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@jonmarty
Last active June 17, 2018 22:57
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An explanation of mathematical neurons in the context of computational neuroscience and an example of a Morris Lecar Neuron
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"cells": [
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"source": [
"## Morris Lecar Model\n",
"\n",
"Computational Neuroscience is a branch of neuroscience which makes use of mathematical models and theoretical analysis in attempting to understand the principles that govern brain function. Central to the field is the development and use of mathematical models of individual neurons, which attempt to replicate the response of neurons to environmental conditions and external stimuli. Variations and combinations of these models allow for the modelling of entire neurological systems. One such mathematical model is the Morris-Lecar neuron.\n",
"\n",
"The Morris-Lecar neuron is a model of a neuron with three ion channels and an external applied current $I$. The conductance varies across the $K^+$ and $Ca^{2+}$ ion channels, but is static across the $L^+$ channel. The $Ca^{2+}$ ion channel which has an instantaneously responding conductance relative to voltage, is used for excitation (entering an excited, spiking state). The $K^+$ ion channel whose conductance has a delayed response to changes in voltage, is used for recovery (returning to resting state).\n",
"\n",
"According to the roles of each ion channel, the formal system of differential equations describing the system is:\n",
"\n",
"$C\\frac{dV}{dt} = I - g_L(V-V_L) - g_{Ca}M_{ss}(V-V_{Ca}) - g_KN(V-V_K)$\n",
"\n",
"$\\frac{dN}{dt} = \\frac{N_{ss}(V) - N}{\\tau_N(V)}$\n",
"\n",
"where C is the capacitance of the cell membrane, V is the voltage across the membrane, $g_L$, $g_{Ca}$, and $g_K$ are the conductances across each of the ion channels, $V_L$, $V_{Ca}$, and $V_K$ are the equilibrium voltages of each of the ion channels, N is the recovery variable, and:\n",
"\n",
"$M_{ss} = (1+tanh[(V-V_1)/V_2])/2$\n",
"\n",
"$N_{ss} = (1+tanh[(V-V_3)/V_4])/2$\n",
"\n",
"Additionally, $\\tau_N$ serves as the time constant for the relaxation caused by the $K^+$ ion channel in response to changes in voltage. It can formally be written as:\n",
"\n",
"$\\tau_N(V) = \\tau_0sech[(V-V_3)/2V_4]$\n",
"\n",
"where $\\tau_0$ sets the time scale of the analysis (this is equivalent to the $\\frac{1}{\\phi cosh[(V-V_3)/2V_4]}$ used below, where $\\phi$ is the reference frequency, and is the reciprocal of $\\tau_0$)\n",
"\n",
"In order to gain a better understanding of this model, let's first look at what the variables stand for.\n",
"\n",
"* N is the instantaneous probability that a K^+ ion channel is in its open (conducting state)\n",
"* The equation for $\\frac{dN}{dt}$ describes the process by which protein channels transition between non-conducting and conducting states\n",
"* $M_ss$ and $N_ss$ are the open-state probability functions for the $Ca^{2+}$ and $K^+$ ion channels\n",
"\n",
"In addition to this notebook, I have put together an interactive simulator of the Morris Lecar model at https://jonmarty.shinyapps.io/MorrisLecar.\n",
"\n",
"In this notebook, we will be viewing the response of a Morris-Lecar neuron to various input currents.\n",
"\n",
"To begin, we set the parameters for the neuron:"
]
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"cell_type": "code",
"execution_count": 1,
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"collapsed": false
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"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from scipy.stats import zscore\n",
"from copy import copy\n",
"\n",
"global V\n",
"global N\n",
"# Assign values to variables\n",
"C = 6.69810502993 # Capacitance of membrane\n",
"V_1 = 30 # Tuning parameters for steady state and time constant\n",
"V_2 = 15\n",
"V_3 = 0\n",
"V_4 = 30\n",
"phi = 0.025 # reference frequency\n",
"V_L = -50 # Equilibrum potentials for ion channels\n",
"V_Ca = 100\n",
"V_K = -70\n",
"g_Ca = 1.1 # leak, conductances through membrane for each ion\n",
"g_K = 2\n",
"g_L = 0.5\n",
"V = -52.14 # Membrane potential\n",
"N = 0.02 # Recovery variance\n",
"V_init = copy(V)\n",
"N_init = copy(N)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
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"source": [
"We instantiate the system of differential equations as a set of lambda functions:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
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"outputs": [
],
"source": [
"#Define functions\n",
"M_ss = lambda: (1/2) * (1 + np.tanh((V - V_1) / V_2))\n",
"N_ss = lambda: (1/2) * (1 + np.tanh((V - V_3) / V_4))\n",
"T_N = lambda: 1 / (phi * np.cosh((V - V_3) / (2 * V_4)))\n",
"\n",
"#Define differential equations\n",
"dV = lambda I: (I - g_L * (V - V_L) - g_Ca * M_ss() * (V - V_Ca) - g_K * N * (V - V_K)) / C\n",
"dN = lambda: (N_ss() - N) / T_N()\n",
"\n",
"#Equations for the input of each channel\n",
"L = lambda: - g_L * (V - V_L)\n",
"Ca = lambda: - g_Ca * M_ss() * (V - V_Ca)\n",
"K = lambda: - g_K * N * (V - V_K)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
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"source": [
"We define functions to run a simulation of a neuron based on an inputted current, as well as plot the results:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
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"outputs": [
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"source": [
"import pandas as pd\n",
"\n",
"def run_model(current):\n",
" global V\n",
" global N\n",
" \n",
" #Reset variables\n",
" V = copy(V_init)\n",
" N = copy(N_init)\n",
" \n",
" data = {\n",
" \"t\" : [],\n",
" \"I\" : [],\n",
" \"V\" : [],\n",
" \"N\" : [],\n",
" \"L\" : [],\n",
" \"Ca\" : [],\n",
" \"K\" : [],\n",
" \"N_ss\" : [],\n",
" \"T_N\" : []\n",
" }\n",
"\n",
" for t, I in zip(range(len(current)), current):\n",
" #Update variables\n",
" V = V + dV(I)\n",
" N = N + dN()\n",
" #Update DataFrame\n",
" data[\"t\"].append(t)\n",
" data[\"I\"].append(I)\n",
" data[\"V\"].append(V)\n",
" data[\"N\"].append(N)\n",
" data[\"L\"].append(L())\n",
" data[\"Ca\"].append(Ca())\n",
" data[\"K\"].append(K())\n",
" data[\"N_ss\"].append(N_ss())\n",
" data[\"T_N\"].append(T_N())\n",
" \n",
" return pd.DataFrame.from_dict(data)\n",
"def plot_model(data):\n",
" for col in data.keys():\n",
" if col in [\"t\", \"I\", \"L\"]: continue\n",
" plt.plot(data[col]/mean(data[col]))\n",
" plt.legend(loc=\"upper right\")\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"Having defined the model and set its parameters, we can move on to experimentation.\n",
"\n",
"First, we experiment with a random input current"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
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"outputs": [
{
"data": {
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"
},
"execution_count": 4,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"#Generate an input stimulus\n",
"scale = 5\n",
"length = 1000\n",
"center = 5e-10\n",
"current = list(scale * np.random.random((length)) + center)\n",
"\n",
"plt.plot(current)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 5,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"data = run_model(current)\n",
"plot_model(data)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"As the cell is subjected to a constant above-zero input current, we can see that the recovery variable, $N$, increases. This stops the voltage in the cell from growing uncontrollably.\n",
"\n",
"Next, we look at a square pulse stimulus:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"# Generate an input stimulus\n",
"value = 5\n",
"length = 1000\n",
"begin = 450\n",
"end = 550\n",
"current = [0 for _ in range(length)]\n",
"current[begin:end] = [value for _ in range(end-begin)]\n",
"plt.plot(current)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"
},
"execution_count": 7,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"data = run_model(current)\n",
"plot_model(data)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"The above graph is a good visualization for the similarities between the release of current from a dielectric and from a neuron's membrane. We can see that our model neuron's membrane experiences exponential decay in the release of current, just as a dielectric does. This demonstrates how the membrane of a neuron acts as a dielectric.\n",
"\n",
"Finally, we will be looking at a sinusoidal stimulus:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 8,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"# Generate an input stimulus\n",
"scale = 5e-1\n",
"step = np.pi/25\n",
"base = 5e-1\n",
"length = 1000\n",
"current = [scale * np.sin(step*i) + base for i in range(length)]\n",
"plt.plot(current)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 9,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"data = run_model(current)\n",
"plot_model(data)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"As we can see from the above graph, the injection of a 0.5 Ampere sinusoidal stimulus causes the cell's voltage to oscillate. This is caused by the interplay between the recovery variable $N$ and the voltage $V$. As the voltage increases, the recovery variable moves to counteract it by increasing the influence of the $K^+$ ion gate on the voltage. However, this response is delayed. This delay allows for the system of oscillate between voltage levels. More technically, we would say that the sinusoidal stimulus caused the system to bifurcate from a resting state to an oscillating, or firing, state. This state can also be visualized based on the phase portrait shown below. As the system begins to oscillate, it moves from a single point (resting state) to an elliptical path (oscillating state)."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 10,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"plt.plot(data[\"N\"], data[\"V\"])\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"collapsed": false
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