Problems: Module 2

Non-excitable membranes simply have a membrane potential; it exists but does not drive their function. Excitable membranes are designed to let that potential fluctuate deliberately, and the fluctuation is how the cell does its job. One point per side, so describing only one type scores half. (slide 3)

Pressure sensors: anatomically visceral receptors, functionally baroreceptors. (slides 7–8)

Heart rate command: motor, autonomic, sympathetic.

Hot metal: anatomically somatic receptors, functionally thermoreceptors.

Route into the CNS: sensory, or afferent.

Leg commands: motor, somatic.

Electrochemical equilibrium is the membrane potential at which the chemical driving force and the electrical driving force offset each other in opposite directions. Neither gradient is zero, and the concentrations are not equal; the two forces simply cancel, so there is no net movement. (slides 12–14)

One point per blank. The diagram is not reproduced here, so learn what each feature looks like on a trace instead.

slides 29–39

Each Nernst potential is 3 points: 1 for the answer, 2 for work. Watch the sign of z for chloride. (slide 14)

Chord conductance is 7 points: 2 for work, 1 per ionic term, 1 for V_m, 1 for the gap. (slide 23)

Hypokalemia: lower outside K⁺ enlarges the concentration gradient, so more K⁺ leaves, leaving the inside more negative. V_m becomes more negative.

Hyperkalemia: higher outside K⁺ shrinks the gradient, so less K⁺ leaves and more positive charge stays inside. V_m becomes less negative. Each prediction is 2 points and each rationale 2 points, and rationale scores even if the prediction is wrong.

Why it’s dangerous: a smaller gap means threshold is easier to reach, so the membrane is more excitable. Too small and it becomes irritable, firing at inappropriate times, giving hyper-reactive nerve signaling and cardiac arrhythmias. A larger gap means less excitable.

Ouabain (3): V_m becomes less negative, but only gradually, because K⁺ leak channels carry most of the resting conductance and the pump contributes modestly. (slide 22)

Electrogenic (2): it moves Na⁺ out and K⁺ in, but lopsidedly, 3 out for 2 in, so the inside loses one net positive charge per cycle.

No equilibrium (1): the pumps keep carrying K⁺ back in, restoring the gradient the leak channels dissipate.

Amplitude: decays with distance, because nothing boosts or refreshes it once initiated. (slide 31)

Refractory: none at all, because graded potentials do not use channels with inactivation gates, which are what make refractory periods. (slides 38–40)

Threshold: none required to start one. (slides 29–30)

X three times: temporal summation, 3 × 4 = +12 mV.

X and Y together: spatial summation, +4 − 5 = −1 mV. (slide 32)

Dendrite (4): λ is small, because graded potentials decay quickly and are subthreshold by the axon hillock. With r_i roughly fixed, a small λ requires a small r_m, meaning a leaky membrane that loses current as the signal travels. (slide 31)

Myelin (2): raises r_m, since the wrapping stops ions leaking across the membrane. (slide 41)

Distance (3): unmyelinated axons leak current quickly, so it falls below threshold over a short distance and the action potential must regenerate at every adjacent patch. In myelinated axons the high r_m raises λ, so current travels much farther above threshold and regenerates only at the nodes of Ranvier. (slides 40–41)

Absolute (2): activation gate open, inactivation gate closed. The channel cannot open again until it resets, no matter how strong the stimulus. (slides 38–39)

Relative (1): the membrane is hyperpolarized, so the gap to threshold is larger and the membrane less excitable.

Mid-axon (2): propagates in both directions, because there is no trailing patch of refractory membrane to block one side. (slide 40)

Coding (2): refractory periods cap the firing rate so action potentials stay distinct. Without them, they would merge like summing graded potentials and the brain could not read their frequency.

Cooling (3): slower gates lengthen the absolute refractory period, which lowers maximum firing frequency, so the brain perceives the cold as less intense. The beginning of numbing.

Terminal (2): voltage-gated Ca²⁺ channels, Ca²⁺ flowing in. (slide 43)

Toxin (2): neurotransmission is blocked, so the skeletal muscle cell is never stimulated and cannot contract. (slide 44)

Receptors (4): ligand-gated ion channels on a neuron, G protein-coupled receptors on cardiac muscle. The ligand-gated channel is faster because far fewer steps must happen. (Module 1 slide 16)

Mixed channel (4): net EPSP. Ion flow is proportional to V_m − E_X. At V_m ≈ −70 mV, E_Na ≈ +60 mV sits 130 mV away while E_K ≈ −90 mV sits only 20 mV away, so far more Na⁺ enters than K⁺ leaves. (slide 16)

Na⁺ permeability rises steeply right at threshold and peaks with the action potential, because voltage-gated Na⁺ channels respond almost instantly. It falls as the channels inactivate at the peak.

K⁺ permeability rises later and more gradually and stays elevated after the spike, because K⁺ channels are slow to open and slow to close.

Overshoot: K⁺ keeps leaving while its channels are still open after repolarization, so V_m dips below −70 mV until they close.

Relative refractory period: Na⁺ channels are resetting one by one and the membrane is hyperpolarized, so the gap between V_m and threshold (−55 mV on the figure) is larger. A larger-than-normal stimulus is needed to close it. (M2 slide 39)

(a) The lines cross near 1 µm. Above that diameter myelinated axons conduct much faster, reaching about 50 m/s at 10 µm against under 10 m/s unmyelinated. Below it myelin gives no advantage, which is why the thinnest axons are left unmyelinated.

(b) The large-diameter axon has λ = 3 mm and a low internal resistance r_a; the small axon has λ = 1 mm and a high r_a. Lower internal resistance lets passive current travel farther before decaying to 37%, so thicker axons conduct faster.

(c) Velocity rises steeply with temperature, reaching about 5× the 20°C baseline near 40°C, because warmth speeds diffusion of ions. Past about 40–45°C the curves crash to zero: heat beyond physiological limits stops conduction. (M2 slide 42)

1: A fires twice with a long gap. Each EPSP decays before the next arrives, so they do not add.

2: A fires twice in quick succession. Temporal summation stacks the second EPSP on the first.

3: A and B fire together. Spatial summation adds the two EPSPs.

4: A A B B in rapid succession combines both kinds of summation, the depolarization reaches threshold at the axon hillock, and an action potential fires.

5: C alone gives an IPSP (downward). A + C together cancel, so V_m barely changes. Summation applies to IPSPs too. (M2 slide 32)

z = +2 halves the constant. V_m is more negative than E_Ca, so Ca²⁺ flows into the cell, with chemical and electrical gradients both pointing in.

The gap widened from 24.4 mV, so the membrane is less excitable. A larger stimulus is needed to reach threshold.

More excitable than baseline (24.4), less than at 8.0 mM (15.6).

The ion with the most open channels pulls V_m toward its Nernst potential. Matching Na⁺ to K⁺ depolarizes the cell by almost 60 mV.

(a) Temporal summation: 5 × 3 = +15 mV.

(b) Spatial summation: 3 + 3 − 4 = +2 mV.

(c) −70 + 15 = −55 mV. It reaches threshold, so yes. Threshold is “meets or exceeds.”

The length constant doubles. Passive current travels twice as far before decaying to 37%.

It has almost no affinity for resting, closed Na⁺ channels. It binds open (depolarizing) and inactivated (repolarizing) voltage-gated Na⁺ channels, blocking further Na⁺ influx. The pain neuron cannot depolarize, so pain signals stop reaching the brain. From the Assignment 2 key, Track 1.

Both give a net EPSP. The muscle case is more lopsided because its V_m sits closer to E_K.

False. Both gradients are still present, equal in strength and opposite in direction, so there is no net movement. (slides 12–14)

Its job is to change voltage on purpose. Precise control over which ions cross, when, and how fast takes many channel types: leak channels to set rest, ligand-gated channels for graded potentials, voltage-gated channels for action potentials. A non-excitable membrane only needs a steady potential. (M2 slide 3)

Depolarization (up): positive ions enter, as Na⁺ influx. Hyperpolarization (down below baseline): positive ions leave or negative ions enter, as K⁺ efflux or Cl⁻ influx. Repolarization: return to baseline, typically K⁺ efflux after a depolarization. (M2 slide 3)

Pain receptors in the fingertip (somatic receptors) → sensory, afferent neurons → CNS (spinal cord and brain) integrates → somatic motor, efferent neurons → skeletal muscle (effector) pulls the hand away. (M2 slide 7)

Both are structures sensitive to their environment. Module 1: a membrane protein that binds a ligand, such as a G protein-coupled receptor binding norepinephrine. Module 2: a specialized cell that turns a stimulus into an electrical signal, such as a thermoreceptor or baroreceptor. (M2 slide 8)

Na⁺: chemical in (more outside), electrical in (positive ion drawn to the negative inside), electrochemical strongly in. K⁺: chemical out (more inside), electrical in, electrochemical out because the chemical gradient is slightly stronger. (M2 slide 12)

E_K becomes less negative. K⁺ dominates resting conductance, so resting potential moves the same way: less negative, closer to threshold, more excitable. (M2 slides 14, 23)

It assumes the membrane is permeable to only one ion. Real membranes are permeable to several ions at once. Nernst potentials are still useful because they show which way each ion wants to move at a given V_m, and the chord conductance and Goldman equations are built from them. (M2 slide 15)

Driving force is V_m − E_Cl = −70 − (−47) = −23 mV. The inside is more negative than chloride’s equilibrium, so electrical repulsion of the negative ion outweighs its inward chemical gradient and Cl⁻ moves out. The lecture’s “more negative than E_X means it flows in” rule is written for cations; flip it for an anion. (M2 slide 16)

K⁺ leak channels: many, always open, steady K⁺ loss makes the inside negative. The main contributor. Na⁺ leak channels: few, a small trickle in that keeps V_m slightly above E_K. Na⁺-K⁺ pump: restores the gradients and, being electrogenic (3 out, 2 in), adds a little negativity. (M2 slide 22)

Each term is weighted by that ion’s share of total conductance, and at rest most open channels are K⁺ leak channels, so K⁺'s weight is about 0.70. If g_Na matched g_K, the two weights would be equal and V_m would land between E_K and E_Na: in the Assignment 2 neuron, about −21 mV, a large depolarization. (M2 slide 23)

Spatial summation of an EPSP and an IPSP. If they are equal in size they cancel and V_m barely changes; otherwise the net change is their sum (for +4 and −5 mV, −1 mV). (M2 slides 30, 32)

Graded potentials decay with distance because nothing refreshes them. A signal far out on a dendrite has more membrane to cross before reaching the axon hillock, so it arrives smaller and is less likely to meet threshold. (M2 slide 31)

Spatial: several synapses fire at the same time. Temporal: one synapse fires repeatedly before earlier potentials decay. Both together: two excitatory terminals each firing in rapid bursts, as in panel 4 of slide 32 (A A B B), which reaches threshold. (M2 slide 32)

Rest: both closed, Na⁺ channels resting and ready. Threshold: Na⁺ channels begin opening, K⁺ still closed. Depolarization: many Na⁺ open, K⁺ closed. Peak (+30 mV): Na⁺ inactivating, K⁺ finally opening. Repolarization and hyperpolarization: Na⁺ inactivated then resetting, K⁺ open then slowly closing. (M2 slide 38)

Voltage-gated K⁺ channels are slow to close. K⁺ keeps leaving after V_m reaches resting, carrying it below −70 mV until the channels close. (M2 slides 38–39)

At the peak, Na⁺ channels close with the activation gate open and the inactivation gate closed. In that state they cannot open again whatever the voltage or stimulus strength. Only when they reset to resting and ready (activation closed, inactivation open) can a new action potential start. (M2 slides 38–39)

Na⁺ spreading from an active patch reaches both neighbors, but the patch behind is still refractory and cannot fire. Only the patch ahead can, so the signal moves away from the axon hillock. (M2 slide 40)

Velocity falls sharply. Without myelin, membrane resistance drops, current leaks out, the length constant shrinks, and the action potential must regenerate at every patch of membrane. Voltage-gated channels are concentrated at the nodes, so a stripped internode may fail to conduct at all. (M2 slides 41–42)

Thick and myelinated fastest, then thin and myelinated, then thick and unmyelinated, assuming the thin axon is above about 1 µm where myelin helps and temperature is equal. Myelin gives the largest gain (10–150 against 0.5–2 m/s); diameter adds to it. (M2 slides 41–42)

The action potential only opens voltage-gated Ca²⁺ channels at the terminal. Ca²⁺ entry is the signal for vesicles to undergo exocytosis. Block the channels and the electrical signal never becomes a chemical one, so nothing reaches the next cell. (M2 slide 43)