{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulating a bead trajectory\n",
    "Along with calibrating forces, ``Tweezepy`` also contains methods for simulating bead trajectories."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a single-molecule force spectroscopy experiment, a bead is well-described by Langevin dynamics: the bead's position, $x$, fluctuates over time, $t$, as it randomly diffuses in a harmonic potential, $E(x) = 1/2\\kappa x^2$, where $\\kappa$ is the trap stiffness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x202e4d5ee50>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "kappas = np.array([1,5,10])\n",
    "def energy(x,k):\n",
    "    kT = 4.1\n",
    "    return 1/2 * k * x**2 / kT\n",
    "x = np.linspace(-10,10,num=1000)\n",
    "for kappa in kappas:\n",
    "    plt.plot(x,energy(x,kappa),label = kappa,lw=2)\n",
    "plt.xlabel('Bead position (nm)')\n",
    "plt.ylabel(r'Energy ($k_BT$)')\n",
    "plt.legend(title=r'$\\kappa$ (pN/nm)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot shows the energy (in $k_BT$) as a function of the bead's position (in nm). Collisions between the bead and water molecules create a stochastic (Langevin) force, $F_L$, that obeys the fluctuation-dissipation relation, $\\langle F_L(t+t')F_L(t)\\rangle = 2\\gamma k_BT\\delta(t')$, where $\\gamma$ is the drag coefficient and $\\delta(t)$ is the Dirac delta function.\n",
    "\n",
    "For a micron-scale bead in water, inertial effects can become important at sampling rates, $f_s\\gtrsim10^6$, well below the sampling rate of most SMFS video-tracking experiments. Thus, the bead's motion is well-described by the overdamped Langevin equation:\n",
    "\n",
    "$$\\kappa x(t) + \\gamma \\dot{x}(t) = F_L(t)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To simulate the bead, we can rewrite the overdamped Langevin equation so that changes in the bead's position, $\\Delta x = x(t+t') - x(t)$, are induced by $F_L$ over a simulation time step, $t'$:\n",
    "\n",
    "$$\\Delta x = \\frac{\\Delta t}{\\gamma}\\left(F_L(t) - \\kappa x(t)\\right)$$\n",
    "\n",
    "$$ x(t+t') = x(t) + \\Delta x$$\n",
    "\n",
    "For each time step, $F_L$ is drawn from a norm distribution with mean, $\\langle F_L\\rangle = 0$, and variance, $\\langle F_L^2\\rangle = 2\\gamma k_BT\\Delta t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Bead position (nm)')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tweezepy import simulate_trace\n",
    "fc = 10 # corner frequency\n",
    "gamma = 1e-5 # dissipation due to viscous drag, in pN s/nm\n",
    "             # 1e-5 is a typical value for an MT experiment\n",
    "kappa = gamma*2*np.pi*fc # kappa in pN/nm\n",
    "fsim = 100 # sampling frequency in Hz\n",
    "N  = 102400 # number of points in trajectory\n",
    "seed = 0\n",
    "time = np.arange(N)/fsim\n",
    "xtrace = simulate_trace(gamma,kappa,fsim,N, seed = seed)\n",
    "plt.plot(time, xtrace)\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel('Bead position (nm)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In an actual experiment, the exposure time of the camera will introduce motion blur. To capture this effect, we can downsample the bead trajectory. To accomplish this, we simulate the bead at 1000 times the sampling frequency and then downsample by finding the average position of every 1000 bead positions. This is done automatically in the ``downsampled_trace`` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x203007548e0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tweezepy import downsampled_trace\n",
    "xtrace = simulate_trace(gamma,kappa,fsim,N, seed = seed)\n",
    "xtrace_ds = downsampled_trace(gamma,kappa,fsim,N, seed = seed)\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(8,3),\n",
    "                      ncols=2,\n",
    "                      gridspec_kw={'width_ratios':[3,1],\n",
    "                                   'wspace':0})\n",
    "ax[0].plot(time, xtrace, label = 'No downsampling')\n",
    "ax[0].plot(time, xtrace_ds, label = 'Downsampled')\n",
    "ax[1].hist(xtrace,bins=100,orientation = 'horizontal')\n",
    "ax[1].hist(xtrace_ds,bins=100,orientation = 'horizontal')\n",
    "ax[0].set_xlabel('Time (s)')\n",
    "ax[0].set_ylabel('Bead position (nm)')\n",
    "ax[1].set_xticks([])\n",
    "ax[1].set_yticks([])\n",
    "ax[0].legend(bbox_to_anchor = (1.3,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot shows that motion blur reduces the variance of the bead positions without shifting the equilibrium bead position. Specifically, the variance of the measured positions with blur, $\\text{var}(\\bar{x})$ is related to the variance of the bead positions without blur, $\\text{var}(x)$, by\n",
    "\n",
    "$$\\text{var}(\\bar{x}) = \\text{var}(x)S(\\alpha)$$\n",
    "\n",
    "where $\\alpha\\equiv\\tau_0\\kappa/\\gamma$ and $\\tau_0$ is the camera integration time. The motion blur correction, $S(\\alpha)$, is\n",
    "\n",
    "$$S(\\alpha)= \\frac{2}{\\alpha} - \\frac{2}{\\alpha^2}\\left(1-\\exp(-\\alpha)\\right)$$\n",
    "\n",
    "The motion blur affects the power spectral density (PSD) at high frequencies and Allan variance (AV) at short observation times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x203031f4130>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tweezepy import AV,PSD\n",
    "psd = PSD(xtrace,fsim,bins = 35)\n",
    "fig, axes = psd.plot(data_label='no downsampling')\n",
    "psd = PSD(xtrace_ds,fsim,bins = 35)\n",
    "fig, axes = psd.plot(fig=fig,data_label='downsampling')\n",
    "axes[0].legend()\n",
    "av = AV(xtrace,fsim)\n",
    "fig, axes = av.plot(data_label='no downsampling')\n",
    "av = AV(xtrace_ds,fsim)\n",
    "fig, axes = av.plot(fig=fig,data_label='downsampling')\n",
    "axes[0].legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "f94fc5ffea663767ae62903b10257b44f00e90761e17ce479a3f3bec4d89dc46"
  },
  "kernelspec": {
   "display_name": "Python 3.8.3 64-bit ('base': conda)",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
