{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "## **Enzyme Kinetics** : \n", "#### _Accurate numerical solution_ - compared to the **Michaelis-Menten** model approximation and to the alternative **Morrison** model.\n", "\n", "#### Two Coupled Reactions: `E + S <-> ES`, and `ES -> E + P` , using real-life kinetic parameters. \n", "#### Scenario with **_small amount of Enzyme_**, relative to the initial Substrate concentration.\n", "In the follow-up experiments `enzyme_1_b` and `enzyme_1_c`, the enzyme concentration gets progressively increased.\n", "\n", "Two other reactions being assumed negligible, and not included, are : \n", "1) the reverse direction of the 2nd reaction \n", "2) the non-catalyzed E + S <-> P reaction" ] }, { "cell_type": "markdown", "id": "604b150b-7812-4fd3-9403-69a06dd7e397", "metadata": {}, "source": [ "### THE REACTION: \n", "the enzyme `Adenosine deaminase` with the substrate `2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine`, \n", "and the initial concentration values choosen below, all satisfy the customary Michaelis-Menten assumptions that `[E] << [S]` and that the reaction rate constants satisfy `k1_reverse >> k2_forward` \n", "\n", "For this reaction: k1_forward = 18, k1_reverse = 100, k2_forward = 49 \n", "\n", "Source of kinetic parameters: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*" ] }, { "cell_type": "markdown", "id": "c123db4f-c802-47f0-a3d3-0b857314d8e5", "metadata": {}, "source": [ "### TAGS : \"uniform compartment\", \"chemistry\", \"numerical\", \"enzymes\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "6e9d0902-6fc9-4692-ac39-0651d08902ca", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Nov. 17, 2024\"\n", "LIFE123_VERSION = \"1.0.0.rc.0\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "1e0ae9a9-9d0c-4edf-a5f2-1c589419e6cf", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "a29db1c7", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n", "\n", "import ipynbname\n", "import pandas as pd\n", "\n", "from life123 import check_version, ChemData, UniformCompartment, ReactionEnz, GraphicLog, PlotlyHelper" ] }, { "cell_type": "code", "execution_count": 4, "id": "af15ecf0-e083-4fef-b68e-abe794dcc86e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": 5, "id": "121fdfdd", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'enzyme_1_a.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = ipynbname.name() + \".log.htm\" # Use the notebook base filename for the log file\n", " # IN CASE OF PROBLEMS, set manually to any desired name\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": null, "id": "3713fa4d-e9bb-4e33-8734-c1d4d23cf177", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "34d1cefc-f644-410a-9fe4-5204964742ac", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "91a729ee-ad2f-4771-bc84-49ecb9d6a851", "metadata": {}, "source": [ "# 1. Accurate numerical solution" ] }, { "cell_type": "code", "execution_count": 6, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"])" ] }, { "cell_type": "code", "execution_count": 7, "id": "90f9ec41-6e1b-4558-9400-47e35ece6efc", "metadata": {}, "outputs": [], "source": [ "# Our Enzyme\n", "chem_data.add_chemical(name=\"Adenosine deaminase\", label=\"E\") \n", "\n", "# Our Substrate\n", "chem_data.add_chemical(name=\"2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine\", label=\"S\");" ] }, { "cell_type": "code", "execution_count": 8, "id": "0f9c3501-0b99-47d9-87fa-3a027ede3799", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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namelabel
0PP
1ESES
2Adenosine deaminaseE
32,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purineS
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" ], "text/plain": [ " name label\n", "0 P P\n", "1 ES ES\n", "2 Adenosine deaminase E\n", "3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem_data.all_chemicals()" ] }, { "cell_type": "markdown", "id": "f8d4ea7f-0591-467c-9df3-d95f53df75f5", "metadata": {}, "source": [ "### Specify the Kinetic Parameters" ] }, { "cell_type": "markdown", "id": "6b0b902c-c2bb-4731-9235-3f94ae9ec247", "metadata": {}, "source": [ "Source: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*" ] }, { "cell_type": "code", "execution_count": 9, "id": "78077d8c", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: E + S <-> ES (kF = 18 / kR = 100 / delta_G = 4,250.9 / K = 0.18) | 1st order in all reactants & products\n", "1: ES <-> E + P (kF = 49 / kR = 0) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'E', 'ES', 'P', 'S'}\n" ] } ], "source": [ "# Reaction E + S <-> ES , with 1st-order kinetics, \n", "chem_data.add_reaction(reactants=[\"E\", \"S\"], products=[\"ES\"],\n", " forward_rate=18., reverse_rate=100.) \n", "\n", "# Reaction ES <-> E + P , with 1st-order kinetics, ignoring the reverse reaction\n", "chem_data.add_reaction(reactants=[\"ES\"], products=[\"E\", \"P\"],\n", " forward_rate=49., reverse_rate=0) \n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 10, "id": "373afeb1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `enzyme_1_a.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": null, "id": "8913269e-9c1b-493f-8d28-c53f8cb7b5e4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "d23a97ea-f252-4e11-a3e9-aea74f58591e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9a4febb2-2780-4754-9c70-c2041b1afc07", "metadata": {}, "source": [ "## Set the initial concentrations of all the chemicals\n", "### in the scenario we're exploring, there's LITTLE ENZYME relative to initial substrate concentration \n", "In the follow-up experiments `enzyme_1_b` and `enzyme_1_c`, the enzyme concentration gets progressively increased." ] }, { "cell_type": "code", "execution_count": 11, "id": "8c9e3f86-b9a5-41da-9e1b-75258017808a", "metadata": {}, "outputs": [], "source": [ "S0 = 20.\n", "E0 = 1." ] }, { "cell_type": "code", "execution_count": 12, "id": "aae96512-3d86-4ab0-b167-92943523b7ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (P). Conc: 0.0\n", " Species 1 (ES). Conc: 0.0\n", " Species 2 (E). Conc: 1.0\n", " Species 3 (S). Conc: 20.0\n", "Set of chemicals involved in reactions: {'E', 'ES', 'P', 'S'}\n" ] } ], "source": [ "# Here we use the \"slower\" preset for the variable steps, a very conservative option prioritizing accuracy over speed\n", "uc = UniformCompartment(chem_data=chem_data, preset=\"slower\")\n", "uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n", "uc.describe_state()" ] }, { "cell_type": "markdown", "id": "ef2c10f2-ec7f-497a-bdbf-4fea30ba31a1", "metadata": { "tags": [] }, "source": [ "#### Advance the reactions to equilibrium" ] }, { "cell_type": "code", "execution_count": 13, "id": "e6ad72b8-722a-4606-a611-7dc600529f30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "827 total step(s) taken in 0.03 min\n", "Number of step re-do's because of negative concentrations: 2\n", "Number of step re-do's because of elective soft aborts: 1\n", "Norm usage: {'norm_A': 706, 'norm_B': 710, 'norm_C': 706, 'norm_D': 706}\n", "System Time is now: 1.5039\n" ] } ], "source": [ "# Perform the reactions\n", "uc.single_compartment_react(duration=1.5, initial_step=0.05)" ] }, { "cell_type": "code", "execution_count": 14, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (828) - only showing 1 every 6 lines\n" ] }, { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=P
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"landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Small amout of E relative to S(0)
Changes in concentration for `E + S <-> ES` and `ES <-> E + P` (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.001277774292219279, 1.5039403419420914 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Highlight a detail about the initial buildup of ES\n", "uc.plot_history(colors=['green', 'red', 'violet', 'darkturquoise'], \n", " title_prefix=\"DETAIL at early times\",\n", " range_x=[0, 0.5], range_y=[0, 2.])" ] }, { "cell_type": "markdown", "id": "ba28bbea-b725-4e1a-9c64-7dbad40cf2c8", "metadata": {}, "source": [ "#### Notice how the bound enzyme `ES` (red) quickly builds up at the very beginning, from time 0 to roughly 0.01 ... and that, in the longer term, the enzyme returns to its unbound state `E`" ] }, { "cell_type": "code", "execution_count": null, "id": "0b89741b-e652-4030-abca-8567b3200ded", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "327163fb-5f35-474c-836e-32c17d487030", "metadata": { "tags": [] }, "source": [ "### What is the initial rate of production of the final reaction product `P`? \n", "One could take the numerical derivative (gradient) of the time values of [P] - but no need to! **Reaction rates are computed in the course of the simulation, and stored in a rate-history dataframe**" ] }, { "cell_type": "code", "execution_count": 16, "id": "39db903a-7619-4c60-8a6c-1b36b37ba84b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMErxn0_raterxn1_rate
00.000000360.0000000.000000
10.000500274.5432008.820000
20.000750243.26927512.075109
30.000763241.91175312.216716
40.000769241.23749312.287060
............
8221.4688050.2539410.285397
8231.4758320.2442910.274566
8241.4828590.2350050.264142
8251.4898860.2260680.254109
8261.4969130.2174680.244454
\n", "

827 rows × 3 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME rxn0_rate rxn1_rate\n", "0 0.000000 360.000000 0.000000\n", "1 0.000500 274.543200 8.820000\n", "2 0.000750 243.269275 12.075109\n", "3 0.000763 241.911753 12.216716\n", "4 0.000769 241.237493 12.287060\n", ".. ... ... ...\n", "822 1.468805 0.253941 0.285397\n", "823 1.475832 0.244291 0.274566\n", "824 1.482859 0.235005 0.264142\n", "825 1.489886 0.226068 0.254109\n", "826 1.496913 0.217468 0.244454\n", "\n", "[827 rows x 3 columns]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates = uc.get_rate_history() # We'll be interested in rxn1_rate (the reaction that leads to `P`)\n", "rates" ] }, { "cell_type": "code", "execution_count": 17, "id": "f63a5168-1dc7-4b6b-a164-78a5b607e4fa", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's take a look at how the reaction rate varies with time\n", "PlotlyHelper.plot_pandas(df=rates, \n", " title=\"Reaction rate, dP/dt, over time\",\n", " x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n", " x_label=\"time\", y_label=\"dP/dt\")" ] }, { "cell_type": "code", "execution_count": 18, "id": "d19d0316-7bd0-411d-9ca1-065c7c5795b9", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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"text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A closer peek at its maximum value\n", "PlotlyHelper.plot_pandas(df=rates, \n", " title=\"Reaction rate, dP/dt, over time (DETAIL at early times)\",\n", " x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n", " range_x=[0,0.05], range_y=[33., 34.5])" ] }, { "cell_type": "code", "execution_count": null, "id": "dd087a54-e737-44ce-b499-56cdbc61a23b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "bfacc983-b8af-467d-87b2-2fee868d8254", "metadata": {}, "source": [ "As we saw earlier, the time it took for `ES` to build up was about 0.01 \n", "**Ignoring the brief initial transient phase, the reaction rate starts at about 34.1**" ] }, { "cell_type": "code", "execution_count": null, "id": "485514fa-5259-4319-9aea-8adac65ae24f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "e0886793-ace6-49dc-bbef-d2aa0c040001", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "078285f0-00aa-4fbb-9a67-7de0184d6cec", "metadata": {}, "source": [ "# 2. Comparing the results to the Michaelis-Menten model approximation" ] }, { "cell_type": "markdown", "id": "5c15fd87-ee4d-41f5-bcc5-de1dce1a59ec", "metadata": {}, "source": [ "### Let's compute some parameters used by the Michaelis-Menten model \n", "for background reference, see: https://vallance.chem.ox.ac.uk/pdfs/KineticsLectureNotes.pdf (p. 20)" ] }, { "cell_type": "code", "execution_count": 19, "id": "251dfcc1-0cc2-4bad-af3a-afa2feed4e4c", "metadata": {}, "outputs": [], "source": [ "rxn = ReactionEnz(enzyme=\"E\", substrate=\"S\", product=\"P\",\n", " k1_F=chem_data.get_forward_rate(0), k1_R=chem_data.get_reverse_rate(0), \n", " k2_F=chem_data.get_forward_rate(1))" ] }, { "cell_type": "code", "execution_count": 20, "id": "e279ef7d-61ca-469f-8418-60ad0b1222e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.277777777777779" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kM # For the data in this experiment, it comes out to (49. + 100.) / 18." ] }, { "cell_type": "code", "execution_count": 21, "id": "5b073f95-a8ed-4885-8b88-85a04341ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kcat" ] }, { "cell_type": "code", "execution_count": 22, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = rxn.compute_vmax(E_tot=E0) # kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 23, "id": "09dfe215-e89d-4562-8a54-72973c6d2b2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "34.656188605108056" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "initial_rxn_rate = rxn.compute_rate(S_conc=S0) # (vmax * S0) / (kM + S0)\n", "initial_rxn_rate" ] }, { "cell_type": "markdown", "id": "fbc8da21-6dbf-4957-a4f6-437b50de003f", "metadata": {}, "source": [ "Not too far from the value of about 34.1 we saw earlier... \n", "To keep in mind that the initial part of the reaction is affected by transients" ] }, { "cell_type": "code", "execution_count": null, "id": "1d9b8b04-e789-477e-be6a-d180d6f23eaf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2f8ba6c4-1d82-450d-86b6-0e96d695632a", "metadata": {}, "source": [ "### Now, let's look at the reaction rate that produces `P` as a function of [S]; we'll compare what we computed earlier vs. what is given by the approximation of the **Michaelis-Menten model**" ] }, { "cell_type": "markdown", "id": "a5f993a2-84fd-4ca6-838b-c7af9aeaef86", "metadata": {}, "source": [ "First, we'll merge the concentration history and and the rate history into a single dataframe `df`" ] }, { "cell_type": "code", "execution_count": 24, "id": "94f14cc7-e188-4a6d-b833-1f588ce34d40", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESEScaptionP_rate
00.0000000.0000000.0000001.00000020.000000Set concentration0.000000
10.0005000.0000000.1800000.82000019.8200001st reaction step8.820000
20.0007500.0022050.2464310.75356919.75136412.075109
30.0007630.0023560.2493210.75067919.74832312.216716
40.0007690.0024320.2507560.74924419.74681112.287060
........................
8221.46880519.9474370.0058240.9941760.0467380.285397
8231.47583219.9494430.0056030.9943970.0449540.274566
8241.48285919.9513720.0053910.9946090.0432370.264142
8251.48988619.9532280.0051860.9948140.0415860.254109
8261.49691319.9550140.0049890.9950110.0399970.244454
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827 rows × 7 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S caption \\\n", "0 0.000000 0.000000 0.000000 1.000000 20.000000 Set concentration \n", "1 0.000500 0.000000 0.180000 0.820000 19.820000 1st reaction step \n", "2 0.000750 0.002205 0.246431 0.753569 19.751364 \n", "3 0.000763 0.002356 0.249321 0.750679 19.748323 \n", "4 0.000769 0.002432 0.250756 0.749244 19.746811 \n", ".. ... ... ... ... ... ... \n", "822 1.468805 19.947437 0.005824 0.994176 0.046738 \n", "823 1.475832 19.949443 0.005603 0.994397 0.044954 \n", "824 1.482859 19.951372 0.005391 0.994609 0.043237 \n", "825 1.489886 19.953228 0.005186 0.994814 0.041586 \n", "826 1.496913 19.955014 0.004989 0.995011 0.039997 \n", "\n", " P_rate \n", "0 0.000000 \n", "1 8.820000 \n", "2 12.075109 \n", "3 12.216716 \n", "4 12.287060 \n", ".. ... \n", "822 0.285397 \n", "823 0.274566 \n", "824 0.264142 \n", "825 0.254109 \n", "826 0.244454 \n", "\n", "[827 rows x 7 columns]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = uc.add_rate_to_conc_history(rate_name=\"rxn1_rate\", new_rate_name=\"P_rate\")\n", "df" ] }, { "cell_type": "code", "execution_count": 25, "id": "4bcb86d9-6991-48b1-be23-117f8df8bd4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESEScaptionP_rateMichaelis_rate
00.0000000.0000000.0000001.00000020.000000Set concentration0.00000034.656189
10.0005000.0000000.1800000.82000019.8200001st reaction step8.82000034.564299
20.0007500.0022050.2464310.75356919.75136412.07510934.528950
30.0007630.0023560.2493210.75067919.74832312.21671634.527380
40.0007690.0024320.2507560.74924419.74681112.28706034.526599
...........................
8221.46880519.9474370.0058240.9941760.0467380.2853970.275111
8231.47583219.9494430.0056030.9943970.0449540.2745660.264664
8241.48285919.9513720.0053910.9946090.0432370.2641420.254610
8251.48988619.9532280.0051860.9948140.0415860.2541090.244934
8261.49691319.9550140.0049890.9950110.0399970.2444540.235622
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827 rows × 8 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S caption \\\n", "0 0.000000 0.000000 0.000000 1.000000 20.000000 Set concentration \n", "1 0.000500 0.000000 0.180000 0.820000 19.820000 1st reaction step \n", "2 0.000750 0.002205 0.246431 0.753569 19.751364 \n", "3 0.000763 0.002356 0.249321 0.750679 19.748323 \n", "4 0.000769 0.002432 0.250756 0.749244 19.746811 \n", ".. ... ... ... ... ... ... \n", "822 1.468805 19.947437 0.005824 0.994176 0.046738 \n", "823 1.475832 19.949443 0.005603 0.994397 0.044954 \n", "824 1.482859 19.951372 0.005391 0.994609 0.043237 \n", "825 1.489886 19.953228 0.005186 0.994814 0.041586 \n", "826 1.496913 19.955014 0.004989 0.995011 0.039997 \n", "\n", " P_rate Michaelis_rate \n", "0 0.000000 34.656189 \n", "1 8.820000 34.564299 \n", "2 12.075109 34.528950 \n", "3 12.216716 34.527380 \n", "4 12.287060 34.526599 \n", ".. ... ... \n", "822 0.285397 0.275111 \n", "823 0.274566 0.264664 \n", "824 0.264142 0.254610 \n", "825 0.254109 0.244934 \n", "826 0.244454 0.235622 \n", "\n", "[827 rows x 8 columns]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's add a column with the rate estimated by the Michaelis-Menten model\n", "df[\"Michaelis_rate\"] = rxn.compute_rate(S_conc=df[\"S\"])\n", "df" ] }, { "cell_type": "code", "execution_count": 26, "id": "6e8cdb8c-0e8e-461f-81a0-f7b75de1d322", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
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AswQQFmdDQ8EgAAEIQAACEIAABCAAAYSFNgABCEAAAhCAAAQgAAEIOEsAYXE2NBQMAhCAAAQgAAEIQAACEEBYaAMQgAAEIAABCEAAAhCAgLMEEBZnQ0PBIAABCEAAAhCAAAQgAAGEhTYAAQhAAAIQgAAEIAABCDhLAGFxNjQUDAIQgAAEIAABCEAAAhBAWGgDEIAABCAAAQhAAAIQgICzBBAWZ0NDwSAAAQhAAAIQgAAEIAABhIU2AAEIQAACEIAABCAAAQg4SwBhcTY0FAwCEIAABCAAAQhAAAIQQFhoAxCAAAQgAAEIQAACEICAswQQFmdDQ8EgAAEIQAACEIAABCAAAYSFNgABCEAAAhCAAAQgAAEIOEsAYXE2NBQMAhCAAAQgAAEIQAACEEBYaAMQgAAEIAABCEAAAhCAgLMEEBZnQ0PBIAABCEAAAhCAAAQgAAGEhTYAAQhAAAIQgAAEIAABCDhLAGFxNjQUDAIQgAAEIAABCEAAAhBAWGgDEIAABCAAAQhAAAIQgICzBBAWZ0NDwSAAAQhAAAIQgAAEIAABhIU2AAEIQAACEIAABCAAAQg4SwBhcTY0FAwCEIAABCAAAQhAAAIQQFhoAxCAAAQgAAEIQAACEICAswQQFmdDQ8EgAAEIQAACEIAABCAAAYSFNgABCEAAAhCAAAQgAAEIOEsAYXE2NBQMAhCAAAQgAAEIQAACEEBYaAMQgAAEIAABCEAAAhCAgLMEEBZnQ0PBIAABCEAAAhCAAAQgAAGEhTYAAQhAAAIQgAAEIAABCDhLAGFxNjQUDAIQgAAEIAABCEAAAhBAWGgDEIAABCAAAQhAAAIQgICzBBAWZ0NDwSAAAQhAAAIQgAAEIAABhIU2AAEIQAACEIAABCAAAQg4SwBhcTY0FAwCEIAABCAAAQhAAAIQQFhoAxCAAAQgAAEIQAACEICAswQQFmdDQ8EgAAEIQAACEIAABCAAAYTFsA28+voewxxI7hOBt/Ycprbu3KcOHOzzqdrU1YDAkK4u9dYjRqhfbN1rkAtJfSMwYli3etPh3er1Hft9qzr1NSTw9iMPN8yB5BCwTwBhMWSKsBgC9Cw5wuJZwC1UF2GxANHDLBAWD4NuqcoIiyWQZGOVAMJiiBNhMQToWXKExbOAW6guwmIBoodZICweBt1SlREWSyDJxioBhMUQJ8JiCNCz5AiLZwG3UF2ExQJED7NAWKob9O8/8k/qhJNPUWPGntCRSiAsHcHORdsQQFgMmwjCYgjQs+QIi2cBt1BdhMUCRA+zQFiqG3SEpbqxo+TFEUBYDNkiLIYAPUuOsHgWcAvVRVgsQPQwC4SlukFHWKobO0peHAGExZAtwmII0LPkCItnAbdQXYTFAkQPs0BYPAy6pSozJMwSSLKxSgBhMcSJsBgC9Cw5wuJZwC1UF2GxANHDLBAWD4NuqcoIiyWQZGOVAMJiiBNhMQToWXKExbOAW6guwmIBoodZICweBr1FlbuHbFJDuzcFZ8jP3UM29//cvTn4XQ75e//P+fYJu2TmberJpzYMKMXonjerNcvmZwqG5PP61h1q+cK5mdJxcr0JICyG8UVYDAF6lhxh8SzgFqqLsFiA6GEWCEt1g55mDsuQru0N2dikhnRtU13yc0M0+l/b3HxNBKSr8Xd5PduRX1h++tIrAwRl8tRZauu2HZmkBWHJFi1fzkZYDCONsBgC9Cw5wuJZwC1UF2GxANHDLBCW6gR9x/Yutb3hFLt2bldjxmxUj/3rj9Spp/Wp40/Y15SQwb0g2ep38NCx6tChUepQX4+Sn/v6Gj83fj946JjgdzkOHDw2+DnvkDARjaiwzL93qVrwrRVq0V03qgnjxgbXieuJeW71wuBv1918t1qx6okBlTvj9HHqvnnXxqYN5ysnjJ80dUDa48ccTU9Ntqbi7NkIi2FoEBZDgJ4lR1g8C7iF6iIsFiB6mAXC0tmgi4S8/HJX0NtxxBGb1M4d0gvS3wOyo2En73znxqBX5OXNXYGkyD99LF58kTr11KfVySf/OLEShxrC0deQD5EMkY/fCkn/z4GQiJw0/i7nZjmKEBYtJFpYZlz+qabASC+MHHoIWFIPS/R1LUM6b5GVaRefp6Zfen6zumdNmZ6pdycLJ84tlwDCYsgbYTEE6FlyhMWzgFuoLsJiAaKHWSAsxQRdBOOVhoiIYIhw7Nq5Qw1piMiQrk1q9Oh+MZF/UQlJUxoRi37B6AmEY926d6q1a45Q69eNURs3jlEjR/WpG+e8Xf3e0cekyS73OTaFRSQi3EMSVygRjyUPP9oUizhhWb/hJXXRlXMG9NRIXiIkF3z8bDXpA6fF/j03BBI6RwBhMQwJwmII0LPkCItnAbdQXYTFAkQPs0BYsgVdi4j0hvRPSv9tb8iRozc2pKR/joiISE/PttSZRyVE94TEDcVKyvQH/zZEzZg+POiNGX/KIbVq9b7U189zoomwRCfdz/3SZWrKuRMHFUNEY+u2nQNe1z0lccKybOVaNevWe2Kro3tVpKfmZxu3BOfkmeyfhxVpyiOAsBiyRlgMAXqWHGHxLOAWqouwWIDoYRYIS3/QixIREQ8ZjiWH/Hzw4DHB0Cs9HEvPB7HV9KQen5oyIqjP1df0qpnXHLCV9aB8TIQlPIdFpESO6Cph0V6X6NCuVsISHlqWBCA6DyZNmsJgkrE1AgiLIUqExRCgZ8kRFs8CbqG6CIsFiB5mUXdhKVpEwvNCdG9I3jkhWZtf0iphS77dHfS0vOOYPvXgsn3B/0UctoRFyiZyEp74rntKwhKRRlj0kLCkHpskDnHzWopgRp7FE0BYDBkjLIYAPUuOsHgWcAvVRVgsQPQwi6oKS3iyup4jInNDZI6IzBWR1/LMEdE9Ip0UkbTNsNWyxp+cPELJELE75+9XF3z6YNosM51nU1i0oOh5LHHioVf20hITFRhdeL26WFh2pDfljNPfFZzyvxZ9d8CKYPra0ZXEMsHgZGcIICyGoUBYDAF6lhxh8SzgFqqLsFiA6GEWLgpLWEZ27ZQNC/W+IZtU3nki4aFZBw6+e8BSvWX1iNhuXq2ERWRFpEV6V3741F7blw7ysykskp8WEN3TEh2yJXNQZOnjsIiE56O0WtZY8g+vEhYFgqwU0kQ6kinCYogdYTEE6FlyhMWzgFuoLsJiAaKHWZQtLO1kRARFJqufdtrTqaPRe6AhIL9ZMav/5+LmiKQulAMnvv/0w4K5LA8t36fO/OAh6yXKKyzWC0KGEAgRQFgMmwPCYgjQs+QIi2cBt1BdhMUCRA+zsCksWkYaq/U2ekKeCZby7d9RPV/PSHjlLD1hvex5IlVuEvNuH6ruuH1YMCRMhobZPhAW20TJzwYBhMWQIsJiCNCz5AiLZwG3UF2ExQJED7PIIix6AntXY9leEZI3djWEJFjGt7G8b3f/cr7SM5JmOV9kpPjG9tyzQ9Q5k4obFoawFB9DrpCdAMKSndmAFAiLIUDPkiMsngXcQnURFgsQPcwiLCzygCu9IyIhQxs9I7p3ZGhDRuS1LEO19JyR8FK+wdyRnLuqexiatlVuNYdFJy5yWBjC0jZEnNABAgiLIXSExRCgZ8kRFs8CbqG6CIsFiDXPQgvJ0O51wUT2N3ZtVqMbGyAedeQ6tX37ttS7rkvvSO+BU4Nd1vvF5JjmviLyuvydo3gCaYRFljeWZY6L2JMFYSk+xlwhOwGEJTszelgMmfmcHGHxOfr56o6w5ONWp1RxQtLTs0kNG/pMc/d12YG93RFe2ldPYqd3pB218v+eRlj0amEy6V4m39s8EBabNMnLFgGExZAkPSyGAD1LjrB4FnAL1UVYLEB0PAs9h0T2F5FekS2v7Gj0ijzTGL7VP2RLZCSLkIiYKDVGDR86Rm1/4+hgR/b+1zjqQkAWQhh33GFBdTa8uFeNHGVvE0mEpS6tpF71QFgM44mwGAL0LDnC4lnALVQXYbEAscNZ6FW2RExkUvuwoZsbK21tVkf0bGz8vC71HJLo/BG9slackGSZdN9hPFw+JwG9iaTt5Y0RlpwBIVmhBLwXlugGRnpjozD18AZG0b8jLIW2z9pljrDULqSFVwhhKRyxlQsk9ZLoYVtpVtkKzyGJDtmS37McCEsWWtU8d/YNw9Q3Fwy1Po8FYalme6h7qb0XFpGR5QvnNuMsvx85eqS6b961wWuXzLxNvb51R/Oc6N8Rlrq/RezWD2Gxy9OH3BAWd6Ks55JI74j0kuilf6WXRA/barf0r94MUeaO6Ent/StuHWt1UjvC4k67yVqSNHNYJM+Vj3SrSz83PNg80uY8FoQla8Q4vwwC3gtLFLL0uDz/wqamoJw1Zbq6etqFasq5E4NTl61cq+5YsFitWTY/+B1hKaOZ1ucaCEt9YllWTRCWskj3XycqJbLylgzdkpW3REra7dQe7SVpNWyryJohLEXSLTbvtMKi57HI/BWZx2LrqJuwyBfPTz61YQCeuV+6rPlcZ4tbOB95drzg42er6ZeeX0T2XuaJsETCLo3shLG/H/SwrN/wkrroyjlq0V03qgnjxgZnRl9DWLx83+SuNMKSG523CREW+6HXUvLKyzvUW45a15jcnk9K9F4kvY3eElkK2KWlfxEW++2mrBzTCouURzaQlPa8avU+Nf6UQ1aKWEdhETB65Ix88Tzr1ntUkdKCsFhpigMyQVh+g0Ma19ZtO1V4jkoaYdnXa+cGYT+05OgigeFDh6jeg4caDzculo4yuUigq1GoYcOGqP3cazKFZ9s2pdY90xXsQ3LEEc+ozZu2NSa3P6O6up5OOXyrpzFES/YkGdP/T8nPxwY/K9WTqSydOHlIo+F0d3c1JIqbTSf4l3XNCz7ZpVas6FLfvKdPXfw5O7Ee0bjf1OmQHpawsMjPMrz/XSceq265/oq2VR0/aaqadvF5asG3VgTnypfYq594uvm7vDa6583NkTfRHp3wc2V03nT4C/G2BfH8BIQl0gDCc1bSCMvrO+yuf+55e6x99XveNFzt3N3bWGLUzgdL7YFRwcYDdpc64k3D1Nad+6ERQ+DZ9V0NGelSQxvzSF55ebt6Z2M54J07Nqt3vvPpYPhWqzklfY3d2WUuSV9DQOT/g8GO7f1LAMvfqnwMG9qtDh/e2OG+cb/hqC+BBX/frW64bqj69GcOqvl/f8BKRY8cOcIonxdeUOonPzHKIlfik05S6sQTBye1ISxhIZErSJ66x0Z+D4/O0b9Hh4SJrKz90fqm2My/d6la8vCjzd9zVdqjRAhLJNi6q/C51QuDvzCHxaN3QwlVZUhYCZBrdgmGhCklY/Wfe7arIST9Q7i0mOjJ7u3mlchEd5EQ+d/F4VtFNFmGhBVB1b089QaSMhxMhoXZOEyHhH3iE0otXWqjJNny+M53lDo/ZspIVFhEFKS3JG3vhvSwtBs+Fjf/OSos0edJqV2avLNRqO/Z3guLNCA9gV7CLN2EcuiVw1glrL6NvxM1Q1g6Qb3a1/RJWMJzS4YPWx/sWbJr5yY19p3PtO0tia6+1b8Kl78bJiIs1X3fZ5nDEt5Acstre6xU2lRYrruusXjFc1aKkimTW25pCMD4wUniJt2nlZVWUqGnEugrhod+xc1hETmJO9rJUCYINT7Ze2EJ77EicWYflhq3dgeqhrA4EISKFaGOwiJiIvuWDG8M49ryyvaGmKxr7PD+eHMDxVbDuKK9JbrnpGJhLby4CEvhiAu7QBZhkULYnnhvKiyFgcmZcdyQsCxZxfWCiJBMfN+E5hyYND0s9KZkoT74XO+FxQwfyxqb8vMtPcLiW8TN61tlYckrJnppYL1Xifx/qDGnJOvmieb0q5sDwlLd2GUVFtmLRfZkuXP+fnXBpw8aVxxhGYgwTjSir0VH50T37JMcRZx++tIrA0b1yGszLv9UcyVa4+DVOAOExTC4LGtsCNCz5AiLZwG3UN0qCItNMXFpaWAL4etYFghLx9CXfmHZ7V52vb982gE1+59upGMAACAASURBVCbzRRYQlvbCoufB6DNldI4cejqBng8tr7VaJSw6mb/0xlOhCyIshsFCWAwBepYcYfEs4Baq65KwhOeY7N29LhjKJbu+y6T3VityxfWYICYWGkeLLBCWYvm6lLueeG9rx/u6CYtLsaIs+QkgLPnZBSkRFkOAniVHWDwLuIXqdkJY9Kpcz64fEqzKJRPfZY5Ju8nviImFgFvKAmGxBLIC2dje8d4nYUmaCK/DnmVyfgWaSqWLiLAYhg9hMQToWXKExbOAW6hu0cKih3Pt3rVZvbplszpu7OPB6lxjxmwMek3iDsTEQmALzgJhKRhwgdlnncMiRRl33GHB8t8/fGqvescxZvt8+SQsBYaRrC0TQFgMgSIshgA9S46weBZwC9W1JSzhXpO3vuVx1T1kk9q9a33b4VysymUhiB3IAmHpAHRLl8wjLJ+cPELJ0LCHlu9TMjTM5EBYTOiRtigCCIshWYTFEKBnyREWzwJuobp5hEX3mrz6yg41bOgzzWWD0/aa7Os9q7nRooUqkEUHCCAsHYBu6ZJ5hEUm3QeT7xuT7mXyvcmBsJjQI21RBBAWQ7IIiyFAz5IjLJ4F3EJ12wmLlpNfvPqyGtr9TOPfuuZcExGUuEP3moiYyJLBTIC3ECjHskBYHAtIwcXRK4Wd+7GD6t4H9htdDWExwkfiggggLIZgERZDgJ4lR1g8C7iF6oaFReTkufWNDRcbu8DLRPjhQ9e0HNIVnmvSe2BC0Guyr/dDFkpFFq4TQFhcj5Dd8umVwsafckitWr3PKHOExQgfiQsigLAYgkVYDAF6lhxh8SzgBtWVBxC9Stf+vS8r1fdYajlhSJcB+JokRVhqEsiU1dArhcnpW17bkzJV/GkIixE+EhdEAGExBIuwGAL0LDnC4lnAU1Y3a8+J9JTIsK7gXzCk691B7wkHBDQBhKW6bSHPHBap7TmTRii5l0gPi/S05D0QlrzkSFckAYTFkC7CYgjQs+QIi2cBj6ludM7J7l3r1KRJ/b0nPT3bBqUQERky5D1q1+7xav+Bs5hvQhNKRQBhSYXJyZPyCoteKUzmsMhclryHj8Kid65/bvXCltjOmjJdXfDxs9X0S8/Pizcx3bKVa9WsW+9RUoa05bFeCIczRFgMg4OwGAL0LDnC4lfAX97cFXzj+ePndwST4WXFrvec9nggJ3ET4vWck/2NyfBaTpTqUW89YoT6xda9fsGjtkYEEBYjfB1NnFdY9EphV1/Tq2Zek3+lsLoJi0jG1m07AxEIH7Jp5OieN6s1y+anFgRfhKXIeuZ9cyEsecn9Jh3CYgjQs+QIS30DHt7nZO9ukRNZratfTuI2YAxPiJc5J0nDutqtElZfotTMhADCYkKvmmmXfLtbzZg+POhdMVkprI7CMrpnpHrXiceqW66/IgjudTffrZ5/YVNDZHYEwpL2KPJBPtzDkrY8RZ1XZD3zlhlhyUsOYTEk52dyhKU+cdfzTn7eWE54WGM54aOObL1il6zOJUsIZ50Qj7DUp82UWROEpUzablzL1kphdRSWq6dd2BxuJdGS3pVpF5+nljz8aCAscbIg5+hDzpVhYPpBfsG3VjT/tuiuG9WEcWOD3/VQLv1H3YMTbiEiSytWPTEofbgM0fKkyTepFeq66jJLeVc/8bQK1yFczktm3qaefGpDM7vjxxytli+c2xS9uLKX8Q5AWAwp08NiCNCz5AhLNQOue0/kgWD4sDVth3ZF9zkxWUoYYalmm+l0qRGWTkeg/OvrlcJGjupTG17MP4TUXFheaFT+J+UDUCc1rnnioOuKZIiwrFj1b+ptRx3R/Pvb33ZUorBImonvm9DskZGH+PvmXRsIS3h4mbz++tYdzQd6fZ6+iJx/wtjfD9LKIbKy9kfrm706IiJx0tRKXiSfyVNnqZuuvbQpSq1gh4e+6fPalTOuh6VV2csINsJiSBlhMQToWXKEpRoB1xPjn/zBTvWWIx9r9p5MmrR6UAXi5p3Ia7YOhMUWSb/yQViqG++8c1ikxuOOO0yJuJisFGYuLJ9olGRpBwLwncY1B0+G18Jy3LFvVxddOWfAvJVWshDuOQkLSHjSfVg44iqsh57pHgpdlinnTmyeLkIx90uXBb/rSfdxwiLnhNOlBazzb5U2rpzRxQValT1PudKWX5+HsGQlFjkfYTEE6FlyhMXNgOs9T9LMPelfSvhUtb93YvC//F7kgbAUSbe+eSMs1Y2tibDolcIeWr5PnfnBfEsbmwvLdQ34z3UgALc0rjl+0HXDD9rSsyC9LDKXJU3vRjSzaM9DnLDoXhidNjykKjzMLJx3K2GR86LDyM44fVyz16Yd6CRhaVXOuB6WVmVHWNpFwYG/IywOBKFCRUBYOh+s6PCuPW+sUx/+8GONpYVXD1pWODwxfu/+P+vIksIIS+fbTBVLgLBUMWr9ZTYRFr1S2OybetXl0/KtFGYuLG6xj+sZkBK2E5Y8PSzRoWTRnotWvR3thoFpqus3vBT0FOl5Ne1ox12zXTmThCVvL0+7Mqb5Oz0saSi1OAdhMQToWXKEpfyA66WFf/hEY/7J0Mcbw7seT9z3RG/IKBPj+yfIf6j8AkeuiLB0PASVLADCUsmwGRf6mwuGKpEWkRWRljyH78IizFrNYWk1JCwqBzLXRA49JEx6eH760isDViaT12Zc/in14qZXY4eEiVi9+svXmvNpJL80w7x07OPObVdOKfeRo0cO6MVpVXa96ECe9pY2DcKSllTCeQiLIUDPkiMsxQdcC4rMP5HVu44/7uFgWeG4+SdlD+/KU3uEJQ810iAsfrYBvVKYDAeTYWF5DoSln1qrVcL0xpHRIWHR1bxkOFhYWOTn6PAuvUJXUg+L7lEJxzJt70qS3LQrpy6LpG+1SljcKmh52lyaNAhLGkotzkFYDAF6lhxhsR9wERT5kN7w/E41Ytjjzb1PkgRl/4EPBUsL72/0nticHG+/Zv05IixFka13vghLveObVDtZMOScSSOUyUphdRMWP1tC/WqNsBjGFGExBOhZcoTFPOBhQZH5J6e/Z0XQexK3OaPe+6RT80/Ma4uw2GDoYx4IS3WjbjKHRWp99FGHB5WXpY1FXLIeCEtWYp07P2kivC5R3DyczpXW7MoIixk/hbAYAvQsOcKSPeB6iNf3vtsdLDHcaoiXCMp+6T05IDvHn1qJHpR2ROhhaUeIv8cRQFiq2y5MhUV6WKSnJe9KYQhLddtOnUuOsBhGF2ExBOhZcoSlfcBlFa8nGkO8opPk44Z4hXtQXJgg37522c9AWLIzI4VqDI/sVm86vFu9vmM/OCpGwFRYLv3ccLXykW517wP71bkfO5i59ghLZmQkKIEAwmIIGWExBOhZcoQlPuAyB0X+7X5jfTAPJWmZ4ToM8cra5BGWrMQ4XwggLP62g3m3D1V33D5MXX1Nr5p5TfaljREWf9uOyzVHWAyjg7AYAvQsOcLSH3AZrvDE2iHqJxteVm856jH1ntNkqeHVasyYjQNahF7FS+agVGWSvO0mjbDYJupHfgiLH3GOq6X0rkgvi/SuSC9L1gNhyUqM88sggLAYUkZYDAF6ltxXYQnPQ5EelKSJ8rIPSv88lInB//K77wfC4nsLyFd/hCUftzqk0ksbjz/lkFq1OvvSxghLHVpB/eqAsBjGFGExBOhZcp+EJTrMa/Lk5YP2QtE7yQc9KI3lhqVHhWMgAYSFFpGHAMKSh5obaUznsMg8wHHHHZZ7aWOExY12QCkGEkBYDFsEwmII0LPkdRYWvdywbNg4vNGLcvak/uWG44Z5iZyIpNR1orzNZo2w2KTpT14IS3VjbSosUnMRFhGXPEsbIyzVbTt1LjnCYhhdhMUQoGfJ6yYs0osiyw3v3rWuMRflcRXXi8IwL7NGjrCY8fM1NcJS3cjbEJZPTh4RLGSSZ2ljhKW6bafOJUdYDKOLsBgC9Cx51YVF96L84IlutXf34+rPpzwQ24siPScM87LTuBEWOxx9ywVh8S3iA+s7Y/pwteTb3Wr2Tb3q8mnZVgpDWPxuO67WHmExjAzCYgjQs+RVFJbwil4yYV73ovT0bGtGT/ei+LyaV1FNGWEpimy980VY6h3fdrXTSxuLrIi0ZDkQliy0OLcsAgiLIWmExRCgZ8mrIiwylGDJoqFqzxvrGit6LVdTpixXp5329IBoyQT5vfs/Huwqz1yU4hoywlIc2zrnjLDUObrt62aytDHC0p4vZ5RPAGExZI6wGAL0LLmrwiKTM1c+0ti8scVQL1nRS/ZC0ZPlWXK4nMaLsJTDuW5XQViqG1Ebc1ikZ/ycSSNUnqWNEZbqtp06lxxhMYwuwmII0LPkLgmLno+yauUu9ba3rAh2l58yZZmKG+q1Z99n6EXpUFtFWDoEvuKXRViqG0AbwqKXNhYKW17bkwkGwpIJFyeXRKBUYRk/aaqa+6XL1JRzJw6o3vx7l6olDz+q1iybX1K17V0GYbHH0oecOi0sIikyVEB2mJf5KH/xF/cP2htFhnrJssO7932WfVEcaJQIiwNBqGAREJYKBu03RbYhLJKVXtr4h0/tVe84pi81EIQlNSpOLJGAE8KybOVaNevWe9RzqxeWWHU7l0JY7HD0JZdOCIsMDXhwUbd69ZXNwdLDcZIic1B0LwpDvdxqjQiLW/GoSmkQlqpEqrhy5l3aGGEpLibknJ+AE8Jy3c13q7U/Wt+RHpZLZt6mnnxqQ5Pg8WOOVssXzh1AdPLUWepnG7cEr0X/jrDkb3w+pixLWLSk/Pj5l9V7T18eSEp00rxMmGc+ivutEGFxP0YulhBhcTEq5ZYp79LGCEu5ceJq6QgULiy696RdceKGirVLY+PvZ02ZPkCU5PeJ75ugbrn+iiB7EZrXt+5oSozIy5GjR6r75l0b/B1hsREFf/IoUlj0yl4/37I5VlJk0vze/ec1Js5PDP6X3zncJ4CwuB8jF0uIsLgYlXLLlHdpY4Sl3DhxtXQECheWcDGS5rCkK2o5Z0lvz/MvbGoKigjM1dMubM67EQG7Y8HipuQgLOXEpS5XsS0s0pNyzzeGqnaSIj0p0qPCUT0CCEv1YuZCiREWF6KQrwy25rDkXdoYYckXN1IVS6BUYSm2KnZylx6Ud514bNDDsn7DS+qiK+eoRXfdqCaMGxtcIPoawmKHuy+52BCW8HCv48Y+pr74xa8OGO6le1KQlHq0KoSlHnEsuxYIS9nE7V3PlrDkXdoYYbEXS3KyRwBhCbGU3pUVq55oTv5PIyz2QkFOEEgmsHGjUsuWKbV8+UY1ZszqmInzPY3EUxr/Jv/mf2hCAAIQgEAVCSxevFideuqp6uSTTzYq/rZtSh1xRH8WfekXCTO6JokhUBSBwoVFhoGlPTq5SpgsrbzgWyta9qZIPehhSRtNzosjkKWHJbpPSnR1L3pS/Ghj9LD4EWfbtaSHxTbRauaXZ2ljeliqGeu6l7pwYQkDlOFWf3zWe9X0S88fwDXp9bLgR3tWwtdlDktZUfDjOu2ERe84v2TR0GAzx8mTl6upUxcOgKNX99q972I/oHleS4TF8waQs/oIS05wNUuWZ2ljhKVmjaAm1SlVWFzcOFJkSY7oUsY6vqwSVpOW7kg1koRFr/D1q5+vaQ73GjNmY7PU7JPiSAA7UAyEpQPQa3BJhKUGQbRQhUs/NzzYLPjO+fvVBZ8+mCpHhCUVJk4qmYATwtKpjSP18K445uFlltmHpeRWWePLhYUlvMLXR86+v9GTcn9jfspvJUV2nH9j7+eVyAqbOda4UbSpGsLib+xNao6wmNDrbFpbk+6lFnpp46uv6VUzrzmQqmIISypMnFQygVKFJWnoV3Sp4JIZGF2OVcKM8HmXeM+2w9T/+d4BteTbO9UJx68YNHlexEQEZefu65EU71pHfIURFhpCHgIISx5qbqSxKSx5ljZGWNxoB5RiIIFShUX3pEQ3iZShYued84HmZo1VChLCUqVoda6s8qHx4KJutXd3/5Cv8LwUPXl+z77PBLLCAYEwAYSF9pCHAMKSh5obaWwKiww3lnks4085pFat3peqgghLKkycVDKBUoVF6hY3DGvaxecNmohfMofcl0NYcqOrfUJZ5Wve3wwLNnWMG/Kl56Ww63ztm4JRBREWI3zeJkZYvA39gIrLQi6yUtjIUX1qw4t7U0FBWFJh4qSSCZQuLCXXr/DLISyFI67UBcKrfJ10wgODhnz1qTFq997Pql17PsOQr0pFtnOFRVg6x77KV0ZYqhw9u2XXSxuLsIi4tDsQlnaE+HsnCBQuLDLcq8o9KO2CgrC0I+TH3/UE+h8/v1nNuGqOmjRp9YAJ9LIEsQz5GvW756itO/epAwfbf2j4QY5atiOAsLQjxN/jCCAstAtNIOvSxggLbcdFAoULi1Ra9jLZum1nUP9Obg5ZRAAQliKoViNP3ZtyzzeGqj/8g8G9KXGrfLXbh6UaNaeUZRJAWMqkXZ9rISzVjaXNOSxCQS9tfO8D+9W5H2u/tDHCUt22U+eSlyIsGqCedC+/n3H6OHXfvGsrzxZhqXwIM1dAz02J603Rq3zJcsQiLNEDYcmM2/sECIv3TSAXAIQlFzYnEtkWlqxLGyMsTjQDChEhUKqwhK8tGzI++dSG4KXoqmFVihLCUqVomZV1ybe7lexAHzc3RU+gb7f7PMJiFgMfUyMsPkbdvM4IiznDTuVgW1jks2vG9OFB74r0srQ7EJZ2hPh7Jwh0TFjCla3ykDGEpRPNtrxrhlf6uuQvB85N0csRZ9kzBWEpL3Z1uRLCUpdIllsPhKVc3i5fTS9tfOYHD6mHlrdf2hhhcTma/pbNCWHR+PWQsUV33agmjBtbiaggLJUIU+ZCyg1e5qbE7Zsiw75EUvIsR4ywZA6F9wkQFu+bQC4ACEsubLVMJF+8vf/09EsbIyy1bAaVr1RpwhIeAlaX+SsSfYSl8u+BZgX0JPr7vvmGeu/py9WXv/yV2JW+TDZ3RFjq017KqgnCUhbpel0HYalXPE1rc/RRhwdZbHltT9usEJa2iDihAwRKEZbrbr5brf3RerVm2fygipOnzlJHjh7JpPsOBJxLDibQatiX9Kbs2vP5Rm/Kx63sm4Kw0AKzEkBYshLjfCGAsFS3HdiewyIkzpk0Qsny+7Lbvex63+pAWKrbdupc8lKEReaoXPDxs5u72evd7uuwxDE9LNV9e8iwL5lE/6ufrwk2eJw6dWGzMmkn0WetPcKSlRjnIyy0gTwEEJY81NxIU4Sw6L1Y0ixtjLC40Q4oxUACpQiLbB4ZXQks7rUqBgdhqV7UZMUUvXdK3LCvLJPos9YeYclKjPMRFtpAHgIISx5qbqQpQlhm3zBMfXPBUDX7pl51+bQD9LC4EWpKkYEAwpIBVtypCIshwJKSy7Av6VFZ+uAWddzYxwbMT5FhX7v3flbt3vdZK8O+WlUJYSkp4DW6DMJSo2CWWBWEpUTYFbhUICsNaRFZEWlpddDDUoGAelhEhMUw6AiLIcCCk0fnp0yZskz19GwLrqpX+2q3d4rNIiIsNmn6kRfC4kecbdcSYbFNtNr5rXykO9jxPs3SxghLtWNd19KXJixpAFZxTgvCkiay5Z+jReVHP3g56E2Jzk/Zted6ZbLaV94aISx5yfmbDmHxN/YmNUdYTOjVL61MuJeJ9zLhXibe08NSvxjXvUalCEudISIsbkVXi4pMpBdRmTRpdbOA0pNS5PyUNCQQljSUOCdMAGGhPeQhgLDkoeZGmiLmsMiy/eOOOyyoYLuljelhcaMdUIqBBBAWwxaBsBgCtJRc5qfccfswddIJD6gvfvGr6rTTng5yzrMbvaUixWaDsBRJt555Iyz1jGvRtUJYiiZcXP5FCIuUVoRFxOWHT+1V7zimL7ECCEtxsSXn/AQKFxZZDSztwZCwtKQ4TxOQFb9kaWIRlfCKX2VOpM8SDYQlCy3OFQIIC+0gDwGEJQ81N9IUJSx6aeOHlu8L5rIkHQiLG+2AUgwkULiwhC8nG0b+8Vnvbe7Hov+W9HoVgkUPS2eiJKIy72+GqT/6yP2DREWGfZU5kT4LAYQlCy3ORVhoA3kJICx5ydU3nUy6l8n3d87fry749EGEpb6hrmXNShWWpL1X5t+7VC15+FG1Ztn8ykFGWMoNWVVFRVNCWMptL3W4Gj0sdYhi+XVAWMpn7voV590+NBg6ffU1vWrmNcl7sdDD4nok/SyfE8KybOVaNevWexRDwvxshGlqXXVRQVjSRJlz4gggLLSLPAQQljzU6p1GPkdnTB+uzv3YQSU73icdCEu920FVa1eqsCQN/RJhuWPBYnpYqtqKCix3XUQFYSmwkdQ8a4Sl5gEuqHoIS0FgS8i2qDkssjiNzGNptxcLwlJCkLlEZgKlCovuSZn7pcvUlHMnNgsrQ8XOO+cD6pbrr8hcgU4nYEhYMRGom6ggLMW0Ex9yRVh8iLL9OiIs9pmWlWNRwiLL/r//9MPUyFF9asOLe+lhKSugXMcKgVKFRUq8fsNL6qIr5wwo/LSLzxs0Ed9K7UrIBGGxC1m+AZIu66pNpk9LgTksaUlxniaAsNAW8hBAWPJQcyNNUcIitTv6qMODSrbai4UeFjfaAaUYSKB0YalbABAWOxGVb35EVOKWJ3Z51a+stUdYshLjfISFNpCHAMKSh1r908hu97Lrvex2L7vexx0IS/3bQRVriLAYRg1hMQOod6b/nRHfqtTyxHlrjbDkJedvOoTF39ib1BxhMaFX37Rp9mJBWOob/yrXDGExjB7Ckg+gFpVf/XyNuvPOGc2d6WXDxzr1qETpICz52ovPqRAWn6Ofv+4IS352dU45+4Zh6psLhqrZN/Wqy6fFL22MsNS5BVS3bgiLYewQlmwARVQeXNStvrNkS9CjMnXqwiCDuouKpoSwZGsvnM1O97SBfAQQlnzcXEhV5ByWQFYa0iKyItISdyAsLrQCyhAlgLAYtgmEJT1AWflr6YNb1CV/OWeAqOze+1n1xt6/Uof6RqXPrKJnIiwVDVwHi00PSwfhV/jSCEt1g1eksMhO97Ljfau9WBCW6radOpccYTGMLsLSHqAWlY+cfb+aPfsrzQS7910cDP+S3hVfDoTFl0jbqyfCYo+lTzkhLNWNdpHCovdikQn3MvGeHpbqthPfSo6wGEYcYUkGmLTyl4+ioikhLIZvOA+TIyweBt1ClREWCxBrmMWO7V1q3HGt92Khh6WGga9BlRAWwyAiLIMB6gn1+/c8HEyoHzNmY3BS74F3q607F3vVoxKlg7AYvuE8TI6weBh0C1VGWCxArGkWIiwiLrJ5pGwiGT0QlpoGvuLVQlgMA4iwDAQ47/ah6vvfe0XNuGrgPJU6r/yVpQkhLFloca4QQFhoB3kIICx5qPmRRu/F8tDyferMDw7eiwVh8aMdVK2WCIthxBCWfoB6nsr5f/41ddVVfxe8JnNTZEL9zj2zDCnXJznCUp9YllUThKUs0vW6DsJS3XgWOYdFqMike5l8f+8D+4PJ99EDYalu26lzyREWw+j6LixJGz/6PE+lVZNCWAzfcB4mR1g8DLqFKiMsFiB2KIuihUXvxXL1Nb1q5jWD92JBWDoUeC7bkgDC8hs88+9dqpY8/Khas2z+IGCTp85SP9u4JXj9+DFHq+UL5zbP8VlYZPiX7Kfy6KNnM08l5Y0GYUkJitOaBBAWGkMeAghLHmpupClaWNrtxYKwuNEOKMVAAt4Ly7KVa9WsW+8JqIzuefMgYblk5m3q9a07mpIi8nLk6JHqvnnXBml8FJak/VSYp9L+9oKwtGfEGQMJICy0iDwEEJY81PxIo5c2lvkrMo8leiAsfrSDqtXSe2HRAUvqYTlrynR19bQL1ZRzJwaniuDcsWBxU2x8Epak4V87d89inkrKdz7CkhIUpzUJICw0hjwEEJY81PxI89yzQ5RMvE/aiwVh8aMdVK2WCMtvIhYnLOs3vKQuunKOWnTXjWrCuLHBmdHXfBGWuOFfzFPJ/nZHWLIz8z0FwuJ7C8hXf4QlHzcfUum9WKSuW17bQw+LD0GvQR0RFkNheW1H/E6xNWgbQRWkV+WLn9+ioqt/7dl3g9rbe3FdqllaPY5403C1Y3dvYwW1wWvfl1YILlQpAkNUl+p587DGHkb7K1VuCttZAsO7h6jDR3Sr7Y37DUe1CHz34aXqpHGnqLHHn1hYwY8/ZoTavl2pn23ep0aNGniZo0aOKOy6ZAyBvAQQFkNh2d87eA3zvMFwKd2mTUrNn9+ldu64X335y19pTqo/ePDLjYftLzSK2uNScStTlmFDh6gDBw+pPnylMjHreEG7lBreaDd1vdd0nG9NC9A1pEs1nEUdOMDNpmoh/s5DS9SEd5+qTjzxpMKK/id/0qUef6xLff/7fepDHx7YRoYPazQcDgg4RgBhaSEs8icf57AkTap/bftKr3ept/HeZUiYDYp+5cGQML/ibau2DAmzRbL8fIpeJUxq1GovFuawlB9zrtieAMLSRlh8WiVMT6p/+9vmB70qPT3bAkFh9a/2b6S0ZyAsaUlxniaAsNAW8hBAWPJQ8yeNzEu94/ZhKm4vFoTFn3ZQpZp6LyzhZY114M475wPqluuvaMbRh31YdK/KA/d/pDn8i0n19t/KCIt9pnXPEWGpe4SLqR/CUgzXuuSq92K54NMH1Z3zB86PQ1jqEuV61cN7YTENZ9VXCdO9KuNO/B9q9uyvBDjoVTFtFcnpEZbi2NY1Z4SlrpEttl4IS7F8q557q71YEJaqR7ee5UdYDONaZWGJ61V5Y+9fqV17Ps9cFcN2kZQcYSkIbI2zRVhqHNwCq4awFAi34KzLmMOi92J5xzF96odP7R1QI4Sl4ACTfS4CCEsubL9NVEVhSepV2bbrG2pf74cMiZC8FQGEhfaRlQDCkpUY5wsBhKW67aAMYRE6Rx91eAApuhcLwlLdtlPnkiMshtGthUd1TQAAFD5JREFUmrDE9aqwU71hI8iQHGHJAItTAwIICw0hDwGEJQ81N9KUJSzvP/2wYK816WGRnhZ9ICxutANKMZAAwmLYIqoiLEm9KixVbNgAMiZHWDIC43SEhTaQiwDCkgubV4k+OXmEkrksDy3fp8784G/3lENYvGoGlakswmIYqioIi9yQvnrHqyq8ApjMVdn+xu2GtSd5VgIIS1ZinE8PC20gDwGEJQ81v9Ik7cWCsPjVDqpSW4TFMFKuC4ustX5w/9fVnXfOCGoqK4AxV8Uw6AbJERYDeJ4mRVg8DbxhtREWQ4AeJE/aiwVh8SD4FawiwmIYNFeFRYaA/fVVP1czZ8xUU6YsC2op+6rsaPSqHOobZVhrkuclgLDkJedvOoTF39ib1BxhMaHX2bRlzWFJ2osFYels/Ll6PAGExbBluCgschPa+p//oGZcNSfYBJJ9VQyDbDE5wmIRpidZISyeBNpyNREWy0BLzK4sYUnaiwVhKTHYXCo1AYQlNar4E10Slh3bu9Sdf/uGGnfiTeqqq/4uKPDe/R8P5qqItHB0ngDC0vkYVK0ECEvVIuZGeREWN+KQpxRlCYvei2X8KYfUqtX7mkVFWPJEjTRFE0BYDAm7Iix6CFh4Yr2Iikyu53CHAMLiTiyqUhKEpSqRcqucCItb8XC1NHF7sSAsrkbL73IhLIbxd0FYZOLcmw6fq2bP/kpQG+lNYbliw8AWlBxhKQhsjbNFWGoc3AKrhrAUCLdGWY877jAlozPCe7EgLDUKcI2qgrAYBrOTwiK9Kksf3BIMAZs6dWFQE5YrNgxowckRloIB1zB7hKWGQS2hSghLCZBrcIm4vVgQlhoEtoZVQFgMg9opYRFZmTt7g/raV89nYr1hDMtMjrCUSbse10JY6hHHsmuBsJRN3N71yprDIiWO24sFYbEXS3KyRwBhMWTZCWGRVcD6ehkCZhi6jiRHWDqCvdIXRVgqHb6OFR5h6Rh64wuXKSxxe7EgLMYhJIMCCCAshlDLFpaF92xR7zrpr5t7q+zcPUvt3DPLsBYkL4sAwlIW6fpcB2GpTyzLrAnCUiZtu9cqU1ji9mJBWOzGk9zsEEBYDDmWJSzRVcBkYr2sAibLFnNUhwDCUp1YuVJShMWVSFSrHAhLteLVqdLG7cWCsHQqGly3FQGExbB9lCEsKx/pVtte+3qwa70crAJmGLQOJkdYOgi/opdGWCoauA4XG2HpcAAqcvm4vVgQlooEz7NiIiyGAS9aWGR86e//3jXNjSBZBcwwYB1OjrB0OAAVvDzCUsGgOVBkhMWBIFSgCLKksSxtLMeW1/YE/yMsFQich0VEWAyDXpSwyE1k6YOvqP924Z8Eq4Ad6hulZL4KG0EaBqzDyRGWDgeggpdHWCoYNAeKjLA4EIScRShzDosUUe/FsuHFvWrkqD6EJWfcSFYsAYTFkG8RwhK3ZDEbQRoGypHkCIsjgahQMRCWCgXLoaIiLA4FI2NRyhaW6F4s9LBkDBinl0IAYTHEbFtYZDzp5hdvVpdeMicomUyql8n1Mm+Fo/oEEJbqx7DsGiAsZROvx/UQlurGsWxhie7FgrBUt+3UueQIi2F0bQqLLC846nd/O1+FJYsNg+NgcoTFwaA4XiSExfEAOVo8hMXRwDhYrNk3DFPy/HH1Nb1q5jUHGBLmYIwoklIIi2ErsCUsS5e8oiaeeYE67bSnma9iGBOXkyMsLkfHzbIhLG7GxfVSISyuR8id8um9WC6fdkDNvqkXYXEnNJQkRABhMWwOpsISnVzPksWGAXE8OcLieIAcLB7C4mBQKlAkhKUCQXKkiNG9WBgS5khgKMYAAgiLYYMwERaZXP/w0kfUf7/6UtXTs031Hni32rpzMfNVDGPicnKExeXouFk2hMXNuLheKoTF9Qgll6/sOSzRvVgQluq2nTqXHGExjG5eYRFZefY/bmlOrmd/FcNAVCQ5wlKRQDlUTITFoWBUqCgIS4WCFSlq2cIS3YsFYalu26lzyREWw+jmERb5NmPH69eqT5z/1eDqTK43DEKFkiMsFQqWI0VFWBwJRMWKgbBULGCh4pYtLHLp8F4sJ4/t30iSAwIuEUBYDKORVVhWfXenOu2UjzYn12/bdXewdDGHHwQQFj/ibLOWCItNmv7khbD4E2sbNQ3vxfKJ80bYyJI8IGCVAMJiiDOLsMhKYH/2p+cEO9czud4QfEWTIywVDVwHi42wdBB+hS+NsFQ4eB0oengvlksuHt6BEnBJCLQmgLAYtpC0woKsGIKuSXKEpSaBLLEaCEuJsGt0KYSlRsEsoSp6LxZZ1vjLs4aVcEUuAYFsBBCWbLwGnZ1GWJ7+90fUB864LFgJbF/vh9SvGyuBHeobZXhlkleRAMJSxah1tswIS2f5V/XqCEtVI6dUJ+awhPdiufuuodWFR8lrSwBhMQxtO2HZ9OJd6sz3XR1chZXADGHXIDnCUoMgllwFhKVk4DW5HMJS3UB2QlhWPtKtZFjYmR88pJ5YO6S68Ch5bQkgLIahTRIWWSZw/VO3qE99ck5wBVYCMwRdk+QIS00CWWI1EJYSYdfoUghLdYPZCWEJ78Xy7HqEpbqtp74lR1gMYxsnLLLHyuYXkRVDtLVMjrDUMqyFVgphKRRvbTNHWGob2kIqpvdiGTmqT23f1lXINcgUAiYEEBYTeo20UWERWdn162nqjz5yf5Dztl3fULv3XWx4FZLXhQDCUpdIllcPhKU81nW6EsJSp2iWUxe9F0tfXznX4yoQyEIAYclCK+bcsLDs3LE9kJX3nr48mFT/+o7vqd4D7za8AsnrRABhqVM0y6kLwlIO57pdBWGpW0SLr885k0YoGRqGsBTPmitkJ4CwZGc2IIUWFpGVo0adq44c/Qx7rBgyrXNyhKXO0S2mbghLMVzrnivCUt0Id2IOi9DSe7EgLNVtO3UuOcKSIrqTp85SP9u4JTjz+DFHq+UL5zZTibB0D9kUyIr8z4aQKYB6fArC4nHwc1YdYckJzvNkCEt1G0CnhEXvxYKwVLft1LnkCEub6F4y8zb1+tYdTUkReTly9Eh137xrg5S//PWPkZU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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's see how our computed rate compares with the approximations from the Michaelis-Menten model\n", "PlotlyHelper.plot_pandas(df=df, x_var=\"S\", fields=[\"P_rate\", \"Michaelis_rate\"],\n", " title=\"Reaction rate, dP/dt, as a function of Substrate concentration\",\n", " y_label=\"dP/dt\", legend_header=\"Rates\",\n", " vertical_lines_to_add=18.9, colors=[\"blue\", \"yellow\"])" ] }, { "cell_type": "markdown", "id": "3d6b91c7-dc26-4a04-8a27-4d1b10f4d96e", "metadata": {}, "source": [ "Let's recall that our reactions started with [S]=20 \n", "Virtually overlapped plots, except at the very right! (very early times, when [S] is greater than about 19)" ] }, { "cell_type": "markdown", "id": "6e3f2c52-49ce-4e48-97ab-24c2274fa2cc", "metadata": {}, "source": [ "## In this scenario, the Michaelis-Menten model is remarkable accurate EXCEPT at the very early times of the reaction (the large values of `S`), which is the brief initial transient phase when `ES` builds up from zero" ] }, { "cell_type": "markdown", "id": "291b603e-45fd-4cb9-a479-82ee4e4ba936", "metadata": {}, "source": [ "#### This is as expected, because the kinetic parameters of this reaction satisfy the Michaelis-Menten assumptions that `[E] << [S]` and that the rates satisfy `k1_reverse >> k2_forward`" ] }, { "cell_type": "code", "execution_count": null, "id": "413400e9-c049-4661-a1ec-d0e7bf3ef4ea", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "1c05908a-d2ac-43d7-8a74-b7ff62f66f1f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6db0551d-719f-43d7-93c5-eeba71814e4c", "metadata": { "tags": [] }, "source": [ "# 3. Comparing the results to the Morrison model" ] }, { "cell_type": "markdown", "id": "1271df18-1ef6-4907-a939-4605a9396a22", "metadata": {}, "source": [ "#### Following section 7.1 of _\"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023_, we'll test out an the alternative **Morrison** approach, which is expected to perform better than the **Michaelis-Menten** model when the Enzyme concentration isn't so small. But, in this scenario, we only have small amounts of enzyme - and we'll see below that no significant improvement is gained by switching model." ] }, { "cell_type": "code", "execution_count": 27, "id": "e6184d05-da5e-4539-b44f-5a15fcaa7a1b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESEScaptionP_rateMichaelis_rateMorrison_rate
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10.0005000.0000000.1800000.82000019.8200001st reaction step8.82000034.56429934.292188
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827 rows × 9 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S caption \\\n", "0 0.000000 0.000000 0.000000 1.000000 20.000000 Set concentration \n", "1 0.000500 0.000000 0.180000 0.820000 19.820000 1st reaction step \n", "2 0.000750 0.002205 0.246431 0.753569 19.751364 \n", "3 0.000763 0.002356 0.249321 0.750679 19.748323 \n", "4 0.000769 0.002432 0.250756 0.749244 19.746811 \n", ".. ... ... ... ... ... ... \n", "822 1.468805 19.947437 0.005824 0.994176 0.046738 \n", "823 1.475832 19.949443 0.005603 0.994397 0.044954 \n", "824 1.482859 19.951372 0.005391 0.994609 0.043237 \n", "825 1.489886 19.953228 0.005186 0.994814 0.041586 \n", "826 1.496913 19.955014 0.004989 0.995011 0.039997 \n", "\n", " P_rate Michaelis_rate Morrison_rate \n", "0 0.000000 34.656189 34.292188 \n", "1 8.820000 34.564299 34.292188 \n", "2 12.075109 34.528950 34.291025 \n", "3 12.216716 34.527380 34.290945 \n", "4 12.287060 34.526599 34.290905 \n", ".. ... ... ... \n", "822 0.285397 0.275111 0.276209 \n", "823 0.274566 0.264664 0.265721 \n", "824 0.264142 0.254610 0.255628 \n", "825 0.254109 0.244934 0.245914 \n", "826 0.244454 0.235622 0.236566 \n", "\n", "[827 rows x 9 columns]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df[\"Morrison_rate\"] = rxn.compute_rate_morrison(E_tot=E0,\n", " S_tot=df[\"S\"] + df[\"ES\"])\n", "df" ] }, { "cell_type": "code", "execution_count": 28, "id": "2c115147-d5e1-4b9b-81ba-0080de480128", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
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"ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Reaction rate, dP/dt, as a function of Substrate concentration" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0.03999702266555944, 20 ], "title": { "text": "S" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.925343811394892, 36.581532416502945 ], "title": { "text": "dP/dt" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's take a closer look at the rightmost portion\n", "PlotlyHelper.plot_pandas(df=df, x_var=\"S\", fields=[\"P_rate\", \"Michaelis_rate\", \"Morrison_rate\"],\n", " title=\"Reaction rate, dP/dt, as a function of Substrate concentration\",\n", " y_label=\"dP/dt\", legend_header=\"Rates\",\n", " vertical_lines_to_add=18.9,\n", " colors=[\"blue\", \"yellow\", \"orange\"],\n", " range_x=[17, 20], range_y=[32,35])" ] }, { "cell_type": "markdown", "id": "d09def65-ccfe-4a46-91a1-dda169d31809", "metadata": {}, "source": [ "# In this scenario, the Morrison model appears to be only very mildly better than the Michaelis-Menten one at the early reaction times (large [S], close to the initial value of 20.) - and virtually identical everywhere else. \n", "Then why even bother with it? In the next two experiments, `enzyme_2` and `enzyme_3`, we'll see how the Morrison model becomes progressively better than Michaelis-Menten at increasingly higher amounts of enzyme." ] }, { "cell_type": "code", "execution_count": null, "id": "2b6f6e1a-f620-457a-b4f6-cb0fde4fc035", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }