# Lateral Membrane Heterogeneity Regulates Viral-Induced Membrane Fusion during HIV Entry

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## Abstract

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## 1. Introduction

_{B}T (k

_{B}T ~ 4 × 10

^{−21}J). It strongly depends on the distance between the fusing membranes: the smaller the distance, the lower the barrier. Fusion efficiency is determined by the height of the energy barrier (the lower the barrier, the more effective fusion is). In the process of cell infection by viruses, the barrier is partly compensated by the action of specific proteins known as “fusion proteins” [22,23], which undergo conformational transition aimed to bring the viral and the target cell membranes in a closer juxtaposition. In the case of HIV, the rearrangement is triggered by interaction of subunits of the fusion protein with CD4 receptors and CCR5 co-receptors on the surface of the target cell membrane [24,25]. Such an interaction results in exposure of the hydrophobic fusion peptide with its subsequent incorporation into the target cell membrane. In the present work, we attempt to elucidate how interaction of fusion peptides with raft boundaries can affect efficiency of virus induced fusion. Our calculations are based on the liquid crystal elasticity theory adapted to lipid membranes (detailed description of the methodology is available in the works [26,27]). In the framework of this theory, the membrane is treated as a continuous liquid crystal medium subjected to elastic deformations. The deformations are caused by fusion peptides incorporated into the membrane, along with the hydrophobic thickness mismatch at the raft boundary. The elastic parameters of the membrane as a whole take into account, in particular, the specific interactions of lipids with each other and with the proteins embedded in the membrane. We assume that CD4 receptors nucleate rafts around them, and the boundaries of the rafts in the opposing monolayers of the cell membrane are misaligned (shifted relative to each other) (see Figure 1a), according to the results obtained in [9]. HIV fusion peptides incorporate deeply into the target cell membrane, inducing negative curvature in the membrane [28]. Due to such mode of incorporation, the peptides are capable of changing the energy barriers associated with the membrane topological rearrangement, inclusively those related to stalk formation. In our calculations, we assume that the membrane fusion occurs at the expense of cooperative action of several HIV fusion proteins (see Figure 1b,c). Presently, there is limited understanding of this issue in the available publications [24,29]. Some authors suggest that one or two trimers participate in the fusion, whereas others claim that several trimers are needed [30,31]. We also take into account the evaluations carried out in the work [20], according to which the total work done by proteins should be of the order of 100 k

_{B}T. At the same time, the estimate of the energy liberated in the process of the conformational transition of one fusion protein trimer amounts to several tens of k

_{B}T [18]. These estimates also indirectly indicate the cooperative effect of several proteins in the process of fusion. Together with the axial symmetry of the fusion stalk structure, that leaves us with few peptides, located around some center-stalk. That picture justifies the assumption of the cooperative action of several fusion peptides leading to the ring-like insertion into the membrane. The assumption of cooperative action of several fusion peptides allow greatly simplifying the calculations by means of considering cylindrically symmetrical ring of fusion peptides, known as fusion rosette [32].

_{h}= 2πR

_{1fp}Lσ

_{0}≈ 60–80 k

_{B}T, where R

_{1fp}~ 1 nm is the characteristic diameter of the fusion peptide; L ~ 2 nm is the characteristic length of the fusion peptide; σ

_{0}~ 40–50 mN/m is the surface tension on water/hydrophobic peptide interface. Thus, according to our calculations presented below, the total elastic stress developed in fusing membranes is hardly sufficient to pull a single fusion peptide out of the target membrane.

## 2. Results

#### 2.1. Dependence of the Equilibrium Position of the Fusion Peptide Upon Incorporation Depth

_{FP}, is assumed to be smaller than the shift L of the monolayer raft boundaries. The dependence of the membrane equilibrium energy on the position R of the peptide with respect to the center of coordinates is shown in Figure 2b.

_{B}T, K = 10 k

_{B}T/nm

^{2}[40,41] for the monolayer splay and tilt moduli, respectively. The surface tension σ of a monolayer is assumed at 0.01 k

_{B}T/nm

^{2}. The raft monolayer thickness h

_{r}was taken equal to 2 nm; the surrounding membrane monolayer thickness h

_{s}was 1.5 nm [2]. The only difference of the raft from the surrounding membrane was in the equilibrium thickness. The equilibrium width L of transient zone between the domain boundaries in the two juxtaposed monolayers of the membrane were also found by means of minimization of the membrane deformation energy, and equaled 2 nm.

#### 2.2. Dependence of the Stalk Formation Energy Barrier on the Presence of a Raft

_{TM}and R

_{FP}, respectively. The transmembrane domains are modeled as annular inclusions penetrating the entire depth of the viral membrane bilayer, whereas the fusion peptides—as annular inclusions incorporated into one monolayer of the target membrane to relatively large depth (see Figure 3).

_{0}, at which the hydration repulsion forces [42] equilibrate the attraction force applied by the proteins. It is also assumed that, in the course of fusion, the distance ΔH between the annulus of transmembrane domains and the annulus of fusion proteins in the target cell gets smaller, whereas the distance between the membranes in the area remote from the fusion rosette remains unchanged and equal to H

_{0}(see Figure 3). Due to the large size of fusion proteins and their transmembrane (TM) domains as well as their high density in the viral membrane, we assume that the deviation of transmembrane domains from the initial equilibrium position can be neglected. An energy barrier associated with the hydration repulsion forces has to be crossed in order to bring the membranes closer [43]. In the conditions when fusion peptides tend to decrease the distance between the membranes, the hydration repulsion of the bilayers presumably results in a lateral displacement of the lipid polar heads from the membrane contact area [20]. Thus, hydrophobic defects are formed in the contact monolayers of the bilayers undergoing fusion [44]; the radius of the hydrophobic defect is designated as ρ in Figure 3. Such defects can act as nucleation centers for monolayer fusion, since their formation results in local disordering of the hydration layers and occurrence of hydrophobic attraction between the contact monolayers [45], ultimately resulting in stalk formation.

_{0}= 60 k

_{B}T/nm

^{3}, hydration interaction characteristic length ξ

_{h}= 0.35 nm. The hydrophobic attraction characteristic length ξ

_{f}was assumed equal to 1 nm in compliance with the experimental data reported in [45]. The half-width of the transmembrane domain R

_{TM}, as well as the half-width of the fusion peptide R

_{FP}were assumed equal to 1 nm.

_{T}on the reaction coordinate H

_{0}− ΔH. The hydrophobic patch radius was variable. An example of the dependence of total energy on the reaction coordinate is shown in Figure 4a. The dependencies allow calculating the energy barrier to the stalk formation. The barrier height W

_{B}is calculated as a difference between the maximal energy on the trajectory and the initial energy:

_{B}= W

_{max}− W

_{initial}

_{initial}was not equal to zero since membrane deformations caused by incorporation of fusion peptides and compensation of the hydrophobic mismatch at the raft boundary are already factored into it. Then, we varied the length L of the raft transient zone and calculated the energy barrier for each value of L at fixed radius R of the protein annulus and distance H

_{0}between the membranes. Figure 4b illustrates an example of the dependence of the barrier height upon L.

_{0}, the energy barrier is minimized against the transient zone width L. This corresponds to the minimum of the red curve in Figure 4b (designated as W

_{raft}). Then, we compare the obtained value with the barrier height in the absence of the raft (designated as W

_{noraft}). Two values: the minimal height of the barrier W

_{raft}and difference ΔW are of crucial importance for our analysis. The latter is defined as

_{noraft}− W

_{raft}

_{raft}and ΔW on the initial distance H

_{0}between the membranes at different values of the fusion rosette radius R.

_{0}between the membranes, presence of a raft boundary near the fusion site can decrease the energy barrier to stalk formation, thus facilitating fusion. At small values of H

_{0}, the energy is lower in the absence of rafts, and vice versa.

## 3. Discussion

_{0}between the membranes, presence of the raft boundary can either decrease or increase the energy barrier to stalk formation (Figure 5). Decrease of H

_{0}value results in reduction of the energy barrier W

_{raft}, and simultaneously with that presence of the raft boundary becomes less favorable for fusion (ΔW becomes negative). The equilibrium distance H

_{0}between the membranes is determined by the balance of hydration repulsion forces and the attraction induced by fusion peptides, and it can vary depending on the number of proteins in the fusion rosette and on the curvature of the membranes undergoing fusion. According to various estimates [17,20,51], this value is of the order of several nanometers. According to Figure 5, small H

_{0}values correspond to the situation when rafts are not favorable for fusion, while the large values—to the situation when rafts facilitate it. The critical height of the barrier, at which rafts still favor fusion, decreases with the increasing radius R of the rosette and amounts to 45 k

_{B}T at R = 4 nm and 35 k

_{B}T at R = 3 nm. These values are in excellent agreement with the theoretical estimates obtained earlier [20,21]. Thus, we have obtained that, in the case of fusion between HIV and target cell membranes raft boundary in the vicinity of the fusion site can facilitate fusion. As can be readily seen from a typical curve shown in Figure 4b, asymmetry of the raft boundary provides additional relaxation of the deformation energy and results in decrease of the barrier by several k

_{B}T.

## 4. Materials and Methods

#### 4.1. Energy of the Membranes with Peptide Inclusions

**n**, characterizing the average orientation of lipid molecules, is introduced. The field of directors is defined on a certain surface within the monolayer. The shape of the surface is determined by the unit vectors

**N**normal to it (directed towards the inter-monolayer surface of the membrane). We take into account two deformation modes—tilt and splay. The deformations are attributed to the so-called neutral surface, where the splay and lateral extension deformations are independent on each other. According to the experimental data obtained in [59], the neutral surface lies in the transient area between the lipid polar heads and hydrophobic chains at the depth of ~0.5 nm from the external surface of the lipid monolayer. Splay deformation is qualitatively described by divergence of the director along the neutral surface, whereas the tilt deformation is described by the tilt vector field

**t**=

**n**/(

**nN**) −

**N**≈

**n**−

**N**. We assume the membrane deformation is small, and hence the energy of deformed monolayer counted from the state of planar monolayer can be expressed as [41]

_{0}is the area of the neutral surface in the initial undisturbed state. We introduce Cartesian system of coordinates with the origin at the right-hand side boundary of the bilayer raft (see Figure 2a). The axes are selected so that the Oy axis is perpendicular to the membrane surface, whereas the Ox axis is perpendicular to the raft boundary and lies in the membrane plane. Smallness of deformations implies that the director projection upon the Ox axis is much smaller than unity. All the functions defining the membrane shape and its deformations depend on only one spatial coordinate in the unidimensional case. The vector fields of directors, normals to the neutral surface, and tilts can be replaced with their projections on the Ox axis:

**n**→ n

_{x}= n,

**N**→ N

_{x}= N,

**t**→ t

_{x}= t. Director divergence transforms into its component directed along the Ox axis: div(

**n**) → dn/dx. In addition to that, we only take credit for local volumetric incompressibility condition [41]:

_{0}is the undisturbed monolayer thickness. The thickness of undisturbed raft is designated as h

_{r}, and differs from the thickness of undisturbed monolayer of the surrounding membrane, designated as h

_{s}. The location of the intermonolayer surface m(x) is defined as the distance from the Oxy plane to the intermonolayer surface measured in the given point x along a perpendicular to the plane Oxy. We define the location of the neutral surface of the upper monolayer h

_{a}(x) and of the lower monolayer h

_{b}(x) in a similar manner. Equation (4) along with the definitions of tilt vector (

**t**=

**n**−

**N**), monolayer thickness (Δh

_{a}= h

_{a}(x) − m(x), Δh

_{b}= m(x) − h

_{b}(x)), and normal to the neutral surface of a monolayer (

**N**=

_{a}**grad**(h

_{a}(x)),

**N**= −

_{b}**grad**(h

_{b}(x))), relate the tilt angles t

_{a}(x) and t

_{b}(x) in the upper and lower monolayers with directors, a(x) and b(x) in these monolayers, as well as position of the intermonolayer surface, m(x). Thus, local incompressibility condition applied to two monolayers of the membrane decreases the number of independent functions characterizing the state of a membrane segment from five (a(x), b(x), h

_{a}(x), h

_{b}(x), m(x)) to three (a(x), b(x), m(x)). These three functions are sufficient to rewrite the elastic energy functional, Equation (3). In order to find the functional extremals, we vary it with respect to independent functions a(x), b(x), m(x) and obtain a system of three differential Euler–Lagrange equations, whose solutions are then substituted into the elastic energy functional, Equation (3). The expressions for functions a(x), b(x), m(x), obtained by solving the system of Euler–Lagrange equations contain free coefficients, which are determined by minimizing the energy with specified boundary conditions. The boundary conditions are dependent on the geometry of incorporation of fusion proteins and hydrophobic thickness mismatch at the raft boundaries. See more details of the methodology used for calculating the elastic energy in the works [8,9,60]. Incorporation of fusion peptide into the membrane is accompanied by lateral shift of the adjacent lipid molecules, and in general case—by tilt of the lipid molecules at the boundary to a certain angle with respect to the neutral surface of undeformed membrane. We designate the projection of director at the inner boundary of fusion protein layer (r = R − R

_{FP}) as n

_{l}, at the outer boundary (r = R + R

_{FP})—as n

_{r}(Figure 6a,b). Besides that, fusion peptide can rotate in the membrane as a whole. To account for that, we designate the projection of the director describing this rotation as n

_{FP}. Obviously, n

_{FP}= (n

_{l}+ n

_{r})/2, i.e., n

_{FP}is an average of the directors at the inner and outer boundaries of the fusion peptide layer.

_{FP}, and monolayer thickness, h

_{0}, as

_{0}in Equation (5) is assumed equal to half sum of the monolayer thicknesses of the raft and the surrounding membrane

_{a}(R + R

_{FP}) − h

_{a}(R − R

_{FP}) = 2R

_{FP}n

_{FP}

_{a}(R + 0) − h

_{a}(R − 0) = 0

#### 4.2. Stalk Energy

_{e}, from the hydration repulsion between the hydrophilic surfaces of the contact monolayers, W

_{h}, and from the attraction of the hydrophobic patches formed in the opposing membranes, W

_{f}:

_{T}= W

_{e}+ W

_{h}+ W

_{f}

_{TM}(Figure 6c). Besides that, tilt of the transmembrane domains within the fusion rosette causes relative displacement of the neutral surfaces of monolayers on the inner (r = R − R

_{TM}) and outer (r = R + R

_{TM}) boundaries of the ring. Thus, we have the following boundary conditions

_{TM}) = −n

_{TM}, b(R ± R

_{TM}) = n

_{TM}, h

_{a}

_{,b}(R + R

_{TM}) − h

_{a}

_{,b}(R + R

_{TM}) = −2n

_{TM}R

_{TM}

_{0}), lipid molecules are horizontally oriented, i.e., the director must be equal to −1. Besides fixing the director at the boundary of the hydrophobic spot, we also restrain the separation ΔH of the neutral surfaces of the contact monolayers of fusing membranes along the central circles of the protein rings, at r = R. Additionally, the distance between these neutral surfaces is maintained equal to H

_{0}far from the fusion site, at r → ∞.

_{f}is the characteristic length of hydrophobic interactions in water [45]; l is the distance between the hydrophobic spots; σ

_{0}is the surface tension of the macroscopic phase separation boundary (water/lipid carbohydrate chains). The hydration repulsion energy is calculated according to [42,43] as

_{0}is the disjoining (or wedging) pressure, corresponding to maximal possible repulsion of contacting hydrophilic surfaces; ξ

_{h}is the characteristic length of decay of hydration repulsion. The integration in the Equation (13) is performed over the hydrophilic surface of the contact monolayers. In order to evaluate the integral in Equation (13), we use Derjaguin approximation [61], according to which the integration in the Equation (13) can be limited to the area in which the distance between the membranes changes by the value of ξ

_{h}, having replaced the deformed hydrophilic surfaces of contact monolayers with horizontal planes. If there are no hydrophilic surfaces in the membranes, integration in Equation (13) starts from r = 0. In case there are hydrophobic spots in the membranes, integration is performed from r = r + L

_{h}, making allowance for smearing of the boundary between the hydrophobic spot and the bulk membrane. Such smearing is caused by several factors—fluctuations of polar heads of lipids (the characteristic size of a polar head is ~0.8 nm), finite characteristic length of decay of the order parameter of the hydrophobic and hydrophilic interaction (~0.35 nm and 1 nm, respectively). We selected the value of L

_{h}~ 1 nm.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HIV | human immunodeficiency virus |

TM | transmembrane (domain) |

## References

- Simons, K.; Ikonen, E. Functional rafts in cell membranes. Nature
**1997**, 387, 569–572. [Google Scholar] [CrossRef] [PubMed] - García-Sáez, A.J.; Chiantia, S.; Schwille, P. Effect of line tension on the lateral organization of lipid membranes. J. Biol. Chem.
**2007**, 282, 33537–33544. [Google Scholar] [CrossRef] [PubMed] - Brown, D.A.; London, E. Functions of lipid rafts in biological membranes. Annu. Rev. Cell Dev. Biol.
**1998**, 14, 111–136. [Google Scholar] [CrossRef] [PubMed] - Lingwood, D.; Kaiser, H.J.; Levental, I.; Simons, K. Lipid rafts as functional heterogeneity in cell membranes. Biochem. Soc. Trans.
**2009**, 37, 955–960. [Google Scholar] [CrossRef] [PubMed] - Teissier, É.; Pécheur, E.I. Lipids as modulators of membrane fusion mediated by viral fusion proteins. Eur. Biophys. J.
**2007**, 36, 887–899. [Google Scholar] [CrossRef] [PubMed] - Yang, S.T.; Kiessling, V.; Simmons, J.A.; White, J.M.; Tamm, L.K. HIV gp41–mediated membrane fusion occurs at edges of cholesterol-rich lipid domains. Nat. Chem. Biol.
**2015**, 11, 424–431. [Google Scholar] [CrossRef] [PubMed] - Yang, S.T.; Kreutzberger, A.J.; Kiessling, V.; Ganser-Pornillos, B.K.; White, J.M.; Tamm, L.K. HIV virions sense plasma membrane heterogeneity for cell entry. Sci. Adv.
**2017**, 3, e1700338. [Google Scholar] [CrossRef] [PubMed] - Kuzmin, P.I.; Akimov, S.A.; Chizmadzhev, Y.A.; Zimmerberg, J.; Cohen, F.S. Line tension and interaction energies of membrane rafts calculated from lipid splay and tilt. Biophys. J.
**2005**, 88, 1120–1133. [Google Scholar] [CrossRef] [PubMed] - Galimzyanov, T.R.; Molotkovsky, R.J.; Bozdaganyan, M.E.; Cohen, F.S.; Pohl, P.; Akimov, S.A. Elastic membrane deformations govern interleaflet coupling of lipid-ordered domains. Phys. Rev. Lett.
**2015**, 115, 088101. [Google Scholar] [CrossRef] [PubMed] - Galimzyanov, T.R.; Molotkovsky, R.J.; Kuzmin, P.I.; Akimov, S.A. Stabilization of bilayer structure of raft due to elastic deformations of membrane. Biol. Membr.
**2011**, 28, 307–314. [Google Scholar] [CrossRef] - Galimzyanov, T.R.; Lyushnyak, A.S.; Aleksandrova, V.V.; Shilova, L.A.; Mikhalyov, I.I.; Molotkovskaya, I.M.; Akimov, S.A.; Batishchev, O.V. Line Activity of Ganglioside GM1 Regulates the Raft Size Distribution in a Cholesterol-Dependent Manner. Langmuir
**2017**, 33, 3517–3524. [Google Scholar] [CrossRef] [PubMed] - Galimzyanov, T.R.; Molotkovsky, R.J.; Cohen, F.S.; Pohl, P.; Akimov, S.A. Comment on “Elastic membrane deformations govern interleaflet coupling of lipid-ordered domains” Reply. Phys. Rev. Lett.
**2016**, 116, 079802. [Google Scholar] [CrossRef] [PubMed] - Perlmutter, J.D.; Sachs, J.N. Interleaflet interaction and asymmetry in phase separated lipid bilayers: Molecular dynamics simulations. J. Am. Chem. Soc.
**2011**, 133, 6563–6577. [Google Scholar] [CrossRef] [PubMed] - Risselada, H.J.; Marrink, S.J. The molecular face of lipid rafts in model membranes. Proc. Natl. Acad. Sci. USA
**2008**, 105, 17367–17372. [Google Scholar] [CrossRef] [PubMed] - Pantano, D.A.; Moore, P.B.; Klein, M.L.; Discher, D.E. Raft registration across bilayers in a molecularly detailed model. Soft Matter
**2011**, 7, 8182–8191. [Google Scholar] [CrossRef] - Molotkovsky, R.J.; Kuzmin, P.I.; Akimov, S.A. Membrane fusion. Two possible mechanisms underlying a decrease in the fusion energy barrier in the presence of fusion proteins. Biol. Membr.
**2015**, 32, 79–92. [Google Scholar] [CrossRef] - Molotkovsky, R.J.; Galimzyanov, T.R.; Jiménez-Munguía, I.; Pavlov, K.V.; Batishchev, O.V.; Akimov, S.A. Switching between Successful and Dead-End Intermediates in Membrane Fusion. Int. J. Mol. Sci.
**2017**, 18, 2598. [Google Scholar] [CrossRef] [PubMed] - Chernomordik, L.V.; Kozlov, M.M. Mechanics of membrane fusion. Nat. Struct. Mol. Biol.
**2008**, 15, 675–683. [Google Scholar] [CrossRef] [PubMed] - Efrat, A.; Chernomordik, L.V.; Kozlov, M.M. Point-like protrusion as a prestalk intermediate in membrane fusion pathway. Biophys. J.
**2007**, 92, L61–L63. [Google Scholar] [CrossRef] [PubMed] - Kuzmin, P.I.; Zimmerberg, J.; Chizmadzhev, Y.A.; Cohen, F.S. A quantitative model for membrane fusion based on low-energy intermediates. Proc. Natl. Acad. Sci. USA
**2001**, 98, 7235–7240. [Google Scholar] [CrossRef] [PubMed] - Ryham, R.J.; Klotz, T.S.; Yao, L.; Cohen, F.S. Calculating transition energy barriers and characterizing activation states for steps of fusion. Biophys. J.
**2016**, 110, 1110–1124. [Google Scholar] [CrossRef] [PubMed] - Harrison, S.C. Viral membrane fusion. Nat. Struct. Mol. Biol.
**2008**, 15, 690–698. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jahn, R.; Lang, T.; Südhof, T.C. Membrane fusion. Cell
**2003**, 112, 519–533. [Google Scholar] [CrossRef] - Melikyan, G.B. HIV entry: A game of hide-and-fuse? Curr. Opin. Virol.
**2014**, 4, 1–7. [Google Scholar] [CrossRef] [PubMed] - Jakobsdottir, G.M.; Iliopoulou, M.; Nolan, R.; Alvarez, L.; Compton, A.A.; Padilla-Parra, S. On the whereabouts of HIV-1 cellular entry and its fusion ports. Trends Mol. Med.
**2017**, 23, 932–944. [Google Scholar] [CrossRef] [PubMed] - Akimov, S.A.; Volynsky, P.E.; Galimzyanov, T.R.; Kuzmin, P.I.; Pavlov, K.V.; Batishchev, O.V. Pore formation in lipid membrane I: Continuous reversible trajectory from intact bilayer through hydrophobic defect to transversal pore. Sci. Rep.
**2017**, 7, 12152. [Google Scholar] [CrossRef] [PubMed] - Akimov, S.A.; Volynsky, P.E.; Galimzyanov, T.R.; Kuzmin, P.I.; Pavlov, K.V.; Batishchev, O.V. Pore formation in lipid membrane II: Energy landscape under external stress. Sci. Rep.
**2017**, 7, 12509. [Google Scholar] [CrossRef] [PubMed] - Tristram-Nagle, S.; Chan, R.; Kooijman, E.; Uppamoochikkal, P.; Qiang, W.; Weliky, D.P.; Nagle, J.F. HIV fusion peptide penetrates, disorders, and softens T-cell membrane mimics. J. Mol. Biol.
**2010**, 402, 139–153. [Google Scholar] [CrossRef] [PubMed] - Wilen, C.B.; Tilton, J.C.; Doms, R.W. HIV: Cell binding and entry. Cold Spring Harb. Perspect. Med.
**2012**, 2, a006866. [Google Scholar] [CrossRef] [PubMed] - Gallo, S.A.; Finnegan, C.M.; Viard, M.; Raviv, Y.; Dimitrov, A.; Rawat, S.S.; Puri, A.; Durell, S.; Blumenthal, R. The HIV Env-mediated fusion reaction. Biochim. Biophys. Acta
**2003**, 1614, 36–50. [Google Scholar] [CrossRef] - Kielian, M.; Rey, F.A. Virus membrane-fusion proteins: More than one way to make a hairpin. Nat. Rev. Microbiol.
**2006**, 4, 67–76. [Google Scholar] [CrossRef] [PubMed] - Chernomordik, L.V.; Frolov, V.A.; Leikina, E.; Bronk, P.; Zimmerberg, J. The pathway of membrane fusion catalyzed by influenza hemagglutinin: Restriction of lipids, hemifusion, and lipidic fusion pore formation. J. Cell Biol.
**1998**, 140, 1369–1382. [Google Scholar] [CrossRef] [PubMed] - Bajimaya, S.; Frankl, T.; Hayashi, T.; Takimoto, T. Cholesterol is required for stability and infectivity of influenza A and respiratory syncytial viruses. Virology
**2017**, 510, 234–241. [Google Scholar] [CrossRef] [PubMed] - Yang, Q.; Zhang, Q.; Tang, J.; Feng, W.H. Lipid rafts both in cellular membrane and viral envelope are critical for PRRSV efficient infection. Virology
**2015**, 484, 170–180. [Google Scholar] [CrossRef] [PubMed] - Ohkura, T.; Momose, F.; Ichikawa, R.; Takeuchi, K.; Morikawa, Y. Influenza A virus hemagglutinin and neuraminidase mutually accelerate their apical targeting through clustering of lipid rafts. J. Virol.
**2014**, 88, 10039–10055. [Google Scholar] [CrossRef] [PubMed] - Huarte, N.; Carravilla, P.; Cruz, A.; Lorizate, M.; Nieto-Garai, J.A.; Kräusslich, H.G.; Pérez-Gil, J.; Requejo-Isidro, J.; Nieva, J.L. Functional organization of the HIV lipid envelope. Sci. Rep.
**2016**, 6, 34190. [Google Scholar] [CrossRef] [PubMed] - Webb, S.R.; Smith, S.E.; Fried, M.G.; Dutch, R.E. Transmembrane domains of highly pathogenic viral fusion proteins exhibit trimeric association in vitro. mSphere
**2018**, 3, e00047-18. [Google Scholar] [CrossRef] [PubMed] - Vishwanathan, S.A.; Thomas, A.; Brasseur, R.; Epand, R.F.; Hunter, E.; Epand, R.M. Large changes in the CRAC segment of gp41 of HIV do not destroy fusion activity if the segment interacts with cholesterol. Biochemistry
**2008**, 47, 11869–11876. [Google Scholar] [CrossRef] [PubMed] - Akimov, S.A.; Aleksandrova, V.V.; Galimzyanov, T.R.; Bashkirov, P.V.; Batishchev, O.V. Interaction of amphipathic peptides mediated by elastic membrane deformations. Biol. Membr.
**2017**, 34, 162–173. [Google Scholar] [CrossRef] - Rawicz, W.; Olbrich, K.C.; McIntosh, T.; Needham, D.; Evans, E. Effect of chain length and unsaturation on elasticity of lipid bilayers. Biophys. J.
**2000**, 79, 328–339. [Google Scholar] [CrossRef] - Hamm, M.; Kozlov, M.M. Elastic energy of tilt and bending of fluid membranes. Eur. Phys. J. E
**2000**, 3, 323–335. [Google Scholar] [CrossRef] - Leikin, S.L.; Kozlov, M.M.; Chernomordik, L.V.; Markin, V.S.; Chizmadzhev, Y.A. Membrane fusion: Overcoming of the hydration barrier and local restructuring. J. Theor. Biol.
**1987**, 129, 411–425. [Google Scholar] [CrossRef] - Rand, R.P.; Parsegian, V.A. Hydration forces between phospholipid bilayers. Biochim. Biophys. Acta
**1989**, 988, 351–376. [Google Scholar] [CrossRef] - Frolov, V.A.; Zimmerberg, J. Cooperative elastic stresses, the hydrophobic effect, and lipid tilt in membrane remodeling. FEBS Lett.
**2010**, 584, 1824–1829. [Google Scholar] [CrossRef] [PubMed] - Israelachvili, J.; Pashley, R. The hydrophobic interaction is long range, decaying exponentially with distance. Nature
**1982**, 300, 341–342. [Google Scholar] [CrossRef] [PubMed] - Aeffner, S.; Reusch, T.; Weinhausen, B.; Salditt, T. Energetics of stalk intermediates in membrane fusion are controlled by lipid composition. Proc. Natl. Acad. Sci. USA
**2012**, 109, E1609–E1618. [Google Scholar] [CrossRef] [PubMed] - Yi, L.; Fang, J.; Isik, N.; Chim, J.; Jin, T. HIV gp120-induced interaction between CD4 and CCR5 requires cholesterol-rich microenvironments revealed by live cell fluorescence resonance energy transfer imaging. Biol. Chem.
**2006**, 281, 35446–35453. [Google Scholar] [CrossRef] [PubMed] - Luo, C.; Wang, K.; Liu, D.; Li, Y.; Zhao, Q. The functional roles of lipid rafts in T cell activation, immune diseases and HIV infection and prevention. Cell. Mol. Immunol.
**2008**, 5, 1–7. [Google Scholar] [CrossRef] [PubMed] - Carter, G.C.; Bernstone, L.; Sangani, D.; Bee, J.W.; Harder, T.; James, W. HIV entry in macrophages is dependent on intact lipid rafts. Virology
**2009**, 386, 192–202. [Google Scholar] [CrossRef] [PubMed] - Van Wilgenburg, B.; Moore, M.D.; James, W.S.; Cowley, S.A. The productive entry pathway of HIV-1 in macrophages is dependent on endocytosis through lipid rafts containing CD4. PLoS ONE
**2014**, 9, e86071. [Google Scholar] [CrossRef] [PubMed] - Leikin, S.; Parsegian, V.A.; Rau, D.C.; Rand, R.P. Hydration forces. Annu. Rev. Phys. Chem.
**1993**, 44, 369–395. [Google Scholar] [CrossRef] [PubMed] - McMahon, H.T.; Gallop, J.L. Membrane curvature and mechanisms of dynamic cell membrane remodelling. Nature
**2005**, 438, 590–596. [Google Scholar] [CrossRef] [PubMed] - Zimmerberg, J.; Kozlov, M.M. How proteins produce cellular membrane curvature. Nat. Rev. Mol. Cell Biol.
**2006**, 7, 9–19. [Google Scholar] [CrossRef] [PubMed] - Shnyrova, A.V.; Bashkirov, P.V.; Akimov, S.A.; Pucadyil, T.J.; Zimmerberg, J.; Schmid, S.L.; Frolov, V.A. Geometric catalysis of membrane fission driven by flexible dynamin rings. Science
**2013**, 339, 1433–1436. [Google Scholar] [CrossRef] [PubMed] - Martens, S.; Kozlov, M.M.; McMahon, H.T. How synaptotagmin promotes membrane fusion. Science
**2007**, 316, 1205–1208. [Google Scholar] [CrossRef] [PubMed] - McMahon, H.T.; Kozlov, M.M.; Martens, S. Membrane curvature in synaptic vesicle fusion and beyond. Cell
**2010**, 140, 601–605. [Google Scholar] [CrossRef] [PubMed] - Ahn, A.; Gibbons, D.L.; Kielian, M. The fusion peptide of Semliki Forest virus associates with sterol-rich membrane domains. J. Virol.
**2002**, 76, 3267–3275. [Google Scholar] [CrossRef] [PubMed] - Freitas, M.S.; Gaspar, L.P.; Lorenzoni, M.; Almeida, F.C.; Tinoco, L.W.; Almeida, M.S.; Maia, L.F.; Degrève, L.; Valente, A.P.; Silva, J.L. Structure of the Ebola fusion peptide in a membrane-mimetic environment and the interaction with lipid rafts. J. Biol. Chem.
**2007**, 282, 27306–27314. [Google Scholar] [CrossRef] [PubMed] - Leikin, S.; Kozlov, M.M.; Fuller, N.L.; Rand, R.P. Measured effects of diacylglycerol on structural and elastic properties of phospholipid membranes. Biophys. J.
**1996**, 71, 2623–2632. [Google Scholar] [CrossRef] - Galimzyanov, T.R.; Molotkovsky, R.J.; Kheyfets, B.B.; Akimov, S.A. Energy of the interaction between membrane lipid domains calculated from splay and tilt deformations. JETP Lett.
**2013**, 96, 681–686. [Google Scholar] [CrossRef] - Derjaguin, B.V. Interaction forces between hydrophobic and hydrophilic self-assembled monolayers. Kolloid Zeits.
**1934**, 69, 155–164. [Google Scholar] [CrossRef]

**Figure 1.**Schematic representation of the initial stage of T-cell infection by HIV. (

**a**) Viral membrane in the vicinity of the target cell membrane; the target cell membrane consists of lipids of raft (highlighted in red) and non-raft (shown in blue) phases. (

**b**) Interaction of fusion proteins with CD4 receptors (green) and CCR5 co-receptors (midnight blue) on the cell surface accompanied by conformational transitions of fusion proteins and incorporation of fusion peptides (shown in black) into the cellular membrane. (

**c**) Formation of stalk—a structure, in which the contact monolayers of membranes already fused, while the distal ones have not yet.

**Figure 2.**(

**a**) Schematic representation of the model of a peptide incorporated into the membrane with the raft. The raft area is shaded in pink and outlined by bold lines, the surrounding membrane is shown in white and outlined by thin lines. L designates the shift of the monolayer raft boundaries. The area occupied by fusion peptides is shown in gray. The width of the fusion peptide is 2R

_{FP}. The distance from the center of fusion peptide to the center of coordinates is designated as R. (

**b**) Dependence of the equilibrium energy of the membrane W (expressed as the energy per unit length of the raft boundary) upon the coordinate R of the fusion peptide. The blue curve corresponds to the case of the half-width R

_{FP}equal to 1 nm, the red one—to the case of the half-width R

_{FP}equal to 0.5 nm. The equilibrium thicknesses of the raft monolayer and the monolayer of the surrounding membrane are designated as h

_{r}and h

_{s}, respectively.

**Figure 3.**Schematic representation of the model. Distance ΔH between fusion peptides and transmembrane domains of proteins in membranes is used as the reaction coordinate. Transmembrane domains (half-width of R

_{TM}) are schematically shown by gray rectangles, fusion peptides (half-width of R

_{FP}) are shown by gray triangles. H

_{0}is the equilibrium distance between the membranes, ρ is the radius of the hydrophobic face formed in the area of maximal proximity of the membranes. Raft area is highlighted in pink. The viral membrane is shown on the top, and the cellular membrane is shown at the bottom.

**Figure 4.**(

**a**) Dependence of the system total energy W

_{T}(shown in red) on the reaction coordinate H

_{0}− ΔH. The blue curve is the deformation energy of the two membranes, the black one is the energy of hydration repulsion of the membranes and hydrophobic interaction of the defects. The graph corresponds to the values of R = 3 nm, L = 3 nm, H

_{0}= 3 nm. (

**b**) Dependence of the energy barrier W

_{B}to stalk formation on the width L of the raft transient zone (shown in red). The energy barrier in the absence of raft in the target cell membrane is shown in blue. The graph corresponds to the values of R = 3 nm, H

_{0}= 4 nm.

**Figure 5.**Dependence of W

_{raft}(blue curve) and ΔW (red curve) on the initial distance H

_{0}between the membranes at different values of the fusion rosette radius R. (

**a**): R = 3 nm; (

**b**) R = 4 nm. The height of the barrier corresponding to intersection of the red line with the abscissa corresponds to the minimal energy needed to achieve the stalk state in the presence of a raft (shown by vertical dashed lines).

**Figure 6.**Schematic representation of fusion peptide domains (shown as magenta ellipse) in a bilayer. (

**a**) intermediate incorporation depth; (

**b**) deep incorporation; (

**c**) transmembrane domain (shown as yellow rectangle). Black arrows show the boundary director orientations.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Molotkovsky, R.J.; Alexandrova, V.V.; Galimzyanov, T.R.; Jiménez-Munguía, I.; Pavlov, K.V.; Batishchev, O.V.; Akimov, S.A.
Lateral Membrane Heterogeneity Regulates Viral-Induced Membrane Fusion during HIV Entry. *Int. J. Mol. Sci.* **2018**, *19*, 1483.
https://doi.org/10.3390/ijms19051483

**AMA Style**

Molotkovsky RJ, Alexandrova VV, Galimzyanov TR, Jiménez-Munguía I, Pavlov KV, Batishchev OV, Akimov SA.
Lateral Membrane Heterogeneity Regulates Viral-Induced Membrane Fusion during HIV Entry. *International Journal of Molecular Sciences*. 2018; 19(5):1483.
https://doi.org/10.3390/ijms19051483

**Chicago/Turabian Style**

Molotkovsky, Rodion J., Veronika V. Alexandrova, Timur R. Galimzyanov, Irene Jiménez-Munguía, Konstantin V. Pavlov, Oleg V. Batishchev, and Sergey A. Akimov.
2018. "Lateral Membrane Heterogeneity Regulates Viral-Induced Membrane Fusion during HIV Entry" *International Journal of Molecular Sciences* 19, no. 5: 1483.
https://doi.org/10.3390/ijms19051483