`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: May 26, 2023

In [1]:

import set_path      # Importing this module will add the project's home directory to sys.path

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

In [ ]:

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()

In [7]:

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

# All of these settings are currently close to the default values... but subject to change; set for repeatability
dynamics.set_thresholds(norm="norm_A", low=0.5, high=0.8, abort=1.44)
dynamics.set_thresholds(norm="norm_B", low=0.08, high=0.5, abort=1.5)
dynamics.set_step_factors(upshift=1.5, downshift=0.5, abort=0.5)
dynamics.set_error_step_factor(0.5)

dynamics.single_compartment_react(initial_step=0.01, target_end_time=1.5,
                                  variable_steps=True, explain_variable_steps=False)

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

INFO: the tentative time step (0.01) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.005) [Step started at t=0, and will rewind there]
43 total step(s) taken

Plots of changes of concentration with time¶

In [8]:

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

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

Equilibrium ¶

In [9]:

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

2 S <-> U
Final concentrations:  [U] = 72.65 ; [S] = 18.19
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99404
    Formula used:  [U] / [S]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.1489 %
Reaction IS in equilibrium (within 1% tolerance)

S <-> X
Final concentrations:  [X] = 36.52 ; [S] = 18.19
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00759
    Formula used:  [X] / [S]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 0.3793 %
Reaction IS in equilibrium (within 1% tolerance)

Out[9]:

True

In [ ]:

2. Now, let's suddenly increase [U]¶

In [10]:

dynamics.describe_state()

SYSTEM STATE at Time t = 1.604933:
3 species:
  Species 0 (U). Conc: 72.64754791961869
  Species 1 (X). Conc: 36.515929976181866
  Species 2 (S). Conc: 18.188974184580783

In [11]:

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

SYSTEM STATE at Time t = 1.604933:
3 species:
  Species 0 (U). Conc: 100.0
  Species 1 (X). Conc: 36.515929976181866
  Species 2 (S). Conc: 18.188974184580783

In [12]:

dynamics.get_history(tail=3)

Out[12]:

	SYSTEM TIME	U	X	S	caption
42	1.297039	72.238529	37.297254	18.225687
43	1.604933	72.647548	36.515930	18.188974
44	1.604933	100.000000	36.515930	18.188974	Set concentration of `U`

Again, take the system to equilibrium¶

In [13]:

dynamics.set_step_factors(upshift=1.2, downshift=0.5, abort=0.4)  # Needs to tighten to time advance, to prevent mild instability


dynamics.single_compartment_react(initial_step=0.01, target_end_time=3.0,
                                  variable_steps=True, explain_variable_steps=False)

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

19 total step(s) taken

In [14]:

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

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

In [15]:

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

2 S <-> U
Final concentrations:  [U] = 92.63 ; [S] = 23.18
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99634
    Formula used:  [U] / [S]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.09147 %
Reaction IS in equilibrium (within 1% tolerance)

S <-> X
Final concentrations:  [X] = 46.26 ; [S] = 23.18
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99594
    Formula used:  [X] / [S]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 0.2029 %
Reaction IS in equilibrium (within 1% tolerance)

Out[15]:

True

In [ ]:

3. Let's again suddenly increase [U]¶

In [16]:

dynamics.describe_state()

SYSTEM STATE at Time t = 3.152333:
3 species:
  Species 0 (U). Conc: 92.63103996217262
  Species 1 (X). Conc: 46.26386257327225
  Species 2 (S). Conc: 23.178961663145174

In [17]:

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

SYSTEM STATE at Time t = 3.152333:
3 species:
  Species 0 (U). Conc: 150.0
  Species 1 (X). Conc: 46.26386257327225
  Species 2 (S). Conc: 23.178961663145174

In [18]:

dynamics.get_history(tail=3)

Out[18]:

	SYSTEM TIME	U	X	S	caption
62	2.886100	92.695247	46.170745	23.143666
63	3.152333	92.631040	46.263863	23.178962
64	3.152333	150.000000	46.263863	23.178962	Set concentration of `U`

Yet again, take the system to equilibrium¶

In [19]:

dynamics.single_compartment_react(initial_step=0.01, target_end_time=4.5,
                                  variable_steps=True, explain_variable_steps=False)

#dynamics.get_history()

#dynamics.explain_time_advance()

20 total step(s) taken

In [20]:

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

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

In [21]:

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

Out[21]:

True

In [ ]:

4. Now, instead, let's DECREASE [U]¶

In [22]:

dynamics.describe_state()

SYSTEM STATE at Time t = 4.709733:
3 species:
  Species 0 (U). Conc: 134.37031316880427
  Species 1 (X). Conc: 67.07941550667395
  Species 2 (S). Conc: 33.62278239213483

In [23]:

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

SYSTEM STATE at Time t = 4.709733:
3 species:
  Species 0 (U). Conc: 80.0
  Species 1 (X). Conc: 67.07941550667395
  Species 2 (S). Conc: 33.62278239213483

In [24]:

dynamics.get_history(tail=3)

Out[24]:

	SYSTEM TIME	U	X	S	caption
83	4.443500	134.497997	66.882281	33.564550
84	4.709733	134.370313	67.079416	33.622782
85	4.709733	80.000000	67.079416	33.622782	Set concentration of `U`

Take the system to equilibrium¶

In [25]:

dynamics.single_compartment_react(initial_step=0.01, target_end_time=6.,
                                  variable_steps=True, explain_variable_steps=False)

19 total step(s) taken

In [26]:

#dynamics.history.get_dataframe()
#dynamics.explain_time_advance()

In [27]:

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

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

In [28]:

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

Out[28]:

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)¶

Initialize the system¶

Set the initial concentrations of all the chemicals¶

1. Take the initial system to equilibrium¶

Plots of changes of concentration with time¶

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

Equilibrium¶

2. Now, let's suddenly increase [U]¶

Again, take the system to equilibrium¶

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

3. Let's again suddenly increase [U]¶

Yet again, take the system to equilibrium¶

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

4. Now, instead, let's DECREASE [U]¶

Take the system to equilibrium¶

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

`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)¶

Equilibrium ¶