`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: Feb. 5, 2023

In [1]:

# Extend the sys.path variable, to contain the project's root directory
import set_path
set_path.add_ancestor_dir_to_syspath(2)  # The number of levels to go up 
                                         # to reach the project's home, from the folder containing this notebook

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()

dynamics.single_compartment_react(time_step=0.0005, stop_time=0.015,
                                  dynamic_substeps=2, rel_fast_threshold=15)

df = dynamics.get_history()
df

single_compartment_react(): setting abs_fast_threshold to 300.0
30 total step(s) taken

Out[6]:

	SYSTEM TIME	A	X	B	caption
0	0.00000	5.000000	100.000000	0.000000	Initial state
1	0.00025	4.000000	99.000000	2.000000	Interm. step, due to the fast rxns: [0]
2	0.00050	3.209000	98.209000	3.582000
3	0.00075	2.580486	97.580486	4.839029	Interm. step, due to the fast rxns: [0]
4	0.00100	2.079295	97.079295	5.841410
5	0.00125	1.678503	96.678503	6.642994	Interm. step, due to the fast rxns: [0]
6	0.00150	1.357274	96.357274	7.285452
7	0.00175	1.099350	96.099350	7.801299	Interm. step, due to the fast rxns: [0]
8	0.00200	0.891957	95.891957	8.216086
9	0.00225	0.725002	95.725002	8.549996	Interm. step, due to the fast rxns: [0]
10	0.00250	0.590476	95.590476	8.819049
11	0.00275	0.481997	95.481997	9.036005	Interm. step, due to the fast rxns: [0]
12	0.00300	0.394471	95.394471	9.211058
13	0.00325	0.323816	95.323816	9.352368	Interm. step, due to the fast rxns: [0]
14	0.00350	0.266757	95.266757	9.466485
15	0.00375	0.220664	95.220664	9.558671	Interm. step, due to the fast rxns: [0]
16	0.00400	0.183420	95.183420	9.633160
17	0.00450	0.123219	95.123219	9.753562
18	0.00500	0.086089	95.086089	9.827823
19	0.00550	0.063173	95.063173	9.873654
20	0.00600	0.049025	95.049025	9.901950
21	0.00650	0.040288	95.040288	9.919424
22	0.00700	0.034891	95.034891	9.930217
23	0.00750	0.031558	95.031558	9.936884
24	0.00800	0.029499	95.029499	9.941002
25	0.00850	0.028227	95.028227	9.943546
26	0.00900	0.027441	95.027441	9.945118
27	0.00950	0.026956	95.026956	9.946089
28	0.01000	0.026656	95.026656	9.946689
29	0.01050	0.026470	95.026470	9.947059
30	0.01100	0.026356	95.026356	9.947288
31	0.01150	0.026285	95.026285	9.947430
32	0.01200	0.026241	95.026241	9.947517
33	0.01250	0.026214	95.026214	9.947571
34	0.01300	0.026198	95.026198	9.947604
35	0.01350	0.026187	95.026187	9.947625
36	0.01400	0.026181	95.026181	9.947638
37	0.01450	0.026177	95.026177	9.947646
38	0.01500	0.026175	95.026175	9.947650

A, as the scarse limiting reagent, stops the reaction.
When A is low, B is also low.

In [7]:

dynamics.explain_time_advance()

From time 0 to 0.004, in 16 substeps of 0.00025 (each 1/2 of full step)
From time 0.004 to 0.015, in 22 FULL steps of 0.0005

Equilibrium ¶

In [8]:

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

A + X <-> 2 B
Final concentrations:  [B] = 9.948 ; [A] = 0.02617 ; [X] = 95.03
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.9994
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.01508 %
Reaction IS in equilibrium (within 1% tolerance)

Out[8]:

True

Plots of changes of concentration with time¶

In [9]:

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

Now, let's suddenly increase [A]¶

In [10]:

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

SYSTEM STATE at Time t = 0.015:
3 species:
  Species 0 (A). Conc: 50.0
  Species 1 (X). Conc: 95.02617476453239
  Species 2 (B). Conc: 9.947650470935224

In [11]:

dynamics.get_history(tail=5)

Out[11]:

	SYSTEM TIME	A	X	B	caption
35	0.0135	0.026187	95.026187	9.947625
36	0.0140	0.026181	95.026181	9.947638
37	0.0145	0.026177	95.026177	9.947646
38	0.0150	0.026175	95.026175	9.947650
39	0.0150	50.000000	95.026175	9.947650	Set concentration of `A`

Again, take the system to equilibrium¶

In [12]:

dynamics.single_compartment_react(time_step=0.0005, stop_time=0.035,
                                  dynamic_substeps=2, rel_fast_threshold=15)

df = dynamics.get_history()
df

single_compartment_react(): setting abs_fast_threshold to 300.0
40 total step(s) taken

Out[12]:

	SYSTEM TIME	A	X	B	caption
0	0.00000	5.000000	100.000000	0.000000	Initial state
1	0.00025	4.000000	99.000000	2.000000	Interm. step, due to the fast rxns: [0]
2	0.00050	3.209000	98.209000	3.582000
3	0.00075	2.580486	97.580486	4.839029	Interm. step, due to the fast rxns: [0]
4	0.00100	2.079295	97.079295	5.841410
...	...	...	...	...	...
97	0.03300	0.612358	45.638533	108.722934
98	0.03350	0.609293	45.635467	108.729065
99	0.03400	0.606800	45.632975	108.734050
100	0.03450	0.604774	45.630949	108.738103
101	0.03500	0.603126	45.629301	108.741398

102 rows × 5 columns

In [13]:

dynamics.explain_time_advance()

From time 0 to 0.004, in 16 substeps of 0.00025 (each 1/2 of full step)
From time 0.004 to 0.015, in 22 FULL steps of 0.0005
From time 0.015 to 0.026, in 44 substeps of 0.00025 (each 1/2 of full step)
From time 0.026 to 0.035, in 18 FULL steps of 0.0005

In [14]:

# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium(tolerance=2)

A + X <-> 2 B
Final concentrations:  [B] = 108.7 ; [A] = 0.6031 ; [X] = 45.63
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.95133
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 1.217 %
Reaction IS in equilibrium (within 2% tolerance)

Out[14]:

True

In [15]:

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]

Let's again suddenly increase [A]¶

In [16]:

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

SYSTEM STATE at Time t = 0.035:
3 species:
  Species 0 (A). Conc: 30.0
  Species 1 (X). Conc: 45.62930114786792
  Species 2 (B). Conc: 108.74139770426417

In [17]:

dynamics.get_history(tail=5)

Out[17]:

	SYSTEM TIME	A	X	B	caption
98	0.0335	0.609293	45.635467	108.729065
99	0.0340	0.606800	45.632975	108.734050
100	0.0345	0.604774	45.630949	108.738103
101	0.0350	0.603126	45.629301	108.741398
102	0.0350	30.000000	45.629301	108.741398	Set concentration of `A`

Yet again, take the system to equilibrium¶

In [18]:

dynamics.single_compartment_react(time_step=0.0005, stop_time=0.070,
                                  dynamic_substeps=2, rel_fast_threshold=15)

df = dynamics.history.get()
df

single_compartment_react(): setting abs_fast_threshold to 300.0
70 total step(s) taken

Out[18]:

	SYSTEM TIME	A	X	B	caption
0	0.00000	5.000000	100.000000	0.000000	Initial state
1	0.00025	4.000000	99.000000	2.000000	Interm. step, due to the fast rxns: [0]
2	0.00050	3.209000	98.209000	3.582000
3	0.00075	2.580486	97.580486	4.839029	Interm. step, due to the fast rxns: [0]
4	0.00100	2.079295	97.079295	5.841410
...	...	...	...	...	...
200	0.06800	2.330535	17.959837	164.080327
201	0.06850	2.327192	17.956493	164.087015
202	0.06900	2.324126	17.953427	164.093146
203	0.06950	2.321315	17.950616	164.098768
204	0.07000	2.318737	17.948039	164.103923

205 rows × 5 columns

In [19]:

dynamics.explain_time_advance()

From time 0 to 0.004, in 16 substeps of 0.00025 (each 1/2 of full step)
From time 0.004 to 0.015, in 22 FULL steps of 0.0005
From time 0.015 to 0.026, in 44 substeps of 0.00025 (each 1/2 of full step)
From time 0.026 to 0.035, in 18 FULL steps of 0.0005
From time 0.035 to 0.051, in 64 substeps of 0.00025 (each 1/2 of full step)
From time 0.051 to 0.07, in 38 FULL steps of 0.0005

In [20]:

# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium(tolerance=2)

A + X <-> 2 B
Final concentrations:  [B] = 164.1 ; [A] = 2.319 ; [X] = 17.95
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.94321
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 1.42 %
Reaction IS in equilibrium (within 2% tolerance)

Out[20]:

True

In [21]:

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(t_start=0, t_end=0.01, var1="A", var2="B")

Min abs distance found at row: 2

Out[22]:

(0.0004607037505267594, 3.333333333333333)

In [23]:

dynamics.curve_intersection(t_start=0.0151, t_end=0.02, var1="A", var2="B")

Min abs distance found at row: 41

Out[23]:

(0.01538932900514749, 36.64921682364508)

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 [ ]:

A up-regulates B ,¶

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