5D · Module 2 Review: Excitable Membranes

Practice this module: MCQ · Flashcards · Problems, Module 2

Membranes and the nervous system¶

Non-excitable: steady −10 to −20 mV, the potential simply exists. Excitable: designed to fluctuate (−90 to +30 mV) and use it to work. Red blood cells are not excitable.
Sensory = afferent (in). Motor = efferent (out). Somatic motor → skeletal muscle. Autonomic → cardiac, smooth, glands, fat. Sympathetic prepares for stress.
Receptors: visceral (organs, e.g. baroreceptors in chest vessels), somatic (skin, muscle, joints, e.g. thermoreceptors), special senses.

Na⁺ at rest: chemical in, electrical in, they sum. K⁺: chemical out, electrical in, chemical wins.
Electrochemical equilibrium: two nonzero gradients cancel. It does not need equal concentrations or 0 mV.
E_X = −(61.5/z) log₁₀([X]_i/[X]_o). Watch z: −1 for Cl⁻, +2 for Ca²⁺.
Cation flows in when V_m is more negative than E_X, out when less negative. Flow ∝ |V_m − E_X|.

Worked example: the Assignment 2 neuron

E_K = -61.5\log\tfrac{140}{5} = -89.0 \qquad E_{Na} = -61.5\log\tfrac{12}{135} = +64.6 \qquad E_{Cl} = +61.5\log\tfrac{9}{115} = -68.0

V_m = 0.700(-89.0) + 0.025(64.6) + 0.275(-68.0) = -62.3 + 1.62 - 18.7 = -79.4\ \text{mV};\ \text{gap to } -55 = 24.4\ \text{mV}

Hyperkalemia at [K⁺]_o = 8: E_K −76.45, V_m −70.6, gap 15.6 mV, more excitable and arrhythmia-prone. Hypokalemia does the reverse.

K⁺ leak channels (main), a few Na⁺ leak channels, and the electrogenic Na⁺-K⁺ pump (3 out, 2 in). Voltage-gated channels are closed. “Pick 2”: pump and K⁺ leak channels.
K⁺ sets resting potential because it has the most open channels (weight 0.70 in chord conductance).
Ouabain: V_m becomes less negative, but only gradually.

Ligand-gated channels. Na⁺ in = EPSP; K⁺ out or Cl⁻ in = IPSP.
No threshold, no refractory period, decay with distance (small length constant, low r_m).
Axon hillock integrates. Temporal = one synapse repeatedly (+4 × 3 = +12 mV). Spatial = several at once (+4 − 5 = −1 mV). Both work on IPSPs.
A mixed Na⁺/K⁺ channel gives a net EPSP, because V_m sits far from E_Na and close to E_K.

Na⁺ channels: fast open, then inactivated (activation gate open, inactivation gate closed). K⁺ channels: slow open, slow close.
Absolute refractory: no stimulus works. Relative: hyperpolarized and resetting, a bigger stimulus works. Refractory periods keep APs distinct so the brain can read frequency; cooling lengthens them.
Speed: myelin (raises r_m and λ), larger diameter, higher temperature. ATP concentration is not a factor.
Terminal: voltage-gated Ca²⁺ channels → Ca²⁺ in → exocytosis. Neuron target: ligand-gated channel (fast). Cardiac target: GPCR (slow).