Generate a controlled step or load recorded step, arbitrary, or chaotic current waveforms.
Choose the current and voltage columns in one file. The voltage column becomes the fitting target.
Select a model, inspect its parameters, and define the HH membrane currents.
Exponential midpoint improves numerical accuracy in the tested protocols and is slower. It supports Na, KDR, and leak with alpha-beta gates. Other channels require Euler. This setting controls internal integration; output sampling is unchanged.
Run the selected model, then inspect traces and extracted features below.
The fit will start from the values currently shown in the model controls.
Completed runs with the same target, objective, fitted parameters, bounds, and starting vector can be overlaid.
Choose what the figure contains. The preview follows the latest simulation and selected optimizer runs.
A two-variable spiking model with membrane potential \(v\) and recovery current \(u\), integrated with fourth-order Runge–Kutta.
When \(v\ge v_\text{th}\), the state resets:
Defaults: \(k_1{=}0.04,\ k_2{=}5,\ k_3{=}140,\ v_\text{th}{=}30\) mV. Injected current is multiplied by \(I_\text{scale}\).
The membrane is represented as a capacitor in parallel with a selected set of ionic conductances:
Each channel \(c\) is defined by maximal conductance \(\bar g_c\), reversal potential \(E_c\), and zero or more gates \(g_j\). The classic configuration uses fast Na⁺, delayed-rectifier K⁺, and leak.
Each gate \(g\in[0,1]\) relaxes toward a voltage- or calcium-dependent steady state.
Alpha/beta rates
Steady state and time constant
Calcium-gated activation
Calcium-source channels feed a single intracellular pool that relaxes toward a baseline concentration:
Inward calcium current is negative and raises \([\mathrm{Ca}]_i\). Defaults: \([\mathrm{Ca}]_\text{base}{=}0.05\) µM, \(\tau_\text{Ca}{=}80\) ms, and \(\gamma{=}0.02\).
The same extractor is applied to model and recorded voltage:
Fixed extractor settings: 0.2 ms derivative sustain, 10 ms threshold lookback, 30 ms width tail, 20 ms AHP tail, 0.1 mV AHP-recovery criterion, 20 ms pre-stimulus rest window, and 1 ms current smoothing for automatic step detection.
The custom objective first matches spike count, then compares the timing and shape of paired spikes.
Different counts: a count penalty and bounded timing guide direct the search. These candidates rank below every equal-count candidate.
Same count: normalized feature errors are weighted and combined. A penalty covers model features that are missing where the target is measurable.
Nm and Nt are model and target counts. Each normalized feature error D̃k is weighted by wk; Mincomplete penalizes missing model features.
Spike count is evaluated first. A dynamic structural gate is set above the maximum possible equal-count score, so a wrong-count trace cannot outrank an equal-count trace. A bounded spike-time distribution term guides the search within the same wrong-count level. Paired per-spike terms are included only when model and recorded spike counts agree:
Each measurable target pair is capped before averaging:
\(d=|N_m-N_e|\), \(c=100\), and \(C_{\rm match}=\max(c,H)\sum_{k\ne{\rm count}}w_k\) is the equal-count loss ceiling. With empirical spike-time Wasserstein distance \(W_1\), \(T_{W_1}=0.25G\,W_1/(W_1+100\,\mathrm{ms})<G\), preserving strict spike-count dominance. After the global search, deterministic current-mapping repair searches the best under-count and over-count basins independently, then ranks every evaluated exact-count candidate using the paired objective above. The bounded search does not prove a global optimum. \(M_\text{incomplete}\) penalizes a model measurement that is missing where the target is measurable; unavailable target measurements are excluded from \(A_k\). \(\phi_k\) covers spike timing, amplitude, threshold, time-to-peak, half-width, and AHP depth. The scales \(s_k\) make millivolt and millisecond differences comparable, while normalized weights satisfy \(\sum_k w_k=1\).