{ "metadata": { "name": "", "signature": "sha256:24d8bbfdbd22db2a05986039d2951737f00d73534fbf13eda009a452e3469e82" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%load_ext autoreload\n", "%autoreload 2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "%run nb_init.py" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "2015-01-26 09:33:26,838 -leg_joint -INFO -successfully imported leg_joint\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Energetical aspects of the model\n", "\n", "\n", "## Total energy of the epithelium\n", "\n", "According to the [Farhadifar et\n", "al. paper](http://dx.doi.org/10.1016/j.cub.2007.11.049), in the case\n", "of a regular hexagonal latice, energy is given by:\n", "\n", "$$\n", "E = N\\frac{K}{2} (A - A_0)^2 + N\\frac{\\Gamma}{2} L^2 +\n", "6N\\frac{\\Lambda}{2}\\ell\n", "$$\n", "\n", "In our model, the area dependant term is replaced by a volume\n", "term :\n", "$$ E = N\\frac{K_v}{2} (V - V_0)^2 + N\\frac{\\Gamma}{2}\n", "L^2 + 3N\\Lambda\\ell $$\n", "\n", "Here the $V = A(\\rho - R_L) = Ah $ where $R_L$ is the lumen radius and $\\rho$ the radius of the apical sheet of the epithelium.\n", "As they did, we define the adimentional contractility $\\bar\\Gamma = \\Gamma/K_vA_0h_0^2$ and line tension\n", "$\\bar\\Lambda = \\Lambda /K_v (A_0^{3/2}h_0^2)$, where $h_0$ is such that $V_0 = A_0h_0$.\n", "\n", "\n", "As the epithelium is distributed over a cylinder, the radius of the cylinder determines the number of cells forming a ring around it, $ N_\\perp $, so we have: $ \\ell = \\frac{2\\pi}{N_\\perp}\\rho $ if the cells are aligned along the $z$ axis.\n", "The perimeter $L$ of a cell is equal to $6\\ell$ and the area $A$\n", "equals $(3\\sqrt{3}/2)\\ell^2$. We define the constant $\\mu = 6\\left(2/3\\sqrt{3}\\right)^{1/2}$,\n", "then $\\ell = \\frac{\\mu}{6}A^{1/2}$ and $L^2 = \\mu^2 A$. \n", "\n", "The normalized energy $\\bar E = E/NK_v(A_0h_0)^2$ then reads:\n", "$$\n", "\\bar E = \\frac{1}{2} \\left(\\frac{V - V_0}{V_0}\\right)^2\n", "+ \\frac{\\bar\\Gamma}{2A_0}\\mu^2 A\n", "+ \\frac{\\bar\\Lambda}{A_0^{1/2}} \\frac{\\mu}{2} A^{1/2} \n", "$$\n", "\n", "We define the dilatation factor $\\delta$ such that $\\delta = \\rho/\\rho_0 = h/h_0$, $A/A_0 = \\delta^2$ and $V/V_0 = \\delta^3$.\n", "The previous equation becomes:\n", "\n", "$$\n", "\\bar E = \\frac{1}{2} \\left(\\delta^3 - 1\\right)^2\n", "+ \\frac{\\mu^2\\bar\\Gamma}{2}\\delta^2\n", "+ \\frac{\\mu\\bar\\Lambda}{2}\\delta \n", "$$\n", "\n", "The same calculus in the 2D case gives:\n", "$$\n", "\\bar E_{2D} = \\frac{1}{2} (\\delta^2 - 1)^2\n", "+ \\frac{\\mu^2\\bar\\Gamma}{2}\\delta^2\n", "+ \\frac{\\mu\\bar\\Lambda}{2}\\delta \n", "$$\n", "\n", "We can implement those functions rightaway:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pylab as plt\n", "mu = 6 * np.sqrt(2. / (3 * np.sqrt(3)))\n", "\n", "def elasticity(delta):\n", " return (delta**3 - 1 )**2 / 2.\n", "\n", "def contractility(delta, gamma):\n", " return gamma * mu**2 * delta**2 / 2.\n", "\n", "def tension(delta, lbda):\n", " return lbda * mu * delta / 2.\n", "\n", "def isotropic_energy(delta, gamma, lbda):\n", " \n", " energy = (elasticity(delta)\n", " + contractility(delta, gamma)\n", " + tension(delta, lbda))\n", " return energy\n", "\n", "def isotropic_energy_2D(delta, gamma, lbda):\n", " elasticity = (delta**2 - 1)**2 / 2.\n", " contractility = gamma * mu**2 * delta**2 / 2.\n", " tension = lbda * mu * delta / 2.\n", " return elasticity + contractility + tension\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "delta = np.linspace(0, 1.2, 200)\n", "#aspects = np.logspace(-6, 0, 40, base=2)\n", "fig, ax = plt.subplots(figsize=(6, 4))\n", "ax.plot(delta, isotropic_energy_2D(delta, 0.04, 0.12), 'b-', lw=2, alpha=0.8, label='2D case')\n", "ax.plot(delta, isotropic_energy(delta, 0.04, 0.12), 'k-', lw=2, alpha=0.8, label='3D case')\n", "\n", "#for aspect in aspects:\n", "# ax.plot(delta, isotropic_energy(delta, aspect, 0.04, 0.12), 'b-',\n", "# label=(r'$R_L/R_0 = %.3e$' % aspect), alpha= aspect * 0.6)\n", "ylbl = ax.set_ylabel(r'Normalized energy $\\bar E$')\n", "xlblb = ax.set_xlabel('')\n", "xlblb = ax.set_xlabel(r'Scaling factor $\\delta$')\n", "\n", "ax.legend(loc='upper left')\n", "\n", "fig.savefig(lj.data.get_image('isotropic_energy_vs_scaling.svg'))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/home/guillaume/anaconda/envs/python3/lib/python3.4/site-packages/matplotlib-1.4.x-py3.4-linux-x86_64.egg/matplotlib/figure.py:1644: UserWarning: This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n", " warnings.warn(\"This figure includes Axes that are not \"\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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NGuUpGzduHOPGjSs+6mPMI488QmJiImeccQYtWrTgwIEDLF68mPvvv59nn32WhQsX0rlz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\n+tCrVy+6du1Kly5diImJaZT8GWM4cuQIO3bsYPv27Xz55Zf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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Epithelium ground state and phase diagramm\n", "\n", "### Gradient expression\n", "\n", "The ground state of the regular epithelium is attained when enregy is minimal with respect to $\\delta$:\n", "\n", "$$\n", "\\frac{\\partial \\bar E}{\\partial \\delta} = 0\n", "$$\n", "\n", "That is (dropping the top bar notation):\n", "\n", "$$\n", "3 \\delta^2(\\delta^3 - 1)\n", "+ \\mu^2\\Gamma\\delta\n", "+ \\frac{\\mu\\Lambda}{2} = 0\n", "$$\n", "\n", "\n", "In 2D:\n", "\n", "$$\n", "2 \\delta(\\delta^2 - 1)\n", "+ \\mu^2\\Gamma\\delta\n", "+ \\frac{\\mu\\Lambda}{2} = 0\n", "$$\n", "\n", "\n", "Once again let's code this:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def isotropic_grad_poly(lbda, gamma):\n", " grad_poly = [3, 0, 0,\n", " -3,\n", " mu**2 * gamma,\n", " mu * lbda / 2.]\n", " return grad_poly\n", "\n", "def isotropic_grad(delta, lbda, gamma):\n", " grad_poly = isotropic_grad_poly(lbda, gamma)\n", " return np.polyval(grad_poly, delta)\n", "\n", "\n", "def isotropic_grad_poly_2D(lbda, gamma):\n", " grad_poly = [2, 0,\n", " mu**2 * gamma - 2,\n", " mu * lbda / 2.]\n", " return grad_poly\n", "\n", "def isotropic_grad_2D(delta, lbda, gamma):\n", " grad_poly = isotropic_grad_poly_2D(lbda, gamma)\n", " return np.polyval(grad_poly, delta)\n", "\n", "\n", "## The (archetypal) case I simulations in the article are for\n", "## the following values:\n", "gamma_case1 = 0.04\n", "lbda_case1 = 0.12\n", "# We can plot the above function for a range of values for aspect\n", "\n", "deltas = np.linspace(0, 1.1, 200)\n", " \n", "fig, ax = plt.subplots(1, 1, figsize=(6.,4.))\n", "grad = isotropic_grad(deltas, lbda_case1, gamma_case1)\n", "line = ax.plot(deltas, grad, 'k-', alpha=0.8, lw=2, label='3D case')\n", "\n", "grad2D = isotropic_grad_2D(deltas, lbda_case1, gamma_case1)\n", "line = ax.plot(deltas, grad2D, 'b-', alpha=0.8, lw=2, label='2D case')\n", "\n", "\n", "zero_x = ax.plot(deltas, np.zeros_like(deltas), 'k-') \n", "ylbl = ax.set_ylabel(r'Isotropic gradient amplitude'\n", " '$\\partial E / \\partial \\delta$')\n", "xlblb = ax.set_xlabel(r'Scaling factor $\\delta$')\n", "ax.legend(loc='upper left')\n", "plt.draw()\n", "fig.savefig(lj.data.get_image('isotropic_gradient_vs_scaling.svg'))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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g3kDtfwcdnYiIiJQ6Lf6YW4mSI+fcvTnPzew6oAnQ2Tm3Js+1jsBnwGafMYqI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\nJyeHjz/+mFmzZrFxY5m1mGndujUTJkxg0qRJdOwY9V8Bl1R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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Phase diagram\n", "\n", "In order for the apical junction to find a stable configuration, the energy must have a minimum as a function of\n", "$\\delta$. We can look at several cases and deduce the necessary conditions on $\\bar\\Gamma$ and $\\bar\\Lambda$ for this to apply.\n", "\n", "\n", "#### Soft network\n", "\n", "The tissue will behave as a soft network if the energy minimum for equilibrium volumes equal the initial volume ($\\delta = 1$), and contractility and elasticity can compensate each over. There exist a minimum energy in this case if:\n", "$$ \\mu^2 \\Gamma \\delta + \\mu\\Lambda / 2 < 0 $$\n", "The boundary between soft and cristal-like network is given by the line $\\Gamma = - 2 \\Lambda / 2\\mu$ in the $(\\Gamma, \\Lambda)$ plane.\n", "\n", "\n", "\n", "\n", "#### Case $\\Lambda \\geq 0$, $\\Gamma \\geq 0$\n", "\n", "To fix the correct conditions we have to look in the $(\\Gamma, \\Lambda)$ plane for real values of the gradient roots.\n", "\n", "We can seek the maximum possible values of $\\Gamma$ for a given $\\Lambda$. We have:\n", "$$\n", "\\Gamma = - \\frac{\\Lambda}{2\\mu\\delta} + \\frac{3}{\\mu^2}\\delta(1 - \\delta^3)\n", "$$\n", "\n", "$\\Gamma$ is maximal with respect to $\\delta$ if\n", "$$\n", "\\begin{align*}\n", "\\frac{\\partial \\Gamma}{\\partial \\delta} = \\frac{\\Lambda}{2\\mu\\delta^2} + 3\\frac{1 - 4\\delta^3}{\\mu^2} = 0\\\\\n", "\\Leftrightarrow -12\\delta^5 + 3\\delta^2 + \\Lambda\\mu / 2 = 0\n", "\\end{align*}\n", "$$\n", "\n", "The phase space boundary for valid values of $\\Gamma$ and $\\Lambda$ is given by the values of $\\Gamma$ for the roots of the above polynomial as a function of $\\Lambda$.\n", "\n", "If $\\Lambda = 0$, this gives $\\delta_m(\\Lambda = 0) = 4^{-1/3}$ and $\\Gamma_m(\\Lambda = 0) \\simeq 0.123$. With a similar reasoning for $\\Lambda$, we have $\\delta_m(\\Gamma = 0) = (2 / 5)^{1/3}$ and $\\Lambda_m(\\Gamma = 0) \\simeq 0.525$\n", "\n", "We can solve numerically for the other values of $\\Lambda$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "### This function does a brute force search for the roots of \n", "## the gradient in the lambda, gamma plane\n", "def find_grad_roots(lbda, gamma):\n", " p = isotropic_grad_poly(lbda, gamma)\n", " roots = np.roots(p) \n", " good_roots = np.real([r for r in roots if np.abs(r) == r])\n", " np.sort(good_roots)\n", " if len(good_roots) == 1:\n", " return good_roots\n", " elif len(good_roots) > 1:\n", " return good_roots[0]\n", " else:\n", " return np.nan\n", "\n", "def find_boundary_roots(lbda):\n", " delta_poly = [-12, 0, 0, 3, 0, lbda * mu / 2]\n", " roots = np.roots(delta_poly)\n", " good_roots = np.real([r for r in roots if (np.abs(r) == r) and (0 < r < 1)])\n", " np.sort(good_roots)\n", " return good_roots[0]\n", "\n", "def get_boundary_gamma(lbda):\n", " lbda = np.atleast_1d(lbda)\n", " dm = np.array([find_boundary_roots(l) for l in lbda])\n", " gamma = -lbda/(2 * mu * dm) + 3 * dm * (1 - dm**3) / mu**2\n", " return gamma\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "### Compute the boundary line\n", "\n", "lbda_max = 6 * (2 / 5.)**(2/3.) * 0.6 / mu\n", "gamma_max = 3 * 4**(-1 / 3.) * 0.75 / mu**2\n", "\n", "b_lbdas = np.linspace(0, lbda_max, 100)\n", "b_gammas = get_boundary_gamma(b_lbdas)\n", "print('''Maximum value for Lambda: %.3f \\n'''\n", " '''Maximum value for Gamma: %.3f''' % (lbda_max, gamma_max))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Maximum value for Lambda: 0.525 \n", "Maximum value for Gamma: 0.102\n" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "### Compute the value of delta over a grid in the (Lambda, Gamma) plane\n", "lbdas, gammas = np.meshgrid(np.linspace(0, lbda_max * 1.1, 512),\n", " np.linspace(0, gamma_max * 1.5, 512))\n", "roots = []\n", "for l, g in zip(lbdas.ravel(), gammas.ravel()):\n", " roots.append(find_grad_roots(l, g))\n", "roots = np.array(roots).reshape(gammas.shape)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "### 2D case\n", "\n", "gammas_2D = np.linspace(0, 2/mu**2, 20)\n", "lambdas_max_2D = ((4 - 2 * gammas_2D * mu**2) / 3.)**(3./2.) / mu\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "### Plot everything\n", "\n", "fig, ax = plt.subplots()\n", "roots[np.isnan(roots)] = 0.5\n", "lbdas, gammas = np.meshgrid(np.linspace(0, lbda_max * 1.1, 512), np.linspace(0, gamma_max * 1.5, 512))\n", "contour_set = ax.contourf(lbdas, gammas, roots.clip(0.5, 1), 256, cmap='gray')\n", "fig.colorbar(contour_set, ticks=[0.5, 0.6, 0.7, 0.8, 0.9, 1.])\n", "\n", "boundary = ax.plot(b_lbdas, b_gammas, 'g-', lw=3, alpha=0.8, label='3D case')\n", "boundary2D = ax.plot(lambdas_max_2D, gammas_2D, 'b-', \n", " lw=3, alpha=0.8, label='2D case')\n", "\n", "ax.plot(lbda_case1, gamma_case1, 'ko')\n", "\n", "ax.set_xlabel(r'Line tension $\\bar\\Lambda$')\n", "ax.set_ylabel(r'Contractility $\\bar\\Gamma$')\n", "ax.set_title('Values of $\\delta$')\n", "\n", "ax.legend(loc='upper right')\n", "fig.savefig(lj.data.get_image('phase_space_boundaries.svg'))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Xjz/+uOq8O3fuZPDgwXTv3p1jjz2WQw45hN27dzN9+nSWLFnCmWeeSY8e3srW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\n6kFsw8q82ohbytf5dquLhFv/uzvXzeL6x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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now get the values of the optimal scaling $\\delta_o$ and of the ground state energy $E_0$\n", "with a simple root finding on the `isotropic_grad` function:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "delta_o = find_grad_roots(lbda_case1, gamma_case1)\n", "\n", "print(\"Optimum scaling factor = %.3f\" % delta_o)\n", "ground_energy = isotropic_energy(delta_o, gamma_case1, lbda_case1)\n", "print(\"Ground energy = %.3f\" % ground_energy)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Optimum scaling factor = 0.887\n", "Ground energy = 0.462\n" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### Computation of the scaling factor\n", "\n", "Let's note $A_i$ and $\\rho_i$ the initial area and radius, \n", "before relaxation, and $A_f, \\rho_f$ the same variables after the isotropic relaxation is applied.\n", "We now want to multiply all the distances by a factor $c$ such that $h_fA_f = \\delta_o^3h_0A_0$, with $\\rho_f = c\\rho_i$ \n", "and $A_f = c^2A_i$.\n", "\n", "By noting $\\delta_i = h_i / h_0$, we simply have $c = \\delta_o / \\delta_i$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now have the two phase space boundaries given by Faradhifar on figure 1. When we pass to\n", "the simulation we'll use all that to ensure that optimisation will converge and that we start the simultations\n", "close to the ground state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gradient computation at junction vertices\n", "\n", "In order to find the local energy minimum, as shown below, we use a conjugate gradient method\n", "(namely the [`fmin_lbfgs`](http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html#broyden-fletcher-goldfarb-shanno-algorithm-method-bfgs) algorithm from SciPy). So we need to compute said gradient at each junction vertex that concur to the optimization.\n", "\n", "In order to compute the local minimum of the energy, we calculate its\n", "gradient at junction vertex $i$ whose position in the 3D space is defined by the vector $\\mathbf{r_i}$ pointing from the coordinate system's origin. An edge between two vertices is noted\n", "$\\mathbf{r_{ij}} = \\mathbf{r_j} - \\mathbf{r_i}$. The coefficients noted $c_{ij}$ correspond to the terms of the graph's adjacency matrix, such that they are equal to 1 if an edge exists between vertices $i$ and $j$, and 0 otherwise.\n", "\n", "$$\n", "\\begin{aligned} \n", " \\mathbf{\\nabla_i} E &= (\\frac{\\partial E}{\\partial x},\n", " \\frac{\\partial E}{\\partial y},\n", " \\frac{\\partial E}{\\partial z}) \\\\\n", " \\mathbf{\\nabla_i} E &= \\sum_\\alpha \\left(K (V_\\alpha - V_0) \n", " \\mathbf{\\nabla_i} V_\\alpha \n", " + \\Gamma L_\\alpha \\mathbf{\\nabla_i} L_\\alpha \\right)c_{i \\alpha} \n", " + \\sum_i \\Lambda_{ij} \\mathbf{\\nabla_i} \\ell_{ij}c_{ij}\n", "\\end{aligned}\n", "$$\n", "\n", "We have \n", "$$\n", "\\begin{aligned} \n", " \\mathbf{\\nabla_i}\\ell_{ij} &= \\frac{\\mathbf{r}_{ij}}{\\ell_{ij}}c_{ij}\\\\\n", " \\mathbf{\\nabla_i}L_\\alpha &= \\sum_{kn} \\mathbf{\\nabla_i} \n", " \\ell_{kn} c_{\\alpha k} c_{\\alpha n}\n", " = \\sum_{j} \\mathbf{\\nabla_i}\\ell_{ij} c_{ij} c_{\\alpha i} c_{\\alpha j}\n", " = \\sum_{j} \\frac{\\mathbf{r_{ij}}}{\\ell_{ij}}c_{ij}c_{\\alpha i} c_{\\alpha j}\\\\\n", " \\mathbf{\\nabla_i}V_{\\alpha} &= \\sum_{km}\\mathbf{\\nabla_i}V_{\\alpha km}\n", " c_{\\alpha k}c_{\\alpha m}c_{km}\n", " = \\sum_{km} \\mathbf{\\nabla_i}h_\\alpha A_{\\alpha km}\n", " c_{\\alpha k}c_{\\alpha m}c_{km}\n", " = A_\\alpha \\mathbf{\\nabla_i}h_\\alpha + \n", " h_\\alpha \\sum_{km} \\mathbf{\\nabla_i} A_{\\alpha km}c_{\\alpha k}\n", " c_{\\alpha m}c_{km}\\\\\n", " \\mathbf{\\nabla_i}V_{\\alpha} &= \n", " \\frac{h_\\alpha}{2} \\sum_{km}\\mathbf{u}_{\\alpha km} \n", " \\times \\frac{\\mathbf{r}_{km}}{\\nu}c_{\\alpha k}c_{\\alpha m}c_{km}\n", " + \\sum_{j}\\left(A_{\\alpha ij}\\frac{\\mathbf{r_i}}{2\\rho_i} \n", " + \\frac{h_\\alpha}{2}\\mathbf{r}_{\\alpha j} \\times \\mathbf{u}_{\\alpha ij}\\right)\n", " c_{\\alpha j}c_{ij}\\\\\n", "\\end{aligned}\n", "$$\n", "\n", "With the normal perpendicular to the $(\\mathbf{r_k}, \\mathbf{r_m})$ plane noted:\n", "\n", "$$\n", "\\mathbf{u}_{\\alpha km} = \\frac{\\mathbf{r}_{\\alpha k} \\times \\mathbf{r}_{\\alpha m}}{||\\mathbf{r}_{\\alpha k} \\times \\mathbf{r}_{\\alpha m}||}\n", "$$ \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Implementation in the simulation engine\n", "\n", "## Initial state\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "!ls" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0 - Introduction.ipynb\t\t\t 5 - Joint.ipynb\t\t\t nb_init.py\r\n", "1 - Epithelium architecture.ipynb\t 8 - Parameters exploration.ipynb sandbox.ipynb\r\n", "2 - Energy minimisation.ipynb\t\t Analysis.ipynb\t\t\t saved_graphs\r\n", "3 - Cell division and type 1 transition.ipynb Figures.ipynb\r\n", "4 - Single cell apoptosis.ipynb\t\t latest.ipynb\r\n" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "import tempfile" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "d = tempfile.mkdtemp()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "d" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "'/tmp/tmpgyfdubak'" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "### The script `nb_init` does all the imports\n", "%run nb_init.py\n", "\n", "## Epithelium instantiation\n", "eptm = lj.Epithelium(graphXMLfile=lj.data.small_xml(),\n", " save_dir='saved_graphs',\n", " identifier='tuto',\n", " copy=True)\n", "\n", "## Scaling so that we start at global epithelium\n", "#eptm.isotropic_relax()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "2015-01-26 10:07:01,023 -leg_joint -INFO -successfully imported leg_joint\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "2015-01-26 10:07:01,024 -leg_joint.epithelium -INFO -Instanciating epithelium tuto\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "2015-01-26 10:07:01,075 -leg_joint.epithelium -INFO -Initial cells\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "2015-01-26 10:07:01,075 -leg_joint.epithelium -INFO -Initial junctions\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "2015-01-26 10:07:01,319 -leg_joint.epithelium -INFO -Update geometry\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### We can gather information like the average cell surface\n", "\n", "To do so, we use graph-tool's filtering mechanism. We use two attributes of the `Epithelium` object:\n", "`is_cell_vert` and `is_alive`, which are graph-tools boolean `PropertyMaps`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Create a filter with only the 'live' cell vertices\n", "vfilt = eptm.is_cell_vert.copy() \n", "vfilt.a *= eptm.is_alive.a\n", "## Filtering\n", "eptm.graph.set_vertex_filter(vfilt)\n", "\n", "area = eptm.cells.areas.fa.mean()\n", "height = eptm.rhos.fa.mean() - eptm.rho_lumen\n", "eptm.delta_o = eptm.find_grad_roots()\n", "print('Square root of the ratio between the prefered area\\n'\n", " 'and the actual average area: %.6f\\n' \n", " % (np.sqrt(area / eptm.params[\"prefered_area\"])))\n", "print('Ratio between the prefered height\\n'\n", " 'and the actual average height: %.6f\\n' \n", " % (height / eptm.params['prefered_height']))\n", "print('Scaling factor with respect to elastic volume equilibrium: %.6f\\n'\n", " % eptm.delta_o)\n", "\n", "# Remove the filter\n", "eptm.graph.set_vertex_filter(None)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Square root of the ratio between the prefered area\n", "and the actual average area: 0.886593\n", "\n", "Ratio between the prefered height\n", "and the actual average height: 0.886593\n", "\n", "Scaling factor with respect to elastic volume equilibrium: 0.886593\n", "\n" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "All three numbers should be equal by definition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Energy profile as a function of scaling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The graph bellow corresponds to the analytical computations above" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(6, 4))\n", "lbda = eptm.paramtree.relative_dic['line_tension']\n", "gamma = eptm.paramtree.relative_dic['contractility']\n", "deltas = np.linspace(0.4, 1.2)\n", "ax.plot(deltas, eptm.isotropic_energy(deltas), 'k-',\n", " label='Analytical total')\n", "ax.plot(eptm.delta_o, eptm.isotropic_energy(eptm.delta_o), 'ro')\n", "ax.set_xlabel('Normalized energy')\n", "ax.set_ylabel('Scaling');\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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0NNdcc43XpeRJOMxBEhERkSJk3759zJ07t9COHoECkoiIiATZtGnTKFWqVKFeV1ABSURE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\nVptZl1DWHAz56beZ1fH/XUnwf94ZZnZ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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison between anaytical and computed solutions\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "deltas = np.linspace(0.5, 1.2, 20)\n", "fig, ax = plt.subplots(figsize=(5, 8))\n", "lbda = eptm.paramtree.relative_dic['line_tension']\n", "gamma = eptm.paramtree.relative_dic['contractility']\n", "ax.plot(deltas, eptm.isotropic_energy(deltas), 'k-',\n", " label='Analytical total')\n", "ax.plot(eptm.delta_o, eptm.isotropic_energy(eptm.delta_o), 'ro')\n", "ax.plot(deltas, elasticity(deltas), 'b-',\n", " label='Analytical volume elasticity')\n", "ax.plot(deltas, contractility(deltas, gamma), c='orange', ls='-',\n", " label='Analytical contractility')\n", "ax.plot(deltas, tension(deltas, lbda), 'g-',\n", " label='Analytical line tension')\n", "\n", "ax.set_xlabel(r'Isotropic scaling $\\delta$')\n", "ax.set_ylabel(r'Isotropic energie $\\bar E$')\n", "\n", "eptm.update_rhotheta()\n", "area0 = eptm.params['prefered_area']\n", "h_0 = eptm.params['prefered_height']\n", "\n", "\n", "### Cells only area and height\n", "eptm.set_vertex_state([(eptm.is_cell_vert, False),\n", " (eptm.is_alive, False)])\n", "area_avg = eptm.cells.areas.fa.mean()\n", "rho_avg = eptm.rhos.fa.mean()\n", "eptm.set_vertex_state()\n", "\n", "### Set height and area to height0 and area0\n", "scale = (area0 / area_avg)**0.5\n", "eptm.scale(scale)\n", "eptm.rho_lumen = rho_avg * scale - h_0\n", "eptm.update_geometry()\n", "\n", "\n", "energy = eptm.calc_energy()\n", "\n", "norm = (eptm.params['prefered_area']**2\n", " * eptm.params['prefered_height']**2\n", " * eptm.params['vol_elasticity']\n", " * (eptm.is_cell_vert.a * eptm.is_alive.a).sum())\n", "\n", "cell = eptm.graph.vertex(60)\n", "\n", "energies = np.zeros((deltas.size, 3))\n", "#scales = np.linspace(0.5, 1.2, 20) / eptm.delta_o\n", "for n, delta in enumerate(deltas):\n", " eptm.scale(delta)\n", " eptm.update_geometry()\n", " Ec, Ev = eptm.calc_cells_energy()\n", " El, Er = eptm.calc_junctions_energy()\n", " energies[n, :] = [Ev.sum(), El.sum(), Ec.sum()]\n", " eptm.scale(1 / delta)\n", "\n", "eptm.isotropic_relax()\n", "\n", "\n", "energies = np.array(energies) / norm\n", "ax.plot(deltas, energies[:, 0], 'bo:', lw=2, alpha=0.8,\n", " label='Computed volume elasticity')\n", "ax.plot(deltas, energies[:, 1], 'go:', lw=2, alpha=0.8,\n", " label='Computed line tension')\n", "ax.plot(deltas, energies[:, 2], ls=':',\n", " marker='o', c='orange', label='Computed contractility')\n", "ax.plot(deltas, energies.sum(axis=1), 'ko:', lw=2, alpha=0.8,\n", " label='Computed total')\n", "\n", "ax.legend(loc='upper left', fontsize=10)\n", "ax.set_ylim(0, 1.2)\n", "\n", "plt.savefig(lj.data.get_image('scaling_comparison.svg'))\n", "\n", "\n", "print(eptm.delta_o, deltas[energies.sum(axis=1).argmin()] * eptm.delta_o)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.886592687387 0.769935754836\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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1xx+5uER1+yML1vlXf7nBOnC8uzVbDx8+zJ49e1i1ahVQumD94MGDiY+Pr7BC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"text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that at initialisation time, we also\n", "invoked the `isotropic_relax` method,\n", "and we start with an hexagonal lattice, so we should be fairly close to\n", "the ground state energy, except from the cells closer to edges along the $z$ axis." ] } ], "metadata": {} } ] }