Atomistic Simulations of Ion Channels - Computational Neuroscience: A Comprehensive Approach - page 49

catenary-shaped region of high dielectric is embedded in a region of low dielectric.
The force on a test ion at different locations in the models is calculated using both
methods, which provides a sensitive test with instructive results. The force on an
ion in the center of a spherical cavity with a radius of 20 A in 0.5 M NaCl solution
(Debye length 4.3 A) is nearly 0, both in BD and PB. As the ion is moved closer to
the wall, the repulsive force from BD persists up to about 2 Debye lengths from the
walls, whereas the PB solution shows a force of almost 0. Close to the wall, the BD
force increases steeply but the PB force is a factor of 4 less. The problem appears
to be that counter ions in the PB case provide shielding, even though there is no
physical space for counter ions [82]. In the two more complicated cases (a channel-
like cylinder with rounded edges and a catenary shape) similar effects were seen.
In wider channels the difference in maximum force between PB and BD decreased.
Thus, when force profiles are integrated, PB underestimates the height of the barri-
ers in the electrostatic potential energy profile. In a second paper, PNP theory was
compared with BD in the same model cylindrical channels and also in a potassium
channel-like geometry [34]. When the channel diameter became less than 2 Debye
lengths (n.b. the Debye length is 8 A in 150 mM KCl), the PNP approach severely
overestimated shielding. Overall the results provide clear examples of the dangers of
failing to treat ions as discrete entities within confined spaces.

2.3.2 Gramicidin A

Gramicidin A is a peptide ion channel that has long served as a model for theoretical
work on ion channels, partly because of its simple structure and partly because it was
the only high-resolution structure known ( Figure 2.1A) . It has an unusual structure
with a mixture of L and D amino acids. Because it can be chemically synthesized it
has been modified in many ways. Two examples are the replacement of tryptophans
with fluorinated equivalents [5] and the incorporation of a photoactive switch [19].
Although the structure of gramicidin is rather unusual, it does provide a pore lined
with carbonyl groups, similar to those found in potassium channels. There is a vast
literature on theoretical studies of gramicidin A, and I only present a few papers
that illustrate important points learned from gramicidin A. Other reviews include
[92, 111, 68, 4, 119].
In a pioneering study, Aqvist and Warshel [7] calculated a free energy profile for
sodium in the gramicidin channel based on the electrostatic Protein Dipoles Langevin
Dipoles (PDLD) model, a semi-microscopic model midway between an all-atom rep-
resentation and a continuum model, and found reasonable well depths and barriers.
They compared the results from this model with free energy perturbation calcula-
tions of the solvation of Na + in bulk water and inside the channel, yielding similar
results when the induced dipoles due to the low dielectric membrane environment
were taken into account. An important aspect of this work is that the low dielec-
tric environment from the membrane was taken into account explicitly. This allows
an estimate of the significant effect of this term (ca. 10 kcal/mol), which has not
always been included in later simulations. Several molecular dynamics simulations
have suggested that ion permeation is coupled to motions of the channel. Roux and