Protein_electrostatics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Odds and Ends in Protein Electrostatics\n",
    "_Stefan Hervø-Hansen, Division of Theoretical Chemistry, Lund University._\n",
    "\n",
    "This notebook is a continuation of intresting topics within protein electrostatics. Topics include the EXG protein and protein engineering in colaboration with Jakob Winther & Kresten Lindorff-Larsen, statistical thermodynamics of charged systems with Mikael Lund, and topics mentioned at the protein electrostatics meetings; in particular the 2018 meeting in Belgrade, Serbia and the 2019 meeting in Telluride, Colorado, USA.\n",
    "\n",
    "\n",
    "## Import modules and convience functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.image as mpimg\n",
    "import mdtraj as md\n",
    "from scipy import stats\n",
    "from scipy import optimize\n",
    "from adjustText import adjust_text\n",
    "from IPython.display import Markdown\n",
    "\n",
    "# Simulation related packages\n",
    "from simtk.openmm import app\n",
    "import simtk.openmm as mm\n",
    "import openmmtools as mmtools\n",
    "import parmed as pmd\n",
    "\n",
    "def pairwise(iterable):\n",
    "    \"s -> (s0, s1), (s2, s3), (s4, s5), ...\"\n",
    "    a = iter(iterable)\n",
    "    return zip(a, a)\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Energetics of Ion Pairs in Different Dielectrics\n",
    "<img src=\"figures/Ionpair_illustration.jpeg\" alt=\"Transfer of ionpair\" width=250 align='right' style='padding-left:20px'/>\n",
    "\n",
    "This is a primative continuum model (Coulomb and Born), which describes the process of transfering ion-pairs between different dielectric enviroments. In specific, we here look at the transfer from water (78.4, at 298 Kelvin) to a lower dielectric.\n",
    "$$\n",
    "\\Delta G = \\underbrace{\\frac{1}{4\\pi \\epsilon_0 \\epsilon_r} \\frac{q_{1}q_{2}}{r}}_{\\text{Coulomb energy}} + \n",
    "\\underbrace{\\sum_{i=1}^{2}\\frac{-q_{i}^2}{8\\pi\\epsilon_0 r_{i,0}} \\left( \\frac{1}{\\epsilon_{\\text{water}}} - \\frac{1}{\\epsilon_r} \\right)}_{\\text{Solvation energy}} \\tag{eq. 1}\n",
    "$$\n",
    "Noteable it can be seen given the simple model and the parameters chosen it is an unfavorable process transfering ion pairs from a high dielectic to a low dielectric. However the free energy penalty of the ion pair being on the surface (blue area highlighted) is much smaller than being buried (orange area highlighted) and thus ion pairs on protein surfaces are able to found in stable proteins.\n",
    "\n",
    "### Energy Functions and Calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 518.4x345.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 338,
       "width": 511
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def BornEnergy(q, r0, eps=78.4):\n",
    "    '''\n",
    "    Calculates the Born energy of a single ion.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    q: float, charge of ion in elementary charges.\n",
    "    r0: float, radius of ion in Angstrom.\n",
    "    eps: float, unitless dielectric constant (default: 78.4).\n",
    "    '''\n",
    "    k = 1.38935406579333*10**(-4) / 2 # [m^2*N/(e^2*mol)], k = Na/(8*pi*epsilon)\n",
    "    r0 *= 10**(-10)\n",
    "    return (-k*q**2/r0) * (1/78.4 - 1/eps)\n",
    "\n",
    "def CoulombEnergy(q1, q2, r, eps=78.4):\n",
    "    '''\n",
    "    Calculates the Coulomb energy between two ions.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    q1: float, charge of ion 1 in elementary charges.\n",
    "    q2: float, charge of ion 2 in elementary charges.\n",
    "    r: float, distance between ion 1 and 2 in Angstrom.\n",
    "    eps: float, unitless dielectric constant (default: 78.4).\n",
    "    '''\n",
    "    r *= 10**(-10)\n",
    "    k = 1.38935406579333*10**(-4) #  [m^2*N/(e^2*mol)], k = Na/(4*pi*epsilon)\n",
    "    return k*(q1*q2/(r*eps))\n",
    "\n",
    "\n",
    "eps_list = np.arange(0.1, 80, 1)\n",
    "Energy = {\n",
    "    'Born': [],\n",
    "    'Coulomb': [],\n",
    "    'Total': []\n",
    "}\n",
    "\n",
    "unit_Joule_to_kcal = 2.39*10**(-4)\n",
    "for eps in eps_list:\n",
    "    E_Coulomb = CoulombEnergy(q1=1, q2=-1, r=3.5, eps=eps) * unit_Joule_to_kcal\n",
    "    E_Born = BornEnergy(q=1, r0=1.75, eps=eps) * 2 * unit_Joule_to_kcal\n",
    "    E_Total = E_Coulomb + E_Born\n",
    "    \n",
    "    Energy['Coulomb'].append(E_Coulomb)\n",
    "    Energy['Born'].append(E_Born)\n",
    "    Energy['Total'].append(E_Total)\n",
    "    \n",
    "\n",
    "# Plotting.\n",
    "fig, ax = plt.subplots(figsize=(7.2,4.8))\n",
    "\n",
    "ax.plot(eps_list, Energy['Total'], label='Total', linewidth=3)\n",
    "ax.plot(eps_list, Energy['Coulomb'], label='Coulomb energy', linewidth=3)\n",
    "ax.plot(eps_list, Energy['Born'], label='Born energy',  linewidth=3)\n",
    "ax.hlines(0, -100, 100, alpha=0.25, linestyle='dashed')\n",
    "ax.axvspan(xmin=6, xmax=7, ymin=-50, ymax=50, alpha=0.2, color='C1')\n",
    "ax.axvspan(xmin=20, xmax=30, ymin=-50, ymax=50, alpha=0.2, color='C0')\n",
    "\n",
    "# Graphical settings.\n",
    "ax.minorticks_on()\n",
    "ax.set_ylim(-50, 50)\n",
    "ax.set_xlim(0.1, 80)\n",
    "ax.legend(loc=0, fontsize=14)\n",
    "ax.set_xlabel('Dieletric constant ε', fontsize=16)\n",
    "ax.set_ylabel('Free energy ΔG [kcal/mol]', fontsize=16)\n",
    "ax.tick_params(which='major', direction='in', length=4, width=2, colors='black',\n",
    "               grid_color='black', grid_alpha=0.5, labelsize=14)\n",
    "ax.tick_params(which='both', direction='in')\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig('figures/Solvation_of_ionpair.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Diprotic acid model: Salt bridge vs Hydrogen bond\n",
    "<img src=\"figures/Diprotic_acid_illustration.jpeg\" alt=\"Diprotic acid model\" width=300 align='right'/>\n",
    "To characterize the energetics of ion pairs in proteins, we have investigated the titration behaviour of an Asp-His pair in an otherwise charge depleted protein named EXG (PDB ID, <a href=\"https://www.rcsb.org/structure/6QFS\" target=\"_blank\">6QFS</a>) derived from a cellulose binding domain in <i>Cellulomonas fimi</i>. To do this we utilized a diprotic acid model (visualized) in which the diprotic acid can adapt 4 microstates consisting of the possible combinations of Asp and His being deprotonated and protonated. Within this scheme we can see that in the transition going from fully protoated to fully deprotoated, the two intermediate states are characterized by either being in a neutral state (PD) or zwitterionic state (DP). The population of these states has been measured using Monte Carlo simulations in the pH interval 2.0-9.5.\n",
    "\n",
    "Due to only two titratable acids being present in the system, we can write a partition function which contains all information on the energics between the protonation states within the grand ensemble of protons\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "Z &= 1+ e^{-\\beta \\left( G_{01}^{0} - \\mu_{ \\mathrm{H}^{+}} \\right)}\\\n",
    "+ e^{-\\beta \\left( G_{10}^{0} - \\mu_{ \\mathrm{H}^{+}} \\right)}\\\n",
    "+ e^{-\\beta \\left( G_{11}^{0} - 2 \\mu_{ \\mathrm{H}^{+}} \\right)} \\\\\n",
    "  &= 1 + 10^{ \\left( \\mathrm{p}K_{10}^{00} -  \\mathrm{pH} \\right)} \\\n",
    "+ 10^{ \\left( \\mathrm{p}K_{01}^{00} -  \\mathrm{pH} \\right)} \\\n",
    "+ 10^{ \\left( \\mathrm{p}K_{11}^{10} + \\mathrm{p}K_{10}^{00} - 2 \\mathrm{pH} \\right)}\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "$$\n",
    "The last equality is obtained due to the energy of protonating a group at a certain pH is given by $G_a = G_a^0 - \\mu_{\\text{H}^+} = - \\beta^{-1} \\ln 10 (\\text{p}K_{\\text{a}} - \\text{pH})$. In the above expression we have changes the ground state to be the fully deprotonated state, thus from the partition we can write an expression for the population of the individual states at any given pH value:\n",
    "$$\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\left\\langle \\left( 00 \\right) \\right\\rangle &= \\frac{1}{Z} \\\\\n",
    "\\left\\langle \\left( 10 \\right) \\right\\rangle &= \\frac{10^{ \\left( \\mathrm{p}K_{10}^{00} -  \\mathrm{pH} \\right)}}{Z} \\\\\n",
    "\\left\\langle \\left( 01 \\right) \\right\\rangle &= \\frac{10^{ \\left( \\mathrm{p}K_{01}^{00} -  \\mathrm{pH} \\right)}}{Z} \\\\\n",
    "\\left\\langle \\left( 11 \\right) \\right\\rangle &= \\frac{10^{ \\left( \\mathrm{p}K_{11}^{10} + \\mathrm{p}K_{10}^{00} - 2 \\mathrm{pH} \\right)}}{Z}\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "$$\n",
    "By fitting the four equations simultaniously under the constain of the thermodynamic cycle presented $(\\mathrm{p}K_{01}^{11} + \\mathrm{p}K_{01}^{00} = \\mathrm{p}K_{11}^{10} + \\mathrm{p}K_{10}^{00})$ we can obtain thermodynamic parameters which describe the entire system.\n",
    "### Boltzmann Weights, Partition Function, & Minimization Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Boltzmann weight for each state and the partition function\n",
    "def QPD(k):\n",
    "    return 10**(k[0] - pH)\n",
    "def QDP(k):\n",
    "    return 10**(k[1] - pH)\n",
    "def QPP(k):\n",
    "    return 10**((k[0] + k[1] - k[2]) - 2*pH)\n",
    "def QDD(k):\n",
    "    return 1\n",
    "def Z(k):\n",
    "    return 1 + QPD(k) + QDP(k) + QPP(k)\n",
    "\n",
    "# Minimization function\n",
    "def target(k):\n",
    "    minimization =  sum((1/Z(k) - DD)**2) + sum((QPD(k)/Z(k) - PD)**2) + sum((QDP(k)/Z(k) - DP)**2) + sum((QPP(k)/Z(k) - PP)**2)\n",
    "    return minimization\n",
    "\n",
    "# Macroscopic titration function\n",
    "def macroscopic(pH, pka1, pka2):\n",
    "    return (10**(pka2 - pH) + 2 * 10**(pka1+pka2 - 2*pH)) / (1+10**(pka2 - pH) + 10**(pka1+pka2 - 2*pH))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pK<sub>a</sub> Fitting and Bjerrum Diagram\n",
    "We here fit the populations sampled by Monte Carlo simultions to the population expression derived from the Boltzmann distribution using both the microscopic cycle (previously shown) and though a macroscopic cycle, which is characterized by not distinguishing between proton locations, but only considers the net dissociation of protons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'target' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-7a326c0aa3d6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     37\u001b[0m     \u001b[0mDD\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mblock\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m     \u001b[0mtotal\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mPD\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mPP\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mDP\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mDD\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 39\u001b[0;31m     \u001b[0mmicro\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptimize\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtarget\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtol\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[0;36m7\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     40\u001b[0m     \u001b[0mmacro\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptimize\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurve_fit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmacroscopic\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpH\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtotal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmaxfev\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1200\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'target' is not defined"
     ]
    }
   ],
   "source": [
    "Nblocks = 4\n",
    "pHs = np.arange(2.00, 10.00, 0.5)\n",
    "states = np.zeros(shape=(Nblocks, len(pHs), 4)) # PD, PP, DP, DD\n",
    "\n",
    "for i,pH in enumerate(pHs):\n",
    "    titration = np.loadtxt('data/titration_data/39D66H/reordered_cpouts.pH_{:.2f}.dat'.format(pH), usecols=(3))\n",
    "    statesPerBLock = len(titration)/(2*Nblocks)\n",
    "    count = 0\n",
    "    block = 0\n",
    "    for Asp, His in pairwise(titration):\n",
    "        if Asp > 0 and His > 0:     # PD\n",
    "            states[block][i][0] += 1\n",
    "        elif Asp > 0 and His == 0:  # PP\n",
    "            states[block][i][1] += 1\n",
    "        elif Asp == 0 and His == 0: # DP\n",
    "            states[block][i][2] += 1\n",
    "        elif Asp == 0 and His > 0:  # DD\n",
    "            states[block][i][3] += 1\n",
    "        else: # This condition should never happen\n",
    "            raise Exception(\"State could not be catagorized\")\n",
    "        count += 1\n",
    "        if count == statesPerBLock:\n",
    "            block += 1\n",
    "            count = 0\n",
    "                       \n",
    "states = states/statesPerBLock # Normalization\n",
    "\n",
    "\n",
    "results_micro = np.empty(shape=(Nblocks, 6))\n",
    "results_macro = np.empty(shape=(Nblocks, 2))\n",
    "\n",
    "for i,block in enumerate(states):\n",
    "    pH = pHs\n",
    "    PD = block[:,0]\n",
    "    PP = block[:,1]\n",
    "    DP = block[:,2]\n",
    "    DD = block[:,3]\n",
    "    total = 1*PD + 2*PP + 1*DP + 0*DD\n",
    "    micro = optimize.minimize(target, x0=np.array([7,4,6]), tol=10**(-7)).x\n",
    "    macro = optimize.curve_fit(macroscopic, pH, total, p0=[3,6], maxfev=1200)[0]\n",
    "\n",
    "    results_macro[i] = macro\n",
    "    results_micro[i] = np.array([micro[0], micro[1], -micro[2]+micro[0],\n",
    "                                 -micro[2]+micro[1], micro[2]*0.6*np.log(10)*4.18400, micro[2]])\n",
    "    \n",
    "arg_mean = results_micro.mean(axis=0)[0:5]                # mean\n",
    "arg_ste = results_micro.std(axis=0)[0:5]/np.sqrt(Nblocks) # standard error of means.\n",
    "print('''\n",
    "    Microscopic                 Macroscopic\n",
    "       (2)            (PP)__\n",
    "    DD ---- DP              \\\\\n",
    "(1) |       |  (3)          (1)           \n",
    "    PD ---- PP                \\\\__(DP+PD)__\n",
    "       (4)                                 \\\\\n",
    "                                           (2)\n",
    "                                             \\\\__(DD)\n",
    "Microscopic pKa values\n",
    "----------------------\n",
    "    1: {:4.2f} ± {:4.2f}\n",
    "    2: {:4.2f} ± {:4.2f}\n",
    "    3: {:4.2f} ± {:4.2f}\n",
    "    4: {:4.2f} ± {:4.2f}\n",
    "    Interaction energy W: {:4.2f} ± {:4.2f} kJ/mol\n",
    "    \n",
    "Macroscopic pKa values\n",
    "----------------------\n",
    "    1: {:4.3f} ± {:4.3f}\n",
    "    2: {:4.3f} ± {:4.3f}\n",
    "'''.format(arg_mean[0], arg_ste[0], arg_mean[1], arg_ste[1], arg_mean[2], arg_ste[2], arg_mean[3], arg_ste[3],\n",
    "           arg_mean[4], arg_ste[4], results_macro.mean(axis=0)[0], results_macro.std(axis=0)[0]/np.sqrt(Nblocks),\n",
    "           results_macro.mean(axis=0)[1], results_macro.std(axis=0)[1]/np.sqrt(Nblocks)))\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6*1.2, 4*1.2))\n",
    "\n",
    "# Plot sampled data\n",
    "pHs = np.arange(2.00, 10.00, 0.5)\n",
    "plt.errorbar(pHs, states.mean(axis=0)[:,1], states.std(axis=0)[:,1]/np.sqrt(Nblocks), marker='o', markersize=4, linestyle='None', color='C0') # PP\n",
    "plt.errorbar(pHs, states.mean(axis=0)[:,2], states.std(axis=0)[:,2]/np.sqrt(Nblocks), marker='o', markersize=4, linestyle='None', color='C1') # DP\n",
    "plt.errorbar(pHs, states.mean(axis=0)[:,0], states.std(axis=0)[:,0]/np.sqrt(Nblocks), marker='o', markersize=4, linestyle='None', color='C2') # PD\n",
    "plt.errorbar(pHs, states.mean(axis=0)[:,3], states.std(axis=0)[:,3]/np.sqrt(Nblocks), marker='o', markersize=4, linestyle='None', color='C3') # DD\n",
    "\n",
    "# Plot fitted model\n",
    "arg =  results_micro[:,[0,1,-1]].mean(axis=0) # arguments partition function.\n",
    "pH = np.arange(min(pHs), max(pHs), 0.01)\n",
    "ax.plot(pH, QPP(arg)/Z(arg), label='PP', linewidth=3, color='C0', alpha=0.70)\n",
    "ax.plot(pH, QDP(arg)/Z(arg), label='DP', linewidth=3, color='C1', alpha=0.70)\n",
    "ax.plot(pH, QPD(arg)/Z(arg), label='PD', linewidth=3, color='C2', alpha=0.70)\n",
    "ax.plot(pH, QDD(arg)/Z(arg), label='DD', linewidth=3, color='C3', alpha=0.70)\n",
    "\n",
    "# Graphical settings\n",
    "ax.minorticks_on()\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xlim(min(pH), max(pH))\n",
    "ax.legend(loc=0, fontsize=16)\n",
    "ax.set_xlabel('pH', fontsize=16)\n",
    "ax.set_ylabel('Protonation state occupation', fontsize=16)\n",
    "ax.tick_params(which='major', direction='in', length=4, width=2, colors='black',\n",
    "               grid_color='black', grid_alpha=0.5, labelsize=14)\n",
    "ax.tick_params(which='minor', direction='in')\n",
    "fig.tight_layout()\n",
    "#fig.savefig('figures/Diprotic_microstate_population.tiff', bbox_inches='tight', dpi=600, format='tiff', pil_kwargs={'compression': 'tiff_lzw'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the Bjerrum diagram we find the zwitterionic state (DP) to be more populated than the neutral state (PD) for the Asp-His pair on the surface of the EXG protein.\n",
    "\n",
    "## pH Depedent Conformational Exchange: Diprotic Acid\n",
    "To gain futher insight into the strong interaction occuring for the D39-H66 pair, we continued by investigating the sampled conformation from the molecular dynamics simulations conducted in between the titration Monte Carlo moves. To do so, we choose to analyse the distance distribution between the side chain carboxylate group of D39 and the side chain pyrrole nitrogen ($\\delta$) and pyridine nitrogen ($\\epsilon$) of H66. Additionally, we analyzed if the movement was correlated by observing the first side chain dihedral angle $\\chi_{1}$. These properties are suspected to be strongly pH depedent, so the analysis were conducted at pH 2.0, 5.0, and 9.0 corresponding to pHs where the different titration species are highly populated (see Bjerrum plot).\n",
    "\n",
    "### pH-dependent Distance Distribution\n",
    "To reduce the complexity of the points for the distance calculation between the Asp and His side chains we choose to use the midpoint between the two side chain carboxylate oxygen of D39 and the pyrrole nitrogen and pyridine nitrogen of H66, resulting in two distance distrubtion for each pH value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pH values for which trajectories exists\n",
    "pHs = [2, 5, 9]\n",
    "\n",
    "# Initiate figure\n",
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(1.5*5.5*1.2, 1.5*4*1.2))\n",
    "axes = [item for sublist in axes for item in sublist]\n",
    "\n",
    "for i, pH in enumerate(pHs):\n",
    "    # Load trajecotry\n",
    "    traj = md.load('trajectories/EXG_39D66H_pH{}.h5'.format(pH))\n",
    "    \n",
    "    coc_dN_dist = []\n",
    "    coc_eN_dist = []\n",
    "    \n",
    "    # Getting index for the indivudal atoms\n",
    "    asp_oxy = traj.topology.select('(resname AS4 and name OD1) || (resname AS4 and name OD2)') # Aspartate side chain carboxyl oxygen\n",
    "    his_dN  = traj.topology.select('resname HIS and name ND1') # Histidine side chain pyrrole nitrogen\n",
    "    his_eN  = traj.topology.select('resname HIS and name NE2') # Histidine side chain pyridine nitrogen\n",
    "    \n",
    "    for frame in range(traj.n_frames):\n",
    "        # Calculate center of charge\n",
    "        coc = (traj.xyz[frame][asp_oxy[0]] + traj.xyz[frame][asp_oxy[1]]) / 2\n",
    "        \n",
    "        # Append calculated distances to list\n",
    "        coc_dN_dist.append(10*np.linalg.norm(coc - traj.xyz[frame][his_dN]))\n",
    "        coc_eN_dist.append(10*np.linalg.norm(coc - traj.xyz[frame][his_eN]))\n",
    "     \n",
    "    for j, distance in enumerate([coc_dN_dist, coc_eN_dist]):\n",
    "        # Create histogram and plot\n",
    "        dist_probability, bin_edges_dist = np.histogram(distance, bins=100, density=True)\n",
    "        bin_centers = (bin_edges_dist[:-1] + bin_edges_dist[1:]) / 2.\n",
    "        \n",
    "        if j == 0:\n",
    "            label = '$\\delta$'\n",
    "        elif j == 1:\n",
    "            label = '$\\epsilon$'\n",
    "        axes[i].plot(bin_centers, dist_probability, label=label)\n",
    "        \n",
    "    axes[i].set_xlim(1.7, 10.0)\n",
    "    axes[i].set_ylim(0.0, 1.2)\n",
    "    axes[i].minorticks_on()\n",
    "    axes[i].set_title('pH {:.1f}'.format(pH), fontsize=18)\n",
    "    axes[i].set_xlabel('Distance (Å)', fontsize=16)\n",
    "    axes[i].set_ylabel('Probability density', fontsize=16)\n",
    "    #axes[i].legend(loc='upper right', title='Histidine nitrogen', fontsize=14)\n",
    "    axes[i].tick_params(which='major', direction='in', length=4, width=2, colors='black',\n",
    "                   grid_color='black', grid_alpha=0.5, labelsize=14)\n",
    "    axes[i].tick_params(which='minor', direction='in')\n",
    "\n",
    "# Legend\n",
    "leg = axes[1].legend(loc='upper left', title='Histidine nitrogen', fontsize=16, bbox_to_anchor=(1.0, 1.05))\n",
    "for line in leg.get_lines():\n",
    "    line.set_linewidth(6.0)\n",
    "leg.get_title().set_fontsize(14)\n",
    "\n",
    "# Image for 4. graph\n",
    "#img = mpimg.imread('trajectories/Asp_His_pair_v4_2.png')\n",
    "#imgplot = axes[3].imshow(img, interpolation='none')\n",
    "axes[3].axis('off')\n",
    "\n",
    "# Save figure\n",
    "fig.tight_layout()\n",
    "#fig.savefig('figures/Distance_distribution.tiff', bbox_inches='tight', dpi=600, format='tiff', pil_kwargs={'compression': 'tiff_lzw'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see a well-defined peak at pH 5.0 at approximately 2.8 Å between the centre of charge of the side chain carboxnyl oxygen of D39 and the pyridine nitrogen on the sidechain of H66, which is in good agreement with salt bridge and hydrogen bonding distances. This distinctive peak is absent at pH 2.0 and 9.0 which points towards the strong interaction is introduced in the zwitterionic and/or neutral state of the Asp-His pair. \n",
    "### pH-dependent Rotamer Distribution\n",
    "We here deviate from the -180 to 180 convension for measurement of $\\chi_{1}$ angles to instead using 0-360 in order to avoid the sampled states to lie in the boarders of the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pHs = [2, 5, 9] # pH values for which trajectories exists\n",
    "variants = ['39D66H', '43D66H', '61D66H'] # EXG variants studied.\n",
    "\n",
    "fig, axes = plt.subplots(nrows=3, ncols=3, figsize=(16, 18)) # Initiate figure\n",
    "\n",
    "for j, variant in enumerate(variants):\n",
    "    for i, pH in enumerate(pHs):\n",
    "        traj = md.load('trajectories/EXG_{}_pH{}.h5'.format(variant, pH)) # Load trajecotry\n",
    "        chi1_matrix = md.compute_chi1(traj, periodic=True, opt=True)      # Compite chi1 angles\n",
    "        \n",
    "        for index,residue in enumerate(chi1_matrix[0]):                   # Find Asp and His index for variants\n",
    "            restype = str(traj.topology.atom(residue[0]))[0:3:1]\n",
    "            if restype == 'AS4':\n",
    "                Asp_index = index\n",
    "            if restype == 'HIS':\n",
    "                His_index = index\n",
    "            \n",
    "        chi1_Asp = np.asarray([np.rad2deg(chi1_matrix[1][i][Asp_index]) for i in range(traj.n_frames)])\n",
    "        chi1_His = np.asarray([np.rad2deg(chi1_matrix[1][i][His_index]) for i in range(traj.n_frames)])\n",
    "        chi1_Asp[chi1_Asp < 0] += 360\n",
    "        chi1_His[chi1_His < 0] += 360\n",
    "        \n",
    "        mod_cmap = plt.cm.get_cmap('nipy_spectral_r')\n",
    "        mod_cmap.set_bad('white')\n",
    "\n",
    "        z, xedge, yedge = np.histogram2d(chi1_Asp, chi1_His, bins=50, density=True)\n",
    "        x = 0.5*(xedge[:-1] + xedge[1:])\n",
    "        y = 0.5*(yedge[:-1] + yedge[1:])\n",
    "        z[z == 0] = np.nan\n",
    "        extent = [yedge[0], yedge[-1], xedge[0], xedge[-1]]\n",
    "        \n",
    "        im = axes[j][i].contourf(x, y, z.T, 50, extent=extent, cmap=mod_cmap)\n",
    "        print('Progress: Variant {Variant}, pH {pH} finished!'.format(Variant=variant, pH=pH))\n",
    "        \n",
    "        axes[j][i].minorticks_on()\n",
    "        axes[j][i].set_xlabel('{} χ₁ (degrees)'.format(variant[2]+variant[0:2]), fontsize=16)\n",
    "        axes[j][i].set_ylabel('{} χ₁ (degrees)'.format(variant[-1]+variant[3:5]), fontsize=16)\n",
    "        axes[j][i].set_xlim(0, 361)\n",
    "        axes[j][i].set_ylim(0, 361)\n",
    "        axes[j][i].tick_params(which='major', direction='in', length=4, width=2, colors='black',\n",
    "                   grid_color='black', grid_alpha=0.5, labelsize=14)\n",
    "        axes[j][i].tick_params(which='minor', direction='in')\n",
    "        \n",
    "        axes[0][i].set_title('pH {:.1f}'.format(pHs[i]), fontsize=20)\n",
    "\n",
    "fig.subplots_adjust(right=0.8)\n",
    "cbar_ax = fig.add_axes([1, 0.1, 0.02, 0.8])\n",
    "cbar = fig.colorbar(im, cax=cbar_ax, format='%.1e')\n",
    "cbar.set_label('Probability density', fontsize=16)\n",
    "cbar.ax.tick_params(labelsize=14)\n",
    "fig.subplots_adjust(hspace=10)\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig('figures/Asp-His_sidechain_dihedrals.tiff', bbox_inches='tight', dpi=600, format='tiff', pil_kwargs={'compression': 'tiff_lzw'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examining the joint distribution of $\\chi_{1}$ angles of D39 and H66 we find at pH 2.0 and 9.0 D39 was mostly found with $\\chi_{1}$ in the p-rotamer ($\\chi_{1}$~60°), whereas at pH 5.0 it mostly sampled the t-rotamer ($\\chi_{1}$ ~180°). The histidine was mostly found in the t-rotamer, sampling also the m-rotamer ($\\chi_{1}$ ~300°) at low pH. When D39 was in the p-rotamer, the aspartate side chain faced the solvent, whereas the t-rotamer state populated at pH 5.0 corresponded to the conformation from the short-distance peak at pH 5 in Figure 4, with the aspartate side chain facing the side chain of H66."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pH depedent conformational exchange: monoprotic single-aspartate residue acid\n",
    "### pH-dependent rotamer distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pHs = [0.5, 8.0] # pH values for which trajectories exists\n",
    "variants = ['39D', '43D', '61D'] # aspartate variants\n",
    "var_indexes = [26, 30, 46] # index for variants list\n",
    "\n",
    "# Initiate figure\n",
    "fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(16, 4))\n",
    "\n",
    "for i, variant in enumerate(variants):\n",
    "    j = 0\n",
    "    for pH in pHs:\n",
    "        # Load trajecotry\n",
    "        traj = md.load('trajectories/EXG_{variant}_pH{pH}.h5'.format(variant=variant, pH=pH))\n",
    "        \n",
    "        chi1_matrix = md.compute_chi1(traj, periodic=True, opt=True)\n",
    "        chi1_Asp = np.asarray([np.rad2deg(chi1_matrix[1][j][var_indexes[i]]) for j in range(traj.n_frames)])\n",
    "        chi1_Asp[chi1_Asp < 0] += 360\n",
    "        \n",
    "        probabilities, edges = np.histogram(chi1_Asp, bins=60, density=True)\n",
    "        centers = 0.5*(edges[1:]+ edges[:-1])\n",
    "        axes[i].plot(centers, probabilities, color='C{}'.format(j), linewidth=3)\n",
    "        print('Progress: Variant {variant}, pH {pH} finished!'.format(variant=variant, pH=pH))\n",
    "        j+=1\n",
    "        \n",
    "for i, ax in enumerate(axes):\n",
    "    ax.set_xlim(0, 360)\n",
    "    ax.set_ylim(0, 0.04)\n",
    "    ax.set_title('{}'.format(variants[i]), fontsize=20)\n",
    "    ax.set_xlabel('χ₁ (degrees)', fontsize=16)\n",
    "    ax.set_ylabel('Probability density', fontsize=16)\n",
    "    ax.tick_params(which='major', direction='in', length=4, width=2, colors='black',\n",
    "                   grid_color='black', grid_alpha=0.5, labelsize=14)\n",
    "    ax.tick_params(which='minor', direction='in')\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('figures/Asp_sidechain_dihedral.tiff', bbox_inches='tight', dpi=600, format='tiff', pil_kwargs={'compression': 'tiff_lzw'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Titration Curves of EXG Variants: pK<sub>a</sub> Values & Hill Coefficients\n",
    "\n",
    "The Henderson–Hasselbalch equation is given by\n",
    "$$\n",
    "\\text{pH} = \\text{p}K_{a} + \\log{\\left(\\frac{[\\text{B}]}{[\\text{A}]}\\right)},\n",
    "$$\n",
    "where $[\\text{A}]$ and $[\\text{B}]$ are the concentrations of acid and base respectively. We define the acid fraction (the protonated fraction), $y_a$, and base fraction (the deprotonated fraction), $y_b$, as\n",
    "$$\n",
    "y_a = \\frac{[\\text{A}]}{[\\text{A}]+[\\text{B}]}, \\quad y_b=\\frac{[\\text{B}]}{[\\text{B}]+[\\text{A}]}, \\quad y_a + y_b = 1.\n",
    "$$\n",
    "<div style=\"padding: 0px; \n",
    "            width: auto; \n",
    "            word-wrap: break-word; \n",
    "            text-align:justify;\">\n",
    "\n",
    "<div style=\"width:image width px; \n",
    "            font-size:80%; \n",
    "            text-align:right; \n",
    "            float: right; padding-left-right-top-bottom:0.5em;\">\n",
    "    <img src=\"figures/hillIllustration.png\" \n",
    "         alt=\"Hill coeffificent in titrations\" \n",
    "         width=300 \n",
    "         style=\"padding-left:0.5em;\"/>\n",
    "\n",
    "</div>\n",
    "Rewriting the Henderson–Hasselbalch equation in terms of the base fraction we obtain\n",
    "$$\n",
    "\\text{pH} = \\text{p}K_{a} + \\log{\\left(\\frac{y_b}{1-y_b}\\right)} \\implies y_b = \\frac{1}{1+10^{\\text{p}K_{a}-\\text{pH}}}.\n",
    "$$\n",
    "To capture deviations in titration behavour due to ultrasensitivity, which is related to the steepness of the transition, we introduce the Hill coefficient ($n$) into the equation above\n",
    "$$\n",
    "y_b = \\frac{1}{1+10^{n \\left(\\text{p}K_{a}-\\text{pH}\\right)}}\n",
    "$$\n",
    "The above equation will serve as fitting equation to obtain $\\text{p}K_{a}$ values and Hill coefficients ($n$) from single residue titration curves.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "\n",
       "| Variant | pKa (Asp) | n (Asp) | pKa (His) | n (His) |\n",
       "|---------|-----------|---------|-----------|---------|\n",
       "|  66H     |    -      |   -     |   6.121 ± 0.093      |  1.009 ± 0.008     |\n",
       "|  39D     |   5.333 ± 0.038      | 1.006 ± 0.008      |     -     |    -    |\n",
       "|  43D     |   4.776 ± 0.015      | 0.995 ± 0.005      |     -     |    -    |\n",
       "|  61D     |   4.486 ± 0.014      | 0.961 ± 0.001      |     -     |    -    |\n",
       "|  39D66H     |    -      |   -     |     -     |    -    |\n",
       "|  43D66H     |   4.663 ± 0.026      | 0.966 ± 0.003      |   6.010 ± 0.104      |  0.989 ± 0.012     |\n",
       "|  61D66H     |   4.186 ± 0.068      | 0.948 ± 0.004      |   6.069 ± 0.044      |  0.996 ± 0.016     |\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 857
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hill modified Henderson–Hasselbalch equation expressed for the deprotonated fraction\n",
    "def DeprotFraction(pH, pka, n):\n",
    "    return 1/(1+10**(n*(pka - pH)))\n",
    "\n",
    "# Number of blocks:\n",
    "Nblocks = 4\n",
    "\n",
    "# Initiate figure\n",
    "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))\n",
    "\n",
    "Table = [] # Empty list used to append table values\n",
    "variants = ['66H', '39D', '43D', '61D', '39D66H', '43D66H', '61D66H'] # EXG variants\n",
    "for k, variant in enumerate(variants):\n",
    "    Table.append(variant)\n",
    "    numTitrationSites = sum(c.isalpha() for c in variant)\n",
    "    if k == 0:\n",
    "        pHs = np.asarray([2.0, 3.0, 4.0, 5.0, 6.0, 6.5, 7.0, 8.0, 9.0, 10.0])\n",
    "    elif numTitrationSites == 1:\n",
    "        pHs = np.arange(0.5, 8.5, 0.5)\n",
    "    else:\n",
    "        pHs = np.arange(2.0, 10.0, 0.5)\n",
    "    \n",
    "    states = np.zeros(shape=(Nblocks, len(pHs), numTitrationSites))\n",
    "    \n",
    "    for i,pH in enumerate(pHs):\n",
    "        titration = np.loadtxt('data/titration_data/{}/reordered_cpouts.pH_{:.2f}.dat'.format(variant,pH), usecols=(3))\n",
    "        statesPerBLock = len(titration)/(numTitrationSites*Nblocks)\n",
    "        count = 0\n",
    "        block = 0\n",
    "        if numTitrationSites == 2:\n",
    "            for Asp, His in pairwise(titration):\n",
    "                if Asp == 0: # D (Asp)\n",
    "                    states[block][i][0] += 1\n",
    "                if His > 0:  # D (His)\n",
    "                    states[block][i][1] += 1\n",
    "                count += 1\n",
    "                if count == statesPerBLock:\n",
    "                    block += 1\n",
    "                    count = 0\n",
    "        else:\n",
    "            for Asp in titration:\n",
    "                if Asp == 0:  # D\n",
    "                    states[block][i][0] += 1\n",
    "                count += 1\n",
    "                if count == statesPerBLock:\n",
    "                    block += 1\n",
    "                    count = 0\n",
    "    \n",
    "    states = states/statesPerBLock # Normalization\n",
    "    \n",
    "    results = np.empty(shape=(Nblocks, 2*numTitrationSites))\n",
    "    for i,block in enumerate(states):\n",
    "        deprot = block[:,0]\n",
    "        if k == 0:\n",
    "            deprot = 1 - deprot # Quick fix for fixing protonation index of His66 variant.\n",
    "        opt_asp = optimize.curve_fit(DeprotFraction, pHs, deprot, p0=[4,1])[0]\n",
    "        if numTitrationSites == 2:\n",
    "            deprot = block[:,1]\n",
    "            opt_his = optimize.curve_fit(DeprotFraction, pHs, deprot, p0=[4,1])[0]\n",
    "            results[i] = np.concatenate((opt_asp, opt_his))\n",
    "        else:\n",
    "            results[i] = opt_asp\n",
    "        \n",
    "    for resid in range(numTitrationSites):\n",
    "        if k == 0: # Quick fix for His66\n",
    "            axes[1].errorbar(pHs, 1-states.mean(axis=0)[:,resid], states.std(axis=0)[:,resid], markersize=8, linestyle='None', marker='o', color='C{}'.format(k))\n",
    "        else:\n",
    "            axes[resid].errorbar(pHs, states.mean(axis=0)[:,resid], states.std(axis=0)[:,resid], markersize=8, linestyle='None', marker='o', color='C{}'.format(k))\n",
    "        if variant == '39D66H':  # Do not plot single titration curve for `39D66H` variant.\n",
    "            continue\n",
    "        pH = np.arange(1.0, 10.0, 0.01)\n",
    "        if resid == 0:\n",
    "            means = results.mean(axis=0)[:2]\n",
    "            stds = results.std(axis=0)[:2]\n",
    "            Table.extend(['{:.3f} ± {:.3f}'.format(means[0], stds[0]), '{:.3f} ± {:.3f}'.format(means[1], stds[1])])\n",
    "        else:\n",
    "            means = results.mean(axis=0)[2:4]\n",
    "            stds = results.std(axis=0)[2:4]\n",
    "            Table.extend(['{:.3f} ± {:.3f}'.format(means[0], stds[0]), '{:.3f} ± {:.3f}'.format(means[1], stds[1])])\n",
    "        if k == 0: # Yet another quick fix for His66\n",
    "            axes[1].plot(pH, DeprotFraction(pH, means[0], means[1]), linewidth=3, alpha=0.75, color='C{}'.format(k))\n",
    "        else:\n",
    "            axes[resid].plot(pH, DeprotFraction(pH, means[0], means[1]), linewidth=3, alpha=0.75, color='C{}'.format(k))\n",
    "               \n",
    "# Beautification\n",
    "for i, ax in enumerate(axes):\n",
    "    ax.minorticks_on()\n",
    "    ax.set_xlabel('pH', fontsize=16)\n",
    "    ax.set_ylabel('Degree of proton dissociation', fontsize=16)\n",
    "    ax.tick_params(which='major', direction='in', length=4, width=2, colors='black',\n",
    "               grid_color='black', grid_alpha=0.5, labelsize=14)\n",
    "    ax.tick_params(which='minor', direction='in')\n",
    "\n",
    "axes[0].set_title('Aspratate', fontsize=20)\n",
    "axes[1].set_title('Histidine', fontsize=20)\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig('figures/SingleResidueTitrationCurves.tiff', bbox_inches='tight', dpi=600, format='tiff', pil_kwargs={'compression': 'tiff_lzw'})\n",
    "\n",
    "Markdown('''\n",
    "| Variant | pKa (Asp) | n (Asp) | pKa (His) | n (His) |\n",
    "|---------|-----------|---------|-----------|---------|\n",
    "|  {}     |    -      |   -     |   {}      |  {}     |\n",
    "|  {}     |   {}      | {}      |     -     |    -    |\n",
    "|  {}     |   {}      | {}      |     -     |    -    |\n",
    "|  {}     |   {}      | {}      |     -     |    -    |\n",
    "|  {}     |    -      |   -     |     -     |    -    |\n",
    "|  {}     |   {}      | {}      |   {}      |  {}     |\n",
    "|  {}     |   {}      | {}      |   {}      |  {}     |\n",
    "'''.format(*Table))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pKa Prediction of Titratable Residues in a Highly Charge-depleated Protein\n",
    "Total correlation plot between predicted pKa values by CpHMD simulation and experimental pKa values by NMR spectroscopy for the EXG system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### EXG DATA ####\n",
    "\n",
    "# Experimental pka values\n",
    "Asp39  = 5\n",
    "Asp43  = 4.37\n",
    "Asp61  = 4.15\n",
    "Asp39d = 4.07\n",
    "Asp43d = 4.32\n",
    "Asp61d = 4.1\n",
    "\n",
    "His66  = 6.39\n",
    "His66d39 = 7.24\n",
    "His66d43 = 6.49 \n",
    "His66d61 = 6.68\n",
    "\n",
    "exp_asp = [Asp39, Asp43, Asp61, Asp39d, Asp43d, Asp61d]\n",
    "exp_his = [His66, His66d39, His66d43, His66d61]\n",
    "\n",
    "# Predicted pka values\n",
    "sim_Asp39 = 5.33\n",
    "sim_Asp43 = 4.78\n",
    "sim_Asp61 = 4.49\n",
    "sim_Asp39d= 3.69\n",
    "sim_Asp43d= 4.66\n",
    "sim_Asp61d= 4.19\n",
    "\n",
    "sim_His66 = 6.1\n",
    "sim_His66d39 = 6.85\n",
    "sim_His66d43 = 6.01\n",
    "sim_His66d61 = 6.07\n",
    "\n",
    "sim_asp = [sim_Asp39, sim_Asp43, sim_Asp61, sim_Asp39d, sim_Asp43d, sim_Asp61d]\n",
    "sim_his = [sim_His66, sim_His66d39, sim_His66d43, sim_His66d61]\n",
    "\n",
    "\n",
    "label_asp = ['D39', 'D43', 'D61', 'H66-D39', 'H66-D43', 'H66-D61']\n",
    "label_his = ['H66', 'H66-D39', 'H66-D43', 'H66-D61']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Begin figure\n",
    "fig = plt.figure()\n",
    "ax = fig.add_axes([0.0, 0.0, 1.0, 1.0])\n",
    "\n",
    "texts = []\n",
    "\n",
    "# Plot\n",
    "ax.scatter(sim_asp, exp_asp, color='red', label='Asp')\n",
    "ax.scatter(sim_his, exp_his, color='blue', label='His')\n",
    "\n",
    "for i, txt in enumerate(label_asp):\n",
    "    if i > 2:\n",
    "        weight = 'normal'\n",
    "    else:\n",
    "        weight = 'normal'\n",
    "    text = ax.annotate(txt, (sim_asp[i], exp_asp[i]), weight=weight,\n",
    "                       bbox=dict(facecolor='none', edgecolor='black', boxstyle='round,pad=0.1'))\n",
    "    texts.append(text)\n",
    "    \n",
    "for i, txt in enumerate(label_his):\n",
    "    text = ax.annotate(txt, (sim_his[i], exp_his[i]),\n",
    "                       bbox=dict(facecolor='none', edgecolor='black', boxstyle='round,pad=0.1'))\n",
    "    texts.append(text)\n",
    "\n",
    "\n",
    "# Statistics and Regression line\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(sim_asp+sim_his,exp_asp+exp_his)\n",
    "f = lambda x: slope*x + intercept\n",
    "g = lambda x: x\n",
    "x = np.array([3.5,10])\n",
    "#ax.plot(x, f(x), label='Linear fit')\n",
    "ax.plot(x, g(x), color='black', alpha=0.5)\n",
    "ax.plot(x, g(x)+0.39, color='gray', alpha=0.5, linestyle='dashed')\n",
    "ax.plot(x, g(x)-0.39, color='gray', alpha=0.5, linestyle='dashed')\n",
    "\n",
    "# Axis modification\n",
    "ax.set_xlim(3.5,7.5)\n",
    "ax.set_ylim(3.5,7.5)\n",
    "ax.minorticks_on()\n",
    "ax.legend(loc=0, fontsize=14, frameon=False)\n",
    "ax.set_xlabel(r'p$K_{\\mathrm{a}}$ Simulation', fontsize=16)\n",
    "ax.set_ylabel(r'p$K_{\\mathrm{a}}$ Experiment', fontsize=16)\n",
    "\n",
    "ax.set_xticks(np.arange(3.5, 8.0, 0.5))\n",
    "ax.tick_params(which='major', direction='in', length=4, width=2, colors='black',\n",
    "               grid_color='black', grid_alpha=0.5, labelsize=14)\n",
    "ax.tick_params(which='minor', direction='in')\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "fig.tight_layout()\n",
    "# Avoid overlapping annotations\n",
    "adjust_text(texts, expand_points=(2.0,2.0), expand_text=(2.0, 2.0), expand_align=(2.2, 2.2),\n",
    "            arrowprops=dict(arrowstyle='->', color='black')) # 1.3,1.3\n",
    "#fig.savefig('figures/Total_pka_correlation.pdf', bbox_inches='tight')\n",
    "\n",
    "print('slope: {}'.format(slope))\n",
    "print('intercept: {}'.format(intercept))\n",
    "print('r_value**2: {}'.format(r_value**2))\n",
    "\n",
    "sim_full = np.append(sim_asp, sim_his)\n",
    "exp_full = np.append(exp_asp, exp_his)\n",
    "\n",
    "pKa_RMSD = np.sqrt(np.sum(np.subtract(sim_full,exp_full)**2)/len(exp_full))\n",
    "print(r'Root-mean-square error (RMSE) of pKa values: {}'.format(pKa_RMSD))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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