Gating Currents in the Voltage-Gated K⁺ Channel

The ionic side is the standard Hodgkin–Huxley delayed rectifier: the channel opens as n⁴, where n is a single activation gating variable relaxing toward its voltage-dependent steady state n∞(V) with time constant τn(V), using the classical rate functions αn(V) = 0.01(V+55) / (1 − e^{−(V+55)/10}) and βn(V) = 0.125·e^{−(V+65)/80}. The ionic current at any moment is I_K(t) = ḡ_K · n(t)⁴ · (V_m(t) − E_K), computed continuously through the pulse and the return to holding potential — which is why you'll see a small "tail current" right after the step back, the same signature used experimentally to confirm a current is carried through open K⁺ channels. The default ḡ_K (88 nS) and E_K (−77 mV) are calibrated so a step to +50 mV settles near 10 nA, a realistic whole-cell amplitude — adjust ḡ_K in the advanced panel to rescale.

The gating current is modelled the simplest way that still reproduces the classic ON/OFF signature: each of the four activation particles is treated as a two-state resting ⇌ activated gate governed by the same αn/βn rates, so n(t) is literally the fraction of particles in the activated state and the charge-movement current is proportional to its rate of change, I_gating(t) ∝ dn/dt. A depolarizing step makes n rise toward a larger n∞, giving a decaying ON transient; stepping back to holding makes n fall again, giving a mirror-image OFF transient of the opposite sign. The default gating-charge scale is calibrated so that, at the same +50 mV reference pulse, the ON gating-current peak lands at roughly 1/100th of the ionic peak (tens to ~100 pA) — consistent with how much smaller real gating currents are than the ionic currents they precede — and the "gating current gain" slider rescales from that point.

Both traces carry independent Gaussian recording noise (adjustable in the advanced panel, default 0.15 nA SD on I_K and 8 pA SD on I_gating), so the small gating-current trace reads visibly noisier relative to its signal than the much larger ionic current does — as in a real patch/voltage-clamp recording, where the gating current sits closer to the noise floor. Clicking "Start sweeps" runs a finite batch of N sweeps (N = the "traces to average" slider) at 2/s for both currents together, shows each raw sweep in gray, and once all N have arrived, overlays the trial-averaged trace in color — exactly the signal-averaging approach used to pull small, noisy gating currents out of the noise floor in a real recording.

When a run's N sweeps complete, its averaged I_K and I_gating traces are stored, the way a storage oscilloscope keeps every exposed trace lit on its screen for a photograph rather than letting it decay: the "stored averages" panel accumulates one I_K trace and one gating-charge Q(t) trace per completed run (Q(t) = the running time-integral of that run's averaged I_gating), all shown together, not just the latest. Run sweeps at several test voltages and each one adds another trace to the display — exactly like recording a family of voltage-clamp pulses on a storage scope before the photograph. Nothing is erased until you press "Reset averages," which clears every stored trace at once (independently of "Reset trace", which only clears the sweep currently in progress). Each stored run also adds one point to the G–V and Q–V plots at that run's test voltage, so those two curves are built up empirically, one stored run at a time, the same way a real family of voltage-clamp pulses is used to construct an I–V or G–V relation. Running the same test voltage again re-exposes (replaces) that voltage's trace and point rather than duplicating them.

G–V is measured from the tail current, not the steady-state current during the pulse. The straightforward formula G = I_K,steady / (V_test − E_K) has a problem: as V_test sweeps across the family of test pulses that make up the curve, it necessarily passes close to E_K somewhere in the middle — exactly where the curve's rising phase is most interesting — and dividing by a driving force near zero there amplifies any noise in I_K enormously, which is why points near E_K can look far jumpier than the rest of the curve. The fix is the standard electrophysiology one: at the instant of repolarization, the current jumps to a value set by that pulse's conductance (n(t2)⁴, which hasn't had time to relax yet) but now driven by the holding potential instead — G = I_tail / (V_hold − E_K). Since V_hold is one fixed value for a whole family of runs (rather than sweeping through the family the way V_test does), this denominator stays comfortably away from zero throughout the whole curve. I_tail itself is read from a single fixed point 0.5 ms after repolarization — early enough that deactivation hasn't relaxed the tail current much, but past the brief capacitive transient right at the step — shown as a thin dotted green line on the I_K panel; it isn't draggable, since a tail-current measurement is meant to be one well-defined instant, not an averaged window.

Q–V, on the other hand, keeps the original Clampfit-style treatment: the two dashed cursors spanning the I_K/I_gating panels mark the window the ON gating charge is averaged over — drag either line to move it, and every stored run's Q-V point is re-measured immediately, so the curve updates live for traces you've already recorded, not just the next one. The window defaults to the last 5 ms of the pulse, backed off 0.5 ms from the step edge, and re-centers there automatically whenever pulse duration changes; it's left wherever you drag it across every other parameter change. Charge has no analogous near-E_K singularity to fix (it's a time integral, not a ratio), which is why it's the one still built from an adjustable window rather than a single fixed point.

One note on residual noise, since it's genuine and worth understanding rather than hiding: trial- averaging N sweeps shrinks the noise band by √N — it doesn't remove it, since a fresh independent noise value is still added at every single time sample. An N-sweep average will always show some sample-to-sample jitter; it's just N-fold-smaller jitter than any one raw sweep. Because the tail current is now a single fixed sample rather than a window average, its noise doesn't shrink any further than that — a wider window would help, the same way it would for any non-cumulative current, but that trade-off (smoother G-V vs. a true instantaneous tail reading) is deliberately not offered here. Q, by contrast, gets essentially no benefit from widening its window either way: it's a running sum of the noisy current, and consecutive values of a running sum are highly correlated, so noise that has already accumulated like a random walk over the integration isn't undone by averaging nearby points on that walk. The two real levers for a smoother Q–V curve are raising N (which reduces the noise entering the integral before it's ever summed) and/or lowering the I_gating recording-noise slider; the charge is also referenced to the sample right at pulse onset rather than to the start of the recording, so the unavoidable ~5 ms of pre-pulse dead time doesn't add its own extra random-walk noise on top. This is also why very small signals — test voltages close to the holding potential, where the true charge moved is tiny to begin with — can show Q-V traces that don't cleanly separate or even cross each other run to run: when the true signal is smaller than the noise floor, the noise dominates what you see, and no amount of re-reading the same few sweeps fixes that — only more trials (raise N) or a genuinely larger signal (a bigger voltage step) will.

Because conductance depends on n⁴ but total charge moved depends only on n itself (one power, not four — each particle moves once whether or not the other three have also moved), the G–V curve comes out steeper and shifted to more positive voltages than the Q–V curve once you've populated both across a range of test voltages. That leftward offset is the classic result: charge moves at voltages where the pore is still mostly closed, i.e. gating precedes conduction. This is a deliberately simplified two-state-per-particle picture (real gating currents show additional kinetic components, e.g. from a Cole–Moore shift and non-independent subunit transitions) — good for building intuition, not a fit to any specific published recording.