{ "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: Nov. 21, 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 = -2,723.4 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'C', 'B', 'A'}\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", "Set of chemicals involved in reactions: {'C', 'B', 'A'}\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_history()" ] }, { "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: [A] = 21.43 ; [B] = 33.81\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: [B] = 33.81 ; [C] = 44.76\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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START_TIMEDelta ADelta BDelta Ctime_stepcaption
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" ], "text/plain": [ " START_TIME Delta A Delta B Delta C time_step caption\n", "197 1.97 -0.914286 0.914286 0.0 0.01 \n", "198 1.98 -0.914286 0.914286 0.0 0.01 \n", "199 1.99 -0.914286 0.914286 0.0 0.01 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_rxn_data(rxn_index=0, tail=3)" ] }, { "cell_type": "code", "execution_count": 13, "id": "1004ce75-b71b-4982-a68d-aa65cf8fcb1b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: C <-> A\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 = -2,723.4 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'C', 'B', 'A'}\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 = -2,723.4 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'C', 'B', 'A'}\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 = -2,723.4 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 18 / delta_G = 4,441.7 / K = 0.16667) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'C', 'B', 'A'}\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_history() # 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: [A] = 10 ; [B] = 30\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: 0.0001018 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: B <-> C\n", "Final concentrations: [B] = 30 ; [C] = 60\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: 3.817e-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: 0.16666698478459493\n", "Discrepancy between the two values: 5.09e-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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