{ "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: June 23, 2024 (using v. 1.0 beta36)" ] }, { "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 life123 import ChemData as chem\n", "from life123 import UniformCompartment\n", "\n", "import plotly.express as px\n", "import plotly.graph_objects as go\n", "from life123 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_2\"],\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": [ "1" ] }, "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: {'A', 'B', 'C'}\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", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "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}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "initial_conc = {\"A\": 100.} \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: {'A', 'B', 'C'}\n" ] } ], "source": [ "dynamics = UniformCompartment(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\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\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: [C] = 44.76 ; [A] = 21.43\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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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 0.0 -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": "code", "execution_count": null, "id": "97b75540-6fad-4dfd-8f60-a079f12bedc8", "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: {'A', 'B', 'C'}\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": [ "1" ] }, "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: {'A', 'C', 'B'}\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 18, "id": "1e4e5e85-1407-440c-ba9c-dff59843b5ac", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "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: {'A', 'B', 'C'}\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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"" } }, "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": "On the left of vertical gray line: FICTIONAL world; on the right: REAL world!" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 3.9999999999999587 ], "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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", 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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\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\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: [C] = 60 ; [A] = 10\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: 0.166667\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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