{ "cells": [ { "cell_type": "markdown", "id": "9995f4b2-2eb3-4af2-a73e-17e60dd97366", "metadata": {}, "source": [ "# Analysis of growth data in the efflux experiment\n", "\n", "(c) 2024 Justin Bois. This work is licensed under a [Creative Commons Attribution License CC-BY 4.0](https://creativecommons.org/licenses/by/4.0/). All code contained herein is licensed under an [MIT license](https://opensource.org/licenses/MIT).\n", "\n", "This document was prepared at [Caltech](http://www.caltech.edu) with support financial support from the [Donna and Benjamin M. Rosen Bioengineering Center](http://rosen.caltech.edu).\n", "\n", "\n", "\n", "*This tutorial was generated from an Jupyter notebook. You can download the notebook [here](efflux_analysis.ipynb).*\n", "\n", "
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\n", "\n", "In this tutorial, we will explore how to analyze the data from the efflux pump experiment. We will then develop some tools for parsing the data set and obtaining growth rates from the curves. Then, we will learn how to compute the growth rate for a given set of parameters and antibiotic concentration. This is necessary to be able to perform a regression to obtain an estimate the parameter $q_{\\mathrm{ex}, 0}^\\mathrm{max}$ for each strain." ] }, { "cell_type": "markdown", "id": "974da43e-1c90-4034-b4cc-4a6efd4e4a75", "metadata": {}, "source": [ "## Data wrangling\n", "\n", "The data will again come from our plate reader in the same format as for the E. coli growth experiment. You can use the parser from that module to load in the data into a data frame. Remember that you need to specify the filename, header row, and last row of the data to do so. Here is that parser for convenience." ] }, { "cell_type": "code", "execution_count": 2, "id": "3f04c235-372b-4ef8-bc30-3fc7a9a097e6", "metadata": {}, "outputs": [], "source": [ "def read_plate_reader(fname, header_row, last_row):\n", " \"\"\"Read in time series data from Bi 1x plate reader.\n", "\n", " Parameters\n", " ----------\n", " fname : str\n", " Path to file outputted from plate reader.\n", " header_row : int\n", " Number of row containing header column (zero-indexed)\n", " last_row : int\n", " Last row of the file containing the time series data (zero-indexed)\n", "\n", " Returns\n", " -------\n", " output : DataFrame\n", " Pandas DataFrame containing time series data.\n", " \"\"\"\n", " # Find out how many rows in input file\n", " with open(fname, \"rb\") as fp:\n", " n_rows = len(fp.readlines())\n", " \n", " # How many lines in footer to skip\n", " skipfooter = n_rows - last_row - 1\n", "\n", " # Read in data frame\n", " df = pd.read_csv(\n", " fname,\n", " sep=\"\\t\",\n", " skiprows=header_row,\n", " skipfooter=skipfooter,\n", " engine=\"python\",\n", " encoding='ISO-8859-1',\n", " )\n", "\n", " # Rename temperature column\n", " df = df.rename(columns={df.columns[df.columns.str.contains('T°')][0]: 'temperature (deg C)'})\n", "\n", " # Parse the time column\n", " df['time (s)'] = pd.to_timedelta(df['Time']).dt.total_seconds()\n", "\n", " # Set start time to zero\n", " df['time (s)'] -= df['time (s)'].min()\n", "\n", " # Time in units of hours\n", " df['time (hr)'] = df['time (s)'] / 3600\n", "\n", " return df" ] }, { "cell_type": "markdown", "id": "4e2cd21b-3793-44df-b918-75e2dec0c889", "metadata": {}, "source": [ "### Well metadata\n", "\n", "In this experiment, we will have two data sets to load in, one from Group A, and one from Group B. You will perform regressions to get growth rates on each data set separately. That is, you will determine $\\lambda_0$ and $\\lambda$ for each time course, reporting relative growth rate and $\\lambda/\\lambda_0$, where the $\\lambda_0$ is determined from the data set from the same plate. That is, you should have a $\\lambda_0$ for Group A and a separate $\\lambda_0$ for Group B.\n", "\n", "For this demonstration, we will work with one data set from a dry run from this experiment in the file `20240527_tet_test.txt`. The analysis is analogous for a second data set. As in the *E. coli* growth module, we need to specify the header row and the last row of data." ] }, { "cell_type": "code", "execution_count": 3, "id": "8a3abe36-0354-451e-b028-cbaaf7cedf74", "metadata": {}, "outputs": [], "source": [ "# This is a dry run of this experiment\n", "fname_A = '20240527_tet_test.txt'\n", "header_row_A = 53\n", "last_row_A = 223\n", "\n", "# Load in the data frame for \"Group A\" (which is just the dry run in this case)\n", "dfA = read_plate_reader(fname_A, header_row_A, last_row_A)" ] }, { "cell_type": "markdown", "id": "43fe6b16-af41-45d9-9326-4f8b14616545", "metadata": {}, "source": [ "It is also useful to have a dictionary with the metadata for each well in the plates, in this case the strain and tetracycline concentration. We have two dictionaries, one for the plate from Group A and one from Group B. Below are dictionaries for the metadata for this experiment. The abbreviated strain is followed by the tetracycline concentration in µM, separated by a dash. Blank wells are labeled as \"blank.\"" ] }, { "cell_type": "code", "execution_count": 4, "id": "355ffb3b-76ba-4c21-8f72-90f8c209630b", "metadata": {}, "outputs": [], "source": [ "well_metadata_A = dict(\n", " A1=\"MG-0.0\",\n", " A2=\"WT-0.21\",\n", " A3=\"MG-0.0\",\n", " A4=\"WT-0.90\",\n", " A5=\"MG-0.0\",\n", " A6=\"WT-3.90\",\n", " A7=\"MG-0.0\",\n", " A8=\"WT-16.90\",\n", " A9=\"MG-0.0\",\n", " A10=\"WT-73.15\",\n", " A11=\"MG-0.0\",\n", " A12=\"WT-208.33\",\n", " B1=\"3.19-0.0\",\n", " B2=\"UV5-0.21\",\n", " B3=\"3.19-0.0\",\n", " B4=\"UV5-0.90\",\n", " B5=\"3.19-0.0\",\n", " B6=\"UV5-3.90\",\n", " B7=\"3.19-0.0\",\n", " B8=\"UV5-16.90\",\n", " B9=\"3.19-0.0\",\n", " B10=\"UV5-73.15\",\n", " B11=\"3.19-0.0\",\n", " B12=\"UV5-208.33\",\n", " C1=\"IW-0.0\",\n", " C2=\"MG-0.21\",\n", " C3=\"IW-0.0\",\n", " C4=\"MG-0.90\",\n", " C5=\"IW-0.0\",\n", " C6=\"MG-3.90\",\n", " C7=\"IW-0.0\",\n", " C8=\"MG-16.90\",\n", " C9=\"IW-0.0\",\n", " C10=\"MG-73.15\",\n", " C11=\"IW-0.0\",\n", " C12=\"MG-208.33\",\n", " D1=\"WT-0.0\",\n", " D2=\"3.19-0.21\",\n", " D3=\"WT-0.0\",\n", " D4=\"3.19-0.90\",\n", " D5=\"WT-0.0\",\n", " D6=\"3.19-3.90\",\n", " D7=\"WT-0.0\",\n", " D8=\"3.19-16.90\",\n", " D9=\"WT-0.0\",\n", " D10=\"3.19-73.15\",\n", " D11=\"WT-0.0\",\n", " D12=\"3.19-208.33\",\n", " E1=\"UV5-0.0\",\n", " E2=\"IW-0.21\",\n", " E3=\"UV5-0.0\",\n", " E4=\"IW-0.90\",\n", " E5=\"UV5-0.0\",\n", " E6=\"IW-3.90\",\n", " E7=\"UV5-0.0\",\n", " E8=\"IW-16.90\",\n", " E9=\"UV5-0.0\",\n", " E10=\"IW-73.15\",\n", " E11=\"UV5-0.0\",\n", " E12=\"IW-208.33\",\n", " F1=\"MG-0.21\",\n", " F2=\"WT-0.21\",\n", " F3=\"MG-0.90\",\n", " F4=\"WT-0.90\",\n", " F5=\"MG-3.90\",\n", " F6=\"WT-3.90\",\n", " F7=\"MG-16.90\",\n", " F8=\"WT-16.90\",\n", " F9=\"MG-73.15\",\n", " F10=\"WT-73.15\",\n", " F11=\"MG-208.33\",\n", " F12=\"WT-208.33\",\n", " G1=\"3.19-0.21\",\n", " G2=\"UV5-0.21\",\n", " G3=\"3.19-0.90\",\n", " G4=\"UV5-0.90\",\n", " G5=\"3.19-3.90\",\n", " G6=\"UV5-3.90\",\n", " G7=\"3.19-16.90\",\n", " G8=\"UV5-16.90\",\n", " G9=\"3.19-73.15\",\n", " G10=\"UV5-73.15\",\n", " G11=\"3.19-208.33\",\n", " G12=\"UV5-208.33\",\n", " H1=\"IW-0.21\",\n", " H2=\"blank\",\n", " H3=\"IW-0.90\",\n", " H4=\"blank\",\n", " H5=\"IW-3.90\",\n", " H6=\"blank\",\n", " H7=\"IW-16.90\",\n", " H8=\"blank\",\n", " H9=\"IW-73.15\",\n", " H10=\"blank\",\n", " H11=\"IW-208.33\",\n", " H12=\"blank\",\n", ")\n", "\n", "well_metadata_B = dict(\n", " A1=\"MG-0.0\",\n", " A2=\"WT-0.44\",\n", " A3=\"MG-0.0\",\n", " A4=\"WT-1.88\",\n", " A5=\"MG-0.0\",\n", " A6=\"WT-8.13\",\n", " A7=\"MG-0.0\",\n", " A8=\"WT-35.17\",\n", " A9=\"MG-0.0\",\n", " A10=\"WT-152.19\",\n", " A11=\"MG-0.0\",\n", " A12=\"WT-312.50\",\n", " B1=\"3.19-0.0\",\n", " B2=\"UV5-0.44\",\n", " B3=\"3.19-0.0\",\n", " B4=\"UV5-1.88\",\n", " B5=\"3.19-0.0\",\n", " B6=\"UV5-8.13\",\n", " B7=\"3.19-0.0\",\n", " B8=\"UV5-35.17\",\n", " B9=\"3.19-0.0\",\n", " B10=\"UV5-152.19\",\n", " B11=\"3.19-0.0\",\n", " B12=\"UV5-312.50\",\n", " C1=\"IW-0.0\",\n", " C2=\"MG-0.44\",\n", " C3=\"IW-0.0\",\n", " C4=\"MG-1.88\",\n", " C5=\"IW-0.0\",\n", " C6=\"MG-8.13\",\n", " C7=\"IW-0.0\",\n", " C8=\"MG-35.17\",\n", " C9=\"IW-0.0\",\n", " C10=\"MG-152.19\",\n", " C11=\"IW-0.0\",\n", " C12=\"MG-312.50\",\n", " D1=\"WT-0.0\",\n", " D2=\"3.19-0.44\",\n", " D3=\"WT-0.0\",\n", " D4=\"3.19-1.88\",\n", " D5=\"WT-0.0\",\n", " D6=\"3.19-8.13\",\n", " D7=\"WT-0.0\",\n", " D8=\"3.19-35.17\",\n", " D9=\"WT-0.0\",\n", " D10=\"3.19-152.19\",\n", " D11=\"WT-0.0\",\n", " D12=\"3.19-312.50\",\n", " E1=\"UV5-0.0\",\n", " E2=\"IW-0.44\",\n", " E3=\"UV5-0.0\",\n", " E4=\"IW-1.88\",\n", " E5=\"UV5-0.0\",\n", " E6=\"IW-8.13\",\n", " E7=\"UV5-0.0\",\n", " E8=\"IW-35.17\",\n", " E9=\"UV5-0.0\",\n", " E10=\"IW-152.19\",\n", " E11=\"UV5-0.0\",\n", " E12=\"IW-312.50\",\n", " F1=\"MG-0.44\",\n", " F2=\"WT-0.44\",\n", " F3=\"MG-1.88\",\n", " F4=\"WT-1.88\",\n", " F5=\"MG-8.13\",\n", " F6=\"WT-8.13\",\n", " F7=\"MG-35.17\",\n", " F8=\"WT-35.17\",\n", " F9=\"MG-152.19\",\n", " F10=\"WT-152.19\",\n", " F11=\"MG-312.50\",\n", " F12=\"WT-312.50\",\n", " G1=\"3.19-0.44\",\n", " G2=\"UV5-0.44\",\n", " G3=\"3.19-1.88\",\n", " G4=\"UV5-1.88\",\n", " G5=\"3.19-8.13\",\n", " G6=\"UV5-8.13\",\n", " G7=\"3.19-35.17\",\n", " G8=\"UV5-35.17\",\n", " G9=\"3.19-152.19\",\n", " G10=\"UV5-152.19\",\n", " G11=\"3.19-312.50\",\n", " G12=\"UV5-312.50\",\n", " H1=\"IW-0.44\",\n", " H2=\"blank\",\n", " H3=\"IW-1.88\",\n", " H4=\"blank\",\n", " H5=\"IW-8.13\",\n", " H6=\"blank\",\n", " H7=\"IW-35.17\",\n", " H8=\"blank\",\n", " H9=\"IW-152.19\",\n", " H10=\"blank\",\n", " H11=\"IW-312.50\",\n", " H12=\"blank\",\n", ")" ] }, { "cell_type": "markdown", "id": "c3128eab-ccee-4504-bf63-b59c05777fa9", "metadata": {}, "source": [ "### Tidy data\n", "\n", "To more easily work with this data set, we will put it in **tidy format**, where each row in the data frame is a single absorbance measurement and each column is a property associated with that measurement, such as time, time stamp, temperature, well, well metadata, and, of course absorbance. The function below converts the data to tidy format given the well metadata." ] }, { "cell_type": "code", "execution_count": 5, "id": "ee11d66d-1739-40db-bc0d-6db786c95572", "metadata": {}, "outputs": [], "source": [ "def conc(well, well_metadata):\n", " \"\"\"Return abx concentration for a given well\"\"\"\n", " strain_conc = well_metadata[well]\n", " if strain_conc == \"blank\":\n", " return 0.0\n", " else:\n", " ind = strain_conc.find(\"-\")\n", " return float(strain_conc[ind + 1 :])\n", "\n", "\n", "def strain(well, well_metadata):\n", " \"\"\"Return strain for a given well\"\"\"\n", " strain_conc = well_metadata[well]\n", " if strain_conc == \"blank\":\n", " return \"blank\"\n", " else:\n", " ind = strain_conc.find(\"-\")\n", " return strain_conc[:ind]\n", "\n", "\n", "def tidy(df, well_metadata, group):\n", " \"\"\"Convert data frame to tidy format.\"\"\"\n", " # Convert to tall format\n", " df_tidy = df.melt(\n", " id_vars=[\"Time\", \"temperature (deg C)\", \"time (s)\", \"time (hr)\"],\n", " var_name=\"well\",\n", " value_name=\"absorbance\",\n", " )\n", "\n", " # Add metadata columns\n", " df_tidy[\"conc\"] = df_tidy[\"well\"].apply(conc, args=(well_metadata,))\n", " df_tidy[\"strain\"] = df_tidy[\"well\"].apply(strain, args=(well_metadata,))\n", " df_tidy[\"group\"] = group\n", "\n", " df_tidy = df_tidy.sort_values(\n", " by=[\"group\", \"strain\", \"conc\", \"well\", \"time (hr)\"], ignore_index=True\n", " )\n", "\n", " return df_tidy" ] }, { "cell_type": "markdown", "id": "e283c95f-dc48-4cd9-bf87-f2a1512d1b8e", "metadata": {}, "source": [ "We can put it to use to tidy our data frame." ] }, { "cell_type": "code", "execution_count": 6, "id": "348715ab-915c-4a4e-ba85-9bd82b9cf002", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Timetemperature (deg C)time (s)time (hr)wellabsorbanceconcstraingroup
00:05:1037.00.00.0B10.0850.03.19A
10:11:1037.1360.00.1B10.0850.03.19A
20:17:1037.1720.00.2B10.0850.03.19A
30:23:1037.01080.00.3B10.0850.03.19A
40:29:1037.01440.00.4B10.0850.03.19A
\n", "
" ], "text/plain": [ " Time temperature (deg C) time (s) time (hr) well absorbance conc \\\n", "0 0:05:10 37.0 0.0 0.0 B1 0.085 0.0 \n", "1 0:11:10 37.1 360.0 0.1 B1 0.085 0.0 \n", "2 0:17:10 37.1 720.0 0.2 B1 0.085 0.0 \n", "3 0:23:10 37.0 1080.0 0.3 B1 0.085 0.0 \n", "4 0:29:10 37.0 1440.0 0.4 B1 0.085 0.0 \n", "\n", " strain group \n", "0 3.19 A \n", "1 3.19 A \n", "2 3.19 A \n", "3 3.19 A \n", "4 3.19 A " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dfA = tidy(dfA, well_metadata_A, \"A\")\n", "\n", "# Take a look\n", "dfA.head()" ] }, { "cell_type": "markdown", "id": "111542c7-e693-4dc9-a6aa-e8c4360a78dd", "metadata": {}, "source": [ "For simplicity, I have labeled the antibiotic concentration column `\"conc\"`, but recall that the concentration is in units of µM." ] }, { "cell_type": "markdown", "id": "31e6b6b9-e79e-4196-82f4-6aa74c528504", "metadata": {}, "source": [ "### Checking the blanks\n", "\n", "As before, we can check the blanks. To do this, we first pull out the part of the data frame that contains blanks. We then use Pandas's convenient **groupby** operation to group the data frame by well. We can iterate over the `GroupBy` object with a `for` loop, which gives us a group name (which will be the well in this case) and a sub-data frame that has just the data for that well. We can then add the trace of that blank to the plot." ] }, { "cell_type": "code", "execution_count": 7, "id": "d9955e6b-d358-4b9a-b3b4-273e7703f9c1", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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We can therefore define our blank concentration to be the average of all blank measurement." ] }, { "cell_type": "code", "execution_count": 8, "id": "1c82f536-2e72-48fc-8d44-cf7ac69387cd", "metadata": {}, "outputs": [], "source": [ "blank_absorbance = dfA_blank['absorbance'].mean()" ] }, { "cell_type": "markdown", "id": "2cef47cd-9f05-4724-b985-65759be8cb67", "metadata": {}, "source": [ "We can now add a column to the data frame for the OD600, which is the background substracted absorbance." ] }, { "cell_type": "code", "execution_count": 9, "id": "c5c7f0f6-c88f-49a9-85ad-639307daedcc", "metadata": {}, "outputs": [], "source": [ "dfA['OD600'] = dfA['absorbance'] - blank_absorbance" ] }, { "cell_type": "markdown", "id": "6727fba6-39bc-44f2-b598-249b34f3d86a", "metadata": {}, "source": [ "### Make plots\n", "\n", "We can now use this kind of groupby structure to make all kinds of plots. 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Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1099" } }, "output_type": "display_data" } ], "source": [ "p = bokeh.plotting.figure(\n", " frame_width=350,\n", " frame_height=200,\n", " x_axis_label=\"time (hr)\",\n", " y_axis_label=\"OD600\",\n", " y_axis_type=\"log\",\n", " toolbar_location=\"above\",\n", ")\n", "\n", "# Color scheme\n", "strains = [\"MG\", \"3.19\", \"IW\", \"WT\", \"UV5\"]\n", "colors = {strain: color for strain, color in zip(strains, bokeh.palettes.Category10_5)}\n", "\n", "# Pull out only entries for zero antibiotic concentration (and not blanks)\n", "inds = (dfA[\"conc\"] == 0.0) & (dfA[\"strain\"] != \"blank\")\n", "dfA_0abx = dfA.loc[inds, :]\n", "\n", "# Items we will place in the legend\n", "legend_items = []\n", "\n", "# Groupby and iterate, adding to plot\n", "for strain, sub_df in dfA_0abx.groupby(\"strain\"):\n", " # Lines for a given strain\n", " lines = []\n", "\n", " # Get each well for the strain and add a line to the plot\n", " for well, subsub_df in sub_df.groupby(\"well\"):\n", " lines.append(\n", " p.line(subsub_df[\"time (hr)\"], subsub_df[\"OD600\"], color=colors[strain])\n", " )\n", "\n", " # Add the lines to the legend\n", " legend_items.append((strain, lines))\n", "\n", "# Create the legend from the items\n", "legend = bokeh.models.Legend(items=legend_items, click_policy=\"hide\")\n", "\n", "# Add the legend to the plot\n", "p.add_layout(legend, \"right\")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "98f8cbe9-6abf-4b07-a7c2-b3852a2203ed", "metadata": {}, "source": [ "We could also plot the growth for all concentrations of tetracycline for the MG1655 strain." ] }, { "cell_type": "code", "execution_count": 11, "id": "6853680c-93fe-4caa-96f5-3a8ff7310413", "metadata": {}, "outputs": [ { "data": { "text/html": [ 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for the strain and add a line to the plot\n", " for well, subsub_df in sub_df.groupby(\"well\"):\n", " lines.append(\n", " p.line(subsub_df[\"time (hr)\"], subsub_df[\"OD600\"], color=colors[conc])\n", " )\n", "\n", " # Add the lines to the legend\n", " legend_items.append((str(conc), lines))\n", "\n", "# Create the legend from the items\n", "legend = bokeh.models.Legend(items=legend_items, click_policy=\"hide\")\n", "\n", "# Add the legend to the plot\n", "p.add_layout(legend, \"right\")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "55c64088-4cca-4734-9f43-c03d30295e2a", "metadata": {}, "source": [ "Apparently, above an antibiotic concentration of 0.9, the cells do not grow." ] }, { "cell_type": "markdown", "id": "e4ba5c2f-6ac7-4662-a016-7f4f6b2b8387", "metadata": {}, "source": [ "### Obtaining growth rates\n", "\n", "We can use the groupby operations to perform curve fits as well. We need to modify our `fit_growth()` function from the *E. coli* growth module for use here to simply return the growth rate (we do not care about the initial absorbance)." ] }, { "cell_type": "code", "execution_count": 12, "id": "03178d10-85a0-48e1-b305-060f5123f322", "metadata": {}, "outputs": [], "source": [ "def exp_growth(t, A0, lam):\n", " return A0 * np.exp(lam * t)\n", "\n", "\n", "def fit_growth(df, t_start, t_end):\n", " \"\"\"Obtain estimates for A0 and λ for a given sub-trace\"\"\"\n", " # If no time window, return zero\n", " if t_start == t_end:\n", " return 0.0\n", " \n", " # Parameter guesses\n", " A0_guess = 0.01\n", " lam_guess = 1.0 # 1/hr\n", "\n", " # Pull out data\n", " sub_df = df.loc[(df[\"time (hr)\"] >= t_start) & (df[\"time (hr)\"] <= t_end), :]\n", " t = sub_df[\"time (hr)\"].values\n", " A = sub_df['OD600'].values\n", "\n", " # Perform optimization\n", " popt, _ = scipy.optimize.curve_fit(exp_growth, t, A, p0=(A0_guess, lam_guess))\n", "\n", " # Just return growth rate \n", " return popt[1]" ] }, { "cell_type": "markdown", "id": "9c98a723-6a9f-436e-8756-be6875cf3e7a", "metadata": {}, "source": [ "Now that we have our curve fitting function in hand, we can, for example, get growth rates for each strain in the absence of antibiotic (an important calculation; these are the $\\lambda_0$ values). It turns out that Pandas GroupBy objects are really slick for doing this automatically using the `apply()` method. We pass in the function we want to call, and then specify other arguments to the function.\n", "\n", "Looking at the plot, the exponential growth phase seems to be between 6 and 10 hours." ] }, { "cell_type": "code", "execution_count": 13, "id": "08a74da6-0bb0-4d3f-8c9d-6ef3c709c996", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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strainwellgrowth rate (1/hr)
03.19B10.506579
13.19B110.439572
23.19B30.565789
33.19B50.545540
43.19B70.574230
53.19B90.586322
6IWC10.531716
7IWC110.447853
8IWC30.533252
9IWC50.537041
10IWC70.535596
11IWC90.479817
12MGA10.512562
13MGA110.515497
14MGA30.487880
15MGA50.497014
16MGA70.471504
17MGA90.491036
18UV5E10.527472
19UV5E110.516805
20UV5E30.514496
21UV5E50.502841
22UV5E70.499688
23UV5E90.463137
24WTD10.509833
25WTD110.458630
26WTD30.499100
27WTD50.479537
28WTD70.488544
29WTD90.492815
\n", "
" ], "text/plain": [ " strain well growth rate (1/hr)\n", "0 3.19 B1 0.506579\n", "1 3.19 B11 0.439572\n", "2 3.19 B3 0.565789\n", "3 3.19 B5 0.545540\n", "4 3.19 B7 0.574230\n", "5 3.19 B9 0.586322\n", "6 IW C1 0.531716\n", "7 IW C11 0.447853\n", "8 IW C3 0.533252\n", "9 IW C5 0.537041\n", "10 IW C7 0.535596\n", "11 IW C9 0.479817\n", "12 MG A1 0.512562\n", "13 MG A11 0.515497\n", "14 MG A3 0.487880\n", "15 MG A5 0.497014\n", "16 MG A7 0.471504\n", "17 MG A9 0.491036\n", "18 UV5 E1 0.527472\n", "19 UV5 E11 0.516805\n", "20 UV5 E3 0.514496\n", "21 UV5 E5 0.502841\n", "22 UV5 E7 0.499688\n", "23 UV5 E9 0.463137\n", "24 WT D1 0.509833\n", "25 WT D11 0.458630\n", "26 WT D3 0.499100\n", "27 WT D5 0.479537\n", "28 WT D7 0.488544\n", "29 WT D9 0.492815" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Pull out only entries for zero antibiotic concentration (and not blanks)\n", "inds = (dfA[\"conc\"] == 0.0) & (dfA[\"strain\"] != \"blank\")\n", "dfA_0abx = dfA.loc[inds, :]\n", "\n", "# Include include_groups=False to silence deprecation warning\n", "# reset_index() to convert to dataframe\n", "growth_rates_0abx = (\n", " dfA_0abx.groupby([\"strain\", \"well\"])\n", " .apply(fit_growth, t_start=6, t_end=10, include_groups=False)\n", " .reset_index(name='growth rate (1/hr)')\n", ")\n", "\n", "# Take a look\n", "growth_rates_0abx" ] }, { "cell_type": "markdown", "id": "8501f51f-6810-4a77-a9a5-49cef1de1ae5", "metadata": {}, "source": [ "We now have growth rates for each curve without antibiotics! We can make a plot of these to make sure there are no outliers." ] }, { "cell_type": "code", "execution_count": 14, "id": "ffb8e6b3-2501-494f-8fdf-0fc503a69aa5", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1706" } }, "output_type": "display_data" } ], "source": [ "bokeh.io.show(iqplot.strip(growth_rates_0abx, q='growth rate (1/hr)', cats='strain'))" ] }, { "cell_type": "markdown", "id": "6cc76fcd-ae23-46d7-a50b-27c980e4417e", "metadata": {}, "source": [ "The IW and 3.19 strains both have two growth rates that are low, but they are only off by about 20%. We can take $\\lambda_0$ to be the median of our measurements (the median being immune to outliers) to get our $\\lambda_0$ values." ] }, { "cell_type": "code", "execution_count": 15, "id": "f4d70862-2345-404a-90b9-f572e3efd10b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "strain\n", "3.19 0.555665\n", "IW 0.532484\n", "MG 0.494025\n", "UV5 0.508669\n", "WT 0.490680\n", "Name: growth rate (1/hr), dtype: float64" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lam0 = (\n", " growth_rates_0abx.groupby(\"strain\")[\"growth rate (1/hr)\"]\n", " .apply(np.median)\n", ")\n", "\n", "# Take a look\n", "lam0" ] }, { "cell_type": "markdown", "id": "705d77f5-eb9c-4d21-902e-9a69f291c081", "metadata": {}, "source": [ "We can similarly obtain growth rates for all concentrations of antibiotics in the MG1655 strain. We need to refer to the plot to give time windows. For tetracycline concentration above 1 µM, we saw no growth, so we do not need to fit those, and we can put `[0, 0]` for the time window. We have already updated the fitting function to return zero for the growth rate if there is a time window of zero width." ] }, { "cell_type": "code", "execution_count": 16, "id": "4502c963-7b9f-43ac-a6cc-ace926f39058", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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concwellgrowth rate (1/hr)
00.21C20.383576
10.21F10.428159
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30.90F30.180286
43.90C60.000000
53.90F50.000000
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716.90F70.000000
873.15C100.000000
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11208.33F110.000000
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" ], "text/plain": [ " conc well growth rate (1/hr)\n", "0 0.21 C2 0.383576\n", "1 0.21 F1 0.428159\n", "2 0.90 C4 0.242548\n", "3 0.90 F3 0.180286\n", "4 3.90 C6 0.000000\n", "5 3.90 F5 0.000000\n", "6 16.90 C8 0.000000\n", "7 16.90 F7 0.000000\n", "8 73.15 C10 0.000000\n", "9 73.15 F9 0.000000\n", "10 208.33 C12 0.000000\n", "11 208.33 F11 0.000000" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Pull out only entries MG1655 with nonzero ABX concentration\n", "dfA_MG = dfA.loc[(dfA[\"strain\"] == \"MG\") & (dfA['conc'] > 0), :]\n", "\n", "# Time windows based on plots\n", "time_windows = {\n", " 0.21: [6, 10.5],\n", " 0.9: [14, 17],\n", " 3.9: [0, 0],\n", " 16.9: [0, 0],\n", " 73.15: [0, 0],\n", " 208.33: [0, 0],\n", "}\n", "\n", "# Compute curve fits (have to loop this time because we need time windows)\n", "# Instantiate dictionary with results\n", "growth_rates_MG = {'conc': [], 'well': [], 'growth rate (1/hr)': []}\n", "\n", "# Loop through groupby object to do curve fits\n", "for (conc, well), sub_df in dfA_MG.groupby(['conc', 'well']):\n", " # Update concentration and well\n", " growth_rates_MG['conc'].append(conc)\n", " growth_rates_MG['well'].append(well)\n", "\n", " # Obtain growth rate\n", " lam = fit_growth(sub_df, t_start=time_windows[conc][0], t_end=time_windows[conc][1])\n", " growth_rates_MG['growth rate (1/hr)'].append(lam)\n", "\n", "# Convert to data frame\n", "growth_rates_MG = pd.DataFrame(growth_rates_MG)\n", "\n", "# Take a look\n", "growth_rates_MG" ] }, { "cell_type": "markdown", "id": "01dcaffb-26f9-4124-b032-e777667a59ee", "metadata": {}, "source": [ "We can then compute the growth rate as the average." ] }, { "cell_type": "code", "execution_count": 17, "id": "d4ce5271-ca37-452e-abd7-aa95c2fec351", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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concgrowth rate (1/hr)
00.210.405868
10.900.211417
23.900.000000
316.900.000000
473.150.000000
5208.330.000000
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" ], "text/plain": [ " conc growth rate (1/hr)\n", "0 0.21 0.405868\n", "1 0.90 0.211417\n", "2 3.90 0.000000\n", "3 16.90 0.000000\n", "4 73.15 0.000000\n", "5 208.33 0.000000" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lam_MG = growth_rates_MG.groupby('conc')['growth rate (1/hr)'].mean().reset_index()\n", "\n", "# Take a look\n", "lam_MG" ] }, { "cell_type": "markdown", "id": "e6b6c8fa-fc3b-4fba-8130-ca6901440709", "metadata": {}, "source": [ "Finally, to get the relative growth rate, we divide by $\\lambda_0$. " ] }, { "cell_type": "code", "execution_count": 18, "id": "52bdf9e2-3095-410a-8311-b0231e28b27d", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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concgrowth rate (1/hr)relative growth rate
00.210.4058680.821553
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" ], "text/plain": [ " conc growth rate (1/hr) relative growth rate\n", "0 0.21 0.405868 0.821553\n", "1 0.90 0.211417 0.427947\n", "2 3.90 0.000000 0.000000\n", "3 16.90 0.000000 0.000000\n", "4 73.15 0.000000 0.000000\n", "5 208.33 0.000000 0.000000" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lam_MG['relative growth rate'] = lam_MG['growth rate (1/hr)'] / lam0['MG']\n", "\n", "# Take a look\n", "lam_MG" ] }, { "cell_type": "markdown", "id": "e690c70e-db3b-4c79-8cd5-8b9fde1c1c95", "metadata": {}, "source": [ "We can do similar analysis for all of the other strains to get our growth rates." ] }, { "cell_type": "markdown", "id": "00b48f87-ad74-465c-9779-e1809507c435", "metadata": {}, "source": [ "## Theoretical model for growth rate as a function of abx concentration\n", "\n", "In the handout associated with the experiment, we worked out a theoretical model for growth rate as a function of external antibiotic concentration $a_\\mathrm{ex}$. To solve for the growth rate, we have to find the solution to the dimensionless equation\n", "\n", "\\begin{align}\n", "0 = \\;&(K + \\tilde{q}_\\mathrm{ex, 0}^\\mathrm{max} - 1)\\tilde{\\lambda}^3 \\nonumber \\\\\n", "&+ (2 - (1-K)(\\tilde{P}_\\mathrm{in} + \\tilde{P}_\\mathrm{out}) - (1-\\kappa)(\\tilde{q}_\\mathrm{ex, 0}^\\mathrm{max} + K)) \\tilde{\\lambda}^2 \\nonumber \\\\\n", "&-(1+\\kappa(\\tilde{q}_\\mathrm{ex, 0}^\\mathrm{max} + K) - (2 - (1-\\kappa)K)\\tilde{P}_\\mathrm{out}-(1 - (1-2K)\\kappa)\\tilde{P}_\\mathrm{in}\\,\\tilde{a}_\\mathrm{ex})\\tilde{\\lambda} \\nonumber \\\\\n", "&+ (1+\\kappa K)(\\kappa \\,\\tilde{P}_\\mathrm{in} \\tilde{a}_\\mathrm{ex} - \\tilde{P}_\\mathrm{out}),\n", "\\end{align}\n", "\n", "as derived in the handout. Upon finding the solution, we can get the dimensional growth rate by multiplying by $\\lambda_0$.\n", "\n", "By playing with parameters, the above cubic equation may have zero, one, two, or three roots on the interval $0 \\le \\lambda \\le 1$. Though I will not derive it here, we can show that the following are true.\n", "\n", "- Zero roots: In this situation there is no growth and bacteria die.\n", "- One root: The value of $\\lambda$ corresponding to this root represents a stable growth rate.\n", "- Two roots: The greater of the two roots is stable and the lesser is unstable. There can be a population of cells growing at a rate given by the greater of the two roots and another population that is not growing.\n", "- Three roots: The minimal and maximal roots are stable; the middle one is unstable. There is a population of cells growing at the faster rate and one growing at a slower rate.\n", "\n", "In the case of two or three roots, the population growing at the faster rate will overwhelm the slow growers and will be the population we can see growing in the experiment. Therefore, our task is to find the largest root of the above cubic equation that is less than one. If no such root exists, the growth rate is zero.\n", "\n", "Fortunately, Numpy has a built in function for finding roots of polynomials, `np.polynomial.Polynomial.roots()`. We can use this to find all three roots of the above cubic equation. The functions below accomplish this. Note that the default values for parameters known from the literature are included in the `growth_rate()` function." ] }, { "cell_type": "code", "execution_count": 19, "id": "c760605c-7771-465d-a49b-72b76c5895ac", "metadata": {}, "outputs": [], "source": [ "def solve_growth_rate_dimensionless(\n", " aex, kappa, K, qmax, Pin, Pout, return_all_roots=False\n", "):\n", " \"\"\"Solve for the growth rate for a single antibiotic\n", " concentation in dimensionless units. All parameters\n", " are dimensionless. If `return_all_roots` is True,\n", " returns all physically viable steady state growth rates.\n", " Otherwise, only the single stable growth rate is returned.\n", " \"\"\"\n", " # No antibiotic: max growth rate\n", " if aex == 0.0:\n", " lam = np.array([1.0])\n", " else:\n", " # Coefficients for cubic polynomial\n", " a3 = K + qmax - 1\n", " a2 = 2 - (1 - K) * (Pin * aex + Pout) - (1 - kappa) * (qmax + K)\n", " a1 = (\n", " -1\n", " - kappa * (qmax + K)\n", " + (2 - (1 - kappa) * K) * Pout\n", " + (1 - (1 - 2 * K) * kappa) * Pin * aex\n", " )\n", " a0 = (1 + kappa * K) * (kappa * Pin * aex - Pout)\n", "\n", " # Set up the cubic polynomial\n", " cubic = np.polynomial.Polynomial([a0, a1, a2, a3])\n", "\n", " # Solve the cubic\n", " lam = np.sort([r for r in cubic.roots() if np.isreal(r) and 0 <= r <= 1])\n", "\n", " # No roots, return 0\n", " if len(lam) == 0:\n", " return 0.0\n", "\n", " if return_all_roots:\n", " return lam if len(lam) > 1 else lam[0]\n", " else:\n", " return lam[-1]\n", "\n", "\n", "def growth_rate(\n", " aex, # µM\n", " qmax, # µM/hr\n", " lam0, # 1/hr\n", " rmin=19.3, # µM\n", " kappa_t=0.061, # 1/µM\n", " Pin=2.85, # 1/hr\n", " Pout=2.85, # 1/hr\n", " Kd=1.0, # µM\n", " KM=10.0, # µM\n", "):\n", " \"\"\"Solve for the growth rate for antibiotic concentration, or\n", " array of antibiotic concentrations, aex. Assumes all\n", " concentration units are µM and all time units are hours.\n", " \"\"\"\n", " # Nondimensionalize\n", " kappa = kappa_t * rmin / lam0\n", " K = KM / Kd\n", " qmax = qmax / Kd / lam0\n", " Pin = Pin / lam0\n", " Pout = Pout / lam0\n", " aex = aex / Kd\n", "\n", " if np.isscalar(aex):\n", " result = solve_growth_rate_dimensionless(\n", " aex, kappa, K, qmax, Pin, Pout, return_all_roots=False\n", " )\n", " else:\n", " result = [\n", " solve_growth_rate_dimensionless(\n", " aex_val, kappa, K, qmax, Pin, Pout, return_all_roots=False\n", " )\n", " for aex_val in aex\n", " ]\n", " result = np.array(result)\n", "\n", " # Return dimensional growth rate\n", " return result * lam0" ] }, { "cell_type": "markdown", "id": "1b38bcac-8348-475f-854c-08f6e969a1fd", "metadata": {}, "source": [ "As an example, we can compute the growth rate for $q_\\mathrm{ex, 0}^\\mathrm{max} = 500$ with $\\lambda_0 = 0.5$. 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root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1752" } }, "output_type": "display_data" } ], "source": [ "aex = np.linspace(0, 2, 2000)\n", "lam = growth_rate(aex, 500, 0.5)\n", "\n", "p = bokeh.plotting.figure(\n", " frame_width=350,\n", " frame_height=200,\n", " x_axis_label='aex (µM)',\n", " y_axis_label='λ (1/hr)',\n", " x_range=[0, 2],\n", ")\n", "\n", "p.line(aex, lam, line_width=2)\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "0dbe1481-8e09-4075-ae61-7c9a960e522f", "metadata": {}, "source": [ "The `growth_rate()` function is useful when doing a regression to find estimates for $q_{\\mathrm{ex},0}^\\mathrm{max}$ for each stain using the $\\lambda/\\lambda_0$ versus $a_\\mathrm{ex}$ curves you obtain in this experiment. The function you will use in `scipy.optimize.curve_fit()` is shown below." ] }, { "cell_type": "code", "execution_count": 21, "id": "c3893a3f-0d46-4164-9aaf-f85a8d191510", "metadata": {}, "outputs": [], "source": [ "def fit_function(aex, qmax):\n", " \"\"\"lam0 has to be externally defined as the abx-free growth rate.\"\"\"\n", " return growth_rate(aex, qmax, lam0)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }