# Switching between Successful and Dead-End Intermediates in Membrane Fusion

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## Abstract

**:**

## 1. Introduction

_{B}T (k

_{B}T ~ 4 × 10

^{−21}J). This means that, without an additional impact on the system, the membrane would not merge within a physically reasonable time ranging from a few seconds to a few tens of seconds. In biological systems, special proteins known as fusion proteins are responsible for this additional intervention into the system [2,8]. The most thoroughly characterized fusion proteins are those of the synaptic system, participating in the process of Ca

^{2+}-dependent exocytosis [9,10], and fusion proteins of various envelope viruses, such as influenza virus [11,12,13], HIV [14,15], vesicular stomatitis virus [16], etc.

## 2. Results

_{TM}and R

_{FP}, respectively. The TM domains are modeled as annular inclusions piercing the entire depth of the bilayer of the viral membrane, whereas fusion peptides—as annular inclusions incorporated into one of the monolayers to a certain depth depending on the specifics of the peptide structure (see Figure 2). For trimeric configuration of fusion proteins, the annular structure of fusion peptides can be formed by aligning two peptides of each trimer along the fusion rosette circle, and directing the third peptide outward the circle center. Let us introduce a cylindrical coordinate system Ohr, with the origin O, the axis Or lying in the plane of the inter-monolayer surface of the bottom membrane, and the axis Oh along the rotational symmetry axis of the system. Due to cylindrical symmetry, the system is effectively unidimensional, i.e., all the values only depend on r.

_{0}, at which the attraction force imposed by the proteins is equilibrated by the repulsion forces induced by membrane hydration [46]. Further evolution of the system can only be driven by thermal fluctuations of the lipid bilayers. Two possible trajectories of the system evolution corresponding to different modes of interaction of proteins with the membrane are considered. In the first case, the membranes are brought into tight contact at the expense of conformational transitions of the fusion proteins causing juxtaposition of their transmembrane domains with the fusion peptides. It is assumed that, in the course of fusion, the distance is ∆H between the ring of the transmembrane domains in the viral membrane and the ring of the fusion peptides in the target membrane, while the distance between the membranes away from the fusion rosette remains equal to H

_{0}(see Figure 2a). An energy barrier associated with hydration-induced repulsion has to be crossed in order to bring the membranes in close proximity [47]. It is assumed that, under the conditions when fusion proteins attempt to bring the membranes in juxtaposition, strong hydration repulsion results in lateral displacement of the lipid head groups from the area of contact of the membranes [6]. Thus, hydrophobic defects are generated in the contacting monolayers of the merging membranes [48]; the radius of the hydrophobic defect is designated as ρ on Figure 2a. Such defects can serve as monolayer fusion nucleation centers, since their formation induces local loss of order of the hydration layers and appearance of hydrophobic attraction between them [49]. The attraction between hydrophobic defects in the contact monolayers of the merging membranes leads to stalk formation (Figure 1a).

_{T}of the membranes upon the process coordinate. In the case of stalk, the coordinate is the change of distance ∆H between the fusion peptides and the transmembrane domains of the fusion proteins located in the target membrane and in the viral membrane, respectively (Figure 2a), while the radius of the hydrophobic patch ρ can vary freely. As we demonstrated earlier, the process of formation of a pore through the membrane is described by at least two coordinates [44,45,50,51]. In the case of the π-shaped structure, we selected the height of the hydrophobic part of the pore L, and the pore radius R

_{p}(Figure 2b) as the system coordinates. The energy contributors vary significantly between the two scenarios.

_{B}T and K = 10 k

_{B}T/nm

^{2}[52,53] for leaflet splay and tilt moduli, respectively. The monolayer surface tension σ is assumed equal to 0.01 k

_{B}T/nm

^{2}. The equilibrium thickness of the monolayer h

_{0}is assumed at 1.5 nm, which is consistent with the values observed for 1,2-dioleoyl-sn-glycero-3-phosphocholine, 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine etc. For hydration-induced repulsion parameters, we used the following values from the work [54]: disjoining pressure P

_{0}= 60 k

_{B}T/nm

^{3}, characteristic length of hydration repulsion ξ

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

_{f}is considered equal to 1 nm [49]. The equilibrium distance between the fusing membranes H

_{0}is assumed at 5 nm. This distance reflects steric interactions associated with the fusion protein ectodomains that have to be accommodated between the membranes. As the membranes are brought together, the HA protein undergoes a conformational rearrangement [18], in the course of which one of the parts of the HA ectodomain, namely HA1 subdomain, moves away thereby decreasing the effective diameter of the ectodomain just to the diameter of HA2 subdomain, which is about 5 nm [18]. Note that the energy of the π-shaped structure is independent on the intermembrane distance, while the stalk and hemifusion diaphragm energy grows up for increasing distance [55]. The half-width of the TM domain R

_{TM}is assumed at 1 nm.

_{p}, is presented. The height of the hydrophobic part of the pore L also varies in this process from L = 3 nm corresponding to the equilibrium thickness of the bilayer 2h

_{0}, to zero. The vertical drop of energy at the point R

_{p}= 1.1 nm of the plot corresponds to change of the height of the hydrophobic belt L at constant pore radius R

_{p}.

_{initial}), final state (W

_{final}), and energy maximum (W

_{max}) are shown.

_{FP}, and the depth of incorporation of the fusion peptide. The cases of R = 3 and R = 4 nm are analyzed for three different depths of incorporation of the fusion peptide (shallow, intermediate and deep insertion); the half-width of the fusion peptide is varied from 0 to 1 nm. Figure 4 presents dependencies of energy barriers on R

_{FP}at fixed R for the three depths of insertion. Figure 4a corresponds to R = 3 nm, Figure 4b—to R = 4 nm.

_{FP}= 0.5 nm.

_{B}= W

_{max}− W

_{initial}

_{RB}= W

_{max}− W

_{final}

_{RB}= W

_{B}+ W

_{initial}− W

_{final}

_{B}T (blue curve in Figure 3a). The hydrophobic patch radius at that point is ~1 nm. This means that, in order to create a hydrophobic defect with the area of 1 nm

^{2}, the system has to cross the energy barrier exceeding 12 k

_{B}T. According to Figure 5, the inner radius of the hydrophilic pore is ~1 nm. We consider that for fusion, the width of the hydrophobic belt must also be no smaller than ~1 nm. Its area then exceeds 18 nm

^{2}. It means that the energy barrier associated with formation of such a belt is larger than 100 k

_{B}T and cannot be crossed at the expense of thermal fluctuations within the characteristic time of fusion (~1 min) [6].

## 3. Discussion

_{FP}and depth of insertion, i.e., the value of the boundary director. According to Figure 4, the behavior of the system is determined by the depth of incorporation of the peptide: decreased depth of incorporation hinders fusion due to increase of the energy barrier to stalk formation. Pore formation proves the least favorable in the case of intermediate depth of insertion and the most favorable in case of shallow insertion. The larger the half-width of the fusion peptide, the more favorable is pore formation. For the biologically relevant sizes of the fusion peptide (R

_{FP}≥ 0.5 nm), shallow incorporation of the fusion peptide facilitates formation of the π-shaped structure, and deep insertion facilitates membrane fusion. In the case of intermediate incorporation, the fusion rosette radius R plays a definitive role: the larger the fusion rosette, the more favorable stalk formation becomes.

_{B}T. The reverse barrier corresponding to pore closure depends on the depth of incorporation of the fusion peptide (see Figure 6). In the case of intermediate depth, it is almost insensitive to the changes of half-width R

_{FP}and amounts to about 10–15 k

_{B}T, i.e., it can be relatively rapidly crossed at the expense of thermal fluctuations. In other cases, for biologically adequate sizes of the fusion peptide (R

_{FP}≥ 0.5 nm) the energy barrier would exceed 50 k

_{B}T, i.e., too high to be crossed at the expense of thermal fluctuations in reasonable time. Therefore, π-shaped structure turns out to be a dead end final state in the case of shallow and deep insertion: both fusion and return into the initial state are hindered. In the case of intermediate depth of incorporation, a return to the initial state proves possible. Thus, in the case of intermediate depth a scenario with periodic opening and closure of a pore in the target membrane preceding stalk-mediated fusion is possible. These reversible changes, as well as a significant height of the stalk formation energy barrier (~50 k

_{B}T) must substantially slow down fusion of membranes in case of the intermediate depth of insertion of fusion peptides.

_{o}) phase (“rafts”) with the local lipid composition different from that of the bulk lipid [58]. The liquid ordered domains are also known to be thicker than the surrounding membrane [59], which results in line tension of the domain boundary [43]. According to recent experimental studies, the raft boundary structure plays an important role in the process of viral fusion [60]. In particular, the HIV fusion peptide tends to be preferentially inserted along the raft boundaries, and phase separation with formation of such boundaries substantially enhances fusion efficiency. By contrast, no enhancement of fusion efficiency was observed in the membranes consisting exclusively of the L

_{o}phase without any phase separation boundaries. These trends, however, do not apply to the influenza virus. This difference in the behavior of the HIV and influenza virus fusion peptides can be attributable to different depths of insertion of the corresponding fusion peptides into the host cell membranes. A correlation can be found between the difference in the insertion depths and the difference in the spontaneous curvatures induced by the insertion: deeper penetration (as in case of the HIV) is similar to induction of negative spontaneous curvature, whereas more shallow incorporation (e.g., influenza virus) induces nearly zero spontaneous curvature. According to our prior results [59], membrane components with non-zero spontaneous curvature (regardless of the sign) preferentially distribute into the phase separation boundaries, so that such boundaries can serve as local concentrators of the fusion peptides with deep insertion and define their orientation in the membrane. Besides that, regardless of the preferences of the fusion peptides, the phase separation boundary has excess energy that can be characterized by the line tension of the boundary and is proportional to its total length. One of the viable options for minimizing the boundary energy is to bend the domain surface to form a hemispherical bulge protruding from the membrane plane. If it happens in the area between the viral membrane and the host cell membrane, minimal distance between the membranes would decrease, facilitating the fusion process through stalk intermediate. Thus, formation of a domain with a high line tension of the boundary should further facilitate fusion. We suppose that incorporation into the target membrane of the fusion peptides with preference towards the phase separation boundary can serve to nucleate domain formation in the target membrane. In other words, under appropriate conditions the fusion peptides can induce formation of phase separation boundaries rather than preferentially partitioning into the pre-existing boundaries. A detailed theoretical model of the process of fusion of phase-separating membranes is an intended topic of our further investigations.

## 4. Materials and Methods

#### 4.1. Stalk Energy

_{e}, the energy of hydration repulsion between the membranes W

_{h}, and the energy of interaction between hydrophobic defects in different membranes W

_{f}:

_{T}= W

_{e}+ W

_{h}+ W

_{f}.

**n**characterizing the average orientation of lipid molecules is introduced for description of the membrane monolayer deformations. The vector field is defined on a certain surface inside the monolayer parallel to its external boundary, known as a dividing surface. The shape of the surface is defined by a field of unit vectors

**N**normal to it; the normal vectors are considered to be directed towards the inter-monolayer surface of the membrane. We consider only the following two main deformation modes: tilt and splay. We assign all deformations and elastic moduli to a specific dividing surface, so-called neutral surface, defined as the surface where energy contributions from splay and lateral stretch/compression deformations are independent of each other. According to the experimental results of [63], the neutral surface is situated in the area of junction between the polar head groups and acyl chains, at the depth of ~0.5 nm from the outer monolayer boundary. The splay deformation is quantitatively described by divergence of the director over the dividing surface, whereas tilt deformations are described by the tilt vector

**t**=

**n**/(

**nN**) −

**N**≈

**n**−

**N**. If the deformations are assumed small and zero energy is assigned to the undeformed planar bilayer, the energy of deformed monolayer can be expressed as [53]

_{0}is the neutral surface area in the initial undeformed state. Smallness of deformations means that the projection of the director on the axis Or is much smaller than unity. All vectors are replaced with their projections on this axis. In order to define the state of two monolayers in the membrane, five functions need to be introduced: projections of the directors of the upper and the lower monolayer on the Or axis, a(r) and b(r), respectively; distance from the Or plane to the neutral surfaces of the upper and lower monolayers, h

_{a}(r) and h

_{b}(r), respectively; distance from the Or plane to the inter-monolayer surface, m(r). Besides that, we assume the hydrophobic zone of the monolayer to be locally volumetrically incompressible, i.e., that the volume of any element of the monolayer does not change upon deformation. This assumption is justified by a large value of the volumetric compressibility module. The local incompressibility condition is written as follows [53]:

_{0}is the thickness of undeformed monolayer. Equation (6) in combination with the definitions of the tilt vector (

**t**=

**n**−

**N**), monolayer thickness (∆h

_{a}= h

_{a}(r) − m(r), ∆h

_{b}= m(r) − h

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

**N**=

_{a}**grad**(h

_{a}(r)),

**N**= −

_{b}**grad**(h

_{b}(r))), relates the tilt vectors t

_{a}(r) and t

_{b}(r) in the upper and lower monolayer with the directors a(r) and b(r) in these leaflets and the location of the inter-monolayer surface m(r). Thus, by imposing the conditions of local volumetric incompressibility to the two leaflets of the membrane, the number of independent functions characterizing the state of the membrane can be reduced from five (a(r), b(r), h

_{a}(r), h

_{b}(r), m(r)) to three (a(r), b(r), m(r)). We express the elastic energy functional Equation (5) through these three functions, and search its extrema by varying the functional with respect to the independent functions a(r), b(r), m(r) and thus obtaining three Euler-Lagrange differential equations. The solutions of these equations are then substituted into the elastic energy functional Equation (5). The expressions for a(r), b(r), and m(r) obtained by solving the Euler-Lagrange differential equations contain indefinite coefficients, which are determined by minimizing the energy taking into account the boundary conditions, which are defined by the geometry of the fusion peptides, TM domains and hydrophobic regions in the contact monolayers. More detailed descriptions of the methods used for elastic energy calculations are provided in the works [43,61,64,65].

_{TM}becomes non-zero. (Figure 7a). Besides that, the tilt of the TM domains in the fusion rosette causes relative shift of the neutral surfaces of the membrane leaflets on the outer (r = R − R

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

_{TM}) boundary of the ring (Figure 2a). Thus, the following boundary conditions apply:

_{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}.

_{FP}) as n

_{l}, and its value on the outer boundary (r = R + R

_{FP}) as n

_{r}(Figure 7b–d). Besides, the fusion peptide can rotate in the membrane as a whole; we denote the projection of the director describing this rotation as n

_{FP}. Obviously, n

_{FP}= (n

_{l}+ n

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

_{FP}is a mean of the directors on the inner and outer boundaries of the fusion peptide ring. Using geometric interpretation of the director, the difference between the directors on the inner and outer boundaries of the fusion peptide ring (director “jump”) can be expressed through the width of the ring 2R

_{FP}and the monolayer thickness h

_{0}as follows:

_{a}(R + R

_{FP}) − h

_{a}(R − R

_{FP}) = 2R

_{FP}n

_{FP}

_{a}(R + R

_{FP}) − h

_{a}(R − R

_{FP}) = 0

_{0}, lipid molecules are horizontal, and the director is equal to −1. Besides introducing the boundary director, we fix the distance ∆H between the neutral surfaces of the contact monolayers of the two membranes at r = R, and distance H

_{0}between the neutral surfaces of the contact monolayers of the two membranes at r → ∞.

_{f}is the characteristic length of hydrophobic interactions in water [49], l is the distance between the hydrophobic regions, and σ

_{0}is the surface tension of the macroscopic boundary separating water and acyl chains of lipids. Hydration repulsion energy is calculated as described in [46,47]:

_{0}is the disjoining pressure characterizing the amplitude of hydration repulsion, ξ

_{h}the characteristic length of hydration interactions; the integration is performed over the hydrophilic surface of the contact monolayers. For evaluation of the integral in Equation (13), we apply Derjaguin–Landau–Verwey–Overbeek theory, according to which integration in the equation can be limited to the region in which the distance between the membrane changes by the value of ξ

_{h}, with a replacement of the deformed hydrophilic surfaces of the contact leaflets by horizontal planes. If there are no hydrophobic regions in the membranes, integration in Equation (13) starts from r = 0. When the membranes do contain hydrophobic regions, integration starts at r = r + L

_{h}, to make an allowance for the effect of blurring of the boundary between the hydrophobic patch and the bulk membrane. This blurring is caused by several factors—fluctuations of polar head groups of lipids (the head group size ~0.8 nm), finite persistence length of the order parameters of hydrophobic and hydrophilic interaction (~0.35 nm and 1 nm, respectively). We selected a medium value of L

_{h}~ 0.8 nm.

#### 4.2. Energy of the π-Shaped Structure

_{e}, and the energy W

_{f}of the water-filled hydrophobic cylinder piercing the target membrane (Figure 2b):

_{T}= W

_{e}+ W

_{f}.

_{h}. The deformation energy of the membrane with a pore is calculated based on the elasticity theory approaches, similarly to calculations of the membrane deformation energy in the stalk configuration. More details about the formalism applied are available in [44,45,50].

_{a}

_{0}, Z

_{a}

_{0}) and (R

_{b}

_{0}, Z

_{b}

_{0}), corresponding to two monolayers. The energy of the “horizontal bilayer” region of both viral and target membrane is calculated exactly in the same way as the energy of deformations in the case of stalk, described above.

_{z}(h). We use designation v(h) for director projection onto the Oh axis. The distance from the Oh axis to the surface of lipid tail ends, M(h), characterizes the shape of this surface. The solutions obtained in the horizontal and vertical regions are conjugated along the circumferences (R

_{a}

_{0}, Z

_{a}

_{0}) and (R

_{b}

_{0}, Z

_{b}

_{0}) delineating them based on the considerations of continuity of neutral surfaces and director. The boundary conditions read:

_{a}(R

_{a}

_{0}) = Z

_{a}

_{0}, R(Z

_{a}

_{0}) = R

_{a}

_{0}, a

^{2}(R

_{a}

_{0}) − v

_{a}

^{2}(Z

_{a}

_{0}) = 1,

_{b}(R

_{b}

_{0}) = Z

_{b}

_{0}, R(Z

_{b}

_{0}) = R

_{b}

_{0}, b

^{2}(R

_{b}

_{0}) − v

_{b}

^{2}(Z

_{b}

_{0}) = 1,

_{a}, v

_{b}are projection of the director onto Oh axis.

_{p}, coaxial with Oh. The energy of water-filled hydrophobic cylinder is calculated in [51,66] based on Marcelja theory [67]. In our notation, the energy of the cylinder reads:

_{p}L) is the cylinder side surface area; I

_{0}, I

_{1}are Bessel functions of order zero and one, respectively. For the vertical region, the boundary conditions at the edge of the hydrophobic belt are stated as follows:

_{p}, and height of the hydrophobic belt L.

#### 4.3. Algorithm of Evaluation of the Process Trajectory Likelihood

_{TM}, R

_{FP}—and minimized the energy W

_{T}with respect to all free parameters, which include the indefinite coefficients occurring in the solutions of Euler–Lagrange differential equations and geometric parameters that are not fixed, such as the radius of the hydrophobic region ρ or tilt of protein domains in the membrane, n

_{TM}and n

_{FP}. Thus, we obtained the dependence of the total energy W

_{T}only on the process coordinates—∆H in the case of stalk, and L and R

_{p}in the case of π-shaped structure. Thereafter, for each of the two scenarios we determined the energy barrier, i.e., the maximal energy needed for the system to transition from the initial state (common for both scenarios) to the final state. For stalk-mediated fusion, the end state is achieved when the distal monolayers of the merging membranes form a bilayer, and ∆H = 0 (Figure 1a); for the case of the π-shaped structure, the end state occurs when hydrophilic pore forms in the target membrane, and L = 0 (Figure 1b). After that we compare the energy barriers obtained at fixed geometric parameters. We assume that the system selects a scenario in accordance with Boltzmann weight factor of the trajectory, i.e., the process with a lower energy barrier is more likely. This method allowed us to determine how the fusion protein structural properties could be modified in order to increase or decrease the membrane fusion probability.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

HA | hemagglutinin |

HIV | human immunodeficiency virus |

TM | transmembrane (domain) |

## References

- Baker, P.F. Cell Fusion. Ciba Foundation Symposium No. 103. Pp. 291. (Pitman, 1984.). Exp. Physiol.
**1984**, 69, 894. [Google Scholar] [CrossRef] - Harrison, S.C. Viral membrane fusion. Nat. Struct. Mol. Biol.
**2008**, 15, 690–698. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chernomordik, L.V.; Melikyan, G.B.; Chizmadzhev, Y.A. Planar lipid bilayers as a model for studying fusion of biological-membranes. Biol. Membr.
**1987**, 4, 117–164. [Google Scholar] - Kozlov, M.M.; Markin, V.S. Possible mechanism of membrane fusion. Biofizika
**1983**, 28, 242–247. [Google Scholar] [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] - Jahn, R.; Lang, T.; Südhof, T.C. Membrane fusion. Cell
**2003**, 112, 519–533. [Google Scholar] [CrossRef] - Martens, S.; McMahon, H.T. Mechanisms of membrane fusion: Disparate players and common principles. Nat. Rev. Mol. Cell Biol.
**2008**, 9, 543–556. [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] - Frolov, V.A.; Cho, M.S.; Bronk, P.; Reese, T.S.; Zimmerberg, J. Multiple Local Contact Sites are Induced by GPI-Linked Influenza Hemagglutinin During Hemifusion and Flickering Pore Formation. Traffic
**2000**, 1, 622–630. [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] - Batishchev, O.V.; Shilova, L.A.; Kachala, M.V.; Tashkin, V.Y.; Sokolov, V.S.; Fedorova, N.V.; Baratova, L.A.; Knyazev, D.G.; Zimmerberg, J.; Chizmadzhev, Y.A. pH-dependent formation and disintegration of the influenza A virus protein scaffold to provide tension for membrane fusion. J. Virol.
**2016**, 90, 575–585. [Google Scholar] [CrossRef] [PubMed] - Melikyan, G.B.; Markosyan, R.M.; Hemmati, H.; Delmedico, M.K.; Lambert, D.M.; Cohen, F.S. Evidence that the transition of HIV-1 gp41 into a six-helix bundle, not the bundle configuration, induces membrane fusion. J. Cell Biol.
**2000**, 151, 413–424. [Google Scholar] [CrossRef] [PubMed] - Markosyan, R.M.; Cohen, F.S.; Melikyan, G.B. Time-resolved imaging of HIV-1 Env-mediated lipid and content mixing between a single virion and cell membrane. Mol. Biol. Cell
**2005**, 16, 5502–5513. [Google Scholar] [CrossRef] [PubMed] - Ge, P.; Tsao, J.; Schein, S.; Green, T.J.; Luo, M.; Zhou, Z.H. Cryo-EM model of the bullet-shaped vesicular stomatitis virus. Science
**2010**, 327, 689–693. [Google Scholar] [CrossRef] [PubMed] - Chizmadzhev, Y.A. The mechanisms of lipid-protein rearrangements during viral infection. Bioelectrochemistry
**2004**, 63, 129–136. [Google Scholar] [CrossRef] [PubMed] - Skehel, J.J.; Wiley, D.C. Receptor binding and membrane fusion in virus entry: The influenza hemagglutinin. Annu. Rev. Biochem.
**2000**, 69, 531–569. [Google Scholar] [CrossRef] [PubMed] - Gruenke, J.A.; Armstrong, R.T.; Newcomb, W.W.; Brown, J.C.; White, J.M. New insights into the spring-loaded conformational change of influenza virus hemagglutinin. J. Virol.
**2002**, 76, 4456–4466. [Google Scholar] [CrossRef] [PubMed] - Danieli, T.; Pelletier, S.L.; Henis, Y.I.; White, J.M. Membrane fusion mediated by the influenza virus hemagglutinin requires the concerted action of at least three hemagglutinin trimers. J. Cell Biol.
**1996**, 133, 559–569. [Google Scholar] [CrossRef] [PubMed] - Bentz, J. Minimal aggregate size and minimal fusion unit for the first fusion pore of influenza hemagglutinin-mediated membrane fusion. Biophys. J.
**2000**, 78, 227–245. [Google Scholar] [CrossRef] - Floyd, D.L.; Ragains, J.R.; Skehel, J.J.; Harrison, S.C.; van Oijen, A.M. Single-particle kinetics of influenza virus membrane fusion. Proc. Natl. Acad. Sci. USA
**2008**, 105, 15382–15387. [Google Scholar] [CrossRef] [PubMed] - White, J.M.; Delos, S.E.; Brecher, M.; Schornberg, K. Structures and mechanisms of viral membrane fusion proteins: Multiple variations on a common theme. Crit. Rev. Biochem. Mol. Biol.
**2008**, 43, 189–219. [Google Scholar] [CrossRef] [PubMed] - Harrison, S.C. Viral membrane fusion. Virology
**2015**, 479, 498–507. [Google Scholar] [CrossRef] [PubMed] - 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] - Kroemer, G.; Galluzzi, L.; Brenner, C. Mitochondrial membrane permeabilization in cell death. Physiol. Rev.
**2007**, 87, 99–163. [Google Scholar] [CrossRef] [PubMed] - Frolov, V.A.; Dunina-Barkovskaya, A.Y.; Samsonov, A.V.; Zimmerberg, J. Membrane permeability changes at early stages of influenza hemagglutinin-mediated fusion. Biophys. J.
**2003**, 85, 1725–1733. [Google Scholar] [CrossRef] - Engel, A.; Walter, P. Membrane lysis during biological membrane fusion: Collateral damage by misregulated fusion machines. J. Cell Biol.
**2008**, 183, 181–186. [Google Scholar] [CrossRef] [PubMed] - Risselada, H.J.; Marelli, G.; Fuhrmans, M.; Smirnova, Y.G.; Grubmüller, H.; Marrink, S.J.; Müller, M. Line-tension controlled mechanism for influenza fusion. PLoS ONE
**2012**, 7, e38302. [Google Scholar] [CrossRef] [PubMed] - Risselada, H.J.; Bubnis, G.; Grubmüller, H. Expansion of the fusion stalk and its implication for biological membrane fusion. Proc. Natl. Acad. Sci. USA
**2014**, 111, 11043–11048. [Google Scholar] [CrossRef] [PubMed] - Katsov, K.; Müller, M.; Schick, M. Field theoretic study of bilayer membrane fusion: II. Mechanism of a stalk-hole complex. Biophys. J.
**2006**, 90, 915–926. [Google Scholar] [CrossRef] [PubMed] - Lee, K.K. Architecture of a nascent viral fusion pore. EMBO J.
**2010**, 29, 1299–1311. [Google Scholar] [CrossRef] [PubMed] - Calder, L.J.; Rosenthal, P.B. Cryomicroscopy provides structural snapshots of influenza virus membrane fusion. Nat. Struct. Mol. Biol.
**2016**, 23, 853–858. [Google Scholar] [CrossRef] [PubMed] - Chlanda, P.; Mekhedov, E.; Waters, H.; Schwartz, C.L.; Fischer, E.R.; Ryham, R.J.; Cohen, F.S.; Blank, P.S.; Zimmerberg, J. The hemifusion structure induced by influenza virus haemagglutinin is determined by physical properties of the target membranes. Nat. Microbiol.
**2016**, 1, 16050. [Google Scholar] [CrossRef] [PubMed] - Lai, A.L.; Tamm, L.K. Shallow boomerang-shaped influenza hemagglutinin G13A mutant structure promotes leaky membrane fusion. J. Biol. Chem.
**2010**, 285, 37467–37475. [Google Scholar] [CrossRef] [PubMed] - Qiao, H.; Armstrong, R.T.; Melikyan, G.B.; Cohen, F.S.; White, J.M. A specific point mutant at position 1 of the influenza hemagglutinin fusion peptide displays a hemifusion phenotype. Mol. Biol. Cell
**1999**, 10, 2759–2769. [Google Scholar] [CrossRef] [PubMed] - Li, Y.; Han, X.; Lai, A.L.; Bushweller, J.H.; Cafiso, D.S.; Tamm, L.K. Membrane structures of the hemifusion-inducing fusion peptide mutant G1S and the fusion-blocking mutant G1V of influenza virus hemagglutinin suggest a mechanism for pore opening in membrane fusion. J. Virol.
**2005**, 79, 12065–12076. [Google Scholar] [CrossRef] [PubMed] - Lai, A.L.; Park, H.; White, J.M.; Tamm, L.K. Fusion peptide of influenza hemagglutinin requires a fixed angle boomerang structure for activity. J. Biol. Chem.
**2006**, 281, 5760–5770. [Google Scholar] [CrossRef] [PubMed] - Lorieau, J.L.; Louis, J.M.; Bax, A. The complete influenza hemagglutinin fusion domain adopts a tight helical hairpin arrangement at the lipid: Water interface. Proc. Natl. Acad. Sci. USA
**2010**, 107, 11341–11346. [Google Scholar] [CrossRef] [PubMed] - Worch, R.; Krupa, J.; Filipek, A.; Szymaniec, A.; Setny, P. Three conserved C-terminal residues of influenza fusion peptide alter its behavior at the membrane interface. Biochim. Biophys. Acta
**2017**, 1861, 97–105. [Google Scholar] [CrossRef] [PubMed] - White, J.M.; Whittaker, G.R. Fusion of enveloped viruses in endosomes. Traffic
**2016**, 17, 593–614. [Google Scholar] [CrossRef] [PubMed] - Qiang, W.; Sun, Y.; Weliky, D.P. A strong correlation between fusogenicity and membrane insertion depth of the HIV fusion peptide. Proc. Natl. Acad. Sci. USA
**2009**, 106, 15314–15319. [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] - 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] - 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] - Akimov, S.A.; Aleksandrova, V.V.; Galimzyanov, T.R.; Bashkirov, P.V.; Batishchev, O.V. Mechanism of pore formation in stearoyl-oleoyl-phosphatidylcholine membranes subjected to lateral tension. Biol. Membr.
**2017**, 34, 270–283. [Google Scholar] [CrossRef] - Akimov, S.A.; Molotkovsky, R.J.; Galimzyanov, T.R.; Radaev, A.V.; Shilova, L.A.; Kuzmin, P.I.; Batishchev, O.V.; Voronina, G.F.; Chizmadzhev, Y.A. Model of membrane fusion: Continuous transition to fusion pore with regard of hydrophobic and hydration interactions. Biol. Membr.
**2014**, 31, 14–24. [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] - 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] - Kozlovsky, Y.; Chernomordik, L.V.; Kozlov, M.M. Lipid intermediates in membrane fusion: Formation, structure, and decay of hemifusion diaphragm. Biophys. J.
**2002**, 83, 2634–2651. [Google Scholar] [CrossRef] - Chernomordik, L.V.; Kozlov, M.M. Protein-lipid interplay in fusion and fission of biological membranes. Annu. Rev. Biochem.
**2003**, 72, 175–207. [Google Scholar] [CrossRef] [PubMed] - Sarkar, A.; Kellogg, G.E. Hydrophobicity-shake flasks, protein folding and drug discovery. Curr. Top. Med. Chem.
**2010**, 10, 67–83. [Google Scholar] [CrossRef] [PubMed] - Simons, K.; Ikonen, E. Functional rafts in cell membranes. Nature
**1997**, 387, 569–572. [Google Scholar] [CrossRef] [PubMed] - 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] - 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] - 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] - Staneva, G.; Osipenko, D.S.; Galimzyanov, T.R.; Pavlov, K.V.; Akimov, S.A. Metabolic precursor of cholesterol causes formation of chained aggregates of liquid-ordered domains. Langmuir
**2016**, 32, 1591–1600. [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] - 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] - Glaser, R.W.; Leikin, S.L.; Chernomordik, L.V.; Pastushenko, V.F.; Sokirko, A.I. Reversible electrical breakdown of lipid bilayers: Formation and evolution of pores. Biochim. Biophys. Acta
**1988**, 940, 275–287. [Google Scholar] [CrossRef] - Marcelja, S. Structural contribution to solute-solute interaction. Croat. Chem. Acta
**1977**, 49, 347–358. [Google Scholar]

**Figure 1.**Schematic representation of two scenarios of influenza virus fusion with the host cell membrane: (

**a**) a trajectory involving the interim stage of stalk formation, leading to fusion of contact monolayers and formation of a hemifusion diaphragm; (

**b**) a trajectory leading to reorientation of the fusion peptides at the edge of the pore and formation of a leaky structure (π-shaped structure). The viral membrane is on the top, the host cell membrane—at the bottom. Transmembrane domains are represented by light-yellow rectangles, fusion peptides—by red ellipses.

**Figure 2.**Schematic representation of the two alternative scenarios of evolution of the modeled system. (

**a**) Stalk-mediated fusion: the distance ∆H between the fusion peptides and the transmembrane domains of the fusion proteins in the membranes is assumed as the reaction coordinate; (

**b**) Formation of the dead-end state (π-shaped structure): the reaction coordinates are the pore radius R

_{p}and the length L of the hydrophobic part of the pore. The transmembrane domains (with the half-width of R

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

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

_{0}is the equilibrium distance between the membranes, ρ is the radius of the hydrophobic spot formed in the area of maximal proximity of the membranes.

**Figure 3.**Dependence of the total energy (W

_{T}) of the membrane on the process coordinates for the scenarios with formation of stalk (

**a**); and π-shaped structure (

**b**). The geometric parameters are as follows: the radius of fusion rosette R = 3 nm, half-width of the fusion peptide annulus R

_{FP}= 0.1 nm, shallow insertion. In the case of stalk, the red curve corresponds to the total energy W

_{T}, the blue curve—to the sum (W

_{h}+ W

_{f}), i.e., the total energy less the deformation energy. For the case of π-shaped structure, only the dependence on the pore radius R

_{p}is shown; the energy is minimized with respect to the hydrophobic belt height L for each fixed R

_{p}.

**Figure 4.**Dependencies of the height of the energy barrier (W

_{B}) for formation of the stalk (solid curves) and the π-shaped structure (dashed curves) on the half-width of the fusion peptide R

_{FP}. (

**a**) fusion rosette radius R = 3 nm; (

**b**) fusion rosette radius R = 4 nm. The red curves correspond to shallow insertion, the blue curves—to intermediate insertion, and the black curves—to deep insertion.

**Figure 5.**Calculated shape of the membranes for different depths of insertion of fusion peptides. (

**a**) Shallow insertion; (

**b**) intermediate insertion; (

**c**) deep insertion. Fusion peptide is shown in gray, the dotted line is the position of the inter-monolayer surface.

**Figure 6.**Dependence of the energy barrier for transition from the π-shaped structure to the initial unperturbed state (W

_{RB}) on the half-width of the fusion peptide R

_{FP}for different fusion rosette radii. (

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

**b**) R = 4 nm. The red, blue and black curves correspond to shallow, intermediate and deep insertion, respectively.

**Figure 7.**Schematic representation of a fusion peptide in a bilayer. (

**a**) transmembrane domain; (

**b**) case of shallow incorporation of the fusion peptide; (

**c**) intermediate incorporation; (

**d**) deep incorporation. The black arrows designate the directions of the boundary directors. Transmembrane domain is represented by light-yellow rectangle, fusion peptides—by red ellipses.

© 2017 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.; 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.
https://doi.org/10.3390/ijms18122598

**AMA Style**

Molotkovsky RJ, Galimzyanov TR, Jiménez-Munguía I, Pavlov KV, Batishchev OV, Akimov SA.
Switching between Successful and Dead-End Intermediates in Membrane Fusion. *International Journal of Molecular Sciences*. 2017; 18(12):2598.
https://doi.org/10.3390/ijms18122598

**Chicago/Turabian Style**

Molotkovsky, Rodion J., Timur R. Galimzyanov, Irene Jiménez-Munguía, Konstantin V. Pavlov, Oleg V. Batishchev, and Sergey A. Akimov.
2017. "Switching between Successful and Dead-End Intermediates in Membrane Fusion" *International Journal of Molecular Sciences* 18, no. 12: 2598.
https://doi.org/10.3390/ijms18122598