Poisson-Nernst-Planck theory approach to the calculation of current through biological ion channels

Overview

Ion channels are specialized proteins on the plasma membrane that allow charged ions to pass down their electrochemical gradient. Their main function is to maintain the membrane potential which is critical for cell viability. These channels are either gated or non-gated and can transport more than a thousand ions within milliseconds for the cellular event to occur.
Compared to the gated ion channels, the non-gated channels, also known as leakage or passive channels, have no gating mechanism.

The relative difference in electrical charge, or voltage, between the inside and the outside of a cell membrane, is called the membrane potential. It is generated by differences in permeability of the membrane to various ions and the concentrations of these ions across the membrane.
The Inside of a Neuron is More Negative
The membrane potential of a cell can be measured by inserting a microelectrode into a cell and comparing the charge to a reference electrode in the extracellular fluid. The...

A postsynaptic neuron usually receives numerous impulses from several other presynaptic neurons. The axon hillock of the postsynaptic neuron integrates all these signals and determines the likelihood of firing an action potential.
Sometimes a single EPSP is strong enough to induce an action potential in the postsynaptic neuron. However, multiple presynaptic inputs must often create EPSPs around the same time for the postsynaptic neuron to be sufficiently depolarized to fire an action potential.

Ion channels are specialized proteins on the plasma membrane that allow charged ions to pass down their electrochemical gradient. Their main function is to maintain the membrane potential which is critical for cell viability. These channels are either gated or non-gated and can transport more than a thousand ions within milliseconds for the cellular event to occur.
Compared to the gated ion channels, the non-gated channels, also known as leakage or passive channels, have no gating mechanism.

An electrochemical gradient is a fundamental concept in biology and chemistry. It regulates the movement of ions across cell membranes. This movement is influenced by two factors:
The electrical gradient: The electrical gradient across cell membranes refers to the difference in electric charge between the inside and outside of a cell.  This difference drives the movement of ions towards or away from the cells. For instance, if the inside of the cell is more negatively charged relative to the...