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Merged
MichaelClerx merged 2 commits into from
Aug 25, 2026
Merged

Added levels 1 and 2 to the model tour #28

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3c807b5
Added levels 1 and 2 to the model tour. Closes #26.
MichaelClerx Aug 25, 2026
be0e0aa
Improved model tour text
MichaelClerx Aug 25, 2026
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76 changes: 68 additions & 8 deletions tutorial/tour.ipynb
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Expand Up @@ -228,23 +228,85 @@
"The given $R_f$ value is typical for Axon, HEKA, and Sutter."
]
},
{
"cell_type": "markdown",
"id": "13f7b3c8-ac0f-4c59-8b0a-4e082e81487a",
"metadata": {},
"source": [
"## Level 2: Fast capacitance and compensation\n",
"\n",
"<img src=\"./img/vc-level-2-post.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",
"\n",
"Compared to level 3, only equations 5 and 7 are changed:"
]
},
{
"cell_type": "markdown",
"id": "7c991600-9683-45a6-8545-5c480c518215",
"metadata": {},
"source": [
"\\begin{align}\n",
"2.5 && \\dot{V}_\\text{rc} &= \\frac{R_f I_1 + b - V_\\text{rc}}{(\\tau_\\text{rc} - a)} \\\\\n",
" && a &= \\alpha R_s^* (C_p - C_p^*) \\\\\n",
" && b &= R_f (C_p - C_p^*) \\frac{\\dot{V}_s - \\beta \\dot{V}_e}{1 - \\beta}\n",
"\\end{align}\n",
"\n",
"\\begin{align}\n",
"2.7. && \\tau_o \\dot{I}_\\text{obs} = I_1 + (C_p - C_p^*) \\dot{V}_r - I_\\text{obs}\n",
"\\end{align}"
]
},
{
"cell_type": "markdown",
"id": "c6cd0eeb-a098-44e9-8865-8584ce368ce9",
"metadata": {},
"source": [
"New parameters are\n",
"\n",
"| Parameter | Units | Meaning | Typical value |\n",
"|-----------|-------|-------------------------------------------------|---------------|\n",
"| $C_p$ | pF | True pipette or parasitic capacitance, unknown | 5 pF |\n",
"| $C_p^*$ | pF | Estimated fast capacitance, read from amplifier | 5 pF |\n",
"\n",
"Note that the true capacitance artefact is more complex.\n",
"Similarly, most amplifiers have more complex compensation, including multiple capacitances and time delays."
]
},
{
"cell_type": "markdown",
"id": "9c446bf1-678e-4502-a12e-e22b411c4217",
"metadata": {},
"source": [
"## Level 1: Stray capacitance\n",
"\n",
"The level 1 model adds a \"stray capacitance\" over the measurement resistor $R_f$.\n",
"It is equivalent to level 0, described below, but uses 1st order approximations for all filters.\n",
"\n",
"Full equations can be found in the \"simplifications\" notebook."
]
},
{
"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 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)"
"- Arbitrary equations for the output filters and the stimulus filter (allowing e.g. Bessel formulations)\n",
"\n",
"And, as in level 1, we now have\n",
"\n",
"- A stray capacitance on the measurement resistor $\\tilde{C}_f$"
]
},
{
Expand Down Expand Up @@ -313,8 +375,6 @@
"\n",
"| Parameter | Units | Meaning | Typical value |\n",
"|---------------|-------|----------------------------------------------------|---------------|\n",
"| $C_p$ | pF | True pipette capacitance, unknown | 5 pF |\n",
"| $C^*_p$ | pF | Estimated pipette capacitance, read from amplifier | 5 pF |\n",
"| $\\tilde{C}_f$ | pF | Compensated stray capacitance on measuring resistor, unknown | 5e-3 pF |\n",
"| $\\tau_a$ | ms | Time constant of measurement op-amp, unknown | 13e-6 ms |\n",
"| $t_r$ | ms | Stimulus filter setting | 0.04 ms |\n",
Expand All @@ -339,7 +399,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.12"
"version": "3.13.13"
}
},
"nbformat": 4,
Expand Down