Neuroscience & Neuroanatomy - Brain Systems & Action Potentials

The Nernst equation calculates the equilibrium potential ($E_{ion}$) for a single ion across a semipermeable membrane. It is given by: $E_{ion}=\frac{RT}{zF}\ln \frac{[ion{]}_{out}}{[ion{]}_{in}}$, where $R$ is the gas constant, $T$ is absolute temperature, $z$ is the ion's valence, $F$ is Faraday's constant, and $[ion{]}_{out}$ and $[ion{]}_{in}$ are the extracellular and intracellular concentrations, respectively.

The GHK equation calculates the resting membrane potential ($V_m$) by considering the relative permeabilities and concentration gradients of multiple ions (typically K+, Na+, and Cl-). It is given by: $V_m=\frac{RT}{F}\ln \left(\frac{P_K[K^{+}{]}_{out}+P_{Na}[N{a}^{+}{]}_{out}+P_{Cl}[C{l}^{-}{]}_{in}}{P_K[K^{+}{]}_{in}+P_{Na}[N{a}^{+}{]}_{in}+P_{Cl}[C{l}^{-}{]}_{out}}\right)$, where $P_{ion}$ represents the membrane permeability for each ion.

The resting membrane potential is primarily determined by the selective permeability of the neuronal membrane to potassium ions (K+) through K+ leak channels, and the action of the Na+/K+ ATPase pump, which maintains the concentration gradients.

Depolarization is initiated when the membrane potential reaches threshold, causing a rapid influx of Na+ ions through voltage-ggated Na+ channels. This makes the inside of the membrane more positive, rising sharply from the resting potential.

Repolarization occurs as voltage-gated Na+ channels inactivate and voltage-gated K+ channels open, allowing K+ ions to efflux out of the cell. This outflow of positive charge restores the negative membrane potential.

Hyperpolarization (or undershoot) is caused by the slow closure of voltage-gated K+ channels. This prolonged K+ efflux leads to a transient period where the membrane potential becomes even more negative than the resting potential before returning to baseline.

1. An action potential arrives at the presynaptic terminal. 2. Voltage-gated Ca2+ channels open, leading to Ca2+ influx. 3. Ca2+ binds to synaptotagmin on synaptic vesicles. 4. Vesicles fuse with the presynaptic membrane (mediated by SNARE proteins). 5. Neurotransmitters are released into the synaptic cleft via exocytosis.

EPSPs (Excitatory Postsynaptic Potentials) are depolarizations (e.g., due to Na+ influx) that make the postsynaptic neuron more likely to fire an action potential. IPSPs (Inhibitory Postsynaptic Potentials) are hyperpolarizations (e.g., due to Cl- influx or K+ efflux) that make the postsynaptic neuron less likely to fire an action potential.