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"# IN-PROGRESS (INCOMPLETE)\n",
"\n",
"## Macromolecules : Binding Affinity and Fractional Occupancy. Regulation of the rates of reactions catalyzed by the macromolecule\n",
"\n",
"### Reaction `A <-> B` catalyzed when ligand `L` binds to `site 1` of macromolecule `M1`\n",
"\n",
"In Part 1 we consider the un-catalyzed reaction `A <-> B` \n",
"In Part 2 we'll see what happens when catalysis is added"
]
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"LAST_REVISED = \"Nov. 11, 2024\"\n",
"LIFE123_VERSION = \"1.0.0.rc.0\" # Library version this experiment is based on"
]
},
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"cell_type": "code",
"execution_count": 2,
"id": "85d0e9c4-0d6e-4056-85a4-3cacefaa7f7d",
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"source": [
"#import set_path # Using MyBinder? Uncomment this before running the next cell!"
]
},
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"cell_type": "code",
"execution_count": 3,
"id": "c1ac7763",
"metadata": {
"tags": []
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"source": [
"#import sys\n",
"#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n",
"# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n",
"\n",
"from life123 import ChemData\n",
"from life123 import UniformCompartment\n",
"\n",
"import plotly.express as px"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8d3de311-5010-4b42-a320-e34607c14a0f",
"metadata": {},
"outputs": [],
"source": []
},
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"cell_type": "markdown",
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"source": [
"# PART 1 - Consider just the un-catalyzed reaction `A <-> B` by itself"
]
},
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"id": "34e5c78b-c23a-47c1-8db0-0e2f997dcff6",
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"Number of reactions: 1 (at temp. 25 C)\n",
"0: A <-> B (kF = 1 / kR = 0.13306 / delta_G = -5,000 / K = 7.5156) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A'}\n"
]
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"# Initialize the system\n",
"chem1 = ChemData(names=[\"A\", \"B\"])\n",
"\n",
"# Reaction A <-> B , without catalysis (slow forward rate, relative to what we'll see in Part 2)\n",
"chem1.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=1. , delta_G= -5000)\n",
"\n",
"chem1.describe_reactions()"
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"SYSTEM STATE at Time t = 0:\n",
"2 species:\n",
" Species 0 (A). Conc: 100.0\n",
" Species 1 (B). Conc: 20.0\n",
"Set of chemicals involved in reactions: {'B', 'A'}\n"
]
}
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"# Set the initial concentrations of all the chemicals\n",
"dynamics1 = UniformCompartment(chem_data=chem1, preset=\"fast\")\n",
"\n",
"dynamics1.set_conc(conc={\"A\": 100., \"B\": 20.},\n",
" snapshot=True)\n",
"\n",
"dynamics1.describe_state()"
]
},
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"cell_type": "code",
"execution_count": 6,
"id": "eed45215-960f-4fc5-b8b0-d3353fe2eecd",
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"name": "stdout",
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"63 total step(s) taken in 0.345 sec\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 31, 'norm_B': 18, 'norm_C': 18, 'norm_D': 18}\n",
"System Time is now: 4.5826\n"
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"source": [
"# Take the system to equilibrium\n",
"dynamics1.enable_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# All of these settings are currently close to the default values... but subject to change; set for repeatability\n",
"#dynamics1.set_thresholds(norm=\"norm_A\", low=0.6, high=1.0, abort=1.44)\n",
"#dynamics1.set_thresholds(norm=\"norm_B\", low=0.04, high=0.6, abort=1.5)\n",
"#dynamics1.set_step_factors(upshift=1.2, downshift=0.7, abort=0.4, error=0.3)\n",
"\n",
"dynamics1.single_compartment_react(initial_step=0.02, duration=4.0,\n",
" variable_steps=True)"
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"cell_type": "code",
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"source": [
"#dynamics1.explain_time_advance()"
]
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"execution_count": 8,
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},
"title": {
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Reaction `A <-> B` . Changes in concentrations with time (time steps shown in dashed lines)"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics1.plot_history(colors=['darkturquoise', 'green'], show_intervals=True, title_prefix=\"WITHOUT catalysis\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "0977ca98-2038-4122-8109-008b3a908193",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 14.14 ; [B] = 105.9\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 7.48607\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 7.51557\n",
"Discrepancy between the two values: 0.3926 %\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",
"dynamics1.is_in_equilibrium()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9dcb87c0-35f2-4f75-9b25-457383753281",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "d4d1109a-4fd7-408a-89a4-286f7cffed7d",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "24961bae-dc76-454b-b3eb-8fca0433eec3",
"metadata": {},
"source": [
"# PART 2"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "23c15e66-52e4-495b-aa3d-ecddd8d16942",
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"# Initialize the system\n",
"chem2 = ChemData(names=[\"A\", \"B\", \"L\"])\n",
"\n",
"chem2.add_macromolecules(\"M1\")\n",
"\n",
"chem2.set_binding_site_affinity(\"M1\", site_number=1, ligand=\"L\", Kd=5.0)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "42f86e37-e634-4746-86bd-07036f47301f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"M1 :\n",
" Site 1 - Kd (dissociation const) for L : 5.0\n"
]
}
],
"source": [
"chem2.show_binding_affinities() # Review the values we have given for the dissociation constants"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a9190b2f-aacb-478e-956d-450245338399",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "83fd43d2-6a90-4b24-ae2c-5a65718e416d",
"metadata": {},
"source": [
"## Define 2 reactions, one with and one without catalysis"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "9211536e-74c5-43e5-8c3e-ab619e3c7a0d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 1 (at temp. 25 C)\n",
"0: A <-> B (kF = 1 / kR = 0.13306 / delta_G = -5,000 / K = 7.5156) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A'}\n"
]
}
],
"source": [
"# Reaction A <-> B , without catalysis (same as he had in part 1)\n",
"chem2.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=1. , delta_G= -5000)\n",
"\n",
"# Reaction A <-> B , WITH catalysis (fast forward rate)\n",
"#rxn = chem2.add_reaction(reactants=\"A\", products=\"B\",\n",
"# forward_rate=10. , delta_G= -5000)\n",
"\n",
"#rxn.set_macro_enzyme(macromolecule=\"M1\", site_number=1)\n",
"\n",
"chem2.describe_reactions()"
]
},
{
"cell_type": "markdown",
"id": "e1edaccb-4940-4040-abd9-ccfce973b671",
"metadata": {},
"source": [
"#### Notice the thermodynamics is (as it should be!) the same - and hence the same equilibrium constants - but the kinetics are very different"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "25baaff8-1a2c-488f-bd6a-c351ec75bd5a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "562261e1-3a62-40f5-ac79-5199b3b60565",
"metadata": {},
"source": [
"### Start with no macromolecule ligand `L` present; hence, only the slow reaction is in effect"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "74b8a860-ddaa-4346-a695-5d4b2b334833",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (A). Conc: 100.0\n",
" Species 1 (B). Conc: 20.0\n",
" Species 2 (L). Conc: 0.0\n",
"Macro-molecules, with their counts: {'M1': 1}\n",
"Fractional Occupancy at the various binding sites for each macro-molecule:\n",
" M1 || 1: 0.0 (L)\n",
"Set of chemicals involved in reactions: {'B', 'A'}\n"
]
}
],
"source": [
"# Set the initial concentrations of all the chemicals, including the macromolecule\n",
"\n",
"dynamics2 = UniformCompartment(chem_data=chem2, preset=\"fast\")\n",
"dynamics2.set_conc(conc={\"A\": 100., \"B\": 20.},\n",
" snapshot=True) # The macromolecule ligand L is absent\n",
"\n",
"dynamics2.set_macromolecules() # By default, set counts to 1 for all the registered macromolecules\n",
"\n",
"dynamics2.describe_state()"
]
},
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"cell_type": "code",
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"source": [
"### Take the initial system to equilibrium"
]
},
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"cell_type": "code",
"execution_count": 14,
"id": "3fdc370b-1f0e-4d3b-9ab4-7c2c16e33ffc",
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"name": "stdout",
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"text": [
"63 total step(s) taken in 0.395 sec\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 31, 'norm_B': 18, 'norm_C': 18, 'norm_D': 18}\n",
"System Time is now: 4.5826\n"
]
}
],
"source": [
"dynamics2.enable_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# All of these settings are currently close to the default values... but subject to change; set for repeatability\n",
"#dynamics2.set_thresholds(norm=\"norm_A\", low=0.6, high=1.0, abort=1.44)\n",
"#dynamics2.set_thresholds(norm=\"norm_B\", low=0.04, high=0.6, abort=1.5)\n",
"#dynamics2.set_step_factors(upshift=1.2, downshift=0.7, abort=0.4, error=0.3)\n",
"\n",
"dynamics2.single_compartment_react(initial_step=0.02, duration=4.0,\n",
" variable_steps=True)"
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"cell_type": "code",
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"text": [
"From time 0.012 to 0.03, in 1 step of 0.018\n",
"From time 0.03 to 0.1164, in 6 steps of 0.0144\n",
"From time 0.1164 to 0.138, in 1 step of 0.0216\n",
"From time 0.138 to 0.2762, in 8 steps of 0.0173\n",
"From time 0.2762 to 0.3022, in 1 step of 0.0259\n",
"From time 0.3022 to 0.4473, in 7 steps of 0.0207\n",
"From time 0.4473 to 0.4784, in 1 step of 0.0311\n",
"From time 0.4784 to 0.6028, in 5 steps of 0.0249\n",
"From time 0.6028 to 0.6402, in 1 step of 0.0373\n",
"From time 0.6402 to 0.7596, in 4 steps of 0.0299\n",
"From time 0.7596 to 0.8044, in 1 step of 0.0448\n",
"From time 0.8044 to 0.9477, in 4 steps of 0.0358\n",
"From time 0.9477 to 1.001, in 1 step of 0.0537\n",
"From time 1.001 to 1.087, in 2 steps of 0.043\n",
"From time 1.087 to 1.152, in 1 step of 0.0645\n",
"From time 1.152 to 1.255, in 2 steps of 0.0516\n",
"From time 1.255 to 1.333, in 1 step of 0.0774\n",
"From time 1.333 to 1.456, in 2 steps of 0.0619\n",
"From time 1.456 to 1.549, in 1 step of 0.0929\n",
"From time 1.549 to 1.624, in 1 step of 0.0743\n",
"From time 1.624 to 1.735, in 1 step of 0.111\n",
"From time 1.735 to 1.824, in 1 step of 0.0892\n",
"From time 1.824 to 1.958, in 1 step of 0.134\n",
"From time 1.958 to 2.065, in 1 step of 0.107\n",
"From time 2.065 to 2.386, in 2 steps of 0.16\n",
"From time 2.386 to 2.867, in 2 steps of 0.241\n",
"From time 2.867 to 3.228, in 1 step of 0.361\n",
"From time 3.228 to 3.77, in 1 step of 0.542\n",
"From time 3.77 to 4.583, in 1 step of 0.812\n",
"(62 steps total)\n"
]
}
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"source": [
"dynamics2.diagnostics.explain_time_advance()"
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},
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Reaction `A <-> B` . Changes in concentrations with time (time steps shown in dashed lines)"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics2.plot_history(colors=['darkturquoise', 'green', 'darkblue'], show_intervals=True, title_prefix=\"WITHOUT catalysis\")"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "af8fec87-0f53-4491-b742-e909182781b9",
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"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 14.14 ; [B] = 105.9\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 7.48607\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 7.51557\n",
"Discrepancy between the two values: 0.3926 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
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"execution_count": 17,
"metadata": {},
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],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics2.is_in_equilibrium()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9d774e6b-8952-4664-837c-08ba42f8be48",
"metadata": {},
"outputs": [],
"source": []
}
],
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