`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, 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_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")],
                 forward_rate=8., reverse_rate=2.)

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: 1 (at temp. 25 C)
0: A + X <-> 2 B  (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products
[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_1.log.htm`]

Set the initial concentrations of all the chemicals¶

In [5]:

dynamics = ReactionDynamics(reaction_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

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=0.0005, reaction_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 0.5 (set to 0.00025) [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
55 total step(s) taken

In [7]:

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

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	0.000250	4.000000	99.000000	2.000000
2	0.000500	3.209000	98.209000	3.582000
3	0.000625	2.894743	97.894743	4.210514
4	0.000750	2.612415	97.612415	4.775169
5	0.000875	2.358605	97.358605	5.282790
6	0.001000	2.130295	97.130295	5.739410
7	0.001125	1.924814	96.924814	6.150372
8	0.001250	1.739789	96.739789	6.520422
9	0.001375	1.573112	96.573112	6.853775
10	0.001500	1.422906	96.422906	7.154189
11	0.001625	1.287493	96.287493	7.425013
12	0.001750	1.165380	96.165380	7.669240
13	0.001875	1.055228	96.055228	7.889544
14	0.002000	0.955840	95.955840	8.088319
15	0.002125	0.866144	95.866144	8.267712
16	0.002250	0.785177	95.785177	8.429646
17	0.002375	0.712076	95.712076	8.575848
18	0.002500	0.646066	95.646066	8.707868
19	0.002625	0.586449	95.586449	8.827102
20	0.002750	0.532599	95.532599	8.934801
21	0.002875	0.483952	95.483952	9.032095
22	0.003000	0.440001	95.440001	9.119998
23	0.003125	0.400287	95.400287	9.199426
24	0.003250	0.364399	95.364399	9.271201
25	0.003375	0.331967	95.331967	9.336067
26	0.003500	0.302654	95.302654	9.394693
27	0.003625	0.276158	95.276158	9.447683
28	0.003750	0.252209	95.252209	9.495582
29	0.003875	0.230560	95.230560	9.538881
30	0.004000	0.210988	95.210988	9.578024
31	0.004125	0.193294	95.193294	9.613412
32	0.004250	0.177297	95.177297	9.645406
33	0.004375	0.162834	95.162834	9.674332
34	0.004500	0.149757	95.149757	9.700487
35	0.004625	0.137932	95.137932	9.724135
36	0.004813	0.121895	95.121895	9.756210
37	0.005000	0.108161	95.108161	9.783677
38	0.005188	0.096400	95.096400	9.807201
39	0.005375	0.086326	95.086326	9.827347
40	0.005563	0.077699	95.077699	9.844602
41	0.005750	0.070310	95.070310	9.859381
42	0.005938	0.063980	95.063980	9.872039
43	0.006125	0.058559	95.058559	9.882882
44	0.006313	0.053915	95.053915	9.892169
45	0.006594	0.047949	95.047949	9.904103
46	0.006875	0.043266	95.043266	9.913469
47	0.007156	0.039590	95.039590	9.920821
48	0.007438	0.036704	95.036704	9.926591
49	0.007859	0.033307	95.033307	9.933386
50	0.008281	0.031005	95.031005	9.937989
51	0.008914	0.028667	95.028667	9.942667
52	0.009863	0.026856	95.026856	9.946289
53	0.011287	0.026110	95.026110	9.947779
54	0.013423	0.026209	95.026209	9.947582
55	0.016626	0.026115	95.026115	9.947769

In [9]:

dynamics.explain_time_advance()

From time 0 to 0.0005, in 2 steps of 0.00025
From time 0.0005 to 0.004625, in 33 steps of 0.000125
From time 0.004625 to 0.006313, in 9 steps of 0.000188
From time 0.006313 to 0.007438, in 4 steps of 0.000281
From time 0.007438 to 0.008281, in 2 steps of 0.000422
From time 0.008281 to 0.008914, in 1 step of 0.000633
From time 0.008914 to 0.009863, in 1 step of 0.000949
From time 0.009863 to 0.01129, in 1 step of 0.00142
From time 0.01129 to 0.01342, in 1 step of 0.00214
From time 0.01342 to 0.01663, in 1 step of 0.0032
(55 steps total)

Equilibrium ¶

In [10]:

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

A + X <-> 2 B
Final concentrations:  [B] = 9.948 ; [A] = 0.02612 ; [X] = 95.03
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00855
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.2137 %
Reaction IS in equilibrium (within 1% tolerance)

Out[10]:

True

In [ ]:

Now, let's suddenly increase [A]¶

In [11]:

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

SYSTEM STATE at Time t = 0.016626465:
3 species:
  Species 0 (A). Conc: 50.0
  Species 1 (X). Conc: 95.02611534596562
  Species 2 (B). Conc: 9.947769308068802

In [12]:

dynamics.get_history(tail=5)

Out[12]:

	SYSTEM TIME	A	X	B	caption
52	0.009863	0.026856	95.026856	9.946289
53	0.011287	0.026110	95.026110	9.947779
54	0.013423	0.026209	95.026209	9.947582
55	0.016626	0.026115	95.026115	9.947769
56	0.016626	50.000000	95.026115	9.947769	Set concentration of `A`

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 0.5 (set to 0.00025) [Step started at t=0.016626, and will rewind there]
INFO: the tentative time step (0.00025) 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 0.000125) [Step started at t=0.016626, and will rewind there]
INFO: the tentative time step (0.000125) 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 6.25e-05) [Step started at t=0.016626, and will rewind there]
INFO: the tentative time step (6.25e-05) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 3.125e-05) [Step started at t=0.016626, and will rewind there]
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
78 total step(s) taken

In [14]:

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

A, still the limiting reagent, is again stopping the reaction.
The (transiently) high value of [A] led to a high value of [B]

In [15]:

#dynamics.get_history()

#dynamics.explain_time_advance()

In [16]:

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

A + X <-> 2 B
Final concentrations:  [B] = 108.8 ; [A] = 0.5945 ; [X] = 45.62
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00995
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.2488 %
Reaction IS in equilibrium (within 1% tolerance)

Out[16]:

True

In [ ]:

Let's again suddenly increase [A]¶

In [17]:

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

SYSTEM STATE at Time t = 0.03752232:
3 species:
  Species 0 (A). Conc: 30.0
  Species 1 (X). Conc: 45.62063150861952
  Species 2 (B). Conc: 108.75873698276109

In [18]:

dynamics.get_history(tail=5)

Out[18]:

	SYSTEM TIME	A	X	B	caption
131	0.030573	0.673295	45.699410	108.601180
132	0.032036	0.630941	45.657056	108.685887
133	0.034231	0.602230	45.628346	108.743309
134	0.037522	0.594516	45.620632	108.758737
135	0.037522	30.000000	45.620632	108.758737	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 0.5 (set to 0.00025) [Step started at t=0.037522, and will rewind there]
INFO: the tentative time step (0.00025) 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 0.000125) [Step started at t=0.037522, and will rewind there]
41 total step(s) taken

In [20]:

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

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 [22]:

# Look up the some of the intersections of the [A] and [B] curves
dynamics.curve_intersection("A", "B", t_start=0, t_end=0.01)

Min abs distance found at data row: 2

Out[22]:

(0.0004607037505267594, 3.333333333333333)

In [23]:

dynamics.curve_intersection("A", "B", t_start=0.0151, t_end=0.02)

Min abs distance found at data row: 73

Out[23]:

(0.017062701624030972, 36.64925643602293)

Note: the curve_intersection() function currently cannot location the intersection at t=0.015 (the vertical rise in the red line); this issue will get addressed in future versions...

In [24]:

#dynamics.get_history()

#dynamics.explain_time_advance()

In [25]:

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

A + X <-> 2 B
Final concentrations:  [B] = 164.2 ; [A] = 2.29 ; [X] = 17.91
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00332
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.08288 %
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¶

Now, let's suddenly increase [A]¶

Again, take the system to equilibrium¶

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 ¶