Neuroscience - Central Nervous System Pathways & Action Potentials

Calculates the equilibrium potential ($E_x$) for a single ion across a membrane:

At body temperature ($37^{\circ }\text{C}$), it simplifies to:

Calculates the resting membrane potential ($V_m$) by accounting for multiple permeable ions and their relative membrane permeabilities ($P$):

Typically around $-70\text{ mV}$ in neurons. Maintained primarily by background $K^{+}$ leak channels (high permeability to $K^{+}$ at rest) and electrogenic $N{a}^{+}/K^{+}$-ATPase pumps, which transport $3{\text{ Na}}^{+}$ out for every $2{\text{ K}}^{+}$ brought into the cell.

Triggered when a stimulus brings membrane potential to threshold (around $-55\text{ mV}$). Voltage-gated $N{a}^{+}$ channels open rapidly, resulting in a massive inward $N{a}^{+}$ current that drives $V_m$ toward $+35\text{ mV}$.

Repolarization: Inactivation gates of voltage-gated $N{a}^{+}$ channels close, and delayed rectifier $K^{+}$ channels open ($K^{+}$ efflux).
Hyperpolarization: Slow closure of voltage-gated $K^{+}$ channels causes $V_m$ to temporarily drop below $-70\text{ mV}$ before returning to baseline.

Absolute Refractory Period: Voltage-gated $N{a}^{+}$ channels are inactivated; no action potential can fire regardless of stimulus strength.
Relative Refractory Period: Voltage-gated $K^{+}$ channels are open and $N{a}^{+}$ channels have reset; a larger-than-normal depolarizing stimulus is required to reach threshold.

Action potential propagation along myelinated axons where depolarization 'jumps' between Nodes of Ranvier. Myelination increases membrane resistance ($R_m$) and decreases membrane capacitance ($C_m$), drastically increasing conduction velocity.

Function: Facilitates intended movement ('Go' pathway).
Circuit: Cortex (+ Glutamate) $\to$ Striatum $\to$ Inhibits GPi/SNr (- GABA) $\to$ Disinhibits Thalamus $\to$ Excites Cortex (+ Glutamate).