Neuroscience - Action Potentials & Synaptic Transmission

The baseline electrical potential difference across a neuronal membrane at rest, typically around $-70extmV$. It is maintained primarily by passive $ext{K}^{+}$ leak channels and the active $ext{Na}^{+}/ext{K}^{+}$ ATPase pump.

Calculates the equilibrium potential ($E_X$) for a single permeable ion across a membrane:
$$\begin{gathered} E_X= \\ fracRTzF \\ ln \\ frac[X{]}_o[X{]}_i \end{gathered}$$
At body temperature (37^\\circ\ ext{C}), it simplifies to $$\begin{gathered} E_X= \\ frac61.5z \\ lo{g}_{10} \\ frac[X{]}_o[X{]}_{i}extmV \end{gathered}$$.

Determines the resting membrane potential ($V_m$) by considering multiple permeable ions and their relative membrane permeabilities ($P_i$):
$$\begin{gathered} V_m= \\ fracRTF \\ ln \\ left( \\ frac{P}_{extNa}[ext{Na}^{+}{]}_o+P_{extK}[ext{K}^{+}{]}_o+P_{extCl}[ext{Cl}^{-}{]}_i{P}_{extNa}[ext{Na}^{+}{]}_i+P_{extK}[ext{K}^{+}{]}_i+P_{extCl}[ext{Cl}^{-}{]}_{o}ight) \end{gathered}$$

An electrogenic primary active transporter that pumps $3ext{Na}^{+}$ ions out of the neuron and $2ext{K}^{+}$ ions into the neuron per ATP hydrolyzed, maintaining resting ionic concentration gradients.

Cycles through three functional states:
1. Deactivated (Closed): Activation gate closed, inactivation gate open (at RMP).
2. Activated (Open): Both gates open (upon reaching threshold).
3. Inactivated (Closed): Inactivation loop blocks pore despite depolarization.

Triggered when membrane potential reaches threshold ($meq-55extmV$), opening voltage-gated $ext{Na}^{+}$ channels. $ext{Na}^{+}$ influx creates a positive feedback loop (Hodgkin cycle) driving $V_m$ toward $$\begin{gathered} E_{extNa} \\ approx+60extmV \end{gathered}$$.

Restoration of negative potential driven by two concurrent processes: voltage-gated $ext{Na}^{+}$ channels spontaneously inactivate, and delayed rectifier voltage-gated $ext{K}^{+}$ channels open, causing massive $ext{K}^{+}$ efflux.

A transient phase where $V_m$ becomes more negative than RMP (nearing $$\begin{gathered} E_{extK} \\ approx-90extmV \end{gathered}$$) because delayed rectifier $ext{K}^{+}$ channels are slow to close, leaving total $ext{K}^{+}$ permeability higher than at rest.