Lecture 5 - Electrical Signals of Nerve Cells (Passive Membrane Properties)

Question 1

By myelinating a cell, you’re increasing the resistance of an axon, which also increases τ. Due to this, an action potential should be stretched out in time and delayed. How does the cell stop this from happening?

Answer 1

Since resistance is increasing, you must decrease capacitance. According to Kirchoff’s resistance law, resistances added in parallel have a lower total resistance than resistances added in series. The opposite is true for capacitance. When wrapping the membrane many times, its like adding capacitors in series, which decreases the equivalent capacitance and restores τ to the value it would be if not myelinated. This is why myelin wraps around the axon many more times than needed to affect resistance.

Question 2

What type of membrane resistance does not come from voltage-gated channels, but rather the “leak” channels?

Answer 2

Passive

Question 3

True or False?:

Voltage change across a membrane is not instantaneous due to membrane resistance.

Answer 3

False

Voltage change across a membrane is not instantaneous due to membrane capacitance.

Question 4

What 4 things are affected by passive membrane properties?

Answer 4

1. The magnitude of change in membrane potential after current entry.
2. The time course of change in membrane potential after current entry.
3. The distance over which the changein voltage travels.
4. Speed of action potential propagation.

Question 5

Suppose you have two cells that are equal in diameter. Cell 1 has a larger specific resistance than cell 2. Which cell has the larger membrane resistance?

Answer 5

Cell 1

Since cell 1 has a larger specific resistance, it has less “leaks” than cell 2 for a given surface area. Since both cells are the same size, cell 1 will have less “leaks” total, meaning it has the highest resistance.

Question 6

What does V_t = V_max x e^-t/τ model?

Answer 6

Membrane Discharging

Question 7

What are the units of resistance?

Answer 7

Ohms (Ω)

Question 8

What is τ equal to?

Answer 8

τ = c_mr_m

Question 9

True or False?:

The dendrites and soma are active while the axon is passive.

Answer 9

False

The dendrites and soma are passive while the axon is active.

Question 10

Describe the plumber’s model of a membrane below that illustrates Ohm’s law.

Answer 10

In this basic water model, a water pump is pumping water at a constant rate (current) of I. Water is going around the circuit, where it encounters a channel that is narrower than the rest of the pipe. As such, there will be a difference in pressure on each side of the channel. If the channel is quite large, it can be said to have a high conductance and low resistance. If this is the case, the pressure difference will be low, proportional to the low resistance. Likewise, if the channel is quite small (low conductance, high resistance), there will be a relatively large difference in pressure, proportional to the high resistance.

Question 11

True or False?:

In one unit of τ time, a membrane will increase its charge by 37% of the interval between its current charge and the maximum.

Answer 11

False

In one unit of τ time, a membrane will increase its charge by 63% of the interval between its current charge and the maximum.

Question 12

True or False?:

Once current enters a cell, it flows in all directions it can. In order to direct this current, r_m is typically lower than r_a.

Answer 12

False

Once current enters a cell, it flows in all directions it can. In order to direct this current, r_a is typically lower than r_m.

Question 13

What type of membrane resistance is made up of voltage-gated channels that are closed at rest?

Answer 13

Active

Question 14

True or False?:

Passive signals are unidirectional.

Answer 14

False

Passive signals can flow in any direction.

Question 15

What does Ohm’s law state?

Answer 15

Electrical Potential = Current x Resistance

V = IR

Question 16

How does myelin affect λ? How does this affect action potential progation?

Answer 16

Myelin makes λ much larger (by increasing r_m) allowing for rapid propagation of the action potential from one node of Ranview to the next.

Question 17

What differs in the propagation of signals between passive parts of the neuron and active parts?

Answer 17

In active parts, the signal is maintained by voltage-gated channels. In passive parts, the signal decays as you move away from the synapse.

Question 18

What type of membrane resistance represents all the channels that are open at rest?

Answer 18

Passive

Question 19

What equation models membrane charging?

Answer 19

V_t = V_max x (1 - e^-t/τ)

Question 20

What equation represents voltage drop from the site of current injection?

Answer 20

V_x = V^_max x e^-x/λ

Question 21

What are the 3 passive electrical properties?

Answer 21

1. Membrane Resistance (r_m)
2. Membrane Capacitance (c_m)
3. Intracellular (Axial) Resistance (r_a)

Question 22

What are the units of charge?

Answer 22

Coulombs (C)

Question 23

What are the units of conductance?

Answer 23

Siemens (S)

Question 24

True or False?:

Typically, neurons have input capacitances of 10-50 pF.

Answer 24

True

Question 25

True or False?:

A cell with a large surface area will have a high capacitance c_m and a low membrane resistance r_m while a cell with a small surface area will have a high membrane resistance r_m and a low capacitance c_m.

Question 26

What type of membrane resistance sets the permeabilities at the resting potential used in the GHK equation?

Answer 26

Passive

Question 27

When you move down the axon from a current-injection electrode, will a passive signal be bigger or smaller than it is at the injection site? Explain.

Answer 27

The signal will be smaller than it is at the injection site. The voltage leaks out across the membrane as it propagates down the axon. The membrane offers an alternative route through which the current can flow. As such, by the time you get to the measuring point, there will be less current than there is at the injection site.

Question 28

What type of membrane resistance represents channels that are opened when the membrane reaches action potential threshold?

Answer 28

Active

Question 29

What are passive electrical properties?

Answer 29

Passive electrical properties are the membrane properties that allow neurons to conduct electrical impulses without using voltage-gated ion channels.

Question 30

True or False?:

The ionic equivalent of capacitance is the hydrophobic plasma membrane itself.

Answer 30

True

Question 31

True or False?:

For every unit of λ that you move away from the site of current injection, the voltage will drop to 37% of its value.

Answer 31

True

Question 32

How does the length constant affect spatial summation in order to determine whether a subthreshold input will elicit an action potential?

Answer 32

When λ is larger, signals decay less when they actively propagate from their origin to the axon intial segment. When λ is smaller, they decay a lot more. If λ is big, EPSPs will be able to depolarize the membrane by a greater amount when they reach the axon initial segment than they would be able to if λ was small. As such, cells with a longer λ are more likely to have passive signals that summate to the threshold for an action potential.

Question 33

What is the relationship between capacitance, charge, and electrical potential?

Answer 33

Capacitance = Charge / Electrical Potential

C = Q/E

Question 34

What is the formula for membrane length constant (λ)?

Answer 34

λ = (r_m/r_a)^1/2

Question 35

What are the units of electrical potential?

Answer 35

Volts (V)

Question 36

What is the specific capacitance C_M for a cell?

Answer 36

1 µF/cm²

Question 37

What are the units of current?

Answer 37

Amperes (A)

Question 38

The flow of anions like chloride results in “charge” moving in which direction?

Answer 38

The Opposite Direction

Question 39

What is input resistance r_input?

Answer 39

Input resistance is the resistance for the entire cell plus the access resistance.

r_input = r_m + r_access

Question 40

True or False?:

The ionic equivalent of voltage is the membrane potential.

Answer 40

False

The ionic equivalent of voltage is driving force.

Question 41

What is access resistance r_access?

Answer 41

Access resistance is the resistance of your recording pipette.

Question 42

Why do large axons have larger length constants? Explain using math.

Answer 42

They have larger length constants because λ is inversly proportional to r_a, which gets smaller as an axon gets larger more than r_m gets smaller.

λ = (r_m/r_a)^1/2

r_m ∝ 1/suface area (perimeter) = 1/2πr (r_m decreases as r increases)

r_a ∝ 1/area = 1/πr² (r_a decreases as r increases)

λ ∝ [(1/2πr)/(1/πr²)]^1/2

λ ∝ (a/2)^1/2

Question 43

What acts as a capacitor in cells?

Answer 43

The Lipid Bilayer Membrane

Question 44

Explain what’ll happen to V, i_R, and i_C when a square wave current i is applied to the circuit model of a membrane showed below. What do the resistor and capacitor represent?

Answer 44

Kirchoff’s current law (ew, physics) states that current in parallel will add together. Therefore, i_R + i_C = i. When the current is first applied, it will go the capacitor. But as the charge on the capacitor builds up, it’ll be harder to add more charge. So, i_C will gradually decrease and i_R will gradually increase until the capacitor is fully charged, at which point i_R = i. Since voltage is the difference between each side of the circuit and only i_R crosses it, V will be proportional to i_R. When the current is turned off, the capacitor will start to discharge (hence the -i_C). This charge will then cross the resistor. Since i = 0, i_R = -i_C. The absolute values of i_R and i_C (and consequently, V) will start high and gradually lower until they all reach 0.

The resistor represents ion channels (or lack thereof) and the capacitor represents the lipid bilayer membrane.

Question 45

What does the membrane time constant (τ) determine?

Answer 45

τ determines the rate of change in V_m (proportional to i_R). It is equal to the time it takes to charge a membrane to 63% of its max [(1-1/e)*V_max] or decharge it to 37% of its max..

Question 46

How does the time constant affect temporal summation in order to determine whether a subthreshold input will elicit an action potential?

Answer 46

A cell with a long τ will stretch out passive signals while a cell with a short τ will have shorter passive signals. When the signals are longer, there is a higher likelihood of signals overlapping in order to summate to the treshold. When the signals are shorter, it is more likely that one signal will return to baseline before the next signal comes in, leaving no opportunity for summation.

Question 47

What are the units of capacitance?

Answer 47

Farads (F)

Question 48

What does membrane resistance (r_m) determine?

Answer 48

Membrane resistance determines how much the membrane potential will change in response to addition of current. (Due to Ohm’s law - you have R = r_m, you inject current I, you then find V)

Question 49

What is the difference between specific resistance R_M and membrane resistance r_m?

Answer 49

R_M describes the resistance of a unit area (how leaky the membrane is) and has units of Ω/cm². r_m is the resistance of an entire cell (with channel) and has units Ω.

Question 50

Suppose you have two cells that have the same specific resistance. Cell 1 has a much larger diameter than cell 2. Which cell has the larger membrane resistance?

Answer 50

Cell 2

Since both cells have the same density of “leaks”, the bigger cell 1 will have more “leaks” overall, meaning it has the lower membrane resistance.

Question 51

True or False?:

Extracellular resistance is a very important factor to take into account.

Answer 51

False

Extracellular resistance exists but it is negligible.

Question 52

When you turn off a hyperpolarizing command potential, how do capacitance, charge, and voltage change as you return back to base conditions?

Answer 52

For the lipid membrane, capacitance is constant and will not change. As such (in accordance with the formula C = Q/V), capacitance can be used as a measure of the amount of charge the membrane is able to hold per unit of voltage. As voltage increases, so does the amount of charge the membrane holds. When the hyperpolarizing current is turned off, the absolute voltage of the membrane will decrease. This means that the membrane will be able to hold less charge than before and will have to release some charge in the form of an outward (positive) capacitive current spike.

Question 53

What is axial resistance (r_a) determined by?

Answer 53

Axial resistance is determined by the specific resistance of the cytoplasm and the diameter of the central core.

Question 54

What is a capacitor?

Answer 54

A capacitor is a device that stores energy in the electric field created between a pair of conductors, separated by an insulating layer, on which equal but opposite electric charges have been placed.

Question 55

Will a wide axon have a high or low r_a?

Answer 55

A wide axon will have a low r_a because there is a large area for the current to flow.

Question 56

What are the 3 conditions for getting current to flow and how are they met in neurons?

Answer 56

1. Something has to carry the charge. (Ions)
2. The charge needs to have a passageway. (Typically, Open Ion Channels)
3. The charge must have a driving force. (Concentration Gradient, Electrostatic Potential/Voltage)

Question 57

True or False?:

The ionic equivalent of conductance is ion channels.

Answer 57

True

Question 58

True or False?:

The passive cell membrane can be modeled as a resistor and capacitor in parallel.

Answer 58

True

Question 59

True or False?:

Internal axial resistance (r_a) contributes to how far and how fast an impules will travel.

Answer 59

True