Electrochemistry and circuit components of axons
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Electrochemistry and circuit components of axons
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[post_date] => 2025-01-09 08:14:12
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
In a nerve cell, ion channels open and close based on their environment and other factors. When a channel is open, it behaves as an Ohmic resistor (V=IR). When it is closed, an insulator. The currents through the ion channels are determined by the electrical potential and ion concentration differences between the cytoplasm inside the cell and the surrounding interstitial fluid. If only sodium and potassium ions were present, the “reversal potential,” Vm, would be predicted by the Goldman-Hodgkin-Katz equation, (Equation 1).
Equation 1. Reversal potential
The reverse potential is the potential that, if it were applied to the cell, would result in potassium and sodium crossing the membrane at rates that yield no net current. Each permeability, Px, is proportional to the number ion X channels open at that node.
Table 1 shows the typical concentrations of sodium and potassium ions inside and outside of the cell.
Table 1. Typical ion concentrations, [mM]
As the ions enter and exit the cytoplasm, they change the electric field within the axon, creating a new electrical potential. The cytoplasm conducts a current down its length in response to that electrical potential, much like a copper wire.
[post_title] => Electrochemistry and circuit components of axons
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[question] => If we treat the interstitial fluid and cytoplasm as two separate wires and the channels as resistors in an equivalent circuit diagram, would adding more of these transmembrane “resistors” increase or decrease the total equivalent resistance at the node?
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[answer] => 3
[description] => Reason for the Correct Answer:
Look at Figure 1. All of the inside ends of the channel “resistors” are “wired” to each other through the cytoplasm and all of the outside ends are wired to each other by the interstitial fluid.
This is a parallel circuit.
Resistors in parallel add as a sum of reciprocals
For instance, if there are N channels and all of the channels have the same resistance, r = r1 = r2 = r3== rN, then 
.
Solving for the equivalent resistance, 
. This means that increasing N decreases Requiv. because the resistors/channels are in parallel.
Alternatively: adding more channels is like poking more holes in the membrane. It gives more ions an opportunity to cross the membrane, decreasing the total resistance to current flow.
)
[answers] => Array
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[0] => Array
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[each_answer] => A. Total resistance would increase, because the resistors are in series.
)
[1] => Array
(
[each_answer] => B. Total resistance would increase, because the resistors are in parallel.
)
[2] => Array
(
[each_answer] => C. Total resistance would decrease, because the resistors are in parallel.
)
[3] => Array
(
[each_answer] => D. Total resistance would decrease, because the resistors are in series.
)
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => Tetraethylammonium (TEA) is a toxin that inactivates potassium channels. If a neuron with the values in Table 1 were exposed to enough TEA to close all potassium channels, which of the following best approximates the value of Vm?
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
Permeability to an ion species is proportional to the number of its channels that are open.
With no potassium channels open, PK+ = 0.
This reduces the Goldman-Hodgkin-Katz equation to 
. The permeability terms cancel from the numerator and denominator.
lugging in, this reduces nicely to:
)
[answers] => Array
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[0] => Array
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[each_answer] => A. -90mV
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[1] => Array
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[each_answer] => B. -60mV
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[2] => Array
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[each_answer] => C. 60mV
)
[3] => Array
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[each_answer] => D. 90mV
)
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => Current is said to be flowing into the cytoplasm when ions move across the membrane. What makes this “current” in the same sense as current flowing in a battery-wire-resistor circuit?
[value] => Array
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[answer] => 4
[description] => Reason for the Correct Answer:
Current is not specific to a single species of charge carrier, such as the electron.
Light is a form of time-varying electric field, but no current is flowing.
Ions are charged particles, and current is by definition the movement of charge through space.
)
[answers] => Array
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[0] => Array
(
[each_answer] => A. This is an abuse of nomenclature. The ion and wire currents are not, in fact, two examples of the same “current” phenomenon.
)
[1] => Array
(
[each_answer] => B. The ions carry electrons even though they might have net positive charge, and “current” is the movement of electrons.
)
[2] => Array
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[each_answer] => C. The ions create a local change in the electric field, which means that current is flowing.
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[3] => Array
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[each_answer] => D. The ions carry net charge with them as they move, and current is defined as charge moving in space.
)
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[3] => Array
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[quiz_unique_key] => 2261298308
[question] => Suppose that an axon transmits constant voltage signals between two nodes of Ranvier, a distance L apart. A 10% increase in which parameter would require the neuron to dissipate the most power? (Hold all other variables constant.)
[value] => Array
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[answer] => 2
[description] => Reason for the Correct Answer:
Current will flow from one node of Ranvier to the next.
Cytoplasm is a bulk material with a characteristic resistivity, p.
Resistance, R, = 
, where the cross-sectional area of the axon A = r2.
So, power 
. Increasing the length between nodes of Ranvier or the resistivity would decrease the power required, and increasing the internal axon radius would quickly increase power dissipated.
)
[answers] => Array
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[each_answer] => A. Length between nodes of Ranvier, L
)
[1] => Array
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[each_answer] => B. Internal axon radius, r
)
[2] => Array
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[each_answer] => C. Cytoplasmic resistivity,
)
[3] => Array
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[each_answer] => D. All of the above would change power consumption equally
)
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[quiz_unique_key] => 2377279144
[question] => If a node of Ranvier were held at its reversal potential by a battery and there were twice as many sodium channels open as there are potassium channels, which of the following is true immediately after the potential is turned on?
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[answer] => 1
[description] => Reason for the Correct Answer:
Both sodium and potassium ions will move down their concentration gradients.
If a cell is held at its reversal potential, the net flow of current will be zero.
The total amount of current flowing into the cell through the sodium channels must equal the amount current flowing out through the potassium channels.
Dividing the total current of each type of ion by the number of channels of that type gives the average current flowing through that channel type:
, and 
Where 
is the number of potassium channels, 
is the average current through a potassium channel, and 
is the total current through the potassium channels. Similarly for sodium, and 
There are half as many potassium channels open as there are sodium channels, but the same amount of current must flow through the potassium channels in total. This means that on average, twice as much current flows through an individual potassium channels as flows through an individual sodium channel.
)
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[0] => Array
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[each_answer] => A. More current flows through an individual potassium channel than an individual sodium channel, on average.
)
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[each_answer] => B. The total current through the potassium channels is greater than the total current through the sodium channels.
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[each_answer] => C. The potassium channels dissipate more power than the sodium channels.
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[each_answer] => D. More data is needed to answer this question.
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[559164|1] => C
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[559164|5] => A
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