Neuronal Summation and Action Potentials Notes

Temporal summation

• Two ways to add synaptic inputs to the postsynaptic neuron: temporal summation and spatial summation.
• Temporal summation (focus of this slide): inputs from the same presynaptic neuron arriving in quick succession can summate.
  • Four neurons are shown (A, B green for EPSP, C for IPSP; postsynaptic neuron D in yellow).
  • EPSP = excitatory postsynaptic potential, a depolarizing graded potential.
  • IPSP = inhibitory postsynaptic potential, a hyperpolarizing graded potential.
  • In the example, neuron A fires, releasing neurotransmitter, and then fires again very soon after.
  • If two EPSPs from the same neuron occur in rapid succession, they sum to push the membrane potential toward threshold.
  • If A fired alone (first image) and nothing follows, the membrane depolarizes briefly and returns to rest before any subsequent signal.
  • If two signals occur in quick succession (second image on the right), the depolarizations add up, potentially triggering an action potential.
  • Analogy: sending an email, then sending another one right after; both may be received and processed together, amplifying the response.
• Threshold concept in temporal summation:
  • The postsynaptic neuron must reach a threshold to fire an action potential.
  • Threshold is given as approximately $V_{ ext{th}} \,\approx\,-55\text{ mV}$ (some sources use -50 mV; either value is acceptable in this context).
• Numerical example for temporal summation:
  • If two EPSPs occur close in time and from the same neuron, they sum; for example, an EPSP of $10\text{ mV}$ and another of $20\text{ mV}$ from the same neuron sum to $30\text{ mV}$.
  • Starting from rest $V_{ ext{rest}} = -70\text{ mV}$, a total depolarization of $+30\text{ mV}$ would bring the membrane potential to $V = -70\text{ mV} + 30\text{ mV} = -40\text{ mV}$, which exceeds threshold and can trigger an action potential.
• Action potentials are large, rapid changes in membrane potential; see the AP description below.

Spatial summation

• Spatial summation involves inputs arriving at the postsynaptic neuron from different presynaptic neurons at the same time.
  • The first example (A and B) shows two EPSPs summing to reach threshold.
  • The second example (A and C) shows two signals with opposite effects: EPSP (depolarizing) from A and IPSP (hyperpolarizing) from C; these can cancel each other out.
  • Important condition: stimuli must come from different presynaptic neurons located in different spatial positions around the postsynaptic neuron.
• Simple arithmetic example for spatial summation:
  • If neuron A causes an EPSP of $10\text{ mV}$ and neuron B causes an EPSP of $20\text{ mV}$, the total depolarization is $10 + 20 = 30\text{ mV}$, which can push from $-70\text{ mV}$ to $-40\text{ mV}$, surpassing threshold.

Action potentials (APs): overview

• Action potentials are large, rapid changes in membrane potential.
• Magnitude: about $100\text{ mV}$ change from rest to peak: from $V<em>{ ext{rest}} = -70\text{ mV}$ to a peak around $V</em>{ ext{peak}} \approx +30\text{ mV}$.
• Time scale: approximately $t_{ ext{AP}} \approx 4\text{ ms}$.
• APs travel along the axon to the synaptic terminal; initiation requires the axon hillock to reach threshold.
• Voltage-gated ion channels are essential for APs.
• Nobel Prize (1963) awarded to Hodgkin, Huxley, and Eccles for their work on action potentials in the giant squid axon; discovery highlighted the roles of Na+ and K+ ions in nerve signaling.
• The giant squid axon used in experiments can be as large as $\sim 1\ \text{mm}$ in diameter, facilitating experimental access.
• A related video/animation demonstrates sodium and potassium channel dynamics (blue: Na+ permeability increasing as Na+ channels open; ENa ≈ $+60\ ext{ mV}$; peak AP near +30 mV due to Na+ channel inactivation and K+ conductance).
• Key terms:
  • AP abbreviation: AP = action potential.
  • VG = voltage-gated (ion channels).
  • Resting potential commonly around $V_{ ext{rest}} = -70\text{ mV}$.
  • Threshold around $V_{ ext{th}} \approx -55\text{ mV}$.

Phases of the action potential

• Depolarization phase:
  • Caused by rapid opening of voltage-gated sodium channels.
  • This creates a positive feedback loop: some Na+ channels open, causing depolarization, which opens more Na+ channels, and so on.
  • Analogy: standing ovation at a concert—initial few rise, prompting others to stand in response.
  • Sodium entry during depolarization is driven by both concentration and electrical gradients; the driving force is greatest when channels open.
  • Na+ equilibrium potential is approximately $E_{ ext{Na}} \approx +60\text{ mV}$, but the membrane potential peaks around $+30\text{ mV}$ because Na+ channels inactivate.
• Na+ channel inactivation and peak:
  • Voltage-gated Na+ channels possess an activation gate (fast to open) and an inactivation gate (slow to close).
  • The inactivation gate closes during depolarization, preventing further Na+ influx, which helps cap the peak at around $+30\text{ mV}$.
  • The channel can be in three states: closed (resting), open, and inactivated.
• Repolarization phase:
  • As the Na+ channels inactivate, voltage-gated K+ channels begin to open (but do so more slowly), allowing K+ to exit the cell.
  • This outward K+ current drives the membrane potential back toward rest, causing repolarization.
• Hyperpolarization phase:
  • Potassium conductance remains elevated after the initial repolarization, causing an undershoot toward the potassium equilibrium potential.
  • The membrane potential approaches the typical EK of about $E_K \approx -90\text{ mV}$ during hyperpolarization.
• Return to resting state:
  • The Na+/K+ pump functions to restore ion gradients and membrane potential to the resting level: it moves $3\ Na^+$ out and $2\ K^+$ in per cycle.
  • This helps reset the neuron to $V_{ ext{rest}} = -70\text{ mV}$ and ready for another potential AP.

Voltage-gated sodium channel: detailed mechanics

• The sodium channel has two gates:
  • Activation gate: fast to open; contributes to rapid depolarization.
  • Inactivation gate: slow to close; terminates depolarization by stopping Na+ influx.
• The channel is voltage-dependent and time-dependent.
• Three states of the VG Na+ channel:
  • Closed (resting) state.
  • Open state (sodium influx occurs).
  • Inactivated state (pore blocked, prevents Na+ entry even if depolarization continues).
• As AP proceeds, channels cycle through these states to shape the AP.

Practical implications and practice tips mentioned in the transcript

• Practice drawing an action potential with the correct timescale (~4 ms) and voltage changes (rest to threshold to peak to rest).
• When labeling the AP, indicate the threshold line (often around $V_{ ext{th}} \approx -55\text{ mV}$) and the peaks relative to rest.
• Remember the typical sequence: resting potential (-70 mV) → depolarization (to about +30 mV) via Na+ influx → inactivation of Na+ channels → repolarization via K+ efflux → hyperpolarization toward ~-90 mV → Na+/K+ pump returns the cell to resting potential.

Key quantities and references to remember

• Resting membrane potential: $V_{ ext{rest}} = -70\text{ mV}$
• Threshold potential: $V_{ ext{th}} \approx -55\text{ mV}$ (range around -50 to -55 mV in textbooks)
• Action potential peak: $V_{ ext{peak}} \approx +30\text{ mV}$
• Na+ equilibrium potential: $E_{ ext{Na}} \approx +60\text{ mV}$
• K+ equilibrium potential: $E_K \approx -90\text{ mV}$
• AP duration: $t_{ ext{AP}} \approx 4\text{ ms}$
• AP amplitude change: from $V<em>{ ext{rest}} = -70\text{ mV}$ to $V</em>{ ext{peak}} \approx +30\text{ mV}$, for a total change of $\Delta V = V<em>{ ext{peak}} - V</em>{ ext{rest}} = 30 - (-70) = 100\text{ mV}$
• Ion pump mechanism: $3\ Na^+\ text{ out}, 2\ K^+\ text{ in}$ via the Na+/K+-ATPase.

Historical and conceptual context

• The discovery of voltage-gated ion channels and the ionic basis of the action potential was awarded the Nobel Prize in Physiology or Medicine in 1963 to Alan Hodgkin, Andrew Huxley, and Sir John Eccles for work on the giant squid axon, demonstrating the roles of Na+ and K+ in nerve signaling.
• The giant squid axon provided a tractable model due to its large diameter (~$1\ \text{mm}$), enabling direct electrophysiological measurements.

Connections to broader principles

• The all-or-none nature of the AP depends on reaching the threshold at the axon hillock and the activation/inactivation dynamics of voltage-gated Na+ channels.
• Temporal and spatial summation are fundamental principles that determine whether a neuron reaches threshold and fires an AP.
• The balance of EPSPs and IPSPs, their timing, and spatial distribution govern neural integration and network behavior.
• The gating mechanics illustrate how voltage dependence and time dependence together shape rapid signaling in neurons.

Quick reference glossary

• EPSP: excitatory postsynaptic potential; depolarizing input.
• IPSP: inhibitory postsynaptic potential; hyperpolarizing input.
• VG: voltage-gated.
• AP: action potential.
• ENa: Na+ equilibrium potential; EK: K+ equilibrium potential.
• Threshold: the membrane potential at which an AP is triggered.
• Resting potential: baseline membrane potential when the neuron is not firing.
• Hyperpolarization: membrane potential briefly becoming more negative than the resting potential.
• Depolarization: membrane potential becoming less negative (more positive).
• Na+/K+ pump: maintains ion gradients by moving 3 Na+ out and 2 K+ in per cycle.