UBC Theses and Dissertations
Non local dielectric effects on the dielectric barrier of an ion channel Krayenhoff, Willem Bruce
In this thesis we study non-local dielectric models on the sub-nanometer scale. In particular, we focus on the effect of non-local electrostatics on the potential barrier of a water-filled ion channel through a lipid cell membrane, and on the interaction between ions within such an ion channel. A polarization energy functional is used with its parameters calibrated to roughly reproduce the wave-vector-dependent dielectric function ǫ(q) of water. The lipid membrane is still modelled as a local dielectric. This energy functional is discretized onto a lattice and minimized using local moves to find the energy and the electric and polarization field configurations for a given charge distribution and dielectric profile. This method is used to successfully reproduce known theoretical results with and without an ion channel. Necessary, but not necessarily sufficient conditions for obtaining good results are also derived. The dielectric barrier of an ion channel is studied with these non-local dielectric properties of water, and it is found that the results are very sensitive to how the water-membrane interface is modeled. We conclude that more molecular dynamics simulations are needed to provide guidance as to how to implement the polarization energy density functional at this inter- face, as well as whether these energy density functionals, which match the properties of bulk water, need to be modified in order to apply inside narrow ion channels. However, in all instances that we explored the self-energy of the ion traversing the ion channel was substantially modified from its self-energy under the local model, suggesting that non-local dielectric effects may be one significant factor determining the dielectric barrier of an ion channel.
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