`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: June 23, 2024 (using v. 1.0 beta36)

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 life123 import ChemData as chem
from life123 import UniformCompartment

from life123 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_2"],
                  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", 1)], 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
chem_data.plot_reaction_network("vue_cytoscape_2")

Number of reactions: 2 (at temp. 25 C)
0: 2 S <-> U  (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products
1: S <-> X  (kF = 6 / kR = 3 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {'X', 'U', 'S'}
[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_3.log.htm`]

Set the initial concentrations of all the chemicals¶

In [5]:

dynamics = UniformCompartment(chem_data=chem_data)
dynamics.set_conc(conc={"U": 50., "X": 100.})
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
Set of chemicals involved in reactions: {'X', 'U', 'S'}

In [ ]:

1. Take the initial system to equilibrium¶

In [6]:

dynamics = UniformCompartment(chem_data=chem_data, preset="fast")
dynamics.set_conc(conc={"U": 50., "X": 100.})
#dynamics.describe_state()

In [7]:

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

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

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

30 total step(s) taken
Number of step re-do's because of negative concentrations: 0
Number of step re-do's because of elective soft aborts: 1
Norm usage: {'norm_A': 23, 'norm_B': 15, 'norm_C': 15, 'norm_D': 15}

Plots of changes of concentration with time¶

In [8]:

dynamics.plot_history(colors=['green', 'orange', 'darkturquoise'])

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()

0: 2 S <-> U
Final concentrations: [S] = 18.18 ; [U] = 72.73
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99995
    Formula used:  [U] / [S]
2. Ratio of forward/reverse reaction rates: 4
Discrepancy between the two values: 0.001174 %
Reaction IS in equilibrium (within 1% tolerance)

1: S <-> X
Final concentrations: [S] = 18.18 ; [X] = 36.36
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00006
    Formula used:  [X] / [S]
2. Ratio of forward/reverse reaction rates: 2
Discrepancy between the two values: 0.002978 %
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 = 1.6638105:
3 species:
  Species 0 (U). Conc: 72.72664619276735
  Species 1 (X). Conc: 36.364832680090714
  Species 2 (S). Conc: 18.18187493437456
Set of chemicals involved in reactions: {'X', 'U', 'S'}

In [11]:

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

SYSTEM STATE at Time t = 1.6638105:
3 species:
  Species 0 (U). Conc: 100.0
  Species 1 (X). Conc: 36.364832680090714
  Species 2 (S). Conc: 18.18187493437456
Set of chemicals involved in reactions: {'X', 'U', 'S'}

In [12]:

dynamics.get_history(tail=3)

Out[12]:

	SYSTEM TIME	U	X	S	caption
29	1.296478	72.327210	37.127853	18.217727
30	1.663810	72.726646	36.364833	18.181875
31	1.663810	100.000000	36.364833	18.181875	Set concentration of `U`

Again, take the system to equilibrium¶

In [13]:

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


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

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

19 total step(s) taken
Number of step re-do's because of negative concentrations: 0
Number of step re-do's because of elective soft aborts: 1
Norm usage: {'norm_A': 42, 'norm_B': 34, 'norm_C': 34, 'norm_D': 34}

In [14]:

dynamics.plot_history(colors=['green', 'orange', 'darkturquoise'])

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()

0: 2 S <-> U
Final concentrations: [S] = 23.16 ; [U] = 92.57
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99637
    Formula used:  [U] / [S]
2. Ratio of forward/reverse reaction rates: 4
Discrepancy between the two values: 0.09086 %
Reaction IS in equilibrium (within 1% tolerance)

1: S <-> X
Final concentrations: [S] = 23.16 ; [X] = 46.23
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99593
    Formula used:  [X] / [S]
2. Ratio of forward/reverse reaction rates: 2
Discrepancy between the two values: 0.2035 %
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 = 3.2112105:
3 species:
  Species 0 (U). Conc: 92.57375924458273
  Species 1 (X). Conc: 46.234703179720654
  Species 2 (S). Conc: 23.16448594557913
Set of chemicals involved in reactions: {'X', 'U', 'S'}

In [17]:

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

SYSTEM STATE at Time t = 3.2112105:
3 species:
  Species 0 (U). Conc: 150.0
  Species 1 (X). Conc: 46.234703179720654
  Species 2 (S). Conc: 23.16448594557913
Set of chemicals involved in reactions: {'X', 'U', 'S'}

In [18]:

dynamics.get_history(tail=3)

Out[18]:

	SYSTEM TIME	U	X	S	caption
49	2.944977	92.638507	46.140467	23.129227
50	3.211210	92.573759	46.234703	23.164486
51	3.211210	150.000000	46.234703	23.164486	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)

#dynamics.get_history()

#dynamics.explain_time_advance()

19 total step(s) taken
Number of step re-do's because of negative concentrations: 0
Number of step re-do's because of elective soft aborts: 1
Norm usage: {'norm_A': 60, 'norm_B': 52, 'norm_C': 52, 'norm_D': 52}

In [20]:

dynamics.plot_history(colors=['green', 'orange', 'darkturquoise'])

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 = 4.5023771:
3 species:
  Species 0 (U). Conc: 134.48228669496106
  Species 1 (X). Conc: 66.874053871657
  Species 2 (S). Conc: 33.56056186372072
Set of chemicals involved in reactions: {'X', 'U', 'S'}

In [23]:

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

SYSTEM STATE at Time t = 4.5023771:
3 species:
  Species 0 (U). Conc: 80.0
  Species 1 (X). Conc: 66.874053871657
  Species 2 (S). Conc: 33.56056186372072
Set of chemicals involved in reactions: {'X', 'U', 'S'}

In [24]:

dynamics.get_history(tail=3)

Out[24]:

	SYSTEM TIME	U	X	S	caption
69	4.280516	134.710837	66.428575	33.548940
70	4.502377	134.482287	66.874054	33.560562
71	4.502377	80.000000	66.874054	33.560562	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)

20 total step(s) taken
Number of step re-do's because of negative concentrations: 0
Number of step re-do's because of elective soft aborts: 1
Norm usage: {'norm_A': 79, 'norm_B': 71, 'norm_C': 71, 'norm_D': 71}

In [26]:

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

In [27]:

dynamics.plot_history(colors=['green', 'orange', 'darkturquoise'])

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

In [ ]:

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]¶

IDEAS TO EXPLORE:¶

`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 ¶