`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

TAGS : "reactions 1D"¶

In [1]:

LAST_REVISED = "May 4, 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, os
#os.getcwd()
#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 ChemData, UniformCompartment, BioSim1D, GraphicLog, check_version

In [4]:

check_version(LIFE123_VERSION)

OK

In [ ]:

In [5]:

# 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 [6]:

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

uc = UniformCompartment(chem_data=chem_data)


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

uc.describe_reactions()

# Send the plot of the reaction network to the HTML log file
uc.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" (red), "B" (darkorange), "Y" (green)}
[GRAPHIC ELEMENT SENT TO LOG FILE `down_regulation_1.log.htm`]

In [7]:

bio = BioSim1D(n_bins=1, reaction_handler=uc)

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

bio.describe_state()

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

Out[7]:

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

In [ ]:

In [8]:

# Let's enable history - by default for all chemicals and all bins (we're only using one)
bio.enable_history(take_snapshot=True, caption="Initial setup")

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

In [9]:

bio.get_bin_history(bin_address=0)

Out[9]:

	SYSTEM TIME	A	B	Y	caption
0	0.0	5.0	100.0	0.0	Initial setup

In [ ]:

Take the initial system to equilibrium¶

In [10]:

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[10]:

	Species	Diff rate	Bin 0
0	A	None	0.013852
1	B	None	90.027705
2	Y	None	4.986148

In [11]:

bio.get_bin_history(bin_address=0)

Out[11]:

	SYSTEM TIME	A	B	Y	caption
0	0.0000	5.000000	100.000000	0.000000	Initial setup
1	0.0005	3.000000	96.000000	2.000000
2	0.0010	1.850000	93.700000	3.150000
3	0.0015	1.159770	92.319540	3.840230
4	0.0020	0.735332	91.470665	4.264668
5	0.0025	0.470552	90.941104	4.529448
6	0.0030	0.303911	90.607822	4.696089
7	0.0035	0.198460	90.396921	4.801540
8	0.0040	0.131501	90.263002	4.868499
9	0.0045	0.088891	90.177782	4.911109
10	0.0050	0.061738	90.123476	4.938262
11	0.0055	0.044420	90.088840	4.955580
12	0.0060	0.033369	90.066737	4.966631
13	0.0065	0.026314	90.052627	4.973686
14	0.0070	0.021809	90.043618	4.978191
15	0.0075	0.018932	90.037864	4.981068
16	0.0080	0.017095	90.034189	4.982905
17	0.0085	0.015921	90.031842	4.984079
18	0.0090	0.015172	90.030343	4.984828
19	0.0095	0.014693	90.029386	4.985307
20	0.0100	0.014387	90.028774	4.985613
21	0.0105	0.014192	90.028383	4.985808
22	0.0110	0.014067	90.028134	4.985933
23	0.0115	0.013987	90.027974	4.986013
24	0.0120	0.013936	90.027872	4.986064
25	0.0125	0.013904	90.027807	4.986096
26	0.0130	0.013883	90.027766	4.986117
27	0.0135	0.013870	90.027739	4.986130
28	0.0140	0.013861	90.027722	4.986139
29	0.0145	0.013856	90.027711	4.986144
30	0.0150	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 [12]:

# 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
Current 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
Discrepancy between the two values: 0.0443 %
Reaction IS in equilibrium (within 1% tolerance)

Out[12]:

True

Plots of changes of concentration with time¶

In [13]:

bio.plot_history_single_bin(bin_address=0, 
                            title="Reaction A + 2 B <-> Y . Concentrations at bin 0")

In [ ]:

Now, let's suddenly increase [A]¶

In [14]:

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

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

Out[14]:

	Species	Diff rate	Bin 0
0	A	None	40.000000
1	B	None	90.027705
2	Y	None	4.986148

In [15]:

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

In [16]:

bio.get_bin_history(bin_address=0)

Out[16]:

	SYSTEM TIME	A	B	Y	caption
0	0.0000	5.000000	100.000000	0.000000	Initial setup
1	0.0005	3.000000	96.000000	2.000000
2	0.0010	1.850000	93.700000	3.150000
3	0.0015	1.159770	92.319540	3.840230
4	0.0020	0.735332	91.470665	4.264668
5	0.0025	0.470552	90.941104	4.529448
6	0.0030	0.303911	90.607822	4.696089
7	0.0035	0.198460	90.396921	4.801540
8	0.0040	0.131501	90.263002	4.868499
9	0.0045	0.088891	90.177782	4.911109
10	0.0050	0.061738	90.123476	4.938262
11	0.0055	0.044420	90.088840	4.955580
12	0.0060	0.033369	90.066737	4.966631
13	0.0065	0.026314	90.052627	4.973686
14	0.0070	0.021809	90.043618	4.978191
15	0.0075	0.018932	90.037864	4.981068
16	0.0080	0.017095	90.034189	4.982905
17	0.0085	0.015921	90.031842	4.984079
18	0.0090	0.015172	90.030343	4.984828
19	0.0095	0.014693	90.029386	4.985307
20	0.0100	0.014387	90.028774	4.985613
21	0.0105	0.014192	90.028383	4.985808
22	0.0110	0.014067	90.028134	4.985933
23	0.0115	0.013987	90.027974	4.986013
24	0.0120	0.013936	90.027872	4.986064
25	0.0125	0.013904	90.027807	4.986096
26	0.0130	0.013883	90.027766	4.986117
27	0.0135	0.013870	90.027739	4.986130
28	0.0140	0.013861	90.027722	4.986139
29	0.0145	0.013856	90.027711	4.986144
30	0.0150	0.013852	90.027705	4.986148
31	0.0150	40.000000	90.027705	4.986148	[A] suddenly increased externally

In [ ]:

Again, take the system to equilibrium¶

In [17]:

bio.react(time_step=0.0005, n_steps=80) 
bio.describe_state()

System Time is now: 0.055
SYSTEM STATE at Time t = 0.055:
1 bins and 3 chemical species:

Out[17]:

	Species	Diff rate	Bin 0
0	A	None	0.979974
1	B	None	11.987653
2	Y	None	44.006174

In [18]:

bio.get_bin_history(bin_address=0)

Out[18]:

	SYSTEM TIME	A	B	Y	caption
0	0.0000	5.000000	100.000000	0.000000	Initial setup
1	0.0005	3.000000	96.000000	2.000000
2	0.0010	1.850000	93.700000	3.150000
3	0.0015	1.159770	92.319540	3.840230
4	0.0020	0.735332	91.470665	4.264668
...	...	...	...	...	...
107	0.0530	0.993822	12.015349	43.992326
108	0.0535	0.990050	12.007805	43.996098
109	0.0540	0.986493	12.000690	43.999655
110	0.0545	0.983138	11.993981	44.003010
111	0.0550	0.979974	11.987653	44.006174

112 rows × 5 columns

In [19]:

# 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
Current 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
Discrepancy between the two values: 6.351 %
Reaction IS in equilibrium (within 7% tolerance)

Out[19]:

True

In [20]:

bio.plot_history_single_bin(bin_address=0, 
                            title="Reaction A + 2 B <-> Y . Concentrations at bin 0")

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 [21]:

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

SYSTEM STATE at Time t = 0.055:
1 bins and 3 chemical species:

Out[21]:

	Species	Diff rate	Bin 0
0	A	None	30.000000
1	B	None	11.987653
2	Y	None	44.006174

In [22]:

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

In [23]:

bio.get_bin_history(bin_address=0)

Out[23]:

	SYSTEM TIME	A	B	Y	caption
0	0.0000	5.000000	100.000000	0.000000	Initial setup
1	0.0005	3.000000	96.000000	2.000000
2	0.0010	1.850000	93.700000	3.150000
3	0.0015	1.159770	92.319540	3.840230
4	0.0020	0.735332	91.470665	4.264668
...	...	...	...	...	...
108	0.0535	0.990050	12.007805	43.996098
109	0.0540	0.986493	12.000690	43.999655
110	0.0545	0.983138	11.993981	44.003010
111	0.0550	0.979974	11.987653	44.006174
112	0.0550	30.000000	11.987653	44.006174	[A] again suddenly increased externally

113 rows × 5 columns

Yet again, take the system to equilibrium¶

In [24]:

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

System Time is now: 0.09
SYSTEM STATE at Time t = 0.09:
1 bins and 3 chemical species:

Out[24]:

	Species	Diff rate	Bin 0
0	A	None	24.262454
1	B	None	0.512561
2	Y	None	49.743720

In [25]:

bio.get_bin_history(bin_address=0)

Out[25]:

	SYSTEM TIME	A	B	Y	caption
0	0.0000	5.000000	100.000000	0.000000	Initial setup
1	0.0005	3.000000	96.000000	2.000000
2	0.0010	1.850000	93.700000	3.150000
3	0.0015	1.159770	92.319540	3.840230
4	0.0020	0.735332	91.470665	4.264668
...	...	...	...	...	...
178	0.0880	24.262455	0.512563	49.743718
179	0.0885	24.262455	0.512562	49.743719
180	0.0890	24.262454	0.512562	49.743719
181	0.0895	24.262454	0.512561	49.743720
182	0.0900	24.262454	0.512561	49.743720

183 rows × 5 columns

In [26]:

# 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
Current 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
Discrepancy between the two values: 0.0003695 %
Reaction IS in equilibrium (within 1% tolerance)

Out[26]:

True

In [27]:

bio.plot_history_single_bin(bin_address=0, 
                            title="Reaction A + 2 B <-> Y . Concentrations at bin 0")

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)¶

TAGS : "reactions 1D"¶

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/down_regulate_2"¶

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

Equilibrium ¶