KandelLab — Principles of Neural Science, in Simulation

I. Cellular Level · Cells

The cellular level focuses on the electrophysiological properties of single neurons. From the equilibrium potentials set by ion concentration gradients, to action potentials driven by voltage-gated channels, to spike-train coding and synaptic integration — these are the foundations for understanding how the nervous system works.

— ✦ —

§1

Nernst Equation

— Ion Equilibrium Potential

E = (RT/zF)·ln([X]₀/[X]ᵢ). The equilibrium potential of a single ion is determined by the concentration gradient across the membrane and the temperature.

§2

Goldman–Hodgkin–Katz Equation

— Resting Membrane Potential

The membrane potential weighted by the permeability of multiple ions. When only one ion is permeable, GHK reduces to the Nernst equation.

§3

Hodgkin–Huxley Model

— Action Potential

A four-variable ODE system: V, m, h, n. The gating dynamics of sodium and potassium channels produce all-or-none action potentials.

§4

Leaky Integrate-and-Fire

— Spiking Neuron Model

τ·dV/dt = -(V-E_L) + R·I. A simplified neuron model whose f-I curve can be solved analytically.

§5

Synapse Model

— EPSP/IPSP and Spatiotemporal Integration

Alpha-function synaptic currents. Temporal and spatial summation of multiple synaptic inputs determine whether the neuron fires.