`A` down-regulates `B` , by being the limiting reagent in reaction `A + 2 B <-> Y` (mostly forward)¶

1st-order kinetics.
If [A] is low and [B] is high, then [B] remains high. If [A] goes high, [B] goes low. However, at that point, A can no longer bring B up to any substantial extent.

Single-bin reaction

Based on experiment reactions_single_compartment/down_regulate_2

LAST REVISED: June 23, 2024 (using v. 1.0 beta34.1)

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 BioSim1D

import plotly.express as px
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 'down_regulation_1.log.htm'

In [4]:

# Initialize the system
chem_data = chem(names=["A", "B", "Y"])     # NOTE: Diffusion not applicable (just 1 bin)

# Reaction A + 2 B <-> Y , with 1st-order kinetics for all species
chem_data.add_reaction(reactants=[("A") , (2, "B", 1)], products=[("Y")],
                       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 + 2 B <-> Y  (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', 'Y', 'B'}
[GRAPHIC ELEMENT SENT TO LOG FILE `down_regulation_1.log.htm`]

In [5]:

bio = BioSim1D(n_bins=1, chem_data=chem_data)

bio.set_uniform_concentration(species_name="A", conc=5.)     # Scarce
bio.set_uniform_concentration(species_name="B", conc=100.)   # Plentiful
# Initially, no "Y" is present

bio.describe_state()

SYSTEM STATE at Time t = 0:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [5.]
  Species 1 (B). Diff rate: None. Conc: [100.]
  Species 2 (Y). Diff rate: None. Conc: [0.]

In [6]:

# Save the state of the concentrations of all species at bin 0 (the only bin in this system)
bio.add_snapshot(bio.bin_snapshot(bin_address = 0))
bio.get_history()

Out[6]:

	SYSTEM TIME	A	B	Y	caption
0	0	5.0	100.0	0.0

Take the initial system to equilibrium¶

In [7]:

bio.react(time_step=0.0005, n_steps=30, snapshots={"frequency": 2, "sample_bin": 0})  # At every other step, take a snapshot 
                                                                                      # of all species at bin 0
bio.describe_state()
bio.get_history()

SYSTEM STATE at Time t = 0.015:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [0.01385228]
  Species 1 (B). Diff rate: None. Conc: [90.02770457]
  Species 2 (Y). Diff rate: None. Conc: [4.98614772]

Out[7]:

	SYSTEM TIME	A	B	Y
0	0.000	5.000000	100.000000	0.000000
1	0.001	1.850000	93.700000	3.150000
2	0.002	0.735332	91.470665	4.264668
3	0.003	0.303911	90.607822	4.696089
4	0.004	0.131501	90.263002	4.868499
5	0.005	0.061738	90.123476	4.938262
6	0.006	0.033369	90.066737	4.966631
7	0.007	0.021809	90.043618	4.978191
8	0.008	0.017095	90.034189	4.982905
9	0.009	0.015172	90.030343	4.984828
10	0.010	0.014387	90.028774	4.985613
11	0.011	0.014067	90.028134	4.985933
12	0.012	0.013936	90.027872	4.986064
13	0.013	0.013883	90.027766	4.986117
14	0.014	0.013861	90.027722	4.986139
15	0.015	0.013852	90.027705	4.986148

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

Equilibrium ¶

In [8]:

# Verify that the reaction has reached equilibrium
bio.reaction_dynamics.is_in_equilibrium(conc=bio.bin_snapshot(bin_address = 0))

0: A + 2 B <-> Y
Final concentrations: [A] = 0.01385 ; [B] = 90.03 ; [Y] = 4.986
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99823
    Formula used:  [Y] / ([A][B])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.0443 %
Reaction IS in equilibrium (within 1% tolerance)

Out[8]:

True

Plots of changes of concentration with time¶

In [9]:

fig = px.line(data_frame=bio.get_history(), x="SYSTEM TIME", y=["A", "B", "Y"], 
              title="Changes in concentrations (reaction A + 2 B <-> Y)",
              color_discrete_sequence = ['red', 'blue', 'green'],
              labels={"value":"concentration", "variable":"Chemical"})
fig.show()

Now, let's suddenly increase [A]¶

In [10]:

bio.set_bin_conc(bin_address=0, species_index=0, conc=40.)
bio.describe_state()

SYSTEM STATE at Time t = 0.015:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [40.]
  Species 1 (B). Diff rate: None. Conc: [90.02770457]
  Species 2 (Y). Diff rate: None. Conc: [4.98614772]

In [11]:

# Save the state of the concentrations of all species at bin 0 (the only bin in this system)
bio.add_snapshot(bio.bin_snapshot(bin_address = 0))
bio.get_history()

Out[11]:

	SYSTEM TIME	A	B	Y
0	0.000	5.000000	100.000000	0.000000
1	0.001	1.850000	93.700000	3.150000
2	0.002	0.735332	91.470665	4.264668
3	0.003	0.303911	90.607822	4.696089
4	0.004	0.131501	90.263002	4.868499
5	0.005	0.061738	90.123476	4.938262
6	0.006	0.033369	90.066737	4.966631
7	0.007	0.021809	90.043618	4.978191
8	0.008	0.017095	90.034189	4.982905
9	0.009	0.015172	90.030343	4.984828
10	0.010	0.014387	90.028774	4.985613
11	0.011	0.014067	90.028134	4.985933
12	0.012	0.013936	90.027872	4.986064
13	0.013	0.013883	90.027766	4.986117
14	0.014	0.013861	90.027722	4.986139
15	0.015	0.013852	90.027705	4.986148
16	0.015	40.000000	90.027705	4.986148

Again, take the system to equilibrium¶

In [12]:

bio.react(time_step=0.0005, n_steps=80, snapshots={"frequency": 2, "sample_bin": 0})  # At every other step, take a snapshot 
                                                                                      # of all species at bin 0
bio.describe_state()
bio.get_history()

SYSTEM STATE at Time t = 0.055:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [0.97997411]
  Species 1 (B). Diff rate: None. Conc: [11.98765279]
  Species 2 (Y). Diff rate: None. Conc: [44.00617361]

Out[12]:

	SYSTEM TIME	A	B	Y
0	0.000	5.000000	100.000000	0.000000
1	0.001	1.850000	93.700000	3.150000
2	0.002	0.735332	91.470665	4.264668
3	0.003	0.303911	90.607822	4.696089
4	0.004	0.131501	90.263002	4.868499
5	0.005	0.061738	90.123476	4.938262
6	0.006	0.033369	90.066737	4.966631
7	0.007	0.021809	90.043618	4.978191
8	0.008	0.017095	90.034189	4.982905
9	0.009	0.015172	90.030343	4.984828
10	0.010	0.014387	90.028774	4.985613
11	0.011	0.014067	90.028134	4.985933
12	0.012	0.013936	90.027872	4.986064
13	0.013	0.013883	90.027766	4.986117
14	0.014	0.013861	90.027722	4.986139
15	0.015	0.013852	90.027705	4.986148
16	0.015	40.000000	90.027705	4.986148
17	0.016	19.349973	48.727651	25.636175
18	0.017	13.059681	36.147067	31.926466
19	0.018	9.783622	29.594949	35.202526
20	0.019	7.749528	25.526760	37.236620
21	0.020	6.361385	22.750475	38.624763
22	0.021	5.355704	20.739113	39.630443
23	0.022	4.596387	19.220478	40.389761
24	0.023	4.005510	18.038724	40.980638
25	0.024	3.535038	17.097780	41.451110
26	0.025	3.153653	16.335011	41.832494
27	0.026	2.840021	15.707747	42.146127
28	0.027	2.579079	15.185862	42.407069
29	0.028	2.359876	14.747456	42.626272
30	0.029	2.174254	14.376212	42.811894
31	0.030	2.016004	14.059712	42.970144
32	0.031	1.880314	13.788333	43.105833
33	0.032	1.763400	13.554504	43.222748
34	0.033	1.662239	13.352182	43.323909
35	0.034	1.574392	13.176488	43.411756
36	0.035	1.497866	13.023437	43.488281
37	0.036	1.431022	12.889749	43.555125
38	0.037	1.372496	12.772696	43.613652
39	0.038	1.321146	12.669996	43.665002
40	0.039	1.276010	12.579724	43.710138
41	0.040	1.236273	12.500251	43.749875
42	0.041	1.201240	12.430185	43.784907
43	0.042	1.170317	12.368338	43.815831
44	0.043	1.142991	12.313686	43.843157
45	0.044	1.118820	12.265345	43.867328
46	0.045	1.097423	12.222550	43.888725
47	0.046	1.078466	12.184636	43.907682
48	0.047	1.061660	12.151024	43.924488
49	0.048	1.046752	12.121209	43.939395
50	0.049	1.033522	12.094748	43.952626
51	0.050	1.021774	12.071252	43.964374
52	0.051	1.011338	12.050381	43.974809
53	0.052	1.002065	12.031835	43.984083
54	0.053	0.993822	12.015349	43.992326
55	0.054	0.986493	12.000690	43.999655
56	0.055	0.979974	11.987653	44.006174

In [13]:

# Verify that the reaction has reached equilibrium
bio.reaction_dynamics.is_in_equilibrium(conc=bio.bin_snapshot(bin_address = 0), tolerance=7)

0: A + 2 B <-> Y
Final concentrations: [A] = 0.98 ; [B] = 11.99 ; [Y] = 44.01
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.74597
    Formula used:  [Y] / ([A][B])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 6.351 %
Reaction IS in equilibrium (within 7% tolerance)

Out[13]:

True

In [14]:

fig = px.line(data_frame=bio.get_history(), x="SYSTEM TIME", y=["A", "B", "Y"], 
              title="Changes in concentrations (reaction A + 2 B <-> Y)",
              color_discrete_sequence = ['red', 'blue', 'green'],
              labels={"value":"concentration", "variable":"Chemical"})
fig.show()

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 [15]:

bio.set_bin_conc(bin_address=0, species_index=0, conc=30.)
bio.describe_state()

SYSTEM STATE at Time t = 0.055:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [30.]
  Species 1 (B). Diff rate: None. Conc: [11.98765279]
  Species 2 (Y). Diff rate: None. Conc: [44.00617361]

In [16]:

# Save the state of the concentrations of all species at bin 0 (the only bin in this system)
bio.add_snapshot(bio.bin_snapshot(bin_address = 0))

Yet again, take the system to equilibrium¶

In [17]:

bio.react(time_step=0.0005, n_steps=70, snapshots={"frequency": 2, "sample_bin": 0})  # At every other step, take a snapshot 
                                                                                      # of all species at bin 0
bio.describe_state()
bio.get_history()

SYSTEM STATE at Time t = 0.09:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [24.26245387]
  Species 1 (B). Diff rate: None. Conc: [0.51256052]
  Species 2 (Y). Diff rate: None. Conc: [49.74371974]

Out[17]:

	SYSTEM TIME	A	B	Y	caption
0	0.000	5.000000	100.000000	0.000000
1	0.001	1.850000	93.700000	3.150000
2	0.002	0.735332	91.470665	4.264668
3	0.003	0.303911	90.607822	4.696089
4	0.004	0.131501	90.263002	4.868499
...	...	...	...	...	...
88	0.086	24.262458	0.512569	49.743715
89	0.087	24.262456	0.512566	49.743717
90	0.088	24.262455	0.512563	49.743718
91	0.089	24.262454	0.512562	49.743719
92	0.090	24.262454	0.512561	49.743720

93 rows × 5 columns

In [18]:

# Verify that the reaction has reached equilibrium
bio.reaction_dynamics.is_in_equilibrium(conc=bio.bin_snapshot(bin_address = 0))

0: A + 2 B <-> Y
Final concentrations: [A] = 24.26 ; [B] = 0.5126 ; [Y] = 49.74
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99999
    Formula used:  [Y] / ([A][B])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.0003695 %
Reaction IS in equilibrium (within 1% tolerance)

Out[18]:

True

In [19]:

fig = px.line(data_frame=bio.get_history(), x="SYSTEM TIME", y=["A", "B", "Y"], 
              title="Changes in concentrations (reaction A + 2 B <-> Y)",
              color_discrete_sequence = ['red', 'blue', 'green'],
              labels={"value":"concentration", "variable":"Chemical"})
fig.show()

A, again the scarse limiting reagent, stops the reaction yet again

Note: A can down-regulate B, but it cannot bring it up.

For additional exploration, see the experiment "reactions_single_compartment/down_regulate_2"¶

In [ ]:

A down-regulates B , by being the limiting reagent in reaction A + 2 B <-> Y (mostly forward)¶