{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## Comparing the dynamics of the reaction `A <-> B` , with and without an enzyme \n", "\n", "### Here, we'll explore a HYPOTHETICAL kinetics scenario where the catalyzed reaction `A` + `E` <-> `B` + `E` follows the kinetics of a 2nd-order *elementary* reaction \n", "\n", "LAST REVISED: June 23, 2024 (using v. 1.0 beta36)" ] }, { "cell_type": "code", "execution_count": 1, "id": "cbb1af2e-3564-460e-a4ae-41e4ec4f719f", "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": "087c0d08", "metadata": { "tags": [] }, "outputs": [], "source": [ "from life123 import ChemData\n", "from life123 import UniformCompartment" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "# 1. WITHOUT ENZYME\n", "### `A` <-> `B`" ] }, { "cell_type": "code", "execution_count": 3, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'A', 'B'}\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics, favorable thermodynamics in the forward direction, \n", "# and a forward rate that is much slower than it would be with the enzyme - as seen in part 2, below\n", "chem_data.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=1., delta_G=-3989.73)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "0e771dda-1c0f-4fc0-ab21-049740643897", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 4, "id": "5563e467-a637-44fa-9ba1-d35ddd82c887", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 20.0\n", " Species 1 (B). Conc: 0.0\n", "Set of chemicals involved in reactions: {'A', 'B'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"fast\")\n", "dynamics.set_conc(conc={\"A\": 20.},\n", " snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "651941bb-7098-4065-a598-e50c0b641ab3", "metadata": { "tags": [] }, "source": [ "### Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 5, "id": "76f24d9a-a788-41d8-90a4-db87386f91aa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "16 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 0\n", "Number of step re-do's because of elective soft aborts: 1\n", "Norm usage: {'norm_A': 10, 'norm_B': 9, 'norm_C': 8, 'norm_D': 8}\n" ] } ], "source": [ "dynamics.enable_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(duration=3.0,\n", " initial_step=0.1, variable_steps=True)" ] }, { "cell_type": "code", "execution_count": 6, "id": "e58db01b-b932-4f60-91c2-a578353a3702", "metadata": {}, "outputs": [], "source": [ "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 7, "id": "4a19ad2a-fbd2-420a-b958-2daf88bcc841", "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
SYSTEM TIME=%{x}
Concentration=%{y}", "legendgroup": "A", "line": { "color": "darkorange", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "A", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.06, 0.15, 0.22199999999999998, 0.294, 0.366, 0.438, 0.546, 0.654, 0.8160000000000001, 0.978, 1.2209999999999999, 1.4639999999999997, 1.8284999999999996, 2.1929999999999996, 2.7397499999999995, 3.559874999999999 ], "xaxis": "x", "y": [ 20, 18.8, 17.129599977578295, 15.937602496609351, 14.848593580178377, 13.853675017848747, 12.944717404432549, 11.699081870626607, 10.61488067407264, 9.199347555387318, 8.058994027366417, 6.680990766576445, 5.70481318711416, 4.667526817306994, 4.083949427158638, 3.5914684013706313, 3.337421980365684 ], "yaxis": "y" }, { "hovertemplate": "Chemical=B
SYSTEM TIME=%{x}
Concentration=%{y}", "legendgroup": "B", "line": { "color": "green", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "B", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.06, 0.15, 0.22199999999999998, 0.294, 0.366, 0.438, 0.546, 0.654, 0.8160000000000001, 0.978, 1.2209999999999999, 1.4639999999999997, 1.8284999999999996, 2.1929999999999996, 2.7397499999999995, 3.559874999999999 ], "xaxis": "x", "y": [ 0, 1.2, 2.870400022421707, 4.062397503390652, 5.151406419821625, 6.146324982151256, 7.055282595567456, 8.300918129373397, 9.385119325927363, 10.800652444612686, 11.941005972633587, 13.319009233423559, 14.295186812885843, 15.33247318269301, 15.916050572841366, 16.408531598629374, 16.66257801963432 ], "yaxis": "y" } ], "layout": { "autosize": true, "legend": { "title": { "text": "Chemical" }, "tracegroupgap": 0 }, "shapes": [ { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0, "x1": 0, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.06, "x1": 0.06, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.15, "x1": 0.15, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.22199999999999998, "x1": 0.22199999999999998, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.294, "x1": 0.294, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.366, "x1": 0.366, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.438, "x1": 0.438, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.546, "x1": 0.546, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.654, "x1": 0.654, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.8160000000000001, "x1": 0.8160000000000001, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.978, "x1": 0.978, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 1.2209999999999999, "x1": 1.2209999999999999, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 1.4639999999999997, "x1": 1.4639999999999997, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 1.8284999999999996, "x1": 1.8284999999999996, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 2.1929999999999996, "x1": 2.1929999999999996, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 2.7397499999999995, "x1": 2.7397499999999995, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 3.559874999999999, "x1": 3.559874999999999, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" } ], "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "sequentialminus": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "WITHOUT enzyme
Reaction `A <-> B` . Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0021039450354609925, 3.56197894503546 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": "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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['darkorange', 'green'], show_intervals=True, title_prefix=\"WITHOUT enzyme\")" ] }, { "cell_type": "markdown", "id": "ef7ed670-39dd-4e44-afec-82dbd6e6a431", "metadata": {}, "source": [ "#### Note how the time steps get automatically adjusted, as needed by the amount of change - including a complete step abort/redo at time=0" ] }, { "cell_type": "code", "execution_count": 8, "id": "550dc065-6f3a-4961-b1ea-d52e0aa0baff", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.7243697199909254, 10.000000000000002)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersect(\"A\", \"B\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 9, "id": "19e66cfc-8e1c-4332-b85d-2b8ced01d4b3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 3.337 ; [B] = 16.66\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.99265\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 5.00001\n", "Discrepancy between the two values: 0.1471 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "6517c7bd-3243-4326-9c7e-0ca04da6d812", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "27401e5d-8f3e-4c27-8438-129d3e3408a2", "metadata": {}, "source": [ "# 2. WITH ENZYME `E`\n", "### `A` + `E` <-> `B` + `E`" ] }, { "cell_type": "markdown", "id": "878edb65-e2f9-46d0-b3ba-3a82c064243b", "metadata": {}, "source": [ "# NOTE: we're exploring a very HYPOTHETICAL scenario where this reaction follows the kinetics of a 2nd-order elementary reaction! \n", "### Also, we'll completely ignore the concomitant (much slower) direct reaction A <-> B (in other experiments, we'll re-include that slower reaction)" ] }, { "cell_type": "code", "execution_count": 10, "id": "ffaef48b-e95b-4cb9-ab9f-c526a159222e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A + E <-> B + E (kF = 10 / kR = 2 / delta_G = -3,989.7 / K = 5) | Enzyme: E | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions (not counting enzymes): {'A', 'B'}\n", "Set of enzymes involved in the above reactions: {'E'}\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"A\", \"B\", \"E\"])\n", "\n", "# Reaction A + E <-> B + E , with 1st-order kinetics, and a forward rate that is faster than it was without the enzyme\n", "# Thermodynamically, there's no change from the reaction without the enzyme\n", "chem_data.add_reaction(reactants=[\"A\", \"E\"], products=[\"B\", \"E\"],\n", " forward_rate=10., delta_G=-3989.73)\n", "\n", "chem_data.describe_reactions() # Notice how the enzyme `E` is noted in the printout below" ] }, { "cell_type": "markdown", "id": "12a8ca3f-a25c-4902-baef-586805338279", "metadata": {}, "source": [ "### Notice how, while the ratio kF/kR is the same as it was without the enzyme (since it's dictated by the energy difference), the individual values of kF and kR now are each 10 times bigger than before" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals (to what they originally were)" ] }, { "cell_type": "code", "execution_count": 11, "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: 20.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (E). Conc: 30.0\n", "Set of chemicals involved in reactions (not counting enzymes): {'A', 'B'}\n", "Set of enzymes involved in reactions: {'E'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\")\n", "dynamics.set_conc(conc={\"A\": 20., \"B\": 0., \"E\": 30.},\n", " snapshot=True) # Plenty of enzyme `E`\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726", "metadata": { "tags": [] }, "source": [ "### Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 12, "id": "dde62826-d170-4b39-b027-c0d56fb21387", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "43 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 3\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 31, 'norm_B': 28, 'norm_C': 28, 'norm_D': 28}\n" ] } ], "source": [ "dynamics.enable_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(duration=0.1,\n", " initial_step=0.1, variable_steps=True)" ] }, { "cell_type": "markdown", "id": "33d9466e-c41e-4e92-a8fd-3b594aa201b0", "metadata": {}, "source": [ "#### Note how the (proposed) initial step - kept the same as the previous run - is now _extravagantly large_, given the much-faster reaction dynamics. However, the variable-step engine intercepts and automatically corrects the problem!" ] }, { "cell_type": "code", "execution_count": 13, "id": "b0543cac-f3cd-453c-ae9b-c00f01e61fa8", "metadata": {}, "outputs": [], "source": [ "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 14, "id": "8cc14786-cc9f-4399-9203-290526d3a326", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
SYSTEM TIME=%{x}
Concentration=%{y}", "legendgroup": "A", "line": { "color": "darkorange", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "A", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.00025000000000000006, 0.0003750000000000001, 0.0005000000000000001, 0.0006250000000000001, 0.0007500000000000001, 0.0008750000000000001, 0.0010000000000000002, 0.0011250000000000003, 0.0012500000000000005, 0.0013750000000000006, 0.0015250000000000005, 0.0016750000000000005, 0.0018550000000000005, 0.002071000000000001, 0.002330200000000001, 0.0025894000000000012, 0.0029004400000000015, 0.0032736880000000016, 0.0036469360000000017, 0.004094833600000002, 0.004542731200000002, 0.004990628800000002, 0.005528105920000003, 0.006065583040000003, 0.006710555584000003, 0.007484522636800003, 0.008413283100160002, 0.009527795656192002, 0.010865210723430403, 0.012470108804116482, 0.014395986500939779, 0.016707039737127734, 0.01948030362055328, 0.022808220280663934, 0.02680172027279672, 0.031593920263356064, 0.03734456025202727, 0.044245328238432725, 0.05252624982211927, 0.06246335572254312, 0.07438788280305174, 0.08869731529966209, 0.1058686342955945 ], "xaxis": "x", "y": [ 20, 18.5, 17.817499988322027, 17.165712471856086, 16.54325538855674, 15.94880886915984, 15.381112438507849, 14.8389623428155, 14.3212089972085, 13.826754548122938, 13.354550545396744, 12.813404753861018, 12.301480830012633, 11.72034478592084, 11.068170663981231, 10.34641737879167, 9.692012324498002, 8.980002859979733, 8.221263685106354, 7.564475729230228, 6.88223271354949, 6.3099966821992295, 5.830029767112873, 5.34693909761987, 4.9573224773808695, 4.58024764562945, 4.232821487988652, 3.932073323218025, 3.691843042719504, 3.5192302209391038, 3.411824172644529, 3.3574032304570443, 3.337375182039971, 3.333337023279125, 3.3333291480230174, 3.3333310196544024, 3.3333300366891363, 3.3333308920950366, 3.3333297935177297, 3.3333317502281075, 3.333327098428005, 3.333341485650293, 3.333284636054847, 3.333567842193264 ], "yaxis": "y" }, { "hovertemplate": "Chemical=B
SYSTEM TIME=%{x}
Concentration=%{y}", "legendgroup": "B", "line": { "color": "green", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "B", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.00025000000000000006, 0.0003750000000000001, 0.0005000000000000001, 0.0006250000000000001, 0.0007500000000000001, 0.0008750000000000001, 0.0010000000000000002, 0.0011250000000000003, 0.0012500000000000005, 0.0013750000000000006, 0.0015250000000000005, 0.0016750000000000005, 0.0018550000000000005, 0.002071000000000001, 0.002330200000000001, 0.0025894000000000012, 0.0029004400000000015, 0.0032736880000000016, 0.0036469360000000017, 0.004094833600000002, 0.004542731200000002, 0.004990628800000002, 0.005528105920000003, 0.006065583040000003, 0.006710555584000003, 0.007484522636800003, 0.008413283100160002, 0.009527795656192002, 0.010865210723430403, 0.012470108804116482, 0.014395986500939779, 0.016707039737127734, 0.01948030362055328, 0.022808220280663934, 0.02680172027279672, 0.031593920263356064, 0.03734456025202727, 0.044245328238432725, 0.05252624982211927, 0.06246335572254312, 0.07438788280305174, 0.08869731529966209, 0.1058686342955945 ], "xaxis": "x", "y": [ 0, 1.5000000000000004, 2.1825000116779734, 2.834287528143915, 3.4567446114432605, 4.05119113084016, 4.618887561492153, 5.161037657184502, 5.678791002791504, 6.173245451877064, 6.645449454603258, 7.186595246138984, 7.69851916998737, 8.279655214079161, 8.93182933601877, 9.653582621208331, 10.307987675502, 11.01999714002027, 11.778736314893647, 12.435524270769774, 13.117767286450512, 13.690003317800773, 14.16997023288713, 14.653060902380131, 15.042677522619133, 15.419752354370553, 15.767178512011352, 16.06792667678198, 16.308156957280502, 16.480769779060903, 16.588175827355478, 16.642596769542962, 16.662624817960037, 16.666662976720882, 16.66667085197699, 16.6666689803456, 16.666669963310866, 16.666669107904966, 16.666670206482273, 16.666668249771895, 16.666672901571996, 16.66665851434971, 16.666715363945155, 16.66643215780674 ], "yaxis": "y" }, { "hovertemplate": "Chemical=E
SYSTEM TIME=%{x}
Concentration=%{y}", "legendgroup": "E", "line": { "color": "violet", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "E", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.00025000000000000006, 0.0003750000000000001, 0.0005000000000000001, 0.0006250000000000001, 0.0007500000000000001, 0.0008750000000000001, 0.0010000000000000002, 0.0011250000000000003, 0.0012500000000000005, 0.0013750000000000006, 0.0015250000000000005, 0.0016750000000000005, 0.0018550000000000005, 0.002071000000000001, 0.002330200000000001, 0.0025894000000000012, 0.0029004400000000015, 0.0032736880000000016, 0.0036469360000000017, 0.004094833600000002, 0.004542731200000002, 0.004990628800000002, 0.005528105920000003, 0.006065583040000003, 0.006710555584000003, 0.007484522636800003, 0.008413283100160002, 0.009527795656192002, 0.010865210723430403, 0.012470108804116482, 0.014395986500939779, 0.016707039737127734, 0.01948030362055328, 0.022808220280663934, 0.02680172027279672, 0.031593920263356064, 0.03734456025202727, 0.044245328238432725, 0.05252624982211927, 0.06246335572254312, 0.07438788280305174, 0.08869731529966209, 0.1058686342955945 ], "xaxis": "x", "y": [ 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30 ], "yaxis": "y" } ], "layout": { "autosize": true, "legend": { "title": { "text": "Chemical" }, "tracegroupgap": 0 }, "shapes": [ { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0, "x1": 0, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.00025000000000000006, "x1": 0.00025000000000000006, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0003750000000000001, "x1": 0.0003750000000000001, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0005000000000000001, "x1": 0.0005000000000000001, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0006250000000000001, "x1": 0.0006250000000000001, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0007500000000000001, "x1": 0.0007500000000000001, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0008750000000000001, "x1": 0.0008750000000000001, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0010000000000000002, "x1": 0.0010000000000000002, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0011250000000000003, "x1": 0.0011250000000000003, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0012500000000000005, "x1": 0.0012500000000000005, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0013750000000000006, "x1": 0.0013750000000000006, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0015250000000000005, "x1": 0.0015250000000000005, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0016750000000000005, "x1": 0.0016750000000000005, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0018550000000000005, "x1": 0.0018550000000000005, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.002071000000000001, "x1": 0.002071000000000001, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.002330200000000001, "x1": 0.002330200000000001, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0025894000000000012, "x1": 0.0025894000000000012, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0029004400000000015, "x1": 0.0029004400000000015, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0032736880000000016, "x1": 0.0032736880000000016, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.0036469360000000017, "x1": 0.0036469360000000017, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.004094833600000002, "x1": 0.004094833600000002, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.004542731200000002, "x1": 0.004542731200000002, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.004990628800000002, "x1": 0.004990628800000002, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.005528105920000003, "x1": 0.005528105920000003, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.006065583040000003, "x1": 0.006065583040000003, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.006710555584000003, "x1": 0.006710555584000003, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.007484522636800003, "x1": 0.007484522636800003, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.008413283100160002, "x1": 0.008413283100160002, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.009527795656192002, "x1": 0.009527795656192002, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.010865210723430403, "x1": 0.010865210723430403, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.012470108804116482, "x1": 0.012470108804116482, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.014395986500939779, "x1": 0.014395986500939779, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.016707039737127734, "x1": 0.016707039737127734, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.01948030362055328, "x1": 0.01948030362055328, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.022808220280663934, "x1": 0.022808220280663934, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.02680172027279672, "x1": 0.02680172027279672, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.031593920263356064, "x1": 0.031593920263356064, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.03734456025202727, "x1": 0.03734456025202727, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.044245328238432725, "x1": 0.044245328238432725, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.05252624982211927, "x1": 0.05252624982211927, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.06246335572254312, "x1": 0.06246335572254312, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.07438788280305174, "x1": 0.07438788280305174, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.08869731529966209, "x1": 0.08869731529966209, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" }, { "line": { "color": "gray", "dash": "dot", "width": 1 }, "type": "line", "x0": 0.1058686342955945, "x1": 0.1058686342955945, "xref": "x", "y0": 0, "y1": 1, "yref": "y domain" } ], "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "sequentialminus": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "WITH enzyme
Reaction `A + E <-> B + E` . Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -6.955889244125788e-05, 0.10593819318803575 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.6666666666666665, 31.666666666666668 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": "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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"WITH enzyme\")" ] }, { "cell_type": "code", "execution_count": 15, "id": "2cf77dd1-040e-4e3a-9867-678479a3dda6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0024674107137523833, 10.000000000000002)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersect(\"A\", \"B\", t_start=0, t_end=0.02)" ] }, { "cell_type": "code", "execution_count": 16, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + E <-> B + E\n", "Final concentrations: [A] = 3.334 ; [E] = 30 ; [B] = 16.67\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.99958\n", " Formula used: ([B][E]) / ([A][E])\n", "2. Ratio of forward/reverse reaction rates: 5.00001\n", "Discrepancy between the two values: 0.008546 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "97efd24d-c771-4354-a924-eb21bc3d070c", "metadata": {}, "source": [ "## Thanks to the (abundant) enzyme, the reaction reaches equilibrium roughly around t=0.02, far sooner than the roughly t=3.5 without enzyme\n", "The concentrations of `A` and `B` now become equal (cross-over) at t=0.00246 , rather than t=0.740" ] }, { "cell_type": "code", "execution_count": 17, "id": "47c6d97b-a778-47c1-9cad-e75433a32f66", "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", " \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", " \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", " \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", " \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", " \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", " \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", " \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", " \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", " \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", "
SYSTEM TIMEABEcaption
00.00000020.0000000.00000030.0Initialized state
10.00025018.5000001.50000030.0
20.00037517.8175002.18250030.0
30.00050017.1657122.83428830.0
40.00062516.5432553.45674530.0
50.00075015.9488094.05119130.0
60.00087515.3811124.61888830.0
70.00100014.8389625.16103830.0
80.00112514.3212095.67879130.0
90.00125013.8267556.17324530.0
100.00137513.3545516.64544930.0
110.00152512.8134057.18659530.0
120.00167512.3014817.69851930.0
130.00185511.7203458.27965530.0
140.00207111.0681718.93182930.0
150.00233010.3464179.65358330.0
160.0025899.69201210.30798830.0
170.0029008.98000311.01999730.0
180.0032748.22126411.77873630.0
190.0036477.56447612.43552430.0
200.0040956.88223313.11776730.0
210.0045436.30999713.69000330.0
220.0049915.83003014.16997030.0
230.0055285.34693914.65306130.0
240.0060664.95732215.04267830.0
250.0067114.58024815.41975230.0
260.0074854.23282115.76717930.0
270.0084133.93207316.06792730.0
280.0095283.69184316.30815730.0
290.0108653.51923016.48077030.0
300.0124703.41182416.58817630.0
310.0143963.35740316.64259730.0
320.0167073.33737516.66262530.0
330.0194803.33333716.66666330.0
340.0228083.33332916.66667130.0
350.0268023.33333116.66666930.0
360.0315943.33333016.66667030.0
370.0373453.33333116.66666930.0
380.0442453.33333016.66667030.0
390.0525263.33333216.66666830.0
400.0624633.33332716.66667330.0
410.0743883.33334116.66665930.0
420.0886973.33328516.66671530.0
430.1058693.33356816.66643230.0
\n", "
" ], "text/plain": [ " SYSTEM TIME A B E caption\n", "0 0.000000 20.000000 0.000000 30.0 Initialized state\n", "1 0.000250 18.500000 1.500000 30.0 \n", "2 0.000375 17.817500 2.182500 30.0 \n", "3 0.000500 17.165712 2.834288 30.0 \n", "4 0.000625 16.543255 3.456745 30.0 \n", "5 0.000750 15.948809 4.051191 30.0 \n", "6 0.000875 15.381112 4.618888 30.0 \n", "7 0.001000 14.838962 5.161038 30.0 \n", "8 0.001125 14.321209 5.678791 30.0 \n", "9 0.001250 13.826755 6.173245 30.0 \n", "10 0.001375 13.354551 6.645449 30.0 \n", "11 0.001525 12.813405 7.186595 30.0 \n", "12 0.001675 12.301481 7.698519 30.0 \n", "13 0.001855 11.720345 8.279655 30.0 \n", "14 0.002071 11.068171 8.931829 30.0 \n", "15 0.002330 10.346417 9.653583 30.0 \n", "16 0.002589 9.692012 10.307988 30.0 \n", "17 0.002900 8.980003 11.019997 30.0 \n", "18 0.003274 8.221264 11.778736 30.0 \n", "19 0.003647 7.564476 12.435524 30.0 \n", "20 0.004095 6.882233 13.117767 30.0 \n", "21 0.004543 6.309997 13.690003 30.0 \n", "22 0.004991 5.830030 14.169970 30.0 \n", "23 0.005528 5.346939 14.653061 30.0 \n", "24 0.006066 4.957322 15.042678 30.0 \n", "25 0.006711 4.580248 15.419752 30.0 \n", "26 0.007485 4.232821 15.767179 30.0 \n", "27 0.008413 3.932073 16.067927 30.0 \n", "28 0.009528 3.691843 16.308157 30.0 \n", "29 0.010865 3.519230 16.480770 30.0 \n", "30 0.012470 3.411824 16.588176 30.0 \n", "31 0.014396 3.357403 16.642597 30.0 \n", "32 0.016707 3.337375 16.662625 30.0 \n", "33 0.019480 3.333337 16.666663 30.0 \n", "34 0.022808 3.333329 16.666671 30.0 \n", "35 0.026802 3.333331 16.666669 30.0 \n", "36 0.031594 3.333330 16.666670 30.0 \n", "37 0.037345 3.333331 16.666669 30.0 \n", "38 0.044245 3.333330 16.666670 30.0 \n", "39 0.052526 3.333332 16.666668 30.0 \n", "40 0.062463 3.333327 16.666673 30.0 \n", "41 0.074388 3.333341 16.666659 30.0 \n", "42 0.088697 3.333285 16.666715 30.0 \n", "43 0.105869 3.333568 16.666432 30.0 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": null, "id": "5e6c18d4", "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }