equations for voltage across membrane to the injected current ion pump
Answers
Answer:
Explanation:
To understand the behavior of this circuit, we first need to review the behavior of the individual 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 balloon 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
neural membrane. C: RC circuit model of a passive neural membrane, with a current source added.
by the current provided by the sodium-potassium pump so that the net current in/out of the cell is
zero. Likewise, once the water balloon is fully inflated, the current provided by the water pump
equals the current spurting out through the holes and the net current in/out of the balloon is zero.
We can think about the net current in/out of the balloon/cell in two different ways; one is
analogous to the current through the battery/resistor branch of the electrical circuit and the other is
analogous to the current through the capacitor of the electrical circuit. We’ll consider these in turn.
The net current in/out of the balloon depends on the difference between the pressure in the
balloon and the pressure exerted by the pump. When these two pressures are equal, the balloon
is in equilibrium, and the net current is zero. The net current also depends on the size/number of
holes. If the pressure in the balloon is greater than that exerted by the pump, then the net current
will be outward. If the holes are big, then this net outward current will be large. The net current
out of the balloon, therefore, increases with increased pressure difference and it increases if the
holes are made bigger. In electrical circuits, this is called Ohm’s Law:
Ig = g (Vm E); (1)
where Ig is current through the resistor, Vm is the membrane potential (i.e., the voltage between
inside and outside of the neuron, modeled as the the voltage drop across both the resistor and the
battery), and g is conductance