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kaizu/HiharaS_CellRep_2012.ipynb

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HiharaS_CellRep_2012.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# HiharaS_CellRep_2012\n",
"\n",
"- Hihara S1, Pack CG, Kaizu K, Tani T, Hanafusa T, Nozaki T, Takemoto S, Yoshimi T, Yokota H, Imamoto N, Sako Y, Kinjo M, Takahashi K, Nagai T, Maeshima K., \"Local nucleosome dynamics facilitate chromatin accessibility in living mammalian cells.\", Cell Rep. 2012 Dec 27;2(6):1645-56. doi: 10.1016/j.celrep.2012.11.008.\n",
"- Nozaki T1, Kaizu K, Pack CG, Tamura S, Tani T, Hihara S, Nagai T, Takahashi K, Maeshima K., \"Flexible and dynamic nucleosome fiber in living mammalian cells.\", Nucleus. 2013 Sep-Oct;4(5):349-56. doi: 10.4161/nucl.26053.\n",
"\n",
"The following version of E-Cell System version 4 was used to run the following script:\n",
"\n",
"https://github.com/ecell/ecell4/tree/07892d0aba588f36c8445490ae286d910e30dae0\n",
"\n",
"This is the specialized version for simulating \"a dog on a leash\" situation."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"from ecell4 import *\n",
"Avogadro_constant = N_A"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"6.022140857e+23"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Avogadro_constant"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Setting paramters. `V` is a simulation volume (litre), `B_conc` is a nucleosome concentration (molar), `r_max` is a length of \"a leash\", and `D_A` is a diffusion constant of EGFP pentamers."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"V = 3.321078080854328e-18\n",
"L = cbrt(V * 1e-3)\n",
"B_conc = 0.5e-3\n",
"r_max = 20e-9 # L * 10 is for free diffusion\n",
"D_A = 7e-12"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Deriving the dependent parameters."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"L_2 = L * 0.5\n",
"N_A, N_B = 100, int(V * B_conc * Avogadro_constant)\n",
"N_tot = N_A + N_B\n",
"\n",
"sigma_D = 3.8e-9 * 23.5e-12\n",
"sigma_B = 2 * cbrt(5.5e-9 * 5.5e-9 * 6e-9 * 3 / 4) # 11e-9\n",
"sigma_A = sigma_D / D_A\n",
"D_B = sigma_D / sigma_B\n",
"\n",
"sigma_max, sigma_min = max(sigma_A, sigma_B), min(sigma_A, sigma_B)\n",
"if r_max > 0:\n",
" params = (D_A, sigma_A, D_B, sigma_B)\n",
"else:\n",
" params = (D_A, sigma_A, 0, sigma_B)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Showing the number of tracers and nucleosomes, and their diameters."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(100, 1000, 1.2757142857142858e-08, 1.0288276478101776e-08)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N_A, N_B, sigma_A, sigma_B"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Defining a model and setting an initial condition."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with species_attributes():\n",
" A | {'D': str(D_A), 'radius': str(sigma_A * 0.5)}\n",
" B | {'D': str(D_B), 'radius': str(sigma_B * 0.5)}\n",
"\n",
"m = get_model()\n",
"\n",
"matrix_size = int(max(3, L / sigma_max))\n",
"w = egfrd.EGFRDWorld(Real3(L, L, L), Integer3(matrix_size, matrix_size, matrix_size))\n",
"w.bind_to(m)\n",
"\n",
"w.add_molecules(Species('A'), N_A)\n",
"w.add_molecules(Species('B'), N_B)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Checking if the number of molecules was set properly."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(100, 1000)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w.num_molecules(Species('A')), w.num_molecules(Species('B'))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Displaying the initial situation."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<html>\n",
" <head>\n",
" <script type=\"text/javascript\">\n",
" (function(){\n",
" if(window[\"THREE\"] === undefined || window[\"d3\"] === undefined){\n",
"\t require.config({\n",
"\t paths:{\n",
"\t d3: [\n",
"\t 'https://d3js.org/d3.v3.min',\n",
"\t 'custom/d3.min'\n",
"\t ],\n",
"\t THREE: [\n",
"\t 'https://cdnjs.cloudflare.com/ajax/libs/three.js/r66/three.min',\n",
"\t 'custom/three.min'\n",
"\t ],\n",
" Elegans: [\n",
" 'https://cdn.rawgit.com/domitry/elegans/15e85b0dafdb6f09181c1ee2f0c47218f6fd698d/release/elegans.min',\n",
"\t 'custom/elegans'\n",
"\t ]\n",
"\t },\n",
"\t shim:{\n",
"\t THREE: {\n",
"\t exports: 'THREE'\n",
"\t },\n",
"\t Elegans: {\n",
"\t deps: ['THREE'],\n",
"\t exports: 'Elegans'\n",
"\t }\n",
"\t }\n",
"\t });\n",
"\n",
"\t require([\"d3\", \"THREE\"], function(d3){\n",
"\t window[\"d3\"] = d3;\n",
"\n",
"\t d3.select(document)\n",
"\t .on(\"contextmenu\", function(){\n",
"\t d3.selectAll(\"canvas\").style(\"z-index\", 10);\n",
"\t d3.selectAll(\".download_menu\").style(\"z-index\", 100);\n",
"\t });\n",
"\t });\n",
" }\n",
"\n",
" require([\"Elegans\"], function(){\n",
"\t console.log(\"Begin rendering...\");\n",
"\t var model = {\"plots\": [{\"type\": \"Particles\", \"options\": {\"name\": \"A\", \"size\": 1.2825815329416699, \"color\": \"#a6cee3\"}, \"data\": {\"z\": [8.871003989142618e-08, 8.90309596489202e-08, 1.4691197232326384e-07, 1.1555289480692738e-07, 4.9499938151929415e-08, 1.1102481205930223e-07, 2.6459306874430827e-08, 6.729369601415944e-09, 1.0623368399693475e-07, 1.6604923844729528e-08, 1.2634696526234624e-07, 8.266019127974575e-08, 9.74945626196683e-09, 8.379049709282616e-08, 1.4164163744428749e-09, 3.945403251508692e-08, 2.984217373547346e-08, 6.841009327353911e-08, 5.463311272127272e-08, 2.5564493760792387e-09, 1.3341398466719883e-07, 2.0457968385935938e-08, 1.036886581159891e-08, 1.1240088063962359e-07, 1.1401884551840264e-07, 9.25269580561109e-08, 1.2326938092307424e-07, 3.9949261251622985e-08, 1.0865518529282252e-07, 1.1947005985487642e-07, 8.999285273929804e-08, 1.9206545268874064e-08, 1.106093142825411e-07, 1.4424874845166565e-07, 5.049838749665288e-09, 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"\t // Elegans.Embed.parse(\"#\"+\"viza2caaca6-5023-44fd-9600-908429a11971\",model).render();\n",
"\t var stage = Elegans.Embed.parse(\"#\"+\"viza2caaca6-5023-44fd-9600-908429a11971\",model);\n",
" stage.world.camera.position.set(-22, 23, 32);\n",
" stage.world.camera.rotation.set(-0.6, 0.5, 0.6);\n",
"\t stage.render();\n",
" });\n",
" })();\n",
" </script>\n",
" </head>\n",
" <body>\n",
" <div id=\"viza2caaca6-5023-44fd-9600-908429a11971\"></div>\n",
" </body>\n",
"</html>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"viz.plot_world(w)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Running a simulation with logging."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sim = egfrd.BDSimulator(w)\n",
"sim.set_dt(1e-9)\n",
"sim.set_R(r_max)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"dt = 10e-7\n",
"obs1 = FixedIntervalCSVObserver(dt, \"result%03d.csv\")\n",
"# obs2 = FixedIntervalHDF5Observer(dt, \"test%03d.h5\")\n",
"obs2 = FixedIntervalTrajectoryObserver(dt, [pid for pid, p in w.list_particles(Species(\"A\"))], True, 1e-7)\n",
"# obs2 = FixedIntervalTrajectoryObserver(dt, [pid for pid, p in w.list_particles(Species(\"B\"))], True, 1e-7)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sim.initialize() #XXX: Donot forget this\n",
"sim.run(dt * 100, (obs1, obs2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Displaying trajectories of a part of tracers."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"\t require.config({\n",
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"\t d3: [\n",
"\t 'https://d3js.org/d3.v3.min',\n",
"\t 'custom/d3.min'\n",
"\t ],\n",
"\t THREE: [\n",
"\t 'https://cdnjs.cloudflare.com/ajax/libs/three.js/r66/three.min',\n",
"\t 'custom/three.min'\n",
"\t ],\n",
" Elegans: [\n",
" 'https://cdn.rawgit.com/domitry/elegans/15e85b0dafdb6f09181c1ee2f0c47218f6fd698d/release/elegans.min',\n",
"\t 'custom/elegans'\n",
"\t ]\n",
"\t },\n",
"\t shim:{\n",
"\t THREE: {\n",
"\t exports: 'THREE'\n",
"\t },\n",
"\t Elegans: {\n",
"\t deps: ['THREE'],\n",
"\t exports: 'Elegans'\n",
"\t }\n",
"\t }\n",
"\t });\n",
"\n",
"\t require([\"d3\", \"THREE\"], function(d3){\n",
"\t window[\"d3\"] = d3;\n",
"\n",
"\t d3.select(document)\n",
"\t .on(\"contextmenu\", function(){\n",
"\t d3.selectAll(\"canvas\").style(\"z-index\", 10);\n",
"\t d3.selectAll(\".download_menu\").style(\"z-index\", 100);\n",
"\t });\n",
"\t });\n",
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"\n",
" require([\"Elegans\"], function(){\n",
"\t console.log(\"Begin rendering...\");\n",
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-3.202021308505399e-08]}}], \"options\": {\"range\": {\"z\": [-8.99196665784049e-09, 1.8816102575916267e-07], \"x\": [-1.4308957834501441e-08, 1.8284403458250174e-07], \"y\": [-3.598195351420141e-08, 1.6117103890280177e-07]}, \"autorange\": false, \"save_image\": true, \"grid\": true, \"world_width\": 350, \"world_height\": 350}};\n",
"\t // Elegans.Embed.parse(\"#\"+\"viz5904598c-62d7-4777-a455-301dddb914af\",model).render();\n",
"\t var stage = Elegans.Embed.parse(\"#\"+\"viz5904598c-62d7-4777-a455-301dddb914af\",model);\n",
" stage.world.camera.position.set(-22, 23, 32);\n",
" stage.world.camera.rotation.set(-0.6, 0.5, 0.6);\n",
"\t stage.render();\n",
" });\n",
" })();\n",
" </script>\n",
" </head>\n",
" <body>\n",
" <div id=\"viz5904598c-62d7-4777-a455-301dddb914af\"></div>\n",
" </body>\n",
"</html>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"viz.plot_trajectory(obs2)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# viz.plot_movie_with_attractive_mpl(obs2, marker_size=9, species_list=['A'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Analyzing the mean square displacement of tracers."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy\n",
"data = numpy.array([[tuple(pos) for pos in obs2.data()[i]] for i in range(len(obs2.data()))])\n",
"m, n, _ = data.shape"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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TCVcKDEF28OhBZv7fTG49+1YGnTDI6eaEl5asSlo3GPj0BAr27ueBQZfTIeZM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\n+FFgEBERPwoMIiLi5/8DmxlnadfB3G4AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fc99944e0b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"retval = [0.0]\n",
"for i in range(1, n):\n",
" L = numpy.average([numpy.linalg.norm(data[j][i] - data[j][0]) for j in range(m)])\n",
" retval.append(L * L)\n",
"import matplotlib.pylab as plt\n",
"plt.plot(obs2.t(), retval, 'o-')\n",
"plt.plot(obs2.t(), numpy.array(obs2.t()) * 6 * D_A, '--')\n",
"plt.plot(obs2.t(), numpy.array(obs2.t()) * 6 * 3.1e-12, '.')\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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