analysis_dimers.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "365de1b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c45a0c0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "from scipy.constants import N_A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "39ee4704-44aa-44a2-b2c4-468cec2689b4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Matplotlib is building the font cache; this may take a moment.\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import matplotlib.cm as cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5a24aba2-0e1e-4014-b43c-5b044bb05d38",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bdef5730-2e55-44d6-b4eb-4818b0a34666",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"ticks\", color_codes=True, font_scale=1.)\n",
    "sns.set_style({\"xtick.direction\": \"in\", \"ytick.direction\": \"in\"})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "97cd265b-bace-4578-9ac7-f2ff036d4a0a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import mdtraj as md"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9dd2cb97-7982-47f9-8415-ca88f84c6122",
   "metadata": {},
   "source": [
    "# Dilute boxes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "fe1857e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fix_gr(g_r, r, box):\n",
    "    \"\"\"\n",
    "    Analytical fix to the radial distribution function\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    g_r : array\n",
    "        Radial distribution function\n",
    "    r : array\n",
    "        Radial distance\n",
    "    box : float\n",
    "        Box size\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    \"\"\"\n",
    "\n",
    "\n",
    "\n",
    "def calcB22(g_r, r):\n",
    "    \"\"\"\n",
    "    Calculate the second virial coefficient from the radial distribution function\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    g_r : array\n",
    "        Radial distribution function\n",
    "    r : array\n",
    "        Radial distance\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    B22 : float\n",
    "        Second virial coefficient in nm^3\n",
    "    \"\"\"\n",
    "    return -2*np.pi*np.trapz((g_r -1)*r**2, x=r)\n",
    "\n",
    "def calc_pb(distances, cut=None, log=True, plot=True):\n",
    "    \"\"\"ArithmeticError\n",
    "    Calculate the bound fraction from the pairsiwe distances\n",
    "    \"\"\"\n",
    "    if log: \n",
    "        hist, bin_edges = np.histogram(np.log10(np.concatenate(distances)), \\\n",
    "                density=True, bins=np.linspace(-0.5,1.25,nbins))\n",
    "    else:\n",
    "        hist, bin_edges = np.histogram(np.concatenate(distances), \\\n",
    "                density=True, bins=np.linspace(0,10,nbins))\n",
    "        \n",
    "    bin_centers = np.array([0.5*(bin_edges[i]+bin_edges[i+1]) for i in range(nbins-1)])\n",
    "    if plot: \n",
    "        fig, ax = plt.subplots()\n",
    "        ax.plot(bin_centers, hist)\n",
    "        ax.axvline(cut, c='k', ls='--')\n",
    "        xlabel = '$\\log10(r)$' if log else '$r$ [nm]'\n",
    "        ax.set_xlabel(xlabel)\n",
    "        ylabel = '$P(\\log(r)$)' if log else '$P(r)$'\n",
    "        ax.set_ylabel(ylabel)\n",
    "        ax.set_yscale('log')\n",
    "        ax.set_ylim(5e-4, 10)\n",
    "        plt.tight_layout()\n",
    "\n",
    "    # Calculate the bound fraction\n",
    "    ibound = np.argmin(np.abs(bin_centers - log_rcut))\n",
    "    p_bound = np.trapz(hist[:ibound], dx=bin_centers[1]-bin_centers[0])\n",
    "\n",
    "    return p_bound\n",
    "\n",
    "def calc_kd(pb, V):\n",
    "    return (1 - pb)**2/(V*N_A*pb)*1e24\n",
    "\n",
    "def calc_kd_fromB22(pb, V, B22):\n",
    "    return 1./(N_A*pb*(V - 2*B22))*1e24\n",
    "\n",
    "def calc_kd_fromB22_approx(B22):\n",
    "    \"\"\"\n",
    "    Calculate the dissociation constant from the second virial coefficient\n",
    "    using the approximate expression: \n",
    "    B22 = 1/(2*N_A*Kd)\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    B22 : float\n",
    "        Second virial coefficient in nm^3\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    Kd : float\n",
    "        Dissociation constant in M\n",
    "    \"\"\"\n",
    "    conversion = 1e-24\n",
    "    return -1./(2*N_A*B22*conversion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "51d7343b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B22 = -1.132 nm^3\n",
      "K_d = 0.733 M\n",
      "p_b = 0.000\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nbins = 100\n",
    "log_rcut = -0.25\n",
    "fig, ax = plt.subplots(figsize=(5,4))\n",
    "\n",
    "system = \"argon\"\n",
    "t = 50\n",
    "dcd = \"data/%s_n50_L20_T%g_prod.dcd\"%(system, t)\n",
    "pdb = \"data/%s_n50_L20_T%g_final.pdb\"%(system, t)\n",
    "try:\n",
    "    # load trajectory\n",
    "    traj = md.load_dcd(dcd, top=pdb, stride=1)\n",
    "\n",
    "    # calculate rdf\n",
    "    bins, g_r = md.compute_rdf(traj, list(itertools.combinations(range(50), 2)), \\\n",
    "                       r_range=[0,1.5], n_bins=nbins)\n",
    "    ax.plot(bins, g_r, label='T=%g K'%t)\n",
    "    \n",
    "    # compute B22 from rdf \n",
    "    B22 = calcB22(g_r, bins)\n",
    "    print (\"B22 = %.3f nm^3\"%B22)\n",
    "\n",
    "    # compute approximate form of Kd from B22\n",
    "    Kd_approx = calc_kd_fromB22_approx(B22)\n",
    "    print (\"K_d = %.3f M\"%Kd_approx)\n",
    "\n",
    "    # compute pairwise distances\n",
    "    distances = md.compute_distances(traj, \\\n",
    "                    atom_pairs=list(itertools.combinations(range(20), 2)))\n",
    "\n",
    "    # estimate population bound from histogram\n",
    "    p_bound = calc_pb(distances, cut=log_rcut, log=True, plot=True)\n",
    "    print (\"p_b = %.3e\"%p_bound)\n",
    "\n",
    "except Exception as e:\n",
    "    print (e)\n",
    "\n",
    "ax.axhline(1,0,2,ls='dashed', lw=1, color='k')\n",
    "ax.set_xlim(0.0,1.5)\n",
    "ax.set_xlabel('$r$ (nm)')\n",
    "ax.set_ylabel(r'$g(r)$')\n",
    "ax.legend(loc=1,ncols=2, fontsize=10)\n",
    "ax.set_title(system.capitalize())\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "de2f6d9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No such file: data/argon_n50_L20_T10_final.pdb\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/w_/6y6c02w52ydcq3xnpj_nt2tr0000gn/T/ipykernel_95933/2727992347.py:41: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
      "  ax.legend(loc=1,ncols=2, fontsize=10)\n",
      "/var/folders/w_/6y6c02w52ydcq3xnpj_nt2tr0000gn/T/ipykernel_95933/2727992347.py:51: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
      "  ax2.legend(loc=1,ncols=2, fontsize=10)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "temps = range(10,190,10)\n",
    "nbins = 150\n",
    "log_rcut = -0.25\n",
    "\n",
    "B22_all = {}\n",
    "p_bound_all = {}\n",
    "\n",
    "for system in [\"neon\", \"argon\", \"krypton\", \"xenon\", \"methane\"]:\n",
    "    B22 = []; p_bound = []\n",
    "    fig, ax = plt.subplots(figsize=(5,4))\n",
    "    fig2, ax2 = plt.subplots(figsize=(5,4))\n",
    "    for t in temps:\n",
    "        dcd = \"data/%s_n50_L20_T%g_prod.dcd\"%(system, t)\n",
    "        pdb = \"data/%s_n50_L20_T%g_final.pdb\"%(system, t)\n",
    "        try:\n",
    "            traj = md.load_dcd(dcd, top=pdb, stride=2)\n",
    "            bins, g_r = md.compute_rdf(traj, list(itertools.combinations(range(50), 2)), \\\n",
    "                               r_range=[0,1.5], n_bins=nbins)\n",
    "            ax.plot(bins, g_r, label='T=%g K'%t)\n",
    "            B22.append([t, -2*np.pi*np.trapz((g_r -1)*bins**2, x=bins)])\n",
    "\n",
    "            distances = md.compute_distances(traj, \\\n",
    "                                atom_pairs=list(itertools.combinations(range(20), 2)))\n",
    "            hist, bin_edges = np.histogram(np.log10(np.concatenate(distances)), \\\n",
    "                                density=True, bins=np.linspace(-0.5,1.25,nbins))\n",
    "            bin_centers = np.array([0.5*(bin_edges[i]+bin_edges[i+1]) for i in range(nbins-1)])\n",
    "            ax2.plot(bin_centers, hist, label='T=%g K'%t)\n",
    "            ibound = np.argmin(np.abs(bin_centers - log_rcut))\n",
    "            p_bound.append([t, np.trapz(hist[:ibound], dx=bin_centers[1]-bin_centers[0])])\n",
    "        except Exception as e:\n",
    "            print (e)\n",
    "\n",
    "    B22_all[system] = np.array(B22)\n",
    "    p_bound_all[system] = np.array(p_bound)\n",
    "\n",
    "    ax.axhline(1,0,2,ls='dashed', lw=1, color='k')\n",
    "    ax.set_xlim(0.0,1.5)\n",
    "    ax.set_xlabel('$r$ (nm)')\n",
    "    ax.set_ylabel(r'$g(r)$')\n",
    "    ax.legend(loc=1,ncols=2, fontsize=10)\n",
    "    ax.set_title(system.capitalize())\n",
    "    fig.tight_layout()\n",
    "\n",
    "    ax2.axvline(log_rcut, ls='--', color='k')\n",
    "    ax2.set_yscale('log')\n",
    "    ax2.set_xlabel('distance (nm)')\n",
    "    ax2.set_ylabel('p(d)')\n",
    "    #ax2.set_xlim(0, 17)\n",
    "    ax2.set_ylim(1e-4, 4)\n",
    "    ax2.legend(loc=1,ncols=2, fontsize=10)\n",
    "    ax2.set_title(system.capitalize())\n",
    "    fig2.tight_layout()\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "0f13e0a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$K_D$ (M$^{-1}$)')"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(temps, calc_kd(np.array(pb), 20**3), 'o', ms=10)\n",
    "plt.plot(temps, calc_kd_fromB22(np.array(pb), 20**3, np.array(B22)), 'x', ms=10)\n",
    "plt.xlabel('T (K)')\n",
    "#plt.xlabel('$p_{bound}$')\n",
    "plt.ylabel('$K_D$ (M$^{-1}$)')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}