{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Errors in serial dilution: How can dispensing technology impact assay data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### [Sonya M. Hanson and John D. Chodera](http://www.choderalab.org/) Computational Biology Program, Memorial Sloan Kettering Cancer Center, New York NY 10065"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a 2013 paper by Ekins et al, [Dispensing Processes Impact Apparent Biological Activity as Determined by Computational and Statistical Analyses. PLoS ONE 8(5): e62325, 2013](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0062325), a surprisingly large discrepancy in IC50 assay results is noted between the assay performed using a **Tecan Genesis** liquid handling workstation compared with a **LabCyte Echo** acoustic dispensing unit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> *It would appear that tip-based dispensing is producing erroneous data based on our and other analyses which we see here reflected in the models and initial lack of correlations with molecular properties.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This discrepancy was so large and so surprising that it was quickly picked up and discussed at length by numerous industry blogs, most notably [In the Pipeline by Derek Lowe](http://blogs.sciencemag.org/pipeline/archives/2013/05/03/drug_assay_numbers_all_over_the_place), which called the report a \"truly disturbing paper\".  Speculation abounded as to the precise cause: including sticky compounds, plastic leaching out of pipette tips, colloidal aggregation, mis-calibrated pipettes, and sloppy experiments.  But could a simple physical process rooted in the intrinsic variability in the assay explain this difference?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a biochemical or cell-based assay to determine the potency of a compound of interest, solutions of the compound at several concentrations are prepared and the assay readout at a number of these concentrations can be fit to yield the $K_i$, $IC_{50}$, or $EC_{50}$ (depending on the assay configuration)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a traditional manual assay or liquid handling workstation (such as the **Tecan Genesis**), the most straightforward approach to preparing a number of these compound concentrations is to prepare a **serial dilution series** starting from an original compound stock solution (often 10 mM stock in DMSO).  In a serial dilution, a volume $V_0$ of one solution is transferred into the next well and diluted with another volume $V_1$ of diluent, allowing a series of solutions spanning orders of magnitude in compound concentration to be prepared in a serial manner."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](img/dilution-simple.png \"dilution-simple.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **LabCyte Echo**, on the other hand, uses a direct dispensing technology to transfer a programmed volume (from 2.5 nL to microliters) directly into the assay wells, allowing a dilution series over several orders of magnitude in concentration to be created directly without the need for serial dilution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](img/direct-simple.png \"direct-simple.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the Ekins et al paper explores the impact assay discrepancies has on QSAR models parameterized to the data, here we focus on the origin of the differences in assay results, and show how a simple model that captures **the errors introduced at each step** of the assay can lead us to identify a possible culprit behind the large discrepancy between the two assay configurations.  Understanding the origin of this discrepancy---which ends up being a source of bias in one of the assay configurations---can allow us to anticipate assay issues ahead of time, take steps to mitigate them, or even to correct for them after the fact."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we introduce a simple kind of assay modeling in **this IPython notebook** that computational and experimental chemists alike can employ, as a tool that can easily be used to model and understand sources of uncertainty and  biases inherent in any experimental assay.  This kind of modeling could be used, for example, during assay development to ensure that the assay configuration will meet the dynamic range and accuracy needed for the assay, or it could be used after the fact by assay data consumers to understand the expected uncertainty and bias in the experimental dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###First to set up the general python working environment and define our key dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First import a few general packages to be able to deal with numbers (*numpy* and more specificially *numpy.random*) and to allow us to set specific errors between fixed volume values (*scipy.interpolate*)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.random import normal\n",
    "from scipy.interpolate import interp1d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next import a few packages to allow us to plot (*matplotlib.pyplot*), make nice-looking plots (*seaborn*), and view this plots inside our ipython notebooks (*%pylab inline*)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set(style='white')\n",
    "sns.set_context('talk')\n",
    "\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset we are using to illustrate how to model and interpret errors comes from the paper mentioned above (  [Dispensing Processes Impact Apparent Biological Activity as Determined by Computational and Statistical Analyses. PLoS ONE 8(5): e62325, 2013](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0062325)), all of which was originally described in two patents from Astrazeneca ([WO2009010794A1](https://www.google.com/patents/WO2009010794A1)and [US7718653](http://www.google.com/patents/US7718653)). The table in this paper is shown below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/data_combined.png\" alt=\"Drawing\" style=\"width: 800px;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# data from Fig 1 of Ekins et al.\n",
    "echo_IC50s = np.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 = np.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 = np.log10(echo_IC50s)\n",
    "genesis_pIC50s = np.log10(genesis_IC50s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now if we plot this data to see how the $IC_{50}$ values obtained with the two different technologies compare to each other, with a line representing if they were identical, we see there are significant discrepencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hansons/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
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ooh6dFv4x0fNlgVSLetLdnyTe5MFUbnb7AXCtu9+f+TH8X1nZqv1IIJp7vmLK41lbER/y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\nRCR3CiMREcnd/wfshOySipPwvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10478dc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot this data to show the relationship of pIC50's measured by different technologies\n",
    "plt.subplot(111, aspect='equal');\n",
    "plt.plot([-9, -4], [-9, -4], 'k-');\n",
    "plt.scatter(echo_pIC50s, genesis_pIC50s,color='k',marker='x',s=40, linewidth=2);\n",
    "plt.xlabel('pIC50 (acoustic)');\n",
    "plt.ylabel('pIC50 (tips)');\n",
    "plt.legend(['ideal', 'actual'], loc='lower right');\n",
    "plt.title('Relationship of pIC50s measured by different technologies');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###1. Calculating $IC_{50}$ for EphB4 system from assay data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This data is for $IC_{50}$s of ligands with the enzyme EphB4. From the [EphB4 DataSheet](http://www.proqinase.com/kinase-database/pdfs/2843.pdf), we know the Km for ATP by EphB4 is 1.71 uM . Note that we're assuming that EphB4 obeys Michaelis-Menten kinetics here, and that V0/Vmax is what is measured."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Km = 1.71e-6 # Km of ATP for EphB4 (M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's assume true Ki for an arbitrary compound is 10 nM, a substrate concentration of 4 µM ATP, and that we're using 0.25 ng of ~42.4 kDa enzyme, which gives us 6 µM. We will dispense 2 µL of diluted compound into an assay plate well into which 10 µL of enzyme mix has been dispense."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "true_Ki = 10e-9 # arbitrary compound Ki (M)\n",
    "\n",
    "substrate_concentration = 4e-6 # ATP concentration (M)\n",
    "\n",
    "enzyme_concentration = 6e-6 # EphB4 assay concentration (M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's suppose the 10 µL 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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can calculate enzyme activities (V0/Vmax) directly from the values above using the following equation (derived using the assumptions of Michaelis-Menten kinetics for a competitive inhibitor):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{V_{0}}{V_{max}} = \\frac{[S]}{K_{m}(1+\\frac{[I]}{K_{i}})+[S]}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#define the function 'competitive_inhibition' using this equation\n",
    "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already defined everything in this equation except our inhibitor concentration *[I]*, which is exactly the focus of the later parts of this notebook. Here we will define an ideal dilution series to create our inhibitor concentrations:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](img/dilution.png \"dilution.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions):\n",
    "    # Initialize concentrations and volumes with zero vectors with Cinitial and Vinitial as first value\n",
    "    concentrations = np.zeros([ndilutions], np.float64)\n",
    "    volumes = np.zeros([ndilutions], np.float64)\n",
    "    concentrations[0] = Cinitial\n",
    "    volumes[0] = Vinitial\n",
    "    \n",
    "    # and Vbuffer as initial volume for all but first.\n",
    "    for n in range(1,ndilutions):\n",
    "        volumes[n] = Vbuffer\n",
    "        \n",
    "    # Create dilution series.\n",
    "    for n in range(1,ndilutions):\n",
    "        concentrations[n] = concentrations[n-1] * Vtransfer / (Vtransfer + Vbuffer)\n",
    "        volumes[n] += Vtransfer\n",
    "        volumes[n-1] -= Vtransfer\n",
    "        \n",
    "    # Remove Vtransfer from last.\n",
    "    volumes[ndilutions-1] -= Vtransfer\n",
    "    \n",
    "    return [volumes, concentrations]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's use this dilution series to create an 8-point dilution series with an initial concentration of 10 mM, an initial volume of 100 µL and Vtransfer and Vbuffer = 50 µL."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Cinitial = 600e-6 # initial dilution concentration (M) = 600 uM, to match maximum assay concentration of Echo assay\n",
    "\n",
    "ndilutions = 8 # number of dilutions, including initial dilution\n",
    "\n",
    "Vinitial = 100e-6 # working volume (L)\n",
    "\n",
    "Vtransfer = 50e-6 # volume transferred from previous dilution (L)\n",
    "\n",
    "Vbuffer = 50e-6 # volume of diluent (buffer) added (L)\n",
    "\n",
    "[assay_volumes, assay_compound_concentrations] = dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Now we have an 8-point dilution series from 600.000000 uM to 4.687500 uM.\n"
     ]
    }
   ],
   "source": [
    "print \"Now we have an %s-point dilution series from %f uM to %f uM.\" % (ndilutions, assay_compound_concentrations.max()/1e-6, assay_compound_concentrations.min()/1e-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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x7GLAgcBVkpZk7v593wBOlbRx9r7y/n1rAJ+neX0E+7xCofADYCppWZVJwNRsm5lZx2lk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\nWE5SZmbWsZykzMysYzlJmZlZx/r/qy/pnxOCanoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bbca790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1,ax2) = plt.subplots(2,1,sharex=True)\n",
    "\n",
    "ax1.scatter(range(ndilutions), assay_compound_concentrations/1e-6, lw=4)\n",
    "\n",
    "ax1.set_title(\"Normal plot\")\n",
    "ax1.set_ylabel('concentration (uM)')\n",
    "ax1.axis([- 0.5, ndilutions - 0.5, 0.0, Cinitial * 1.2/1e-6])\n",
    "\n",
    "ax2.semilogy(range(ndilutions), assay_compound_concentrations,'ko')\n",
    "\n",
    "ax2.set_title(\"Semilogy plot\")\n",
    "ax2.set_ylabel('concentration (M)')\n",
    "ax2.axis([- 0.5, ndilutions - 0.5, 0.0, Cinitial * 1.2])\n",
    "\n",
    "plt.xlabel('dilution number')\n",
    "f.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use these ideal assay_compound_concentrations to calculate what our activity would be for each inhibitor concentration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#initialize the activity values with a zero vector\n",
    "activity = np.zeros([ndilutions], np.float64)\n",
    "\n",
    "#calclulate activity with our competitive inhibition model and our ideal assay_compound_concentrations\n",
    "for i in range(ndilutions):\n",
    "    activity[i] = competitive_inhibition(substrate_concentration, assay_compound_concentrations[i], enzyme_concentration, true_Ki, Km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AC4H7gHcBR2bmlohYGhFLy7obgZOA5RQ79/YETiiPPTJcH8ArgVcBrwc2RcQD5ePqqs9F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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10478dd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogx(assay_compound_concentrations, activity, 'ro');\n",
    "plt.xlabel('ideal $[I]$ (M)');\n",
    "plt.ylabel('$V_{0}/V_{max}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course this is data without error bars, and is not how a real experiment would work. If we assumed both the Genesis (tip-based) and Echo (direct dispensing) methods gave us exactly the right answer for the activity, then these activity values would give us the $pIC_{50}$ values on the 'ideal' line in the first graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###2. Adding the inaccuracy and imprecision of the Tecan Genesis liquid-handling robot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "In reality, every experimental operation---such as a volume transfer---will be imperfect, leading to imperfect assay results.  We can model this---and its often surprising impact on the assay results---by making a simple model for the random and systematic variation with each operation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Liquid-handling robots can't transfer the specified volume exactly. Each transfer operation has some (a) inaccuracy (modeled as a constant bias factor for all dispensing operations) and (b) imprecision (random error associated with each volume transfer). It is important to consider these factors separately, as often liquid handlers are calibrated for precision, rather than accuracy, which means bias can creep in. We'll ignore other contributions to error, such as compound stickiness, insolubility, etc., though in future iterations including them may be useful."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![https://en.wikipedia.org/wiki/Accuracy_and_precision](img/accuracy_precision_simple.png \"https://en.wikipedia.org/wiki/Accuracy_and_precision\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we generate this dilution series using a Tecan Genesis robot used in the assay.\n",
    "\n",
    "Published manufacturer specifications for the imprecision of the Tecan Genesis are available online:\n",
    "\n",
    "[imprecision data for Tecan Genesis](http://www.frankshospitalworkshop.com/equipment/documents/automated_analyzer/user_manuals/Tecan%20Genesis%20RMP%20-%20User%20manual.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](img/GenesisImprecision.png \"GenesisImprecision.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tecan does not generally publish inaccuracy specifications, however, since a well-calibrated instrument can essentially eliminate inaccuracy with custom corrections applied to different volume ranges.  In order to illustrate the role inaccuracy can play, we will instead employ inaccuracy data published for a similar class of liquid handling instrument---the Beckman NX/FX span-8:\n",
    "\n",
    "[inaccuracy/imprecision data for Biomek NX/FX](https://www.beckmancoulter.com/wsrportal/bibliography?docname=BR-10150B.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we define a pipetting error function for the Tecan Genesis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tecan_genesis_pipetting_model(volume):\n",
    "    # Imprecision from Tecan Genesis manual.\n",
    "    # Inaccuracy estimated from Beckman Biomek NX/FX span-8.\n",
    "    \n",
    "    imprecision_function = interp1d(\n",
    "        [1.5e-6,100e-6], # volume range (L)\n",
    "        [0.03, 0.005]) # published relative imprecision for corresponding volumes Tecan Genesis\n",
    "    inaccuracy_function = interp1d(\n",
    "        [0.5e-6, 1e-6, 100e-6], # volume range (L)\n",
    "        [0.05, 0.03, 0.03]) # published relative inaccuracies for corresponding volumesfor Beckman NX/FX span-8\n",
    "    \n",
    "    return [inaccuracy_function(volume), imprecision_function(volume)]    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just for reference, this is what the ideal pipetting model looks like in comparison:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ideal_pipetting_model(volume):\n",
    "\n",
    "    imprecision_function = interp1d(\n",
    "        [1.5e-6, 100e-6], # volume range (L)\n",
    "        [0.0, 0.0]) # relative imprecision for corresponding volumes\n",
    "    inaccuracy_function = interp1d(\n",
    "        [0.5e-6, 1e-6, 100e-6], # volume range (L)\n",
    "        [0.0, 0.0, 0.0]) # relative inaccuracies for corresponding volumes\n",
    "    \n",
    "    return [inaccuracy_function(volume), imprecision_function(volume)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now consider a single *realization* of the automated pipetting process to generate a dilution series, utilizing the robot pipetting imprecision and inaccuracy model we defined above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main difference between our ideal *dilution_series* function here are that we are adding the inaccuracy in the form of the *transfer_bias*, which is a normal distribution around our inaccuracy value, to the *Vbuffer* and *Vtransfer* values. We are also then distributing this value according to a normal distribution around our imprecision value for both the *Vbuffer* and *Vtransfer* values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, pipetting_model, Cstock=10e-3):    \n",
    "\n",
    "    # Use pipetting error function to determine inaccuracy and imprecision for transferred volumes.\n",
    "    [transfer_inaccuracy, transfer_imprecision] = pipetting_model(Vtransfer)    \n",
    "    [buffer_inaccuracy, buffer_imprecision] = pipetting_model(Vbuffer)    \n",
    "\n",
    "    # Draw bias for this instrument recalibration.\n",
    "    # We allow the relative bias to be of different scale between the different volumes pipetted,\n",
    "    # but must be same direction.\n",
    "    bias = normal() # draw random normal variate that will scale inaccuracy to determine relative bias\n",
    "    \n",
    "    # Initialize storage for actual concentrations and volumes.\n",
    "    actual_concentrations = np.zeros([ndilutions], np.float64)\n",
    "    actual_volumes = np.zeros([ndilutions], np.float64)\n",
    "    \n",
    "    # Fill initial well of with appropriate dilution of stock solution.\n",
    "    Vinitial_transfer = (Cinitial / Cstock) * Vinitial # compute transferred volume of stock solution\n",
    "    Vinitial_buffer = Vinitial - Vinitial_transfer # compute transferred buffer volume\n",
    "    [initial_transfer_inaccuracy, initial_transfer_imprecision] = pipetting_model(Vinitial_transfer)\n",
    "    [initial_buffer_inaccuracy, initial_buffer_imprecision] = pipetting_model(Vinitial_buffer)    \n",
    "    Vtransfer_actual = Vinitial_transfer * ((1+initial_transfer_inaccuracy*bias) + initial_transfer_imprecision*normal())\n",
    "    Vbuffer_actual = Vinitial_buffer * ((1+initial_buffer_inaccuracy*bias) + initial_buffer_imprecision*normal())                        \n",
    "    actual_volumes[0] = Vtransfer_actual + Vbuffer_actual       \n",
    "    actual_concentrations[0] = Cstock * Vtransfer_actual / actual_volumes[0]\n",
    "                                \n",
    "    # Create dilution series.\n",
    "    for n in range(1,ndilutions):\n",
    "        Vtransfer_actual = Vtransfer * ((1+transfer_inaccuracy*bias) + transfer_imprecision*normal())\n",
    "        Vbuffer_actual   = Vbuffer   * ((1+buffer_inaccuracy*bias)   + buffer_imprecision  *normal())\n",
    "        Vtot = Vtransfer_actual + Vbuffer_actual\n",
    "        actual_concentrations[n] = actual_concentrations[n-1] * Vtransfer_actual / Vtot\n",
    "        actual_volumes[n]   += Vtot\n",
    "        actual_volumes[n-1] -= Vtransfer_actual\n",
    "    \n",
    "    # Remove volume Vtransfer from last so that all wells have same intended volume.\n",
    "    Vtransfer_actual = Vtransfer * ((1+transfer_inaccuracy*bias) + transfer_imprecision*normal())\n",
    "    actual_volumes[ndilutions-1] -= Vtransfer_actual\n",
    "    \n",
    "    return [actual_volumes, actual_concentrations]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "[actual_volumes, actual_concentrations] = \\\n",
    "    ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the deviations in concentrations generated by this imprecision and inaccuracy for this single realization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ERKRFZQ2RA4HPu/vngAXAee6+J3EFQvVCREQ6VNYQGUlcAx3i9O/vT7++CDim3kWJiEhr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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c8e7910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Set 'ideal_concentrations' and 'ideal_volumes' to the ideal assay_compound_concentrations and assay_volumes from before.\n",
    "ideal_concentrations = assay_compound_concentrations\n",
    "ideal_volumes = assay_volumes\n",
    "\n",
    "plt.semilogy(range(ndilutions), ideal_concentrations, 'ko', range(ndilutions), actual_concentrations, 'ro');\n",
    "plt.xlabel('dilution number');\n",
    "plt.ylabel('concentration (M)');\n",
    "plt.legend(['ideal','actual']);\n",
    "plt.axis([-0.5, ndilutions - 0.5, 0.0, Cinitial * 1.2]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the trend that the magnitude of the concentration error increases with subsequent dilutions.  To better see this effect, we plot the relative errors in concentration, volume, and total quantity of compound per well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Fsn4LCIsYbePuA2sRnIiI5C/rpIC/A36UPB8BtAD/QZhJ9uc1iEtERBpE1kTx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\nZNkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c4c7e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([-0.5, ndilutions], [1, 1], 'k--');\n",
    "plt.plot(range(ndilutions), actual_concentrations / ideal_concentrations, 'ro', \\\n",
    "         range(ndilutions), actual_volumes / ideal_volumes, 'go', \\\n",
    "         range(ndilutions), (actual_volumes*actual_concentrations)/(ideal_volumes*ideal_concentrations), 'bo');\n",
    "plt.legend(['exact', 'concentration', 'volume', 'quantity'], loc='upper left');\n",
    "plt.axis([-0.5, ndilutions - 0.5, 0.5, 1.5]);\n",
    "plt.ylabel('relative quantity');\n",
    "plt.xlabel('dilution number');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this was only a single *realization* of the pipetting process, it is difficult to draw conclusions about the *typical* errors in creating a dilution series with a liquid handler.  We can do this by simulating *many* independent realizations of the same experiment, and then estimate the **coefficient of variation (CV)** from the variation among experiments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, let's repeat the experiment 5000 times:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nreplicates = 5000\n",
    "\n",
    "actual_volumes_n = np.zeros([nreplicates, ndilutions], np.float64)\n",
    "actual_concentrations_n = np.zeros([nreplicates, ndilutions], np.float64)\n",
    "\n",
    "for replicate in range(nreplicates):\n",
    "    [actual_volumes_replicate, actual_concentrations_replicate] = \\\n",
    "        ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
    "        \n",
    "    actual_volumes_n[replicate,:] = actual_volumes_replicate\n",
    "    actual_concentrations_n[replicate,:] = actual_concentrations_replicate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's use this to compute the CV, using numpy.std, which calculates the standard deviation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the CV as a function of dilution number reveals surprising trends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YMOD/EWulTl2Odfi9D/z7mecLZ+zLL4d2G35qaDeYsS+/7PU02RG3Qm2IiN9HxDHFNNed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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c472090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(ndilutions), concentrations_cv*100, 'ro', \\\n",
    "         range(ndilutions), volumes_cv*100, 'go', \\\n",
    "         range(ndilutions), quantity_cv*100, 'bo')\n",
    "plt.xlabel('dilution number')\n",
    "plt.ylabel('CV (%)')\n",
    "plt.xlim([-0.5, ndilutions - 0.5])\n",
    "plt.legend(['concentration', 'volume', 'quantity'], loc='lower right');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the error in volume is relatively constant with dilution number, the CV (imprecision) in both concentration and quantity of compound increases with dilution number: up to 6% in the final sample."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about bias?  Is there significant deviation from the expected average concentration due to this process?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the mean of all these values for this 5000 replicate test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ku/+qGW+mpJLG8iw+BX9pev62UqPEQFsys5UIjxYfc/c7Wh1PFa8AywCfAy4y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\nREQkmf8H/7rsrx559ogAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c3ff510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 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",
    "#Let's define DILUTIONS to make plotting easier.\n",
    "dilutions = np.arange(ndilutions)\n",
    "\n",
    "# Plot relative biases.\n",
    "plt.plot([0, ndilutions], [0, 0], 'k--', dilutions, concentrations_bias*100, 'ro', \\\n",
    "     dilutions, volumes_bias*100, 'go', dilutions, quantity_bias*100, 'bo')\n",
    "plt.xlabel('dilution number')\n",
    "plt.ylabel('RB (%)')\n",
    "plt.legend(['none','concentration', 'volume', 'quantity'], loc='lower right')\n",
    "plt.axis([-0.5, ndilutions - 0.5, -100, 100]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We see that the process is essentially free of bias, which is expected if the bias for each realization of the experiment is chosen randomly for this model.  In reality, if multiple experiments are run with the same instrument without recalibration, the same bias in dispensing volumes would lead to biased assay results, but for the purposes of this simulation, we are sampling over many random recalibrations of the same instrument."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Now lets see how our estimation of enzyme activity is affected by including imprecision and inaccuracy, running many assay replicates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we need to add one more step of pipetting that includes our pipetting imprecision and inaccuracy as we transfer  a *compound_volume* (2 uL) of our dilution series into the enzyme assay solution of volume *mix_volume* (10 uL):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.00000000e-04   5.00000000e-05   2.50000000e-05   1.25000000e-05\n",
      "   6.25000000e-06   3.12500000e-06   1.56250000e-06   7.81250000e-07]\n"
     ]
    },
    {
     "data": {
      "image/png": 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Pd/L7HPB0YPs2tx3r/BcVDLkGfEfSLyQtJiWBRyXNyUuvnwxsQPrFX/d5SRdI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\nEjEzs9KcRMzMrDQnETMzK+3/AxhqcQXw+poTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c3ff810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compound_volume = 2.0e-6 # volume of compound dilution added to assay (L)\n",
    "mix_volume = 10.0e-6 # volume of enzyme assay mix added to assay (L)\n",
    "ideal_assay_concentrations = ideal_concentrations * ( compound_volume/(compound_volume + mix_volume) ) # ideal (L)\n",
    "\n",
    "# Plot the concentration range in the final assay\n",
    "plt.semilogy(range(ndilutions), ideal_assay_concentrations, 'ko');\n",
    "plt.xlabel('dilution number');\n",
    "plt.ylabel('concentration (M)');\n",
    "plt.legend(['ideal']);\n",
    "plt.axis([-0.5, ndilutions - 0.5, 1e-8, Cinitial * 1.2]);\n",
    "print ideal_assay_concentrations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "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",
    "    dispense_volume = np.zeros([ndilutions], np.float64)\n",
    "    dispense_compound_concentration = np.zeros([ndilutions], np.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",
    "        dispense_volume[i] = compound_volume_dispensed + mix_volume_dispensed\n",
    "        dispense_compound_concentration[i] = compound_concentrations[i] * compound_volume_dispensed / dispense_volume[i]\n",
    "\n",
    "    return [dispense_volume, dispense_compound_concentration]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fNNd/IXCyuy+t5x4ivUL6zf9P2WPWRtfSGM8oYC/gGNKGmaNogv/rNYTssRWp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\nmy8tMlA0jAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c19bf90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#initialize the activity values with a zero vector\n",
    "activity = np.zeros([nreplicates,ndilutions], np.float64)\n",
    "\n",
    "#calclulate activity with our competitive inhibition model and our new actual_concentrations for nreplicates\n",
    "for replicate in range(nreplicates):\n",
    "    # create a dilution series\n",
    "    [actual_volumes, actual_concentrations] = ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
    "    # combine aliquot of compound dilution with assay mix\n",
    "    [dispense_volumes, dispense_compound_concentrations] = robot_dispense(compound_volume, mix_volume, actual_concentrations, tecan_genesis_pipetting_model)\n",
    "    # measure V_0/V_max for each dilution\n",
    "    for i in range(ndilutions):\n",
    "        activity[replicate,i] = competitive_inhibition(substrate_concentration, dispense_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
    "\n",
    "#plot a subset of V_0/V_max realizations\n",
    "plt.semilogx(ideal_assay_concentrations, activity[::10].transpose(), 'r-');\n",
    "plt.xlabel('ideal [I] (M)');\n",
    "plt.ylabel('$V_{0}/V_{max}$');\n",
    "plt.axis([10**(-6.2), 10**(-3.9), 0, 0.06]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's not hard to see that the activity will vary over a substantial range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To determine the distribution of $IC_{50}$s consistent with the newly imposed experimental errors, we next use a nonlinear fit to each realization of the experiment to extract an $IC_{50}$ using this relationship to Ki for competitive inhibition, where we have already defined *[S]* and *Km* as constants:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$IC_{50} = K_{i}(1+\\frac{[S]}{K_{m}})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#define the function 'competitive_inhibition_IC50' using this equation\n",
    "def competitive_inhibition_IC50(substrate_concentration, inhibitor_concentration, enzyme_concentration, IC50, Km):\n",
    "    Ki = IC50/(1 + substrate_concentration/Km)\n",
    "    return competitive_inhibition(substrate_concentration, inhibitor_concentration, enzyme_concentration, Ki, Km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fit_ic50(inhibitor_concentrations, activities, Ki_guess):\n",
    "    \n",
    "    def objective(inhibitor_concentrations, IC50):\n",
    "        ndilutions = len(inhibitor_concentrations)\n",
    "        activities = np.zeros([ndilutions], np.float64)\n",
    "        for i in range(ndilutions):\n",
    "            activities[i] = competitive_inhibition_IC50(substrate_concentration, inhibitor_concentrations[i], enzyme_concentration, IC50, Km)\n",
    "            \n",
    "        return activities - activities.min()\n",
    "    \n",
    "    # fit the IC50 using a good initial guess for curve_fit        \n",
    "    import scipy.optimize\n",
    "    IC50_guess = Ki_guess*(1 + substrate_concentration/Km)\n",
    "    [popt, pcov] = scipy.optimize.curve_fit(objective, inhibitor_concentrations, activities - activities.min(), p0=[IC50_guess], maxfev=1000)\n",
    "    \n",
    "    return popt[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4tWXzzym/7NPGOPtiVdVmNnA68J7M/P0YT/Uh4Ar++wPz35lmb+ZO7IuI2BrYDdgpIn4G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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ce41c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "IC50s_tips = np.zeros([nreplicates], np.float64)\n",
    "for replicate in range(nreplicates):\n",
    "    IC50s_tips[replicate] = fit_ic50(ideal_assay_concentrations, activity[replicate,:], true_Ki)\n",
    "pIC50s_tips = np.log10(IC50s_tips)\n",
    "    \n",
    "nhist = 20\n",
    "plt.hist(pIC50s_tips, nhist);\n",
    "plt.xlabel('measured pIC50 (M)');\n",
    "plt.ylabel('P(pIC50)');\n",
    "plt.yticks([]);\n",
    "plt.xlim(-8, -7);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The imprecision and inaccuracy in the measured $pIC_{50}$s may not be uniform across the whole $K_i$ range, however.  To see if there is variation as a function of true inhibitor $K_i$, we can characterize imprecision and inaccuracy as a function of $pK_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def robot_IC50s(true_Ki):\n",
    "    nreplicates = 1000\n",
    "    IC50s = np.zeros([nreplicates], np.float64)\n",
    "    for replicate in range(nreplicates):\n",
    "        [actual_volumes, actual_concentrations] = ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
    "        [dispense_volumes, dispense_compound_concentrations] = robot_dispense(compound_volume, mix_volume, actual_concentrations, tecan_genesis_pipetting_model)\n",
    "        activities = np.zeros([ndilutions], np.float64)\n",
    "        for i in range(ndilutions):\n",
    "            activities[i] = competitive_inhibition(substrate_concentration,  dispense_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
    "        IC50s[replicate] = fit_ic50(ideal_assay_concentrations, activities, true_Ki)\n",
    "    return IC50s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#define arbitrary pKi array\n",
    "pKis = np.array([-12, -11, -10, -9, -8, -7, -6, -5, -4, -3], np.float64);\n",
    "Kis = 10**pKis\n",
    "nKis = len(pKis)\n",
    "\n",
    "#initialize with zeros\n",
    "genesis_pIC50_bias = np.zeros([nKis], np.float64)\n",
    "genesis_pIC50_CV = np.zeros([nKis], np.float64)\n",
    "\n",
    "for (i, Ki) in enumerate(Kis):\n",
    "    IC50s = robot_IC50s(Ki)    \n",
    "    pIC50s = np.log10(IC50s)\n",
    "    pIC50_true = np.log10(Kis[i]*(1 + substrate_concentration/Km))\n",
    "    genesis_pIC50_bias[i] = pIC50s.mean() - pIC50_true;\n",
    "    genesis_pIC50_CV[i] = pIC50s.std() / abs(pIC50s.mean())   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the bias in the measured $pIC_{50}$ values to examine the bias and CV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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paqhbRC4BPlPttX45sFtEbAzsDNw1qHCSpGarW0QOBmYCOwHfAu4EbgGOAT4xmGiSpKar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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d025310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot relative error in measured Ki values as a function of true Ki.\n",
    "plt.plot([pKis.min(), pKis.max()], [0, 0], 'k-', pKis, genesis_pIC50_bias, 'ro');\n",
    "plt.xlabel('pKi');\n",
    "plt.ylabel('bias in measured pIC50');\n",
    "plt.axis([pKis.min()-0.5, pKis.max()+0.5, -1.5,1.5]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d002c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pKis, genesis_pIC50_CV*100, 'ko');\n",
    "plt.xlabel('pKi');\n",
    "plt.ylabel('pIC50 CV (%)');\n",
    "plt.axis([pKis.min(), pKis.max(), 0, 10]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###3. Compare this to inaccuracy and imprecision for acoustic dispensing with the LabCyte Echo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Preparation of a dilution series by direct dispensing with the LabCyte Echo is a different process.  In the protocol described in [2], various quantities of 10 mM stock up to 120 uL were dispensed using the Echo, and then backfilled to 120 uL with DMSO.\n",
    "\n",
    "According to published [inaccuracy/imprecision specifications for LabCyte Echo](http://www.labcyte.com/sites/default/files/support_docs/Echo%205XX%20Specifications.pdf), the Echo has an inaccuracy of 10% and an imprecision of 8% over the entire dispense range of 2.5 nL to 10 uL.  We consider a 8-point dilution series spanning 2.5 nL (the smallest quantity the Echo can dispense) to 120 nL (the largest quantity dispensed in the assay) from 10 mM stock solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](img/Echo.png \"Echo.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unlike for tip-based dispensing, here we aren't creating a dilution series, we will be directly dispensing the assay amounts into the assay wells. We will apply the inaccuracy and imprecision in a similar way as before, to determine the normal distribution around which to define *dispense_volumes* and *backfill_volume*. The *backfill_volume* is the volume of DMSO added to the mix in addition to the compound stock (also in DMSO) so that the concentration of DMSO remains constant throughout the assay."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](img/direct_dispense.png \"direct_dispense.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# define echo_assay_dispense function that mimics the process of dispensing from the Echo into mix_volume\n",
    "def echo_assay_dispense(C0, mix_volume, backfill_volume, dispense_volumes):\n",
    "    # Manufacturer specifications for LabCyte Echo relative inaccuracy and imprecision\n",
    "    echo_inaccuracy = 0.10\n",
    "    echo_imprecision = 0.08\n",
    "\n",
    "    ndilutions = len(dispense_volumes)\n",
    "    echo_volume = np.zeros([ndilutions], np.float64)\n",
    "    echo_concentration = np.zeros([ndilutions], np.float64)\n",
    "    echo_bias = echo_inaccuracy * normal()\n",
    "    \n",
    "    for i in range(ndilutions):\n",
    "        # Compute intended dispensing volumes.\n",
    "        compound_volume_intended = dispense_volumes[i]\n",
    "        backfill_volume_intended = backfill_volume - compound_volume_intended\n",
    "        \n",
    "        compound_volume_dispensed = compound_volume_intended * ((1+echo_bias) + echo_imprecision*normal())\n",
    "        backfill_volume_dispensed = backfill_volume_intended * ((1+echo_bias) + echo_imprecision*normal())\n",
    "        \n",
    "        # Dispense the assay mix with a Tecan Genesis\n",
    "        [genesis_inaccuracy, genesis_imprecision] = tecan_genesis_pipetting_model(mix_volume)\n",
    "        bias = normal()\n",
    "        actual_mix_volume = mix_volume * ((1+genesis_inaccuracy*bias) + genesis_imprecision*normal())\n",
    "\n",
    "        # Compute assay volume and concentration\n",
    "        echo_volume[i] = actual_mix_volume + backfill_volume_dispensed + compound_volume_dispensed\n",
    "        echo_concentration[i] = C0 * compound_volume_dispensed / echo_volume[i]\n",
    "\n",
    "    return [echo_volume, echo_concentration]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's use this *echo_assay_dispense* function to create an 8-point dilution series with DMSO compound stock concentration as 10 mM, a final assay volume of 12 µL, and an 8-point titration of dispense volumes in multiples of 15 nL. To make sure our DMSO concentration does not vary as we vary our compound concentration, we'll always backfill up to 120 nL total DMSO."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  2.08333333e-06   4.16666667e-06   8.33333333e-06   1.66666667e-05\n",
      "   3.33333333e-05   5.00000000e-05   6.66666667e-05   1.00000000e-04]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d002c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "echo_C0 = 10e-3 # DMSO stock concentration (M)\n",
    "\n",
    "assay_volume = 12e-6 # final assay volume (L)\n",
    "\n",
    "echo_dispense_volumes = 2.5e-9 * np.array([1, 2, 4, 8, 16, 24, 32, 48]) # rougly logarithmic dispense volumes in multiples of 2.5 nL \n",
    "\n",
    "ndilutions_echo = len(echo_dispense_volumes)\n",
    "\n",
    "backfill_volume = 120e-9 # total Echo dispense volume including compound and DMSO backfilling (L)\n",
    "\n",
    "mix_volume = assay_volume - backfill_volume # assay mix volume to be added by liquid handler (L)\n",
    "\n",
    "#Check our concentrations are as expected\n",
    "echo_ideal_concentrations = (echo_C0*echo_dispense_volumes/assay_volume)\n",
    "plt.semilogy(range(ndilutions_echo), echo_ideal_concentrations, 'ko');\n",
    "plt.xlabel('dilution number');\n",
    "plt.ylabel('concentration (M)');\n",
    "plt.legend(['ideal']);\n",
    "plt.axis([-0.5, ndilutions_echo - 0.5, 1e-8, echo_C0 * 1.2]);\n",
    "print echo_ideal_concentrations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "[echo_volumes, echo_concentrations] = echo_assay_dispense(echo_C0, mix_volume, backfill_volume, echo_dispense_volumes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Let's plot a single realization of an Echo dispense experiment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BTwKXERXvnmtVcDJA9IMH2aT5On0Kr+TX17WeFiMesNse+AqxDPj5LYhLete/+oFjOef7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\nREQyKVGIiEim/w+Y4c4Oz/LbSwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e121fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([0,ndilutions_echo], [1, 1], 'k--', range(ndilutions_echo), echo_volumes / assay_volume,'ro',\\\n",
    "         range(ndilutions_echo), echo_concentrations / echo_ideal_concentrations, 'go');\n",
    "plt.legend(['exact', 'assay well volume rel err', 'concentration rel err'], loc='lower right')\n",
    "plt.axis([-0.5, ndilutions_echo - 0.5, 0.5, 1.5])\n",
    "plt.ylabel('relative quantity')\n",
    "plt.xlabel('dilution number');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We simulate many realizations of the same experiment to quantify imprecision and bias in the dilution series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# initialize with zeros\n",
    "actual_volumes_n = np.zeros([nreplicates, ndilutions_echo], np.float64)\n",
    "actual_concentrations_n = np.zeros([nreplicates, ndilutions_echo], np.float64)\n",
    "\n",
    "# initialize volume array with assay_volume value\n",
    "volume_array = np.ones([ndilutions_echo]) * assay_volume\n",
    "\n",
    "for replicate in range(nreplicates):\n",
    "    [actual_volumes_replicate, actual_concentrations_replicate] = echo_assay_dispense(echo_C0, mix_volume, backfill_volume, echo_dispense_volumes)\n",
    "    actual_volumes_n[replicate,:] = actual_volumes_replicate\n",
    "    actual_concentrations_n[replicate,:] = actual_concentrations_replicate\n",
    "volumes_cv = (actual_volumes_n / assay_volume).std(0)\n",
    "concentrations_cv = (actual_concentrations_n / echo_ideal_concentrations).std(0)\n",
    "quantity_cv = ((actual_volumes_n * actual_concentrations_n) / (assay_volume * echo_ideal_concentrations)).std(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now plot the CVs to examine the imprecision in the resulting compound concentrations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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E+HGvNtbPL0Sv/RewcEQcSLos9f+RDoevKjWqCprH4dB76VZg/Yj4BHA+sDXw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\nlZmmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e09be10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define dilutions to make plotting easier.\n",
    "dilutions = np.arange(ndilutions_echo)\n",
    "\n",
    "plt.plot(dilutions, concentrations_cv*100, 'rs', dilutions, volumes_cv*100, 'go', dilutions, quantity_cv*100, 'bo')\n",
    "plt.xlabel('dilution number')\n",
    "plt.ylabel('CV (%)')\n",
    "plt.xlim([-0.5,ndilutions_echo - 0.5])\n",
    "plt.legend(['concentration', 'volume', 'quantity'], loc='center right');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We again quantify the bias:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qZa1FeDLxBiHOw4ArYh9gy4mtlBMJ/X4NoY76NObT/Sn4pYLYAriNMPBh/yaH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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e13f410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute relative bias.\n",
    "volumes_bias = (actual_volumes_n / assay_volume).mean(0) - 1\n",
    "concentrations_bias = (actual_concentrations_n / echo_ideal_concentrations).mean(0) - 1\n",
    "quantity_bias = ((actual_volumes_n * actual_concentrations_n) / (assay_volume * echo_ideal_concentrations)).mean(0) - 1\n",
    "\n",
    "# Plot relative biases.\n",
    "plt.plot([0, ndilutions_echo], [0, 0], 'k--', dilutions, concentrations_bias*100, 'rs', \\\n",
    "     dilutions, volumes_bias*100, 'go', dilutions, quantity_bias*100, 'bo')\n",
    "plt.xlabel('dilution number')\n",
    "plt.ylabel('RB (%)')\n",
    "plt.legend(['none','concentration', 'volume', 'quantity'], loc='lower right')\n",
    "plt.axis([-0.5, ndilutions_echo - 0.5, -100, 100]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, bias over many random calibrations of the same instrument is expected to be zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets see how our estimation of enzyme activity is affected by including imprecision and inaccuracy, running many assay replicates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fgM/nW47UofOBK4mrYVZMp8J6gZkdDVzn7gcUbJtEnCRzAnE+s9nuvszMLgKO\nBR4mrv72SPqUW4jLLUs/VeH76DvAm4jvo/PSrwCLgW9UtXCpGT34LDqOuFzzYOBQM/uUu19W7s9V\nsGTIzAIwE7iEuPxn2/bBwCJiUPwM+Aiw0Mxe7e7nFbR7H3AKcBXxf/Cfq1e91Ipuvo/OL2h3bvq8\nHwBvoz1kpJ/o6WdRQftXAZdXEiqgU2FZOx/4NHEW5sLzkicALe4+191b3H0+sAY4uej51wEvmdl9\nwDTim0L6n56+j34MnGhmS4nX7X7Y+yVLjenpe6hNACqeqVg9lmxd4e4Xmtnkou3jgZVF2zzd3r7B\nvZU4CkP6t56+j14k9nyl/+rRe+jlHe5PAxUNNQb1WDLl7qs72NVEXEK5UKnllkX0PpIey/s9pGCp\njs1A8ZDPRmBTDrVI/dL7SHqqKu8hBUt1rCLe7FjI2L1LKtIZvY+kp6ryHtI1lupYAjSY2RziML8Z\nwCjikGKRcul9JD1VlfeQeiy95+WRFO6+HZhKHOm1DjgbONXdK54qQfodvY+kp6r+HtKa9yIikin1\nWEREJFMKFhERyZSCRUREMqVgERGRTClYREQkUwoWERHJlIJFREQypWAREZFMKVhERCRTmitMpIiZ\ntQJT3P3WEvsOBJ4Bxrj7Mz38OZOJczcNTqfaKFUHwAPufrSZXQk0uPs0M7sbeHO6v+Tz02PsA9yZ\ntj0q/Xlrgf3dPSlq+0Xge8A33P0b6RK2F7v723vyOqX/UY9FZHejgaV5F5GaBrwz/T6hfd6nU4D3\nlfH87wDz0sW/2uxDeygVel/hz3D3PwDPmdmMbtQt/ZiCRaSIu6919x1515Ha4O4b0u9D+iDdtqHD\nZwFmdgDwYeCnRbtuB04r0XYC8Ai7LmV7KfDVbtYu/ZROhYkUKTwVZmZNwOXAe4B/AhcVtd0b+EG6\nfyfwW+Cz7v5cuv8Y4umlo4h/yD0InOXuf6rCS/kkcLu7F68YeD1wDvDFgm3vBW4CDmbXNc6XAUPN\nbKq739SbxUrfoR6LSOfmAm8E/gX4EPCZov0/Aw4ATkwfewGLAMxsKPHD+h7gtcBxwEDg+9UoHDgZ\n2O06UVrfWDM7vGDbe4Brixu6eytwG3GqdZGyKFhEOmBmw4DTgc+5+/3ufh/w6YL9hxCvS8xw94fT\nXsh0YJKZvYW45OuFwFfc/Wl3fwiYBxxe/LN6ofaBwBHAoyV2Pw/cRXo6zMxGEMPzxg4OtyrdL1IW\nBYtIx8YFATWEAAACFklEQVQRexgPFWx7oOD7w4jXI540s01mtgl4Nn3OOHdfA8wHPm1m88zsHuAy\nqvN7t19ax/Ml9iXAdbRfZzkNuM3dN3dwrHXEVQZFyqJrLCIda7vWUHgxu/Ci/iBgG7FnUCgQR1O9\nkhhEfwRuBq4ihlE1Loa3DVXuKMSuB36YXrR/D7Cgk2MNLDieSJcULCIdc2A7cCzw/9JtRxbsXwUM\nBoa4+6MAZrYv8HPgPOIw4S3uPqXtCWY2lV2DqhKVLPe6jjiYYESpne7+NzN7kHjq7njisOaOjCD2\nxETKomAR6YC7bzKzecAPzOyfxN7Jjwr2u5ktBK4ysznAC8DFgAGPES/Y729m7ySG1BTgzB6UVHYg\nuXtiZg8Brwd+10Gz64CvAHe7+8ZOfsYR7HoKUKRTusYi0rnPEk9j3ZA+fsyuPYczgIeJI63uS/f9\nS3on/K+BK4FfAiuIPYOpwN5mNjZ9fiW9kMIbJMtxI/DWEsdocx1xFNu1HezHzAYAb6LjC/siuwlJ\nUsn7VESqpbOpZdL9k+l8SpgDiKfrxrj7+m7W8A7gMncf353nS/+kHotIbRtuZvsVbzSz4cDwzp7o\n7v8g9pY+3oOffxZFN4WKdEXBIlLbfkm8ybLYQuA3dH1q7DzgjPRmzYqY2ZHAPu7+35U+V/o3nQoT\nEZFMqcciIiKZUrCIiEimFCwiIpIpBYuIiGRKwSIiIpn6X6kEykezWnf3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e052390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#initialize the activity values with a zero vector\n",
    "activity = np.zeros([nreplicates,ndilutions_echo], np.float64)\n",
    "\n",
    "#calclulate activity with our competitive inhibition model and our new actual_concentrations for nreplicates\n",
    "for replicate in range(nreplicates):\n",
    "    [actual_volumes, actual_concentrations] = echo_assay_dispense(echo_C0, mix_volume, backfill_volume, echo_dispense_volumes)\n",
    "    for i in range(ndilutions_echo):\n",
    "        activity[replicate,i] = competitive_inhibition(substrate_concentration, actual_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
    "\n",
    "#plot\n",
    "plt.semilogx(echo_ideal_concentrations, activity[::10].transpose(), 'r-');\n",
    "plt.xlabel('ideal [I] (M)');\n",
    "plt.ylabel('$V_{0}/V_{max}$');\n",
    "plt.axis([10**(-6.2), 10**(-3.9), 0, 0.06]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check our $pIC_{50}$ histogram using the same `fit_ic50` function from before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bbca2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "IC50s_echo = np.zeros([nreplicates], np.float64)\n",
    "for replicate in range(nreplicates):\n",
    "    IC50s_echo[replicate] = fit_ic50(echo_ideal_concentrations, activity[replicate,:], true_Ki)                        \n",
    "pIC50s_echo = np.log10(IC50s_echo)\n",
    "    \n",
    "nhist = 20\n",
    "plt.hist(pIC50s_echo, nhist);\n",
    "plt.xlabel('measured pIC50 (M)');\n",
    "plt.ylabel('P(pIC50)');\n",
    "plt.yticks([]);\n",
    "plt.xlim(-8, -7);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the imprecision and inaccuracy in the measured pIC50s may not be uniform across the whole $K_i$ range, however, so we will characterize imprecision and inaccuracy as a function of $pK_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def echo_IC50s(true_Ki):\n",
    "    nreplicates = 1000\n",
    "    IC50s = np.zeros([nreplicates], np.float64)\n",
    "    for replicate in range(nreplicates):\n",
    "        [assay_volumes, actual_concentrations] = echo_assay_dispense(echo_C0, mix_volume, backfill_volume, echo_dispense_volumes)\n",
    "        activities = np.zeros([ndilutions_echo], np.float64)\n",
    "        for i in range(ndilutions_echo):\n",
    "            activities[i] = competitive_inhibition(substrate_concentration, actual_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
    "        IC50s[replicate] = fit_ic50(echo_ideal_concentrations, activities, true_Ki)\n",
    "    return IC50s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Initialize with zeros.\n",
    "echo_pIC50_bias = np.zeros([nKis], np.float64)\n",
    "echo_pIC50_CV = np.zeros([nKis], np.float64)\n",
    "\n",
    "for (i, Ki) in enumerate(Kis):\n",
    "    IC50s = echo_IC50s(Ki)    \n",
    "    pIC50s = np.log10(IC50s)\n",
    "    pIC50_true = np.log10(Kis[i]*(1 + substrate_concentration/Km))\n",
    "    echo_pIC50_bias[i] = pIC50s.mean() - pIC50_true;\n",
    "    echo_pIC50_CV[i] = pIC50s.std() / abs(pIC50s.mean())  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RsQNwAuVSJ2PdnJkbLmmwybBURUSSpqGJfm/WvTvrCOAMoADuB7akvEvrBmDnfgSVJE09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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd6acd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot relative error in measured Ki values as a function of true Ki.\n",
    "plt.plot([pKis.min(), pKis.max()], [0, 0], 'k-', pKis, echo_pIC50_bias, 'ro');\n",
    "plt.xlabel('pKi');\n",
    "plt.ylabel('bias in measured pIC50');\n",
    "plt.axis([pKis.min()-0.5, pKis.max()+0.5, -1.5,1.5]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AfsB7I+Ltg40n9ZYFQ5q4kSvwLQY81fb4wMx8KDO/S1ll7bTWmIY0KVkwpIl7\n3YIvImIGZX3y9pXd2gvKHpQFar7Wts3xC00qFgxp4o6IiC0iYj3KcqWXZuato70wM2cBBwLviIhd\nWpsdv9CkYsGQJu504DTKUq63M8bylpl5OuV+jK9ExDS8SkqTjEu0ShPQug9js8z8+bCzSINiC0OS\nVIkFQ5JUiV1SkqRKbGFIkiqxYEiSKrFgSJIqsWBIkiqxYEiSKrFgSJIq+f/UqVNTKEVj1wAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e085210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot CV.\n",
    "plt.plot(pKis, echo_pIC50_CV*100, 'ko');\n",
    "plt.xlabel('pKi');\n",
    "plt.ylabel('measured pIC50 CV (%)');\n",
    "plt.axis([pKis.min(), pKis.max(), 0, 10]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Add to model: dilution by system liquid of the Tecan Genesis liquid-handling robot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Tecan Genesis supports the use of both disposable tips and fixed tips. When operating with fixed tips, syringes use a system liquid (generally water or buffer) to aspirate and dispense during liquid transfers.  While an air gap remains between the liquid being transferred and the system liquid, the system liquid is used to flush the tips into waste after transfers in order to remove any liquid residue before the next transfer. Because a small quantity of system liquid residue remains coating the tip after washing, fixed tips can actually *dilute* the sample being transferred unless special protocols are used to prevent this. A good description of this phenomonen can be found in [Dilution effect in multichannel liquid-handling system equipped with fixed tips:Problems and solutions for bioanalytical sample preparation. J. Lab. Autom. 12(6): 2007](http://dx.doi.org/10.1016/j.jala.2007.07.002), including the diagram below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](img/dilution_effect_diagram.png \"dilution_effect_diagram.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The magnitude of this dilution effect was noted in a 2006 paper by Dong et al at BMS, [The use of a dual dye photometric calibration method to identify possible sample dilution from an automated multichannel liquid-handling system. J. Lab. Autom. 11(2): 2006](http://dx.doi.org/10.1016/j.jala.2006.02.005), which quite surprisingly can have a large impact on dilution series preparation. The relevant table from this paper is below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](img/DilutionError_small.png \"DilutionError_small.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Define a function to interpolate the dilution effect between the measured values of Dong et al. 2006\n",
    "# (extended to 1 uL volumes)\n",
    "volume = np.array([1, 20, 200]) * 1e-6 # volumes at which dilution effect was quantified (L)\n",
    "dilution_effect = np.array([-0.0630, -0.0630, -0.0496]) # relative inaccuracy due to dilution with system liquid at corresponding volumes\n",
    "\n",
    "dilution_function = interp1d(volume, dilution_effect) # interpolation function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We introduce a modified model of our dilution series that now incorporates this dilution effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the only difference between this function and our `ROBOT_dilution_series` function is that `actual_concentrations[n]` value now includes our `dilution_function` term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def DILUTE_ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, pipetting_model, Cstock=10e-3):\n",
    "\n",
    "    # Use pipetting error function to determine inaccuracy and imprecision for transferred volumes.\n",
    "    [transfer_inaccuracy, transfer_imprecision] = pipetting_model(Vtransfer)    \n",
    "    [buffer_inaccuracy, buffer_imprecision] = pipetting_model(Vbuffer)    \n",
    "\n",
    "    # Draw bias for this instrument recalibration.\n",
    "    # We allow the relative bias to be of different scale between the different volumes pipetted,\n",
    "    # but must be same direction.\n",
    "    bias = normal() # draw random normal variate that will scale inaccuracy to determine relative bias\n",
    "    \n",
    "    # Initialize storage for actual concentrations and volumes.\n",
    "    actual_concentrations = np.zeros([ndilutions], np.float64)\n",
    "    actual_volumes = np.zeros([ndilutions], np.float64)\n",
    "    \n",
    "    # Fill initial well of with appropriate dilution of stock solution.\n",
    "    Vinitial_transfer = (Cinitial / Cstock) * Vinitial # compute transferred volume of stock solution\n",
    "    Vinitial_buffer = Vinitial - Vinitial_transfer # compute transferred buffer volume\n",
    "    [initial_transfer_inaccuracy, initial_transfer_imprecision] = pipetting_model(Vinitial_transfer)\n",
    "    [initial_buffer_inaccuracy, initial_buffer_imprecision] = pipetting_model(Vinitial_buffer)    \n",
    "    Vtransfer_actual = Vinitial_transfer * ((1+initial_transfer_inaccuracy*bias) + initial_transfer_imprecision*normal())\n",
    "    Vbuffer_actual = Vinitial_buffer * ((1+initial_buffer_inaccuracy*bias) + initial_buffer_imprecision*normal())                        \n",
    "    actual_volumes[0] = Vtransfer_actual + Vbuffer_actual       \n",
    "    actual_concentrations[0] = (1+dilution_function(Vtransfer_actual)) * Cstock * Vtransfer_actual / actual_volumes[0]\n",
    "                                \n",
    "    # Create dilution series.\n",
    "    for n in range(1,ndilutions):\n",
    "        Vtransfer_actual = Vtransfer * ((1+transfer_inaccuracy*bias) + transfer_imprecision*normal())\n",
    "        Vbuffer_actual   = Vbuffer   * ((1+buffer_inaccuracy*bias)   + buffer_imprecision  *normal())\n",
    "        Vtot = Vtransfer_actual + Vbuffer_actual\n",
    "        actual_concentrations[n] = \\\n",
    "            (1+dilution_function(Vtransfer)) * actual_concentrations[n-1] * Vtransfer_actual / Vtot\n",
    "        actual_volumes[n]   += Vtot\n",
    "        actual_volumes[n-1] -= Vtransfer_actual\n",
    "    \n",
    "    # Remove volume Vtransfer from last so that all wells have same intended volume.\n",
    "    Vtransfer_actual = Vtransfer * ((1+transfer_inaccuracy*bias) + transfer_imprecision*normal())\n",
    "    actual_volumes[ndilutions-1] -= Vtransfer_actual\n",
    "\n",
    "    return [actual_volumes, actual_concentrations]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Once again, we simulate many replicates of the same experiment, this time including the dilution effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#initialize with zeros\n",
    "actual_volumes_n = np.zeros([nreplicates, ndilutions], np.float64)\n",
    "actual_concentrations_n = np.zeros([nreplicates, ndilutions], np.float64)\n",
    "\n",
    "for replicate in range(nreplicates):\n",
    "    [actual_volumes_replicate, actual_concentrations_replicate] = DILUTE_ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
    "    actual_volumes_n[replicate,:] = actual_volumes_replicate\n",
    "    actual_concentrations_n[replicate,:] = actual_concentrations_replicate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can quantify the impact on imprecision by visualizing the CVs as a function of dilution number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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1p+uLiEibZXU9vQisT+ge6s4Y4JXeXNDd55vZGGAmkAAHuvtbDcW2AOYBN5jZJ4AZhMV9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\nE1cUKEREyqwEa2c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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e032550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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",
    "dilutions = np.arange(ndilutions)\n",
    "plt.plot(dilutions, concentrations_cv*100, 'ro', dilutions, volumes_cv*100, 'go', dilutions, quantity_cv*100, 'bo')\n",
    "plt.xlabel('dilution number')\n",
    "plt.ylabel('CV (%)')\n",
    "plt.xlim([-0.5, ndilutions -0.5])\n",
    "plt.legend(['concentration', 'volume', 'quantity'], loc='lower right');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also examine the bias."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0XnujWlxE7AFMIt1l/DfgBElXtTeq6rIZv/8C7N+J5SEi4ijgm6Sbmkt2kvSH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e032710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 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",
    "plt.plot([0, ndilutions], [0, 0], 'k--', dilutions, concentrations_bias*100, 'rs',\\\n",
    "     dilutions, volumes_bias*100, 'go', dilutions, quantity_bias*100, 'bo');\n",
    "plt.xlabel('dilution number');\n",
    "plt.ylabel('RB (%)');\n",
    "plt.legend(['none', 'concentration', 'volume', 'quantity'], loc='upper right');\n",
    "plt.axis([-0.5, ndilutions - 0.5, -100, 100]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now see that over many realizations with random calibrations, significant bias in both the concentration and quantity of compound accumulates with dilution number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def dilute_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",
    "    dispense_volume = np.zeros([ndilutions], np.float64)\n",
    "    dispense_compound_concentration = np.zeros([ndilutions], np.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",
    "        dispense_volume[i] = compound_volume_dispensed + mix_volume_dispensed\n",
    "        d = dilution_function(compound_volume_dispensed)\n",
    "        dispense_compound_concentration[i] = (1+d) * compound_concentrations[i] \\\n",
    "            * compound_volume_dispensed / dispense_volume[i]\n",
    "\n",
    "    return [dispense_volume, dispense_compound_concentration]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QwtYF5C/SbSmwSNcVYwsx/pp0Jsu+wAzynQ3YFziXdFrlnwhhHCEMWM9rRHo8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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d2f47d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#initialize the activity values with a zero vector\n",
    "activity = np.zeros([nreplicates,ndilutions], np.float64)\n",
    "ideal_assay_concentrations = ideal_concentrations * ( compound_volume/(compound_volume + mix_volume) ) # ideal (L)\n",
    "\n",
    "#calclulate activity with our competitive inhibition model and our new actual_concentrations for nreplicates\n",
    "for replicate in range(nreplicates):\n",
    "    [actual_volumes, actual_concentrations] = DILUTE_ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
    "    [dispense_volumes, dispense_compound_concentrations] = dilute_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, dispense_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
    "\n",
    "#plot\n",
    "plt.semilogx(ideal_assay_concentrations, activity[::10].transpose(), 'r-');\n",
    "plt.xlabel('ideal [I] (M)');\n",
    "plt.ylabel('$V_{0}/V_{max}$');\n",
    "plt.axis([10**(-6.2), 10**(-3.9), 0, 0.06]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ETgTekpl/mOCp3g1cxH+/Yf4bc+yXuR/7IiK2B3YDdomInwIPpvy386aBFT4A/fq9iIgW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\nVcLAl6RKGPiSVAkDX5Iq8f8BXaOrUU73K0kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cacd8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "IC50s_tips_dilute = np.zeros([nreplicates], np.float64)\n",
    "for replicate in range(nreplicates):\n",
    "    IC50s_tips_dilute[replicate] = fit_ic50(ideal_assay_concentrations, activity[replicate,:], true_Ki)\n",
    "pIC50s_tips_dilute = np.log10(IC50s_tips_dilute)\n",
    "    \n",
    "nhist = 20\n",
    "plt.hist(pIC50s_tips_dilute, nhist);\n",
    "plt.xlabel('measured pIC50 (M)');\n",
    "plt.ylabel('P(pIC50)');\n",
    "plt.yticks([]);\n",
    "plt.xlim(-8, -7);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  5.44388770e-04   2.53719967e-04   1.19835059e-04   5.62280758e-05\n",
      "   2.65327592e-05   1.24845095e-05   5.84155092e-06   2.76197767e-06]\n"
     ]
    }
   ],
   "source": [
    "def dilute_robot_IC50s(true_Ki):\n",
    "    nreplicates = 1000\n",
    "    IC50s = np.zeros([nreplicates], np.float64)\n",
    "    for replicate in range(nreplicates):\n",
    "        [actual_volumes, actual_concentrations] = DILUTE_ROBOT_dilution_series(Vinitial, Cinitial, Vtransfer, Vbuffer, ndilutions, tecan_genesis_pipetting_model)\n",
    "        [dispense_volumes, dispense_compound_concentrations] = dilute_robot_dispense(compound_volume, mix_volume, actual_concentrations, tecan_genesis_pipetting_model)\n",
    "        activities = np.zeros([ndilutions], np.float64)\n",
    "        for i in range(ndilutions):\n",
    "            activities[i] = competitive_inhibition(substrate_concentration, dispense_compound_concentrations[i], enzyme_concentration, true_Ki, Km)\n",
    "        IC50s[replicate] = fit_ic50(ideal_assay_concentrations, activities, true_Ki)\n",
    "    return IC50s\n",
    "\n",
    "print actual_concentrations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  8.64553314e-05   4.32276657e-05   2.16138329e-05   1.08069164e-05\n",
      "   5.40345821e-06   2.70172911e-06   1.35086455e-06   6.75432277e-07]\n"
     ]
    }
   ],
   "source": [
    "print ideal_concentrations * ( compound_volume/(compound_volume + mix_volume) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  6.00000000e-04   3.00000000e-04   1.50000000e-04   7.50000000e-05\n",
      "   3.75000000e-05   1.87500000e-05   9.37500000e-06   4.68750000e-06]\n"
     ]
    }
   ],
   "source": [
    "print ideal_concentrations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#initialize with zeros\n",
    "dilute_genesis_pIC50_bias = np.zeros([nKis], np.float64)\n",
    "dilute_genesis_pIC50_CV = np.zeros([nKis], np.float64)\n",
    "\n",
    "for (i, Ki) in enumerate(Kis):\n",
    "    IC50s = dilute_robot_IC50s(Ki)    \n",
    "    pIC50s = np.log10(IC50s)\n",
    "    pIC50_true = np.log10(Kis[i]*(1 + substrate_concentration/Km))\n",
    "    dilute_genesis_pIC50_bias[i] = pIC50s.mean() - pIC50_true;\n",
    "    dilute_genesis_pIC50_CV[i] = pIC50s.std() / abs(pIC50s.mean())   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/GRGfBvYGXtOnLN8D1oiIAyi3+b6J0v28YMJ5XwEujogvAj8HjgbOz8w/9inHpKr/E64b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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10deea9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot relative error in measured Ki values as a function of true Ki.\n",
    "plt.plot([pKis.min(), pKis.max()], [0, 0], 'k-', pKis, dilute_genesis_pIC50_bias, 'ro');\n",
    "plt.xlabel('pKi');\n",
    "plt.ylabel('bias in measured pIC50');\n",
    "plt.axis([pKis.min()-0.5, pKis.max()+0.5, -1.5,1.5]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dcdf890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pKis, dilute_genesis_pIC50_CV*100, 'ko');\n",
    "plt.xlabel('pKi');\n",
    "plt.ylabel('pIC50 CV (%)');\n",
    "plt.axis([pKis.min(), pKis.max(), 0, 10]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Now compare Tecan Genesis and LabCyte Echo errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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i10pvYUTEdGB62XGY2cgzyABzfYbWnskmZ7NqU2uTB4gJYPJIbv1UoYVhZjZk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\nhpmZFeKEYWZmhThhmJlZIU4YZmZWyP8D2faX35kZo84AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d5f9250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pKis, echo_pIC50_CV*100, 'go');\n",
    "plt.plot(pKis, genesis_pIC50_CV*100, 'bo');\n",
    "plt.plot(pKis, dilute_genesis_pIC50_CV*100, 'ko');\n",
    "plt.xlabel('pKi');\n",
    "plt.ylabel('pIC50 CV (%)');\n",
    "plt.legend(['echo','disposable dips','fixed tips with dilution effect'])\n",
    "plt.axis([pKis.min(), pKis.max(), 0, 10]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qPe1ARE4D3hKRxeNr8ZzWkT8m20/AyIYVJABV/ZDssQjBWgk+wFMmEhH3LV8w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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d64a5d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "echo_pIC50_err = (echo_pIC50_CV*np.abs(pKis))\n",
    "genesis_pIC50_err = (genesis_pIC50_CV*np.abs(pKis))\n",
    "dilute_genesis_pIC50_err = (dilute_genesis_pIC50_CV*np.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='bo');\n",
    "errorbar(pKis + echo_pIC50_bias, pKis + dilute_genesis_pIC50_bias, xerr=2*echo_pIC50_err, yerr=2*dilute_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');\n",
    "plt.legend(['ideal', 'ideal', 'model', 'dilute model'], loc='lower right');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "figsize(10,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TJEmaBJ1irdls3rbQ5zTYJEmS+mQQsQYGmyRJUl8MKtbAYJMkSVq0QcYaGGySJEmLMuhY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cdf80d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Doing the pIC50 interpolation correctly using function:\n",
    "def compute_pIC50_from_pKi(pKis):\n",
    "    Kis = 10**pKis\n",
    "    return np.log10(Kis*(1 + substrate_concentration/Km))\n",
    "\n",
    "# Interpolate bias and CV for Echo and Genesis.\n",
    "echo_bias_interpolation = interp1d(compute_pIC50_from_pKi(pKis) + echo_pIC50_bias, echo_pIC50_bias);\n",
    "echo_CV_interpolation = interp1d(compute_pIC50_from_pKi(pKis) + echo_pIC50_CV, echo_pIC50_CV);\n",
    "genesis_bias_interpolation = interp1d(compute_pIC50_from_pKi(pKis) + genesis_pIC50_bias, genesis_pIC50_bias);\n",
    "genesis_CV_interpolation = interp1d(compute_pIC50_from_pKi(pKis) + genesis_pIC50_CV, genesis_pIC50_CV);\n",
    "dilute_genesis_bias_interpolation = interp1d(compute_pIC50_from_pKi(pKis) + dilute_genesis_pIC50_bias, dilute_genesis_pIC50_bias);\n",
    "dilute_genesis_CV_interpolation = interp1d(compute_pIC50_from_pKi(pKis) + dilute_genesis_pIC50_CV, dilute_genesis_pIC50_CV);\n",
    "\n",
    "# Compute error bars for Echo and Genesis.\n",
    "echo_pIC50_err = (echo_CV_interpolation(echo_pIC50s)*np.abs(echo_pIC50s))\n",
    "genesis_pIC50_err = (genesis_CV_interpolation(genesis_pIC50s)*np.abs(genesis_pIC50s))\n",
    "dilute_genesis_pIC50_err = (dilute_genesis_CV_interpolation(genesis_pIC50s)*np.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*dilute_genesis_pIC50_err, fmt='ro', markersize=5, zorder=5);\n",
    "plot([-9, -6], [-9, -6], 'k-');\n",
    "xlabel('pIC50 (acoustic)');\n",
    "ylabel('pIC50 (tips)');\n",
    "legend(['ideal', 'original'], loc='lower right');\n",
    "title('95% confidence intervals shown');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lybEB3rd8+fKXANtZ4DKu2gVbZl4EeA42SZI0tJpibebqLO8DnnjooYe2upTbvGpzHjZJ\nkqRRMF+sNRqN6xb7nAabJElSl/Qi1sBgkyRJ6opexRoYbJIkSUvWy1gDg02SJGlJeh1rYLBJkiQt\nWj9iDQw2SZKkRelXrIHBJkmStGD9jDUw2CRJkhak37EGBpskSVLHBhFrYLBJkiR1ZFCxBgabJElS\nW4OMNTDYJEmSWhp0rIHBJkmSNK86xBoYbJIkSXOqS6yBwSZJknSQOsUaGGySJEkHqFusgcEmSZK0\nTx1jDQw2SZIkoL6xBgabJElSrWMNDDZJkjTm6h5rYLBJkqQxNgyxBgabJEkaU8MSa2CwSZKkMTRM\nsQYGmyRJGjPDFmtgsEmSpDEyjLEGBpskSRoTwxprYLBJkqQxMMyxBgabJEkaccMea2CwSZKkETYK\nsQYGmyRJGlGjEmtgsEmSpBE0SrEGBpskSRoxoxZrYLBJkqQRMoqxBgabJEkaEaMaa2CwSZKkETDK\nsQYGmyRJGnKjHmtgsEmSpCE2DrEGBpskSRpS4xJrYLBJkqQhNE6xBgabJEkaMuMWa2CwSZKkITKO\nsQYGmyRJGhLjGmtgsEmSpCEwzrEGBpskSaq5cY81MNgkSVKNGWslg02SJNWSsbafwSZJkmrHWDuQ\nwSZJkmrFWDuYwSZJkmrDWJubwSZJkmrBWJufwSZJkgbOWGvNYJMkSQNlrLVnsEmSpIEx1jpjsEmS\npIEw1jpnsEmSpL4z1hbGYJMkSX1lrC2cwSZJkvrGWFscg02SJPWFsbZ4BpskSeo5Y21pDDZJktRT\nxtrSGWySJKlnjLXuMNgkSVJPGGvdY7BJkqSuM9a6y2CTJEldZax1n8EmSZK6xljrDYNNkiR1hbHW\nOwabJElaMmOttww2SZK0JMZa7xlskiRp0Yy1/jDYJEnSohhr/WOwSZKkBTPW+stgkyRJC2Ks9Z/B\nJkmSOmasDYbBJkmSOmKsDY7BJkmS2jLWBstgkyRJLRlrg2ewSZKkeRlr9WCwSZKkORlr9WGwSZKk\ngxhr9WKwSZKkAxhr9WOwSZKkfYy1ejLYJEkSYKzVmcEmSZKMtZoz2CQNtaLg+KKgUX0cP+jxSMPI\nWKs/g02SpDFmrA0Hg03S0CoK1gBbmm7aUt0mqQPG2vA4dNADkKTFqMJseoJdrGIzAJtZNbmbZdNF\nAY0GGwc7QqnejLXhYrBJqqUO1qOtnWAXl3ISy9kJwBms50S2soeJtUXBhfM9sNHg8m6OVRo2xtrw\nMdgk1dX2dndYxeZ9sQawnJ2sZhNncfpkm8cXXRifNJSMteHkGjZJksaEsTa8nGGTVFcr2mzfsplV\nk2ewft8s2w6OZROrAbYBK3s8PmmoGGvDzWCTVEvt1pkVBRt2s2z6RLaymk0AbGI1e5gA2OA6NWk/\nY234GWyShlKjwcaigD1MrK3WrEE5s7bBI0Sl/Yy10WCwSRpaVbRdyP4DDFY6sybtZ6yNDoNN0lCr\nAs2jPqVZjLXRYrBJGmrFVHE8+2fYVjTWNZxh09gz1kaPp/WQJGmEGGujyWCTNLSKqeLga4mWt0lj\nyVgbXQabpKFUhdk0MNl08yQwbbRpHBlro801bJJqqVqb1sraVtuKqWL+a4m6zk0jxlgbfQabpLpq\ney3RFryWqMaGsTYeahNsEfEN4Dhgb3XTFZl5wgCHJElSrRlr46MWwRYRNwECOCoz9wx6PJJqoe21\nRDlw/VozryWqkWesjZdaBBtwAnCVsSZpRrt1ZsVUsYHyoIO5bHCdmkaZsTZ++hZsEXEIcPgcm/YC\nJwG/iYgvUP6r+lLgrzLzW/0an6Th0ljX2FhMFVAefHDgtUTXNbyWqEaWsTae+nlaj1OA3XN8bAUa\nwJeAJwDLgS8DH4uIG/dxfJKGTBVmzbs+VxprGmXG2vjq2wxbZl5A60Bs/p/s30bEacA9gIt7OjBJ\nkoaAsTbearGGLSJOBbZn5oXV14cChwG/GujAJNVetVbN03RopBlrqkWwAUcBz4mIPwZ2Aa8DtmXm\n1wY7LEmSBstYE9Qn2F4N3JxyHdvNgIuAPx3kgCRJGjRjTTNqEWyZeT3wwupDkqSxZ6ypmRd/lySp\nZow1zWawSZJUI8aa5mKwSZJUE8aa5mOwSZJUA8aaWjHYJEkaMGNN7RhskiQNkLGmThhskiQNiLGm\nThlskiQNgLGmhTDYJEnqM2NNC2WwSZLUR8aaFsNgkySpT4w1LZbBJklSHxhrWgqDTZKkHjPWtFQG\nmyRJPWSsqRsMNkmSesRYU7cYbJIk9YCxpm4y2CRJ6jJjTd1msEmS1EXGmnrBYJMkqUuMNfWKwSZJ\nUhcYa+olg02SpCUy1tRrBpskSUtgrKkfDDZJkhbJWFO/GGySJC2CsaZ+MtgkSVogY039ZrBJkrQA\nxpoGwWCTJKlDxpoGxWCTJKkDxpoGyWCTJKkNY02DZrBJktSCsaY6MNgkSZqHsaa6MNgkSZqDsaY6\nMdgkSZrFWFPdGGySJDUx1lRHBpskSRVjTXVlsEmShLGmejPYJEljz1hT3RlskqSxZqxpGBhskqSx\nZaxpWBhskqSxZKxpmBhskqSxY6xp2BhskqSxYqxpGBlskqSxYaxpWBlskqSxYKxpmBlskqSRZ6xp\n2BlskqSRZqxpFBhskqSRZaxpVBhskqSRZKxplBhsktRjRcHxRUGj+jh+0OMZB8aaRo3BJkk9VBSs\nAbY03bSluk09YqxpFB066AFI0qiqwmwaYIJdrGIzwORmVk0XxTIaDTYOdIAjyFjTqDLYJGkJ2uzi\nXAtlrF3KSSxnJwBnsJ578+XnF8VRF7Z67kaDy7s30tFnrGmUGWyStDTb291hFZv3xRrAcnbyON4X\nZ3F6u8cWSx3cuDDWNOpcwyZJGmrGmsaBM2yStDQrWmzbQrlmjTNYv2+WbQfH8j4el8Aj+jHAUWas\naVwYbJK0BK3WmRUFG4Dp3SzjRLaymk0AbGI1e5h4o2vUlsZY0zgx2CSpRxoNNhblKrS1e5iYPIvT\nAbYBGzxCdGmMNY0bg02SeqiKtgvZf3DCSmfWlsZY0zjyoANJ0tAw1jSunGGTpB6rZtQ8RccSGWsa\nZ86wSZJqz1jTuDPYJEm1ZqxJBpskqcaMNalksEmSaslYk/Yz2CRJtWOsSQcy2CRJtWKsSQcz2CRJ\ntWGsSXMz2CRJtWCsSfMz2CRJA2esSa0ZbJKkgTLWpPYMNknSwBhrUme8lqgk9VgxVRwPbK++XNFY\n17h8kOOpC2NN6pwzbJLUQ8VUsQbY0nTTluq2sWasSQtjsElSj1RhNg1MNt08CUyPc7QZa9LCuUtU\nkpag2t05n7WtthVTxYWtnnsUd50aa9LiGGyStDTb299lTpMdPLZY5HPXkrEmLZ67RCVJPWesSUvj\nDJskLc2KFtu2cOD6tWbbgJXdH079GGvS0hlskrQErdaZFVPFBsqDDuayYRTXqM1mrEnd4S5RSeqR\nxrrGRuBUytm0GduAU6ttI81Yk7rHYJOkHqrCrHnX50pjTdJCGWySpK4y1qTucw2bJPVYtVZtpE7R\nMR9jTeoNZ9gkSV1hrEm9Y7BJkpbMWJN6y2CTJC2JsSb1nsEmSVo0Y03qD4NNkrQoxprUPwabJGnB\njDWpvww2SdKCGGtS/xlskqSOGWvSYBhskqSOGGvS4BhskqS2jDVpsAw2SVJLxpo0eAabJGlexppU\nDwabJGlOxppUHwabJOkgxppULwabJOkAxppUPwabJGkfY02qJ4NNkgQYa1KdGWySJGNNqrlDBz2A\nGRHxKOA1wG2BbwKnZuZlgx2VJI0+Y02qv1rMsEXEScA7gKdl5s2B84D3D3ZUkjT6jDVpONQi2IBT\ngY2Z+YXq6zcCT4iIYoBj0jyKguOLgkb1cfygxyNpcYw1aXj0bZdoRBwCHD7Hpr3AScBHIuJC4O7A\npcBpmdno1/jUmaJgDbC26aYtRcGGRoONgxqTpIUz1qTh0s8ZtlOA3XN8fA2YAJ4FvBA4BvgK8OEq\n8lQTVaxNT7Br8jTO5DTOZIJdk8B0tU3SEKhibRpjTRoafZthy8wLmCcQI+IbwL9l5lerr18GPB8I\n4L/7NcZx18HuzbUT7OJSTmI5OwE4g/WcyFb2MLG2KLiw1YMbDS7v1lglLU4VaxcD96luMtakIVCX\no0QTuHHT1zcAiupD/bO93R1WsXlfrAEsZyer2cRZnD7ZweP9+5QGqIq1LwH3rm7ahrEmDYW6BNs5\nwLsj4j3AVuBVQGbmNwc6KkkaEXPE2k7gJGNNGg61CLbM3BIRpwP/DNyOcg3bIwc7qrG0os32LZtZ\nNXkG6/fNsu3gWDaxGsp/qa/s8fgkLcI8sXanRqNx7eBGJWkhahFsAJn5HuA9gx7HOGu3xqwo2LCb\nZdMnspXVbAJgE6vZwwTABteoSfVjrEmjoTbBpvprNNhYFLCHibXVmjUoZ9Y8rUdNVQeSzKwtXGFU\njxdjTRodBpsWpIq2C9kfASuNAKl+jDVptNTlSgeqeBUBdUt1brwtTTdt8Xx548FYk0aPM2xasGpG\nzVN01FjTSY5ZxWYANrNqcjfLpouinCkd7AjVK8aaNJoMthrxsk/qlCc51lyMNWl0GWw14YyIFsiT\nHOsAxpo02gy2PnFGRFKvGGvS6DPY+scZEXWTJzkWYKxJ48Jgk4aQJzkWGGvSODHY+scZEfWNJzke\nfcaaNF4Mtj5xRkT95kmOR5exJo0fg60mnBFRL3jOvNFjrEnjyWCrEWdEJLVirEnjy0tTSdIQMNak\n8eYMW824C0vSbMaaJGfYJKnGjDVJsIAZtoiYoPwfxlHAXuAq4NLM3NOjsammiqniePavs1vRWNdw\nnZ3UA8aapBktgy0iDgMeDzyH8n8Yvwb2AIcAE0AREf8FnA1szsy9vR2uJI0HY01Ss3l3iUbEg4Ct\nwF8A/wwE8FuZedvMvDVwI+AkYDPwbOBbEXFK74esQSqmijXAlqabtlS3SeoSY03SbK1m2J4LPCYz\nt821sZpN+3r18U8RcQ9gCviPro+yxqqLuu/fPTjCp+Gowmx61s2TwHQxVdBY1/B8cdISGWuS5jJv\nsGXmoxfyRJn5NeCRSx6RBqZam9bK2lbbiqniwlYPdq2b1JqxJmk+Czno4FbANZl5TUTcC3g48JXM\n/FjPRldzRcEaDoyYLUUx1Fcm2N7+LvOa7ODxnq5EmoexJqmVjk7rERGPBL4PnBwRK4CLgCcA74+I\n5/RuePVVxdr0BLsmT+NMTuNMJthV7h4st0lSR4w1Se10OsP2d8DLM/OCiHgNsDMz7xoRK4ENwFt6\nNsIBqdamtbJ2gl1cykksZycAZ7CeE9nKHibWVpeYmldN17qtaLN9C+VM2ly2ASu7Oxxp9BlrkjrR\nabDdifJoUCjflD9Uff514JhuD6om2u4eXMXmfbEGsJydrGYT1cXbh273YLs1ZsVUsYGDDzqYscE1\natLCGGuSOtVpsF0J3DMijgTuAjyzuv3hwPd6MTDVT2NdY2MxVUC5bm9mpm0bZawN67q9keZJjuvL\nWJO0EJ0G2z8A768+vzgz/zMipoC/BU7tycgGr+3uwc2smjyD9ftm2XZwLJtYDSO8e7CKtgvZHwEr\njQBpYYw1SQvVUbBl5lsj4ovAHYBPVDd/FvhUZv5nj8Y2UO3WmBUFG3azbPpEtrKaTQBsYjV7mADY\nsNg1as6IqFuq8+YdeBTzVOFs6IAZa5IWo+PTemTmpRHRAP4sIq4HvjbfSXXHQaPBxqKAPUysrdas\nwczuweE9rUdHqois3Ro87edJjuvJWJO0WB0FW0TcGjgPuB+wm/JaoreIiE8Bj83Mn/VuiPVVRduB\nuweXcPTnUmZExumKC/Ikx8PIWJO0FJ3OsG0ErgNWZOZ3ACLit4FzgDOBJ/VkdEOgCqMlzzY5I6IF\n8iTHQ8RYk7RUnQbbg4GTZ2INIDO/HRGnUZ5EV230dEbkrK8/Ae72xKZbhv2KC9LIMNYkdcNCTutx\ne+CyWbcfAfykqyMaXb2ZEfnyM+DHd2OCXayqTpW3mVWTu1k2XRTlbtslvK7qy5McDwFjTVK3dBps\nrwbOjojlwOcod4/eG3gV8I6IeODMHTPzs10fpeZ3ybMZwSsuqA1Pclx/xpqkbuo02N5Z/TnXJajW\nVR8zOrrWP8IxAAAgAElEQVQ+6Rha/IzIjydh05a5H7XnjqzirJG64oKWzpMcD5axJqnbOj0PmxG2\nREuaEfniWtjTbgmcdCBPcjwYxpqkXpg32CLihpn565nPWz3JzP20ePPOiPzoru/hK2vObfHQsbzi\nglRHxpqkXmk1w/ariLhNZv4I+FWL+zUoz8umJZpzRuSsb1zOWfM/pldXXNBo8CTH/WOsSeqlVsH2\nB8Ceps/n0+jecLRQ43zFBakujDVJvTZvsGXmRU1fPhB4Q2b+X/N9IuLmwBTwmZ6MbgwtZkak21dc\nkNQ5Y01SP7Raw3YCcDRlPLwCyIjYM+tudwNOBZ7XqwFKUl0Za5L6pdUu0WXAJ5q+3jzHfX4B/ENX\nR6RF6dYlsiR1xliT1E/tdoneACAirgDunZle1UDS2DPWJPXbvOdXi4jbz3yemXfoJNYi4g5dGpck\n1ZKxJmkQWu0S/UBEfB54c/NF3+cSEXcDng3cD7hnF8dXe9VF3WcW+6/wxKTS6DLWJA1Kq2A7mfJg\ngosj4ofA+cA3KS/2fgPgVsCJlEeQ3hZ4A/BXPR2tJA2IsSZpkFqtYfsNsD4i3gKsAh4OPBo4CtgL\nXAV8BXg98G+ZeU3vh1svxVSxhvLKBDO2FFOF12qURoyxJmnQ2l5LNDN/SXnx93e2u+84qWJt9rU/\nJ4HpYqrAaJNGg7EmqQ46uvj7OKrWprWyttW26hJT83Ktm1R/xpqkujDY5re9/V3mNdnB4z1nmlRj\nxpqkOpn3tB6SNK6MNUl14wzb/Fa02b6FciZtLtuAld0djqR+MNYk1VHbYIuI36Y8xccxwI2Aa4Af\nAF/IzJFdh9VujVkxVWzg4IMOZmxwjZo0fIw1SXXV6uLvy4B/BR4K7KA8jce1lNF2NHBsRHwUeFJm\nzr4o/MhrrGtsLKYKKA8+mJlp20YZax4hKg0ZY01SnbWaYTsb+C3gDpm5Y/bG6tJV/0o5y/S43gyv\n3qpou5D9BxisdGZNGj7GmqS6axVsDwNOnivWADLzexFxOvC5noxMC+IlsqTFMdYkDYNWwbaLcuH9\nZS3uc2fg510d0ZCpwshTdEhDyFiTNCxaBdurgX+OiN8BPgNcCfyK/WvYHkh57dCX9HqQas1LZGlU\nFAUHzhQ36NlMsbEmaZi0upbodERcSXkB+NOBmzZt/iVwMfAXmXleb4eoVrxElrRwxpqkYdPytB6Z\nuQXYEhE3AI6gjLZrgN2Z2ejD+Mael8jSuCgKDp4pLtjQaNDVf3QYa5KGUavTetwT+FpmXp+Ze4Fd\nEXE48Fzg6Ij4FvD2zPxZn8Y6rrxElkZeFWvTE+xiFZsB2Myqyd0smy4K6Fa0GWuShlWrGbYvA7cB\nfgRQrWX7NPAd4FvAGuCMiPiDzPzvXg9U0vCq1qa1snaCXVzKSSxnJwBnsJ4T2coeJtYWBfPOFHe6\nzs1YkzTMFnJpqtcC78nMUwGq3aRnA28G/rAHY1PJS2RpFLSdKV7F5n2xBrCcnaxmE2dxeruZ4raz\nxMaapGG3kGCbBF4w80Vm7o2INwJf7fqotI+XyJKWxliTNApu0Gb7sqbPvw4cOWv77SjP16YBqY4C\nPZVyNm3GNuBUjxBVjaxo87FtM6vYwbH7HrCDY9nEaih/n1s9dl7GmqRR0WqGbQ/wzYi4GkjgMOCt\nEXHXzPxlRDwDeAXwL70fplrxElmqu3brzIqCDbtZNn0iW1nNJgA2sZo9TABsWMz52Iw1SaOk1XnY\nlkXEbYC7NH3cGfhNdZeXAu8HXt7rQUoabY0GG4sC9jCxtlqzBuXM2qJO62GsSRo17c7DdhVwFeXR\nobO33b5Xg9LCeYksDbsq2g6cKXZmTZKANsEWEYcAfwZ8svl8axGxBvgZ8F5PoCupLow1SaNq3oMO\nIuK3gPOBzcAJszbfC3g38NGIuHHvhidpnDQaXN5oUFQfC5pdM9YkjbJWR4n+DeVRoHfNzM83b6jO\nxXZP4G7Ai3o3PElqz1iTNOpaBdsTgOdlZs61MTO/QXlettW9GJgkdcJYkzQOWgXbbYFvtnn8l6Hp\nxEmS1EfGmqRx0SrYvg/cqc3jjwP+t3vDkaTOGGuSxkmrYPs3YF1E3GiujdXBBq8EPtaLgUnSfIw1\nSeOm1Wk9XgN8EfhKRLyF8n+OVwNHAPcFnlM9fqrXg5SkGcaapHE07wxbdd61k4HPAeuBr1Ce0PIS\nypm1TwH3y8wf9WGckpoUBccXBY3q4/hBj6dfjDVJ46rdlQ5+CjwrItYCd6ScXfsJcHlmXt+H8UkS\nYKxJGm8tg21GZl5LeV0/SQNWFKwB1jbdtKUoFnfNzWFhrEkad/MGW0RsBhq0vz5lIzM9F5vUB1Ws\nTU+wi1VsBmAzqyZ3s2y6KMrrcQ52hN1nrElS6xm2a+kw2Lo3HGm8dbAebe0Eu7iUk1jOTgDOYD0n\nspU9TKytLp4+r8VcTH2QjDVJKs0bbJn5lD6OQx2q3tC3V1+uGLY3YLW1vd0dVrF5X6wBLGcnq9nE\nWZw+2cHj2/0DrDaMNUnar6M1bDMi4h6U1w+9HvhaZrquTVLXGWuSdKCOgi0ibg2cB9wP2A0cAtwi\nIj4FPLY6BYi6oNUM2jguNh9DK9ps37KZVZNnsH7fLNsOjmVTeUnfbcDKHo+vp4qp4nj2sp2jgR/u\nu9lYkzT2Op1h2whcB6zIzO8ARMRvA+cAZwJP6snotM/MYnOApgXnk5tZNV0Uy0Zysfk4areLuyjY\nsJtl0yeyldVsAmATq9nDBMCGod9F/ivgnzHWJGmWToPtwcDJM7EGkJnfjojTgIt6MbBxU82sPQF4\natPNnywK3gWcSzWzNteC83vz5ecXxVEjtdhcc2s02FgUsIeJtdWaNShn1oZ+prV4ebGGT/KmfbG2\ngt/wGF7beI2xJkmdBtuVwO2By2bdPnMiXS3ddjhg9ozNrDp+N8teBbxq5k5zLTh/HO+Lszh9ZBab\nq7Uq2i5k/67zlcMe5MXLizVcwDSXVjfcFfgzDuMQziqmiusa6xpDHaOStFSdBturgbMjYjnlpaqu\no1wM/CrgHRHxwJk7ZuZnuz7KEdDJ5YNanK6h5+OTeqmYKub//f8V8EneNCvWypWypbXFVDHvDHJj\nXWOoY1WSOtFpsL2z+vMtc2xbV33MmPf6pGNuKadr2HfbZlYxz4LzdovVNUKqGbVhmjWd+/d/Lweu\nWTs41gDana5kmH4OkrQonV6aygirid0sY64F58O+S0xjaC/wNtrFmiSJBZ6HTUvSjdM1PAF46h4m\njq9m3S6HfQclSHV24O//r4DXcx7XcUK19TfVmrW5DP3pSiRpqQy2PunS6Rr+vig4l/27hx7qzJqG\nQfM6s6aT4p5Q3bSTx/BaDuGseR6+wXVqksadwVYTo3y6BmnGvFcweE3j2mKquI7y9DUH/v57hKgk\neYBAnVRh1rzrZ+XsWGs0uLzRoKg+nHXQ0Gh3uakqzA78/TfWJAkw2CT1gdcGlaSlcZdozQzh6Rqk\nlhYSa9VaNX//JWkWZ9g0dIqC44uCRvXR9oTEGhxn1iSpOww2ST1hrElS9xhsGipFwRpgS9NNW6rb\nVCPGmiR1l2vYNDSqMJueYBer2AzAZlZN7mbZdFHsO8pWA2asSVL3GWyqjQ7Wo62dYBeXctK+q0Gc\nwXpOZCt7mFhbFMx7gXBof/JiLZ2xJkm9YbCpTlpd4BuAVWzeF2sAy9nJajZRnWy43eM9+rCHjDVJ\n6p1aBFtEfBx4QNNNNwBuApycmV8czKik+iqmiuPZH6grBn3pJmNNknqrFsGWmQ9r/joizgEOMdbG\nzoo227dsZtXkGazfN8u2g2PZxGrwAuEDY6xJUu/VItiaRcQjgT9g//UENSbarTErCjbsZtn0iWxl\nNZsA2MRq9jAB5TVXx2KNWjFVrKG85uaMLcVUMZBrbhprktQffQu2iDgEOHyOTXsz82fVfQ4F3gj8\ndWb+X7/GpuHQaLCxKGAPE2urNWswc4HwMTlCtIq16Vk3TwLTxVRBP6PNWJOk/unnDNspwPlz3H4F\ncMfq88cD12Tm+/s1KA2XKtouZP/6rZWjNLNWrU1rZW2rbcVU0fpI2S6tdTPWJKm/+hZsmXkB7U/U\n+1QYj5kSaR5tj5RtoS9HyhprktR/tVnDFhGHAw8E/nzQY6mzfh8dWJ0bbf/r1WA2qxqDp+gYAGNN\nkgajNsFG+QZwZWZeNeiBDFKrIKvTYnP1TNsjZZn/gJyeHilrrEnS4NQp2G4PXDnoQdTVIBabV5eC\nOjAQi/FZ4D8I7WZMi6liAwf/HszY0KsZV2NNkgaraDQagx7DkkTEHYDvAsdl5hWDHc3iVTNrT6Bc\nxzez8Pxy4F3AuSxxZmWhb+TzXLeT3SwDONVoG5ymmdYDj5Tt0UyrsSZJ3bPYbqnTDNu4m2ux+PHA\nq6qPVha82Nzrdg6vxrrGxupo0P1HyjqzJkkjzWDrkw5O19BvXrdTLRlrklQfBlv/LOV0DZ1ot1hd\nI6SaUetZFBtrklQvBtuIWMQuMa/bqTkZa5JUPwZb/3TjdA2tDkpYEK/bqbkYa5JUTwZbn3TpdA1/\nX0wV57J/9+pDe7XY3Ot2jh9jTZLqq92lotQn1SkZTqWMohnbgFMHdWLcKsyad32uNNZGk7EmSfXm\nDFuNdHK6hl4vNtf4MdYkqf4MNrXkdTtHm7EmScPBYKsZZ9DUL8aaJA0Pg01DpzoJ8cxu4xW9OvBi\nlBlrkjRcPOhAGjPGmiQNH4NNQ6W68PmWppu2VLepA8aaJA0ng01DowqzaQ48wfAkMG20tWesSdLw\ncg2baqNam9bK2lbbqlOizGuc17oZa5I03Aw21cn29neZ12QHjx/Lo2+NNUkafu4SlUaYsSZJo8EZ\nNtXJijbbt3Dg+rVm2zjwMlpjz1iTpNFhsKk22q0xK6aKDZQHHcxlwzivUZvNWJOk0eIuUQ2NxrrG\nRuBUytm0GduAU6ttwliTpFFksGmoVGHWvOtzpbG2n7EmSaPJYJNGhLEmSaPLNWwaOtVatbE8Rcd8\njDVJGm0Gm1ryQuv1Z6xJ0uhzl6hqpyg4vihoVB/trn4w1ow1SRoPBpvm5YXW681Yk6TxYbBpToO6\n0HpRcHAklrepibEmSePFNWxjqo4XWq/CbBpggl2sYjPA5GZWTRfFMhoNPH0HxpokjSODbXz1/ULr\nHaxHWwtlrF3KSSxnJwBnsJ578+XnF8VRLSMRoNFgpA+KMNYkaTwZbOqnjiJxFZv3xRrAcnbyON4X\nZ3F6J48f2dN9GGuSNL4MtvHlhdaHiLEmSePNYBtTA7rQekeRuJlVnMH6fbNsOziW9/G4BB6xiNcc\nesaaJMlg05wa6xobi6kCynVlMzNt2yhjbVGL/9utLysKNgDTu1nGiWxlNZsA2MRq9jDxxlFfnzYX\nY02SBAabWqii7UL2rz1b2csrHTQabCzKFWhr9zAxeRanw0wkjuERosaaJGmGwaZaqaLtwEh0Zg2M\nNUkaawabWvJC6/1nrEmSZjPYVDvVjNpYRqKxJkmai5emkmrCWJMkzcdgk2rAWJMktWKwSQNmrEmS\n2jHYpAEy1iRJnTDYpAEx1iRJnTLYpAEw1iRJC2GwSX1mrEmSFspgk/rIWJMkLYbBJvWJsSZJWiyD\nTeoDY02StBQGm9RjxpokaakMNqmHjDVJUjcYbFKPGGuSpG4x2KQeMNYkSd106KAHIM1WTBXHA9ur\nL1c01jUuH+R4FspYkyR1mzNsUhcZa5KkXjDYVCvFVLEG2NJ005bqttoz1iRJvWKwqTaqMJsGJptu\nngSm6x5txpokqZdcw6a+qdamtbK21bZiqriw3WsMYr2bsSZJ6jWDTf20vf1d5jXZ4eOLJbzGghlr\nkqR+cJeotEjGmiSpX5xhUz+taLN9CweuX2u2DVjZ3eEsnrEmSeong0190259WTFVbKA86GAuG+py\nPjZjTZLUb+4SVW001jU2AqdSzqbN2AacWm0bOGNNkjQIBptqpQqz5l2fK401SdK4M9ikDhhrkqRB\ncg2baqdaq9bX03O0YqxJkgbNGTapBWNNklQHBps0D2NNklQXBps0B2NNklQnBps0i7EmSaobg01q\nYqxJkurIYJMqxpokqa4MNgljTZJUbwabxp6xJkmqO4NNY81YkyQNA4NNY8tYkyQNC4NNY8lYkyQN\nE4NNY8dYkyQNG4NNY8VYkyQNI4NNY8NYkyQNK4NNY8FYkyQNM4NNI89YkyQNO4NNI81YkySNAoNN\nI8tYkySNCoNNI8lYkySNEoNNI8dYkySNGoNNI8VYkySNIoNNI8NYkySNKoNNI8FYkySNMoNNQ89Y\nkySNOoNNQ81YkySNA4NNQ8tYkySNC4NNQ8lYkySNE4NNQ8dYkySNG4NNQ8VYkySNI4NNQ8NYkySN\nK4NNQ8FYkySNM4NNtWesSZLGncGmWjPWJEky2FRjxpokSSWDTbVkrEmStJ/Bptox1iRJOpDBplox\n1iRJOpjBptow1iRJmtuhgx4AQEQcArweeAJwY+Bi4FmZ+d2BDkx9Y6xJkjS/usywPRl4BHAicCtg\nO/D2gY5IfWOsSZLUWl2C7WeUYzkUOATYC1wz0BGpL4w1SZLa69su0Wq35+FzbNqbmR+IiJWUb9bX\nA1cC9+/X2DQYxpokSZ3p5wzbKcDuOT62RsQLgPsCdwJuCXwSeG8fx6Y+M9YkSepc32bYMvMC5gnE\niLgUeG1mXl59/Vzg5xFx18z8Zr/GqP4w1iRJWpi6rGH7FeXRoTP2Vh/XDWY46hVjTZKkhavFaT2A\nc4EXRsQngB8CrwG+npk52GGpm4w1SZIWpy7B9mbKAxIuAm4GfA545CAHpO4y1iRJWrxaBFtmNoBX\nVR8aMcaaJElLU5c1bBpRxpokSUtnsKlnjDVJkrrDYFNPGGuSJHWPwaauM9YkSeoug01dZaxJktR9\nBpu6xliTJKk3DDZ1hbEmSVLvGGxaMmNNkqTeMti0JMaaJEm9Z7Bp0Yw1SZL6w2DTohhrkiT1j8Gm\nBTPWJEnqL4NNC2KsSZLUfwabOmasSZI0GAabOmKsSZI0OAab2jLWJEkaLINNLRlrkiQNnsGmeRlr\nkiTVg8GmORlrkiTVh8GmgxhrkiTVi8GmAxhrkiTVj8GmfYw1SZLqyWATYKxJklRnBpuMNUmSas5g\nG3PGmiRJ9WewjTFjTZKk4WCwjSljTZKk4WGwjSFjTdIoiojlEfHziLjJHNu+FREPWuLzPyUiLlnK\nc0iLdeigB6D+MtYkjarM3AEcPs/mRvUhDSWDbYwYa5K6pSiKGwLH9unldjYajV+3u1NE3AH4DnAz\nYCXw98BRwL8ChzXdbwJ4E/BHwDXA2Zn5umrbMuDNwMnVY7cDz8rML3Tx+5EWzGAbE8aapG6pYi2B\nO/TpJa8oiiI6ibbKCuCdlNH2GeAM4I5N2/8F+DHl+I8CPhIR/5uZ5wDrgb3Anas/NwCvBR649G9D\nWjyDbQwYa5LGzJOAT2TmpwEi4rXA6dXntwH+GDgyM38JfC8iXg+sAc4BXkI567aXMuiuBo7p8/il\ngxhsI85Yk9RtjUbj10VRBDXbJdrkCOAHM19kZiMivld9uRwogMsjYuYuNwB2VZ8fQ7m7dBL4FrC7\nur80UAbbCDPWJPVKFVCXD3oc8/gecK9Zt922+vOHwHXAUZn5G4CIuAXlujeAc4G3ZuY/VtueBJzQ\n8xFLbRhsI8pYkzTGzgPOiIiHA+dT7g5dDpCZOyPic8D6iPgb4KbA+yhn5J5MeZTpNQARMUm5/u2w\ng15B6jPPwzaCjDVJY6xBOfP3OOD1wE+B+wLN509bBdwauAL4NmWsnVZtWwO8MCJ2AW8BXgjcKiKO\nwFODaICKRmO4f/eqw7i/CxyXmVcMdjSDZ6xJklRfi+0WZ9hGiLEmSdJoMthGhLEmSdLoMthGgLEm\nSdJoM9iGnLEmSdLoM9iGmLEmSdJ4MNiGlLEmSdL4MNiGkLEmSdJ4MdiGjLEmSdL4MdiGiLEmSdJ4\n8lqiQ8JYk6TuiYi3Aj/JzJe1ud/fAHfOzCcv4bXuAHwHuFlmXrPY59F4M9iGgLEmaegVxTLKa3gC\nbKbR2DXI4WTmszq832t6PRapEwZbzRlrkoZeGWuXAsdWt5xBUZxIo7G72y8VEQ8BXgPciXJW6yWZ\n+fGI2Av8E7AaWA/cGfhxZr4wIm4LvBP4XSCBzwL3ysxTIuIVwF0z87ERcQ7wM+BE4CTgW8CazLw0\nIm4ATAGPAY6hvOj8qzJzY7e/R40n17DVmLEmaUSsYn+sUX2+utsvEhF3BT4EvAo4AngJ8P6IuFt1\nlxsBRwFnAo3qA+BcYAdwJPBM4MlN25j1+Z8Dp1X33U4ZhwBPBB4FPCgzbw68GNgQETft4reoMeYM\nW00Za5K0YE8ALsjMD1ZffzwiPkwZWQDnZuZ1wC8iAoCIWA48AFiZmb8GvhoRb6OcbZtRNH3+ocz8\nevXY9wJvqG7/IHA+8OOIuB1wLXBjYKLL36PGlDNsNWSsSRoxmyn/PzZjJ7CpB69zJPC9Wbd9j3IX\nJcBVs7YVwNHALzLz6qbbd7R4jZ80fX4d+99Hbwi8pdq+BfiT6nbfZ9UV/iLVjLEmaeSUBxicCDyn\n+ujJ+jXK0Lr9rNvuCPzvzEhmj4zy/7E3i4hbNt1+uznuN9fjm83sGj06M08C1nU0YqlD7hKtEWNN\n0sgqA+3MHr/Ke4GXRMSfAh8B/ghYCTwQeP6s+xYAmXllRFwArI+I51AerPCXwH/Pvi8H7hqd7XDK\n3aDXR8Qy4PXV7YcB1y/6O5IqzrDVhLEmSUuTmZcDjwReDuwBXgesyswvz3H35tmyp1POxP0EeAdw\nAfDrpvs15vh89vO8HFgB7AI+Rbmm7ZvA5ByvJy1Y0WgM9+9QdULC7wLHZeYVgx3N4hhrkjQ4EfFg\n4KLMvL76+nXAMZn5560fKS3cYrvFGbYBM9YkaeDOBJ4eEUVE/DblKUc+MeAxSQcw2AbIWJOkWlgN\nPIXyZLcXAmdn5r8OdETSLB50MCDGmiTVQ2ZeCpw86HFIrTjDNgDGmiRJWgiDrc+MNUmStFAGWx8Z\na5IkaTEMtj4x1iRJ0mIZbH1grEmSpKUw2HrMWJMk9VtE3DQijhr0ONQ9BlsPGWuSBEXBmqJga1Gw\nt/rYWhSs6cdrR8QnIuLJ1ecfi4i/7Mfrdioifj8itrXYvjci7rKIp/4s1XtPRDwxIj6z2DGqHjwP\nW48Ya5JUxhowPevmewDTRQGNBht7PIR91//MzIf3+LXqZBn7L3D/HuA9gx2Olspg6wFjTZL2eXab\nbV0Ntoj4A2AD5cXcPw4c3rTtIuD9mXlWRKwGXgHcCtgO/G1mfioingL8P+Aw4BTgcuCvMvOi6jke\nArwGuBPwHeAlmfnxatvzgLXAb1Fe+P15mfnViLgJ8AbgIcDRwJXACzPzQ9XQDouIs4DHAz8Dnp+Z\nH5zje1tOeRmtk4HdwKsz85w57ncesBx4f0S8CPg5cFpm3iciXgHcDgjgJOAy4NTM/HpE3BA4G1gJ\n/Br4QrVtd9sfvHrOXaJdZqxJ0gHuvshtCxYRRwIfBF4H3Bz4EAdewaABNCLipsC7gMdn5gTwTxwY\njo+sHnsL4M3AhyLiVhFx1+r2VwFHAC+hjKK7RcQK4JXAAzLzVsCngTdWz/cCykC6J2VAvgt4S9Pr\n3ZHyveLWwDOBTRFxp1nf2yHAFuDrwG2AxwB/HxG/P/vnkJmPAnYAj8nMt8zeDjyJMjpvCZwPbImI\nw4C/ACYpY28FZXg+d47HawAMti4y1iRpoP4E+J/MfE9m7q2uB3rxHPdrAL8ETo2I3wX+JTOPa9p+\nSWa+PTOvz8x3AN+tnvsJwAWZ+cHq+T8OfBh4IuWM1A2r5zwReGVm/n71fGcCjwWuAW4P/AI4pun1\nfpCZr61e73zgk5Szbc3uAxwLvDQzr8vMyygj8xkL/zFxXmZ+LDOvo4zMmwH3r34md6K8ruqRwCMy\n8xWLeH71gMHWJcaaJM3pskVuW4yjgR/Muu27s++Umb+k3N15JOVu06uqXYczLp/1kJ2Us1pHAt+b\nte17wO0ycwfwMOBewOeBHdXuVShnst4D/Ah4H2UcFU3PsWPWc36/er1myylnDXdHxJ6I2AP8NXDb\n2d9fB/Z9f5m5F/ghcOvM3AS8lDLYLge+EhH3WcTzqwcMti4w1iRpXv+0yG2L8X3KGaxmt5t9p4i4\nGXCzzHw0MAH8OfCKiLhvdZdjZj3k9pRRtWOO578jZfAtA36RmQ+j3F36YuAdEXE05UEX24AjM/N3\nOPj7PnrW18cBV8y67UrKmbgjZj6q1549E9eJfd9fRBxKGX07I+J44MLMvC9wFOWRpu9exPOrBzzo\nYImMNUmaX6PBxqKcS3o2+9esXQb8Uw+OEN0CvDEinkG5TuyRlLNZb6+2z8xqHQ6cHxF/mpnnR8RV\nlLtJd1XbHxDx/9u78zg7q/qO458QYjCCCCKypmHRL0WWUHFDoEGpZRGqSNmkslSJoFSCiIgoSxEQ\ngYoVRQENKlWaCi9ZyyJFWUQEARH1G9kSZZMsgGxhyfSPcy5cJnNnSWbm3pl836/XvDLPfZb7e+7N\nzP3OOed5jnahdHfuR2ntupRygcKRkv4JuAR4H2WA/lbAesBVkqbYvk3SXEoX41P1+Z6ljJ9bm9IN\n2QhLAJPqBQtnUFrptgamdju3m4CnJR0GnE4JVJcDFwJH9/BaLKCMwevJrpLOonx2fYHS8ncTpcVu\nD0nbA3Nq7XNaHCOGWVrYlkDCWkRE37q6+HZXF5O7ulimfk0eitt52J4P7EAJO49Rxndd3lxK3e4h\nYB/gdEl/pYSeg2zfXbe7ra6fA+wPbGf7cdv3UELgF4H5lIsb9rR9q+2bKd2JF0h6EjgF2M32E8A0\nyhi4ecD5db8ngA1qTbdQPkfmUq5c3cl2o2u3UfMLwI7AFEoX5q3AT6nhrwfnAmdJ+jxNtzaprge+\nBFvuH+oAABSCSURBVDwKvAPYoXaNfrXW8lvgceBdlMAaHWBMV1dX31t1MEmTKGMU1rF9/3A9b8Ja\nRMToU8edfdj2P7S7lqEg6WjKmLvFuVghBsHi5pa0sC2GhLWIiBihxvS9SXSiBLYBSliLiBjVuncf\njjaj/fxGrVx0MAAJaxERo5vtcynjv0Yl28e2u4ZYPGlh66eEtYiIiGiXBLZ+SFiLiIiIdkpg60PC\nWkRERLRbAlsvEtYiIiKiEySwtZCwFhERAyWp+9RVbSVpnb63Gh6dVMtgGc73O1eJ9iBhLSJi8Iw5\ndswB9DQ11dFdgz7bgaSjgMOAp4EzgfVtf2QQj38EINuLzAAg6RTKLTM+I2kicBewap1sflhI+hyw\nge19JO0MfJ4ymwGS7qfM6HDZYhz3TOAh28dK+iYwx/YXJF0LzLB9Rh/7b0aZ3muNunwZcIHts3vb\nb7DU9+MSYBJldoj1KHPI/tH23y3mMV96vwepzF4lsHWTsBYRMXhqWPtWt4c3Bb415tgxDEFo2w84\nxPb0QT5uQ2/3MFuFMt0TtmdT5hAdVrZPbFpcmVf2pC3J/ddeun+b7QN7erwPKwLjGgu2d1iCWhbH\n3wPLAyva7pL0ArCt7WuX4Jgvvd/DIYGtScJaRMSgO6iPdYMW2CSZ0oLyDUlvpczN+RbgX4DbgR/b\n/rykVYA7gSNsnytpY+A/KUHyT8BnbV9ejzkROAd4JzATuKPFcx8K7EWZ4H0i8FngXkpIeDtl7s6Z\nwK7Aw8CRtmfUfacBhwCvobTKTbP9627HPw14je2pdfkGYLbtPevyFcAP6/m/hTJf6TeBcZIetL1G\nPdR7JZ0IrAv8DNjb9mM9nM+mlBbKjSmfi49T5jBF0nTgUduf6bbPtTS1tkn6JPAhYDfKnK7jJT1R\na7ygsa2k9SnzmG5BmaP1TNtfaTrm9ZR5VNcDfg3sY3tWDzWvDJwOvI/awmr7y5L2qecyDnhK0njK\njA+X1qm6TqPMA7sfMIHSEneI7b/W4x5IabVdBfgVZY7aD9L0ftvevXs9gy1j2KqEtYiIIbHJYq4b\nMNsCZgO72j646fFngY8A02o4+yZwXQ1rKwBXAj8CXg8cDPyghgiA/wb+WNd9DNiJHlqUbJ8GnAec\n3uLD+121tpXqc3xP0ob1eY4DtrS9CnANJUB0dwmwLYCk5YGNgK3r8gTg3XUbgC7btwAfB25rCmtj\nah3vASYC69BDoJb0KuCi+rUicAKwfdMmrVrVenzc9qPAdsBc26+1Pa+xbX2uqygTzr8R2AGYKmlq\n0yF2Bz4ArFXP4XM9PDfA94EXKYFwCrC3pH3rzZAbr8UE22Pr9m+zfQrw6Xr8LSmhcAIlwCNpO+D4\nWsNKwC3AD/rxfg+6BDYS1iIiRjvbNwP/AVxGGdN1QF21I/CI7TNtL7T9M0pQ2a8Okn87pcXtudrq\ndTa9z8fZat0jwDG2X7D9v8AVlJan54BXUULKZOA421N62P86YJVa09bA1cBCSaIEsN/YntOthu61\ndAFn2J5re349Rk8XArwbmGD7RNsv2r4auLAf59ibVvtsRQmFR9p+3raBk4F9m2r+ge1Ztp+odbyp\n+0EkrUYJhYfafqa2wJ1CCdl91fyvlNf9AdtPAkdQwt54YE9guu1bbC+khOuDm/YdtrlZl/ou0YS1\niIgh9RtKV2OrdcPpLMqH8VlN3YATgQ0lzW/abiyly2414MlG11h1X318oO6z3dz69CdgNduzJW1P\nGbg+DZgn6Qvdx+DZfl7SlZRWNgH/ByygtCRtDFzczzqaz/N5es4Bq1O7P5vr7+fxB2IM8AbggRqG\nGmZTWtMamseJvUDPjU0T6/HuKRkW6nZz+1HHREqL54tNjz1XH1+V0p0OgO2nKd2yw26pbmFLWIuI\nGHLfWMx1Q+EM4MfAnpLeVR97EPiF7ZUaX5RANK2uW17SSk3HWIvetRqAv0a35UnAbEmvp4TC7Sld\nbkcA59QWo+4upQS2KZTAdg2ldW07Xu4OHYhWtT4ArCmpOSM0n3er/V4Exjctv74fzz8bWEPS2KbH\n16GM8xuIhyhhbtWm93EipQWvLw8COzfttwqlu/4eymvx0rlLWkHSyZLGUQLiklzIMSBLbWBLWIuI\nGHr1KtCplMH6jTFOdwBTh+K2Hq1I+hhl3Nd+lG6t6ZJeTeki3UDSHpLGStqQMk7pA7Vb7VrgVEnL\nSdoI+CitP6QXULr3ejJR0qckLStpR2Abyri59YCrJG1m+zlKi9AzwFM9HOMySmBbw/ZdlMD2fmCs\n7Ttb1NPblaqtuvOuB+YAx0h6laStKBcP9LRf8/czge0kjZe0LuW2GY3XagGwXA06zW6mdBcfX59r\nA8oA//Oajt9nt6PtP1G6jU+u79XKlHB+Ql/7AufWc12t1ncCpcuaWsdHJE2WtCxwJPBO288Dz9L6\n/R50S2VgS1iLiBg+XUd3fbvr6K7JXUd3LVO/Jg9TWGsMbJ9IGc90kO2nKGPZ/gqcUAfAbwccSAkp\nV1DGeX23HmMPSkvRXygXIFxIazOAXesVm90H4P8ZmFyPcyKwi+1769i6o4ALJD1Z69ytWzcsALb/\nAtxNCVTYvpfSXXhp93Ou318LIGm+pOVavT49PM+LlLF9WwPzak0XdNuvp+9PonSxPkJ5raY3rbuD\ncgXsXEnrNT3XC5QLOTahtKpdDZxt+6stauztNiJ7Ui5cuJ8SHh8APtHLcRpOpIS9myiv5+bAjnVM\n4/8BhwPnU/5/bFyfB175fg+5MV1dw9aaNyQkTaL0ra9j+/6+tk9Yi4iI4SRpCmXc3CKD5WPpM9Dc\n0rBUtbAlrEVERMRItNQEtoS1iIhoo5HdnRVtt1Tc1iNhLSIi2qVOf/TmdtcRI9uob2FLWIuIiIiR\nblQHtoS1iIiIGA1GbWBLWIuIiIjRYlQGtoS1iIiIGE1GXWBLWIuIiIjRpiOuEq3TPRwD7AssR7mT\n9CH1jtT9lrAWERERo1GntLAdCuxFmcR2IrA88J2BHGDhwoWQsBYRERGjUKcEtl2Ak2zPtP00ZXLV\nXSS9tr8HmDVr1k9IWIuIiIhRaNi6RCWNBVboYdVCYCzwTNNjXfWxdYHb+3P8rq6uTeq3CWsREREx\nqgznGLZtgCt7eHwWpfvzMEnXAXOA4yhBbrkBPkfCWkRERIw6wxbYbF9Niy5YSeOAFYHrgaeBk4Hd\ngMf6ceixAOPGjXtkzTXX3Hb8+PGrSxqcoiMiIiIG11r137ED2akjrhIF1gROsX0YgKS3As8DM/ux\n7+oAa6+99hsBD1mFEREREYNndeCe/m7cKYFtb2CKpJ0p49xOBc62vbAf+/4K2Ap4CHhx6EqMiIiI\nWGJjKWHtVwPZqVMC21eA9YDZlLFr5wGf6c+OthdQulIjIiIiRoJ+t6w1jOnq6hqKQiIiIiJikHTK\nfdgiIiIiooUEtoiIiIgOl8AWERER0eES2CIiIiI6XAJbRERERIfrlNt6LBFJywLHAPtSprO6EDjE\n9lNtLCv6qc4zewqwB+X9+yVwoO372lpY9EnS5cCWTQ8tA7wa2ML2Te2pKgZC0geBE4E1gLuAqbZ/\n096qoj8k/RZYh3I7LID7bW/cxpJiMUjaH/iy7Tf0tt2oCGzAocBewHuAPwPnUOYn3b2dRUW/7QPs\nCEymzCV7OnA28N52FhV9s71987Kk6cDYhLWRQdJmlN+X77d9o6TDgRlA5vfrcJJeTXmfVrU9v931\nxOKRtC5wGvBcX9uOli7RXYCTbM+0/TRwJLCLpNe2ua7onyco/xeXpdwBeiFlTtkYQSR9gPJH08fb\nXUv021Tg27ZvrMunAXtIGtPGmqJ/NgYeTlgbuWrv0veAM4E+f+ZGTAtbPbEVeli1kPIh/0zTY131\nsXWB24e+uuhLb++f7f+RtBPwJ8r0Yg8C7x7O+qK1Pt67J+o2y1I+7D+doQidpY/fnZsBl0j6KbAJ\ncBvwCdu5o3oH6Md797ykG4H1Ke/dp2z/YRhLjF7043fnEcCdwOXAv/Z1vJHUwrYNMK+HrzuAi4DD\nJE2StDxwHOU/9HJtqjUW1er9u13SYcA7gDcBrwOuAM5vU52xqJbvXdM2uwNP254x/OVFH3r73bky\ncCBlKsA1gVuBi+oHTbRfbz97XcDNlLG/E4FbgMsk5XOvc/T2ufdW4MPAp+lH6xqMkqmpJI2jDJrd\ng9KVdjLwdWBy/trofJJuA063Pb0uLwf8lfL+3dXO2qJ/JF0NXGT7a+2uJfqvDlq/xPYRdXlZ4Clg\nM9u/a2txMWCSHgP+0fYv211LtFY/424BDqhjR6cAM/q66GAktbD1Zk3gFNtr2X4zpWn4eWBme8uK\nfnqWV7aGLqxfL7SnnBgISSsAWwP/3e5aYsDMK3/2lqH8tZ8xbB1O0lRJ721aXhYYR/l9Gp3tbZSr\ney+VNB+4GFhZ0jxJa7XaacSMYevD3sAUSTtT+otPBc62vbD33aJD/Aj4jKT/BR6itJbeadvtLSv6\naXPgQdsPt7uQGLDpwPcknUfpZjsecFq2R4RVgYMlbQfMBb4M/N72He0tK/pi+zrgNY1lSX8P/M/S\n0sL2FcqA9dmUAXy3UcZkxMjwNeC7wLXAA5S/PD7QzoJiQP6GcqFIjDC2LwY+CZxL+dB/G/nZGylO\noAxWvxl4BJgE/FM7C4rFNoYyJrH3jUbDGLaIiIiI0Wy0tLBFREREjFoJbBEREREdLoEtIiIiosMl\nsEVERER0uAS2iIiIiA6XwBYRERHR4RLYIiIiIjrcaJnpICJGCEnTgfG292x67LXA54APAWtRbsT7\nI+BE2081bTcXWKnbITe3/eu6fipwJPB6yk1FP257bi+1jANuBHa1PWvJz25o1LkG59q+s35/DbCc\n7ef62O/HwNds/2zoq4yIoZQWtogYbl003dVb0uuAm4AtgYOAvwX+Dfhn4CJJY+t2q1HC2luA1Zq+\n7qjrdwJOAaYBWwBvBH7QRy3TgBs6OaxV1wCr1+9vAFbrK6xVRwHfqME0IkawtLBFxHDrPrn4icBC\nYFvbC+pjsyTdA9wF7ALMADYEHrf9+xbHnQacYfsCAEl7A/dLerPtmd03lvRqyhR27xiEcxoOYwBs\nPw/8pT872P69pD8Du9N3eI2IDpbAFhGDStJCYH9K1+QawE+BA2w/0sO244G9gMObwhpQZiCvkyLf\nWR/aEHCL51wGeDtlXuHG/rMlzaa0ti0S2IA9gYds39t0nB2AYymteC8C1wMftf1AXT8FOAnYGPgz\ncJzt8+q6NwGnUVoKnwN+CHzW9oKeujElnQS8w/Y2kpalzKn7IWB5SovjwbZ/J+n+Wt7lko4Bft58\nLEkT677vAZ6izAv6OduNVsyfAAeTwBYxoqVLNCKGwpeAT1PC0krAhS22WxdYgTKB9SJs32D7ibq4\nITBO0pWSHpJ0jaS313UrARNYdBL6h4E1Wzz3DsCVjQVJ69Q6zwU2ALav9X2xrhdwBSWAbkppGfyO\npLdJWpkS7h6r57wXsDMlwPWmEao+WZ9vR2AjykTsjYC1ef13T+DU5p1r4L2K8sf3FpSWtI9QXvuG\nK4HNa40RMUKlhS0ihsIJti8GkLQvcLekTW3f0W27xgUEj/fjmBvU7Y8EHgWmAtdI2ojSGgbwbLd9\nFgDjWxzvrcClTctjgU/ZPrMuz5Y0A5hSlz8K3Gb783X57jr+bjzwYeAFYP/aZfl7SQcBF0s6sh/n\ntg7wDDDL9qOSPgEIwPackhWZb/up+n3DtsDawDttzweQ9HFgxaZt7qW0+G1OU0CNiJElgS0ihsJ1\njW9s3ytpHqXlqHtgm1P/7X7lZ0/eB4yz/UxdnirpXcB+lC5BWDScjQeebnG8VZueH9t3S3pG0mdr\nrX8LbALcUjfZEPhV8wFsfxVA0l7A7TWsNdxICYGvSFjdNMbynQnsBjwo6UZKN+Z3etmvse+GwL2N\nsFZruqhbjQslza/nGxEjVLpEI2IovNBteSwvt4I1uweYR4uB/5K+JekAANsvNIW1hj9Qrp6cR2mh\nWr3b+tWBB1rUuJCm34GSNq7H+zvqGDLKVacNC3jlxRLNnulh3dimf7tY1Et/MNcLKSYBu9YaDgdu\nlvSaFs9HPWZ/rhRt1LCwn9tGRAdKYIuIodAYd4WkN1O66Lq3rmH7ReC/gIMlLde8rnZ17gc8UZdn\nSfpY0/plKC1gf6gD7H8JbN20/m8o3YU3tqjxYeANTcsHADfZ3t32GbZ/AazPy0FsJrBZtxr/S9IX\nKCFrsqRXNa3eghKS/sjLwaq5q3JdapCr3Zi72v6J7amUMXLrU8Jjb2YC60h66biSPiHpiqblZYCV\n6/lGxAiVLtGIGArH19tJzAfOAK7q5XYcx1IG3P9U0heB+yiB7xTgauD8ut2FwDGS7qNcoXko8Drg\n7Lr+P4HvS/oNJUB9HbjU9j0tnvdWSjBqeAD4UO1m/QuwB/B+Xr4y9ZvApyQdRbmp79aUW45sCfwO\nOJpyEcKXKBc6fB04v45Be47SCneUpK9Sxp5ty8vdrSsD/y7pUUoI24vSlfu7uv5JYCNJN3U7hyvq\n63VOfe1Wo9yAuLll8C2U0Hlbi9chIkaAtLBFxFA4BzgLuBa4m3IT3IZX3Di3zkTwbuB2Svj6LfDv\n9Ri7NN2e4nDg+8B3gV9TWqje07iK1PaFlAsSTqOMoXuIcsVkK5fS1CJHGQf3c8oMCb+khK7dgDdJ\nmlBvrrsz5dYbd1IC4162b7H9NPCPlMB0a61zBqWFkFrj/sBOlHvLbUe5PUjDyU3n9gfgg8BOTbM0\n/AdwPCXcvvT62V5Ya5pAGV/3PeCsxti6aivgF83j3CJi5BnT1dXT0IqIiMVT78M2xfbP211LbyRN\nAGYB29j+bbvrGSqSbgC+0bhfXESMTGlhi4ilUm0VO5UyHdaoJGlTyji9H7a7lohYMglsEbE0OxV4\np6RJ7S5kiBwLTK1dpxExgqVLNCIiIqLDpYUtIiIiosMlsEVERER0uAS2iIiIiA6XwBYRERHR4RLY\nIiIiIjpcAltEREREh/t/QomuHWNZG8cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cd57a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 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='o');\n",
    "errorbar(echo_pIC50s, genesis_pIC50s, fmt='ro', markersize=5, zorder=5);\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, markersize=8, fmt='bo');\n",
    "errorbar(echo_pIC50s - echo_bias_interpolation(echo_pIC50s), genesis_pIC50s - dilute_genesis_bias_interpolation(genesis_pIC50s), xerr=2*echo_pIC50_err, yerr=2*dilute_genesis_pIC50_err, markersize=8, fmt='go');\n",
    "plot([-9, -6], [-9, -6], 'k-');\n",
    "xlabel('pIC50 (acoustic)');\n",
    "ylabel('pIC50 (tips)');\n",
    "legend(['ideal', 'original', 'disposable tips','fixed tips with dilution effect'], loc='lower right');\n",
    "title('95% confidence intervals shown');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.56162824385\n"
     ]
    }
   ],
   "source": [
    "def rmse(tips,acoustic):\n",
    "    return np.sqrt(((tips - acoustic) ** 2).mean())\n",
    "\n",
    "rootmeansquareerror = rmse(genesis_pIC50s,echo_pIC50s)\n",
    "print rootmeansquareerror"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.56468259099\n"
     ]
    }
   ],
   "source": [
    "rootmeansquareerror_withbias = rmse(genesis_pIC50s - genesis_bias_interpolation(genesis_pIC50s),echo_pIC50s - echo_bias_interpolation(echo_pIC50s))\n",
    "print rootmeansquareerror_withbias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.37475877374\n"
     ]
    }
   ],
   "source": [
    "rootmeansquareerror_withbias_withdilution = rmse(genesis_pIC50s - dilute_genesis_bias_interpolation(genesis_pIC50s),echo_pIC50s - echo_bias_interpolation(echo_pIC50s))\n",
    "print rootmeansquareerror_withbias_withdilution"
   ]
  }
 ],
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