Lecture.ipynb

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    "---\n",
    "# Lecture 7: Molecular Dynamics Simulations in Python\n",
    "---\n",
    "\n",
    "## 1. Introduction <a id='l_overview'></a>\n",
    "\n",
    "This lecture was created as part of a CPS Teaching Fellowship. We are introducing a novel approach to study advanced scientific programming. The goal of today's lecture is to present Molecular Dynamics (MD) simulations of macromolecules. We will learn how to run these simulations using the Python programmming language. We will use many `numpy` functions and a few new modules, such as `openmm` for MD simulations. These are the important concepts that we will cover:\n",
    "\n",
    "- [Newton's Laws of Motion](#l_newton) \n",
    "- [Simulation of Dynamics of Particles](#l_sims)\n",
    "- [Proteins -- Different Levels of Structure](#l_proteins)\n",
    "- [Molecular Mechanics](#l_mm)\n",
    "- [MD Simulations of Proteins](#l_md)\n",
    "\n",
    "\n",
    "## 2. Newton's Laws of Motion <a id='l_newton'></a>\n",
    "\n",
    "Newton's 2nd law connects the kinematics (movements) of a body with its mechanics (total force acting on it) and defines the dynamic evolution of its position: \n",
    "\n",
    "$$m\\frac{d^2r(t)}{dt^2} = F = - \\nabla{U(r)},$$\n",
    "\n",
    "where $m$ is the mass, $r$ is the position, $F$ is the force and $U(r)$ is the potential energy, which depends only on the position of the body. \n",
    "If one knows the forces acting upon the body, one can find the position of the body at any moment $r(t)$, i.e. predict its dynamics. This can be done by solving Newton's equation of motion. It is a second order ODE that can be solved analytically for a few simple cases: constant force, harmonic oscillator, periodic force, drag force, etc.\n",
    "However, a more general approach is to use computers in order to solve the ODE numerically.\n",
    "\n",
    "\n",
    "## 3. Simulation of Dynamics of Particles <a id='l_sims'></a>\n",
    "\n",
    "There are [many methods](https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations#Methods) for solving ODEs. The second order ODE is transformed to the system of two first order ODEs as follows:\n",
    "\n",
    "$$\\frac{dr(t)}{dt} = v(t)$$\n",
    "\n",
    "$$m\\frac{dv(t)}{dt} = F(t)$$\n",
    "\n",
    "We use a finite difference approximation that comes to a simple forward Euler Algorithm: \n",
    "\n",
    "$$ v_{n+1} = v_n + \\frac{F_n}{m} dt$$\n",
    "\n",
    "$$ r_{n+1} = r_n + v_{n+1} dt$$\n",
    "\n",
    "Here we discretize time t with time step $dt$, so $t_{n+1} = t_n + dt$, and $r_{n} = r(t_n)$, $v_{n} = v(t_n)$, where $n$ is the timestep number. Using this method, computing dynamics is straightforward."
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    "\n",
    "<img src=\"pics/Toronto-04.png\" width=\"300\" align=\"right\">\n",
    "### Example 3.1. Simulation of a projectile on Earth.\n",
    "---\n",
    "\n",
    "We want to know the dynamics of a green apple ($m = 0.3$ kg) tossed horizontally at 10 cm/s speed from the top of the Toronto CN Tower (553 m) for the first 10 seconds."
   ]
  },
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "\n",
    "# Setup the figure and axes...\n",
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "\n",
    "## Adjust axes limits according to your problem. Here we don't need more than a couple of meters left or right, and 600 meters up\n",
    "ax.set(xlim=(-2, 2), ylim=(0, 600), xlabel='Position, meters', ylabel='Height, meters', title='Apple falling from CN tower')\n",
    "\n",
    "# parameters of the problem\n",
    "T = 10. #s\n",
    "m = 0.3 #kg\n",
    "g = 9.8 #m/s^2\n",
    "v0x = -0.1 #m/s\n",
    "H = 553. #m\n",
    "\n",
    "# setting a timestep to be 50 ms\n",
    "dt = 0.05 #s\n",
    "N = int(T / dt)\n",
    "\n",
    "# Allocating arrays for 2D problem\n",
    "v = np.zeros((N+1, 2))\n",
    "r = np.zeros((N+1, 2))\n",
    "f = np.zeros((N+1, 2))\n",
    "\n",
    "# initial conditions:\n",
    "r[0] = np.array([0., H])\n",
    "v[0] = np.array([-v0x, 0.])\n",
    "\n",
    "# the only force is gravity\n",
    "f[:] = np.array([0., -m * g])\n",
    "\n",
    "## Run dynamics:\n",
    "for n in range(N):\n",
    "    v[n+1] = v[n] + f[n]/m * dt\n",
    "    r[n+1] = r[n] + v[n+1] * dt\n",
    "\n",
    "## drawing the first data point  \n",
    "scat = ax.scatter(r[0,0], r[0,1], marker='o', c='g', s=200)\n",
    "\n",
    "## animating \n",
    "def animate(i):\n",
    "    scat.set_offsets(r[i])\n",
    "\n",
    "ani = animation.FuncAnimation(fig, func=animate, frames=N)\n",
    "## this function will create a lot of *.png files in a folder 'CNtower_frames'\n",
    "## and create an HTML page with a simulation\n",
    "ani.save('CNtower.html', writer=animation.HTMLWriter(fps= 1//dt))\n",
    "plt.close()\n",
    "#ani.save('CNtower.mp4', fps= 1//dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the dynamics using embedded HTML. It's interactive and you can play a movie step by step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
       "css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_imgf69805cf42f4414192beeb744d231ec1\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_sliderf69805cf42f4414192beeb744d231ec1\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"animf69805cf42f4414192beeb744d231ec1.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.pause_animation()\"><i class=\"fa fa-pause\">\n",
       "          </i></button>\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.play_animation()\"><i class=\"fa fa-play\"></i>\n",
       "          </button>\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.next_frame()\"><i class=\"fa fa-step-forward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"animf69805cf42f4414192beeb744d231ec1.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form action=\"#n\" name=\"_anim_loop_selectf69805cf42f4414192beeb744d231ec1\" class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_f69805cf42f4414192beeb744d231ec1\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_f69805cf42f4414192beeb744d231ec1\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_f69805cf42f4414192beeb744d231ec1\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_f69805cf42f4414192beeb744d231ec1\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_f69805cf42f4414192beeb744d231ec1\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_f69805cf42f4414192beeb744d231ec1\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgf69805cf42f4414192beeb744d231ec1\";\n",
       "    var slider_id = \"_anim_sliderf69805cf42f4414192beeb744d231ec1\";\n",
       "    var loop_select_id = \"_anim_loop_selectf69805cf42f4414192beeb744d231ec1\";\n",
       "    var frames = new Array(200);\n",
       "    \n",
       "  for (var i=0; i<200; i++){\n",
       "    frames[i] = \"CNtower_frames/frame\" + (\"0000000\" + i).slice(-7) +\n",
       "                \".png\";\n",
       "  }\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animf69805cf42f4414192beeb744d231ec1 = new Animation(frames, img_id, slider_id, 52.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML('CNtower.html')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "When a closed system of particles are interacting through pairwise potentials, the force on each particle $i$ depends on its position with respect to every other particle $j$:\n",
    "\n",
    "$$m_i\\frac{d^2r_i(t)}{dt^2} = \\sum_jF_{ij}(t) = -\\sum_j\\nabla_i{U(|r_{ij}(t)|)}$$\n",
    "\n",
    "where $r_{ij} = \\sqrt{(x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2}$ is the distance between particle $i$ and $j$, and $i,j \\in (1,N)$.\n",
    "\n",
    "### Example 3.2. Simulation of 3-body problem with Hooke's law:\n",
    "\n",
    "We want to know the dynamics of 3 particles $m = 1$ kg connected to each other with invisible springs with $K_s = 5$ N/m, and $r_0 = 1$ m initially located at (0, 2), (2, 0) and (-1, 0) on the 2D plane for the first 10 seconds of their motion.\n",
    "\n",
    "**Hint:**\n",
    "The pairwise potential is (Hooke's Law): $$U(r_{ij}) = \\frac{K_s}{2}(r_{ij} - r_0)^2$$\n",
    "\n",
    "The negative gradient of the potential is a force from $j$-th upon $i$-th: \n",
    "\n",
    "$$\\mathbf{F_{ij}} = - \\nabla_i{U(r_{ij})} = - K_s (r_{ij} - r_0) \\nabla_i r_{ij} = - K_s (r_{ij} - r_0) \\mathbf{r_{ij}} / r_{ij}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Setup the figure and axes...\n",
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "ax.set(xlim=(-3.5, 3.5), ylim=(-3.5, 3.5), ylabel='meters', xlabel='meters', title='3-Body problem')\n",
    "\n",
    "# parameters of the problem\n",
    "T = 10. #s\n",
    "m = 1.0 #kg\n",
    "ks = 5 #N/m\n",
    "r0 = 1. #m\n",
    "\n",
    "# setting a timestep to be 50 ms\n",
    "dt = 0.05 #s\n",
    "N = int(T / dt)\n",
    "\n",
    "# Allocating arrays for 2D problem: first axis - time. second axis - particle's number. third - coordinate\n",
    "v = np.zeros((N+1, 3, 2))\n",
    "r = np.zeros((N+1, 3, 2))\n",
    "f = np.zeros((N+1, 3, 2))\n",
    "\n",
    "# initial conditions for 3 particles:\n",
    "r[0,0] = np.array([0., 2.])\n",
    "r[0,1] = np.array([2., 0.])\n",
    "r[0,2] = np.array([-1., 0.])\n",
    "\n",
    "def compute_forces(n):\n",
    "    '''The function computes forces on each pearticle at time step n'''\n",
    "    for i in range(3):\n",
    "        for j in range(3):\n",
    "            if i != j:\n",
    "                rij = r[n,i] - r[n,j]\n",
    "                rij_abs = np.linalg.norm(rij)\n",
    "                f[n, i] -= ks * (rij_abs - r0) * rij / rij_abs \n",
    "## Run dynamics:\n",
    "for n in range(N):\n",
    "    compute_forces(n)\n",
    "    v[n+1] = v[n] + f[n]/m * dt\n",
    "    r[n+1] = r[n] + v[n+1] * dt\n",
    "\n",
    "## drawing and animating \n",
    "scat = ax.scatter(r[0,:,0], r[0,:,1], marker='o', c=['b', 'k', 'r'], s=1000)\n",
    "\n",
    "def animate(i):\n",
    "    scat.set_offsets(r[i])\n",
    "\n",
    "ani = animation.FuncAnimation(fig, animate, frames=N)\n",
    "plt.close()\n",
    "## this function will create a lot of *.png files in a folder '3Body_frames'\n",
    "ani.save('3body.html', writer=animation.HTMLWriter(fps= 1//dt))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, looking at the trajectory representation in real time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
       "css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
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    "HTML('3body.html')"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While we now have a basic knowledge of the purpose and methodology of simulations, we still need to understand what proteins are and why they are important.\n",
    "\n",
    "---\n",
    "## 4. Proteins, structure and functions <a id='l_proteins'></a>\n",
    "---\n",
    "<img src=\"pics/Protein_structure.png\" width=\"400\" align=\"right\">\n",
    "\n",
    "[Protein structure](https://en.wikipedia.org/wiki/Protein_structure) is the three-dimensional arrangement of atoms in a protein, which is a chain of amino acids. Proteins are polymers – specifically polypeptides – formed from sequences of 20 types of amino acids, the monomers of the polymer. A single amino acid monomer may also be called a residue, indicating a repeating unit of a polymer. To be able to perform their biological function, proteins fold into one or more specific spatial conformations driven by a number of non-covalent interactions such as:\n",
    "\n",
    "- hydrogen bonding \n",
    "- ionic interactions \n",
    "- Van der Waals forces\n",
    "- hydrophobic packing \n",
    "\n",
    "To understand the functions of proteins at a molecular level, it is often necessary to determine their three-dimensional structure using techniques such as X-ray crystallography, NMR spectroscopy, and others.\n",
    "\n",
    "### 4.1 Levels of structure:\n",
    "\n",
    "**Primary structure** of a protein refers to the sequence of amino acids in the polypeptide chain.\n",
    "\n",
    "**Secondary structure** refers to highly regular local sub-structures of the actual polypeptide backbone chain. There are two main types of secondary structure: the α-helix and the β-strand or β-sheets.\n",
    "\n",
    "**Tertiary structure** refers to the three-dimensional structure of monomeric and multimeric protein molecules. The α-helixes and β-sheets are folded into a compact globular structure. \n",
    "\n",
    "**Quaternary structure** is the three-dimensional structure consisting of two or more individual polypeptide chains (subunits) that operate as a single functional unit (multimer).\n",
    "\n",
    "\n",
    "### 4.2 Functions:\n",
    "\n",
    "- *Antibodies* - bind to specific foreign particles, ex: IgG \n",
    "- *Enzymes* - speed up chemical reactions, ex: Lysozyme\n",
    "- *Messengers* - transmit signals, ex: Growth hormone \n",
    "- *Structural components* - support for cells, ex: Tubulin\n",
    "- *Transport/storage* - bind and carry small molecules, ex: Hemoglobin\n",
    "\n",
    "\n",
    "**Lysozyme** is a protein-enzyme (found in tears, saliva, mucus and egg white) that is a part of the innate immune system with antimicrobial activity characterized by the ability to damage the cell wall of bacteria. Bacteria have polysaccharides (sugars) in their cell wall, that bind to the groove, and lysozyme cuts the bond and destroys bacteria.  \n",
    "\n",
    "|  ![Protein Sequence in DNA](pics/LysozymeSequence.png) | ![Protein Structure](pics/LysozymeStructure.gif) | ![Protein Strucure with Sugar](pics/LysozymeRock.gif) |\n",
    "|:-:|:-:|:-:|\n",
    "|  Sequence | Structure | Function  |\n",
    "\n",
    "Figure credit: [C.Ing](https://github.com/cing/HackingStructBiolTalk) and [wikipedia](https://en.wikipedia.org/wiki/Protein_structure)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 5. Molecular Mechanics <a id='l_mm'></a>\n",
    "---\n",
    "\n",
    "Since we now know what proteins are and why these molecular machines are important, we consider the method to model them. The basic idea is to create the same kind of approach as we used in the 3-body simulation. Now, our system consists of thousands particles (atoms of the protein plus atoms of surrounding water) and they all are connected via a complex potential energy function.\n",
    "\n",
    "An all-atom potential energy function $V$ is usually given by the sum of the bonded terms ($V_b$) and non-bonded terms ($V_{nb}$), i.e.\n",
    "\n",
    "$$V = V_{b} + V_{nb},$$\n",
    "\n",
    "where the bonded potential includes the harmonic (covalent) bond part, the harmonic angle and\n",
    "the two types of torsion (dihedral) angles: proper and improper. As it can be seen, these functions are mostly harmonic potentials \n",
    "\n",
    "$$V_{b} = \\sum_{bonds}\\frac{1}{2}K_b(b-b_0)^2 + \\sum_{angles}K_{\\theta}(\\theta-\\theta_0)^2 + \\sum_{dihedrals}K_{\\phi}(1-cos(n\\phi - \\phi_0)) + \\sum_{impropers}K_{\\psi}(\\psi-\\psi_0)^2$$\n",
    "\n",
    "For example, $b$ and $\\theta$ represent the distance between two atoms and the angle between two\n",
    "adjacent bonds; $\\phi$ and $\\psi$ are dihedral (torsion) angles. These can be evaluated for all the\n",
    "atoms from their current positions. Also, $K_b$, $K_\\theta$, $K_\\phi$, and $K_\\psi$ are the spring constants, associated\n",
    "with bond vibrations, bending of bond angles, and conformational fluctuations in dihedral and\n",
    "improper angles around some equilibrium values $b_0$, $\\theta_0$, $\\phi_0$, and $\\psi_0$, respectively. \n",
    "\n",
    "The non-bonded part of the potential energy function is represented by the electrostatic and van der Waals potentials, i.e.\n",
    "\n",
    "$$V_{nb} = \\sum_{i,j}\\left(\\frac{q_{i}q_{j}}{4\\pi\\varepsilon_{0}\\varepsilon r_{ij}} + \\varepsilon_{ij}\\left[\\left(\\frac{\\sigma^{min}_{ij}}{r_{ij}}\\right)^{12}-2\\left(\\frac{\\sigma^{min}_{ij}}{r_{ij}}\\right)^{6}\\right]\\right)$$\n",
    "\n",
    "where $r_{ij}$ is the distance between two interacting atoms, $q_i$ and $q_j$ are their electric charges; $\\varepsilon$ and\n",
    "$\\varepsilon_0$ are electric and dielectric constant; $\\varepsilon_{ij} = \\sqrt{\\varepsilon_i\\varepsilon_j}$ and\n",
    "$\\sigma_{ij} = \\frac{\\sigma_i + \\sigma_j}{2}$ are van der Waals parameters for atoms $i$ and $j$.\n",
    "\n",
    "**Importantly, each force field has its own set of parameters, which are different for different types of atoms.**\n",
    "\n",
    "![](pics/ff.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Molecular dynamics of proteins <a id='l_md'></a>\n",
    "---\n",
    "\n",
    "[**Molecular dynamics (MD)**](https://en.wikipedia.org/wiki/Molecular_dynamics) is a computer simulation method for studying the physical movements of atoms and molecules, i.e. their dynamical evolution. \n",
    "\n",
    "In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using  [molecular mechanics force fields](#l_mm). \n",
    "\n",
    "\n",
    "\n",
    "Now with all that intellectual equipment, we can start running legit Molecular Dynamics simulations. All we need is an initial structure of the protein and software that computes its dynamics efficiently.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Procedure:\n",
    "1. Load initial coordinates of protein atoms (from `*.pdb` file)\n",
    "2. Choose force field parameters (in potential function V from section 5).\n",
    "3. Choose parameters of the experiment: temperature, pressure, box size, solvation, boundary conditions\n",
    "4. Choose integrator, i.e. algorithm for solving equation of motion\n",
    "5. Run simulation, save coordinates time to time (to `*.dcd` file).\n",
    "6. Visualize the trajectory \n",
    "7. Perform the analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are the Python libraries we are going to need today:\n",
    "\n",
    "1. [nglview](http://nglviewer.org/nglview/latest/index.html#installation) - module to visualize molecules\n",
    "2. [mdanalysis](https://www.mdanalysis.org/pages/installation_quick_start/) - module to analyze MD trajectory\n",
    "3. [openmm](http://docs.openmm.org/latest/userguide/application.html#installing-openmm) - module to run MD simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "version_minor": 0
      },
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from simtk.openmm.app import *\n",
    "from simtk.openmm import *\n",
    "from simtk.unit import *\n",
    "import MDAnalysis as md\n",
    "import nglview as ng\n",
    "from sys import stdout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These files are already preloaded to your `data` folder."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdb0_file = 'data/villin_water.pdb'\n",
    "pdb1_file = 'data/polyALA.pdb'\n",
    "pdb2_file = 'data/polyGLY.pdb'\n",
    "pdb3_file = 'data/polyGV.pdb'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PDB files contain 3D structures of proteins that were resolved by experimental techniques. They can be downloaded from [ProteinDataBank](https://www.wwpdb.org/). Here we can see what a `.pdb` file looks like: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REMARK    GENERATED BY TRJCONV\n",
      "\n",
      "HEADER    Villin N68H in explicit water\n",
      "\n",
      "REMARK    THIS IS A SIMULATION BOX\n",
      "\n",
      "CRYST1   49.163   45.981   38.869  90.00  90.00  90.00 P 1           1\n",
      "\n",
      "MODEL        0\n",
      "\n",
      "ATOM      1  N   LEU     1      25.160  14.160  19.440  1.00  0.00\n",
      "\n",
      "ATOM      2  H1  LEU     1      24.350  13.730  19.870  1.00  0.00\n",
      "\n",
      "ATOM      3  H2  LEU     1      25.980  13.680  19.760  1.00  0.00\n",
      "\n",
      "ATOM      4  H3  LEU     1      25.180  15.100  19.810  1.00  0.00\n",
      "\n",
      "ATOM      5  CA  LEU     1      25.090  13.920  17.980  1.00  0.00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "file0 = open(pdb0_file, 'r')\n",
    "counter = 0\n",
    "for line in file0:\n",
    "    if counter < 10:\n",
    "        print(line)\n",
    "    counter += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look at the protein via `nglview`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/klyshko/Applications/anaconda3/lib/python3.7/site-packages/MDAnalysis/topology/PDBParser.py:330: UserWarning: Element information is absent or missing for a few atoms. Elements attributes will not be populated.\n",
      "  warnings.warn(\"Element information is absent or missing for a few \"\n"
     ]
    },
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      "text/plain": [
       "NGLWidget()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "Tab(children=(Box(children=(Box(children=(Box(children=(Label(value='step'), IntSlider(value=1, min=-100)), la…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "u = md.Universe(pdb0_file)\n",
    "ng.show_mdanalysis(u, gui=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 6.1. MD simulation of protein folding into alpha-helix\n",
    "---\n",
    "\n",
    "Run a simulation of fully extended polyalanine `polyALA.pdb` for 400 picoseconds in a vacuo environment with T=300 K and see if it can fold to any secondary  structure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#\"Progress (%)\",\"Step\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\"\n",
      "2.5%,5000,5277.1591796875,292.65647692668705\n",
      "5.0%,10000,5248.111328125,274.7734911374804\n",
      "7.5%,15000,5233.80322265625,292.5302550802924\n",
      "10.0%,20000,5160.2373046875,310.7545135140518\n",
      "12.5%,25000,5176.20166015625,270.7016430126723\n",
      "15.0%,30000,5110.03466796875,306.7496597544093\n",
      "17.5%,35000,5358.77783203125,287.87668498160053\n",
      "20.0%,40000,5234.97998046875,306.6754668334164\n",
      "22.5%,45000,5109.7314453125,277.9522965283394\n",
      "25.0%,50000,5150.640625,288.8731486891316\n",
      "27.5%,55000,5298.50634765625,330.0983963213737\n",
      "30.0%,60000,5151.90234375,302.08526171987603\n",
      "32.5%,65000,5053.84423828125,305.26542421723934\n",
      "35.0%,70000,4939.3330078125,310.7949258695294\n",
      "37.5%,75000,4892.923828125,323.52527914924934\n",
      "40.0%,80000,4967.5576171875,298.0353351619747\n",
      "42.5%,85000,4951.75830078125,308.40950802727457\n",
      "45.0%,90000,4850.55908203125,287.9668199775539\n",
      "47.5%,95000,4875.8623046875,309.31722794641234\n",
      "50.0%,100000,4803.8212890625,282.8968325975807\n",
      "52.5%,105000,4757.81982421875,327.962613041576\n",
      "55.0%,110000,4894.1923828125,304.73234029374\n",
      "57.5%,115000,4839.11376953125,299.74439864748337\n",
      "60.0%,120000,4765.73779296875,298.0570390137095\n",
      "62.5%,125000,4653.646484375,292.27513210482573\n",
      "65.0%,130000,4761.24365234375,281.2627064283929\n",
      "67.5%,135000,4818.3466796875,331.9352701265175\n",
      "70.0%,140000,4682.9990234375,284.622219731552\n",
      "72.5%,145000,4747.23388671875,320.80815499138834\n",
      "75.0%,150000,4833.13330078125,299.30487092033894\n",
      "77.5%,155000,4882.5048828125,298.9295420129181\n",
      "80.0%,160000,4696.947265625,296.3128776360789\n",
      "82.5%,165000,4831.3486328125,312.1585191038542\n",
      "85.0%,170000,4718.20361328125,280.5663220660269\n",
      "87.5%,175000,4791.93896484375,307.84622840719334\n",
      "90.0%,180000,4789.97265625,302.7172337489902\n",
      "92.5%,185000,4820.0537109375,287.9221703565977\n",
      "95.0%,190000,4709.40234375,302.8284004990198\n",
      "97.5%,195000,4814.1748046875,303.28907545803054\n",
      "100.0%,200000,4813.11962890625,281.4738533396843\n"
     ]
    }
   ],
   "source": [
    "### 1.loading initial coordinates\n",
    "pdb = PDBFile(pdb1_file) \n",
    "\n",
    "### 2.choosing a forcefield parameters\n",
    "ff = ForceField('amber10.xml')  \n",
    "system = ff.createSystem(pdb.topology, nonbondedMethod=CutoffNonPeriodic)\n",
    "\n",
    "### 3. Choose parameters of the experiment: temperature, pressure, box size, solvation, boundary conditions, etc\n",
    "temperature = 300*kelvin\n",
    "frictionCoeff = 1/picosecond\n",
    "time_step = 0.002*picoseconds\n",
    "total_steps = 400*picoseconds / time_step\n",
    "\n",
    "### 4. Choose an algorithm (integrator)\n",
    "integrator = LangevinIntegrator(temperature, frictionCoeff, time_step)\n",
    "\n",
    "### 5. Run simulation, saving coordinates time to time:\n",
    "\n",
    "### 5a. Create a simulation object\n",
    "simulation = Simulation(pdb.topology, system, integrator)\n",
    "simulation.context.setPositions(pdb.positions)\n",
    "\n",
    "### 5b. Minimize energy\n",
    "simulation.minimizeEnergy()\n",
    "\n",
    "### 5c. Save coordinates to dcd file and energies to a standard output console:\n",
    "simulation.reporters.append(DCDReporter('data/polyALA_traj.dcd', 1000))\n",
    "simulation.reporters.append(StateDataReporter(stdout, 5000, step=True, potentialEnergy=True,\\\n",
    "                                              temperature=True, progress=True, totalSteps = total_steps))\n",
    "\n",
    "### 5d. Run!\n",
    "simulation.step(total_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Visualization**\n",
    "\n",
    "Let's look at the trajectory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ad1a62eb2fa04423b7af14755af2e6e5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "NGLWidget(max_frame=199)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ecc7a8c73a61495cb4fc0e76cbaf5852",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tab(children=(Box(children=(Box(children=(Box(children=(Label(value='step'), IntSlider(value=1, min=-100)), la…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### 6. Visualization\n",
    "sys = md.Universe(pdb1_file, 'data/polyALA_traj.dcd')\n",
    "ng.show_mdanalysis(sys, gui=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 6.2. Analysis of MD trajectory.\n",
    "---\n",
    "\n",
    "**End-to-end distance**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "### analysis of end-to-end distance\n",
    "\n",
    "## choose terminal atoms \n",
    "N_terminus = sys.select_atoms('resid 1 and name N')\n",
    "C_terminus = sys.select_atoms('resid 25 and name C')\n",
    "\n",
    "## go through the whole trajectory and compute distance between them for every frame\n",
    "dist = []\n",
    "for frame in sys.trajectory:\n",
    "    dist.append(np.linalg.norm(N_terminus.positions - C_terminus.positions))\n",
    "\n",
    "## the result is in the dist array    \n",
    "dist = np.array(dist) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Number of hydrogen bonds:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[]\n",
      "[]\n",
      "[]\n",
      "[[123, 107, 'ALA13:H', 'ALA11:O', 2.9577059877155665, 131.93423521880456]]\n",
      "[[113, 97, 'ALA12:H', 'ALA10:O', 2.1374486184213484, 141.93410583481094], [123, 107, 'ALA13:H', 'ALA11:O', 2.1950973223355206, 124.27929762696895]]\n",
      "[[3, 17, 'ALA1:H3', 'ALA2:O', 2.0130550964820433, 132.84132472444526], [153, 137, 'ALA16:H', 'ALA14:O', 1.8937674954665695, 143.3319358533161]]\n",
      "[[3, 17, 'ALA1:H3', 'ALA2:O', 1.939028380621704, 151.93035576267874]]\n",
      "[[3, 17, 'ALA1:H3', 'ALA2:O', 1.9744333029157237, 150.90062476870742]]\n",
      "[]\n",
      "[[73, 57, 'ALA8:H', 'ALA6:O', 2.337432132408794, 131.28731063763829]]\n"
     ]
    }
   ],
   "source": [
    "from MDAnalysis.analysis import hbonds ## module for analysis of hydrogen bonds\n",
    "\n",
    "## compute information about hbonds and write it to the 'hb.timeseries'\n",
    "hb = hbonds.hbond_analysis.HydrogenBondAnalysis(sys)\n",
    "hb.run()\n",
    "\n",
    "## print information for the first 10 frames\n",
    "for frame in hb.timeseries[:10]:\n",
    "    print(frame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## go through the 'hb.timeseries' file and calculate number of bonds for each time frame \n",
    "## (it's the length of array frame)\n",
    "hb_number = []\n",
    "for frame in hb.timeseries:\n",
    "    hb_number.append(len(frame))\n",
    "    \n",
    "## the result is in the number array     \n",
    "hb_number = np.array(hb_number)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot end-to-end distance and number of hydrogen bonds vs time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,5))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot( dist, '-k' )\n",
    "plt.xlabel('timesteps')\n",
    "plt.ylabel('end-to-end distance, A')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(hb_number, 'g-')\n",
    "plt.ylabel('# of hydrogen bonds')\n",
    "plt.xlabel('timesteps')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**[Ramachandran plot](https://en.wikipedia.org/wiki/Ramachandran_plot):**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/klyshko/anaconda3/lib/python3.6/site-packages/MDAnalysis/analysis/dihedrals.py:286: UserWarning: Cannot determine phi and psi angles for the first or last residues\n",
      "  warnings.warn(\"Cannot determine phi and psi angles for the first \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(30, 150, 'beta region')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from MDAnalysis.analysis import dihedrals  ## module for dihedrals analysis\n",
    "\n",
    "ram1 = dihedrals.Ramachandran(sys).run(0,30) ## analyse for first 30 steps (black color)\n",
    "ram2 = dihedrals.Ramachandran(sys).run(170,200) ## analyse for last 30 steps (blue color)\n",
    "\n",
    "## ramachandran plot\n",
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "ram1.plot(ax=ax, color='k', marker='.')\n",
    "ram2.plot(ax=ax, color='b', marker='.')\n",
    "ax.arrow(20, 20, -40, -40, width=2, head_width=8, head_length=12, fc='b', ec='b')\n",
    "ax.text(30, 20, 'alpha region', color='blue', fontsize=20)\n",
    "ax.arrow(20, 150, -40, 0, width=2, head_width=8, head_length=12, fc='k', ec='k')\n",
    "ax.text(30, 150, 'beta region', fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 1. Simulation of a projectile.\n",
    "\n",
    "<img src=\"pics/brady.JPG\" width=\"15%\" align='right'>\n",
    "Read through sections 2-3 and example 3.1 of the lecture. Write a program that simulates the 2-s motion of the NFL ball ($m = 15$ ounces) thrown by quaterback [T.Brady](https://en.wikipedia.org/wiki/Tom_Brady) from height $H=8$ ft at speed $v=60$ MPH which is 30 degrees to the horizontal. Save the simulation as `brady.html`. \n",
    "\n",
    "**Hint**. Be careful with units. You need SI.\n",
    "\n",
    "Use the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## GO PATS!\n",
    "\n",
    "# Setup the figure and axes...\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "## Adjust axes limits according to your problem. Here we don't need more than a couple of meters left or right, and 600 meters up\n",
    "ax.set(xlim=(-2, 50), ylim=(0, 15), xlabel='Position, meters', ylabel='Height, meters', title='NFL Ball Throw')\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "# parameters of the problem\n",
    "T = 2. #s\n",
    "m = 0.425 #kg\n",
    "g = 9.8 #m/s^2\n",
    "v0 = 26.8224 #m/s\n",
    "H = 2.4384 #m\n",
    "theta = np.pi/6 #rad\n",
    "\n",
    "# setting a timestep to be 50 ms\n",
    "dt = 0.05 #s\n",
    "N = int(T / dt)\n",
    "\n",
    "# Allocating arrays for 2D problem\n",
    "v = np.zeros((N+1, 2))\n",
    "r = np.zeros((N+1, 2))\n",
    "f = np.zeros((N+1, 2))\n",
    "\n",
    "# initial conditions:\n",
    "r[0] = np.array([0., H])\n",
    "v[0] = np.array([v0 * np.cos(theta), v0 * np.sin(theta)])\n",
    "\n",
    "# the only force is gravity\n",
    "f[:] = np.array([0., -m * g])\n",
    "\n",
    "## Run dynamics:\n",
    "for n in range(N):\n",
    "    v[n+1] = v[n] + f[n]/m * dt\n",
    "    r[n+1] = r[n] + v[n+1] * dt\n",
    "\n",
    "## drawing the first data point \n",
    "ax.axvline(0, ymin = 0, ymax = 6, color = 'gray', linewidth = 0.5)\n",
    "scat = ax.scatter(r[0,0], r[0,1], marker='o', c='k', s=125)\n",
    "\n",
    "\n",
    "## animating \n",
    "def animate(i):\n",
    "    scat.set_offsets(r[i])\n",
    "\n",
    "plt.tight_layout()\n",
    "ani = animation.FuncAnimation(fig, func=animate, frames=N)\n",
    "ani.save('brady.html', writer=animation.HTMLWriter(fps= 1//dt))\n",
    "plt.close()\n",
    "#ani.save('brady.mp4', fps= 1//dt)\n",
    "\n",
    "HTML('brady.html')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 2. Simulation of an N-body problem.\n",
    "\n",
    "Read through sections 2-3 and example 3.2 of the lecture. Write a program that simulates the 10-s dynamics of **4** particles, each with $m = 0.5$ kg, connected to each other with invisible springs with $K_s = 8$ N/m, and $r_0 = 2$ m initially located at (0,0), (0, 2), (2, 0) and (2, 2) on the 2D plane. Save the simulation as `4body.html`.\n",
    "\n",
    "\n",
    "Use the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up animation axes\n",
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "ax.set(xlim=(-2, 4), ylim=(-2, 4), ylabel='meters', xlabel='meters', title='4-Body problem')\n",
    "\n",
    "# system parameters\n",
    "T = 10. #s\n",
    "m = 0.5 #kg\n",
    "ks = 8 #N/m\n",
    "r0 = 2.\n",
    "\n",
    "# define the time step of the simulation\n",
    "dt = 0.05 #s\n",
    "N = int(T / dt)\n",
    "\n",
    "# define the array of velocity, position, and force, for each time, particle, and direction\n",
    "v = np.zeros((N+1, 4, 2))\n",
    "r = np.zeros((N+1, 4, 2))\n",
    "f = np.zeros((N+1, 4, 2))\n",
    "\n",
    "# set the initial position for each particle\n",
    "r[0,0] = np.array([0., 0.])\n",
    "r[0,1] = np.array([0., 2.])\n",
    "r[0,2] = np.array([2., 0.])\n",
    "r[0,3] = np.array([2., 2.])\n",
    "\n",
    "def compute_forces(n):\n",
    "    '''The function computes forces on each pearticle at time step n'''\n",
    "    for i in range(4):\n",
    "        for j in range(4):\n",
    "            if i != j:\n",
    "                rij = r[n,i] - r[n,j]\n",
    "                rij_abs = np.linalg.norm(rij)\n",
    "                f[n, i] -= ks * (rij_abs - r0) * rij / rij_abs \n",
    "## Run dynamics:\n",
    "for n in range(N):\n",
    "    compute_forces(n)\n",
    "    v[n+1] = v[n] + f[n]/m * dt\n",
    "    r[n+1] = r[n] + v[n+1] * dt\n",
    "\n",
    "## drawing and animating \n",
    "scat = ax.scatter(r[0,:,0], r[0,:,1], marker='o', c=['b', 'k', 'r', 'g'], s=1000)\n",
    "\n",
    "def animate(i):\n",
    "    scat.set_offsets(r[i])\n",
    "\n",
    "# create the animation\n",
    "ani = animation.FuncAnimation(fig, animate, frames=N)\n",
    "plt.close()\n",
    "ani.save('4body.html', writer=animation.HTMLWriter(fps = 1//dt))\n",
    "\n",
    "HTML('4body.html')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 3. Your first MD simulation.\n",
    "\n",
    "Read through section 6 and example 6.1-6.2 of the lecture. Run 3 simulations of fully extended polyglycine `data/polyGLY.pdb` for 1 nanosecond in vacuum (no water) with $T_1=100 K$, $T_2=300 K$, and $T_3=500 K$ and visually compare how extended the final structure is at each temperature.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Similar to Example 6.1 only with 3 temperatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4. MD simulation analysis.\n",
    "\n",
    "Perform a quantitative analysis of the trajectories you obtained in Exercise 3. Use, for example, the end-to-end distance or the function `radius_of_gyration()` from the `MDAnalysis` module, which returns the [radius of gyration](https://en.wikipedia.org/wiki/Radius_of_gyration) of the protein."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import MDAnalysis as md\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "pdb_file = 'data/polyGLY.pdb'\n",
    "dcd_file = 'polyGLY_traj_300K.dcd'  \n",
    "sys = md.Universe(pdb_file, dcd_file)\n",
    "\n",
    "CA_atoms = sys.select_atoms('name CA')\n",
    "\n",
    "# Number of Ca atoms\n",
    "N = len(CA_atoms)\n",
    "M = len(sys.trajectory)\n",
    "\n",
    "#Calculate pairwise distances\n",
    "'''\n",
    "from scipy.spatial.distance import pdist\n",
    "X = []\n",
    "for frame in sys.trajectory:\n",
    "    X.append(pdist(CA_atoms.positions))\n",
    "X = np.array(X)\n",
    "'''\n",
    "\n",
    "## More intuitive way to do that:\n",
    "X = np.empty((M, int(N * (N - 1) / 2)))\n",
    "\n",
    "# using counter\n",
    "k = 0 \n",
    "\n",
    "# for each frame of the trajectory\n",
    "for frame in sys.trajectory:\n",
    "    x = []\n",
    "    # double loop for every pair i,j of atoms avoiding the duplicates\n",
    "    for i in range(len(CA_atoms)):\n",
    "        for j in range(len(CA_atoms)):\n",
    "            if j > i :\n",
    "                # find distance of the vector connecting two atoms\n",
    "                d = np.linalg.norm(CA_atoms[i].position - CA_atoms[j].position)\n",
    "                x.append(d)\n",
    "    # making an numpy array and add that to the X\n",
    "    x = np.array(x)\n",
    "    X[k] = x\n",
    "    k += 1 \n",
    "\n",
    "# Checking the dimensionality\n",
    "print(X.shape, (M, int(N * (N - 1) / 2)))\n",
    "    \n",
    "from sklearn.decomposition import PCA \n",
    "\n",
    "# Total number of components (N*(N-1)/2)\n",
    "total_num_components = int(N * (N - 1) / 2)\n",
    "skl_PCA = PCA(n_components = total_num_components).fit(X)\n",
    "\n",
    "\n",
    "\n",
    "# number of components needed to have grater than 90% variance\n",
    "num_components = 0\n",
    "\n",
    "#calculate the total variance using the first i components\n",
    "for i in range(total_num_components):\n",
    "    total_variance = np.sum(skl_PCA.explained_variance_ratio_[:i])\n",
    "    if total_variance > 0.90:\n",
    "        num_components = i\n",
    "        break\n",
    "\n",
    "\n",
    "print(\"The number of principal components neded to ave variance > 90% is\", num_components)\n",
    "\n",
    "\n",
    "# Transform the data\n",
    "skl_X_transformed = skl_PCA.transform(X) ## apply a transformation\n",
    "\n",
    "colors = np.array([np.linspace(0,1,len(skl_X_transformed)), np.linspace(1, 0,len(skl_X_transformed)), np.zeros(len(skl_X_transformed))])\n",
    "# Use the first two PCs to plot the data in 2D\n",
    "plt.scatter(skl_X_transformed[:,0], skl_X_transformed[:,1], c=colors.T)\n",
    "plt.xlabel(\"PC #1\")\n",
    "plt.ylabel(\"PC #2\")\n",
    "plt.title(\"Data in 2D\")\n",
    "plt.show()"
   ]
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