branes such as ‘clumps’ or ‘nets’ being assigned negativevalues for clarity. An incomplete membrane is one thatdoes not create separate sections of the simulation box,and thus would not hinder the flow of water or smallmolecules across it. The amplitude is plotted as a way tovisualize the morphology changes stemming from theincreasing density. Figure 3 plots the initially set densityof the lipid layer vs. the measured amplitude of the layerat equilibrium. From the insets, it can clearly be observedhow the amplitude can be used to track the evolution ofthe morphological mode as a function of the initialdensity.

At low densities the membrane cannot form at all;instead the attractive force between similar lipid beads

and the repulsive force between water and lipid tailbeads cause nearby lipids to cluster together and formmicelles or ‘clumps’, as is evidenced by the lowest-den-sity subfigure of Figure 3; at this stage, there is a rela-tively large negative amplitude, as the clumps floataround with little effect on each other, creating a largedistance between the highest and lowest lipids. When theinitial lipid density is increased, the lipids form anincomplete membrane, referred here as ‘net’ form. Thisevolution occurs due to the strong surface tension andself-adhesion of the lipid membrane. When there areenough lipids to prevent the separation of the lipids intoindividual micelles, yet few enough that a flat bilayermembrane is not energetically favorable, the lipid struc-ture forms a ‘net’-like assembly, where many small holesinitiate and converge to form large, circular holes in thetypical membrane structure. The ‘net’ mode has a smallnegative value, as the surface tension felt by the netkeeps it very flat and taut. The process of net formationfrom the initial layer structure is detailed in Figure 4,including periodic images to more clearly demonstratethe net-like structure. It can be perceived from the pro-gression seen in Figure 4 that the number of lipids isinsufficient to keep a stable flat membrane, as holesspontaneously form. At first, the system changes rapidly,with holes forming and then merging repeatedly. Afterformation, these holes then congregate together to formlarge, stable holes, giving the incomplete membrane theappearance of a ‘net’ as shown in Figure 2(b). The con-figuration in Figure 4(h) was formed after approximately

100 101-40

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0

10

20

30

40

50

60

Lipid Density (3 is normal)

Mem

bran

e A

mpl

itude

Figure 3. Height difference between upper and lower edges of the membrane as the initial lipid density increases, with associatedimages (log scaling for x-axis). A negative value denotes that the membrane is incomplete (does not completely separate the top andbottom sections of the simulation box).

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300,000 timesteps (~73 ns). The simulation was contin-ued until 1,000,000 timesteps (~243 ns), and no furtherevolution or change in structure was detected; thus thesimulation was judged to have reached equilibrium sta-tus. At a normal density of 3, there is a small regionwhere there are enough lipids to form a stable, completemembrane as seen in Figure 2(c), yet not so many thatout-of-plane deformation occurs. It can be said that inthis window, the interior and exterior force of the lipidbilayer are balanced.

At initial lipid densities higher than the normal, amembrane will form, but due to the increased number oflipids the bilayer formed repulses itself as it tries to forma membrane that is larger than the simulation box. Thisleads to ‘rippling’ behavior as the excess repulsive forceof the membrane interior overcomes the bending energy

of the membrane. This ‘rippling’ behavior is seen inFigure 2(d). Once the density reaches a certain pointhowever, ‘bubbles’ appear inside the membrane, reduc-ing the rippling behavior and eventually generating a rel-atively flat, but thick, structure with micelles of waterinside the membrane itself. The formation process of theintra-membrane bubbles seen in Figure 2(e) is illustratedin Figure 5. It can be seen that at high densities, therepulsive interactions between the lipids drive them out-wards, creating a disordered membrane that cannot formstable long-wavelength ripples before the lipids shuntedto the exterior of the membrane self-contact and foldover, forming bubble structures around small amounts ofwater. These bubbles in the interior of the membrane sta-bilize the repulsion forces between lipids by balancingthe surface area and volume of the membrane. Beyond

(a) (b)

(c) (d)

(e) (f)

(h)(g)

Figure 4 Evolution process of the ‘net’ membrane mode. Note the formation of multiple small holes joining together to form large,stable holes. The wire box in subfigure (a) represents the units cell of the simulation.

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the membrane mode with a single layer of bubbles, themembrane starts forming stacked layers of bubbles, asdisplayed in Figure 2(f). Additional increases to the ini-tial lipid density merely increase the eventual thicknessof this layer; as such a mode keeps stable even at extre-mely large densities. In fact, rippled lamellar and bubble-like formations have been observed in cell membranesexposed to magnetic fields for long durations (Chionna

et al., 2005; Dini & Abbro, 2005). Similar unusual ornon-flat membrane structures have also been found inhuman neutrophils exposed to chemoattractant, as shownin Figure 6 (Mckay et al., 1991). Figure 6(a) shows nor-mal cell membranes, with the corresponding simulationalmembrane morphology shown in Figure 6(b). Figure 6(c)shows the abnormal, bulging, and rippled cell mem-branes of neutrophils exposed to chemoattractant, with

(a)

(c)

(e)

(b)

(d)

(f)

Figure 5. Evolution process of the ‘bubbled’ membrane mode. Note the folding over of the membrane to form the ‘bubbles’.

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the corresponding simulational morphology shown inFigure 6(d). Although we have seen the mechanisms offormation for these several types of extraordinary mem-branes, merely noting the effect of the initial density ofthe lipid bilayer cannot help us get a true grasp of theformation and stability of the different biomembranemodes.

3.3. Effect of interaction parameter

Similar to the density of the lipids in the biomembrane,the interaction parameter between the lipid heads, lipidtails, and water beads can be tuned in order to morewidely examine the different behaviors exhibited bybiomembranes, which can be representative of certainfactors indicating problems with a cell or similar artificialstructure. The interaction parameter designates the repul-sion effects which each lipid experiences from lipidsnearby, and changing it mimics the tuning of biomem-branes by inserting different types of lipid, or by electricor magnetic fields (Krishnan, Mojarad, Kukura, & San-doghdar, 2010; Le Meins, Sandre, & Lecommandoux,2011; Mashaghi et al., 2013; Woods, Li, Rosenblatt,Yager, & Schoen, 1989). To simulate this, we varied theinteraction parameter between lipid beads mentioned inthe Methods section. For the previous section, the repul-sive interaction parameters between lipid beads of thesame type are set as aii ¼ 25, and those for two beads ofdifferent types are set as aij ¼ 100. To study the effectsof the interaction parameter, we modulated the self-inter-action parameter between lipid beads of the same type

by a set amount P; that is, aii ¼ 25� P for lipid beadsonly (not water beads) such that P = 1 is the normalvalue. The self-interaction of water beads is unchanged,as are the interactions between water beads and lipidsand those between lipid beads of different type. It hasbeen shown that there is a certain range of parameterswhich allows for the formation of lipid bilayers, but thatrange is fairly flexible (Kranenburg, Nicolas, & Smit,2004). Due to this, we investigated the way the interac-tion parameter influences different behaviors that mayoccur irrespective of density.

Figure 7 demonstrates the effect of changing theparameter P from 0.25 to 4 while keeping the initiallipid density at 3. This Figure reveals that, while keepingdensity at 3 and thus for the same number of lipids, low-ering the interaction parameter causes the membrane toform holes and create a ‘net’ structure, while raising theinteraction parameter forces the membrane to adopt the‘rippled’ mode. This can be explained due to the factthat at an interaction parameter below unit, lipids clustermore compactly under pressure from the water, causingthe membrane to shrink and upsetting the balance ofinterior repulsion and exterior surface tension, so that themembrane must form holes in order to stabilize. At aninteraction parameter greater than unit, the repulsiveforce between lipids increase, pushing the balancebetween repulsion and surface tension in the oppositedirection, such that the membrane bulges and forms rip-ples in order to maintain stability. However, observingthe effect of P for a single density does not help us get acomprehensive sense of the overall effect of the

(a) (b)

(c) (d)

Figure 6. (a) human blood neutrophils with normal lipid density; (b) flat membrane from computational model with normal lipiddensity; (c) human blood neutrophils with abnormal lipid density; (d) bubbled membrane from computational model with abnormallipid density. Figures (a) and (c) adapted with permission from Mckay, Kusel, and Wilkinson (1991).

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interaction parameter. Thus, after running many cases,we formed a ‘phase diagram’-style graph as seen inFigure 8. From this, we can observe that the interactionparameter and the density are two sides of a coin; thatis, increasing P is similar to increasing the initial densityin the effect it has on the morphology of the biomem-

brane. The result that these two seemingly disparate vari-ables have similar effects lies in the fact that increasingeither one results in an increased repulsion effect withinthe membrane itself, creating similar changes to themorphological mode. From this overview, we can usethese results to gather an overview of the many different

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Interaction Parameter

Mem

bra

ne

Am

plit

ud

e

Figure 7. Height difference between upper and lower edges of the membrane at normal density as the interaction parameter changes,with associated images (log scaling for x-axis). A negative value denotes that the membrane is incomplete (does not completelyseparate the top and bottom sections of the simulation box).

100 10110-1

100

Lipid Density

Inte

ract

ion

Para

met

er

Clumping NetFlat

Rippled Bubbled Stacked

Figure 8. Map of the different morphologies as a function of both density and interaction parameter (log scaling).

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morphologies which a biomembrane structure can evolveinto, dependent on the density and chemical makeup ofthe lipids composing it.

4. Concluding remarks

In summary, we have utilized DPD simulations to inves-tigate the effects of various factors such as lipid densityand interaction parameter value on the construction andcharacteristics of the typical lipid biomembrane. Ourfindings show that a smaller-than-normal initial lipiddensity does not create the traditional biomembrane;instead letting the system run to equilibrium results inthe formation of a ‘net’, or at very low densities, a seriesof disparate ‘clumps’. As expected, a normal density andnormal parameter result in a flat, stable biomembrane.When the initial lipid density is higher than normal, themembrane forms, but due to the increased number oflipids, the membrane formed is larger than the simulationbox, leading to ‘rippling’ behavior as the excess repul-sive force of the membrane interior overcomes the bend-ing energy of the membrane. Once the density reaches acertain point however, ‘bubbles’ appear inside the mem-brane, reducing the rippling behavior and eventually gen-erating a relatively flat, but thick, structure with micellesof water inside the membrane itself. Our simulations alsodemonstrate that the forces between lipids in a mem-brane, here represented by the interaction parameter ofthe DPD force field, play a significant role in the forma-tion and behavior of lipid biomembrane assemblies, cre-ating similar structures as the initial lipid densitydistribution. This work provides a comprehensiveapproach to the intricacies of lipid bilayer membranes,and can be used to develop novel cellular manipulationand destruction techniques.

AcknowledgmentsX. Wang acknowledges support from the National ScienceFoundation (No. CMMI-1610812) and University of Georgia(UGA) start-up fund. The facility support for modeling andsimulations from the UGA Advanced Computing ResourceCenter are greatly appreciated. R. Averett acknowledges thesupport from National Heart, Lung, and Blood Institute of theNational Institutes of Health under Award NumberK01HL115486.

Disclosure statementNo potential conflict of interest was reported by the authors.

FundingThis work was supported by the National Science Foundation[grant number CMMI-1610812]; the University of Georgia(UGA).

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