{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Mean Square Displacement (MSD)\n", "\n", "This is a validation for the E-Cell4 library. Here, we test a mean square displacement (MSD) for each simulation algorithms." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy\n", "from ecell4.prelude import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Making a model for all. A single species `A` is defined. The radius is 5 nm, and the diffusion coefficient is 1um^2/s:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "radius, D = 0.005, 1\n", "m = NetworkModel()\n", "m.add_species_attribute(Species(\"A\", radius, D))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a random number generator, which is used through whole simulations below:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "rng = GSLRandomNumberGenerator()\n", "rng.seed(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Distribution along each axis\n", "\n", "First, a distribution along each axis is tested. The distribution after the time `t` should follow the normal distribution with mean 0 and variance `2Dt`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def plot_displacements(ret):\n", " distances = []\n", " for ret_ in ret:\n", " obs = ret_.observers[1]\n", " for data in obs.data():\n", " distances.extend(tuple(data[-1] - data[0]))\n", "\n", " _, bins, _ = plt.hist(distances, bins=30, density=True, facecolor='green', alpha=0.5, label='Simulation')\n", " xmax = max(abs(bins[0]), abs(bins[-1]))\n", " x = numpy.linspace(-xmax, +xmax, 101)\n", " gauss = lambda x, sigmasq: numpy.exp(-0.5 * x * x / sigmasq) / numpy.sqrt(2 * numpy.pi * sigmasq)\n", " plt.plot(x, gauss(x, 2 * D * duration), 'r-', label='Expected')\n", " plt.plot(x, gauss(x, sum(numpy.array(distances) ** 2) / len(distances)), 'k--', label='Fitting')\n", " plt.xlim(x[0], x[-1])\n", " plt.ylim(0, 1)\n", " plt.xlabel('Displacement')\n", " plt.ylabel('Frequenecy')\n", " plt.legend(loc='best', shadow=True)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "duration = 0.1\n", "N = 50\n", "obs = FixedIntervalTrajectoryObserver(0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `egfrd`:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "ret1 = ensemble_simulations(\n", " duration, ndiv=1, model=m, y0={'A': N}, observers=obs,\n", " solver=('egfrd', Integer3(4, 4, 4)), repeat=50)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_displacements(ret1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `spatiocyte`:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "ret2 = ensemble_simulations(\n", " duration, ndiv=1, model=m, y0={'A': N}, observers=obs,\n", " solver=('spatiocyte', radius), repeat=50)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_displacements(ret2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mean square displacement\n", "\n", "A mean square displacement after the time `t` is euqal to the variance above. The one of a diffusion in volume is `6Dt`. `ecell4.FixedIntervalTrajectoryObserver` enables to track a trajectory of a particle over periodic boundaries." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def test_mean_square_displacement(ret):\n", " t = numpy.array(ret[0].observers[1].t())\n", " sd = []\n", " for ret_ in ret:\n", " obs = ret_.observers[1]\n", " for data in obs.data():\n", " sd.append(numpy.array([length_sq(pos - data[0]) for pos in data]))\n", " return (t, numpy.average(sd, axis=0), numpy.std(sd, axis=0))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "duration = 3.0\n", "N = 50\n", "obs = FixedIntervalTrajectoryObserver(0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `egfrd`:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "ret1 = ensemble_simulations(\n", " duration, ndiv=1, model=m, y0={'A': N}, observers=obs,\n", " solver=('egfrd', Integer3(4, 4, 4)), repeat=10)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "t, mean1, std1 = test_mean_square_displacement(ret1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `spatiocyte`:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "ret2 = ensemble_simulations(\n", " duration, ndiv=1, model=m, y0={'A': N}, observers=obs,\n", " solver=('spatiocyte', radius), repeat=10)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "t, mean2, std2 = test_mean_square_displacement(ret2)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(t, 6 * D * t, 'k-', label=\"Expected\")\n", "plt.errorbar(t[::30], mean1[::30], yerr=std1[::30], fmt='go', label=\"eGFRD\")\n", "plt.errorbar(t[::30], mean2[::30], yerr=std2[::30], fmt='ro', label=\"Spatiocyte\")\n", "plt.xlim(t[0], t[-1])\n", "plt.legend(loc=\"best\", shadow=True)\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Mean Square Displacement\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mean square displacement in a cube\n", "\n", "Here, we test a mean square diplacement in a cube. For the periodic boundaries, particles cannot escape from World, and thus the displacement for each axis is less than a half of the World size. In `meso` simulations, unlike `egfrd` and `spatiocyte`, each molecule doesn't have its `ParticleID`. `meso` is just validated in this condition because `FixedIntervalTrajectoryObserver` is only available with `ParticleID`." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def multirun(target, job, repeat, method=None, **kwargs):\n", " from ecell4.extra.ensemble import run_ensemble, genseeds\n", " from ecell4.util.session import ResultList\n", " \n", " return run_ensemble(target, [list(job) + [genseeds(repeat)]], repeat=repeat, method=method, **kwargs)[0]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def singlerun(job, job_id, task_id):\n", " from ecell4_base.core import AABB, Real3, GSLRandomNumberGenerator\n", " from ecell4_base.core import FixedIntervalNumberObserver, FixedIntervalTrajectoryObserver\n", " from ecell4.util.session import get_factory\n", " from ecell4.extra.ensemble import getseed\n", "\n", " duration, solver, ndiv, myseeds = job\n", " rndseed = getseed(myseeds, task_id)\n", "\n", " f = get_factory(*solver)\n", " f.rng(GSLRandomNumberGenerator(rndseed))\n", " w = f.world(ones())\n", " L_11, L_2 = 1.0 / 11, 1.0 / 2\n", " w.bind_to(m)\n", " NA = 12\n", " w.add_molecules(Species(\"A\"), NA, AABB(Real3(5, 5, 5) * L_11, Real3(6, 6, 6) * L_11))\n", "\n", " sim = f.simulator(w)\n", "\n", " retval = [sum(length_sq(p.position() - Real3(L_2, L_2, L_2)) for pid, p in w.list_particles_exact(Species(\"A\"))) / NA]\n", " for i in range(ndiv):\n", " sim.run(duration / ndiv)\n", " mean = sum(length_sq(p.position() - Real3(L_2, L_2, L_2)) for pid, p in w.list_particles_exact(Species(\"A\"))) / NA\n", " retval.append(mean)\n", " return numpy.array(retval)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "duration = 0.15\n", "ndiv = 20\n", "t = numpy.linspace(0, duration, ndiv + 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `egfrd`:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "ret1 = multirun(singlerun, job=(duration, (\"egfrd\", Integer3(4, 4, 4)), ndiv), repeat=50)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "mean1 = numpy.average(ret1, axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `spatiocyte`:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "ret2 = multirun(singlerun, job=(duration, (\"spatiocyte\", radius), ndiv), repeat=50)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "mean2 = numpy.average(ret2, axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `meso`:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "ret3 = multirun(singlerun, job=(duration, (\"meso\", Integer3(11, 11, 11)), ndiv), repeat=50)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "mean3 = numpy.average(ret3, axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mean square displacement at the uniform distribution in a cube is calculated as follows:\n", "\n", "$\\int_0^1\\int_0^1\\int_0^1 dxdydz\\ (x-0.5)^2+(y-0.5)^2+(z-0.5)^2=3\\left[\\frac{(x-0.5)^3}{3}\\right]_0^1=0.25$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(t, 6 * D * t, 'k-', label=\"Expected\")\n", "plt.plot((t[0], t[-1]), (0.25, 0.25), 'k--', label='Uniform distribution')\n", "plt.plot(t, mean1, 'go', label=\"eGFRD\")\n", "plt.plot(t, mean2, 'ro', label=\"Spatiocyte\")\n", "plt.plot(t, mean3, 'bo', label=\"Meso\")\n", "plt.xlim(t[0], t[-1])\n", "plt.ylim(0, 0.3)\n", "plt.legend(loc=\"best\", shadow=True)\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Mean Square Displacement\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mean square displacement in 2D\n", "\n", "Spatial simulation with a structure is only supported by `spatiocyte` and `meso` now. Here, mean square displacement on a planar surface is tested for these algorithms.\n", "\n", "First, a model is defined with a species `A` which has the same attributes with above except for the location named `M`." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "radius, D = 0.005, 1\n", "\n", "m = NetworkModel()\n", "A = Species(\"A\", radius, D, \"M\")\n", "A.set_attribute(\"dimension\", 2)\n", "m.add_species_attribute(A)\n", "M = Species(\"M\", radius, 0)\n", "M.set_attribute(\"dimension\", 2)\n", "m.add_species_attribute(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mean square displacement of a 2D diffusion must follow `4Dt`. The diffusion on a planar surface parallel to yz-plane at the center is tested with `spatiocyte`." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "duration = 0.3\n", "N = 50\n", "obs = FixedIntervalTrajectoryObserver(0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `spatiocyte`:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "ret2 = ensemble_simulations(\n", " duration, ndiv=1, model=m, y0={'A': N}, observers=obs,\n", " structures={'M': PlanarSurface(0.5 * ones(), unity(), unitz())},\n", " solver=('spatiocyte', radius), repeat=50)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "t, mean2, std2 = test_mean_square_displacement(ret2)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(t, 6 * D * t, 'k--', label=\"Expected 3D\")\n", "plt.plot(t, 4 * D * t, 'k-', label=\"Expected 2D\")\n", "plt.errorbar(t, mean2, yerr=std2, fmt='ro', label=\"Spatiocyte\")\n", "plt.xlim(t[0], t[-1])\n", "plt.legend(loc=\"best\", shadow=True)\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Mean Square Displacement\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plottig the trajectory of particles on a surface with `spatiocyte`:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "viz.plot_trajectory(ret2[0].observers[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mean square displacement on a planar surface restricted in a cube by periodic boundaries is compared between `meso` and `spatiocyte`." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "def singlerun(job, job_id, task_id):\n", " from ecell4_base.core import AABB, Real3, GSLRandomNumberGenerator\n", " from ecell4_base.core import FixedIntervalNumberObserver, FixedIntervalTrajectoryObserver\n", " from ecell4.util.session import get_factory\n", " from ecell4.extra.ensemble import getseed\n", "\n", " duration, solver, ndiv, myseeds = job\n", " rndseed = getseed(myseeds, task_id)\n", "\n", " f = get_factory(*solver)\n", " f.rng(GSLRandomNumberGenerator(rndseed))\n", "\n", " w = f.world(ones())\n", " L_11, L_2 = 1.0 / 11, 1.0 / 2\n", " w.bind_to(m)\n", " NA = 12\n", " w.add_structure(Species(\"M\"), PlanarSurface(0.5 * ones(), unity(), unitz()))\n", " w.add_molecules(Species(\"A\"), NA, AABB(ones() * 5 * L_11, ones() * 6 * L_11))\n", "\n", " sim = f.simulator(w)\n", "\n", " retval = [sum(length_sq(p.position() - Real3(L_2, L_2, L_2)) for pid, p in w.list_particles_exact(Species(\"A\"))) / NA]\n", " for i in range(ndiv):\n", " sim.run(duration / ndiv)\n", " mean = sum(length_sq(p.position() - Real3(L_2, L_2, L_2)) for pid, p in w.list_particles_exact(Species(\"A\"))) / NA\n", " retval.append(mean)\n", " return numpy.array(retval)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "duration = 0.15\n", "ndiv = 20\n", "t = numpy.linspace(0, duration, ndiv + 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `spatiocyte`:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "ret2 = multirun(singlerun, job=(duration, (\"spatiocyte\", radius), ndiv), repeat=50)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "mean2 = numpy.average(ret2, axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulating with `meso`:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "ret3 = multirun(singlerun, job=(duration, (\"meso\", Integer3(11, 11, 11)), ndiv), repeat=50)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "mean3 = numpy.average(ret3, axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mean square displacement at the uniform distribution on a plane is calculated as follows:\n", "\n", "$\\int_0^1\\int_0^1 dxdydz\\ (0.5-0.5)^2+(y-0.5)^2+(z-0.5)^2=2\\left[\\frac{(x-0.5)^3}{3}\\right]_0^1=\\frac{1}{6}$" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(t, 4 * D * t, 'k-', label=\"Expected\")\n", "plt.plot((t[0], t[-1]), (0.5 / 3, 0.5 / 3), 'k--', label='Uniform distribution')\n", "plt.plot(t, mean2, 'ro', label=\"Spatiocyte\")\n", "plt.plot(t, mean3, 'bo', label=\"Meso\")\n", "plt.xlim(t[0], t[-1])\n", "plt.ylim(0, 0.2)\n", "plt.legend(loc=\"best\", shadow=True)\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Mean Square Displacement\")\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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 1 }