Lecture 4

Question 1

What is the magnitude and direction of the sodium (Na⁺) gradient created by the Na+/K+ ATPase?

Answer 1

Gradient: Sodium is far more concentrated outside the cell.

Magnitude: The concentration outside is about 10 times higher than inside the cytoplasm (a ~10:1 ratio).

Question 2

What is the magnitude and direction of the potassium (K⁺) gradient created by the Na+/K+ ATPase?

Answer 2

Gradient: Potassium is far more concentrated inside the cell.

Magnitude: The concentration inside the cytoplasm is about 30 times higher than in the extracellular space (a ~30:1 ratio).

Question 3

How does the flow of potassium (K⁺) and sodium (Na⁺) ions directly affect the membrane potential (Vₘ)?

Answer 3

Potassium (K⁺) Flow: When K⁺ leaves the cell, it removes positive charge, causing the membrane to hyperpolarize (Vₘ becomes more negative).

Sodium (Na⁺) Flow: When Na⁺ enters the cell, it adds positive charge, causing the membrane to depolarize (Vₘ becomes more positive).

Question 4

What is the “driving force” that determines how quickly an ion will diffuse across the plasma membrane?

Answer 4

Definition: The difference between the membrane potential (Vₘ) and the ion’s equilibrium potential (Eₓ).

Formula: Driving Force = Vₘ - Eₓ

Interpretation: A larger difference means a stronger push for the ion to move. If Vₘ = Eₓ, the driving force is zero and there is no net flow.

Question 5

What does “conductance” (gₓ) for an ion represent, and what two factors does it depend on?

Answer 5

Definition: The ability of the membrane to allow the facilitated diffusion of a specific ion.

It depends on:
The number of open ion channels for that ion.
The intrinsic transport rate (ability to pass ions) of those open channels.

Question 6

What is the equation that calculates the current (Iₓ) for a specific ion, and what does each term represent?

Answer 6

Equation: Iₓ = gₓ (Vₘ - Eₓ)

Terms:

Iₓ: Ionic Current (the flow of ions per unit time)

gₓ: Conductance (ease of ion flow)

(Vₘ - Eₓ): Driving Force (the electrochemical push)

Question 7

current at equilibrium

Answer 7

Σ(Ix) = I K + I Na + I Cl = 0

Question 8

Under what specific condition does the membrane potential (Vₘ) become stable and stop changing?

Answer 8

Condition: When the sum of all ionic currents (Iₓ) flowing across the membrane is zero.

At this point, the inward and outward flows of charge are balanced, and Vₘ remains constant.

Question 9

What does the chord conductance equation state about the membrane potential (Vₘ)?

Answer 9

Statement: The membrane potential is a weighted mean (average) of the equilibrium potentials (Eₓ) of all permeable ions.

Key Idea: The “weight” for each ion is its relative conductance (gₓ/Σg).

Question 10

What is the general form of the chord conductance equation?

Answer 10

Equation: Vₘ = (gₖ/Σg)Eₖ + (g_Na/Σg)E_Na + (g_Cl/Σg)E_Cl

Where:

gₓ is the conductance for an ion

Σg is the total conductance (gₖ + g_Na + g_Cl)

Eₓ is the equilibrium potential for an ion

Question 11

How does the relative conductance of an ion influence the membrane potential?

Answer 11

Rule: The ion with the largest relative conductance (gₓ/Σg) has the greatest influence on Vₘ.

Example: If potassium conductance (gₖ) is very high, Vₘ will be very close to Eₖ. If g_Na and gₖ are equal, Vₘ will be roughly the average of E_Na and Eₖ.

Question 12

What is the resting membrane potential (RMP), and what is its typical value in excitable cells like neurons and muscle cells?

Answer 12

The stable potential difference across the plasma membrane when a cell is fully repolarized and “at rest.”

Typical Value: -60 mV to -80 mV.

Question 13

Which ion has the greatest influence on the RMP, and through what type of channel does it flow?

Answer 13

Dominant Ion: Potassium (K⁺)

Reason: The potassium conductance (gₖ) is far greater than sodium or chloride conductance at rest.

Channel Type: This occurs mainly through leak potassium channels, which are the most common open channels in the resting membrane.

Question 14

What is the relationship between the Resting Membrane Potential (RMP) and the potassium equilibrium potential (Eₖ)?

Answer 14

The RMP is close to the equilibrium potential of K+.

However, it is slightly depolarized relative to Eₖ.

Reason: This is due to the small contributions from the inward leak of sodium ions and other conductances.

Question 15

Why don’t ion concentrations change over time, even though there is constant ion flux at rest?

Answer 15

State: A Dynamic Equilibrium exists.

Mechanism:

The Na+/K+ ATPase actively pumps out Na⁺ that leaks in and pumps in K⁺ that leaks out.

Chloride is re-equilibrated via secondary active transport.

This active transport exactly balances the passive leak, keeping concentrations constant.

Question 16

Opening of ion channels gated by voltage, ligands or physical
stimuli leads to what

Answer 16

membrane depolarization or hyperpolarization

Question 17

What happens to the membrane potential and membrane conductance when a very small current is injected into a cell?

Answer 17

Membrane Potential: It changes.

Membrane Conductance: It does NOT change. The ion channels that are open at rest (like leak channels) are sufficient to mediate the response. This is called a passive response.

Question 18

Why does the membrane potential (Vₘ) change more slowly than the applied current?

Answer 18

Reason: The plasma membrane acts as a capacitor.

Mechanism: The injected current must first charge this capacitor (by building up charge on either side of the lipid bilayer), which causes the slower, smoother change in Vₘ.

Question 19

How does the membrane’s capacitance affect the speed of the voltage change in response to a current?

Answer 19

The higher the capacitance, the slower the change in Vₘ will be for a given current.

Question 20

What distinguishes a passive response from an active response to a larger current?

Answer 20

Passive Response: Caused by small currents. Involves no change in membrane conductance; only the pre-existing “leak” channels are involved.

Active Response: Caused by larger currents. These currents activate additional voltage-gated conductances, changing the membrane’s properties

Question 21

What is electrotonic conduction, and is it amplified by voltage-gated channels?

Answer 21

Definition: The passive conduction of a change in membrane potential along a neurite (dendrite or axon).

Amplification: No. It is not amplified by voltage-gated ion channels.

Question 22

How does the magnitude of the membrane potential change as it propagates passively from the site of current injection?

Answer 22

Pattern: It decreases (decays) exponentially with increasing distance.

Observation: The change is greatest at the injection site and becomes smaller and smaller as it travels.

Question 23

Why does the passive potential change get smaller as it travels along the neurite?

Answer 23

Reason: As current (ions) flows along the inside of the neurite, some ions escape (“leak”) across the plasma membrane through the open ion channels that are always present.

Result: This loss of current makes the signal smaller and smaller with distance.

Question 24

What is the length constant (lambda, λ), and what does it tell you?

Answer 24

Definition: The distance from a current injection site at which the membrane potential change has decayed to 1/e (about 37%) of its original value.

Significance: It measures the capacity of a neurite to passively propagate a potential change. A large λ means little decay; a small λ means rapid decay

Question 25

What two fundamental properties determine the length constant (λ)?

Answer 25

Membrane Resistance (rₘ): The ability of the membrane to prevent ions from leaking out. Higher rₘ (fewer open channels) results in a larger λ (less decay). Axial Resistance (rₐ): The resistance to ions flowing along the inside of the neurite. Lower rₐ results in a larger λ (less decay).

Question 26

In the garden hose analogy for electrotonic conduction, what do the "leaky walls" and "hose diameter" represent?

Answer 26

Leaky Walls: Represent low membrane resistance (rₘ). More leaks (open channels) mean less water (current) reaches the end. Hose Diameter: Represents the axial resistance (rₐ). A larger diameter means lower rₐ, allowing more water (current) to flow farther with less loss.

Question 27

How does increasing the diameter of a neurite affect the length constant (λ), and why?

Answer 27

Effect: A larger diameter results in a larger length constant (λ) and less electrotonic decay. Reason: Axial resistance (rₐ) decreases dramatically with diameter (rₐ ~ 1/d²). Membrane resistance (rₘ) also decreases with more surface area, but more slowly (rₘ ~ 1/d). Because rₐ decreases faster, the net effect is a larger λ.

Question 28

What is the equation for the length constant (λ), and what do the variables represent?

Answer 28

Equation: λ = √( rₘ / (rₐ + rₒ) ) Variables: rₘ: Membrane Resistance rₐ: Axial (Internal) Resistance rₒ: Extracellular Resistance (often considered negligible)

Question 29

How does increasing the diameter (d) of a neurite affect the axial resistance (rₐ) and membrane resistance (rₘ), and what is the net effect on the length constant (λ)?

Answer 29

Scaling Laws: Axial Resistance (rₐ): Decreases with the square of the diameter (rₐ ~ 1/d²). Membrane Resistance (rₘ): Decreases proportionally with diameter due to increased surface area (rₘ ~ 1/d). Net Effect: Because rₐ decreases much faster than rₘ, the net result is that a larger diameter causes a larger length constant (λ) and therefore less electrotonic decay.

Question 30

What type of response does a small, depolarizing current elicit in a neuron, and why?

Answer 30

Response Type: A passive response. Reason: The depolarization is not large enough to activate voltage-gated ion channels. The potential change is governed solely by the passive properties (capacitance and resistance) of the membrane.

Question 31

What happens when a depolarizing current is large enough, and what is the name of the resulting event?

Answer 31

What Happens: The membrane is depolarized to a point where voltage-gated ion channels are activated. Resulting Event: This triggers an action potential—a very rapid, large depolarization.

Question 32

What is the "action potential threshold," and how is it defined?

Answer 32

Definition: The specific membrane voltage at which there is a 50 percent chance of elicing an action potential. Significance: It is the critical level of depolarization required to activate enough voltage-gated channels to initiate the all-or-none response.

Question 33

What are the key characteristics of a full-blown action potential?

Answer 33

All-or-None Response: It is a maximal, stereotyped event that occurs whenever the threshold is reached, regardless of how strongly it is exceeded. Peak Membrane Potential: The inside of the cell becomes very positive, reaching +30 to +50 mV.

Question 34

Why is the upstroke of an action potential so rapid and "explosive"?

Answer 34

Mechanism: A positive feedback loop. Depolarization to ~-40 mV opens some VGSCs. Na⁺ influx depolarizes the membrane further. This opens more VGSCs, leading to more depolarization. Result: This loop causes nearly all VGSCs to open simultaneously, creating the very fast upstroke.

Question 35

What are the two main consequences of the rapid inactivation of voltage-gated sodium channels (VGSCs)?

Answer 35

Action Potential Shape: It helps terminate the action potential, allowing the membrane to repolarize. Action Potential Initiation: It creates the phenomenon of accommodation, where a slow depolarization may fail to trigger an AP.

Question 36

What is accommodation, and why does a very slow depolarization fail to trigger an action potential?

Answer 36

Definition: The failure to generate an action potential in response to a very slow depolarization. Reason: During a slow depolarization, VGSCs inactivate at a rate that exceeds their activation rate. As some channels open, others inactivate and become unresponsive, preventing the critical mass needed for the positive feedback loop.

Question 37

How does the speed of the initial depolarization affect the action potential threshold?

Answer 37

Faster Depolarization: Lower threshold. The positive feedback loop starts before significant inactivation occurs. Slower Depolarization: Higher threshold. The membrane must be depolarized farther to overcome the competing inactivation of VGSCs.

Question 38

What is the primary function of voltage-gated potassium (K⁺) channels during an action potential?

Answer 38

Function: To repolarize the membrane. Mechanism: When they open, K⁺ flows out of the cell, making the inside more negative and opposing the depolarization. This is a negative feedback loop.

Question 39

How does the opening speed of voltage-gated potassium (K⁺) channels compare to voltage-gated sodium (Na⁺) channels?

Answer 39

Voltage-gated Na⁺ Channels: Open very fast (<1 ms). This speed advantage allows them to initiate the depolarizing upstroke. Voltage-gated K⁺ Channels: Open much more slowly. This delay allows the Na⁺-driven depolarization to occur first. K are activated by depolarization, with a voltage-dependence similar to sodium channels (i.e., they begin to open at around -40 mV).

Question 40

Describe the sequence of ion channel events that creates the rising and falling phases of an action potential.

Answer 40

Rising Phase (Depolarization): Fast-opening Na⁺ channels open, allowing Na⁺ influx. Falling Phase (Repolarization): Slower-opening K⁺ channels open, allowing K⁺ efflux, which repolarizes the membrane.

Question 41

How do the inactivation properties of voltage-gated potassium channels differ from sodium channels?

Answer 41

Voltage-gated Na⁺ Channels: Show rapid and complete inactivation. Voltage-gated K⁺ Channels: Show little and delayed inactivation. They stay open longer to ensure the membrane fully repolarizes.

Question 42

What triggers the rising phase of an action potential, and why is it so steep?

Answer 42

Trigger: A depolarizing current (e.g., synaptic input) brings the membrane to threshold. Rising Phase: Voltage-gated sodium channels (VGSCs) open much faster than potassium channels. This creates a positive feedback loop of Na⁺ influx and depolarization, causing the steep upstroke.

Question 43

What happens at the peak of the action potential?

Answer 43

Sodium Channels: They begin to inactivate rapidly, so Na⁺ influx decreases. Potassium Channels: The slow-opening voltage-gated potassium channels have now opened in significant numbers. Balance: At the peak, K⁺ efflux equals Na⁺ influx, so the membrane potential stops rising and is poised to repolarize.

Question 44

What causes the membrane to repolarize after the action potential peak?

Answer 44

Cause: K⁺ efflux through open potassium channels now exceeds Na⁺ influx (as sodium channels are inactivating). Result: The net outward flow of positive charge makes the inside of the cell more negative, driving the falling phase of the action potential.

Question 45

What is afterhyperpolarization, and what causes it?

Answer 45

Definition: The period when the membrane potential becomes more negative than the original resting potential after an action potential. Cause: Voltage-gated potassium channels inactivate very slowly, so they remain open and continue K⁺ efflux even after the membrane has repolarized to the resting level.

Question 46

How is the voltage clamp technique used to study action potential currents?

Answer 46

Method: A neuron is held at a negative potential (e.g., -75 mV), and the voltage is suddenly stepped to a depolarized level (e.g., 0 mV). Observation: This reveals two distinct currents: a fast, transient inward current followed by a slower, sustained outward current.

Question 47

How can you prove that the delayed outward current is carried by potassium channels?

Answer 47

Method: Apply Tetraethylammonium (TEA), a potassium channel blocker. Result: The delayed outward current is lost, but the fast inward current remains. Conclusion: The outward current is mediated by voltage-gated potassium channels.

Question 48

How can you prove that the fast inward current is carried by sodium channels?

Answer 48

Method: Apply Tetrodotoxin (TTX), a sodium channel blocker. Result: The fast inward current is immediately blocked, but the delayed outward current remains. Conclusion: The inward current is mediated by voltage-gated sodium channels (VGSCs).

Question 49

What is the key conclusion from using TTX and TEA together in a voltage clamp experiment?

Answer 49

Conclusion: The action potential consists of two separate, sequential currents: A fast, TTX-sensitive Na⁺ inward current. A slow, TEA-sensitive K⁺ outward current. These currents can be isolated and studied independently using these specific toxins.

Question 50

What is the absolute refractory period, and why is it impossible to generate another action potential during this time?

Answer 50

Definition: The period from the start of an action potential until the end of repolarization when it is absolutely impossible to trigger a second action potential. Cause: Voltage-gated sodium channels (VGSCs) are inactivated. No matter how much you depolarize the membrane, there are not enough available VGSCs to open and initiate the positive feedback loop.

Question 51

What is the relative refractory period, and why does it occur?

Answer 51

Definition: The period following the absolute refractory period when a second action potential can be generated, but only with a stronger-than-normal stimulus. Cause: The membrane is repolarized, but many VGSCs are still recovering from inactivation. The pool of available VGSCs is smaller, so a larger depolarization is needed to open enough of them to reach threshold.

Question 52

What is the key difference in the state of voltage-gated sodium channels (VGSCs) between the absolute and relative refractory periods?

Answer 52

Absolute Refractory Period: VGSCs are in the inactivated state and cannot be opened. Relative Refractory Period: VGSCs are recovering from inactivation. Some are available, but many are still inactivated, reducing the total number that can be recruited.

Question 53

What are the two components that allow an action potential to propagate along an axon?

Answer 53

Passive Component: The electrotonic (passive) spread of depolarization from the active segment to the adjacent segment. Active Component: The opening of voltage-gated sodium channels (VGSCs) in the adjacent segment, which amplifies the signal into a full action potential via a positive feedback loop.

Question 54

Why does an action potential propagate over long distances without getting smaller (without decrement)?

Answer 54

Reason: The active component (VGSCs) boosts the signal at every point along the axon. Result: The depolarization is regenerated to its full amplitude in each new axonal segment, preventing any decay in size.

Question 55

Why does an action potential normally propagate in only one direction along the axon?

Answer 55

Reason: The refractory period of the segment that just fired. Mechanism: While depolarization spreads passively in both directions, the segment behind the action potential is in its absolute refractory period (VGSCs are inactivated) and cannot generate a new action potential. Only the segment ahead can fire.

Question 56

What determines the speed of action potential conduction?

Answer 56

Active Component: The positive feedback of VGSC opening is inherently fast. Limiting Factor: The speed is largely determined by the passive, electrotonic conduction from one segment to the next, which depends on the axon's physical properties (e.g., diameter, myelination).

Question 57

Why is the conduction velocity of an action potential so important for the nervous system?

Answer 57

Significance: It limits the flow of information within the nervous system. Example - Need for Speed: A fast reflex (like pulling your hand from a hot surface) requires sensory information to reach the brain/spinal cord extremely quickly to limit tissue damage. Example - Less Critical: Chronic pain signals do not require the same speed; their purpose is a slow, persistent reminder (e.g., to prevent over-exercising an injured knee).

Question 58

How does increasing the diameter of an axon increase its conduction velocity?

Answer 58

Mechanism: A larger diameter dramatically lowers the axial resistance (rₐ) inside the axon. Result: This leads to a larger length constant (λ), meaning the passive electrotonic spread of depolarization travels farther and faster, speeding up the overall propagation.

Question 59

What is the primary mechanism vertebrates use to achieve high conduction velocity without needing enormous axon diameters?

Answer 59

Mechanism: Myelination. Benefit: Myelination is a highly effective adaptation that greatly speeds up conduction velocity without a massive increase in the physical size (diameter) of the axon.

Question 60

Which cells form myelin in the central (CNS) and peripheral (PNS) nervous systems, and what is the primary function of the myelin sheath?

Answer 60

Cells: CNS:Oligodendrocytes PNS: Schwann Cells Function: They wrap their processes around an axon to form myelin, a stack of lipid bilayers that insulates the axon, separating the axonal cytoplasm from the extracellular environment.

Question 61

What are the names for the myelinated and unmyelinated segments of an axon?

Answer 61

Myelinated Segments: Internodal Regions (covered by myelin, 0.3 - 2 mm long). Unmyelinated Gaps: Nodes of Ranvier (small, bare regions of axon between myelin sheaths, ~2 μm wide)

Question 62

How does myelination alter the distribution of ion channels along the axon?

Answer 62

At the Nodes of Ranvier: The concentration of voltage-gated sodium (Na⁺) and potassium (K⁺) channels is very high. In the Internodal Regions: The density of ion channels becomes very low, as they are displaced from beneath the myelin sheath.

Question 63

How does the myelin sheath improve the passive (electrotonic) conduction of a signal along the axon?

Answer 63

Increased Membrane Resistance (rₘ): Myelin acts as an insulator, reducing ion leakage. This results in a larger length constant (λ), meaning the signal can travel farther before decaying. Decreased Membrane Capacitance: Myelin reduces the ability to store charge across the membrane. This allows the voltage to change much faster in response to a current.

Question 64

What is "saltatory conduction," and what makes it possible?

Answer 64

Definition: The process where an action potential "jumps" from one Node of Ranvier to the next. Mechanism: Active Regeneration: Voltage-gated sodium channels are only at the nodes. The action potential is actively regenerated at each node. Fast, Passive Spread: In between nodes, the signal travels very quickly via fast, passive electrotonic conduction through the insulated internodal segments.

Question 65

What are the two main advantages of saltatory conduction?

Answer 65

Increased Speed: Conduction is much faster because the signal jumps long distances instead of regenerating at every tiny segment of the axon. Energy Efficiency: The axon only needs to actively pump ions at the widely spaced nodes of Ranvier, not along the entire length.

Question 66

What is a "mixed" nerve, and what is the range of conduction velocities found within it?

Answer 66

Definition: A nerve that consists of a mixture of unmyelinated axons and myelinated axons of various diameters. Velocity Range: Conduction velocities vary widely, from 0.1 m/s (small unmyelinated C fibers) to 120 m/s (large, myelinated A-alpha fibers).

Question 67

How do the diameter and myelination of nerve fibers affect their conduction velocity and function? Provide examples.

Answer 67

Fastest (A-alpha fibers): Large diameter and myelinated. (e.g., carry proprioceptive information). Intermediate (A-beta/delta): Myelinated but smaller diameter. Slowest (C fibers): Unmyelinated and small diameter. (e.g., relay chronic pain).

Question 68

How is nerve conduction velocity measured clinically, and why is it an important diagnostic tool?

Answer 68

Method: An electrical stimulus is applied to a nerve, and the resulting depolarization is recorded further along the nerve to calculate speed. Importance: It is a key diagnostic tool for detecting peripheral neuropathies and demyelinating diseases.

Question 69

What is the effect of demyelination on nerve conduction, and what is a primary example?

Answer 69

Effect: Demyelination causes a slowing of conduction velocity and can eventually lead to complete propagation failure of action potentials. Example: Multiple Sclerosis (MS), an autoimmune disease where the immune system attacks and degrades myelin. This is detected by a decrease in the number of fast-conducting fibers.