Three hands-on modules covering the electrical behavior of the neuronal membrane: the equilibrium potential of an ion species, the passive (RC) properties of the membrane, and how electronic filters separate a signal of interest from noise in a recording. Every plot below responds live — move a slider, watch the trace update.
The equilibrium potential (or Nernst potential) of an ion is the membrane potential at which its net flux across the membrane is zero — the electrical force pulling the ion one way exactly balances the concentration gradient pushing it the other. It depends only on temperature, the ion's valence, and the ratio of its concentration outside to inside the cell.
Electrically, the plasma membrane behaves like a resistor and capacitor in parallel: the lipid bilayer stores charge (capacitance), while ion channels let current leak across it (resistance). Passing a current step through this RC circuit charges and discharges the membrane exponentially. The time constant τ is how long that takes: the time to reach 63% of the maximum potential while charging, or decay 37% while discharging.
Electronic filters select or reject signals by frequency. A low-pass filter passes slow (low-frequency) signals and attenuates fast ones above its cutoff; a high-pass filter does the opposite. The recording below sums three sine components — click a legend entry to isolate it — then filter the composite to recover just the signal you care about.
scipy.signal.butter
+ filtfilt to <1e-8 abs. error.