Interbilayer forces in membrane fusion

Last updated April 01, 2024

Membrane fusion is a key biophysical process that is essential for the functioning of life itself. It is defined as the event where two lipid bilayers approach each other and then merge to form a single continuous structure.^[1] In living beings, cells are made of an outer coat made of lipid bilayers; which then cause fusion to take place in events such as fertilization, embryogenesis and even infections by various types of bacteria and viruses.^[2] It is therefore an extremely important event to study. From an evolutionary angle, fusion is an extremely controlled phenomenon. Random fusion can result in severe problems to the normal functioning of the human body. Fusion of biological membranes is mediated by proteins. Regardless of the complexity of the system, fusion essentially occurs due to the interplay of various interfacial forces, namely hydration repulsion, hydrophobic attraction and van der Waals forces.^[3]

Inter-bilayer forces

Lipid bilayers are structures of lipid molecules consisting of a hydrophobic tail and a hydrophilic head group. Therefore, these structures experience all the characteristic Interbilayer forces involved in that regime.

Hydration repulsion

Two hydrated bilayers experience strong repulsion as they approach each other. These forces have been measured using the Surface forces apparatus (S.F.A), an instrument used for measuring forces between surfaces. This repulsion was first proposed by Langmuir and was thought to arise due to water molecules that hydrate the bilayers. Hydration repulsion can thus be defined as the work required in removing the water molecules around hydrophilic molecules (like lipid head groups) in the bilayer system.^[4] As water molecules have an affinity towards hydrophilic head groups, they try to arrange themselves around the head groups of the lipid molecules and it becomes very hard to separate this favorable combination.

Experiments performed through SFA have confirmed that the nature of this force is an exponential decline.^[5] The potential V_R is given by^[6]

V_{R}=C_{R}\cdot \exp \!\left[{-z \over \lambda _{R}}\right]

where C_R (>0) is a measure of the hydration interaction energy for hydrophilic molecules of the given system, λ_R is a characteristic length scale of hydration repulsion and z is the distance of separation. In other words, it is on distances up to this length that molecules/surfaces fully experience this repulsion.

Hydrophobic attraction

Hydrophobic forces are the attractive entropic forces between any two hydrophobic groups in aqueous media, e.g. the forces between two long hydrocarbon chains in aqueous solutions. The magnitude of these forces depends on the hydrophobicity of the interacting groups as well as the distance separating them (they are found to decrease roughly exponentially with the distance). The physical origin of these forces is a debated issue but they have been found to be long-ranged and are the strongest among all the physical interaction forces operating between biological surfaces and molecules.^[7] Due to their long range nature, they are responsible for rapid coagulation of hydrophobic particles in water and play important roles in various biological phenomena including folding and stabilization of macromolecules such as proteins and fusion of cell membranes.

The potential V_A is given by^[7]

V_{A}=C_{A}\cdot \exp \!\left[{-z \over \lambda _{A}}\right]

where C_A (<0) is a measure of the hydrophobic interaction energy for the given system, λ_A is a characteristic length scale of hydrophobic attraction and z is the distance of separation.

van der Waals forces in bilayers

These forces arise due to dipole–dipole interactions (induced/permanent) between molecules of bilayers. As molecules come closer, this attractive force arises due to the ordering of these dipoles; like in the case of magnets that align and attract each other as they approach.^[7] This also implies that any surface would experience a van der waals attraction. In bilayers, the form taken by van der Waals interaction potential V_VDW is given by^[8]

V_{VDW}=-{H \over 12\pi }*\left({1 \over z^{2}}-{2 \over (z+D)^{2}}+{1 \over (z+2D)^{2}}\right)

where H is the Hamaker constant and D and z are the bilayers thickness and the distance of separation respectively.

Background

For fusion to take place, it has to overcome huge repulsive forces due to the strong hydration repulsion between hydrophilic lipid head groups.^[7] However, it has been hard to exactly determine the connection between adhesion, fusion and interbilayer forces. The forces that promote cell adhesion are not the same as the ones that promote membrane fusion. Studies show that by creating a stress on the interacting bilayers, fusion can be achieved without disrupting the interbilayer interactions. It has also been suggested that membrane fusion takes place through a sequence of structural rearrangements that help to overcome the barrier that prevents fusion.^[7] Thus, interbilayer fusion takes place through

local approach of membrane
structural rearrangements causing hydration repulsion forces to be overcome
complete merging to form a single entity

Interbilayer interactions during membrane fusion

When two lipid bilayers approach each other, they experience weak van der Waals attractive forces and much stronger repulsive forces due to hydration repulsion.^[9] These forces are normally dominant over the hydrophobic attractive forces between the membranes. Studies done on membrane bilayers using Surface forces apparatus (SFA) indicate that membrane fusion can instantaneously occur when two bilayers are still at a finite distance from each other without them having to overcome the short-range repulsive force barrier.^[7] This is attributed to the molecular rearrangements that occur resulting in the bypassing of these forces by the membranes. During fusion, the hydrophobic tails of a small patch of lipids on the cell membrane are exposed to the aqueous phase surrounding them. This results in very strong hydrophobic attractions (which dominate the repulsive force) between the exposed groups leading to membrane fusion.^[10] The attractive van der Waals forces play a negligible role in membrane fusion. Thus, fusion is a result of the hydrophobic attractions between internal hydrocarbon chain groups that are exposed to the normally inaccessible aqueous environment. Fusion is observed to start at points on the membranes where the membrane stresses are either the weakest or the strongest.^[7]

Applications

Interbilayer forces play a key role in mediating membrane fusion, which has extremely important biomedical applications.^[11]

The most important application of membrane fusion is in the production of hybridomas which are cells that arise as a result of the fusion of antibody-secreting and immortal B-cells. Hybridomas are used in the industry for the production of monoclonal antibodies.
Membrane fusion also has a major role in cancer immunotherapy. Currently, one of the approaches in cancer immunotherapy involves vaccination of dendritic cells which express a specific tumor antigen on their membranes. Instead, the hybrid cells obtained from the fusion of dendritic cells with tumor cells can be used. These hybrids would help in the expression of a range of tumor-associated antigens on their membranes.
Understanding membrane fusion better can also lead to improvements in gene therapy.

Related Research Articles

A biological membrane, biomembrane or cell membrane is a selectively permeable membrane that separates the interior of a cell from the external environment or creates intracellular compartments by serving as a boundary between one part of the cell and another. Biological membranes, in the form of eukaryotic cell membranes, consist of a phospholipid bilayer with embedded, integral and peripheral proteins used in communication and transportation of chemicals and ions. The bulk of lipids in a cell membrane provides a fluid matrix for proteins to rotate and laterally diffuse for physiological functioning. Proteins are adapted to high membrane fluidity environment of the lipid bilayer with the presence of an annular lipid shell, consisting of lipid molecules bound tightly to the surface of integral membrane proteins. The cell membranes are different from the isolating tissues formed by layers of cells, such as mucous membranes, basement membranes, and serous membranes.

An intermolecular force (IMF) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. atoms or ions. Intermolecular forces are weak relative to intramolecular forces – the forces which hold a molecule together. For example, the covalent bond, involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of force fields frequently used in molecular mechanics.

<span class="mw-page-title-main">Van der Waals force</span> Interactions between groups of atoms that do not arise from chemical bonds

In molecular physics and chemistry, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and therefore more susceptible to disturbance. The van der Waals force quickly vanishes at longer distances between interacting molecules.

A transmembrane domain (TMD) is a membrane-spanning protein domain. TMDs may consist of one or several alpha-helices or a transmembrane beta barrel. Because the interior of the lipid bilayer is hydrophobic, the amino acid residues in TMDs are often hydrophobic, although proteins such as membrane pumps and ion channels can contain polar residues. TMDs vary greatly in size and hydrophobicity; they may adopt organelle-specific properties.

<span class="mw-page-title-main">Lipid bilayer</span> Membrane of two layers of lipid molecules

The lipid bilayer is a thin polar membrane made of two layers of lipid molecules. These membranes are flat sheets that form a continuous barrier around all cells. The cell membranes of almost all organisms and many viruses are made of a lipid bilayer, as are the nuclear membrane surrounding the cell nucleus, and membranes of the membrane-bound organelles in the cell. The lipid bilayer is the barrier that keeps ions, proteins and other molecules where they are needed and prevents them from diffusing into areas where they should not be. Lipid bilayers are ideally suited to this role, even though they are only a few nanometers in width, because they are impermeable to most water-soluble (hydrophilic) molecules. Bilayers are particularly impermeable to ions, which allows cells to regulate salt concentrations and pH by transporting ions across their membranes using proteins called ion pumps.

A micelle or micella is an aggregate of surfactant amphipathic lipid molecules dispersed in a liquid, forming a colloidal suspension. A typical micelle in water forms an aggregate with the hydrophilic "head" regions in contact with surrounding solvent, sequestering the hydrophobic single-tail regions in the micelle centre.

A chaotropic agent is a molecule in water solution that can disrupt the hydrogen bonding network between water molecules. This has an effect on the stability of the native state of other molecules in the solution, mainly macromolecules by weakening the hydrophobic effect. For example, a chaotropic agent reduces the amount of order in the structure of a protein formed by water molecules, both in the bulk and the hydration shells around hydrophobic amino acids, and may cause its denaturation.

The DLVO theory explains the aggregation and kinetic stability of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium. It combines the effects of the van der Waals attraction and the electrostatic repulsion due to the so-called double layer of counterions. The electrostatic part of the DLVO interaction is computed in the mean field approximation in the limit of low surface potentials - that is when the potential energy of an elementary charge on the surface is much smaller than the thermal energy scale, $. For two spheres of radius each having a charge separated by a center-to-center distance in a fluid of dielectric constant containing a concentration of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or Yukawa potential,$

<span class="mw-page-title-main">Amphiphile</span> Hydrophilic and lipophilic chemical compound

An amphiphile, or amphipath, is a chemical compound possessing both hydrophilic and lipophilic (fat-loving) properties. Such a compound is called amphiphilic or amphipathic. Amphiphilic compounds include surfactants. The phospholipid amphiphiles are the major structural component of cell membranes.

<span class="mw-page-title-main">Cationic liposome</span>

Cationic liposomes are spherical structures that contain positively charged lipids. Cationic liposomes can vary in size between 40 nm and 500 nm, and they can either have one lipid bilayer (monolamellar) or multiple lipid bilayers (multilamellar). The positive charge of the phospholipids allows cationic liposomes to form complexes with negatively charged nucleic acids through ionic interactions. Upon interacting with nucleic acids, cationic liposomes form clusters of aggregated vesicles. These interactions allow cationic liposomes to condense and encapsulate various therapeutic and diagnostic agents in their aqueous compartment or in their lipid bilayer. These cationic liposome-nucleic acid complexes are also referred to as lipoplexes. Due to the overall positive charge of cationic liposomes, they interact with negatively charged cell membranes more readily than classic liposomes. This positive charge can also create some issues in vivo, such as binding to plasma proteins in the bloodstream, which leads to opsonization. These issues can be reduced by optimizing the physical and chemical properties of cationic liposomes through their lipid composition. Cationic liposomes are increasingly being researched for use as delivery vectors in gene therapy due to their capability to efficiently transfect cells. A common application for cationic liposomes is cancer drug delivery.

Membrane lipids are a group of compounds which form the lipid bilayer of the cell membrane. The three major classes of membrane lipids are phospholipids, glycolipids, and cholesterol. Lipids are amphiphilic: they have one end that is soluble in water ('polar') and an ending that is soluble in fat ('nonpolar'). By forming a double layer with the polar ends pointing outwards and the nonpolar ends pointing inwards membrane lipids can form a 'lipid bilayer' which keeps the watery interior of the cell separate from the watery exterior. The arrangements of lipids and various proteins, acting as receptors and channel pores in the membrane, control the entry and exit of other molecules and ions as part of the cell's metabolism. In order to perform physiological functions, membrane proteins are facilitated to rotate and diffuse laterally in two dimensional expanse of lipid bilayer by the presence of a shell of lipids closely attached to protein surface, called annular lipid shell.

Lipid bilayer characterization is the use of various optical, chemical and physical probing methods to study the properties of lipid bilayers. Many of these techniques are elaborate and require expensive equipment because the fundamental nature of the lipid bilayer makes it a very difficult structure to study. An individual bilayer, since it is only a few nanometers thick, is invisible in traditional light microscopy. The bilayer is also a relatively fragile structure since it is held together entirely by non-covalent bonds and is irreversibly destroyed if removed from water. In spite of these limitations dozens of techniques have been developed over the last seventy years to allow investigations of the structure and function of bilayers. The first general approach was to utilize non-destructive in situ measurements such as x-ray diffraction and electrical resistance which measured bilayer properties but did not actually image the bilayer. Later, protocols were developed to modify the bilayer and allow its direct visualization at first in the electron microscope and, more recently, with fluorescence microscopy. Over the past two decades, a new generation of characterization tools including AFM has allowed the direct probing and imaging of membranes in situ with little to no chemical or physical modification. More recently, dual polarisation interferometry has been used to measure the optical birefringence of lipid bilayers to characterise order and disruption associated with interactions or environmental effects.

One property of a lipid bilayer is the relative mobility (fluidity) of the individual lipid molecules and how this mobility changes with temperature. This response is known as the phase behavior of the bilayer. Broadly, at a given temperature a lipid bilayer can exist in either a liquid or a solid phase. The solid phase is commonly referred to as a “gel” phase. All lipids have a characteristic temperature at which they undergo a transition (melt) from the gel to liquid phase. In both phases the lipid molecules are constrained to the two dimensional plane of the membrane, but in liquid phase bilayers the molecules diffuse freely within this plane. Thus, in a liquid bilayer a given lipid will rapidly exchange locations with its neighbor millions of times a second and will, through the process of a random walk, migrate over long distances.

In membrane biology, fusion is the process by which two initially distinct lipid bilayers merge their hydrophobic cores, resulting in one interconnected structure. If this fusion proceeds completely through both leaflets of both bilayers, an aqueous bridge is formed and the internal contents of the two structures can mix. Alternatively, if only one leaflet from each bilayer is involved in the fusion process, the bilayers are said to be hemifused. In hemifusion, the lipid constituents of the outer leaflet of the two bilayers can mix, but the inner leaflets remain distinct. The aqueous contents enclosed by each bilayer also remain separated.

A model lipid bilayer is any bilayer assembled in vitro, as opposed to the bilayer of natural cell membranes or covering various sub-cellular structures like the nucleus. They are used to study the fundamental properties of biological membranes in a simplified and well-controlled environment, and increasingly in bottom-up synthetic biology for the construction of artificial cells. A model bilayer can be made with either synthetic or natural lipids. The simplest model systems contain only a single pure synthetic lipid. More physiologically relevant model bilayers can be made with mixtures of several synthetic or natural lipids.

The presence of ethanol can lead to the formations of non-lamellar phases also known as non-bilayer phases. Ethanol has been recognized as being an excellent solvent in an aqueous solution for inducing non-lamellar phases in phospholipids. The formation of non-lamellar phases in phospholipids is not completely understood, but it is significant that this amphiphilic molecule is capable of doing so. The formation of non-lamellar phases is significant in biomedical studies which include drug delivery, the transport of polar and non-polar ions using solvents capable of penetrating the biomembrane, increasing the elasticity of the biomembrane when it is being disrupted by unwanted substances and functioning as a channel or transporter of biomaterial.

Peptide amphiphiles (PAs) are peptide-based molecules that self-assemble into supramolecular nanostructures including; spherical micelles, twisted ribbons, and high-aspect-ratio nanofibers. A peptide amphiphile typically comprises a hydrophilic peptide sequence attached to a lipid tail, i.e. a hydrophobic alkyl chain with 10 to 16 carbons. Therefore, they can be considered a type of lipopeptide. A special type of PA, is constituted by alternating charged and neutral residues, in a repeated pattern, such as RADA16-I. The PAs were developed in the 1990s and the early 2000s and could be used in various medical areas including: nanocarriers, nanodrugs, and imaging agents. However, perhaps their main potential is in regenerative medicine to culture and deliver cells and growth factors.

The cell membrane is a biological membrane that separates and protects the interior of a cell from the outside environment. The cell membrane consists of a lipid bilayer, made up of two layers of phospholipids with cholesterols interspersed between them, maintaining appropriate membrane fluidity at various temperatures. The membrane also contains membrane proteins, including integral proteins that span the membrane and serve as membrane transporters, and peripheral proteins that loosely attach to the outer (peripheral) side of the cell membrane, acting as enzymes to facilitate interaction with the cell's environment. Glycolipids embedded in the outer lipid layer serve a similar purpose. The cell membrane controls the movement of substances in and out of a cell, being selectively permeable to ions and organic molecules. In addition, cell membranes are involved in a variety of cellular processes such as cell adhesion, ion conductivity, and cell signalling and serve as the attachment surface for several extracellular structures, including the cell wall and the carbohydrate layer called the glycocalyx, as well as the intracellular network of protein fibers called the cytoskeleton. In the field of synthetic biology, cell membranes can be artificially reassembled.

In colloidal chemistry, the critical micelle concentration (CMC) of a surfactant is one of the parameters in the Gibbs free energy of micellization. The concentration at which the monomeric surfactants self-assemble into thermodynamically stable aggregates is the CMC. The Krafft temperature of a surfactant is the lowest temperature required for micellization to take place. There are many parameters that affect the CMC. The interaction between the hydrophilic heads and the hydrophobic tails play a part, as well as the concentration of salt within the solution and surfactants.

Bovine submaxillary mucin (BSM) coatings are a surface treatment provided to biomaterials intended to reduce the growth of disadvantageous bacteria and fungi such as S. epidermidis, E. coli, and Candida albicans. BSM is a substance extracted from the fresh salivary glands of cows. It exhibits unique physical properties, such as high molecular weight and amphiphilicity, that allow it to be used for many biomedical applications.

References

↑ Yang, L. (2002-09-13). "Observation of a Membrane Fusion Intermediate Structure". Science. 297 (5588). American Association for the Advancement of Science (AAAS): 1877–1879. Bibcode:2002Sci...297.1877Y. doi:10.1126/science.1074354. ISSN 0036-8075. PMID 12228719. S2CID 45362358.
↑ Jahn, Reinhard; Grubmüller, Helmut (2002). "Membrane fusion". Current Opinion in Cell Biology. 14 (4). Elsevier BV: 488–495. doi:10.1016/s0955-0674(02)00356-3. ISSN 0955-0674. PMID 12383801.
↑ Helm, Christiane A.; Israelachvili, Jacob N.; McGuiggan, Patty M. (1992-02-18). "Role of hydrophobic forces in bilayer adhesion and fusion". Biochemistry. 31 (6). American Chemical Society (ACS): 1794–1805. doi:10.1021/bi00121a030. ISSN 0006-2960. PMID 1737032.
↑ Rand, R P (1981). "Interacting Phospholipid Bilayers: Measured Forces and Induced Structural Changes". Annual Review of Biophysics and Bioengineering. 10 (1). Annual Reviews: 277–314. doi:10.1146/annurev.bb.10.060181.001425. ISSN 0084-6589. PMID 7020577.
↑ McIntosh, T. J.; Magid, A. D.; Simon, S. A. (1987). "Steric repulsion between phosphatidylcholine bilayers". Biochemistry. 26 (23). American Chemical Society (ACS): 7325–7332. doi:10.1021/bi00397a020. ISSN 0006-2960. PMID 3427075.
↑ Manciu, Marian; Ruckenstein, Eli (2001). "Free Energy and Thermal Fluctuations of Neutral Lipid Bilayers". Langmuir. 17 (8). American Chemical Society (ACS): 2455–2463. doi:10.1021/la0016266. ISSN 0743-7463.
1 2 3 4 5 6 7 Leckband, Deborah; Israelachvili, Jacob (2001). "Intermolecular forces in biology". Quarterly Reviews of Biophysics. 34 (2). Cambridge University Press (CUP): 105–267. doi:10.1017/s0033583501003687. ISSN 0033-5835. PMID 11771120. S2CID 8401242.
↑ Petrache, Horia I.; Gouliaev, Nikolai; Tristram-Nagle, Stephanie; Zhang, Ruitian; Suter, Robert M.; Nagle, John F. (1998-06-01). "Interbilayer interactions from high-resolution x-ray scattering". Physical Review E. 57 (6). American Physical Society (APS): 7014–7024. Bibcode:1998PhRvE..57.7014P. doi:10.1103/physreve.57.7014. ISSN 1063-651X.
↑ Leikin, Sergey L.; Kozlov, Michael M.; Chernomordik, Leonid V.; Markin, Vladislav S.; Chizmadzhev, Yuri A. (1987). "Membrane fusion: Overcoming of the hydration barrier and local restructuring". Journal of Theoretical Biology. 129 (4). Elsevier BV: 411–425. Bibcode:1987JThBi.129..411L. doi:10.1016/s0022-5193(87)80021-8. ISSN 0022-5193. PMID 3455469.
↑ Helm, C.; Israelachvili, J.; McGuiggan, P. (1989-11-17). "Molecular mechanisms and forces involved in the adhesion and fusion of amphiphilic bilayers". Science. 246 (4932). American Association for the Advancement of Science (AAAS): 919–922. Bibcode:1989Sci...246..919H. doi:10.1126/science.2814514. ISSN 0036-8075. PMID 2814514.
↑ Chen, E. H. (2005-04-15). "Unveiling the Mechanisms of Cell-Cell Fusion". Science. 308 (5720). American Association for the Advancement of Science (AAAS): 369–373. Bibcode:2005Sci...308..369C. doi:10.1126/science.1104799. ISSN 0036-8075. PMID 15831748. S2CID 17524831.

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[1] Yang, L. (2002-09-13). "Observation of a Membrane Fusion Intermediate Structure". Science. 297 (5588). American Association for the Advancement of Science (AAAS): 1877–1879. Bibcode:2002Sci...297.1877Y. doi:10.1126/science.1074354. ISSN 0036-8075. PMID 12228719. S2CID 45362358.

[2] Jahn, Reinhard; Grubmüller, Helmut (2002). "Membrane fusion". Current Opinion in Cell Biology. 14 (4). Elsevier BV: 488–495. doi:10.1016/s0955-0674(02)00356-3. ISSN 0955-0674. PMID 12383801.

[3] Helm, Christiane A.; Israelachvili, Jacob N.; McGuiggan, Patty M. (1992-02-18). "Role of hydrophobic forces in bilayer adhesion and fusion". Biochemistry. 31 (6). American Chemical Society (ACS): 1794–1805. doi:10.1021/bi00121a030. ISSN 0006-2960. PMID 1737032.

[4] Rand, R P (1981). "Interacting Phospholipid Bilayers: Measured Forces and Induced Structural Changes". Annual Review of Biophysics and Bioengineering. 10 (1). Annual Reviews: 277–314. doi:10.1146/annurev.bb.10.060181.001425. ISSN 0084-6589. PMID 7020577.

[5] McIntosh, T. J.; Magid, A. D.; Simon, S. A. (1987). "Steric repulsion between phosphatidylcholine bilayers". Biochemistry. 26 (23). American Chemical Society (ACS): 7325–7332. doi:10.1021/bi00397a020. ISSN 0006-2960. PMID 3427075.

[6] Manciu, Marian; Ruckenstein, Eli (2001). "Free Energy and Thermal Fluctuations of Neutral Lipid Bilayers". Langmuir. 17 (8). American Chemical Society (ACS): 2455–2463. doi:10.1021/la0016266. ISSN 0743-7463.

[Israel-7] 1 2 3 4 5 6 7 Leckband, Deborah; Israelachvili, Jacob (2001). "Intermolecular forces in biology". Quarterly Reviews of Biophysics. 34 (2). Cambridge University Press (CUP): 105–267. doi:10.1017/s0033583501003687. ISSN 0033-5835. PMID 11771120. S2CID 8401242.

[8] Petrache, Horia I.; Gouliaev, Nikolai; Tristram-Nagle, Stephanie; Zhang, Ruitian; Suter, Robert M.; Nagle, John F. (1998-06-01). "Interbilayer interactions from high-resolution x-ray scattering". Physical Review E. 57 (6). American Physical Society (APS): 7014–7024. Bibcode:1998PhRvE..57.7014P. doi:10.1103/physreve.57.7014. ISSN 1063-651X.

[9] Leikin, Sergey L.; Kozlov, Michael M.; Chernomordik, Leonid V.; Markin, Vladislav S.; Chizmadzhev, Yuri A. (1987). "Membrane fusion: Overcoming of the hydration barrier and local restructuring". Journal of Theoretical Biology. 129 (4). Elsevier BV: 411–425. Bibcode:1987JThBi.129..411L. doi:10.1016/s0022-5193(87)80021-8. ISSN 0022-5193. PMID 3455469.

[10] Helm, C.; Israelachvili, J.; McGuiggan, P. (1989-11-17). "Molecular mechanisms and forces involved in the adhesion and fusion of amphiphilic bilayers". Science. 246 (4932). American Association for the Advancement of Science (AAAS): 919–922. Bibcode:1989Sci...246..919H. doi:10.1126/science.2814514. ISSN 0036-8075. PMID 2814514.

[11] Chen, E. H. (2005-04-15). "Unveiling the Mechanisms of Cell-Cell Fusion". Science. 308 (5720). American Association for the Advancement of Science (AAAS): 369–373. Bibcode:2005Sci...308..369C. doi:10.1126/science.1104799. ISSN 0036-8075. PMID 15831748. S2CID 17524831.

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Interbilayer forces in membrane fusion

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