`U` ("Up-regulator") up-regulates `X` , by sharing a reaction product `D` ("Drain") across 2 separate reactions:¶

`U <-> 2 D` and `X <-> D` (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 [D]; and when [D] goes up, so does [X].
Conversely, when [U] goes down, so does [D]; and when [D] goes down, so does [X].

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_2.log.htm'

Initialize the system¶

In [4]:

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

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

# Reaction X <-> D , with 1st-order kinetics for all species
chem_data.add_reaction(reactants="X", products="D",
                       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: U <-> 2 D  (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products
1: X <-> D  (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_2.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., "D": 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 (D). Conc: 0.0

In [ ]:

1. Take the initial system to equilibrium¶

In [6]:

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=0.03, target_end_time=0.5,
                                  variable_steps=True, explain_variable_steps=False)

dynamics.get_history()

INFO: the tentative time step (0.03) 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 0.015) [Step started at t=0, and will rewind there]
INFO: the tentative time step (0.015) 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 0.0075) [Step started at t=0, and will rewind there]
INFO: the tentative time step (0.0075) 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 0.00375) [Step started at t=0, and will rewind there]
INFO: the tentative time step (0.00375) 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 0.001875) [Step started at t=0, and will rewind there]
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
60 total step(s) taken

Out[6]:

	SYSTEM TIME	U	X	D	caption
0	0.000000	50.000000	100.000000	0.000000	Initial state
1	0.001875	49.250000	98.875000	2.625000
2	0.002812	48.885547	98.326211	3.902695
3	0.003750	48.526223	97.784102	5.163452
4	0.004687	48.171958	97.248589	6.407496
...	...	...	...	...	...
56	0.245706	24.643947	53.475305	97.236801
57	0.282239	24.546114	52.410700	98.497071
58	0.337037	24.580376	51.371008	99.468240
59	0.419235	24.768894	50.563716	99.898495
60	0.542532	24.971820	50.109144	99.947215

61 rows × 5 columns

In [7]:

dynamics.explain_time_advance()

From time 0 to 0.001875, in 1 step of 0.00187
From time 0.001875 to 0.01219, in 11 steps of 0.000938
From time 0.01219 to 0.01781, in 4 steps of 0.00141
From time 0.01781 to 0.03469, in 8 steps of 0.00211
From time 0.03469 to 0.03785, in 1 step of 0.00316
From time 0.03785 to 0.03943, in 1 step of 0.00158
From time 0.03943 to 0.04418, in 2 steps of 0.00237
From time 0.04418 to 0.04774, in 1 step of 0.00356
From time 0.04774 to 0.04952, in 1 step of 0.00178
From time 0.04952 to 0.05219, in 1 step of 0.00267
From time 0.05219 to 0.05619, in 1 step of 0.004
From time 0.05619 to 0.0582, in 1 step of 0.002
From time 0.0582 to 0.0612, in 1 step of 0.003
From time 0.0612 to 0.0657, in 1 step of 0.00451
From time 0.0657 to 0.06796, in 1 step of 0.00225
From time 0.06796 to 0.07134, in 1 step of 0.00338
From time 0.07134 to 0.0764, in 1 step of 0.00507
From time 0.0764 to 0.07894, in 1 step of 0.00253
From time 0.07894 to 0.08274, in 1 step of 0.0038
From time 0.08274 to 0.08844, in 1 step of 0.0057
From time 0.08844 to 0.09129, in 1 step of 0.00285
From time 0.09129 to 0.09557, in 1 step of 0.00428
From time 0.09557 to 0.1212, in 4 steps of 0.00641
From time 0.1212 to 0.1308, in 1 step of 0.00962
From time 0.1308 to 0.1357, in 1 step of 0.00481
From time 0.1357 to 0.1429, in 1 step of 0.00722
From time 0.1429 to 0.1645, in 2 steps of 0.0108
From time 0.1645 to 0.197, in 2 steps of 0.0162
From time 0.197 to 0.2457, in 2 steps of 0.0244
From time 0.2457 to 0.2822, in 1 step of 0.0365
From time 0.2822 to 0.337, in 1 step of 0.0548
From time 0.337 to 0.4192, in 1 step of 0.0822
From time 0.4192 to 0.5425, in 1 step of 0.123
(60 steps total)

Plots of changes of concentration with time¶

In [8]:

dynamics.plot_curves(colors=['red', 'green', 'gray'])

Equilibrium ¶

In [9]:

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

U <-> 2 D
Final concentrations:  [D] = 99.95 ; [U] = 24.97
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.0024
    Formula used:  [D] / [U]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.06 %
Reaction IS in equilibrium (within 1% tolerance)

X <-> D
Final concentrations:  [D] = 99.95 ; [X] = 50.11
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99459
    Formula used:  [D] / [X]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 0.2705 %
Reaction IS in equilibrium (within 1% tolerance)

Out[9]:

True

In [ ]:

2. Now, let's suddenly increase [U]¶

In [10]:

dynamics.set_chem_conc(species_name="U", conc=70., snapshot=True)
dynamics.describe_state()

SYSTEM STATE at Time t = 0.54253165:
3 species:
  Species 0 (U). Conc: 70.0
  Species 1 (X). Conc: 50.10914435037049
  Species 2 (D). Conc: 99.94721484673187

In [11]:

dynamics.get_history(tail=3)

Out[11]:

	SYSTEM TIME	U	X	D	caption
59	0.419235	24.768894	50.563716	99.898495
60	0.542532	24.971820	50.109144	99.947215
61	0.542532	70.000000	50.109144	99.947215	Set concentration of `U`

Again, take the system to equilibrium¶

In [12]:

dynamics.single_compartment_react(initial_step=0.03, target_end_time=1,
                                  variable_steps=True, explain_variable_steps=False)

INFO: the tentative time step (0.03) 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 0.015) [Step started at t=0.54253, and will rewind there]
INFO: the tentative time step (0.015) 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 0.0075) [Step started at t=0.54253, and will rewind there]
INFO: the tentative time step (0.0075) 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 0.00375) [Step started at t=0.54253, and will rewind there]
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
32 total step(s) taken

In [13]:

#dynamics.get_history()
#dynamics.explain_time_advance()

In [14]:

dynamics.plot_curves(colors=['red', 'green', 'gray'])

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()

U <-> 2 D
Final concentrations:  [D] = 145.1 ; [U] = 36.37
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.98913
    Formula used:  [D] / [U]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.2717 %
Reaction IS in equilibrium (within 1% tolerance)

X <-> D
Final concentrations:  [D] = 145.1 ; [X] = 72.21
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00937
    Formula used:  [D] / [X]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 0.4683 %
Reaction IS in equilibrium (within 1% tolerance)

Out[15]:

True

In [ ]:

3. Let's again suddenly increase [U]¶

In [16]:

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

SYSTEM STATE at Time t = 1.0973722:
3 species:
  Species 0 (U). Conc: 100.0
  Species 1 (X). Conc: 72.21103524746438
  Species 2 (D). Conc: 145.09842911303875

In [17]:

dynamics.get_history(tail=3)

Out[17]:

	SYSTEM TIME	U	X	D	caption
92	0.981912	36.771516	71.151097	145.362231
93	1.097372	36.373447	72.211035	145.098429
94	1.097372	100.000000	72.211035	145.098429	Set concentration of `U`

Yet again, take the system to equilibrium¶

In [18]:

dynamics.single_compartment_react(initial_step=0.03, target_end_time=1.6,
                                  variable_steps=True, explain_variable_steps=False)

INFO: the tentative time step (0.03) 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 0.015) [Step started at t=1.0974, and will rewind there]
INFO: the tentative time step (0.015) 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 0.0075) [Step started at t=1.0974, and will rewind there]
INFO: the tentative time step (0.0075) 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 0.00375) [Step started at t=1.0974, and will rewind there]
INFO: the tentative time step (0.00375) 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 0.001875) [Step started at t=1.0974, and will rewind there]
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
45 total step(s) taken

In [19]:

#dynamics.get_history()
#dynamics.explain_time_advance()

In [20]:

dynamics.plot_curves(colors=['red', 'green', 'gray'])

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(tolerance=2)

U <-> 2 D
Final concentrations:  [D] = 208.9 ; [U] = 52.56
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.97443
    Formula used:  [D] / [U]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.6392 %
Reaction IS in equilibrium (within 2% tolerance)

X <-> D
Final concentrations:  [D] = 208.9 ; [X] = 103.3
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.02304
    Formula used:  [D] / [X]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 1.152 %
Reaction IS in equilibrium (within 2% tolerance)

Out[21]:

True

In [ ]:

4. Now, instead, let's DECREASE [U]¶

In [22]:

dynamics.set_chem_conc(species_name="U", conc=5., snapshot=True)
dynamics.describe_state()

SYSTEM STATE at Time t = 1.6127957:
3 species:
  Species 0 (U). Conc: 5.0
  Species 1 (X). Conc: 103.26703387633307
  Species 2 (D). Conc: 208.9136350590719

In [23]:

dynamics.get_history(tail=3)

Out[23]:

	SYSTEM TIME	U	X	D	caption
138	1.530598	53.067054	101.964742	209.210614
139	1.612796	52.564398	103.267034	208.913635
140	1.612796	5.000000	103.267034	208.913635	Set concentration of `U`

Take the system to equilibrium¶

In [24]:

dynamics.single_compartment_react(initial_step=0.03, target_end_time=2.3,
                                  variable_steps=True, explain_variable_steps=False)

INFO: the tentative time step (0.03) 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 0.015) [Step started at t=1.6128, and will rewind there]
INFO: the tentative time step (0.015) 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 0.0075) [Step started at t=1.6128, and will rewind there]
INFO: the tentative time step (0.0075) 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 0.00375) [Step started at t=1.6128, and will rewind there]
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
37 total step(s) taken

In [25]:

#dynamics.get_history()
#dynamics.explain_time_advance()

In [26]:

dynamics.plot_curves(colors=['red', 'green', 'gray'])

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

In [27]:

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

Out[27]:

True

In [ ]:

U ("Up-regulator") up-regulates X , by sharing a reaction product D ("Drain") across 2 separate reactions:¶

U <-> 2 D and X <-> D (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¶

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 a reaction product `D` ("Drain") across 2 separate reactions:¶

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

Equilibrium ¶