{ "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", "#### Same as experiments `enzyme_1_a` and `enzyme_1_b` but with _a lavish amount of Enzyme_ relative to the initial Substrate concentration. \n", "Experiment `enzyme_2` had a ten-fold increase in enzyme, relative to `enzyme_1_a`. Here, we _another x10 increase!_\n", "\n", "#### Two Coupled Reactions: `E + S <-> ES`, and `ES -> E + P` , using real-life kinetic parameters. \n", "\n", "Please refer to `enzyme_1_a` and `enzyme_1_b` for more details." ] }, { "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` (same as in experiment `enzyme_1`) \n", "satisfies the customary Michaelis-Menten assumptions that `k1_reverse >> k2_forward`\n", "\n", "However, the initial concentration values choosen below, do NOT satisfy the expected Michaelis-Menten assumptions that `[E] << [S]` \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 = \"Jan. 12, 2025\"\n", "LIFE123_VERSION = \"1.0.0rc2\" # 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, 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": 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": 5, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"], plot_colors=[\"green\", \"red\"])" ] }, { "cell_type": "code", "execution_count": 6, "id": "90f9ec41-6e1b-4558-9400-47e35ece6efc", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
namelabelplot_color
0PPgreen
1ESESred
2Adenosine deaminaseEviolet
32,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purineSdarkturquoise
\n", "
" ], "text/plain": [ " name label plot_color\n", "0 P P green\n", "1 ES ES red\n", "2 Adenosine deaminase E violet\n", "3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S darkturquoise" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Our Enzyme\n", "chem_data.add_chemical(name=\"Adenosine deaminase\", label=\"E\", plot_color=\"violet\") \n", "\n", "# Our Substrate\n", "chem_data.add_chemical(name=\"2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine\", label=\"S\", plot_color=\"darkturquoise\")\n", "\n", "chem_data.all_chemicals()" ] }, { "cell_type": "markdown", "id": "f8d4ea7f-0591-467c-9df3-d95f53df75f5", "metadata": {}, "source": [ "### Specify the Kinetic Parameters \n", "This part is identical to experiments `enzyme_1` and `enzyme_2`" ] }, { "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": 7, "id": "6c65843f-4c9a-4698-a78b-28fcb02312c0", "metadata": {}, "outputs": [], "source": [ "# Here we use the \"slower\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n", "uc = UniformCompartment(chem_data=chem_data, preset=\"slower\")" ] }, { "cell_type": "code", "execution_count": 8, "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: {\"P\" (green), \"S\" (darkturquoise), \"E\" (violet), \"ES\" (red)}\n" ] } ], "source": [ "# Reaction E + S <-> ES , with 1st-order kinetics, \n", "uc.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", "uc.add_reaction(reactants=\"ES\", products=[\"E\", \"P\"],\n", " forward_rate=49., reverse_rate=0)\n", "\n", "uc.describe_reactions()" ] }, { "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", "### Unlike in experiments `enzyme_1` and `enzyme_2`, the reaction is \"awash\" in enzyme, relative to initial substrate concentration" ] }, { "cell_type": "code", "execution_count": 9, "id": "8c9e3f86-b9a5-41da-9e1b-75258017808a", "metadata": {}, "outputs": [], "source": [ "S0 = 20.\n", "E0 = 100. # A LAVISH AMOUNT! 10 times more than in experiment `enzyme_2` - and x100 as much as experiment`enzyme_1`" ] }, { "cell_type": "code", "execution_count": 10, "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: 100.0\n", " Species 3 (S). Conc: 20.0\n", "Set of chemicals involved in reactions: {'P', 'S', 'E', 'ES'}\n" ] } ], "source": [ "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": 11, "id": "e6ad72b8-722a-4606-a611-7dc600529f30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "998 total variable step(s) taken in 0.04 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: 3\n", "Norm usage: {'norm_A': 997, 'norm_B': 1000, 'norm_C': 996, 'norm_D': 996}\n", "System Time is now: 0.050362\n" ] } ], "source": [ "# Perform the reactions\n", "uc.single_compartment_react(duration=0.05, initial_step=0.01) # A much-shorter duration than in previous experiments in the series" ] }, { "cell_type": "code", "execution_count": 12, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (999) - only showing 1 every 7 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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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": [ -3.4329841180803204e-05, 0.0503618770122383 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -5.555555555555555, 105.55555555555556 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(show_intervals=True, \n", " title_prefix=\"Almost as much E as S(0)\")" ] }, { "cell_type": "markdown", "id": "ba28bbea-b725-4e1a-9c64-7dbad40cf2c8", "metadata": {}, "source": [ "The general shapes of the various curves is reminiscent of their counterparts in experiment `enzyme_1`, but notice: \n", "\n", "1. The product `P` is being produced on a much-faster timescale than before\n", "2. The maximum amount of the bound enzyme `ES` is no longer puny; in fact, it's a good fraction of the initial [S]\n", "3. The buildup of `ES`, at the very beginning, no longer looks instantaneous relatively to the main reaction: by the time `ES` reaches its maximum value, a non-trivial amount of product `P` has been produced\n", "\n", "In short, the \"transient\" is not so \"transient\"!" ] }, { "cell_type": "code", "execution_count": null, "id": "056f50a9-bb38-4d4c-b518-82302370b254", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2d8336ee-4576-4081-9835-9fd7b8bee273", "metadata": {}, "source": [ "### What is the rate of production of the final reaction product `P`? " ] }, { "cell_type": "code", "execution_count": 13, "id": "21d7d644-779b-4ffa-82cd-25d50cdd5300", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionrxn1_rate
00.0000000.0000000.000000100.00000020.000000Set concentration0.000000
10.0000100.0000000.36000099.64000019.64000011st reaction step17.640000
20.0000110.0000180.39552399.60447719.604459219.380617
30.0000110.0000190.39729599.60270519.602686319.467446
40.0000110.0000190.39818199.60181919.601800419.510856
...........................
9930.04791817.7754982.10193397.8980670.122569993102.994725
9940.04839717.8248422.05536497.9446360.119793994100.712859
9950.04888117.8735762.00937097.9906300.11705599598.459109
9960.04937017.9216951.96395298.0360480.11435399696.233637
9970.04986317.9691971.91911498.0808860.11168999794.036596
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998 rows × 8 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 100.000000 20.000000 \n", "1 0.000010 0.000000 0.360000 99.640000 19.640000 1 \n", "2 0.000011 0.000018 0.395523 99.604477 19.604459 2 \n", "3 0.000011 0.000019 0.397295 99.602705 19.602686 3 \n", "4 0.000011 0.000019 0.398181 99.601819 19.601800 4 \n", ".. ... ... ... ... ... ... \n", "993 0.047918 17.775498 2.101933 97.898067 0.122569 993 \n", "994 0.048397 17.824842 2.055364 97.944636 0.119793 994 \n", "995 0.048881 17.873576 2.009370 97.990630 0.117055 995 \n", "996 0.049370 17.921695 1.963952 98.036048 0.114353 996 \n", "997 0.049863 17.969197 1.919114 98.080886 0.111689 997 \n", "\n", " caption rxn1_rate \n", "0 Set concentration 0.000000 \n", "1 1st reaction step 17.640000 \n", "2 19.380617 \n", "3 19.467446 \n", "4 19.510856 \n", ".. ... ... \n", "993 102.994725 \n", "994 100.712859 \n", "995 98.459109 \n", "996 96.233637 \n", "997 94.036596 \n", "\n", "[998 rows x 8 columns]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# We specify the reaction that involves `P`\n", "rates = uc.add_rate_to_conc_history(rate_name=\"rxn1_rate\")\n", "rates" ] }, { "cell_type": "code", "execution_count": 14, "id": "18ac9b9f-c669-43f6-ac36-ed95b76e1ae5", "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": "markdown", "id": "bfacc983-b8af-467d-87b2-2fee868d8254", "metadata": {}, "source": [ "**The initial transient phase is no longer miniscule in duration**" ] }, { "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": 15, "id": "251dfcc1-0cc2-4bad-af3a-afa2feed4e4c", "metadata": {}, "outputs": [], "source": [ "rxn = ReactionEnz(enzyme=\"E\", substrate=\"S\", product=\"P\",\n", " k1_F=uc.get_reactions().get_forward_rate(0), k1_R=uc.get_reactions().get_reverse_rate(0),\n", " k2_F=uc.get_reactions().get_forward_rate(1))" ] }, { "cell_type": "code", "execution_count": 16, "id": "e279ef7d-61ca-469f-8418-60ad0b1222e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.277777777777779" ] }, "execution_count": 16, "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": 17, "id": "5b073f95-a8ed-4885-8b88-85a04341ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kcat" ] }, { "cell_type": "code", "execution_count": 18, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4900.0" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = rxn.compute_vmax(E_tot=E0) # kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 19, "id": "09dfe215-e89d-4562-8a54-72973c6d2b2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3465.6188605108055" ] }, "execution_count": 19, "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": [ "#### Both `vmax` and the initial reaction rate are 10x what they were in experiment `enzyme_1`, because we started with an `E0` 10 times as large" ] }, { "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 rate as a function of [S]; we'll compare what we computed earlier vs. as given by the approximation of the Michaelis-Menten model" ] }, { "cell_type": "code", "execution_count": 20, "id": "ff21ba16-795a-40ba-b6e6-6e33dbeda25a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionrxn1_rateMichaelis_rate
00.0000000.0000000.000000100.00000020.000000Set concentration0.0000003465.618861
10.0000100.0000000.36000099.64000019.64000011st reaction step17.6400003447.122503
20.0000110.0000180.39552399.60447719.604459219.3806173445.270565
30.0000110.0000190.39729599.60270519.602686319.4674463445.178054
40.0000110.0000190.39818199.60181919.601800419.5108563445.131800
..............................
9930.04791817.7754982.10193397.8980670.122569993102.99472571.495562
9940.04839717.8248422.05536497.9446360.119793994100.71285969.899661
9950.04888117.8735762.00937097.9906300.11705599598.45910968.323957
9960.04937017.9216951.96395298.0360480.11435399696.23363766.768545
9970.04986317.9691971.91911498.0808860.11168999794.03659665.233510
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998 rows × 9 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 100.000000 20.000000 \n", "1 0.000010 0.000000 0.360000 99.640000 19.640000 1 \n", "2 0.000011 0.000018 0.395523 99.604477 19.604459 2 \n", "3 0.000011 0.000019 0.397295 99.602705 19.602686 3 \n", "4 0.000011 0.000019 0.398181 99.601819 19.601800 4 \n", ".. ... ... ... ... ... ... \n", "993 0.047918 17.775498 2.101933 97.898067 0.122569 993 \n", "994 0.048397 17.824842 2.055364 97.944636 0.119793 994 \n", "995 0.048881 17.873576 2.009370 97.990630 0.117055 995 \n", "996 0.049370 17.921695 1.963952 98.036048 0.114353 996 \n", "997 0.049863 17.969197 1.919114 98.080886 0.111689 997 \n", "\n", " caption rxn1_rate Michaelis_rate \n", "0 Set concentration 0.000000 3465.618861 \n", "1 1st reaction step 17.640000 3447.122503 \n", "2 19.380617 3445.270565 \n", "3 19.467446 3445.178054 \n", "4 19.510856 3445.131800 \n", ".. ... ... ... \n", "993 102.994725 71.495562 \n", "994 100.712859 69.899661 \n", "995 98.459109 68.323957 \n", "996 96.233637 66.768545 \n", "997 94.036596 65.233510 \n", "\n", "[998 rows x 9 columns]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's add a column with the rate estimated by the Michaelis-Menten model\n", "rates[\"Michaelis_rate\"] = rxn.compute_rate(S_conc=rates[\"S\"])\n", "rates" ] }, { "cell_type": "code", "execution_count": 21, "id": "6e8cdb8c-0e8e-461f-81a0-f7b75de1d322", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=rxn1_rate
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ggAACCCCAAAJWAgRJKy4ORgABBBBAAAEEEEAAAQQQIEgyBhBAAAEEEEAAAQQQQAABBKwECJJWXByMAAIIIIAAAggggAACCCBAkGQMIIAAAggggAACCCCAAAIIWAkQJK24OBgBBBBAAAEEEEAAAQQQQIAgyRhAAAEEEEAAAQQQQAABBBCwEiBIWnFxMAIIIIAAAggggAACCCCAAEGSMYAAAggggAACCCCAAAIIIGAlQJC04uJgBBBAAAEEEEAAAQQQQAABgiRjAAEEEEAAAQQQQAABBBBAwEqAIGnFxcEIIIAAAggggAACCCCAAAIEScYAAggggAACCCCAAAIIIICAlQBB0oqLgxFAAAEEEEAAAQQQQAABBAiSjAEEEEAAAQQQQAABBBBAAAErAYKkFRcHI4AAAggggAACCCCAAAIIECQZAwgggAACCCCAAAIIIIAAAlYCBEkrLg5GAAEEEEAAAQQQQAABBBAgSDIGEEAAAQQQQAABBBBAAAEErAQIklZcHIwAAggggAACCCCAAAIIIECQZAwggAACCCCAAAIIIIAAAghYCRAkrbg4GAEEEEAAAQQQQAABBBBAgCDJGEAAAQQQQAABBBBAAAEEELASIEhacXEwAggggAACCCCAAAIIIIAAQZIxgAACCCCAAAIIIIAAAgggYCVAkLTi4mAEEEAAAQQQQAABBBBAAAGCJGMAAQQQQAABBBBAAAEEEEDASoAgacXFwQgggAACCCCAAAIIIIAAAgRJxgACCCCAAAIIIIAAAggggICVAEHSiouDEUAAAQQQQAABBBBAAAEECJKMAQQQQAABBBBAAAEEEEAAASsBgqQVFwcjgAACCCCAAAIIIIAAAggQJBkDCCCAAAIIIIAAAggggAACVgIESSsuDkYAAQQQQAABBBBAAAEEECBIMgYQQAABBBBAAAEEEEAAAQSsBAiSVlwcjAACCCCAAAIIIIAAAgggQJBkDCCAAAIIIIAAAggggAACCFgJECStuDgYAQQQQAABBBBAAAEEEECAIMkYQAABBBBAAAEEEEAAAQQQsBIgSFpxcTACCCCAAAIIIIAAAggggABBkjGAAAIIIIAAAggggAACCCBgJUCQtOLiYAQQQAABBBBAAAEEEEAAAYKk4xj46c9fd6yB4gj4ETh40QK1/dUJNbF7yk+F1IKAJ4GFC+aq+eNz1fZXdnmqkWoQ8CfwtsX7qG3/slNNTU/7q5SaEPAkcOhb9vVUE9Ug4F+AIOloSpB0BKS4NwGCpDdKKvIsQJD0DEp1XgUIkl45qcyzAEHSMyjVeRUgSDpyEiQdASnuTYAg6Y2SijwLECQ9g1KdVwGCpFdOKvMsQJD0DEp1XgUIko6cIQXJW754g/rdiy9VY2NjjioUb0OAINmGOuc0ESBImihxTFsCBMm25DmviQBB0kSJY9oSIEg6yhMkHQEp7k2AIOmNkoo8CxAkPYNSnVcBgqRXTirzLECQ9AxKdV4FCJKOnARJR0CKexMgSHqjpCLPAgRJz6BU51WAIOmVk8o8CxAkPYNSnVcBgqQjZ0hB0pGC4i0LECRb7gBOnytAkGRwdFmAINnl3qFtBEnGQJcFCJKOvUOQdASkuDcBgqQ3SiryLECQ9AxKdV4FCJJeOanMswBB0jMo1XkVIEg6chIkHQEp7k2AIOmNkoo8CxAkPYNSnVcBgqRXTiorEJg79nS0oeEONTZnu5ozZ+bPuWPPxCXmzn1m1tflODleKbfnm67dcLu6467vzGrVUYcforZsut6qr6Se57a+oG5ef6lVOQ4OW4Ag6di/IQVJdm11HAwtFydIttwBnD5XgCDJ4OiyAEGyy73TzbaNRSFwThQC582VoBeFwCjwzQTDKPzlBsKq1+IeJH/wD4/PCo4Xrb5RPfvTbVZhkiBZtf/CLkeQdOxfgqQjIMW9CRAkvVFSkWcBgqRnUKrzKkCQ9MrZu8pmwl80U5gzSzgzK6ji0CjhUY6v+pqcOkpNTS1SU9MHqenpmT8nJ4+Mq5ucOnLW1+U4Od51aasEwHSQ3HLvg+qya7+k7rnzJrV0yeL4/Fkzl4/fd1v8vVu+9k214Stfn3XZ5531fnXVqvMzyybrlQOOPXXFrLInn3Q8M5tVB1HHyhEkHTuEIOkISHFvAgRJb5RU5FmAIOkZlOq8ChAkvXK2WlnWTGFy6aivUDgVhcDpKATunjxqTwg8aiYYxuEvOxBWhakzSOqgqIPkJz/2oVGwlFlLeemlrHkzkumv65Cq65YQecOVF6tlp71nRLBs+eVWs6FV7ShXvwBB0tE4pCDpSEHxlgUIki13AKfPFSBIMji6LECQ7G7vpO8pjP/uefmohMLJKBCazBLOHLeoUbA6gqSEu+SMYtYFSSDceOvmUeDLCpJbt72oTj/3klkzm1KXBMWVnzhbnXj8MZnfbxSQk9UqQJB05CVIOgJS3JsAQdIbJRV5FiBIegalOq8CBEmvnIWVSRDMu6/Qx2xh1kxh3tLRNkJhFWkfQTK92c6mjWvUiccds1dzJAA+/ZPnZ31dzyxmBcmHH3tSLV+5LvOy9CykzGw+8NCj8TFVNvmpYkaZ5gQIko7WBElHQIp7EyBIeqOkIs8CBEnPoFTnVYAgWZ0zf8ZwZuZQNqBxubcwfU/hm3+fuX9Q32eo7yesfiXdLekjSCbvkZSwKK/0rq3pWcr0EtWiIJlcIpsnmb7P0qRMd3uFlmkBgqTjWAgpSLJrq+NgaLk4QbLlDuD0uQIESQZHlwUIkrN7R88aJh9PoR9FMfpavDmN/aYzyWA4CoKp+wrlvkO5/7DpJaRdHaO+g6Rcp4TG5IY3emYxGe5MgqRe2po3w5lnmnXfZFf9aVexAEHScYQQJB0BKe5NgCDpjZKKPAsQJD2DUp1XgdCDZHIDGgmCWfcZVp01TN9fqINi/Ge8Ic2ieEMagmH1IVtHkNTBUd8nmRUI9U6rOlymg6W+Ir3bazKEyuzju074xfiQL9/+l7N2aNXnTu/sWl2Ikm0KECQd9QmSjoAU9yZAkPRGSUWeBQiSnkGpzqtAX4NkcuYwLxzq+w5twCQEJncjlXsM48CYWEral/sLba67q8fWESTlWnUw1DOT6aWnco+jPCIkGRCT9zsWPf5D6k/u2pq2JUR2dbTZt4sgaW82q0RIQdKRguItCxAkW+4ATp8rQJBkcHRZoEtBMnnPofy/PLoiuay0ysxhcgOa5LMLk+GQWcPujlDXINndK6NlIQgQJB17kSDpCEhxbwIESW+UVORZgCDpGZTqvAo0ESTzZg9nZhKjh9yPzSw5tXnpmcOicCjH8Oq3AEGy3/0XeusJko49TJB0BKS4NwGCpDdKKvIsQJD0DEp1XgVcgmRZQJxruSlN8p5DCYEsK/Xa1b2sjCDZy24bTKMJko5dHVKQZNdWx8HQcnGCZMsdwOlzBQiSDI4uC2QFSd8BMTl7+OaGNEfG9x3KS5aWMnvY5VHSXtsIku3Zc+ZyAYJkuVHhEQRJR0CKexMgSHqjpCLPAgRJz6BUV1lAdjCdmSXcHi8llXsQ91/4nJqY+H9qOqp1fN6PrR5rURQQp6JHWLApTeWuouAeAYIkQ6HLAgRJx94hSDoCUtybAEHSGyUVeRYgSHoGpbpMgaxZxPF5jyj97EP5f9MXAdFUiuPqFiBI1i1M/S4CBEkXvahsSEHSkYLiLQsQJFvuAE6fK0CQZHC4CqRD4ry5z8QzihISZSdT041qsu5B3H/ft6gdrx4eLS09kCWmrh1Fee8CBEnvpFToUYAg6YhJkHQEpLg3AYKkN0oq8ixAkPQMGlh1PkPixO53KNnFNH0fYtEyU5fNdgLrCi6ngwIEyQ52Ck0aCfQ+SKYfoKofrJrs4+QDVH1/nyDJT1NXBAiSXekJ2pEWIEgOd0zoexJn7keUexN3RPchziw3tZlJTC813T05s1GNhEbXjWoIksMdn324coJkH3ppuG3sfZCUkHjz+ktHPSh/P2zpweqqVefHX1u74Xb13NYXRsf4/n5IQZJdW/v9RkCQ7Hf/hdx6gmS4vatnE/XGNXP3LDmNN7MxfPSFLDdNziT6DIkm8gRJEyWOaUuAINmWPOc1Eeh9kExfpMxQ/vBHT4yC47Lll6t1n7lAnXjcMfGhDz/2pFpz3S1qy6br47+7fp8gaTLMOKYJAYJkE8qco4oAQbKKWvtlkjuczpv7SKXZxOQ9ibsnT1BTU1FojP70MZPoS4gg6UuSeuoQIEjaqW6590G18dbNo8/5dqXtjpYMsfITZ6tlp73HrmBARwcXJKVTf/ldx8Yzklu3vahOP/cSdc+dN6mlSxbH3Zb8mvzd5ftSJ0EyoJ+Gnl8KQbLnHRhw8wmS3ezc9LJTvYFNPLtoOJuYXHI6sTsKivFSU/mzP4++IEh2c3zSqhkBgqTZSJCJouUr18UHH3X4IQRJMzbno4IJkhIgn/7J8yp5D2QTQXLnxJRzJ1ABAj4E5s+bE/1L/3T0L/0+aqMOBPwJzB1T0T1xc6KAweD0p2pS0/bI/anov2h3U5X6M/q6UttLK5mefmf0fMVF0fvK0TP/qXcoFYXEaSX3Jx5dWr4PB8wfH4ueIzkVP0eSFwJdE1gQjc8QX8eeukLdcOXF6rJrvxRf3gUfPUPJqsLH77ttdLlyzKoLz4m/p2f/9PFyUHKiSBeqOiOZbo/U/fCjT47aJ/UnA6rcOnfHXd8ZtTWZP9L7t2S1M5Q+DSZI6g5J3hPZRJD8+Us7QxkLXEfPBRbtN1+9+sbu6MM6/7jR864MrvkLxudGG6yMqVdenwju2tq+oHlzfxxvXDN37MfRf8+oMXkkRhQQZSnqnOg+xaLXtMwa7tmwZnLqHdH/HxktPY0CojoonlWU7w/htfiA+epfXpmIrpcoOYT+7ts1vuXABV6afPfdXqqpVMmZZ+5dTIJbeuYweXuafJ4/9JC3xCFSXnrCSAfN9B4oPoJkuj1yDr3nim6DXvWo/55e2irXsHnL/aMZ0arBthJ0C4WCC5J6alsPNNd7IMvKh7S0tYXxxyk9CrC01SMmVXkVYGlrdc6ZXU5nwuJ4FA71ZjamO57OLDedCYbJTWxkcxtZhspLKZa2Mgq6LOBraetv/7ZSmzc3f6V/8RdKnX12dpDctHHNaA8TfYR87h6Fwj37mWSFtryAVjW4SbDNak+y5Vn7sKSDZDo3SHmTupvvGT9n7H2QlA7TG+cIiezKKi+9kyu7tpoPFHZtNbfq4pEEyS72Cm0SAYJk8TiQx2HILqcyiyj3Kc5sbLM9fkxG2UsHRZlZnIweiaE3siEolsm9+X2CpLkVRzYv4DNITrSwKGTFCrsgmbWasM0gqWdCdc8nl7BmbbYjoTHrVRZSmx9Zfs7Y+yCZfEakkPh+TqQOpw889Ggsnq4/pBlJgqSfH6q2aiFItiXPecsEhh4kXWYVk4/GkNAoy0/1BjfyJy93AYKkuyE11CfgK0jW18JqNefN0kk4O+LQJerZn26bNVGUDm1NzEjKOc9edspoea3JjGTIs49ZPd37IFlt+PorRZD0Z0lNbgIESTc/StcnMIQgmQ6LMpsYL0eNlqXK94peWctPZ2YYj2L5aX3DclQzQbIBZE5RWWBIQVKC2k+f/3l8X6KsKJSXvkexjSCZDoXpVY/pZ9NLe6XdP/iHx2eFYPnaJz/2odETJCoPhg4WJEg6dkpIQdKRguItCxAkW+4ATp8rEEqQrBoW9bMU43AY/Sf3KupHZEiI5NWuAEGyXX/OXiwwlCCpdzot27VVP7MxPSOZfPyHFtU7vpqMsayZRDlHcpdYWZUoL337XPKcRbu2NvU4EpPr9H0MQdJRlCDpCEhxbwIESW+UVORZoE9BMvlsRdncxnRmMRkWk0tQuVfR82CqoTqCZA2oVOlNINQg6Q2IiloVIEg68hMkHQEp7k2AIOmNkoo8C3QxSGZtcFO2DDUdFtnYxvNAaak6gmRL8JzWSIAgacRUeFDeBji6UFUrWKwAACAASURBVMjPeXTXK66BIOkoHFKQZLMdx8HQcnGCZMsdwOlzBdoKknop6tzo2Yrj8x6NnrP4dPxf2W6oMzOKM8tQJ3Yfv+dPHpcR6hAnSIbas2FcF0EyjH4M9SoIko49S5B0BKS4NwGCpDdKKvIsUHeQTM4u6sBYNruY3uCGexY9d3qPqiNI9qizBthUguQAO71Hl0yQdOwsgqQjIMW9CRAkvVFSkWcBX0FSAmM8o7jn3sWy2cX0ozNkKerMLCMb3Hju4l5XR5DsdfcF33iCZPBd3OsLJEg6dl9IQdKRguItCxAkW+4ATp8rYBMk08tR50WhcWzO9sLlqFmzi2xyw4A0FSBImkpxXBsCBMk21DmnqQBB0lQq5ziCpCMgxb0JECS9UVKRZ4GsIKkDowTFeXOfif6THVKLn7mo712UP/XsIs9a9NxZA6yOIDnATu/RJRMke9RZA2wqQdKx0wmSjoAU9yZAkPRGSUUeBSQw7r/vY2r++CPRktJ/qhwYWY7qsVOoapYAQZIB0WUBgmSXe4e2ESQdx0BIQZJdWx0HQ8vFCZItdwCnj5efyn2LC8a/GwfGoiWpyfsXd068T7HZDQOoLQGCZFvynNdEgCBposQxbQkQJB3lCZKOgBT3JkCQ9EZJRSUCtpveTE69I6rxaPXK6+8lMDK6OidAkOxcl9CghMCQg+SWex9Ul137JfX4fbcVjollyy9XKz9xtlp22nu8j52HH3tSLV+5Lm6DaXu8N6LDFRIkHTuHIOkISHFvAgRJb5RUtEcgeR+jyWM1su5hlK/ZbLYDPgJNCxAkmxbnfDYCoQZJCX9P/+T5vULisaeuUEcdfojasul64+A2lCBZ53XajMnksQTJqnJ7yoUUJB0pKN6yAEGy5Q7o+enTy1KLNr6RR2jsnpT/TlCyLLXskRoEyZ4PjsCbT5AMvIN7fnkhB8kjDl2i3v3Ot6sLPnpG3Eu3fO2b6oc/ekI9+9NtcZA0fdUZsJIzkqbtqeu4Oq+zapsJklXlCJKOchT3LUCQ9C0aZn1Zs4wLxu/PvFh9H6MExt2TR8bBscpjNQiSYY6lUK6KIBlKT4Z5HSEHyXWfuWC0bFR6T2Yjb7jyYrXx1s1xkMwKcXKMfsmxspxVByxZBqtf99x5k1q6ZHH8V70kVX9Pz3gmR4yE2A1f+fpe5ZNtSLfHpN68UamvVbdZ2vvwo0/GS3mz2rl2w+3qjru+M/reyScdr25ef2n897y2N/ETQZB0VGZG0hGQ4t4ECJLeKIOpSDa+kZnG8fjRGjMb4cifWa+8Zak+MAiSPhSpoy4BgmRdstTrQ8BfkLzbR3Mq1nHmXuUk/EmQvPtvv68OPeQto+8feshbc4OklDl72SmjGUwJV1etOj8OksllsvL157a+MApa+jh9Ejn+l991bFxWB7HNW+4fzYJKQMwKs0WhUuq5aPWN6po/+MQowBZhJZfw6uPK2pk1IykhMq/tFTvLqhhB0opr74NDCpLs2uo4GFouTpBsuQNaPr3N0tSdE6fEs4sus4w2l0uQtNHi2KYFCJJNi3M+GwF/QfK3o9Nutjm1p2P/Iqrn7Nwg+bYlb1Gnn3vJrPsii0JccqYxGQyTm+0kg2DWRegltHpGT4faE487ZnS4BL1NG9fEf9eb7WQFSTkmWc4UTddfVDarnelNhYraXqVdpu3XxxEkbcVSxxMkHQEp7k2AIOmNsvMVmYbG5NJUk3sZ67pwgmRdstTrQ4Ag6UOROuoS8BskJ+pqZkG9KwqDpIQdmYmTWUm5V9JkNjB9svRMXVaQ1LOWumxyaWhyuWyy7qIgKcell5Sed9b7R7OcZdB5QbKonVkzkkVtJ0iW9UIHvk+Q7EAn0IRYgCAZ5kCYWZr642hJ6qPxsxnz7mfUG97IEtWJ+F7GE+JNcLrwIkh2oRdoQ54AQZKx0WUBf0GyW1eZNZMmLSwLklVmJNNLYtMzfUWzg2XLWbXq1m0vxjOr+r7NMu2sc5a1My9IVp0VLWujyfeZkTRRKjgmpCDpSEHxlgUIki13gIfTm4ZGHRJllrHqBjgemmtcBUHSmIoDWxAgSLaAzimNBQiSM89wlFfRPZJFS1vToU3uZZSXXtoqM6I/+IfHZ+0UK1/75Mc+pP55288zl7ZK4P3p8z8b3a8p9ZksV9Udn3VsWTul3YctPXjWrGdR2/VmQ8aDrcKBBMkKaMkiBElHQIp7EyBIeqNspCLT5al9C41ZeATJRoYUJ6koQJCsCEexRgQIkm8GSR3WNHx611bZwVVe6aWt6d1VZVlrMkjK/6eXqeqdXfNmJPUMZHIQmM5G5oXOsnbqtkj5ol1bs3alrWuwEiQdZQmSjoAU9yZAkPRG6b0ieeTG/OgRG7J76vzx70bLVH+s5GvpVwihkSDpffhQYc0CBMmaganeSSDUIOmEQuHOCBAkHbsipCDJrq2Og6Hl4gTJljtgz+mTz2lcEIfGmcdupF/Jexp37X5fpeczduOKy1vBjGS5EUe0J0CQbM+eM5cLECTLjbp2RN4GOLqdWfd5du0aTNtDkDSVyjmOIOkISHFvAgRJb5RWFSXva5w/L5p1zHhOY3r31C5thGN1sRUPJkhWhKNYIwIEyUaYOUlFAYJkRTiKNSJAkHRkJkg6AlLcmwBB0htlbkV6tnH+vO+WLlHdtfuUaJbx+GgH1XfEO6gO+UWQHHLvd//aCZLd76Mht5AgOeTe7/61EyQd+yikIOlIQfGWBQiS/jtAzzbOH39gzyM4HtnrJHqJal92UPWvVF4jQbLciCPaEyBItmfPmcsFCJLlRhzRngBB0tGeIOkISHFvAgRJd0p5RuPMsxplxvH+zA1xdk6cEj9yQ4Lj0JaoVhUmSFaVo1wTAgTJJpQ5R1UBgmRVOco1IUCQdFQmSDoCUtybAEHSjlLvpCqhcSY83l862yghkpe9AEHS3owSzQkQJJuz5kz2AgRJezNKNCdAkHS0DilIsmur42BouThBsrgDZOdUCYtFy1RlhlHubWS20e9gJkj69aQ2vwIESb+e1OZXgCDp15Pa/AoQJB09CZKOgBT3JkCQnE2p72/cZ/5fZT6CQ++kuitaohr64ze8DbKKFREkK8JRrBEBgmQjzJykogBBsiIcxRoRIEg6MhMkHQEp7k1g6EFSgqM8fiPv/kYJjruipal6UxyWqXobeqUVESRLiTigRQGCZIv4nLpUgCBZSsQBLQoQJB3xQwqSjhQUb1lgaEFSb4wzM+P44702xtG7qb6x60M8gqPlsUmQbLkDOH2hAEGSAdJlAYJkl3uHthEkHccAQdIRkOLeBEIPkmXBUe5vlGc27po4OZp1PEVJkOTVDQGCZDf6gVZkCxAkGRldFiBIdrl3aBtB0nEMECQdASnuTSC0IFm2VFUHx3jGMQqRBEdvQ8l7RQRJ76RU6FGAIOkRk6q8CxAkvZNSoUcBgqQjZkhBkl1bHQdDy8X7HiSTm+NkPcOR4NjyAHM4PUHSAY+itQsQJGsn5gQOAgRJBzyK1i5AkHQkJkg6AlLcm0DfgmTycRyybFX+nnzJDKMsUWWpqrch0lpFBMnW6DmxgQBB0gCJQ1oTIEi2Rs+JDQSsguSxp65QmzauUSced8ysqrfc+6DaeOtmtWXT9QanDOsQgmRY/dnnq+l6kBybsyPeFEc2x5HdVWUGMh0cZdZRlqpyj2OfR+LebSdIhtWfoV0NQTK0Hg3regiSYfVnaFfjJUg+/NiTavnKderx+24Lzaf0ekIKkqUXywGdFuhikExukCP/n3zp5zhKcNy1+5T4PkdeYQoQJMPs11CuiiAZSk+GeR0EyTD7NZSr8hIkb/naN9XmLfe3MiO5dsPt6o67vjPqj5NPOl7dvP7SWf1z0eob1QMPPRp/zff3CZKh/Cj0/zq6ECT1ctWZR3I8stdy1Zmlqu+LguP74llHXsMQIEgOo5/7epUEyb723DDaTZAcRj/39SpLg6SebSy7wKwlr2VlfHx/2fLLZwVY+fvZy05RF3z0jLh6CZrPbX1hFC4lVB629GB11arzvXyfIOmjF6nDh0BbQVJmGouWq0pgjGcdoz9lFpLX8AQIksPr8z5dMUGyT701vLYSJIfX53264tIgmbyYvHsku3TBMjv6wx89MQqOEizXfeaC0X2dEozXXHfLKHy6fj+kIMmurV0ayfZtaSpIJmcd07urSlCUwMh9jvb9F3IJgmTIvdv/ayNI9r8PQ74CgmTIvdv/a7MKkn24XJlxfPc73x7PSG7d9qI6/dxL1D133qSWLlkcNz/5Nfm7y/elToJkH0bFMNpYZ5AsmnWUexvlHkcdHoehzVXaCBAkbbQ4tmkBgmTT4pzPRoAgaaPFsU0LBBUkZTZyw1e+Ptr0p4kg2XSH1Xm+tWvXqiuuuEKNjY3VeRrq7oXAU1Er74v+u2vPn9sTrT4o+v9To//O2vPn0b24IhqJAAIIIIAAAggg4E+gNEjKclbTV5u7tsojSC679ku5s4/MSJr2Isf1VcB1RlI2x9ln/G41f/y7Kr3DKrOOfR0V3Wg3M5Ld6AdakS3AjCQjo8sCzEh2uXdoW2mQTBLJstGzPniyWnbae2bJ5X29Kd70TGTyvK73QJaVD2lpa1P9xXnqEagSJPeZf3e8UY4ER7n3Mfl6Y9eZ3OtYT1cNrlaC5OC6vFcXTJDsVXcNrrEEycF1ea8u2CpI5m22I7OBG2/d3MrjPyTEyiv9yA/dC+za2qvxSGMdBEyCZNFGOZNTR8WP5Hh958d4NIdDP1B0bwGCJKOiywIEyS73Dm0jSDIGuizgJUjqR4Q0vbRV3wOZBZx8HAnPkTQbguzaaubU1aPygqSEx+TMY7L9smT1tZ3L481y5P95IVCHAEGyDlXq9CVAkPQlST11CBAk61ClTl8CVkEybwlr+pEavhrXh3pCWtpKkOzDiMtvYzJIyv2OCxdsUvPn3a/k/5Ov5KyjzELyQqBuAYJk3cLU7yJAkHTRo2zdAgTJuoWp30XAKkjqmcfkbJ+cXJa8rrrwnPiRG0N7ESSH1uPdvd4lB/1A7Z68NQqOs+93lGc7vrHrt+L7HeUZj/J3Xgg0KUCQbFKbc9kKECRtxTi+SQGCZJPanMtWwCpISuVZy0lvuPLivTbgsW1IX48PKUj2tQ+G3G7ZJGffBX+612Y53O845FHRvWsnSHavT2jRmwIESUZDlwUIkl3uHdpmHSQhmy1AkGRENC2QFx6np4+OZh3PjO55PIPNcpruFM5XKECQZIB0WYAg2eXeoW0EScZAlwVKg6QsWx3yjGNZ5xEky4T4vg8BvVnOPvP/Uo3N2TGqUj/fUTbMOWi/d6vtr05Em+ZM+TgldSDgTYAg6Y2SimoQIEjWgEqV3gQIkt4oqagGgdIgKeeUZyk+/ZPn49M3vTNrDdfstcqQgiSb7XgdGs6V5c086p1WZfYxuVmOyeM/nBtFBQhUECBIVkCjSGMCBMnGqDlRBQGCZAU0ijQmYBQkdWv0Zjvy9/POer+6atX5jTW0qyciSHa1Z/rZLtvwmLxKgmQ/+3wIrSZIDqGX+3uNBMn+9t0QWk6QHEIv9/carYJk8jLXbrhd3XHXd+IvpXdx7S+HfcsJkvZmlJgt4BIeCZKMpj4IECT70EvDbSNBcrh934crJ0j2oZeG28bKQTJJNuSlryEFyeH+GDR/5XPHnlb77/tFJfc+yv/rlyxVndkwZ3l0r+MJVg1jRtKKi4MbFCBINojNqawFCJLWZBRoUIAg2SA2p7IW8BIk9Vn10td77rxJLV2y2LoxfSxAkOxjr7XTZgmMMvu43z5fjJ71+Mis8Lgzer7jq298yjo8Jq+EINlOv3LWcgGCZLkRR7QnQJBsz54zlwsQJMuNOKI9AeMgmVzKyv2Rb3YYQbK9wduHM8sOq7LTqn7Wo25zHc95JEj2YUQMs40EyWH2e1+umiDZl54aZjsJksPs975ctVGQvOVr31Sbt9yvtmy6Pr6ui1bfqA5bejCb7UQWIQVJdm3192Or73tcuOCrsyp9befHo6WrH4qXr/p+ESR9i1KfLwGCpC9J6qlDgCBZhyp1+hIgSPqSpJ46BIyCpNwDufITZ6tlp70nbsPWbS+q08+9hEeBECTrGJO9rVOWrh6w8Avx8tXkfY+ybPX1nR+LwuNvqanpRbVdH0GyNloqdhQgSDoCUrxWAYJkrbxU7ihAkHQEpHitAkZB8thTV+y1M2vW12ptaUcrZ0ayox3TULOK7nt85fVPxTOPyWc91tksgmSdutTtIkCQdNGjbN0CBMm6hanfRYAg6aJH2boFCJKOwiEFSUeKQRXPWrpax32PNqgESRstjm1SgCDZpDbnshUgSNqKcXyTAgTJJrU5l60AQdJWLHU8QdIRsEfFy5auyv2Pbb4Ikm3qc+4iAYIk46PLAgTJLvcObSNIMga6LGAcJE0u4vH7bjM5LKhjCJJBdWfmxciGOVm7rr782meV3P/Y1NLVMmmCZJkQ329LgCDZljznNREgSJoocUxbAgTJtuQ5r4mAUZA0qWiox4QUJNm19c1RnDf7KLOOsnGOBMiuvQiSXesR2qMFCJKMhS4LECS73Du0jSDJGOiyAEHSsXcIko6AHSueNfs4sfsE9eobsnFOvbuuulIQJF0FKV+XAEGyLlnq9SFAkPShSB11CRAk65KlXh8CpUFSdmc1fbG01VSqm8cNdUYya/ZRb5wjAVKCZB9eBMk+9NIw20iQHGa/9+WqCZJ96alhtpMgOcx+78tVlwbJ5IVctPpGddYHTx49T1J/L+/rfUFwaWdIM5IuDn0smzX7qJ/52PbGOVU8CZJV1CjThABBsgllzlFVgCBZVY5yTQgQJJtQ5hxVBayCZN6zI7fc+6DaeOtmtWXT9VXb0dtyBMl+dZ3MPu6/7xfVPvPvVvL/8pqaXhQvW5XNc7qycU4VVYJkFTXKNCFAkGxCmXNUFSBIVpWjXBMCBMkmlDlHVQEvQfLhx55Uy1euUyxtrdoNlKtbIO+5jxIeu37vo6kNQdJUiuOaFiBINi3O+WwECJI2WhzbtABBsmlxzmcjYBUk85awSpBcc90tzEjayHfw2BDvkZTlqwcs/MJo9lHYu7zzqsuwIEi66FG2TgGCZJ261O0qQJB0FaR8nQIEyTp1qdtVwCpI6pnHTRvXqBOPO2Z0blnyuurCc9QFHz3DtT29Kx/S0tZQgmTe5jmvvC47r57Z6+WrRT8gBMnevX0MpsEEycF0dS8vlCDZy24bTKMJkoPp6l5eqFWQlCvcuu1Fdfq5l8y62BuuvHivDXh6qVGh0QTJCmg1FclavtrnzXNsmQiStmIc35QAQbIpac5TRYAgWUWNMk0JECSbkuY8VQSsg2SVk4RcJqQg2dd+ylu+2vfNc2z7gyBpK8bxTQkQJJuS5jxVBAiSVdQo05QAQbIpac5TRYAgWUUtUYYg6QhYsbgsX5WdV2UHVr37quy4+toby6N7IJcHu3y1iIsgWXEwUax2AYJk7cScwEGAIOmAR9HaBQiStRNzAgcBgqQDnhQlSDoCWhbX9z/KLKR+SYCU2cc+PvvR8vILDydI+tSkLp8CBEmfmtTlW4Ag6VuU+nwKECR9alKXbwGCpKNoSEGyy5vtjM97RO23zxdVMkDKxjmvvvEpJfdB8lKKIMko6KoAQbKrPUO7RIAgyTjosgBBssu9Q9sIko5jgCDpCFhSXJavSoCUjXT0S2Yeh3b/o4kyQdJEiWPaECBItqHOOU0FCJKmUhzXhgBBsg11zmkqQJA0lco5jiDpCJhTPL2BjixflZlHAmS+N0GynrFIre4CBEl3Q2qoT4AgWZ8tNbsLECTdDamhPgGCpKNtSEHSkcJL8awAKeFRQqSESV4EScZA/wQIkv3rsyG1mCA5pN7u37USJPvXZ0NqMUHSsbcJko6AUXHZQEeWrh6w8AuzdmBlAx07W2Yk7bw4ujkBgmRz1pzJXoAgaW9GieYECJLNWXMmewGCpL3ZrBIEyeqAEiAXLtikFu6ziQBZnXFUkiDpAZEqahEgSNbCSqWeBAiSniCpphYBgmQtrFTqSYAg6QgZUpBsatfWrAApS1dfeX1mCSuvagIEyWpulKpfgCBZvzFnqC5AkKxuR8n6BQiS9RtzhuoCBMnqdnFJgqQ5oH4G5D7z/1KNzdkRFyRAmvuVHUmQLBPi+20JECTbkue8JgIESRMljmlLgCDZljznNREIJkhuufdBtfHWzWrLpuv3uu6LVt+oHnjo0fjrJ590vLp5/aWzjnH5PkGyfJjpAJl8BqQ8wkOeATmx+4TyCjjCSIAgacTEQS0IECRbQOeUxgIESWMqDmxBgCDZAjqnNBbofZB8+LEn1fKV6+ILPurwQ/YKkms33K6e2/rCKDxKaDxs6cHqqlXnx2Vcvx9SkDQeNYYH6iWsByyc6R958QxIQ7wKhxEkK6BRpBEBgmQjzJykogBBsiIcxRoRIEg2wsxJKgr0Pkjq686bkVy2/HK17jMXqBOPOyY+VILnmutuGQVO1+8TJPceeVn3QBIgK/6EWhQjSFpgcWijAgTJRrk5maUAQdISjMMbFSBINsrNySwFgg6SW7e9qE4/9xJ1z503qaVLFsc0ya/J312+L3USJGePuAP2XTdrF1YCpOVPpMPhBEkHPIrWKkCQrJWXyh0FCJKOgBSvVYAgWSsvlTsKECQdgqYEyZ+9tNOxC7pT/L//4fXq9/7jZWpsbMy6UfuMf1Xtu+Dzo8d4TOw+Rb2264roHkh2YbXGrFjgoP3G1StvTKrdk1MVa6AYAvUI7DM+pubNmxvtzDxRzwmoFQEHgcUHzFfbX55QU2raoRaKIlCPwFsPXFBPxdSKgAcBgqRjkNw1Ec6H9uv+8+fV6ss/axUkx8b+ZxQe16o5c56Kh+P09DvV5ORNamr6Vz0MT6qwERifNxaHyGk+C9mwcWwDAmNjc6KdmlU0PhmcDXBzCkuB+dE/dOzaHf0uZ3haynF4EwIyPnkh0FWBoIOkoLveA1lWPqSlrTbPkZQdWA9Y+IXRDOTk1FHq5dc+G2+mw6sdAZa2tuPOWcsFWNpabsQR7QmwtLU9e85cLsDS1nIjjmhPIPgg6bora1n5kIKkyTBcMH6/OnDhajU+75H4cAKkiVozxxAkm3HmLPYCBEl7M0o0J0CQbM6aM9kLECTtzSjRnEDvg2Ty8R+abdWF56gLPnrGSNHlOZFSSVH5oQTJ9LMgCZDN/ZCanokgaSrFcU0LECSbFud8NgIESRstjm1agCDZtDjnsxHofZC0udg6jg09SKYD5NT0IvXq6yvVq2+sjO6DXFQHKXVWFCBIVoSjWO0CBMnaiTmBgwBB0gGPorULECRrJ+YEDgIESQc8KRpSkEzfI8mjPBwHR8PFCZINg3M6YwGCpDEVB7YgQJBsAZ1TGgsQJI2pOLAFAYKkI3qIQXL/ff901kY6PAvScZA0VJwg2RA0p7EWIEhak1GgQQGCZIPYnMpagCBpTUaBBgUIko7YXQ6Sjz82pl7aodSzz8xRO3bMUS+/NHOxzz47eytp+b68PnD659WaK26NNtJ5Kv77U08dra66+k/Uzom9nwW5aNG0OvDA2XulH37E7L8fceSbf09+b1G0IvbAqDwvvwIESb+e1OZPgCDpz5Ka/AsQJP2bUqM/AYKkP0tq8i9AkHQ07UqQfCkKiv/7e2Pqr781Vz3+6BwlIdL0dfTRT6mrr/6cWrHitlGA/Nznrla33bbCtIrKx0mglGApLwmmB+75/2QIPeKImWd1HnCgio6dCaD6+3K8DrTJMpUb1OOCBMked17gTSdIBt7BPb88gmTPOzDw5hMkA+/gnl8eQdKxA9sOkjKbeNMN4+rbW2T2cWZmUb8kWMlMoIQv+X8duJKzg4e9bZ369dP/mzrooO1xsZdfW6Me+j+fVtu3HxT/Xc9WppmSM5z6e3kznfL9nzz7Ztt2RLOk6bY6dsOs4slwqq9Vh8zkTKr+noTR+Os9D6UESZ+jiLp8ChAkfWpSl28BgqRvUerzKUCQ9KlJXb4FCJKOom0GyZvWz1N/fPO8USj7lfdOqQ/+5qQ67vgpJf9f9Fq44KuduA9SAqUES3m99NKceCluOsDqECrflwCb/L4cL19Pl3Hs1lHx0cznntlSHTjlAD1Tmg6k+u9NL+ElSPrqderxLUCQ9C1KfT4FCJI+NanLtwBB0rco9fkUIEg6arYRJGWW8JorZBZybtz6cz8yqS65bGK03LPokrKeB7n9lZvj+yDTu7Y60rRWPBlOdQjVM6tZ94pKGJWv1xVKi2ZI88Konh21CaMEydaGHCcuESBIMkS6LECQ7HLv0DaCJGOgywIEScfeaTpISiA658ML4iWnMlsmAVKCpMlLHudxwMJ18aGTU0dFy1g/q2RHVv0KJUiaWJgeowOoni3VgVPKj0Lqns2LdCDVX/e5hDcdRrNmRv/NL82L+nNSHXrYzHhIL+s1vWaOQ8C3AEHStyj1+RQgSPrUpC7fAgRJ36LU51OAIOmo2WSQlBnIVZ8ej5eyHnvclPoft+8ymoU0XcZKkHQcDDnF0zOkbYXR9DLd9H2jXVmiW08vUGubAgTJNvU5d5kAQbJMiO+3KUCQbFOfc5cJECTLhEq+31SQlPshb1w/Hrfmk7+3W13z+YnSlmctY/3Zjm/Hs5G8+iVgEkZf+Od5atfuKfX00zP3jKaX9bpesZ4V1bvrpoOo3lVXb17U1r2irtdJef8CBEn/ptToT4Ag6c+SmvwLECT9m1KjPwGCpKNlE0EyGSIvXT2hLlm9u7TV6WWsr7z+KfXqGytLy3FAfwXK7pFML9NN3zeqd92ta4luWRDNmxEd+mNd+jsi32w5QTKEXgz3GgiS4fZtCFdGkAyhF8O9BoKkY9/WHSRlU50//vK8uJUyCymzkUUvmYV866LfUPKnvOQeSLkXkllIx47uQfGyIOl6YCLqbgAAFT1JREFUCXpWVN8v2nQQzVuam96wKH7UTc8f5eLaV10rT5DsWo/QnqQAQZLx0GUBgmSXe4e2ESQdx0BdQVI+tP/u+fPV9783Fn0onlZ/Et0PWfRIDwmO++/7RbXfPhvjK5LguOPV9eqNXWcaXyH3SBpTdfLAuoOk60VXnRHNe5apTXvyNivSzxVNL8utsmuuTXuGdixBcmg93q/rJUj2q7+G1lqC5NB6vF/XS5B07K86gqR8cP4PUYh8/LGxeDOdr39jZ+GmOunNdF5+bY16+fU11ldGkLQm61SBrgdJVywdKNP3fqZ3z5XjfD/KhdlQt94jSLr5UbpeAYJkvb7U7iZAkHTzo3S9AgRJR1/fQTL9eI+iEOl7Mx2CpONgaLl46EHShTdvsyL9XFFZrqt305U/fT7CxXY2NMTHthAkXUYvZesWIEjWLUz9LgIESRc9ytYtQJB0FPYZJG1CZHIWcmp6UXQf5Bo203Hsy74XJ0jW14N5y3KbnA2VgJl+fqhekitXnrw3dJHcIxotie/KiyDZlZ6gHVkCBEnGRZcFCJJd7h3aRpB0HAO+gmQyRMozIv/8rl2ZHwTTs5BspuPYgQEVJ0h2szOrzob6vDc0/ciWog2K6gihBMlujk1aNSNAkGQkdFmAINnl3qFtBEnHMeAjSMq9kL9z1vzovq456jeWTaoNfzSRGSJlI50DFq5TY3N2xJvpyG6sEiR5ISACBMkwx0Hy3lC9/FauVGZD00ty9b2hO3ao+P3E5WX6uBaTXXIJki49Qdm6BQiSdQtTv4sAQdJFj7J1CxAkHYVdg2QyRJ77EQmRu/ZqkcxCHrT/RWrB+P3x9+qaheQeScfB0HJxgmTLHdDB01dZkltHCF38C0r9wi/MUfvuN6lkdpRnhnZwsAy4SQTJAXd+Dy6dINmDThpwEwmSjp3vEiS/vWWuWvXp8XjmQJ4PKc+JTL+S90LWPQtJkHQcDC0XJ0i23AGBnT7vuaF13xdatjkRITSwgdaByyFIdqATaEKuAEGSwdFlAYKkY+9UDZJ3/pmEyPnx2S9dPaEuWb17VkvauBeSIOk4GFouTpBsuQM4/UggHUKf3zpXzZs7prY+P6lefkmpZ58di4/1/aiWshCafl5oiDvkMgztBQiS9maUaE6AINmcNWeyFyBI2pvNKlElSJaFyCZnIR0vn+IdEiBIdqgzaMosAZt7JMs2J9IhVO4HTT6qxXVzorIQykxouIOaIBlu34ZwZQTJEHox3GsgSDr2rW2QLAqRbcxCOl4+xTskQJDsUGfQlMpB0oWOEOqiN9yyBMnh9n0frpwg2YdeGm4bCZKOfW8TJItCpGykIxvqSJjkuZCOnTLQ4gTJgXZ8Dy7bZkayrcvpSgiVXXDlFT8zNLExkcnuuG3Z9f28BMm+92DY7SdIht2/fb86gqRjD5oGyaIQecC+6+LHeshLNtT52Y5vx382/eIeyabF/Z6PIOnXk9r8CfQhSLpcrWkIreue0LafE+pi14WyBMku9AJtyBMgSDI2uixAkHTsHZMg+f3vyXMiF8RnSm6sI7OPb130G/EspLxefm2Nevn1NY4tql6cIFndrgslCZJd6AXakCUQepB06fW83XHl/s+8jYnqeESLngk94oip+HKSGxEduEjFs6OL5M9opjS0F0EytB4N63oIkmH1Z2hXQ5B07NGyIJl8TmQyRO63z8Z4FnJszo5WZyGTl0+QdBwMLRcnSLbcAZw+V4AgWc/gqPKIlrpDqN4ZV65YwqkOpF0OoQTJesYntfoRIEj6caSWegQIko6uRUEyK0RKcDxwv9VKdmaV12s7P65eenV9fF8kLwRcBAiSLnqUrVOAIFmnbrW62wqheuZTAmZ8H2j0q0/fD9rW41kIktXGEKWaESBINuPMWaoJECSruY1K5QVJuRfmA7+2QMkv63M/Mqk2/NGueAmrXsoqwVECpARJXgj4ECBI+lCkjjoECJJ1qLZXp37UyksvzYl+x808D1ReP3k2+nv0NVmWm348i4+Z0LpCKEGyvbHEmcsFCJLlRhzRngBB0tE+K0jKL9VzPrwg/uWqQ2RXNtRxvFyKd1iAINnhzhl40wiSAx8AictPhs5k4JT7QfNCqO9nhKZ3xj327fPUS6/tjpbhTsUzpCHfD8pI7J8AQbJ/fTakFhMkHXs7HSSTIfJX3jul/tfd/xjdC/mF0VLWtjfUKbpc7pF0HAwtFydIttwBnD5XgCDJ4PAhUBRCn312LD5FeibUVwhlZ1wfPUgdVQQIklXUKNOUAEHSUToZJGUZqyxnlV9cxx4Xhci/elL96yM+GC9plcd5vPzaZzu9lJUg6TgYWi5OkGy5Azg9QZIx0EmBsvtBf7ZtXL2xc1I9E/3uliA6MzMqoXRmyW7VV9ZSXKlLdsZt637QqtdCufYECJLt2XPmcgGCZLlR4RE6SMovnN85a76SDXbkl8f3H7xKHfa2z8dl23w2pM3lESRttLp3LEGye31Ci2YEmJFkJHRZoOgeyaIQqpfiyrUlnxFaVwhte1OiLvdhyG0jSIbcu/2/NoKkYx/qILnq0/PVnX82Vx151L+ov/nb31e/dMztcc1dXsrqeOkU75gAQbJjHUJzRgIESQZDlwXq2mwnaymuOBRtSlTXUlwdQof0fNAujzmbthEkbbQ4tmkBgqSjuATJa64YV3/85Xnq6KOfUn/3d78W/8murI6wFLcWIEhak1GgIQGCZEPQnKaSQF1BslJj9hQyvR80ngmNluLKq64QWrQUt8vPB3Xx71JZgmSXeoO2pAUIko5j4g8un1A3rh9XK1bcpjZsWKUOOmh7b5ayOl46xTsmQJDsWIfQnJEAQZLB0GWBLgbJql5l94PqTYnqXoor94AedFD0nNADp7kftGpn7ilHkHQEpHitAgRJR9450T8EXn31Neqaaz4X1yTPhZTnQ8qMZN9e3CPZtx6b3V6CZL/7L+TWEyRD7t3+X1tIQdKlN6o8H9TXLKi0W5bdph/NwlJcpQiSLqOasnULECQNhC9afaN64KFH4yNPPul4dfP6S0elvvGNf68+/OFvxH/v+/2QBEmDwdD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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=rates, x_var=\"S\", fields=[\"rxn1_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=1.65,\n", " colors=[\"blue\", \"yellow\"])" ] }, { "cell_type": "markdown", "id": "3d6b91c7-dc26-4a04-8a27-4d1b10f4d96e", "metadata": {}, "source": [ "Let's recall that our reactions started out with [S]=20 \n", "The curve overlap is still passable at later times (left part of graph, when [S] drops below about 12), but is rather bad at earlier times (when [S] > 12) \n", "### We no longer have the striking overlap we had in experiment `enzyme_1`" ] }, { "cell_type": "markdown", "id": "6e3f2c52-49ce-4e48-97ab-24c2274fa2cc", "metadata": {}, "source": [ "## In this scenario, with a lot more initial enzyme `E` than in experiment `enzyme_1`, the Michaelis-Menten model suffers from poor accuracy for an non-trivial early time, because the transient early phase (when `ES` builds up from zero) is no longer very brief" ] }, { "cell_type": "markdown", "id": "291b603e-45fd-4cb9-a479-82ee4e4ba936", "metadata": {}, "source": [ "#### This is as expected, because we substantially deviated from the Michaelis-Menten assumptions that `[E] << [S]`" ] }, { "cell_type": "code", "execution_count": null, "id": "2245bc83-14ec-4dac-ab1e-9be2333f8681", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "bab5822d-adb1-465e-8f2b-7792e712bb18", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d15a9824-b994-4165-8e41-6b28ac39c1fd", "metadata": {}, "source": [ "# 3. Comparing the results to the Morrison model" ] }, { "cell_type": "markdown", "id": "632dbff5-e5fb-421b-8891-6e1c5e6baded", "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" ] }, { "cell_type": "code", "execution_count": 22, "id": "d889a598-82b6-49ea-9cba-b0e8e9997c5c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionrxn1_rateMichaelis_rateMorrison_rate
00.0000000.0000000.000000100.00000020.000000Set concentration0.0000003465.618861889.979162
10.0000100.0000000.36000099.64000019.64000011st reaction step17.6400003447.122503889.979162
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30.0000110.0000190.39729599.60270519.602686319.4674463445.178054889.978342
40.0000110.0000190.39818199.60181919.601800419.5108563445.131800889.978321
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998 rows × 10 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 100.000000 20.000000 \n", "1 0.000010 0.000000 0.360000 99.640000 19.640000 1 \n", "2 0.000011 0.000018 0.395523 99.604477 19.604459 2 \n", "3 0.000011 0.000019 0.397295 99.602705 19.602686 3 \n", "4 0.000011 0.000019 0.398181 99.601819 19.601800 4 \n", ".. ... ... ... ... ... ... \n", "993 0.047918 17.775498 2.101933 97.898067 0.122569 993 \n", "994 0.048397 17.824842 2.055364 97.944636 0.119793 994 \n", "995 0.048881 17.873576 2.009370 97.990630 0.117055 995 \n", "996 0.049370 17.921695 1.963952 98.036048 0.114353 996 \n", "997 0.049863 17.969197 1.919114 98.080886 0.111689 997 \n", "\n", " caption rxn1_rate Michaelis_rate Morrison_rate \n", "0 Set concentration 0.000000 3465.618861 889.979162 \n", "1 1st reaction step 17.640000 3447.122503 889.979162 \n", "2 19.380617 3445.270565 889.978385 \n", "3 19.467446 3445.178054 889.978342 \n", "4 19.510856 3445.131800 889.978321 \n", ".. ... ... ... ... \n", "993 102.994725 71.495562 100.506658 \n", "994 100.712859 69.899661 98.280755 \n", "995 98.459109 68.323957 96.082240 \n", "996 96.233637 66.768545 93.911274 \n", "997 94.036596 65.233510 91.768007 \n", "\n", "[998 rows x 10 columns]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates[\"Morrison_rate\"] = rxn.compute_rate_morrison(E_tot=E0,\n", " S_tot=rates[\"S\"] + rates[\"ES\"])\n", "rates" ] }, { "cell_type": "code", "execution_count": 23, "id": "773188b3-f2e5-4fd0-ac47-d79f65fe13b4", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=rxn1_rate
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_pandas(df=rates, x_var=\"S\", fields=[\"rxn1_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=1.65,\n", " colors=[\"blue\", \"yellow\", \"orange\"])" ] }, { "cell_type": "markdown", "id": "7d724ebe-6828-4f55-8fa8-2f5ef04c4090", "metadata": {}, "source": [ "## The Morrison model is **VASTLY better** than the Michaelis-Menten one in this *high-enzyme scenario*!" ] }, { "cell_type": "code", "execution_count": null, "id": "3f002b91-ddce-4486-869a-353dc81a5698", "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 }