`A` up-regulates `B` ,¶

by being the limiting reagent in the reaction `A + X <-> 2B` (mostly forward), where `X` is plentiful¶

1st-order kinetics.
If [A] is low, [B] remains low, too. Then, if [A] goes high, then so does [B]. However, at that point, A can no longer bring B down to any substantial extent.

See also the experiment "1D/reactions/up_regulation_1"

LAST REVISED: May 26, 2024

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.chemicals.chem_data import ChemData as chem
from src.modules.reactions.reaction_dynamics import ReactionDynamics

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_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_1.log.htm'

Initialize the system¶

In [4]:

# Initialize the system
chem_data = chem(names=["A", "X", "B"])

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

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: 1 (at temp. 25 C)
0: A + X <-> 2 B  (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {'A', 'B', 'X'}
[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_1.log.htm`]

Set the initial concentrations of all the chemicals¶

In [5]:

dynamics = ReactionDynamics(chem_data=chem_data)
dynamics.set_conc(conc={"A": 5., "X": 100., "B": 0.},
                  snapshot=True)      # A is scarce, X is plentiful, B is absent
dynamics.describe_state()

SYSTEM STATE at Time t = 0:
3 species:
  Species 0 (A). Conc: 5.0
  Species 1 (X). Conc: 100.0
  Species 2 (B). Conc: 0.0
Set of chemicals involved in reactions: {'A', 'B', 'X'}

Take the initial system to equilibrium¶

In [6]:

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

# This setting is a preset that can be adjusted make the time resolution finer or coarser;
# it will stay in effect from now on, unless explicitly changed later
dynamics.use_adaptive_preset(preset="fast")

dynamics.single_compartment_react(initial_step=0.0005, duration=0.015,
                                  variable_steps=True, explain_variable_steps=False)

* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.0003) [Step started at t=0, and will rewind there]
27 total step(s) taken

In [7]:

dynamics.plot_history(colors=['red', 'darkorange', 'green'], show_intervals=True)

A, as the scarse limiting reagent, stops the reaction.
As long as A is low, B also remains low.

In [8]:

dynamics.get_history()

Out[8]:

	SYSTEM TIME	A	X	B	caption
0	0.000000	5.000000	100.000000	0.000000	Initial state
1	0.000300	3.800000	98.800000	2.400000
2	0.000600	2.900384	97.900384	4.199232
3	0.000900	2.221427	97.221427	5.557147
4	0.001200	1.706432	96.706432	6.587135
5	0.001500	1.314329	96.314329	7.371341
6	0.001800	1.014939	96.014939	7.970122
7	0.002100	0.785843	95.785843	8.428314
8	0.002400	0.610246	95.610246	8.779509
9	0.002700	0.475484	95.475484	9.049033
10	0.003000	0.371960	95.371960	9.256080
11	0.003300	0.292375	95.292375	9.415250
12	0.003600	0.231157	95.231157	9.537685
13	0.003900	0.184048	95.184048	9.631904
14	0.004200	0.147783	95.147783	9.704434
15	0.004500	0.119859	95.119859	9.760283
16	0.004800	0.098352	95.098352	9.803295
17	0.005100	0.081787	95.081787	9.836426
18	0.005400	0.069025	95.069025	9.861949
19	0.005700	0.059193	95.059193	9.881614
20	0.006150	0.047830	95.047830	9.904340
21	0.006600	0.040378	95.040378	9.919244
22	0.007050	0.035490	95.035490	9.929020
23	0.007725	0.030681	95.030681	9.938638
24	0.008737	0.027190	95.027190	9.945620
25	0.010256	0.026007	95.026007	9.947986
26	0.012534	0.026292	95.026292	9.947415
27	0.015952	0.025975	95.025975	9.948051

In [9]:

dynamics.explain_time_advance()

From time 0 to 0.0057, in 19 steps of 0.0003
From time 0.0057 to 0.00705, in 3 steps of 0.00045
From time 0.00705 to 0.007725, in 1 step of 0.000675
From time 0.007725 to 0.008737, in 1 step of 0.00101
From time 0.008737 to 0.01026, in 1 step of 0.00152
From time 0.01026 to 0.01253, in 1 step of 0.00228
From time 0.01253 to 0.01595, in 1 step of 0.00342
(27 steps total)

Equilibrium ¶

In [10]:

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

0: A + X <-> 2 B
Final concentrations: [A] = 0.02597 ; [B] = 9.948 ; [X] = 95.03
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.03037
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.7592 %
Reaction IS in equilibrium (within 1% tolerance)

Out[10]:

True

In [ ]:

STEP 2. Now, let's suddenly increase [A]¶

In [11]:

dynamics.set_single_conc(species_name="A", conc=50., snapshot=True)
dynamics.describe_state()

SYSTEM STATE at Time t = 0.015951562:
3 species:
  Species 0 (A). Conc: 50.0
  Species 1 (X). Conc: 95.02597471866889
  Species 2 (B). Conc: 9.948050562662225
Set of chemicals involved in reactions: {'A', 'B', 'X'}

In [12]:

dynamics.get_history(tail=5)

Out[12]:

	SYSTEM TIME	A	X	B	caption
24	0.008737	0.027190	95.027190	9.945620
25	0.010256	0.026007	95.026007	9.947986
26	0.012534	0.026292	95.026292	9.947415
27	0.015952	0.025975	95.025975	9.948051
28	0.015952	50.000000	95.025975	9.948051	Set concentration of `A`

Notice the discontity in [A] in the last 2 rows

Again, take the system to equilibrium¶

In [13]:

dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.035,
                                  variable_steps=True, explain_variable_steps=False)

* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.0003) [Step started at t=0.015952, and will rewind there]
* INFO: the tentative time step (0.0003) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.00018) [Step started at t=0.015952, and will rewind there]
* INFO: the tentative time step (0.00018) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.000108) [Step started at t=0.015952, and will rewind there]
* INFO: the tentative time step (0.000108) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 6.48e-05) [Step started at t=0.015952, and will rewind there]
* INFO: the tentative time step (6.48e-05) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 3.888e-05) [Step started at t=0.015952, and will rewind there]
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
51 total step(s) taken

In [14]:

dynamics.plot_history(colors=['red', 'darkorange', 'green'], show_intervals=True)

A, still the limiting reagent, is again eventually stopping the reaction...
The (transiently) high value of [A] led to a high value of [B]
Notice how the variable time steps automatically adapt.

In [15]:

#dynamics.get_history()

#dynamics.explain_time_advance()

In [16]:

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

0: A + X <-> 2 B
Final concentrations: [A] = 0.5992 ; [B] = 108.7 ; [X] = 45.63
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.97761
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.5598 %
Reaction IS in equilibrium (within 1% tolerance)

Out[16]:

True

In [ ]:

STEP 3. Let's again suddenly increase [A]¶

In [17]:

dynamics.set_single_conc(species_name="A", conc=30., snapshot=True)
dynamics.describe_state()

SYSTEM STATE at Time t = 0.039055056:
3 species:
  Species 0 (A). Conc: 30.0
  Species 1 (X). Conc: 45.62521424281943
  Species 2 (B). Conc: 108.74957151436116
Set of chemicals involved in reactions: {'A', 'B', 'X'}

In [18]:

dynamics.get_history(tail=5)

Out[18]:

	SYSTEM TIME	A	X	B	caption
76	0.028635	0.690343	45.716318	108.567364
77	0.030829	0.612807	45.638782	108.722436
78	0.034119	0.592086	45.618060	108.763879
79	0.039055	0.599240	45.625214	108.749572
80	0.039055	30.000000	45.625214	108.749572	Set concentration of `A`

Yet again, take the system to equilibrium¶

In [19]:

dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.070,
                                  variable_steps=True, explain_variable_steps=False)

* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.0003) [Step started at t=0.039055, and will rewind there]
* INFO: the tentative time step (0.0003) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.00018) [Step started at t=0.039055, and will rewind there]
* INFO: the tentative time step (0.00018) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.000108) [Step started at t=0.039055, and will rewind there]
28 total step(s) taken

In [20]:

dynamics.plot_history(colors=['red', 'darkorange', 'green'], show_intervals=True)

A, again the scarce limiting reagent, stops the reaction yet again.
And, again, the (transiently) high value of [A] up-regulated [B]

Notes:
A can up-regulate B, but it cannot bring it down.
X will soon need to be replenished, if A is to continue being the limiting reagent.**

In [21]:

# Zoom in on the early part of the last plot
dynamics.plot_history(colors=['red', 'darkorange', 'green'], xrange=[0, 0.02])

In [22]:

# Look up the first intersection of the [A] and [B] curves
dynamics.curve_intersect("A", "B", t_start=0, t_end=0.01)

Out[22]:

(0.00045562195425603814, 3.333333333333333)

In [23]:

# The next intersection isn't particulary meaning; just an artifact of the sudden jump in [A]
dynamics.curve_intersect("A", "B", t_start=0.01, t_end=0.02)

WARNING: curve_intersect(): Discontinuity detected at `SYSTEM TIME` = 0.015951562499999995

Out[23]:

(0.015951562499999995, 9.948050562662225)

In [24]:

# The final intersection
dynamics.curve_intersect("A", "B", t_start=0.016, t_end=0.02)

Out[24]:

(0.01638486713665179, 36.649350187554084)

In [25]:

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

0: A + X <-> 2 B
Final concentrations: [A] = 2.284 ; [B] = 164.2 ; [X] = 17.91
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.01395
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.3487 %
Reaction IS in equilibrium (within 1% tolerance)

Out[25]:

True

In [ ]:

A up-regulates B ,¶

by being the limiting reagent in the reaction A + X <-> 2B (mostly forward), where X is plentiful¶

Initialize the system¶

Set the initial concentrations of all the chemicals¶

Take the initial system to equilibrium¶

Equilibrium¶

STEP 2. Now, let's suddenly increase [A]¶

Again, take the system to equilibrium¶

STEP 3. Let's again suddenly increase [A]¶

Yet again, take the system to equilibrium¶

`A` up-regulates `B` ,¶

by being the limiting reagent in the reaction `A + X <-> 2B` (mostly forward), where `X` is plentiful¶

Equilibrium ¶