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membrane Potential

# membrane Potential - The Membrane Equation Professor David...

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The Membrane Equation Professor David Heeger September 5, 2000 RC Circuits Figure 1A shows an RC (resistor, capacitor) equivalent circuit model for a patch of passive neural membrane. The capacitor represents the fact that cellular membranes are good electrical insulators. The battery represents the sodium-potassium pump that acts to hold the electrical potential of the inside of the cell below that of the outside. This voltage difference is called the resting potential of the neuron. The resistor represents the leakage of current through the membrane. To understand the behavior of this circuit, we first need to review the behavior of the indi- vidual electrical elements. We’ll use a water balloon as an analogy to help develop our intuition. Figure 1B shows a leaky water balloon connected to a water pump. When the pump is off, the balloon is empty. When the pump is first turned on, the balloon starts to fill with water. The bal- loon expands rapidly at first because the force from the incoming water far overpowers the elastic force of the unexpanded balloon. As the balloon is stretched more and more, the elastic force gets greater and greater, so the balloon’s size increses ever more slowly, until it reaches equilibrium. At this point, the current flowing into the balloon from the pump is equal to the current spurting out through the holes, and the water pressure inside the balloon is equal to the pressure exerted by the pump. Increasing the number (or size) of the holes would cause more water current to spurt out. Also, if there were more (or bigger) holes, then the balloon would not inflate quite as much. The behavior of the water balloon is expressed in terms of: (1) water volume, (2) water current, (3) water pressure inside the balloon, (4) the size/number of holes, and (5) the elasticity of the balloon. In the electrical RC circuit, the analogous quantities are: (1) electrical charge, (2) electrical current, (3) electrical potential, (4) electrical conductance, and (5) capacitance. Electrical charge (analogous to water volume), is measured in coulombs. Electrical current is the rate of flow of charge (analogous to the rate of flow of the water in and out of the balloon), and is measured in amperes or amps (1 amp = 1 coul/sec). Electrical resistance (analogous to the size/number of holes in the balloon) is measured in ohms. Electrical conductance is the reciprocal of resistance, and is measured in siemens (siemens = 1/ohms). Electrical potential (analogous to the water pressure) is measured in volts. One volt will move 1 amp of current through a 1 siemen conductor. When we say that a neuron is “at rest”, it is actually in a state of dynamic equilibrium. There is always some current leaking out of the cell. But when at rest, that leak current is exactly balanced 1

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Vm E g C water pump water balloon Vm E g C I inject A B C Figure 1: A: RC circuit model of a passive neural membrane. B: Water balloon model of a passive neural membrane. C: RC circuit model of a passive neural membrane, with a current source added.
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membrane Potential - The Membrane Equation Professor David...

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