{
 "metadata": {
  "name": "Serial dilution accuracy - Echo vs tips"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Modeling a serial dilution experiment on different liquid handling/dispensing devices."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A recent paper by Ekins et al. [Dispensing Processes Impact Apparent Biological Activity as Determined by Computational and Statistical Analyses. PLoS ONE 8(5): e62325, 2013], a large discrepany was observed in IC50 assay values in which either a LabCyte Echo acoustic dispensing unit or a Tecan Genesis liquid handling workstation were used in performing the assays.  This discrepancy may be due to any number of factors, but one of the main features of the Echo is its direct dispensing technology that allows a dilution series over several orders of magnitude in concetration to be created *directly* without the need for serial dilution.  Could the observed discrepancy be explained by the difference in the accuracy with which a serial dilution can be created by these two technologies?  A little modeling of the experiment can quickly find out!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy\n",
      "from pylab import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Dilution and dispensing by a liquid-handling robot"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's model how a liquid-handling robot creates a dilution series for a compound via serial dilution.  An ideal dilution series has no error in transferred volumes and ensures complete mixing between dilution steps."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions):\n",
      "    import numpy\n",
      "    from numpy.random import normal\n",
      "    ideal_concentrations = numpy.zeros([ndilutions], numpy.float64)\n",
      "    ideal_volumes = numpy.zeros([ndilutions], numpy.float64)\n",
      "    ideal_concentrations[0] = C0\n",
      "    ideal_volumes[0] = V0\n",
      "    for n in range(1,ndilutions):\n",
      "        ideal_concentrations[n] = ideal_concentrations[n-1] * Vtransfer / (Vtransfer + Vbuffer)\n",
      "        ideal_volumes[n] = Vtransfer + Vbuffer\n",
      "        ideal_volumes[n-1] -= Vtransfer\n",
      "    ideal_volumes[ndilutions-1] -= Vtransfer\n",
      "    return [ideal_volumes, ideal_concentrations]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's consider a 12-point 2x dilution series, where we start with 10 mM compound stocks."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ndilutions = 8 # number of points in dilution series (including original concentration)\n",
      "V0 = 100e-6 # 100 uL final volume in each well\n",
      "C0 = 10e-3 # 10 mM initial DMSO stock\n",
      "Vtransfer = 50e-6 # 50 uL transfer from previous dilution or stock\n",
      "Vbuffer = 50e-6 # 50 uL buffer\n",
      "[ideal_volumes, ideal_concentrations] = dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions)\n",
      "\n",
      "# Font size settings\n",
      "font = {'family' : 'sans serif',\n",
      "        'weight' : 'normal',\n",
      "        'size'   : 12}\n",
      "matplotlib.rc('font', **font)\n",
      "\n",
      "# Plot ideal concentrations.\n",
      "clf()\n",
      "semilogy(range(ndilutions), ideal_concentrations, 'ko');\n",
      "xlabel('dilution number');\n",
      "ylabel('concentration (M)');\n",
      "axis([-0.5, ndilutions, 0.0, C0*1.05]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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9ht27d2Pw4MFyR3N7QUFB6Nmzp9wx7mrLli1ut5VRUlKC48eP45lnnkHHjh0R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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105a63310>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Real liquid-handling robots can't transfer the specified volume exactly.  Each transfer operation has some inaccuracy (modeled as a constant bias factor for all dispensing operations) and imprecision (random error associated with each volume transfer).  We'll ignore other contributions to error, such as compound stickiness, insolubility, etc."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def robot_dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions, pipetting_model):\n",
      "    [transfer_inaccuracy, transfer_imprecision] = pipetting_model(Vtransfer)    \n",
      "    [buffer_inaccuracy, buffer_imprecision] = pipetting_model(Vtransfer)    \n",
      "    \n",
      "    from numpy.random import normal\n",
      "    actual_concentrations = numpy.zeros([ndilutions], numpy.float64)\n",
      "    actual_volumes = numpy.zeros([ndilutions], numpy.float64)\n",
      "    actual_concentrations[0] = C0\n",
      "    actual_volumes[0] = V0\n",
      "    transfer_bias = transfer_inaccuracy * normal()\n",
      "    buffer_bias = buffer_inaccuracy * normal()    \n",
      "    for n in range(1,ndilutions):\n",
      "        Vtransfer_actual = Vtransfer * ((1+transfer_bias) + transfer_imprecision*normal())\n",
      "        Vbuffer_actual = Vbuffer * ((1+buffer_bias) + buffer_imprecision*normal())\n",
      "        actual_concentrations[n] = actual_concentrations[n-1] * Vtransfer_actual / (Vtransfer_actual + Vbuffer_actual)\n",
      "        actual_volumes[n] = Vtransfer_actual + Vbuffer_actual\n",
      "        actual_volumes[n-1] -= Vtransfer_actual\n",
      "    Vtransfer_actual = Vtransfer * ((1+transfer_bias) + transfer_imprecision*normal())\n",
      "    actual_volumes[ndilutions-1] -= Vtransfer_actual\n",
      "    return [actual_volumes, actual_concentrations]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Suppose we generate this dilution series using a Tecan Genesis robot used in the assay.  \n",
      "\n",
      "I couldn't find published specs for standard bias and error for the Genesis (which appears to be no longer produced), so we'll use data for a Beckman NX/FX span-8 instead:\n",
      "    \n",
      "[inaccuracy/imprecision data for Biomek NX/FX](https://www.beckmancoulter.com/wsrportal/bibliography?docname=BR-10150B.pdf)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def tecan_genesis_pipetting_model(volume):\n",
      "    # Assume published imprecision/inaccuracy for Beckman Biomek NX/FX span-8.\n",
      "    from scipy.interpolate import interp1d\n",
      "    imprecision_function = interp1d([0.5e-6, 1e-6, 5e-6, 10e-6, 50e-6, 100e-6, 250e-6, 950e-6], [0.10, 0.07, 0.05, 0.05, 0.05, 0.05, 0.02, 0.01]) # published imprecision for Beckman NX/FX span-8\n",
      "    inaccuracy_function = interp1d([0.5e-6, 1e-6, 100e-6, 250e-6, 900e-6], [0.05, 0.03, 0.03, 0.02, 0.01]) # published inaccuracy for Beckman NX/FX span-8\n",
      "    return [inaccuracy_function(volume), imprecision_function(volume)]    \n",
      "\n",
      "# Biomek NX or FX specs\n",
      "[actual_volumes, actual_concentrations] = robot_dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
      "\n",
      "# Plot ideal and actual concentrations.\n",
      "clf()\n",
      "semilogy(range(ndilutions), ideal_concentrations, 'ko', range(ndilutions), actual_concentrations, 'ro');\n",
      "xlabel('dilution number');\n",
      "ylabel('concentration (M)');\n",
      "legend(['ideal','actual']);\n",
      "axis([-0.5, ndilutions, 0.0, C0*1.05]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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HrDLL7fXr1zF8+HDcuHEDgYGByMzMhK+vL3bv3g1/f/9nyWtx7J4isg6dTofE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\nIiLRWDSIiEi0/wfFxwHg2375SgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105ea5850>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's plot the relative errors in concentration, volume, and total quantity of compound per well generated in this particular replicate of the dilution series:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf();\n",
      "hold(True);\n",
      "plot([0, ndilutions], [1, 1], 'k-');\n",
      "plot(range(ndilutions), actual_concentrations / ideal_concentrations, 'ro', range(ndilutions), actual_volumes / ideal_volumes, 'go', range(ndilutions), (actual_volumes*actual_concentrations)/(ideal_volumes*ideal_concentrations), 'bo');\n",
      "legend(['exact', 'concentration', 'volume', 'quantity'], loc='lower right');\n",
      "axis([0, ndilutions, 0, 1.5]);\n",
      "ylabel('relative quantity');\n",
      "xlabel('dilution number');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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yuVyr5HD48GGdB6Ut/sXF6gI+jpmu6eLKgZuVGDMwPo6ZrtXqTHBPu3v3Ltav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\njKnh5MAYY0wNJwfGGGNqODkwxhhT838E6bdNPbpuwwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108d59850>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we repeat the experiment many times, we can estimate the CV for each dilution number."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nreplicates = 5000\n",
      "actual_volumes_n = numpy.zeros([nreplicates, ndilutions], numpy.float64)\n",
      "actual_concentrations_n = numpy.zeros([nreplicates, ndilutions], numpy.float64)\n",
      "for replicate in range(nreplicates):\n",
      "    [actual_volumes_replicate, actual_concentrations_replicate] = robot_dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
      "    actual_volumes_n[replicate,:] = actual_volumes_replicate\n",
      "    actual_concentrations_n[replicate,:] = actual_concentrations_replicate\n",
      "\n",
      "# Compute CVs    \n",
      "volumes_cv = (actual_volumes_n / ideal_volumes).std(0)\n",
      "concentrations_cv = (actual_concentrations_n / ideal_concentrations).std(0)\n",
      "quantity_cv = ((actual_volumes_n * actual_concentrations_n) / (ideal_volumes * ideal_concentrations)).std(0)\n",
      "\n",
      "# Plot CVs\n",
      "clf()\n",
      "x = numpy.arange(ndilutions)\n",
      "plot(x, concentrations_cv*100, 'ro', x, volumes_cv*100, 'go', x, quantity_cv*100, 'bo');\n",
      "xlabel('dilution number');\n",
      "ylabel('CV (%)');\n",
      "legend(['concentration', 'volume', 'quantity'], loc='upper left');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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VWLx4MXr37g2FQoEpU6aYTPvxxx/RuXNneHh4YMiQISgoKKhxWWQdUVGD8O67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\n5MBYBIiIHNj/A1uX1ydDW+AeAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108d59a50>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The biases may also be important, so let's plot those too."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compute relative bias.\n",
      "volumes_bias = (actual_volumes_n / ideal_volumes).mean(0) - 1\n",
      "concentrations_bias = (actual_concentrations_n / ideal_concentrations).mean(0) - 1\n",
      "quantity_bias = ((actual_volumes_n * actual_concentrations_n) / (ideal_volumes * ideal_concentrations)).mean(0)- 1\n",
      "\n",
      "# Plot relative biases.\n",
      "clf()\n",
      "x = numpy.arange(ndilutions)\n",
      "plot([0, ndilutions], [0, 0], 'k-', x, concentrations_bias*100, 'ro', x, volumes_bias*100, 'go', x, quantity_bias*100, 'bo');\n",
      "xlabel('dilution number');\n",
      "ylabel('bias (%)');\n",
      "legend(['concentration', 'volume', 'quantity'], loc='lower right');\n",
      "axis([0, ndilutions, -100, 100]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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SokZk++7t6D+2P8JjwtF/bH9s373dbNZXVlaGSZMmwcnJCS4uLpg8eTJiY2PR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\nRRgkRESkyP8DTRSI2DJ7u8YAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108d3df10>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def robot_dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions, pipetting_model):\n",
      "    [transfer_inaccuracy, transfer_imprecision] = pipetting_model(Vtransfer)    \n",
      "    [buffer_inaccuracy, buffer_imprecision] = pipetting_model(Vtransfer)    \n",
      "\n",
      "    # Account for dilution effect.\n",
      "    from scipy.interpolate import interp1d\n",
      "    x = numpy.array([20, 200]) * 1e-6 # L\n",
      "    y = numpy.array([-0.0630, -0.0496]) # doi:10.1016/j.jala.2006.02.005\n",
      "    dilution_function = interp1d(x, y)\n",
      "    \n",
      "    from numpy.random import normal\n",
      "    actual_concentrations = numpy.zeros([ndilutions], numpy.float64)\n",
      "    actual_volumes = numpy.zeros([ndilutions], numpy.float64)\n",
      "    actual_concentrations[0] = C0\n",
      "    actual_volumes[0] = V0\n",
      "    transfer_bias = transfer_inaccuracy * normal()\n",
      "    buffer_bias = buffer_inaccuracy * normal()    \n",
      "    for n in range(1,ndilutions):\n",
      "        Vtransfer_actual = Vtransfer * ((1+transfer_bias) + transfer_imprecision*normal())\n",
      "        Vbuffer_actual = Vbuffer * ((1+buffer_bias) + buffer_imprecision*normal())\n",
      "        actual_concentrations[n] = actual_concentrations[n-1] * Vtransfer_actual / (Vtransfer_actual + Vbuffer_actual) * (1+dilution_function(Vtransfer))\n",
      "        actual_volumes[n] = Vtransfer_actual + Vbuffer_actual\n",
      "        actual_volumes[n-1] -= Vtransfer_actual\n",
      "    Vtransfer_actual = Vtransfer * ((1+transfer_bias) + transfer_imprecision*normal())\n",
      "    actual_volumes[ndilutions-1] -= Vtransfer_actual\n",
      "    return [actual_volumes, actual_concentrations]\n",
      "\n",
      "nreplicates = 5000\n",
      "actual_volumes_n = numpy.zeros([nreplicates, ndilutions], numpy.float64)\n",
      "actual_concentrations_n = numpy.zeros([nreplicates, ndilutions], numpy.float64)\n",
      "for replicate in range(nreplicates):\n",
      "    [actual_volumes_replicate, actual_concentrations_replicate] = robot_dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
      "    actual_volumes_n[replicate,:] = actual_volumes_replicate\n",
      "    actual_concentrations_n[replicate,:] = actual_concentrations_replicate"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compute CVs    \n",
      "volumes_cv = (actual_volumes_n / ideal_volumes).std(0)\n",
      "concentrations_cv = (actual_concentrations_n / ideal_concentrations).std(0)\n",
      "quantity_cv = ((actual_volumes_n * actual_concentrations_n) / (ideal_volumes * ideal_concentrations)).std(0)\n",
      "\n",
      "# Plot CVs\n",
      "clf()\n",
      "x = numpy.arange(ndilutions)\n",
      "plot(x, concentrations_cv*100, 'ro', x, volumes_cv*100, 'go', x, quantity_cv*100, 'bo');\n",
      "xlabel('dilution number');\n",
      "ylabel('CV (%)');\n",
      "legend(['concentration', 'volume', 'quantity'], loc='lower right');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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W6XxGRET/qPKegFarxW+//YYDBw7g2rVrqFevHtq3b4+wsDA4OTnVeMc6nQ6urq6YO3cu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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105eae250>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compute relative bias.\n",
      "volumes_bias = (actual_volumes_n / ideal_volumes).mean(0) - 1\n",
      "concentrations_bias = (actual_concentrations_n / ideal_concentrations).mean(0) - 1\n",
      "quantity_bias = ((actual_volumes_n * actual_concentrations_n) / (ideal_volumes * ideal_concentrations)).mean(0)- 1\n",
      "\n",
      "# Plot relative biases.\n",
      "clf()\n",
      "x = numpy.arange(ndilutions)\n",
      "plot([0, ndilutions], [0, 0], 'k-', x, concentrations_bias*100, 'ro', x, volumes_bias*100, 'go', x, quantity_bias*100, 'bo');\n",
      "xlabel('dilution number');\n",
      "ylabel('bias (%)');\n",
      "legend(['none', 'concentration', 'volume', 'quantity'], loc='upper right');\n",
      "axis([0, ndilutions, -100, 100]);\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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jx4/jypUrcHV1RWBgoNU9Z4uJhIio6kz2GHlbW1sEBwejU6dOaNWqlcUlkdzc\nXAwcOBBOTk7w9fXFqlWrzB0SEVGtUenlv9bi1VdfhUajwcWLF3Hw4EH069cPoaGhaNWqlU47e+1j\niBzYGkuXLTRTpBVbt3kdPvn6E5RICexUdnjt+dfQr0c/c4dVDuM0HWuIEWCcpmYtcVaF1SeSoqIi\nJCYmIjU1FQ4ODujUqRMGDBiA5cuXY/bs2Tptiwt/x7JvIwGMsahksm7zOkycPxHpD6UrZenz//7Z\nkg4wxmk61hAjwDhNzVrirKoqvSHREqWlpcHGxgaBgYFKWWhoKFJTU/W2lxvf4rsfUx5UeAb55OtP\ndA4sAEh/KB3zvplnpoj0Y5ymYw0xAozT1Kwlzqq6rzOSkydPQq1Ww9fX18ThVF1hYSGcnZ11ym5f\nXVZeLACguDjLst437wsgunzxxt82Ms774QvLj9MXlh8jwDhNzRfWEWcVGXRGEhUVhd9//x0AsGTJ\nEgQHB6NVq1ZYvHhxtQZnCCcnJ1y9elWnLD8/H1qtVk/rWACx0Ggamf2xzXd+ekb01Ltvvbr1Mnts\njLP2xsg4a2+cd34MYVAi2bp1K9q1awcA+PDDD7Flyxbs3bsX77//vkEbqU7NmzdHaWkpTpw4oZQl\nJycjJCREb3uVbSSeHai/zlxee/41BBwM0CkLOBCACVETzBSRfozTdKwhRoBxmpq1xFlVBt1H4uLi\ngitXriArKwsdOnRAVlYWgMqGkB6s5557DiqVCosXL8aBAwfw5JNP4o8//kDLli2VNiqVCvZOj+HZ\ngSEWNdF+27rN6zDvm3koLiuGpo4GE6ImWOTkG+M0HWuIEWCcpmYtcd5mshsSw8PD0bt3b5w+fRoi\ngkWLFuHs2bN49NFHcfbsWZMFfL/y8vIwevRobN68GR4eHnj//fcRFRWl08bSb0icE/sBFn66BbdK\nNVDbFGPM+O6YEjvZ3GERUS1nskRy4sQJzJw5E7a2tvjXv/4FLy8vrF69Gvv27cOcOXNMFnB1suRE\nMif2A7wfn4QrpSuUMhebYZg6PYzJhIjMymSJpCaw5ETi79Ebpy7/qqe8D9IvbTBDREREfzPku9Pg\ny3+zs7Px559/IicnR6fT0aNH33+EBAC4VarRW152ky8OIyLLZ1AiWbNmDYYNG4ZmzZohJSUFISEh\nSElJQefOnZlITEBtU6y3vE7dkgccCRFR1Rl0+e/06dPx1Vdf4eDBg3BycsLBgwexaNEitG3btrrj\nqxXGjO+H0bq+AAATzUlEQVQOF5thOmUuNkPx8qtPmCkiIiLDGTRH4uzsrNz05+rqitzcXNy6dQsN\nGjTApUuXqj1IU7DkORLg7wn3RfO3ouymHerULcHLrz5hkRPtvLqMqHYx2WR7YGAgdu/ejQYNGuCh\nhx7C/Pnz4eHhgY4dO+Ly5csmC7g6WXoisQa8uoyo9jHZ+0hefPFF5XW6//jHP9CtWzeEhoZi7Nix\nxkdJVmPhp1t0kggAXCldgUXzt5opIiKyBPd1+e+ZM2dQVFRU7n0floxnJMbzdXkaZ/LXlCtvWu9p\nnL5SvpyIrJ9JL/+9U9OmTe8rILJuvLqMiPSpcGgrKChI+blJkyZ6Pz4+Pg8kSLIMvLqMiPSp8Izk\niy++UH5evnz5AwmGLNvfE+ofYNH8Pry6jIgUfEQK1Ti8uozIdEx21VZJSQlmzpyJwMBAODg4IDAw\nEDNmzEBxsf4xcyJz4tVlRA+WQZPtY8eORVpaGubNmwcfHx9kZGQgPj4eWVlZWLJkSXXHSFQlfHYZ\n0YNl0NCWm5sb0tPT4erqqpTl5uYiICAAeXl51RqgqXBoq/bg05SJTMdkQ1ve3t64du2aTtn169fR\nsGHD+4+OqJrw6jKiB6vCoa2tW7dCpVIBAIYPH44+ffpg/PjxaNKkCTIyMjB//nyMGDHigQVKZChr\nubqMV5ZRTVHh0Javr6+SSABARPQunzp1qvqjNAEObZEl4ZVlZC34hsQ7MJGQJeE8DlkLk82REJFp\n8coyqkmYSIjMgM8to5qEiYTIDKzpyrI5sR/A36M3fF2ehr9Hb8yJ/cDcIZGF4RwJkZlYw1sxeVEA\ncbL9DkwkRFXHiwKIk+1EZBReFECGYCIhogrxogAyBBMJEVWIFwWQIThHQkSV4kUBtRsn2+/AREJU\nc/GigOrDyXYiqhV4UYB5MZEQkdWzposCauJcDhMJEVk9a7ko4PZczqnLv+JM/hqcuvwr3o9Psvpk\nwjkSIqoRrOGiAGucy+Fk+x2YSIjI3HxdnsaZ/DXlypvWexqnr5QvtwScbCcisiDWNJdTFUwkREQP\niLXM5VQVh7aIiB4ga5jLuRPnSO7AREJEVHWcIyEiomrHREJEREZhIiEiIqMwkRARkVGYSIiIyChM\nJEREZBQmEiIiMgoTCRERGcXiE0lERATs7e2h1Wqh1WrRsmVLnfqtW7ciKCgIjo6O6NatGzIyMswU\nKRFR7WTxiUSlUmH+/PkoKChAQUEBjhw5otTl5ORg8ODBiI+PR15eHtq1a4fIyEgzRktEVPtYfCIB\nUOHt+YmJiQgJCcHgwYNha2uL2NhYJCcnIy0t7QFHSERUe1lFIomJiUH9+vXRuXNn7NixQylPTU1F\naGiosuzg4IDAwECkpKSYI0wiolrJxtwB3MucOXMQHBwMW1tbrFq1Cv3790dycjL8/PxQVFSE+vXr\n67R3dnZGYWGh3r5iY2OVnyMiIhAREVGNkRMRWZ/t27dj+/btVVrHrE//jYiIwM6dO/XWde7cWW9d\nnz590K9fP4wfPx6TJk3CzZs3MX/+fKW+devWePvttzFw4ECd9fj0XyKiqjPku9OsZyRVzXp3Cw4O\nRkJCgrJcVFSE9PR0BAcHGxkZEREZyqLnSPLz87Fx40YUFxejtLQUK1euxK5du9C7d28AwMCBA5GS\nkoLExEQUFxcjLi4OYWFhaN68uZkjJyKqPSz6xVY5OTno27cvjh49ijp16qBly5Z455138MQT//da\nyq1bt2L8+PE4c+YMHn30USxduhQ+Pj7l+uLQFhFR1fENiXdgIiEiqjq+IZGIiKodEwkRERmFiYSI\niIzCREJEREZhIiEiIqMwkRARkVGYSIiIyChMJEREZBQmEiIiMgoTCRERGYWJhIiIjMJEQkRERmEi\nISIiozCREBGRUZhIiIjIKEwkRERkFCYSIiIyChMJEREZhYmEiIiMwkRCRERGYSIhIiKjMJEQEZFR\nmEiIiMgoTCRERGQUJhIiIjIKEwkRERmFiYSIiIzCREJEREZhIiEiIqMwkRARkVGYSIiIyChMJERE\nZBQmEiIiMgoTCRERGYWJhIiIjMJEQkRERmEiISIiozCREBGRUZhIiIjIKEwkRERkFCYSIiIyChMJ\nEREZhYmEiIiMwkRCRERGYSIhIiKjmD2RfPrpp2jXrh00Gg1GjRpVrn7r1q0ICgqCo6MjunXrhoyM\nDJ36KVOmwMPDAx4eHpg6deqDCpuIiP7H7ImkUaNGmDlzJkaPHl2uLicnB4MHD0Z8fDzy8vLQrl07\nREZGKvULFy7E2rVrcejQIRw6dAg///wzFi5c+CDDN7nt27ebOwSDME7TsYYYAcZpatYSpyHMnkgG\nDhyIAQMGwN3dvVxdYmIiQkJCMHjwYNja2iI2NhbJyclIS0sDACQkJGDy5Mlo2LAhGjZsiMmTJ2Pp\n0qUPeA9My1oOLsZpOtYQI8A4Tc1a4jSE2RPJbSJSriw1NRWhoaHKsoODAwIDA5GamgoAOHz4sE59\nmzZtlDoiInowLCaRqFSqcmVFRUVwdnbWKXN2dkZBQQEAoLCwEPXq1dOpKywsrN5AiYhIl1Sj8PBw\nUalUej+PP/64Ttvp06dLdHS0TtnEiRNl3LhxOmUhISGSmJgoIiL16tWTvXv3KnV79+4VrVarNxYA\n/PDDDz/83MfnXmxQjaoyBqjvjCQ4OBgJCQnKclFREdLT0xEcHKzUJyUloV27dgCA5ORkhISE6O1f\n9AydERGR8cw+tFVWVobi4mKUlpairKwMJSUlKCsrA/D3RHxKSgoSExNRXFyMuLg4hIWFoXnz5gCA\nESNGYO7cuTh37hyysrIwd+5cREdHm3FviIhqIUOGqKrTrFmzyg17xcXFKfVbtmyRoKAgsbe3l65d\nu8qZM2d01n/rrbfEzc1N3NzcZMqUKQ86fCKiWs/siaS6Xb58WZ5++mlxdHSUpk2bytdff23ukMqZ\nN2+ePPzww2JnZ1dunsiSlJSUyOjRo6Vp06ai1WolLCxMNmzYYO6w9Bo6dKg0aNBAtFqt+Pn5ybvv\nvmvukCqUlpYmdnZ2MmzYMHOHold4eLhoNBpxcnISJycnCQoKMndIFVq1apUEBQWJo6OjBAQEyK5d\nu8wdkg5HR0fl9+jk5CR16tSRCRMmmDssvTIzM+XJJ58UNzc3adCggYwfP15KS0v1tjX70FZ1e/XV\nV6HRaHDx4kWsXLkSY8eOxeHDh80dlo7Kbsq0JKWlpfDx8cHOnTtx9epVvPvuu3j22Wdx5swZc4dW\nTkxMDE6dOoWrV69iw4YNmDdvHn799Vdzh6XXq6++ig4dOuidJ7QEKpUK8+fPR0FBAQoKCnDkyBFz\nh6TX5s2bMXXqVCQkJKCwsBC7du2Cv7+/ucPSUVhYqPweL1y4AHt7ezz77LPmDkuv1157DR4eHjh/\n/jySkpKwY8cOfPbZZ3rb1uhEUlRUhMTERLzzzjtwcHBAp06dMGDAACxfvtzcoemo7KZMS+Lg4IBZ\ns2bBx8cHANCvXz/4+fnhwIEDZo6svODgYGg0GmXZxsYGnp6eZoxIv2+++Qaurq544oknLPqCEEuO\n7bZZs2Zh1qxZ6NChAwDA29s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       "text": [
        "<matplotlib.figure.Figure at 0x108d84650>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we now dispense 2 uL of diluted compound into an assay plate well into which 10 uL of enzyme mix has been dispensed, there is additional error since the imprecision at this volume is higher."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "compound_volume = 2.0e-6 # 2 uL \n",
      "mix_volume = 10.0e-6 # 10 uL\n",
      "def robot_dispense(compound_volume, mix_volume, compound_concentrations, pipetting_model):\n",
      "    [compound_inaccuracy, compound_imprecision] = pipetting_model(compound_volume)\n",
      "    [mix_inaccuracy, mix_imprecision] = pipetting_model(mix_volume)\n",
      "    \n",
      "    from numpy.random import normal\n",
      "    assay_volume = numpy.zeros([ndilutions], numpy.float64)\n",
      "    assay_compound_concentration = numpy.zeros([ndilutions], numpy.float64)\n",
      "    \n",
      "    compound_bias = compound_inaccuracy * normal()\n",
      "    mix_bias = mix_inaccuracy * normal()\n",
      "\n",
      "    for i in range(ndilutions):\n",
      "        compound_volume_dispensed = compound_volume * ((1+compound_bias) + compound_imprecision*normal())\n",
      "        mix_volume_dispensed = mix_volume * ((1+mix_bias) + mix_imprecision*normal())\n",
      "        assay_volume[i] = compound_volume_dispensed + mix_volume_dispensed\n",
      "        assay_compound_concentration[i] = compound_concentrations[i] * compound_volume_dispensed / assay_volume[i]\n",
      "\n",
      "    return [assay_volume, assay_compound_concentration]\n",
      "\n",
      "[assay_volumes, assay_compound_concentrations] = robot_dispense(compound_volume, mix_volume, actual_concentrations, tecan_genesis_pipetting_model)\n",
      "\n",
      "pyplot.clf()\n",
      "pyplot.plot([0,ndilutions], [1, 1], 'k-', range(ndilutions), assay_volumes / (compound_volume+mix_volume), 'ro', range(ndilutions), assay_compound_concentrations / (ideal_concentrations*compound_volume/(compound_volume+mix_volume)), 'go')\n",
      "pyplot.legend(['exact', 'assay well volume rel err', 'concentration rel err'], loc='lower left')\n",
      "pyplot.xlabel('dilution number')\n",
      "pyplot.ylabel('relative error')\n",
      "pyplot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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GDBnCQkND+W2ePHnCIiMjmYuLCzM2NmaOjo5s8eLF/PqkpCTm6enJjI2NmUgk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\nuHXrFmbNmoWRI0fi2rVr+g6LV1JSgid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       "text": [
        "<matplotlib.figure.Figure at 0x108d86050>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's suppose the 10 uL of assay mix in each well was dispensed completely accurately, and contains exact concentrations of enzyme and substrate.  We presume inhibition is measured by an exact read of the reaction V0/Vmax.  The IC50 would be the interpolated point at which V0/Vmax drops to 0.5, as determined from a fit of the competitive inhibition equations to the observed V0/Vmax for the dilution series, using the *ideal* dilution series concentrations in the fit.  Let's assume the true Ki is 10 nM, with Km of 1.71 uM (the Km for ATP by EphB4).  Note that we're assuming that EphB4 obeys Michaelis-Menten kinetics here, and that V0/Vmax is what is measured."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def competitive_inhibition(substrate_concentration, inhibitor_concentration, enzyme_concentration, Ki, Km):\n",
      "    V0_over_Vmax = substrate_concentration / (Km*(1 + inhibitor_concentration/Ki) + substrate_concentration)\n",
      "    return V0_over_Vmax\n",
      "\n",
      "substrate_concentration = 4e-6 # 4 uM ATP\n",
      "enzyme_concentration = 6e-6 # 0.25 ng of ~42.4 kDa enzyme = ~6 uM\n",
      "true_Ki = 10e-9 # 10 nM\n",
      "Km = 1.71e-6 # ATP Km from http://www.proqinase.com/kinase-database/pdfs/2843.pdf\n",
      "\n",
      "activity = numpy.zeros([ndilutions], numpy.float64)\n",
      "for i in range(ndilutions):\n",
      "    activity[i] = competitive_inhibition(substrate_concentration, assay_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
      "\n",
      "pyplot.clf()\n",
      "pyplot.semilogx(ideal_concentrations, activity, 'ro')\n",
      "pyplot.xlabel('ideal [I] (M)')\n",
      "pyplot.ylabel('V0/Vmax')\n",
      "pyplot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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aLfXX19fjq6++woEDBxAfH4+FCxciMzNTOrO60fLly6XnycnJSE5Odn6DiYj6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\nYNO/cOFCMWjQIDFo0CCxaNE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       "text": [
        "<matplotlib.figure.Figure at 0x108d31710>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What does this look like if we run many assay replicates?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nreplicates = 1000\n",
      "activity = numpy.zeros([nreplicates,ndilutions], numpy.float64)\n",
      "for replicate in range(nreplicates):\n",
      "    [actual_volumes, actual_concentrations] = robot_dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
      "    [assay_volumes, assay_compound_concentrations] = robot_dispense(compound_volume, mix_volume, actual_concentrations, tecan_genesis_pipetting_model)\n",
      "    for i in range(ndilutions):\n",
      "        activity[replicate,i] = competitive_inhibition(substrate_concentration, assay_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
      "\n",
      "pyplot.clf()\n",
      "pyplot.semilogx(ideal_concentrations, activity.transpose(), 'r-')\n",
      "pyplot.xlabel('ideal [I] (M)')\n",
      "pyplot.ylabel('V0/Vmax')\n",
      "pyplot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ZM2bg2muvxW+//YbU1FR3x0fkHhUVcg9n5crqczNmAKtWAXv3ahcXUQt33u61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\nEBCgkpKSVFlZWYP1VOnWrZs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y5Mga5Xbv3g2j0Yj4+HgAQJs2bZCUlIRnnnnGlZdEVAuT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\nUuyQ5T0HagAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108d45fd0>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It's not hard to see that the IC50 will vary over a large range!  Let's fit the IC50s to see."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fit_ic50(inhibitor_concentrations, activities):\n",
      "    import numpy, scipy\n",
      "    def objective(inhibitor_concentrations, Ki):\n",
      "        activities = numpy.zeros([ndilutions], numpy.float64)\n",
      "        for i in range(ndilutions):\n",
      "            activities[i] = competitive_inhibition(substrate_concentration, inhibitor_concentrations[i], enzyme_concentration, Ki, Km)\n",
      "        return activities\n",
      "            \n",
      "    Ki_guess = true_Ki\n",
      "    import scipy.optimize\n",
      "    [popt, pcov] = scipy.optimize.curve_fit(objective, inhibitor_concentrations, activities, p0=[Ki_guess])\n",
      "    \n",
      "    return popt[0]\n",
      "\n",
      "IC50s_tips = numpy.zeros([nreplicates], numpy.float64)\n",
      "for replicate in range(nreplicates):\n",
      "    IC50s_tips[replicate] = fit_ic50(ideal_concentrations, activity[replicate,:])\n",
      "pIC50s_tips = numpy.log10(IC50s_tips)\n",
      "    \n",
      "clf()\n",
      "nhist = 20\n",
      "hist(pIC50s_tips, nhist);\n",
      "xlabel('measured pIC50 (M)');\n",
      "ylabel('P(pIC50)');\n",
      "gca().axes.get_yaxis().set_ticks([]); # turn off y ticks"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "[]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x108d98f90>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The error won't be uniform across the whole Ki range, however.  Let's characterize the standard error as a function of Ki."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def robot_IC50s(true_Ki):\n",
      "    nreplicates = 1000\n",
      "    IC50s = numpy.zeros([nreplicates], numpy.float64)\n",
      "    for replicate in range(nreplicates):\n",
      "        [actual_volumes, actual_concentrations] = robot_dilution_series(V0, C0, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
      "        [assay_volumes, assay_compound_concentrations] = robot_dispense(compound_volume, mix_volume, actual_concentrations, tecan_genesis_pipetting_model)\n",
      "        activities = numpy.zeros([ndilutions], numpy.float64)\n",
      "        for i in range(ndilutions):\n",
      "            activities[i] = competitive_inhibition(substrate_concentration, assay_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
      "        IC50s[replicate] = fit_ic50(ideal_concentrations, activities)\n",
      "    return IC50s\n",
      "\n",
      "pKis = numpy.array([-12, -11, -10, -9, -8, -7, -6, -5, -4, -3], numpy.float64);\n",
      "Kis = 10**pKis\n",
      "nKis = len(pKis)\n",
      "genesis_pIC50_bias = numpy.zeros([nKis], numpy.float64)\n",
      "genesis_pIC50_CV = numpy.zeros([nKis], numpy.float64)\n",
      "for (i, Ki) in enumerate(Kis):\n",
      "    IC50s = robot_IC50s(Ki)    \n",
      "    pIC50s = numpy.log10(IC50s)\n",
      "    pKi = pKis[i]\n",
      "    genesis_pIC50_bias[i] = pIC50s.mean() - pKi;\n",
      "    genesis_pIC50_CV[i] = pIC50s.std() / abs(pIC50s.mean())    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can plot the bias in the measured pIC50 values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf();\n",
      "plot([pKis.min(), pKis.max()], [0, 0], 'k-', pKis, genesis_pIC50_bias, 'ro');\n",
      "xlabel('pKi');\n",
      "ylabel('bias in measured pIC50');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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I7h6irpIaNGgQJk2ahNDQUAwcOBASiQTArSq1fv16vQYkIiLTIKpg3Lx5E6GhoQCg2aFW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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108dae390>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The CV is not so bad."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf();\n",
      "plot(pKis, genesis_pIC50_CV*100, 'ko');\n",
      "xlabel('pKi');\n",
      "ylabel('pIC50 CV (%)');\n",
      "axis([pKis.min(), pKis.max(), 0, 10]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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mRs2aNdOYMWNUWlrqWV5cXKxBgwbp7NmzSk9P9xRDSkqKLb7oBagOygGogsWL\nF2vVqlXKycnRjh07lJqaKofDodLSUvXr10+NGzfW8uXL1ahRI8977HRHTsBblANwGQ6HQ88884xa\ntmyp0NBQTZkyxXNHy/z8fH399ddKSEhQgwYNyr2Pw3mozSgHoAqioqI8v7du3VoHDx6UJDVv3lxL\nlizRY489plWrVlkVD6hxlANQBfv27Sv3e4sWLTyPH3jgAf3973/X0KFDy90+mWkl1GaUA3AZhmFo\n7ty5OnDggI4fP660tDSNGDGi3GtGjBihN954Q0OGDNEXX3zheR9QW3EqK3AZDodDDz/8sO677z4d\nPHhQDzzwgJKSkvTVV1+VGx0kJCSorKxMAwcO1KpVq+RwOBg9oNbiIjjgMtq2bat//OMf6tu3r9VR\nAL9hWgkAYEI5AABMmFYCAJgwcgAAmFAOAAATygEAYEI5AABMKAcAgAnlAAAw+T/Pj/0VrQsBuAAA\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108d6a210>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Dispensing by LabCyte Echo"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What about the LabCyte Echo experiments?  According to LabCyte, the Echo has an inaccuracy of 10% and a precision of 8% over the entire dispense range of 2.5 nL to 10 uL.  Let's model how it dispenses directly into the assay plate with an 9-point dilution series spanning 2.5 nL to 120 nL from 10 mM stock solution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def echo_assay_dispense(C0, mix_volume, backfill_volume, ideal_dispense_volumes):\n",
      "    inaccuracy = 0.10 # Specs from: http://www.labcyte.com/sites/default/files/support_docs/Echo%205XX%20Specifications.pdf\n",
      "    imprecision = 0.08 # Specs from: http://www.labcyte.com/sites/default/files/support_docs/Echo%205XX%20Specifications.pdf\n",
      "    from numpy.random import normal\n",
      "    ndilutions = len(ideal_dispense_volumes)\n",
      "    assay_volume = numpy.zeros([ndilutions], numpy.float64)\n",
      "    assay_concentration = numpy.zeros([ndilutions], numpy.float64)\n",
      "    bias = inaccuracy * normal()\n",
      "    for i in range(ndilutions):\n",
      "        compound_volume_intended = ideal_dispense_volumes[i]\n",
      "        backfill_volume_intended = backfill_volume - compound_volume_intended\n",
      "        \n",
      "        compound_volume_dispensed = compound_volume_intended * ((1+bias) + imprecision*normal())\n",
      "        backfill_volume_dispensed = backfill_volume_intended * ((1+bias) + imprecision*normal())\n",
      "        \n",
      "        assay_volume[i] = mix_volume + backfill_volume_dispensed + compound_volume_dispensed\n",
      "        assay_concentration[i] = C0 * compound_volume_dispensed / assay_volume[i]\n",
      "\n",
      "    return [assay_volume, assay_concentration]\n",
      "\n",
      "C0 = 10e-3 # 10 mM stock solution\n",
      "ideal_assay_volume = 120e-9 # 120 nL\n",
      "ideal_dispense_volumes = 2.5e-9 * numpy.array([6, 12, 18, 24, 30, 36, 42, 48]) # 9-point titration, multiples of 2.5 nL\n",
      "ideal_concentrations = (C0*ideal_dispense_volumes/ideal_assay_volume)\n",
      "ndilutions = len(ideal_dispense_volumes)\n",
      "ideal_volumes = numpy.ones([ndilutions]) * ideal_assay_volume\n",
      "backfill_volume = 120e-9 # backfill with DMSO to 120 nL after dispensing compound\n",
      "mix_volume = ideal_assay_volume - backfill_volume # 12 uL assay volume (minus 120 uL)\n",
      "[assay_volumes, assay_concentrations] = echo_assay_dispense(C0, mix_volume, backfill_volume, ideal_dispense_volumes)\n",
      "\n",
      "# Plot this realization.\n",
      "clf();\n",
      "plot([0,ndilutions], [1, 1], 'k-', range(ndilutions), assay_volumes/ideal_assay_volume, 'ro', range(ndilutions), assay_concentrations / ideal_concentrations, 'go');\n",
      "legend(['exact', 'assay well volume rel err', 'concentration rel err'], loc='lower right');\n",
      "ylabel('relative quantity');\n",
      "xlabel('dilution number');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ZvmnTJsNGxMxK/9BQThZPER7UZ7rSacDcy8sL3t7e4svGxgZ79+5Fq1atGjs+xpgRNZVB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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108d8b510>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nreplicates = 1000\n",
      "actual_volumes_n = numpy.zeros([nreplicates, ndilutions], numpy.float64)\n",
      "actual_concentrations_n = numpy.zeros([nreplicates, ndilutions], numpy.float64)\n",
      "for replicate in range(nreplicates):\n",
      "    [actual_volumes_replicate, actual_concentrations_replicate] = echo_assay_dispense(C0, mix_volume, backfill_volume, ideal_dispense_volumes)\n",
      "    actual_volumes_n[replicate,:] = actual_volumes_replicate\n",
      "    actual_concentrations_n[replicate,:] = actual_concentrations_replicate\n",
      "volumes_cv = (actual_volumes_n / ideal_volumes).std(0)\n",
      "concentrations_cv = (actual_concentrations_n / ideal_concentrations).std(0)\n",
      "quantity_cv = ((actual_volumes_n * actual_concentrations_n) / (ideal_volumes * ideal_concentrations)).std(0)\n",
      "\n",
      "# Plot CVs\n",
      "clf()\n",
      "x = numpy.arange(ndilutions)\n",
      "plot(x, concentrations_cv*100, 'ro', x, volumes_cv*100, 'go', x, quantity_cv*100, 'bo');\n",
      "xlabel('dilution number');\n",
      "ylabel('CV (%)');\n",
      "legend(['concentration', 'volume', 'quantity'], loc='lower left');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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w/fr1Eus01Tx08eJFKJVKpKenAwBSU1OhVCqxZcsWdO3aFY6OjggMDMSJEydw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\nkwARkRVjEiAismJMAkREVuz/AZbU1/plXywCAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b3a14d0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How does a competitive inhibition look with the narrow dynamic range afforded by the LabCyte Echo?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "activity = numpy.zeros([ndilutions], numpy.float64)\n",
      "for i in range(ndilutions):\n",
      "    activity[i] = competitive_inhibition(substrate_concentration, assay_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
      "\n",
      "# Plot V0/Vmax for a single realization,\n",
      "clf();\n",
      "semilogx(ideal_concentrations, activity, 'ro');\n",
      "xlabel('ideal [I] (M)');\n",
      "ylabel('V0/Vmax');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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G56G0fPlyBAUF4fLly9i7dy+WLVsGo9Ho1K+iogJbtmxBZWUlTCYTTp8+jby8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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108d6e410>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "V0 only goes up to a maximum of 0.012, but we can still see some curvature that could give a decent fit to Michaelis-Menten for an IC50.  Let's try a number of replicates to see how much variation there is between measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "activity = numpy.zeros([nreplicates,ndilutions], numpy.float64)\n",
      "for replicate in range(nreplicates):\n",
      "    [assay_volumes, assay_compound_concentrations] = echo_assay_dispense(C0, mix_volume, backfill_volume, ideal_dispense_volumes)\n",
      "    for i in range(ndilutions):\n",
      "        activity[replicate,i] = competitive_inhibition(substrate_concentration, assay_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
      "\n",
      "# Plot V0/Vmax for many measurements.\n",
      "clf();\n",
      "semilogx(ideal_concentrations, activity.transpose(), 'r-');\n",
      "xlabel('ideal [I] (M)');\n",
      "ylabel('V0/Vmax');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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c3Oe+Wq1Wem8/rrm5ecB6LBaLQ+9L+/Hdy3vWbXFyhvrExERUVVUhISEBhw8f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\nKXDCgAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105f1c4d0>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Transforming this into IC50s, we see there is a fair amount of error."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "IC50s_echo = numpy.zeros([nreplicates], numpy.float64)\n",
      "for replicate in range(nreplicates):\n",
      "    IC50s_echo[replicate] = fit_ic50(ideal_concentrations, activity[replicate,:])\n",
      "\n",
      "clf()\n",
      "nhist = 20\n",
      "hist(numpy.log10(IC50s_echo), nhist);\n",
      "xlabel('log IC50 (M)');\n",
      "ylabel('P(IC50)');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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SFoul0/mqqqpEVVWVaG1tFUeOHBFDhgwR+/btE0Jw/bxBimUphOvrpleHixBC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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b3a1510>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's characterize the error for the Echo assay as a function of Ki."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def echo_IC50s(true_Ki):\n",
      "    nreplicates = 1000\n",
      "    IC50s = numpy.zeros([nreplicates], numpy.float64)\n",
      "    for replicate in range(nreplicates):\n",
      "        [assay_volumes, assay_compound_concentrations] = echo_assay_dispense(C0, mix_volume, backfill_volume, ideal_dispense_volumes)\n",
      "        activities = numpy.zeros([ndilutions], numpy.float64)\n",
      "        for i in range(ndilutions):\n",
      "            activities[i] = competitive_inhibition(substrate_concentration, assay_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
      "        IC50s[replicate] = fit_ic50(ideal_concentrations, activities)\n",
      "    return IC50s\n",
      "\n",
      "# Run simulation of many experiments.\n",
      "pKis = numpy.array([-12, -11, -10, -9, -8, -7, -6, -5, -4, -3], numpy.float64);\n",
      "Kis = 10**pKis\n",
      "nKis = len(pKis)\n",
      "echo_pIC50_bias = numpy.zeros([nKis], numpy.float64)\n",
      "echo_pIC50_CV = numpy.zeros([nKis], numpy.float64)\n",
      "for (i, Ki) in enumerate(Kis):\n",
      "    IC50s = echo_IC50s(Ki)    \n",
      "    pIC50s = numpy.log10(IC50s)\n",
      "    pKi = pKis[i]\n",
      "    echo_pIC50_bias[i] = pIC50s.mean() - pKi;\n",
      "    echo_pIC50_CV[i] = pIC50s.std() / abs(pIC50s.mean())    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot relative error in measured Ki values as a function of true Ki.\n",
      "clf()\n",
      "plot([pKis.min(), pKis.max()], [0, 0], 'k-', pKis, echo_pIC50_bias, 'ro');\n",
      "xlabel('pKi');\n",
      "ylabel('bias in measured pIC50');\n",
      "axis([pKis.min(), pKis.max(), echo_pIC50_bias.min()-1, echo_pIC50_bias.max()+1]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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qXL9+HceOHcP48eMtmule+/btQ0xMjEUz6HQ6fPfdd7hx4wYeeeQR9OnTB8uX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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10aed6790>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot CV.\n",
      "clf();\n",
      "plot(pKis, echo_pIC50_CV*100, 'ro');\n",
      "xlabel('pKi');\n",
      "ylabel('measured pIC50 CV (%)');\n",
      "axis([pKis.min(), pKis.max(), 0, 10]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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HYmIiEhMT0adPHwCAr6+vrHlqKWDaVCQ5ORleXl7o1q0bsrKy5I6D0NBQk8f2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\nciAiIpH/Bxaq/ch+OrZQAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b3a8690>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Comparison of Tecan Genesis and Labcyte Echo modeled performance"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What do we get when we plot the Tecan Genesis and Echo results against each other?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "echo_pIC50_err = (echo_pIC50_CV*numpy.abs(pKis))\n",
      "genesis_pIC50_err = (genesis_pIC50_CV*numpy.abs(pKis))\n",
      "\n",
      "clf();\n",
      "subplot(111, aspect='equal');\n",
      "hold(True);\n",
      "plot([pKis.min(), pKis.max()], [pKis.min(), pKis.max()], 'k-');\n",
      "plot(pKis, pKis, 'ko');\n",
      "errorbar(pKis + echo_pIC50_bias, pKis + genesis_pIC50_bias, xerr=2*echo_pIC50_err, yerr=2*genesis_pIC50_err, fmt='ro');\n",
      "axis([pKis.min(), pKis.max(), pKis.min(), pKis.max()]);\n",
      "xlabel('acoustic pIC50');\n",
      "ylabel('tips pIC50');\n",
      "title('95% confidence intervals shown');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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1lEoGVZ/ff/8dN27cwPTp01u1X9Y8oxcvxoonThwvd3ODfwuDonbxw82bNyMg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\nQcQYUzsOIsaY2v1/HE/k2j3noVgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10aea27d0>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# data from Fig 1 of Fregau et al.\n",
      "echo_IC50s = numpy.array([0.064, 0.486, 0.003, 0.002, 0.007, 0.003, 0.004, 0.052, 0.01362, 0.207, 0.158, 0.01164, 0.00633, 0.00358]) * 1e-6 # M\n",
      "genesis_IC50s = numpy.array([0.817, 3.03, 0.146, 0.553, 0.973, 0.778, 0.445, 0.17, 0.112, 14.4, 0.25, 0.049, 0.087, 0.152]) * 1e-6 # M\n",
      "\n",
      "echo_pIC50s = numpy.log10(echo_IC50s);\n",
      "genesis_pIC50s = numpy.log10(genesis_IC50s);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's add the error bars we modeled to see if the variation is sufficient to bring the two sets of data into agreement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Interpolate bias and CV for Echo and Genesis.\n",
      "from scipy.interpolate import interp1d\n",
      "echo_bias_interpolation = interp1d(pKis, echo_pIC50_bias);\n",
      "echo_CV_interpolation = interp1d(pKis, echo_pIC50_CV);\n",
      "genesis_bias_interpolation = interp1d(pKis, genesis_pIC50_bias);\n",
      "genesis_CV_interpolation = interp1d(pKis, genesis_pIC50_CV);\n",
      "\n",
      "# Compute error bars for Echo and Genesis.\n",
      "echo_pIC50_err = (echo_CV_interpolation(echo_pIC50s)*numpy.abs(echo_pIC50s))\n",
      "genesis_pIC50_err = (genesis_CV_interpolation(genesis_pIC50s)*numpy.abs(genesis_pIC50s))\n",
      "\n",
      "# Plot with error bars.\n",
      "figure();\n",
      "subplot(111, aspect='equal');\n",
      "hold(True);\n",
      "plot([-9, -4], [-9, -4], 'k-');\n",
      "errorbar(echo_pIC50s, genesis_pIC50s, xerr=2*echo_pIC50_err, yerr=2*genesis_pIC50_err, fmt='ro');\n",
      "plot([-9, -6], [-9, -6], 'k-');\n",
      "#axis('equal');\n",
      "xlabel('pIC50 (acoustic)');\n",
      "ylabel('pIC50 (tips)');\n",
      "title('95% confidence intervals shown');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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8unHjBjw8PNRaXENVurgAz9udXiQ72iRdAcvKACcnnV4BG0xPPhMHTeNVY9jc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\n9INehw0HDWP6Q2fCJi0tDUF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       "text": [
        "<matplotlib.figure.Figure at 0x10ae8c390>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What if we correct for the bias for each instrument?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot.\n",
      "figure();\n",
      "subplot(111, aspect='equal');\n",
      "hold(True);\n",
      "plot([-9, -4], [-9, -4], 'k-');\n",
      "errorbar(echo_pIC50s, genesis_pIC50s, xerr=2*echo_pIC50_err, yerr=2*genesis_pIC50_err, fmt='ro');\n",
      "errorbar(echo_pIC50s - echo_bias_interpolation(echo_pIC50s), genesis_pIC50s - genesis_bias_interpolation(genesis_pIC50s), xerr=2*echo_pIC50_err, yerr=2*genesis_pIC50_err, fmt='go');\n",
      "plot([-9, -6], [-9, -6], 'k-');\n",
      "#axis('equal');\n",
      "xlabel('pIC50 (acoustic)');\n",
      "ylabel('pIC50 (tips)');\n",
      "legend(['ideal', 'original', 'bias corrected'], 'upper right');\n",
      "title('95% confidence intervals shown');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ZSRwOh27cuEFERM2bN6fQ0FCpMiNGjNCI2LBuVAPCgCM7QLmhTu0ClCu7PqBs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\n48na2pqcnZ1p+fLlJBKJiIho6dKlUov/0tPTicP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       "text": [
        "<matplotlib.figure.Figure at 0x108d4b6d0>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The assays are in much better agreement at this point, but it does not appear that the specified imprecision of the Tecan Genesis and Labcyte Echo are sufficient to explain the remaining discrepancies."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "References and further reading"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* Ekins S, Olechno J, Williams AJ (2013) Dispensing Processes Impact Apparent Biological Activity as Determined by Computational and Statistical Analyses. PLoS ONE 8(5): e62325. [doi:10.1371/journal.pone.0062325](http://dx.doi.org/10.1371/journal.pone.0062325)\n",
      "* Gu H and Deng Y. Dilution Effect in Multichannel Liquid-Handling System Equipped with Fixed Tips: Problems and Solutions for Bioanalytical Sample Preparation. J. Assoc. Lab. Auto. 12:355, 2007. [doi:10.1016/j.jala.2007.07.002](http://dx.doi.org/10.1016/j.jala.2007.07.002)\n",
      "* Dong H, Ouyang Z, Liu J, Jemal M. The Use of a Dual Dye Photometric Calibration Method to Identify Possible Sample Dilution from an Automated Multichannel Liquid-handling System. J. Asooc. Lab. Auto. 60, 2006. [doi:10.1016/j.jala.2006.02.005](http://dx.doi.org/10.1016/j.jala.2006.02.005)"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}