{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## Violating the Laws of Physics for Fun and Insight!\n", "### A cascade of reactions `A <-> B <-> C` , mostly in the forward direction\n", "### [PART 1](#impossible_1_part1) : the above, together with a PHYSICALLY-IMPOSSIBLE \"closing\" of the cycle with :\n", "#### `C <-> A`, *ALSO* mostly in the forward direction _(never mind the laws of thermodymics)!_\n", "### [PART 2](#impossible_1_part2) : restoring the law of physics (by letting `C <-> A` adjust its kinetics based on the energy difference.)\n", "\n", "All 1st-order kinetics. \n", "\n", "LAST REVISED: July 14, 2023" ] }, { "cell_type": "markdown", "id": "7ba9c24d-102a-4571-8207-c5766525774f", "metadata": {}, "source": [ "![Temporarily suspending the Laws of Physics](../../docs/impossible_1.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "1d51c42b-fcc0-47c8-9b84-122416b82f4a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "248cf329", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.chemicals.chem_data import ChemData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import plotly.express as px\n", "import plotly.graph_objects as go\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'impossible_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "### Initialize the system" ] }, { "cell_type": "code", "execution_count": 4, "id": "32edd4eb-556d-40d3-8f25-8e515b5beaae", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"B\", \"C\"])\n", "\n", "# Reaction A <-> B, mostly in forward direction (favored energetically)\n", "# Note: all reactions in this experiment have 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=9., reverse_rate=3.)\n", "\n", "# Reaction B <-> C, also favored energetically\n", "chem_data.add_reaction(reactants=\"B\", products=\"C\",\n", " forward_rate=8., reverse_rate=4.)" ] }, { "cell_type": "markdown", "id": "faa20450-8753-4d19-ad1c-0cad77e6d165", "metadata": {}, "source": [ "# Part 1 - \"Turning off the Laws of Physics\"!" ] }, { "cell_type": "code", "execution_count": 5, "id": "95927c4b-8c13-462e-85f6-5d6db3006da2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: A <-> B (kF = 9 / kR = 3 / Delta_G = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `impossible_1.log.htm`]\n" ] } ], "source": [ "# LET'S VIOLATE THE LAWS OF PHYSICS!\n", "# Reaction C <-> A, also mostly in forward direction - MAGICALLY GOING \"UPSTREAM\" from C, to the higher-energy level of \"A\"\n", "chem_data.add_reaction(reactants=\"C\" , products=\"A\",\n", " forward_rate=3., reverse_rate=2.) # PHYSICALLY IMPOSSIBLE! Future versions of Life123 may flag this!\n", "\n", "chem_data.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "15abbc56-c39d-4bb9-b1f1-d3b9911c7749", "metadata": {}, "source": [ "# Notice the absurdity of the energy levels always going down, throughout the cycle (like in an Escher painting!)" ] }, { "cell_type": "markdown", "id": "1c04542a-aba7-466a-9ee8-a2f550c6ced2", "metadata": {}, "source": [ "![Energy levels always going down](../../docs/impossible_1b.jpg)" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 6, "id": "e4ff6a84-f5d5-4645-9c56-d9e981c108df", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': 100.0, 'B': 0.0, 'C': 0.0}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "initial_conc = {\"A\": 100., \"B\": 0., \"C\": 0.} \n", "initial_conc" ] }, { "cell_type": "code", "execution_count": 7, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 100.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (C). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc=initial_conc, snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 8, "id": "50ddd8e3-58c6-41f8-b874-ddc9a1d64d30", "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "200 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(initial_step=0.01, target_end_time=2.0,\n", " variable_steps=False) # To avoid extra complexity, we're sticking to simple fixed-time steps" ] }, { "cell_type": "code", "execution_count": 9, "id": "68172367-1929-4eb2-9350-864eebebb7e1", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves()" ] }, { "cell_type": "code", "execution_count": 10, "id": "fbf24a85-b152-4b24-b350-00bed12e7bb9", "metadata": {}, "outputs": [], "source": [ "# dynamics.explain_time_advance()\n", "\n", "# dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "225e1cd9-8c48-4ed4-8510-268476bae0c0", "metadata": {}, "source": [ "### It might look like an equilibrium has been reached. But NOT! Verify the LACK of final equilibrium state:" ] }, { "cell_type": "code", "execution_count": 11, "id": "5dcb9571-340a-48a0-8711-f4d7ed6dcc0c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [B] = 33.81 ; [A] = 21.43\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.57778\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 3.0\n", "Discrepancy between the two values: 47.41 %\n", "Reaction is NOT in equilibrium (not within 1% tolerance)\n", "\n", "1: B <-> C\n", "Final concentrations: [C] = 44.76 ; [B] = 33.81\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.32394\n", " Formula used: [C] / [B]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 33.8 %\n", "Reaction is NOT in equilibrium (not within 1% tolerance)\n", "\n", "2: C <-> A\n", "Final concentrations: [A] = 21.43 ; [C] = 44.76\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.478723\n", " Formula used: [A] / [C]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 68.09 %\n", "Reaction is NOT in equilibrium (not within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "{False: [0, 1, 2]}" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "f74cae99-4f86-4ce7-ad51-fff15ecdfa56", "metadata": {}, "source": [ "## Not surprisingly, none of the reactions of this physically-impossible hypothetical system are in equilibrium\n", "### Even though the concentrations don't change, it's NOT from equilibrium in the reactions - but rather from a balancing out of consuming and replenishing across reactions. \n", "#### Consider, for example, the concentrations of the chemical `A` at the end time, and contributions to its change (\"Delta A\") from the _individual_ reactions affecting `A`, as available from the diagnostic data:" ] }, { "cell_type": "code", "execution_count": 12, "id": "d3ef9936-020b-4ab3-b762-8a6cffb963b6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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1991.990.9142860.0-0.9142860.01
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" ], "text/plain": [ " START_TIME Delta A Delta B Delta C time_step caption\n", "197 1.97 0.914286 0.0 -0.914286 0.01 \n", "198 1.98 0.914286 0.0 -0.914286 0.01 \n", "199 1.99 0.914286 0.0 -0.914286 0.01 " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_rxn_data(rxn_index=2, tail=3)" ] }, { "cell_type": "markdown", "id": "f5b83b4d-f9be-4bd7-955f-803daa0bb658", "metadata": {}, "source": [ "### Looking at the last row from each of the 2 dataframes above, one case see that, at every reaction cycle, [A] gets reduced by some quantity (0.914286) by the reaction `A <-> B`, while simultaneously getting increased by the SAME amount by the (fictional) reaction `C <-> A`. \n", "### Hence, the concentration of A remains constant - but none of the reactions is in equilibrium!" ] }, { "cell_type": "code", "execution_count": null, "id": "562234fc-6f35-4ad4-ab89-13efa748baa7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d8cdc411-7b4d-4241-a218-9737f6cd2e0a", "metadata": {}, "source": [ "# PART 2 - Let's restore the Laws of Physics!" ] }, { "cell_type": "code", "execution_count": 14, "id": "e743e6a7-a8b1-4aba-b7db-4d7c61277a65", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: A <-> B (kF = 9 / kR = 3 / Delta_G = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 15, "id": "f37675c8-827b-4c3d-bd55-93f776cc4989", "metadata": {}, "outputs": [], "source": [ "dynamics.clear_reactions() # Let's start over with the reactions (without affecting the data from the reactions)" ] }, { "cell_type": "code", "execution_count": 16, "id": "4d98c72b-986e-4122-9b2e-c4592b68d6fb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# For the reactions A <-> B, and B <-> C, everything is being restored to the way it was before\n", "chem_data.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=9., reverse_rate=3.)\n", "\n", "# Reaction , also favored energetically\n", "chem_data.add_reaction(reactants=\"B\", products=\"C\",\n", " forward_rate=8., reverse_rate=4.)" ] }, { "cell_type": "code", "execution_count": 17, "id": "593bbaa1-bdf4-4bfd-a1ce-d0c843ca43f1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 9 / kR = 3 / Delta_G = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 18, "id": "1e4e5e85-1407-440c-ba9c-dff59843b5ac", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# But for the reaction C <-> A, this time we'll \"bend the knee\" to the laws of thermodynamics!\n", "# We'll use the same forward rate as before, but we'll let the reverse rate be picked by the system, \n", "# based of thermodynamic data consistent with the previous 2 reactions : i.e. an energy difference of -(-2,723.41 - 1,718.28) = +4,441.69 (reflecting the \n", "# \"going uphill energetically\" from C to A\n", "chem_data.add_reaction(reactants=\"C\", products=\"A\",\n", " forward_rate=3., delta_G=4441.69) # Notice the positive Delta G: we're going from \"C\", to the higher-energy level of \"A\"" ] }, { "cell_type": "code", "execution_count": 19, "id": "707863ca-48d6-41b2-ad44-8fbce297cb4d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: A <-> B (kF = 9 / kR = 3 / Delta_G = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 18 / Delta_G = 4,441.69 / K = 0.166667) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "2fefd29d-ae6a-4eda-8a8f-81625a99bd30", "metadata": {}, "source": [ "# Notice how, now that we're again following the laws of thermodynamics, the last reaction is mostly IN REVERSE (low K < 1), as it ought to be! \n", "#### (considering how energetically unfavorable it is)" ] }, { "cell_type": "markdown", "id": "6f42feb3-f556-486b-bb8a-29a482ff4d2a", "metadata": {}, "source": [ "### Now, let's continue with this \"legit\" set of reactions, from where we left off in our fantasy world at time t=2:" ] }, { "cell_type": "code", "execution_count": 20, "id": "197dd1e8-9c3e-435a-8bb4-9b8f8cbda54b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "400 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.005, target_end_time=4.0,\n", " variable_steps=False)\n", "\n", "#dynamics.explain_time_advance()\n", "\n", "#dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 21, "id": "f06b91e6-730f-40cc-9566-cef4b16cb169", "metadata": {}, "outputs": [], "source": [ "fig0 = dynamics.plot_curves(suppress=True) # Prepare, but don't show, the main plot" ] }, { "cell_type": "code", "execution_count": 22, "id": "8d6ccc03-3e48-4142-bdbf-ca6d6fe6fda0", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Add a second plot, with a vertical gray line at t=2\n", "fig1 = px.line(x=[2,2], y=[0,100], color_discrete_sequence = ['gray'])\n", "\n", "# Combine the plots, and display them\n", "all_fig = go.Figure(data=fig0.data + fig1.data, layout = fig0.layout) # Note that the + is concatenating lists\n", "all_fig.update_layout(title=\"On the left of vertical gray line: FICTIONAL world; on the right: REAL world!\")\n", "all_fig.show()" ] }, { "cell_type": "markdown", "id": "2e79b987-135d-416d-baa3-797a5d0b56be", "metadata": {}, "source": [ "### Notice how [A] drops at time t=2, when we re-enact the Laws of Physics, because A no longer receives the extra boost from the previous mostly-forward (and thus physically-impossible given the unfavorable energy levels!) reaction `C <-> A`. \n", "### Back to the real world, that (energetically unfavored) reaction now mostly goes IN REVERSE; hence, the boost in [C] as well" ] }, { "cell_type": "markdown", "id": "c81944df-c125-4099-a81f-efc7ae0f9a6e", "metadata": {}, "source": [ "### Now, we have a REAL equilibrium!" ] }, { "cell_type": "code", "execution_count": 23, "id": "f13381bb-d635-4667-b28c-99497370bf27", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [B] = 30 ; [A] = 10\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 3.0\n", "Discrepancy between the two values: 9.469e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: B <-> C\n", "Final concentrations: [C] = 60 ; [B] = 30\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2\n", " Formula used: [C] / [B]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 3.551e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "2: C <-> A\n", "Final concentrations: [A] = 10 ; [C] = 60\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.166667\n", " Formula used: [A] / [C]\n", "2. Ratio of forward/reverse reaction rates: 0.16666696258266173\n", "Discrepancy between the two values: 4.735e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "605b7936-546b-4b0c-bf33-cc5007e5343c", "metadata": {}, "source": [ "### The fact that individual reactions are now in actual, real equilibrium, can be easily seen from the last rows in the diagnostic data. Notice all the delta-concentration values at the final times are virtually zero:" ] }, { "cell_type": "code", "execution_count": 24, "id": "51b6568d-dbbb-4655-9f41-0b1ecc5a18da", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " START_TIME Delta A Delta B Delta C time_step caption\n", "599 3.995 4.261187e-07 0.0 -4.261187e-07 0.005 " ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_rxn_data(rxn_index=2, tail=1)" ] }, { "cell_type": "code", "execution_count": null, "id": "3178f06a", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }