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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Spatiocyte simulations with single-molecule resolution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We showed an example of E-Cell4 spatial representation. \n",
"Next let's simulate the models with more detailed spatial representation called **single molecule resolution**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Spatiocyte lattice-based method\n",
"\n",
"In spatical Gillespie method, we divided the **Space** into smaller **Space**, then we diffuse the molecules in the **Subvolume**.\n",
"However we simulated the molecules in the **Subvolume** as the number of the molecules, and the location of the molecules are NOT determinated.\n",
"\n",
"In other words, the spatical resolution of spatical Gillespie method is equal to the side of the **Subvolume** $l$.\n",
"To improve this resolution we need to make the size of $l$ small, but in this method the $l$ must be larger than the (at least) 10 times the diameter of molecule $R$.\n",
"\n",
"How can we improve the spatical resolution to the size of the molecule?\n",
"The answer is the simulation with single-molecule resolution.\n",
"This method simulate the molecule not with the number of the molecules, but with the spatical reaction diffusion of each molecule.\n",
"\n",
"E-Cell4 has multiple single-molecule resolution method, here we explain about Spatiocyte lattice-based method.\n",
"\n",
"Spatiocyte treat each molecule as hard sphere and diffuse the molecules in hexagonal close-packed lattice.\n",
"\n",
"Spatiocyte has ID for each molecule and the position of the molecule with single-molecule resolution.\n",
"To use the time scale, Spatiocyte has 100 times smaller time-step than spatical Gillespie, because the time scale of diffusion increases with the square of the distance.\n",
"\n",
"Next, let's use Spatiocyte.\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from ecell4 import *\n",
"\n",
"with species_attributes():\n",
" A | B | C | {'D': '1'}\n",
"\n",
"with reaction_rules():\n",
" A + B == C | (0.01, 0.3)\n",
"\n",
"m = get_model()\n",
"w = lattice.LatticeWorld(Real3(1, 1, 1), 0.005) # The second argument is 'voxel_radius'.\n",
"w.bind_to(m)\n",
"w.add_molecules(Species('C'), 60)\n",
"sim = lattice.LatticeSimulator(w)\n",
"obs = FixedIntervalNumberObserver(0.1, ('A', 'B', 'C'))\n",
"sim.run(10, obs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is a distinct difference in the second argument for **LatticeWorld**. This is called **Voxel radius**.\n",
"Spatiocyte defines the locations of the molecules with dividing the Space with molecule size, and call the minimum unit for this Space as **Voxel**.\n",
"\n",
"In most cases the size of the molecule would be good for **Voxel radius**.\n",
"\n",
"In this example, we set 5 $\\mathrm{nm}$ as the radius of the molecule in the Space with the side 1 $\\mathrm{\\mu m}$ .\n",
"\n",
"It takes more time to simulate, but the result is same with ODE or Gillespie."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The diffusion movement of single molecule\n",
"\n",
"Next let's simulate single molecule diffusion to check the resolution.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from ecell4 import *\n",
"\n",
"with species_attributes():\n",
" A | {'D': '1'}\n",
"\n",
"m = get_model()\n",
"w = lattice.LatticeWorld(Real3(1, 1, 1), 0.005)\n",
"w.bind_to(m)\n",
"\n",
"(pid, p), suc = w.new_particle(Species('A'), Real3(0.5, 0.5, 0.5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**new_particle** method places a particle to a coordinate in **LatticeWorld**, and returns the particle's **pid**, the information about the particle **p**, and verify whether the particle is cooked with **suc**.\n",
"If a particle is already placed in the coordinate you can NOT place a particle over it and **suc** will be False and fail.\n",
"\n",
"**p** contains the particle position, species type, radius, and diffusion coefficient.\n",
"You can inspect the **p** with the particle's ID **pid**.\n",
"\n",
"Let's check **p**."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A\n",
"0.005 1.0\n",
"(0.49806291436591293, 0.49652123150307814, 0.5)\n"
]
}
],
"source": [
"pid, p = w.get_particle(pid)\n",
"print(p.species().serial()) # will print: A\n",
"print(p.radius(), p.D()) # will print: (0.005, 1.0)\n",
"print(tuple(p.position())) # will print: (0.49806291436591293, 0.49652123150307814, 0.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**get_particle** method receives the particle ID and returns the ID and particle (of cource the IDs are same).\n",
"You can inspect the coordinate of the particle as **Real3** with **position** method.\n",
"It is hard to directly read the coordinate, here we printed it after converting to tuple.\n",
"As you can see the tuple coodinate is slightly different from original **Real3**. This is because Spatiocyte can place the molecule only on the lattice.\n",
"**LatticeWorld** places the molecule the nearest lattice for the argument **Real3**.\n",
"\n",
"You can visualize the coordinate of the molecule with **viz.plot_world** method, and check the molecule in the center of the World.\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
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"<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://cdnjs.cloudflare.com/ajax/libs/d3/3.4.4/d3.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",
"\t 'https://rawgit.com/domitry/elegans/master/release/elegans',\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 = {\"options\": {\"save_image\": true, \"height\": 500, \"autorange\": false, \"width\": 500, \"range\": {\"x\": [0.0, 1.0], \"y\": [0.0, 1.0], \"z\": [0.0, 1.0]}, \"grid\": true}, \"plots\": [{\"data\": {\"x\": [0.49806291436591293], \"y\": [0.49652123150307814], \"z\": [0.5]}, \"options\": {\"name\": \"A\", \"size\": 0.15, \"color\": \"#a6cee3\"}, \"type\": \"Particles\"}]};\n",
"\t Elegans.Embed.parse(\"#\"+\"viz8b03c1cd-09b9-4cbb-a56c-39e11af65742\",model).render();\n",
" });\n",
" })();\n",
" </script>\n",
" </head>\n",
" <body>\n",
" <div id=\"viz8b03c1cd-09b9-4cbb-a56c-39e11af65742\"></div>\n",
" </body>\n",
"</html>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"{'A': '#a6cee3'}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"viz.plot_world(w, save_image=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And you can use **Observer** to track the trajectory of molecular diffusion process."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<html>\n",
" <head>\n",
" <script type=\"text/javascript\">\n",
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" if(window[\"THREE\"] === undefined || window[\"d3\"] === undefined){\n",
"\t require.config({\n",
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"\t d3: [\n",
"\t 'https://cdnjs.cloudflare.com/ajax/libs/d3/3.4.4/d3.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",
"\t 'https://rawgit.com/domitry/elegans/master/release/elegans',\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 = {\"options\": {\"width\": 500, \"height\": 500, \"autorange\": false, \"grid\": true, \"range\": {\"x\": [-2.3564535657527976, 0.6955079584742688], \"y\": [-1.771946643670098, 1.2800148805569687], \"z\": [-0.2084807621135334, 2.843480762113533]}}, \"plots\": [{\"data\": {\"x\": [0.49806291436591293, 0.5878775382679629, 0.563382640840131, 0.5797125724586856, 0.49806291436591293, 0.59604250407724, 0.6042074698865173, 0.6287023673143491, 0.6287023673143491, 0.6123724356957946, 0.5878775382679629, 0.5552176750308537, 0.48173298274735843, 0.4082482904638631, 0.4245782220824176, 0.5062278801751902, 0.5225578117937447, 0.5715476066494083, 0.5062278801751902, 0.6776921621700127, 0.6287023673143491, 0.6205374015050719, 0.5552176750308537, 0.6123724356957946, 0.5062278801751902, 0.5388877434122993, 0.4409081537009721, 0.4245782220824176, 0.47356801693808115, 0.3837533930360313, 0.48989794855663565, 0.4409081537009721, 0.4409081537009721, 0.45723808531952664, 0.3510935297989222, 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"\t Elegans.Embed.parse(\"#\"+\"viz7d7f5093-d218-4d0d-a477-e08dbe86d533\",model).render();\n",
" });\n",
" })();\n",
" </script>\n",
" </head>\n",
" <body>\n",
" <div id=\"viz7d7f5093-d218-4d0d-a477-e08dbe86d533\"></div>\n",
" </body>\n",
"</html>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"{'1': '#a6cee3'}"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sim = lattice.LatticeSimulator(w)\n",
"obs = FixedIntervalTrajectoryObserver(0.002, (pid,))\n",
"sim.run(1, obs)\n",
"viz.plot_trajectory(obs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we visualized the trajectory with **viz.plot_trajectory** method, you can also obtain it as Real3 list with **data** method.\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1\n",
"501\n"
]
}
],
"source": [
"print(len(obs.data()))\n",
"print(len(obs.data()[0]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**data** method returns nested list.\n",
"First index means the index of the particle.\n",
"Second index means the index of the **Real3**.\n",
"In this case we threw just one particle, so the first result is **1**, and next **501** means time-series coordinate of the only one particle (initial coordinate and the coordinates in 1/0.002 = 500 time points)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Also you can obtain the particles in bulk with **list_particles** method and species type."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A (0.6940220937885672, 0.42723919920032305, 0.79)\n",
"A (0.12247448713915891, 0.8256108849411649, 0.96)\n",
"A (0.47356801693808115, 0.9699484522385713, 0.11)\n",
"A (0.563382640840131, 0.3925981830489455, 0.13)\n",
"A (0.23678400846904057, 0.5051814855409226, 0.195)\n",
"A (0.07348469228349536, 0.002886751345948129, 0.8250000000000001)\n"
]
}
],
"source": [
"w.add_molecules(Species('A'), 5)\n",
"\n",
"particles = w.list_particles(Species('A'))\n",
"for pid, p in particles:\n",
" print(p.species().serial(), tuple(p.position()))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Please remember **list_particles** method, this method can be used for other World as well as **add_molecules** method.\n",
"\n",
"On a different note, in Spatiocyte proper method to inspect the single molecule is **list_voxels**, and the coordinate is described with index of voxel (not Real3)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The diffusion coefficient and the second-order reaction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The models we have addressed are called **second-order reaction**.\n",
"Let's look at the relationship between this second-order reaction and the diffusion coefficient in Spatiocyte."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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ZrKp6TAjjKqvBRHt/SgTSsW88CCBXdP8XNZa/hrN4lHtE2uJkFb4c1UmuxmJM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\np2PeeCAcMRtjwiv6mpgOPCaJPAX0B2o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"text/plain": [
"<matplotlib.figure.Figure at 0x10ad4e4e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ecell4 import *\n",
"\n",
"with species_attributes():\n",
" A | B | C | {'D': '1'}\n",
"\n",
"with reaction_rules():\n",
" A + B > C | 1.0\n",
"\n",
"m = get_model()\n",
"w = lattice.LatticeWorld(Real3(2, 1, 1), 0.005)\n",
"\n",
"w.bind_to(m)\n",
"\n",
"w.add_molecules(Species('A'), 120)\n",
"w.add_molecules(Species('B'), 120)\n",
"\n",
"obs = FixedIntervalNumberObserver(0.005, ('A', 'B', 'C'))\n",
"sim = lattice.LatticeSimulator(w)\n",
"sim.run(1.0, obs)\n",
"\n",
"%matplotlib inline\n",
"\n",
"odew = ode.ODEWorld(Real3(2, 1, 1))\n",
"odew.bind_to(m)\n",
"odew.add_molecules(Species('A'), 120)\n",
"odew.add_molecules(Species('B'), 120)\n",
"odeobs = FixedIntervalNumberObserver(0.005, ('A', 'B', 'C'))\n",
"odesim = ode.ODESimulator(odew)\n",
"odesim.run(1.0, odeobs)\n",
"viz.plot_number_observer(obs, \"-\", odeobs, \"--\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although we used faster kinetic constant than before, the result is same.\n",
"But by contrast with ODE simulation, you can find the difference between them (solid line is Spatiocyte, dash line is ODE)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Is this fault of Spatiocyte? (No)\n",
"Actually Spatiocyte reaction rate couldn't be faster, while ODE reaction rate can be faster infinitely."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is caused by the difference between the definition of reaction rate constant in **ODE solver** and **single molecule simulation method**. \n",
"\n",
"The former is called **macroscopic** or **effective** reaction rate constant, the latter is called **microscopic** or **intrinsic** reaction rate constant.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The **macroscopic** rate represents the reaction rate in mixed molecular state, meanwhile **microscopic** rate represents the reactivity in molecule collision.\n",
"So in **microscopic** perspective, the first thing molecules need to react is collision.\n",
"\n",
"In Spatiocyte however you make this **microscopic** rate faster, you can NOT make the reaction rate faster than diffusion rate.\n",
"This is called **diffusion-limited**.\n",
"This is similar to what the molecules coordinated disproportionately need time to react."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is known that there is a relationship between this macroscopic rate constant $k_\\mathrm{on}$ and microscopic rate constant $k_a$ in 3D space."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"$\n",
"\\frac{1}{k_\\mathrm{on}}=\\frac{1}{k_a}+\\frac{1}{4\\pi RD_\\mathrm{tot}}\n",
"$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, $R$ is the sum of two molecule's radius in collision, $D_\\mathrm{tot}$ is the sum of diffusion coefficients.\n",
"In the case of the above IPython Notebook cell, $k_D=4\\pi RD_\\mathrm{tot}$ is almost 0.25 and **microscopic** rate constant is 1.0.\n",
"So the **macroscopic** rate constant is almost 0.2.\n",
"\n",
"(However unless you specify the configuration for Spatiocyte, the second order reaction rate must be slower than $3\\sqrt{2} RD$, and the dissociation constant $k_D$ is also $3\\sqrt{2} RD$.\n",
"\n",
"The single molecule simulation method can separate molecular **diffusion** and **reaction** in accurate manner contrary to ODE or Gillespie method supposed well mixed system (that is diffusion coefficient is infinite).\n",
"\n",
"However if the microscopic rate constant $k_D$ is small enough, the macroscopic rate constant is almost equal to microscopic one (reaction late-limit)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The structure in the Spatiocyte method"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we explain a way to create a structure like cell membrane.\n",
"Although The structure feature in E-Cell4 is still in development, Spatiocyte supports the structure on some level.\n",
"Let's look a sphere structure as an example.\n",
"\n",
"To restrict the molecular diffusion inside of the sphere, first we create it.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"539805\n"
]
},
{
"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://cdnjs.cloudflare.com/ajax/libs/d3/3.4.4/d3.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",
"\t 'https://rawgit.com/domitry/elegans/master/release/elegans',\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 = {\"options\": {\"height\": 500, \"autorange\": false, \"save_image\": false, \"width\": 500, \"grid\": true, \"range\": {\"x\": [0.0, 1.0], \"y\": [0.0, 1.0], \"z\": [0.0, 1.0]}}, \"plots\": [{\"options\": {\"name\": \"C\", \"color\": \"#a6cee3\", \"size\": 0.15}, \"type\": \"Particles\", \"data\": {\"x\": [0.3347635981803677, 0.7266819570256763, 0.5552176750308537, 0.751176854453508, 0.5143928459844674, 0.7266819570256763, 0.7021870595978444, 0.13880441875771343, 0.7021870595978444, 0.6776921621700127, 0.5797125724586856, 0.187794213613377, 0.05715476066494083, 0.44907311951024936, 0.68585712797929, 0.563382640840131, 0.3592584956081995, 0.3837533930360313, 0.4409081537009721, 0.5062278801751902, 0.7756717518813399, 0.8899812732112214, 0.5388877434122993, 0.8328265125462806, 0.68585712797929, 0.7266819570256763, 0.8654863757833897, 0.4164132562731403, 0.2939387691339814, 0.6368673331236264, 0.3184336665618132, 0.8001666493091716, 0.28577380332470415, 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"\t Elegans.Embed.parse(\"#\"+\"viz8a9a2046-5bd0-4482-8556-a3f28488f3d5\",model).render();\n",
" });\n",
" })();\n",
" </script>\n",
" </head>\n",
" <body>\n",
" <div id=\"viz8a9a2046-5bd0-4482-8556-a3f28488f3d5\"></div>\n",
" </body>\n",
"</html>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"{'C': '#a6cee3'}"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w = lattice.LatticeWorld(Real3(1, 1, 1), 0.005)\n",
"sph = Sphere(Real3(0.5, 0.5, 0.5), 0.45)\n",
"print(w.add_structure(Species('C'), sph)) # will print 539805\n",
"viz.plot_world(w)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with species_attributes():\n",
" A | {'D': '1', 'location': 'C'}\n",
"\n",
"m = get_model()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"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://cdnjs.cloudflare.com/ajax/libs/d3/3.4.4/d3.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",
"\t 'https://rawgit.com/domitry/elegans/master/release/elegans',\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 = {\"options\": {\"height\": 500, \"autorange\": false, \"save_image\": false, \"width\": 500, \"grid\": true, \"range\": {\"x\": [0.0, 1.0], \"y\": [0.0, 1.0], \"z\": [0.0, 1.0]}}, \"plots\": [{\"options\": {\"name\": \"A\", \"color\": \"#1f78b4\", \"size\": 0.15}, \"type\": \"Particles\", \"data\": {\"x\": [0.040824829046386304, 0.22045407685048604, 0.9471360338761623, 0.7593418202627853, 0.3347635981803677, 0.040824829046386304, 0.6368673331236264, 0.05715476066494083, 0.08164965809277261, 0.8164965809277261, 0.8083316151184489, 0.2531139400875951, 0.6613622305514582, 0.7430118886442307, 0.187794213613377, 0.6940220937885672, 0.06531972647421809, 0.8818163074019442, 0.06531972647421809, 0.6123724356957946, 0.46540305112880387, 0.7266819570256763, 0.0, 0.9797958971132713, 0.8164965809277261, 0.7266819570256763, 0.04898979485566357, 0.3674234614174768, 0.9879608629225486, 0.8246615467370034, 0.873651341592667, 0.20412414523193154, 0.09797958971132714, 0.9879608629225486, 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0.626425042070744, 0.9612881982007269, 0.28867513459481287, 0.5715767664977295, 0.7736493607140986, 0.5225019936166114, 0.874685657822283, 0.008660254037844387], \"z\": [0.05, 0.065, 0.72, 0.845, 0.1, 0.03, 0.03, 0.07, 0.09, 0.88, 0.4, 0.995, 0.055, 0.05, 0.12, 0.98, 0.92, 0.28, 0.155, 0.9450000000000001, 0.28500000000000003, 0.20500000000000002, 0.49, 0.495, 0.185, 0.87, 0.74, 0.985, 0.585, 0.56, 0.88, 0.275, 0.085, 0.395, 0.16, 0.9450000000000001, 0.88, 0.405, 0.675, 0.71, 0.16, 0.735, 0.03, 0.055, 0.195, 0.105, 0.06, 0.31, 0.115, 0.9500000000000001, 0.325, 0.89, 0.86, 0.795, 0.375, 0.74, 0.795, 0.025, 0.145, 0.74, 0.04, 0.47500000000000003, 0.23500000000000001, 0.755, 0.295, 0.225, 0.995, 0.53, 0.18, 0.045, 0.975, 0.835, 0.74, 0.20500000000000002, 0.245, 0.405, 0.78, 0.085, 0.9, 0.22, 0.0, 0.41500000000000004, 0.7000000000000001, 0.51, 0.45, 0.47000000000000003, 0.64, 0.545, 0.305, 0.02, 0.745, 0.5700000000000001, 0.28, 0.595, 0.075, 0.8200000000000001, 0.835, 0.01, 0.465, 0.71, 0.76, 0.8300000000000001, 0.025, 0.9500000000000001, 0.895, 0.065, 0.785, 0.37, 0.03, 0.0, 0.335, 0.915, 0.115, 0.865, 0.21, 0.9, 0.84, 0.115, 0.925, 0.595]}}]};\n",
"\t Elegans.Embed.parse(\"#\"+\"vizf723be44-c096-49f1-800c-e47b6eec7deb\",model).render();\n",
" });\n",
" })();\n",
" </script>\n",
" </head>\n",
" <body>\n",
" <div id=\"vizf723be44-c096-49f1-800c-e47b6eec7deb\"></div>\n",
" </body>\n",
"</html>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"{'A': '#1f78b4', 'C': '#a6cee3'}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w.add_molecules(Species('A'), 120)\n",
"viz.plot_world(w, species_list=('A',)) # visualize A-molecules only"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "ValueError",
"evalue": "A world must be bound to a model.",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-5-ec1e9d0ccde6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mpid_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mpid\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mpid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlist_particles\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mSpecies\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'A'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mobs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFixedIntervalTrajectoryObserver\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1e-3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpid_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0msim\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLatticeSimulator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0msim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mobs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mviz\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot_trajectory\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32mecell4/lattice.pyx\u001b[0m in \u001b[0;36mecell4.lattice.LatticeSimulator.__cinit__ (lib/ecell4/lattice.cpp:7203)\u001b[0;34m()\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: A world must be bound to a model."
]
}
],
"source": [
"pid_list = [pid for pid, p in w.list_particles(Species('A'))[: 10]]\n",
"obs = FixedIntervalTrajectoryObserver(1e-3, pid_list)\n",
"sim = lattice.LatticeSimulator(w)\n",
"sim.run(1, obs)\n",
"viz.plot_trajectory(obs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The structure and the reaction"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"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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