Nerve fibers contain ion-channels within their membrane. These ion-channels pass specific ions from the outside of the cell inward or in the opposite direction (depends on the concentration differences between the two sides of the membrane). An ion is actually an electric charge, negative like chlorine or positive like sodium. So the movement of each ion through the membrane, inside or outside, is a movement of an electric charge. This is why this mechanism called an electrochemical system. When the nerve fiber receives input from other nerve fibers, these ion-channels open and the ion can cross from one side of the membrane to the other, causing an electric potential. This electric potential progresses along the length of the nerve fiber - this is an electric current moving in threw the nerve fiber.
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