Interbilayer forces in membrane fusion

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]

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

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 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]

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

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.

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]

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

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