From 53ff2f8b053ce757f1e9bab4faf0d821cfdd4b84 Mon Sep 17 00:00:00 2001
From: Michael Clerx <michael.clerx@nottingham.ac.uk>
Date: Wed, 18 Mar 2026 21:32:37 +0000
Subject: [PATCH 1/2] Added simpler schematics (omitting parts that disappear
 in the simplifications but were good for derivations).

---
 tutorial/img/vc-level-3-post.png | Bin 0 -> 17219 bytes
 tutorial/img/vc-level-4-post.png | Bin 0 -> 13289 bytes
 tutorial/img/vc-level-5-post.png | Bin 0 -> 12854 bytes
 3 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 tutorial/img/vc-level-3-post.png
 create mode 100644 tutorial/img/vc-level-4-post.png
 create mode 100644 tutorial/img/vc-level-5-post.png

diff --git a/tutorial/img/vc-level-3-post.png b/tutorial/img/vc-level-3-post.png
new file mode 100644
index 0000000000000000000000000000000000000000..4fdd584d2348e99f4ae602f006fb276124497973
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From 0a39092b516e726cc99e11b88432b1202b726672 Mon Sep 17 00:00:00 2001
From: Michael Clerx <michael.clerx@nottingham.ac.uk>
Date: Wed, 18 Mar 2026 21:38:44 +0000
Subject: [PATCH 2/2] Added link to model tour in readme

---
 README.md           |   4 +-
 tutorial/tour.ipynb | 355 ++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 358 insertions(+), 1 deletion(-)
 create mode 100644 tutorial/tour.ipynb

diff --git a/README.md b/README.md
index 393b887..c63bc78 100644
--- a/README.md
+++ b/README.md
@@ -27,9 +27,11 @@ Levels 0, 1, and 2 can recreate the _fast_ artefacts seen in patch clamp experim
 To fit experimental data, these fast artefacts are less important, and so **level 3 is good to match data from the fastest currents**.
 For slower currents, levels 4 or 5 can be used.
 
+**For a quick overview of levels 5, 4, 3, and 0, see the [Model Tour](./tutorial/tour.ipynb).**
+
 ## Tutorials
 
-To understand these models, we provide [four tutorial notebooks](./tutorial/README.md).
+To understand these models, we provide four [Tutorial Notebooks](./tutorial/README.md).
 
 The first derives a basic model of a patch clamp amplifier, and the second adds compensation and filtering, leading to the "Level 0" model.
 In the third notebook, this model is used to simulate the early stages of a (manual) patch-clamp experiment.
diff --git a/tutorial/tour.ipynb b/tutorial/tour.ipynb
new file mode 100644
index 0000000..6192c3e
--- /dev/null
+++ b/tutorial/tour.ipynb
@@ -0,0 +1,355 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "cf0eda98",
+   "metadata": {},
+   "source": [
+    "# A quick tour of voltage-clamp models\n",
+    "\n",
+    "The voltage-clamp models are available in different levels of detail, ranging from the \"full\" model (level 0) to a greatly simplified one (level 5).\n",
+    "Here, we provide a quick tour of the most important models, and provide guidance for setting parameter values.\n",
+    "\n",
+    "_This notebook presents, but does not derive or explain the models. For that, please see the tutorial notebooks_."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c9f1d4b0-093e-40a3-aed5-765ecd37038b",
+   "metadata": {},
+   "source": [
+    "## Level 5 model\n",
+    "\n",
+    "This model calculates membrane potential $V_m$ from command potential $V_c$, and observed current $I_\\text{obs}$ from ionic current $I$.\n",
+    "\n",
+    "<img src=\"./img/vc-level-5-post.png\" style=\"margin:auto\" />\n",
+    "\n",
+    "It includes:\n",
+    "\n",
+    "- A voltage offset $E^\\dagger_\\text{off}$, representing the remaining voltage error after zeroing\n",
+    "- A leak current $I_\\text{leak}$\n",
+    "- The effect of series resistance $R_s$ on the membrane potential\n",
+    "- Series resistance compensation, $\\alpha$, and prediction, $\\beta$, both specified as fractions between 0 and 1."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "db45980e-56ec-4a79-b1f2-935834dcdb5c",
+   "metadata": {},
+   "source": [
+    "\\begin{align}\n",
+    "5.1. && C_m \\dot{V}_m = \\frac{V_c + E_\\text{off}^\\dagger - V_m}{(1 - \\beta) R_s} - \\frac{1 - \\alpha}{1 - \\beta}(I + I_\\text{leak})\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "5.2. && I_\\text{obs} = I + I_\\text{leak}\n",
+    "\\end{align}\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6d59f32b-7b30-4c3e-b4a2-0484d787cf74",
+   "metadata": {},
+   "source": [
+    "| Variable        | Units | Meaning                                                   |\n",
+    "|-----------------|-------|-----------------------------------------------------------|\n",
+    "| $V_m$           | mV    | Membrane potential                                        |\n",
+    "| $V_c$           | mV    | The command potential, set by the voltage clamp protocol  |\n",
+    "| $I$             | pA    | The ionic current                                         |\n",
+    "| $I_\\text{obs}$  | pA    | The observed (measured/output) current                    |\n",
+    "| $I_\\text{leak}$ | pA    | A leak current, e.g. $g_\\text{leak}(V_m - I_\\text{leak})$ |\n",
+    "\n",
+    "The variables $I$ and $I_\\text{leak}$ should be supplied by an ionic current model and leak model, respectively.\n",
+    "\n",
+    "| Parameter | Units     | Meaning                                             | Typical value   |\n",
+    "|-----------|-----------|-----------------------------------------------------|-----------------|\n",
+    "| $C_m$     | pF        | The cell capacitance, from the amplifier estimate   | 25 pF           |\n",
+    "| $R_s$     | G$\\Omega$ | The series resistance, from the amplifier estimate  | 0.005 G$\\Omega$ |\n",
+    "| $\\alpha$  | -         | Fraction of $R_s$ compensation, read from amplifier | 0.7             |\n",
+    "| $\\beta$   | -         | Fraction of $R_s$ compensation, read from amplifier | 0.7             |\n",
+    "| $E^\\dagger_\\text{off}$ | mV | Remaining voltage offset after zeroing        | 0 mV            |\n",
+    "\n",
+    "In a simple simulation $E^\\dagger_\\text{off}$ is chosen by the user.\n",
+    "In inference settings, $E^\\dagger_\\text{off}$ may be a parameter inferred from the data."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1fd1aba6-145f-40e3-b757-fa509ffdf4e6",
+   "metadata": {},
+   "source": [
+    "## Level 4 model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d987b0d8-8491-4ec4-96b7-93180d6292fd",
+   "metadata": {},
+   "source": [
+    "<img src=\"./img/vc-level-4-post.png\" style=\"margin:auto\" />\n",
+    "\n",
+    "This level adds\n",
+    "\n",
+    "- A distinction between estimated and true membrane capacitance and series resistance\n",
+    "- A state-estimator used to approximate $V_e$ in the \"prediction\" pathway"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "107f74b6-ed11-4fb2-b9bd-ec57f0940b91",
+   "metadata": {},
+   "source": [
+    "\\begin{align}\n",
+    "4.1. && C_m\\dot{V}_m = \\frac{V_c + E_\\text{off}^\\dagger - V_m - (\\alpha - \\beta) R_s^* C_m^* \\dot{V}_e}{R_s - \\alpha R_s^*} - I_\\text{leak} - I\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "4.2. && \\dot{V}_e &= \\frac{V_c - V_e}{(1 - \\beta) R_s^* C_m^*}   \n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "4.3. && I_\\text{obs} = I + I_\\text{leak} + C_m \\dot{V}_m - C_m^* \\dot{V}_e\n",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bfa3cb04-e71e-442e-aee2-970c7ab3e975",
+   "metadata": {},
+   "source": [
+    "New or changed variables and parameters are\n",
+    "\n",
+    "| Variable | Units | Meaning                                               |\n",
+    "|----------|-------|-------------------------------------------------------|\n",
+    "| $V_e$    | mV    | An estimate of $V_m$ used in the \"prediction\" pathway |\n",
+    "\n",
+    "And\n",
+    "\n",
+    "| Parameter | Units     | Meaning                                                 | Typical value   |\n",
+    "|-----------|-----------|---------------------------------------------------------|-----------------|\n",
+    "| $C_m$     | pF        | The true cell capacitance, unknown in real experiments  | 25 pF           |\n",
+    "| $C^*_m$   | pF        | The estimated cell capacitance, read from amplifier     | 25 pF           |\n",
+    "| $R_s$     | G$\\Omega$ | The true series resistance, unknown in real experiments | 0.005 G$\\Omega$ |\n",
+    "| $R^*_s$   | G$\\Omega$ | The series resistance, read from amplifier              | 0.005 G$\\Omega$ |\n",
+    "\n",
+    "For a straightforward simulation, $C_m$ and $R_s$ can be chosen by the user.\n",
+    "In an inference setting, $C_m$ and $R_s$ may be inferred from the data long with $E^\\dagger_\\text{off}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dceee631-de83-43c3-af45-7b18abb080a0",
+   "metadata": {},
+   "source": [
+    "## Level 3 model\n",
+    "\n",
+    "<img src=\"./img/vc-level-3-post.png\" style=\"margin:auto\" />\n",
+    "\n",
+    "This level adds\n",
+    "\n",
+    "- An explicit measurement resistor $R_f$\n",
+    "- A first-order low-pass filter in the series resistance compensation pathway\n",
+    "- A first-order low-pass filter over the command potential (the \"stimulus filter\")\n",
+    "- A first-order low-pass filter over the output"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d00cfab5-45e6-4588-b0cd-5c1dae9a6401",
+   "metadata": {},
+   "source": [
+    "\\begin{align}\n",
+    "3.1. && C_m\\dot{V}_m = \\frac{V_r + E_\\text{off}^\\dagger - V_m}{R_s} - I_\\text{leak} - I\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "3.2. && V_r = V_s + \\alpha \\frac{R_s^*}{R_f} V_\\text{rc} + \\beta R_s^* C_m^* \\dot{V}_e\n",
+    "              = \\alpha \\frac{R_s^*}{R_f} V_\\text{rc} + \\frac{V_s - \\beta V_e}{1 - \\beta}\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "3.3. && \\dot{V}_e &= \\frac{V_s - V_e}{(1 - \\beta)R_s^*C_m^*}   \n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "3.4 && I_1 &= \\frac{V_r + E_\\text{off}^\\dagger - V_m}{R_s} - C_m^* \\dot{V_e}\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "3.5 && \\tau_\\text{rc} \\dot{V}_\\text{rc} &= R_f I_1 - V_\\text{rc}\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "3.6. && \\tau_s \\dot{V_s} = V_c - V_s\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "3.7. && \\tau_o \\dot{I}_\\text{obs} = I_1 - I_\\text{obs}\n",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c4845a2c-d7a9-4228-a456-28d2f297be46",
+   "metadata": {},
+   "source": [
+    "New variables and parameters are\n",
+    "\n",
+    "| Variable | Units | Meaning                                                     |\n",
+    "|----------|-------|-------------------------------------------------------------|\n",
+    "| $V_r$    | mV    | The voltage on one side of the measurement electrode        |\n",
+    "| $V_s$    | mV    | The filtered command potential                              |\n",
+    "| $V_rc$   | mV    | The filtered voltage used in series resistance compensation |\n",
+    "| $V_s$    | mV    | The voltage on one side of the measurement electrode        |\n",
+    "| $I_1$    | pA    | The output current before filtering                         |\n",
+    "\n",
+    "And\n",
+    "\n",
+    "| Parameter        | Unit      | Meaning                                                    | Typical value |\n",
+    "|------------------|-----------|------------------------------------------------------------|---------------|\n",
+    "| $\\tau_\\text{RC}$ | ms        | Time constant of filter in series resistance compenstation, read from amplifier|0.01 ms|\n",
+    "| $\\tau_s$         | ms        | Time constant of stimlus filter, estimated from fits       | 0.025 ms      |\n",
+    "| $\\tau_o$         | ms        | Time constant of 1st order approximation of output filter  | 0.01 ms       |\n",
+    "| $R_f$            | G$\\Omega$ | The measurement resistor, found in headstage documentation | 0.5 G$\\Omega$ |\n",
+    "\n",
+    "To estimate $\\tau_s$ in a real amplifier, you can record the filtered output voltage and fit to it.\n",
+    "The value above corresponds to the \"slow\" (default) setting on a HEKA EPC-10.\n",
+    "\n",
+    "To estimate $\\tau_o$, you can use $\\tau_o \\approx \\frac{1}{2 \\pi f}$, where $f$ is the filter's cut-off frequency in kHz.\n",
+    "\n",
+    "Note that exact values of $\\tau_s$ and $\\tau_o$ are seldom crucial."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f0982179-7da0-49d0-ae2f-a1ce724babe7",
+   "metadata": {},
+   "source": [
+    "## Level 0: The full model\n",
+    "\n",
+    "Next, we jump straight to the Level 0 model.\n",
+    "\n",
+    "<img src=\"./img/vc-level-0.png\" style=\"margin:auto\" />\n",
+    "\n",
+    "This level adds\n",
+    "\n",
+    "- A pipette (conventional patch clamp) or parasitic (planar patch clamp) capacitance $C_p$, and its amplifier estimate $C^*p$\n",
+    "- A stray capacitance on the measurement resistor $\\tilde{C}_f$, and a finite op-amp speed with time constant $\\tau_a$\n",
+    "- A two-part output filter, where \"Filter 1\" affects series resistance compensation, while \"Filter 2\" does not.\n",
+    "- Arbitrary equations for the output filters and the stimulus filter (allowing e.g. Bessel formulations)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "175b67aa-e550-48f0-acea-c7656a812398",
+   "metadata": {},
+   "source": [
+    "\\begin{align}\n",
+    "0.1. && C_m\\dot{V}_m = \\frac{V_p + E_\\text{off}^\\dagger - V_m}{R_s} - I_\\text{leak} - I\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.2. && (C_p+\\tilde{C}_f)\\dot{V}_p = \\frac{V_o - V_p}{R_f} - \\frac{V_p + E_\\text{off}^\\dagger - V_m}{R_s} + \\tilde{C}_f\\dot{V}_o + C_m^* \\dot{V}_e + C_p^* \\dot{V}_r\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.3. && \\tau_a \\dot{V}_o = V_r - V_p\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.4. && V_r = V_s + \\alpha \\frac{R_s^*}{R_f} V_\\text{rc} + \\beta R_s^* C_m^* \\dot{V}_e\n",
+    "              = \\alpha \\frac{R_s^*}{R_f} V_\\text{rc} + \\frac{V_s - \\beta V_e}{1 - \\beta}\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.5. && \\dot{V}_e &= \\frac{V_s - V_e}{(1 - \\beta)R_s^*C_m^*}   \n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.6. && \\tau_\\text{rc} \\dot{V}_\\text{rc} = V_1 - V_\\text{rc}\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.7. && \\dot{V_s} = f_s(V_c, V_s)\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.8. && \\dot{V}_1 = f_1(V_o - V_r, V_1)\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.9. && \\dot{V}_2 = f_2(V_1, V_2)\n",
+    "\\end{align}\n",
+    "\n",
+    "\\begin{align}\n",
+    "0.10. && I_\\text{obs} = V_2 / R_f\n",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7cc410ae-a332-4fdd-9f04-459790d43ef2",
+   "metadata": {},
+   "source": [
+    "# TODO\n",
+    "\n",
+    "New variables and parameters are\n",
+    "\n",
+    "| Variable | Units | Meaning                                                     |\n",
+    "|----------|-------|-------------------------------------------------------------|\n",
+    "| $V_r$    | mV    | The voltage on one side of the measurement electrode        |\n",
+    "| $V_s$    | mV    | The filtered command potential                              |\n",
+    "| $V_rc$   | mV    | The filtered voltage used in series resistance compensation |\n",
+    "| $V_s$    | mV    | The voltage on one side of the measurement electrode        |\n",
+    "| $I_1$    | pA    | The output current before filtering                         |\n",
+    "\n",
+    "And\n",
+    "\n",
+    "| Parameter        | Unit      | Meaning                                                    | Typical value |\n",
+    "|------------------|-----------|------------------------------------------------------------|---------------|\n",
+    "| $\\tau_\\text{RC}$ | ms        | Time constant of filter in series resistance compenstation, read from amplifier|0.01 ms|\n",
+    "| $\\tau_s$         | ms        | Time constant of stimlus filter, estimated from fits       | 0.025 ms      |\n",
+    "| $\\tau_o$         | ms        | Time constant of 1st order approximation of output filter  | 0.01 ms       |\n",
+    "| $R_f$            | G$\\Omega$ | The measurement resistor, found in headstage documentation | 0.5 G$\\Omega$ |\n",
+    "\n",
+    "To estimate $\\tau_s$ in a real amplifier, you can record the filtered output voltage and fit to it.\n",
+    "The value above corresponds to the \"slow\" (default) setting on a HEKA EPC-10.\n",
+    "\n",
+    "To estimate $\\tau_o$, you can use $\\tau_o \\approx \\frac{1}{2 \\pi f}$, where $f$ is the filter's cut-off frequency in kHz.\n",
+    "\n",
+    "Note that exact values of $\\tau_s$ and $\\tau_o$ are seldom crucial."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2332084c-5e5d-4dc1-aed9-fdc3019ffe8b",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.13.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
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