An ion channel is a protein with a hole down its middle embedded into the
cytoplasmic membrane of a living biological cells. Ion channels facilitate ionic
transport across the membrane, thus bridging the intra- and extra-cellular compartments. Properly functioning channels contribute to the healthy state of an organism, making them one of the main targets for pharmaceutical applications. The description and prediction of a channel’s performance --conductivity, selectivity, blocking etc., -- under arbitrary experimental conditions starting from its crystal structure thus appears as an important challenge in contemporary theoretical research.
The main obstacle for such description arises from the presence of the multiple non-negligible interactions in the system. These include ion-ion, ion-water,
ion-ligands, ion-pore, and other interactions. Their self-consistent consideration is essential in narrow ion channels, where due to inter-ion interactions and atomic confinement, the ions move in a single-file highly-correlated manner. Molecular dynamics, the most detailed computational tool to date, does not allow one routinely to evaluate the properties of such channels, while continuous methods overlook the ion-ion interactions. Therefore, one needs a method that combines atomic details with the ability to estimate ionic currents.
This thesis focuses on the classical treatment of ion channels. Namely, a Brownian Dynamics simulation is described where the interactions of the ion with other ions and the channel are incorporated via the multi-ion potential of the mean force (PMF). This allows one to model the channel’s behaviour under various experimental conditions, while preserving the details of the structure and nanoscale interactions with atomic precision. Secondly, we use the concept of a quasiparticle to describe the highly-correlated ionic motion in the selectivity filter of the KcsA channel. We derive the quasiparticle’s effective potential from the multi-ion atomic PMF, thus connecting the quasiparticle’s properties with the nanoscale features of the channel. We also evaluate the rates of transition between different quasiparticles by virtue of the BD simulation. These ingredients comprehensively describe the quasiparticle’s dynamics which hence serves as an intermediary between the crystal structure and the experimentally observed properties of a narrow ion channel.
Lastly, an analytical method to describe the ion-solvent interaction is proposed. It incorporates the ion-solvent and ion-lattice radial density functions, and
hence automatically accounts for the pore shape, the type of atoms comprising the lattice, the type of solvent, and the ion’s location near the pore entrance. This method paves the way to an analytical decomposition of single-ion PMFs, what is of fundamental importance in predicting the conductive and selective properties of mutated biological ion channels. This method can also find application in designing functionalized artificial nanopores with on-demand transport properties for efficient water desalination.