Using Random Walks to Elucidate Structural Dependence of Na⁺ Diffusion in Na_v 1.7 Channel

Na_v channels play a significant role in neuronal excitability, crucial for propagating action potentials in neurons. However, experimental methods of studying passive-diffusive ion transport through these channels operate on a time scale too large to control the protein's conformational changes. Moreover, existing computational methods either do not operate on the same length- and time scales as the process or take too long to run. We present a Continuous Time Random Walk method to simulate ion transport in the channel as a discretized lattice. We elucidate how diffusion depends on the structure of the channel pore and how the disorder from the channel structure can be incorporated as spatial and temporal parameters for the rates of movement into the walk. We see that constrictions in lattices slow down diffusion. Computed diffusion coefficients show that an increase in spatial disorder slows down the diffusive process when the walk is biased in the direction of ion flow, while an increase in temporal disorder has the opposite effect. However, these parameters do not affect unbiased walks inside the channel. A better understanding of the channel disorder and its impact on ion transport can have significant applications in healthcare research.