Difficulty: Intermediate to Advanced | Prerequisites: Basic cell biology, understanding of ion gradients, familiarity with membrane structure and protein channels
This block of lectures covers the electrical behaviour of neurons: how they maintain a resting voltage, how they generate local signals (graded potentials), and how they fire all-or-none action potentials that travel long distances without losing strength. This is foundational for everything that follows in the nervous system portion of the course, from synaptic transmission to sensory processing. If you understand resting membrane potential, the Nernst equation, the Goldman equation and the sequence of channel events during an action potential, you have the toolkit for the rest of neuroscience in BIO 225.
Neurons maintain a resting membrane potential of roughly -70 mV, set mainly by K+ leak channels. The Nernst equation gives the equilibrium potential for a single ion; the Goldman equation accounts for multiple ions and their permeabilities. Graded potentials are local, proportional signals in dendrites and cell bodies. Action potentials are all-or-none, long-distance signals in axons, driven by the sequential opening of voltage-gated Na+ then K+ channels. Myelination speeds conduction via saltatory conduction.
Membrane potential (Vm)
The voltage difference across a cell membrane, measured in millivolts (mV). Inside of the cell is negative relative to outside. Think of it as the electrical "charge" the cell maintains across its boundary.
Equilibrium potential (Eion) / reversal potential
The membrane potential at which there is zero net flow of a particular ion. Also the voltage at which the direction of ion flow reverses. In simple terms, it is the voltage where a specific ion is perfectly balanced between its concentration gradient pulling it one way and the electrical gradient pulling the other.
Nernst equation
Calculates the equilibrium potential for a single ion based on its concentration gradient across the membrane: Eion = (61.5/z) x log([X]outside / [X]inside) at body temperature.
Goldman equation
Extends the Nernst equation to account for multiple ions and their relative permeabilities, giving the overall membrane potential. The membrane potential moves towards the equilibrium potential of whichever ion the membrane is most permeable to.
Resting membrane potential (RMP)
The membrane potential of a neuron at rest, approximately -70 mV. Maintained primarily by K+ leak channels, with a small contribution from Na+ leak channels and the Na+/K+ pump.
Depolarisation
A change in membrane potential that makes the inside of the cell less negative (more positive). Typically caused by Na+ entry or Cl- exit.
Hyperpolarisation
A change in membrane potential that makes the inside more negative than the resting potential. Caused by K+ exit or Cl- entry.
Repolarisation
Return of the membrane potential back towards the resting value after depolarisation.
Graded potential
A local, proportional change in membrane potential in dendrites and cell bodies. Varies in magnitude with stimulus strength. Decays over distance.
Action potential (AP)
An all-or-none electrical signal that propagates along axons without losing amplitude. Triggered when depolarisation reaches threshold (about -55 mV).
Threshold potential
The membrane potential (roughly -55 mV) that must be reached to trigger an action potential by activating voltage-gated Na+ channels.
Voltage-gated Na+ channel (NaV)
Opens at threshold, allowing rapid Na+ influx (depolarisation). Has two gates: an activation gate (opens at threshold) and an inactivation gate (closes near the peak of the AP, from the cytoplasmic side via a ball-and-chain mechanism).
Voltage-gated K+ channel (KV)
Opens shortly after NaV channels, allowing K+ efflux (repolarisation and hyperpolarisation). Slow to close, which causes the after-hyperpolarisation.
Absolute refractory period
The time during which no stimulus, regardless of strength, can trigger another action potential. Corresponds to NaV channel inactivation.
Relative refractory period
The time during which a stronger-than-normal stimulus is required to trigger an AP. Corresponds to the hyperpolarisation phase.
Myelin sheath
Insulation around axons formed by Schwann cells (PNS) or oligodendrocytes (CNS). Increases the length constant and restricts APs to the nodes of Ranvier.
Saltatory conduction
The "jumping" of action potentials from node to node along a myelinated axon. Faster than continuous conduction.
Electrotonic spread
Passive, local spread of an electrical signal along a neuronal membrane. The signal dissipates with distance. This is how current moves through myelinated internodes.
EPSP (excitatory post-synaptic potential)
A graded depolarisation that increases the likelihood of reaching threshold. Example: ligand-gated Na+ channels opening.
IPSP (inhibitory post-synaptic potential)
A graded hyperpolarisation that decreases the likelihood of reaching threshold. Example: ligand-gated Cl- channels opening.
Structural parts of a neuron:
Dendrites: receive incoming signals (majority of signal reception)
Cell body (soma): contains the nucleus, ER and other organelles
Axon hillock: where signals from many dendrites are integrated
Axon: conducts the action potential. Myelin (Schwann cells) speeds propagation.
Axon terminal: where neurotransmitters are released
Synapse: junction between neurons where NTs are released and bind to postsynaptic receptors
Structural classification:
Multipolar: many processes from cell body, multiple dendrites and one axon (classic neuron shape)
Bipolar: cell body in the middle, one dendritic process and one axonal process
Unipolar / pseudounipolar: one main process from the cell body, with the axon extending in both directions. Somatosensory neurons are typically this type.
Functional classification:
Sensory (afferent) neurons: transmit sensory information from receptors to the CNS. Structure varies by sensory system.
Interneurons: connect neurons to one another. Often short, unmyelinated axons with complex dendrites.
Motor (efferent) neurons: carry impulses from the CNS to effector organs (muscles or glands). Cell bodies in the CNS with long, myelinated axons.
Excitable cells (neurons and muscles) depend on the movement of ions across membranes. Some ions are distributed unequally, and at rest, facilitated diffusion of these ions creates the membrane potential.
Typical neuron ion concentrations:
Ion | Cytoplasmic (mM) | Extracellular (mM) | More... |
|---|---|---|---|
K+ | 400 | 20 | Inside |
Na+ | 50 | 440 | Outside |
Cl- | 51 | 560 | Outside |
Organic anions (A-) | 385 | 0 | Inside (large, impermeable) |
The membrane potential arises because separated charges accumulate along the membrane surfaces. The plasma membrane acts as a capacitor: it stores electrical energy by accumulating charges on two closely spaced, insulated surfaces.
Electrochemical gradient = chemical gradient (concentration) + electrical gradient (voltage). Both forces act on each ion simultaneously. Whether an ion moves in or out depends on the net electrochemical gradient, not just one component.
Nernst equation (for a single ion):
E_{ion} = \frac{61.5}{z} \times \log \frac{[X]_{outside}}{[X]_{inside}}Where R = ideal gas constant (8.315 J/K·mol), T = temperature in Kelvin, z = ion valence, F = Faraday's constant (96,485 J/V·mol), [X] = molar concentration.
Sample calculation for K+: Xo = 40 mM, Xi = 400 mM
Eion = 61.5 / (+1) x log(40/400) = 61.5 x (-1) = -61.5 mV
The equilibrium potential predicts the voltage required to balance the concentration gradient. The direction of ion movement is determined by comparing Eion with the membrane potential (Vm):
If Vm is more positive than Eion, the ion moves in whichever direction makes Vm more negative (towards Eion)
If Vm is more negative than Eion, the ion moves to make Vm more positive (towards Eion)
Ions CAN flow against their concentration gradient via facilitated diffusion if the electrical gradient exceeds the concentration gradient
Goldman equation (for multiple ions):
Accounts for the permeability and concentration of K+, Na+ and Cl- simultaneously. The key principle: the membrane potential always moves towards the equilibrium potential of the ion the membrane is most permeable to.
At rest, permeability to K+ is far greater than to Na+, so the RMP sits close to EK+ but not quite there, because a small Na+ permeability pulls it slightly positive.
The resting membrane potential (approximately -70 mV) is an actively maintained, dynamic equilibrium. Three factors contribute:
Distribution of ions near the plasma membrane: more positive charge outside, more negative charge inside, especially from large, impermeable organic anions (A-)
Na+/K+ pump: contributes only -2 to -5 mV directly, but its indirect effect is critical: it maintains the ionic gradients by active transport (3 Na+ out, 2 K+ in per cycle)
Leak channels (the prominent determinant): constitutively active channels that allow facilitated diffusion ("leak currents") based on steep gradients. There are many more K+ leak channels than Na+ leak channels.
Because PK >> PNa at rest, the RMP approaches (but does not reach) the K+ equilibrium potential. The small Na+ permeability is what prevents the RMP from sitting exactly at EK+ (around -80 mV) and instead holds it at about -70 mV.
At rest, neurons have essentially no permeability to Cl-.
Critical principle: changes in membrane potential come from changes in membrane permeability, not from changes in ion concentration. When channels open, the number of ions that move is too small to alter concentration gradients meaningfully. What changes is which ion's equilibrium potential dominates the Goldman equation.
Graded potentials:
Occur in dendrites and cell bodies
Proportional to stimulus strength (graded)
Transient, local, short-distance signals that lose strength with distance
Caused by ligand-gated ion channels: stronger signal (more neurotransmitter) = larger change in Vm
Can be excitatory (EPSP, e.g. Na+ channels) or inhibitory (IPSP, e.g. Cl- channels)
Length constant (lambda): the distance a graded/electrotonic signal can spread. Lambda = sqrt(rm / ri), where rm = membrane resistance and ri = intracellular resistance.
Summation:
Temporal summation: multiple signals arriving at the same location over time add together
Spatial summation: signals arriving at the same time but at different locations on the membrane add together
Threshold and the axon hillock:
The axon hillock is densely packed with voltage-gated Na+ and K+ channels. If the sum of graded potentials at the axon hillock depolarises the membrane past threshold (about -55 mV), an action potential is initiated. Subthreshold depolarisation does not trigger an AP.
Action potential sequence:
Depolarisation reaches threshold at the axon hillock
Voltage-gated Na+ channels open (activation gate responds to voltage). Na+ rushes in because of its large driving force (ENa+ is far positive of Vm). Rapid depolarisation.
Near the peak of the AP, Na+ channels inactivate (inactivation gate closes from the cytoplasmic side via ball-and-chain mechanism)
Voltage-gated K+ channels open (they begin activating around -40 mV, shortly after Na+ channels, not at the peak). K+ exits the cell. Repolarisation begins.
K+ channels are slow to close, so K+ continues to leave until the membrane potential approaches EK+, causing a brief hyperpolarisation (after-potential). The potential never goes more negative than EK+.
K+ channels close. Na+ leak channels bring the membrane back to RMP.
Action potentials are all-or-none: same magnitude and duration for a given cell. Stimulus strength is encoded by AP frequency, not amplitude. Sustained threshold stimulus = repeated APs. Suprathreshold stimulus = very rapid firing. Some neurons fire at 500 to 1000 Hz.
Driving force: the difference between Vm and Eion. Na+ has the largest driving force at rest because ENa+ is furthest from -70 mV.
Refractory periods:
Absolute refractory period: from onset of AP until end of Na+ channel inactivation. No AP can be triggered, regardless of stimulus strength.
Relative refractory period: during hyperpolarisation. A stronger stimulus is required because the membrane is further from threshold.
Unidirectional propagation: APs travel in one direction because voltage-gated Na+ channels behind the advancing AP are still inactivated. The AP can only activate channels ahead of it.
Myelin sheath:
Insulates sections of the axon (internodes), restricting APs to the nodes of Ranvier
Current flows passively (electrotonic spread) through internodes
Prevents ions from leaving the cytoplasm, increasing the length constant by increasing rm
Lambda = sqrt(rm / ri): higher rm means current spreads further before decaying
Saltatory conduction:
Signals "jump" from node to node along myelinated axons
Electrotonic spread through internodes is faster than ion movement across the membrane at nodes
Nodes of Ranvier are necessary because passive current decays with distance. Without periodic regeneration at the nodes, the signal would die out.
Axon diameter:
Larger diameter axons conduct APs faster
Increasing the diameter decreases intracellular resistance (ri), increasing the length constant
Current spreads farther and decays more slowly in a wider axon
Electrical synapses:
Use gap junctions between the presynaptic and postsynaptic neuron
Current passes directly, allowing very fast transmission
Dendrodendritic synapses are mostly gap junctions
Chemical synapses:
AP arrives at the axon terminal and depolarises the membrane
Voltage-gated Ca2+ channels open. Neurons maintain very low intracellular Ca2+, so Ca2+ rushes in (highly positive equilibrium potential means a large driving force).
Ca2+ binds synaptotagmin, which activates the SNARE protein complex
SNARE proteins fuse the vesicle and plasma membranes (exocytosis)
Neurotransmitter diffuses into the synaptic cleft and binds receptors on the postsynaptic cell
The result is a graded potential (EPSP or IPSP) in the postsynaptic neuron
Nernst equation: Eion = (61.5 / z) x log([X]outside / [X]inside)
Length constant: Lambda = sqrt(rm / ri)
Key diagrams to know:
Action potential waveform: label depolarisation, peak, repolarisation, hyperpolarisation (after-potential), return to RMP. Mark where NaV channels open, inactivate; where KV channels open and close.
NaV channel gating diagram: resting (activation gate closed, inactivation gate open), active (both open), inactivated (activation gate open, inactivation gate closed via ball-and-chain).
Comparison of passive current decay vs. action potential maintenance of amplitude over distance.
Saltatory conduction: electrotonic spread through internodes, AP regeneration at nodes of Ranvier.
Local anaesthetics (e.g. lidocaine) work by blocking voltage-gated Na+ channels, preventing action potentials in sensory neurons so you feel no pain. Multiple sclerosis involves demyelination, which disrupts saltatory conduction and slows or blocks signal transmission, directly illustrating why the myelin sheath matters for normal neural function.
Students often think KV channels wait until the peak of the action potential to open. They do not. KV channels begin opening around -40 mV, shortly after NaV channels open. They simply reach maximal opening after NaV channels do.
Students often confuse changes in permeability with changes in concentration. Membrane potential changes come from changes in which channels are open (permeability), not from meaningful changes in ion concentrations. The number of ions that move during an AP is negligible relative to the total pool.
Students sometimes think the Na+/K+ pump is the main determinant of resting membrane potential. It contributes only about -2 to -5 mV directly. K+ leak channels are the dominant factor.
Students often believe that knowing the permeability of an ion is needed to calculate driving force. It is not. Driving force = Vm minus Eion. Permeability determines how much current flows at that driving force, but the force itself is purely a voltage difference.
⚠️ Be able to use the Nernst equation to calculate equilibrium potentials and predict the direction of ion flow at a given Vm. This appeared as an iClicker question.
⚠️ Know the full sequence of channel events during an action potential: NaV opens, NaV inactivates, KV opens, KV closes. Know the timing overlap.
⚠️ Understand driving force and be able to identify which ion has the largest driving force at rest (Na+). This was tested directly.
⚠️ Distinguish absolute from relative refractory periods and explain the mechanism behind each.
⚠️ Explain why APs are unidirectional (NaV inactivation prevents backward propagation).
⚠️ Know how myelination increases conduction speed (increases rm, increases length constant) and why nodes of Ranvier are necessary (passive current decays).
True or false: The Na+/K+ pump is the main contributor to the resting membrane potential. (False. K+ leak channels are the dominant factor.)
Fill in the blank: The membrane potential at which net ion flow is zero for a given ion is called the ______. (Equilibrium potential / reversal potential)
True or false: At resting membrane potential, Na+ has a larger driving force than K+. (True. ENa+ is furthest from Vm.)
Fill in the blank: The period during which no action potential can be fired regardless of stimulus strength is the ______ refractory period. (Absolute)
True or false: Action potentials increase in amplitude with stronger stimuli. (False. APs are all-or-none; stronger stimuli increase frequency.)
Q: A cell has extracellular [K+] = 4 mM and intracellular [K+] = 135 mM with EK+ = -94 mV. The membrane is permeable to K+. At which membrane potential will net K+ flow be out of the cell: -70 mV, -94 mV, or -100 mV?
A: At -70 mV. The membrane potential is more positive than EK+ (-94 mV), so K+ flows out to move Vm towards -94 mV. At -94 mV there is zero net flow (equilibrium). At -100 mV, K+ would flow in.
Q: Which ion has the largest driving force at a resting membrane potential of -70 mV, given EK+ = -80 mV, ENa+ = +60 mV, ECl- = -70 mV?
A: Na+. Driving force = Vm minus Eion. For Na+: -70 minus (+60) = -130 mV. For K+: -70 minus (-80) = +10 mV. For Cl-: -70 minus (-70) = 0 mV.
Q: Why are action potentials unidirectional?
A: Because NaV channels behind the advancing action potential are in the inactivated state (inactivation gate closed). They cannot reopen until they return to the resting state, so the AP can only activate channels ahead of it.
Q: A neuron has a resting potential of -50 mV and EK+ = -75 mV. If a large number of K+ channels suddenly open, what happens?
A: The membrane hyperpolarises. K+ flows out of the cell because the membrane potential (-50 mV) is more positive than EK+ (-75 mV), moving Vm towards -75 mV.
Q: Explain why myelination increases conduction speed.
A: Myelin insulates the axon, preventing ions from leaking out through internodes. This increases membrane resistance (rm) and therefore the length constant. Current spreads further passively through each internode, and the AP "jumps" between nodes of Ranvier (saltatory conduction), which is faster than continuous conduction.
This material connects directly to the sensory systems unit that follows: sensory neurons use graded potentials (generator and receptor potentials) and action potentials to encode stimuli. Synaptic transmission is the foundation for understanding neurotransmitter diversity and receptor types covered in lectures 17 and beyond.
The electrochemical gradient concepts here also apply to muscle physiology, cardiac electrophysiology and renal tubular transport, all of which use the same ion channel and pump machinery.
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