Membranes electrostatic energy

Recently, Ohki proposed a physical principle underlying membrane fusion processes in terms of molecular interaction. For simplicity, two interacting membranes are considered as two flat hydrocarbon bodies having hydrophilic layers on their surfaces, separated by an aqueous solution at a certain distance R. The thickness of the hydrophilic layer is h which may be different from those of the flat body as well as the aqueous phases in their molecular nature and molecular density. Since the electrostatic interaction gives a repulsive force and is not a main factor for membrane fusion, we assume the electrostatic energy term to be a constant contribution to the total interaction energy at the true adhesion, and the van der Waals interaction energy would contribute mainly to membrane fusion. Then, the van der Waals interaction between the two bodies will be expressed as a function of the separation distance R, the thickness h, and the Hamaker constant A in each phase ... 

In terms of the structure within the membrane, the idealized Hsu and Gierke cluster-network model is used as a picture where the pathways between the clusters are interfacial regions. These pathways are termed collapsed channels since they can be expanded by liquid water to form a liquid-filled channel. In essence, the collapsed channels are sulfonic acid sites surrounded by the polymer matrix having a low enough concentration such that the overall pathway between two clusters remains hydrophobic. In other words, they are composed of bridging ionic sites [31] and the electrostatic energy density is too low compared to the polymer elasticity to allow for a bulk-like water phase to form and expand the channels. In all, for a vapor-equilibrated membrane the structure is that of ionic domains that are hydrophilic and contain some bulk-like water. These clusters are connected by... 

The calculation of binding free energies is arguably the most common application of PB methods. As described earlier, PB methods provide the electrostatic energies and are often supplemented with additional terms representing apolar and other interactions. These calculations are performed on a wide variety of complexes ranging from small molecule-protein interactions to protein-membrane interactions and the energy of supramolecular assembly. ... 

For instance, if the rates of association and dissociation of the complex MS are very high, the chemical reaction at the interface is always very close to equilibrium even if a current flows through the membrane. The overall transport is then limited by the translocation of MS across the membrane. As was mentioned, the translocation of the complex may be treated as a jump over an activation barrier. In the presence of an external voltage V, the shape of the barrier is modified by the electrostatic energy as a consequence, the rate constants for the jump from left to right (Kms) and from right to left (Kms) become unequal. This may be expressed to a first approximation by the following relations [325] ... 

The electrostatic free energy of a macromolecule embedded in a membrane in the presence of a membrane potential V can be expressed as the sum of three separate terms involving the capacitance C of the system, the reaction field Orffr), and the membrane potential field p(r) [73],... 

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