`U` ("Up-regulator") up-regulates `X` , by sharing an upstream reagent `S` ("Source") across 2 separate reactions:¶

`2 S <-> U` and `S <-> X` (both mostly forward)¶

1st-order kinetics throughout.

Invoking Le Chatelier's principle, it can be seen that, starting from equilibrium, when [U] goes up, so does [S]; and when [S] goes up, so does [X].
Conversely, when [U] goes down, so does [S]; and when [S] goes down, so does [X].

This experiment is a counterpart of experiment up_regulate_2, with "upstream" rather than "downstream" reactions.

Note: numerical errors in the same reactions (with the same initial conditions) is explored in the experiment "large_time_steps_2"

LAST REVISED: Feb. 19, 2023

In [1]:

# Extend the sys.path variable, to contain the project's root directory
import set_path
set_path.add_ancestor_dir_to_syspath(2)  # The number of levels to go up 
                                         # to reach the project's home, from the folder containing this notebook

Added 'D:\Docs\- MY CODE\BioSimulations\life123-Win7' to sys.path

In [2]:

from experiments.get_notebook_info import get_notebook_basename

from src.modules.reactions.reaction_data import ReactionData as chem
from src.modules.reactions.reaction_dynamics import ReactionDynamics

import numpy as np
import plotly.express as px
from src.modules.visualization.graphic_log import GraphicLog

In [3]:

# Initialize the HTML logging
log_file = get_notebook_basename() + ".log.htm"    # Use the notebook base filename for the log file

# Set up the use of some specified graphic (Vue) components
GraphicLog.config(filename=log_file,
                  components=["vue_cytoscape_1"],
                  extra_js="https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js")

-> Output will be LOGGED into the file 'up_regulate_3.log.htm'

Initialize the system¶

In [4]:

# Initialize the system
chem_data = chem(names=["U", "X", "S"])

# Reaction 2 S <-> U , with 1st-order kinetics for all species (mostly forward)
chem_data.add_reaction(reactants=[(2, "S")], products="U",
                       forward_rate=8., reverse_rate=2.)

# Reaction S <-> X , with 1st-order kinetics for all species (mostly forward)
chem_data.add_reaction(reactants="S", products="X",
                       forward_rate=6., reverse_rate=3.)

chem_data.describe_reactions()

# Send the plot of the reaction network to the HTML log file
graph_data = chem_data.prepare_graph_network()
GraphicLog.export_plot(graph_data, "vue_cytoscape_1")

Number of reactions: 2 (at temp. 25 C)
0: 2 S <-> U  (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products
1: S <-> X  (kF = 6 / kR = 3 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products
[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_3.log.htm`]

Set the initial concentrations of all the chemicals¶

In [5]:

dynamics = ReactionDynamics(reaction_data=chem_data)
dynamics.set_conc(conc={"U": 50., "X": 100., "S": 0.})
dynamics.describe_state()

SYSTEM STATE at Time t = 0:
3 species:
  Species 0 (U). Conc: 50.0
  Species 1 (X). Conc: 100.0
  Species 2 (S). Conc: 0.0

1. Take the initial system to equilibrium¶

In [6]:

dynamics = ReactionDynamics(reaction_data=chem_data)
dynamics.set_conc(conc={"U": 50., "X": 100., "S": 0.})
#dynamics.describe_state()

dynamics.set_diagnostics()       # To save diagnostic information about the call to single_compartment_react()

dynamics.single_compartment_react(time_step=0.01, stop_time=1.5,
                                  dynamic_substeps=4, rel_fast_threshold=50)

df = dynamics.get_history()
#df
dynamics.explain_time_advance()

single_compartment_react(): setting abs_fast_threshold to 50.0
150 total step(s) taken
From time 0 to 0.44, in 176 substeps of 0.0025 (each 1/4 of full step)
From time 0.44 to 1.5, in 106 FULL steps of 0.01
(for a grand total of the equivalent of 150 FULL steps)

Plots of changes of concentration with time¶

In [7]:

dynamics.plot_curves(colors=['green', 'orange', 'blue'])

Note that [S] is initially 0, and that it builds up thru reverse reactions¶

Equilibrium ¶

In [8]:

# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium(tolerance=3)

2 S <-> U
Final concentrations:  [U] = 72.24 ; [S] = 18.23
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.9635
    Formula used:  [U] / [S]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.9125 %
Reaction IS in equilibrium (within 3% tolerance)

S <-> X
Final concentrations:  [X] = 37.3 ; [S] = 18.23
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.04648
    Formula used:  [X] / [S]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 2.324 %
Reaction IS in equilibrium (within 3% tolerance)

Out[8]:

True

2. Now, let's suddenly increase [U]¶

In [9]:

dynamics.describe_state()

SYSTEM STATE at Time t = 1.5:
3 species:
  Species 0 (U). Conc: 72.23775751588529
  Species 1 (X). Conc: 37.298728471715336
  Species 2 (S). Conc: 18.225756496514013

In [10]:

dynamics.set_chem_conc(species_name="U", conc=100.)
dynamics.describe_state()

SYSTEM STATE at Time t = 1.5:
3 species:
  Species 0 (U). Conc: 100.0
  Species 1 (X). Conc: 37.298728471715336
  Species 2 (S). Conc: 18.225756496514013

In [11]:

dynamics.get_history(tail=3)

Out[11]:

	SYSTEM TIME	U	X	S	caption
281	1.49	72.224080	37.324855	18.226984
282	1.50	72.237758	37.298728	18.225756
283	1.50	100.000000	37.298728	18.225756	Set concentration of `U`

Again, take the system to equilibrium¶

In [12]:

dynamics.single_compartment_react(time_step=0.01, stop_time=3.0,
                                  dynamic_substeps=4, rel_fast_threshold=50)

df = dynamics.get_history()
#df
dynamics.explain_time_advance()

single_compartment_react(): setting abs_fast_threshold to 50.0
151 total step(s) taken
From time 0 to 0.44, in 176 substeps of 0.0025 (each 1/4 of full step)
From time 0.44 to 1.5, in 106 FULL steps of 0.01
From time 1.5 to 1.55, in 20 substeps of 0.0025 (each 1/4 of full step)
From time 1.55 to 3.01, in 146 FULL steps of 0.01
(for a grand total of the equivalent of 301 FULL steps)

In [13]:

dynamics.plot_curves(colors=['green', 'orange', 'blue'])

The (transiently) high value of [U] led to an increase in [X]¶

In [14]:

# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium()

2 S <-> U
Final concentrations:  [U] = 93 ; [S] = 23.22
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00501
    Formula used:  [U] / [S]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.1252 %
Reaction IS in equilibrium (within 1% tolerance)

S <-> X
Final concentrations:  [X] = 46.3 ; [S] = 23.22
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99362
    Formula used:  [X] / [S]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 0.3189 %
Reaction IS in equilibrium (within 1% tolerance)

Out[14]:

True

3. Let's again suddenly increase [U]¶

In [15]:

dynamics.describe_state()

SYSTEM STATE at Time t = 3.01:
3 species:
  Species 0 (U). Conc: 93.00357364838469
  Species 1 (X). Conc: 46.29552051953213
  Species 2 (S). Conc: 23.221817151927773

In [16]:

dynamics.set_chem_conc(species_name="U", conc=150.)
dynamics.describe_state()

SYSTEM STATE at Time t = 3.01:
3 species:
  Species 0 (U). Conc: 150.0
  Species 1 (X). Conc: 46.29552051953213
  Species 2 (S). Conc: 23.221817151927773

In [17]:

dynamics.get_history(tail=3)

Out[17]:

	SYSTEM TIME	U	X	S	caption
448	3.00	93.005965	46.290953	23.221603
449	3.01	93.003574	46.295521	23.221817
450	3.01	150.000000	46.295521	23.221817	Set concentration of `U`

Yet again, take the system to equilibrium¶

In [18]:

dynamics.single_compartment_react(time_step=0.01, stop_time=4.5,
                                  dynamic_substeps=4, rel_fast_threshold=50)

df = dynamics.history.get()
#df
dynamics.explain_time_advance()

single_compartment_react(): setting abs_fast_threshold to 50.0
150 total step(s) taken
From time 0 to 0.44, in 176 substeps of 0.0025 (each 1/4 of full step)
From time 0.44 to 1.5, in 106 FULL steps of 0.01
From time 1.5 to 1.55, in 20 substeps of 0.0025 (each 1/4 of full step)
From time 1.55 to 3.01, in 146 FULL steps of 0.01
From time 3.01 to 3.16, in 60 substeps of 0.0025 (each 1/4 of full step)
From time 3.16 to 4.51, in 135 FULL steps of 0.01
(for a grand total of the equivalent of 451 FULL steps)

In [19]:

dynamics.plot_curves(colors=['green', 'orange', 'blue'])

The (transiently) high value of [U] again led to an increase in [X]¶

In [20]:

# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium(explain=False)

Out[20]:

True

4. Now, instead, let's DECREASE [U]¶

In [21]:

dynamics.describe_state()

SYSTEM STATE at Time t = 4.51:
3 species:
  Species 0 (U). Conc: 134.56867943830346
  Species 1 (X). Conc: 66.80533208508905
  Species 2 (S). Conc: 33.57464670976427

In [22]:

dynamics.set_chem_conc(species_name="U", conc=80.)
dynamics.describe_state()

SYSTEM STATE at Time t = 4.51:
3 species:
  Species 0 (U). Conc: 80.0
  Species 1 (X). Conc: 66.80533208508905
  Species 2 (S). Conc: 33.57464670976427

In [23]:

dynamics.get_history(tail=3)

Out[23]:

	SYSTEM TIME	U	X	S	caption
644	4.50	134.574232	66.794725	33.574148
645	4.51	134.568679	66.805332	33.574647
646	4.51	80.000000	66.805332	33.574647	Set concentration of `U`

Take the system to equilibrium¶

In [24]:

dynamics.single_compartment_react(time_step=0.01, stop_time=6.,
                                  dynamic_substeps=4, rel_fast_threshold=50)

df = dynamics.history.get()
#df
dynamics.explain_time_advance()

single_compartment_react(): setting abs_fast_threshold to 50.0
150 total step(s) taken
From time 0 to 0.44, in 176 substeps of 0.0025 (each 1/4 of full step)
From time 0.44 to 1.5, in 106 FULL steps of 0.01
From time 1.5 to 1.55, in 20 substeps of 0.0025 (each 1/4 of full step)
From time 1.55 to 3.01, in 146 FULL steps of 0.01
From time 3.01 to 3.16, in 60 substeps of 0.0025 (each 1/4 of full step)
From time 3.16 to 4.51, in 135 FULL steps of 0.01
From time 4.51 to 4.65, in 56 substeps of 0.0025 (each 1/4 of full step)
From time 4.65 to 6.01, in 136 FULL steps of 0.01
(for a grand total of the equivalent of 601 FULL steps)

In [25]:

dynamics.plot_curves(colors=['green', 'orange', 'blue'])

The (transiently) LOW value of [U] led to an DECREASE in [X]¶

In [26]:

# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium(explain=False)

Out[26]:

True

IDEAS TO EXPLORE:

Effect of the stoichiometry and the Delta_G on the "amplification" of the signal (from [U] to [X])
Effect of a continuously-varying (maybe oscillating [U]), and its being affected by the reactions' kinetics
Combining this experiment and up_regulate_2 in a "bifan motif"

In [ ]:

U ("Up-regulator") up-regulates X , by sharing an upstream reagent S ("Source") across 2 separate reactions:¶

2 S <-> U and S <-> X (both mostly forward)¶