`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

In [1]:

LAST_REVISED = "May 5, 2025"
LIFE123_VERSION = "1.0.0rc3"        # Library version this experiment is based on

In [2]:

#import set_path                    # Using MyBinder?  Uncomment this before running the next cell!

In [3]:

#import sys
#sys.path.append("C:/some_path/my_env_or_install")   # CHANGE to the folder containing your venv or libraries installation!
# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try:  import set_path   

from experiments.get_notebook_info import get_notebook_basename

from life123 import check_version, ChemData, BioSim1D, GraphicLog

In [4]:

# 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 [5]:

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

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

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

bio.describe_state()

SYSTEM STATE at Time t = 0:
1 bins and 3 chemical species:

Out[5]:

	Species	Diff rate	Bin 0
0	A	None	5.0
1	X	None	100.0
2	B	None	0.0

In [6]:

reactions = bio.get_reactions()

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

reactions.describe_reactions()

# Send the plot of the reaction network to the HTML log file
reactions.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: {"B" (green), "X" (darkorange), "A" (red)}
[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulation_1.log.htm`]

In [ ]:

Enable History¶

In [7]:

# Let's enable history for all the chemicals
bio.enable_history(take_snapshot=True)     # Taking a snapshot to include the current initial state in the history

History enabled for bins None and chemicals None (None means 'all')

In [8]:

bio.get_bin_history(bin_address=0)

Out[8]:

	SYSTEM TIME	A	X	B	caption
0	0.0	5.0	100.0	0.0

In [ ]:

Take the initial system to equilibrium¶

In [9]:

bio.react(time_step=0.0005, n_steps=30)
bio.describe_state()

System Time is now: 0.015
SYSTEM STATE at Time t = 0.015:
1 bins and 3 chemical species:

Out[9]:

	Species	Diff rate	Bin 0
0	A	None	0.026173
1	X	None	95.026173
2	B	None	9.947653

In [10]:

bio.get_bin_history(bin_address=0)

Out[10]:

	SYSTEM TIME	A	X	B
0	0.0000	5.000000	100.000000	0.000000
1	0.0005	3.000000	98.000000	4.000000
2	0.0010	1.828000	96.828000	6.344000
3	0.0015	1.126338	96.126338	7.747325
4	0.0020	0.701002	95.701002	8.597996
5	0.0025	0.441254	95.441254	9.117493
6	0.0030	0.281916	95.281916	9.436168
7	0.0035	0.183906	95.183906	9.632188
8	0.0040	0.123519	95.123519	9.752963
9	0.0045	0.086274	95.086274	9.827453
10	0.0050	0.063287	95.063287	9.873425
11	0.0055	0.049096	95.049096	9.901809
12	0.0060	0.040331	95.040331	9.919337
13	0.0065	0.034918	95.034918	9.930163
14	0.0070	0.031575	95.031575	9.936851
15	0.0075	0.029509	95.029509	9.940982
16	0.0080	0.028233	95.028233	9.943534
17	0.0085	0.027445	95.027445	9.945110
18	0.0090	0.026958	95.026958	9.946084
19	0.0095	0.026657	95.026657	9.946686
20	0.0100	0.026471	95.026471	9.947058
21	0.0105	0.026356	95.026356	9.947287
22	0.0110	0.026285	95.026285	9.947429
23	0.0115	0.026242	95.026242	9.947517
24	0.0120	0.026215	95.026215	9.947571
25	0.0125	0.026198	95.026198	9.947604
26	0.0130	0.026188	95.026188	9.947625
27	0.0135	0.026181	95.026181	9.947638
28	0.0140	0.026177	95.026177	9.947646
29	0.0145	0.026175	95.026175	9.947650
30	0.0150	0.026173	95.026173	9.947653

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

In [ ]:

Equilibrium ¶

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

In [11]:

# 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
Current 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
Discrepancy between the two values: 0.009347 %
Reaction IS in equilibrium (within 1% tolerance)

Out[11]:

True

In [ ]:

Plots of changes of concentration with time¶

In [12]:

bio.plot_history_single_bin(bin_address=0, 
                            title_prefix="Reaction A + X <-> 2B")

In [ ]:

Now, let's suddenly increase [A]¶

In [13]:

bio.set_bin_conc(bin_address=0, chem_index=0, conc=50.)
bio.describe_state()

SYSTEM STATE at Time t = 0.015:
1 bins and 3 chemical species:

Out[13]:

	Species	Diff rate	Bin 0
0	A	None	50.000000
1	X	None	95.026173
2	B	None	9.947653

In [14]:

bio.capture_snapshot(caption="[A] suddenly increased externally")

In [15]:

bio.get_bin_history(bin_address=0)

Out[15]:

	SYSTEM TIME	A	X	B	caption
0	0.0000	5.000000	100.000000	0.000000
1	0.0005	3.000000	98.000000	4.000000
2	0.0010	1.828000	96.828000	6.344000
3	0.0015	1.126338	96.126338	7.747325
4	0.0020	0.701002	95.701002	8.597996
5	0.0025	0.441254	95.441254	9.117493
6	0.0030	0.281916	95.281916	9.436168
7	0.0035	0.183906	95.183906	9.632188
8	0.0040	0.123519	95.123519	9.752963
9	0.0045	0.086274	95.086274	9.827453
10	0.0050	0.063287	95.063287	9.873425
11	0.0055	0.049096	95.049096	9.901809
12	0.0060	0.040331	95.040331	9.919337
13	0.0065	0.034918	95.034918	9.930163
14	0.0070	0.031575	95.031575	9.936851
15	0.0075	0.029509	95.029509	9.940982
16	0.0080	0.028233	95.028233	9.943534
17	0.0085	0.027445	95.027445	9.945110
18	0.0090	0.026958	95.026958	9.946084
19	0.0095	0.026657	95.026657	9.946686
20	0.0100	0.026471	95.026471	9.947058
21	0.0105	0.026356	95.026356	9.947287
22	0.0110	0.026285	95.026285	9.947429
23	0.0115	0.026242	95.026242	9.947517
24	0.0120	0.026215	95.026215	9.947571
25	0.0125	0.026198	95.026198	9.947604
26	0.0130	0.026188	95.026188	9.947625
27	0.0135	0.026181	95.026181	9.947638
28	0.0140	0.026177	95.026177	9.947646
29	0.0145	0.026175	95.026175	9.947650
30	0.0150	0.026173	95.026173	9.947653
31	0.0150	50.000000	95.026173	9.947653	[A] suddenly increased externally

In [ ]:

Again, take the system to equilibrium¶

In [16]:

bio.react(time_step=0.0005, n_steps=40)
bio.describe_state()

System Time is now: 0.035
SYSTEM STATE at Time t = 0.035:
1 bins and 3 chemical species:

Out[16]:

	Species	Diff rate	Bin 0
0	A	None	0.601080
1	X	None	45.627253
2	B	None	108.745494

In [17]:

bio.get_bin_history(bin_address=0)

Out[17]:

	SYSTEM TIME	A	X	B	caption
0	0.0000	5.000000	100.000000	0.000000
1	0.0005	3.000000	98.000000	4.000000
2	0.0010	1.828000	96.828000	6.344000
3	0.0015	1.126338	96.126338	7.747325
4	0.0020	0.701002	95.701002	8.597996
...	...	...	...	...	...
67	0.0330	0.607674	45.633847	108.732305
68	0.0335	0.605484	45.631658	108.736685
69	0.0340	0.603704	45.629877	108.740246
70	0.0345	0.602256	45.628430	108.743141
71	0.0350	0.601080	45.627253	108.745494

72 rows × 5 columns

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

In [18]:

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

Ratio of equilibrium concentrations (B_eq / (A_eq * X_eq)):  3.9999999999983915

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[24], line 6
      4 B_eq = bio.bin_concentration(0, 2)
      5 print("Ratio of equilibrium concentrations (B_eq / (A_eq * X_eq)): ", (B_eq / (A_eq * X_eq)))
----> 6 print("Ratio of forward/reverse rates: ", chem_data.get_forward_rate(0) / chem_data.get_reverse_rate(0))

AttributeError: 'ChemData' object has no attribute 'get_forward_rate'

In [19]:

bio.plot_history_single_bin(bin_address=0, 
                            title_prefix="Reaction A + X <-> 2B")

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

In [ ]:

Let's again suddenly increase [A]¶

In [20]:

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

SYSTEM STATE at Time t = 0.035:
1 bins and 3 chemical species:

Out[20]:

	Species	Diff rate	Bin 0
0	A	None	30.000000
1	X	None	45.627253
2	B	None	108.745494

In [21]:

bio.capture_snapshot(caption="[A] again suddenly increased externally")

In [22]:

bio.get_bin_history(bin_address=0)

Out[22]:

	SYSTEM TIME	A	X	B	caption
0	0.0000	5.000000	100.000000	0.000000
1	0.0005	3.000000	98.000000	4.000000
2	0.0010	1.828000	96.828000	6.344000
3	0.0015	1.126338	96.126338	7.747325
4	0.0020	0.701002	95.701002	8.597996
...	...	...	...	...	...
68	0.0335	0.605484	45.631658	108.736685
69	0.0340	0.603704	45.629877	108.740246
70	0.0345	0.602256	45.628430	108.743141
71	0.0350	0.601080	45.627253	108.745494
72	0.0350	30.000000	45.627253	108.745494	[A] again suddenly increased externally

73 rows × 5 columns

In [ ]:

Yet again, take the system to equilibrium¶

In [23]:

bio.react(time_step=0.0005, n_steps=70)
bio.describe_state()

System Time is now: 0.07
SYSTEM STATE at Time t = 0.07:
1 bins and 3 chemical species:

Out[23]:

	Species	Diff rate	Bin 0
0	A	None	2.316313
1	X	None	17.943565
2	B	None	164.112869

In [24]:

bio.get_bin_history(bin_address=0)

Out[24]:

	SYSTEM TIME	A	X	B	caption
0	0.0000	5.000000	100.000000	0.000000
1	0.0005	3.000000	98.000000	4.000000
2	0.0010	1.828000	96.828000	6.344000
3	0.0015	1.126338	96.126338	7.747325
4	0.0020	0.701002	95.701002	8.597996
...	...	...	...	...	...
138	0.0680	2.326989	17.954242	164.091517
139	0.0685	2.323963	17.951216	164.097568
140	0.0690	2.321189	17.948442	164.103117
141	0.0695	2.318645	17.945898	164.108204
142	0.0700	2.316313	17.943565	164.112869

143 rows × 5 columns

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

In [25]:

# Verify the equilibrium
bio.reaction_dynamics.is_in_equilibrium(conc=bio.bin_snapshot(bin_address = 0), 
                                        tolerance=2)

0: A + X <-> 2 B
Current concentrations: [A] = 2.316 ; [X] = 17.94 ; [B] = 164.1
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.94854
    Formula used:  [B] / ([A][X])
2. Ratio of forward/reverse reaction rates: 4
Discrepancy between the two values: 1.286 %
Reaction IS in equilibrium (within 2% tolerance)

Out[25]:

True

In [26]:

bio.plot_history_single_bin(bin_address=0, 
                            title_prefix="Reaction A + X <-> 2B")

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¶

Enable History¶

Take the initial system to equilibrium¶

Equilibrium¶

Plots of changes of concentration with time¶

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¶

For additional exploration, see the experiment reactions_single_compartment/up_regulate_1¶

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

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

Equilibrium ¶

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