`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.

Single-bin reaction

Based on experiment reactions_single_compartment/up_regulate_1

LAST REVISED: May 6, 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
from src.life_1D.bio_sim_1d import BioSim1D

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_2"],
                  extra_js="https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js")

-> Output will be LOGGED into the file 'up_regulation_1.log.htm'

In [4]:

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

# 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: {'X', 'B', 'A'}
[GRAPHIC ELEMENT SENT TO LOG FILE `up_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="X", conc=100.)   # Plentiful
# Initially, no "B" 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 (X). Diff rate: None. Conc: [100.]
  Species 2 (B). 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	X	B	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: [0.02617327]
  Species 1 (X). Diff rate: None. Conc: [95.02617327]
  Species 2 (B). Diff rate: None. Conc: [9.94765346]

Out[7]:

	SYSTEM TIME	A	X	B
0	0.000	5.000000	100.000000	0.000000
1	0.001	1.828000	96.828000	6.344000
2	0.002	0.701002	95.701002	8.597996
3	0.003	0.281916	95.281916	9.436168
4	0.004	0.123519	95.123519	9.752963
5	0.005	0.063287	95.063287	9.873425
6	0.006	0.040331	95.040331	9.919337
7	0.007	0.031575	95.031575	9.936851
8	0.008	0.028233	95.028233	9.943534
9	0.009	0.026958	95.026958	9.946084
10	0.010	0.026471	95.026471	9.947058
11	0.011	0.026285	95.026285	9.947429
12	0.012	0.026215	95.026215	9.947571
13	0.013	0.026188	95.026188	9.947625
14	0.014	0.026177	95.026177	9.947646
15	0.015	0.026173	95.026173	9.947653

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

Equilibrium ¶

Consistent with the 4/1 ratio of forward/reverse rates (and the 1st order reactions), the systems settles in the following equilibrium:

In [8]:

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

A + X <-> 2 B
Final concentrations: [A] = 0.02617 ; [X] = 95.03 ; [B] = 9.948
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99963
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.009347 %
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", "X", "B"], 
              title="Changes in concentrations (reaction A + X <-> 2B)",
              color_discrete_sequence = ['red', 'darkorange', '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=50.)
bio.describe_state()

SYSTEM STATE at Time t = 0.015:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [50.]
  Species 1 (X). Diff rate: None. Conc: [95.02617327]
  Species 2 (B). Diff rate: None. Conc: [9.94765346]

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	X	B
0	0.000	5.000000	100.000000	0.000000
1	0.001	1.828000	96.828000	6.344000
2	0.002	0.701002	95.701002	8.597996
3	0.003	0.281916	95.281916	9.436168
4	0.004	0.123519	95.123519	9.752963
5	0.005	0.063287	95.063287	9.873425
6	0.006	0.040331	95.040331	9.919337
7	0.007	0.031575	95.031575	9.936851
8	0.008	0.028233	95.028233	9.943534
9	0.009	0.026958	95.026958	9.946084
10	0.010	0.026471	95.026471	9.947058
11	0.011	0.026285	95.026285	9.947429
12	0.012	0.026215	95.026215	9.947571
13	0.013	0.026188	95.026188	9.947625
14	0.014	0.026177	95.026177	9.947646
15	0.015	0.026173	95.026173	9.947653
16	0.015	50.000000	95.026173	9.947653

Again, take the system to equilibrium¶

In [12]:

bio.react(time_step=0.0005, n_steps=40, 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 = 0.035:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [0.60107953]
  Species 1 (X). Diff rate: None. Conc: [45.6272528]
  Species 2 (B). Diff rate: None. Conc: [108.74549439]

Out[12]:

	SYSTEM TIME	A	X	B
0	0.000	5.000000	100.000000	0.000000
1	0.001	1.828000	96.828000	6.344000
2	0.002	0.701002	95.701002	8.597996
3	0.003	0.281916	95.281916	9.436168
4	0.004	0.123519	95.123519	9.752963
5	0.005	0.063287	95.063287	9.873425
6	0.006	0.040331	95.040331	9.919337
7	0.007	0.031575	95.031575	9.936851
8	0.008	0.028233	95.028233	9.943534
9	0.009	0.026958	95.026958	9.946084
10	0.010	0.026471	95.026471	9.947058
11	0.011	0.026285	95.026285	9.947429
12	0.012	0.026215	95.026215	9.947571
13	0.013	0.026188	95.026188	9.947625
14	0.014	0.026177	95.026177	9.947646
15	0.015	0.026173	95.026173	9.947653
16	0.015	50.000000	95.026173	9.947653
17	0.016	21.623388	66.649561	66.700877
18	0.017	12.120737	57.146910	85.706180
19	0.018	7.471301	52.497475	95.005051
20	0.019	4.871324	49.897498	100.205005
21	0.020	3.316949	48.343122	103.313756
22	0.021	2.351873	47.378046	105.243908
23	0.022	1.738886	46.765059	106.469882
24	0.023	1.343971	46.370144	107.259712
25	0.024	1.087238	46.113411	107.773177
26	0.025	0.919361	45.945534	108.108931
27	0.026	0.809169	45.835342	108.329315
28	0.027	0.736661	45.762834	108.474332
29	0.028	0.688871	45.715044	108.569911
30	0.029	0.657340	45.683513	108.632974
31	0.030	0.636520	45.662694	108.674613
32	0.031	0.622768	45.648941	108.702118
33	0.032	0.613680	45.639853	108.720293
34	0.033	0.607674	45.633847	108.732305
35	0.034	0.603704	45.629877	108.740246
36	0.035	0.601080	45.627253	108.745494

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

In [13]:

# Verify the equilibrium
A_eq = bio.bin_concentration(0, 0)
X_eq = bio.bin_concentration(0, 1)
B_eq = bio.bin_concentration(0, 2)
print("Ratio of equilibrium concentrations (B_eq / (A_eq * X_eq)): ", (B_eq / (A_eq * X_eq)))
print("Ratio of forward/reverse rates: ", chem_data.get_forward_rate(0) / chem_data.get_reverse_rate(0))

Ratio of equilibrium concentrations (B_eq / (A_eq * X_eq)):  3.9651079073726363
Ratio of forward/reverse rates:  4.0

In [14]:

fig = px.line(data_frame=bio.get_history(), x="SYSTEM TIME", y=["A", "X", "B"], 
              title="Changes in concentrations (reaction A + X <-> 2B)",
              color_discrete_sequence = ['red', 'darkorange', '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 = 0.035:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [30.]
  Species 1 (X). Diff rate: None. Conc: [45.6272528]
  Species 2 (B). Diff rate: None. Conc: [108.74549439]

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 = 0.07:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [2.31631253]
  Species 1 (X). Diff rate: None. Conc: [17.94356534]
  Species 2 (B). Diff rate: None. Conc: [164.11286933]

Out[17]:

	SYSTEM TIME	A	X	B	caption
0	0.000	5.000000	100.000000	0.000000
1	0.001	1.828000	96.828000	6.344000
2	0.002	0.701002	95.701002	8.597996
3	0.003	0.281916	95.281916	9.436168
4	0.004	0.123519	95.123519	9.752963
...	...	...	...	...	...
68	0.066	2.342097	17.969350	164.061300
69	0.067	2.333888	17.961141	164.077718
70	0.068	2.326989	17.954242	164.091517
71	0.069	2.321189	17.948442	164.103117
72	0.070	2.316313	17.943565	164.112869

73 rows × 5 columns

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

In [18]:

# Verify the equilibrium
A_eq = bio.bin_concentration(0, 0)
X_eq = bio.bin_concentration(0, 1)
B_eq = bio.bin_concentration(0, 2)
print("Ratio of equilibrium concentrations (B_eq / (A_eq * X_eq)): ", (B_eq / (A_eq * X_eq)))
print("Ratio of forward/reverse rates: ", chem_data.get_forward_rate(0) / chem_data.get_reverse_rate(0))

Ratio of equilibrium concentrations (B_eq / (A_eq * X_eq)):  3.9485418139406785
Ratio of forward/reverse rates:  4.0

In [19]:

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

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

Note: 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.

For additional exploration, see the experiment `reactions_single_compartment/up_regulate_1`¶

In [ ]:

A up-regulates B , by being the limiting reagent in the reaction:¶

A + X <-> 2B (mostly forward), where X is plentiful¶