Atomistic Simulations of Ion Channels - Computational Neuroscience: A Comprehensive Approach - page 42

for references), the most popular of which currently is Particle Mesh Ewald [95],
although in my opinion this may not be the final answer for membrane systems due
to its artificial symmetry. More fundamentally, the simple potential functions used
might not be accurate enough for important details of e.g. ion-protein interactions
across a range of ions [66]. Although any potential energy function could be used
in principle, including much more complex versions than the one shown in Eq. 2.1,
parameterizing more complex functions is a daunting task and there might not be
sufficient experimental data to test the parameters.
Certain crucial aspects of ion channel function are hard to incorporate in MD sim-
ulations of periodic systems with tens of thousands of atoms. One problem is that
incorporating transmembrane potential differences is not straightforward, although
a reasonable and promising approximation has been developed [35]. Clearly, this
is crucial if we want to calculate current-voltage curves. A second problem is that
ionic concentrations are difficult to model. Even uniform low salt concentrations are
not straightforward to represent in a simulation, because it is difficult to sample the
motion of the 27 K + and27Cl − ions that would make up a 0.15 M KCl solution
in a simulation with 10,000 water molecules. Such a simulation would also ignore
the effect that the lipids have on the local salt concentration near the bilayer [28],
which differs significantly from the bulk concentration. Biologically relevant con-
centrations of calcium or protons are even more problematic: in a typical simulation
system a physiological calcium concentration in the micromolar range would corre-
spond to much fewer than 1 ion. Modelling the effect of pH has similar problems
with concentration and the additional problem that it is hard to make protons hop
between different groups in a classical potential. Usually, pH is incorporated by cal-
culating the pKa of ionisable residues and adjusting the protonation state of ionisable
amino acids according to the desired pH.
Finally, the starting models used for simulations are rather critical at the moment.
Most simulations of ion channels have been carried out on a handful of crystal struc-
tures, including gramicidin A, OmpF, a mechanosensitive channel, and the potassium
channel KcsA. From an ion channel perspective KcsA is by far the most interesting
of these, but the crystal structure initially had a fairly low resolution, which caused
some uncertainty in the starting structures for the simulations. Simulations have also
been done on homology models of various channels, in which case it becomes even
more important to carefully consider the sensitivity of the results obtained to changes
in the model [26].
Before examining continuum models, I would like to mention a class of simula-
tions based on semi-microscopic models that combine fully atomistic detail in parts
of the system with long-range electrostatic corrections based on a series of models
that treat the environment as a lattice of rotating dipoles [23, 78, 6]. This method
appears quite accurate and flexible, but is not implemented in most of the common
software packages for molecular dynamics simulations.