Unassisted transport of ions across membranes

The permeation rate of ions across membranes can be estimated using a continuum dielectric model of a water-membrane system. In this model, both water and membrane are represented as homogeneous, isotropic media, characterized by dielectric constants and ej, respectively, and separated by a sharp planar boundary. If the ion is represented as a point charge q located at the center of a cavity of radius a, the change in the excess chemical potential associated with the transfer of the ion from bulk water to the center of the membrane (the free energy barrier), is expressed in this model as [58,59]  

To help answer this question, a detailed, molecular simulation of the unassisted ion transport of Na+ and Cr across a GMO bilayer was performed using molecular dynamics [25]. Due to the large free energy barrier, however, the transfer does not occur on the timescales accessible to computer simulations. Therefore, a series of molecular dynamics trajectories were generated in which the ion was restricted to overlapping regions along the interface normal (c-direction). 

The simulations revealed a picture of ion permeation that is in sharp contrast with the continuum dielectric model. As the ion moves across the water-membrane interface into the bilayer, the membrane surface does not remain approximately planar. Instead, a local deformation is formed in which water molecules and polar head groups (normally restricted to the surface of the membrane) follow the ion into the nonpolar interior of the bilayer. Once the ion crosses the midplane of the membrane, the deformation on the incoming side relaxes and simultaneously, a similar deformation forms on the outgoing side. Thus, during the entire transfer process, the ion remains partially solvated by both the polar head groups and water molecules. The key feature of this molecular description of the ion transfer process is that the ion is never fully solvated by the nonpolar hydrocarbon tails. Thus, the calculated is markedly lower than the barrier predicted from the continuum model. For Na , was estimated at 

Once A// is known, the permeability coefficient can be estimated from equation (7) by expanding in the high barrier limit. This leads to the 

The calculated Pmembr for Na is approximately 10 cm s— 1. This value is slightly lower than most experimental estimates for phospholipid bilayers [62-64], Considering, however, that the error in the calculated is approxi- 

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