The pore of the ion channel gramicidin has the dimensions of approximately 10 water molecules in single file.  When certain positively charged ions occupy the pore, water molecules reorient so as to prevent additional ions from entering.  This "single-ion constraint" can be modeled mathematically by boundary conditions involving the integral of the ion probability density within the pore.  These boundary conditions are constructed by taking the diffusion limit of a random walk.  The construction also enables us to visualize particle trajectories associated with the boundary conditions.  By taking limits of sums of single-particle processes, we can also construct trajectories associated with more familiar boundary conditions for the diffusion equation.  Sample trajectories underlying four different classes of boundary conditions will be shown.