{ "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", "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.set_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": [ -0.002338945466491458, 3.5622139454664903 ], "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: for the sake of the demo, we'll completely ignore the concomitant (much slower) direct reaction A <-> B\n", "This in an approximation that we'll drop in later experiments" ] }, { "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.set_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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }