# The PNP Cyclic Peptide Ion Channel Model: Simulate ion flow in a simple model system using Poisson-Nernst-Planck (PNP) theory.

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## What is the PNP Cyclic Peptide Ion Channel Model?

Poisson-Nernst-Planck (PNP) theory couples the Poisson (describing the electrostatic potential of a system of fixed charges) and Smoluchowski equations (describing the diffusion of charged particles) to describe ion flow. Using complex boundary conditions, these equations can be used to model an ion channel. This model approximates proteins as cylindrical tubes embedded in a lipid membrane. The ions, lipids, protein, and water molecules are all described as dielectric continuums, exchanging the electronic and nuclear polarizations of molecules for dielectric constants and the ion distributions for number density functions. The system of equations in PNP theory is solved simultaneously and self-consistently via the finite difference method, whereby continuous functions are mapped onto a discrete grid. Using several different input parameters, the electrostatic potential, ion concentrations, ion flux, and ion current of the system can be found.

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