`U` ("Up-regulator") up-regulates `X` , by sharing a reaction product `D` ("Drain") across 2 separate reactions:¶

`U <-> 2 D` and `X <-> D` (both mostly forward)¶

1st-order kinetics throughout.

Invoking Le Chatelier's principle, it can be seen that, starting from equilibrium, when [U] goes up, so does [D]; and when [D] goes up, so does [X].
Conversely, when [U] goes down, so does [D]; and when [D] goes down, so does [X].

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 UniformCompartment

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 'up_regulate_2.log.htm'

Initialize the system¶

In [4]:

# Initialize the system
chem_data = chem(names=["U", "X", "D"])

# Reaction U <-> 2D , with 1st-order kinetics for all species
chem_data.add_reaction(reactants="U", products=[(2, "D", 1)],
                       forward_rate=8., reverse_rate=2.)

# Reaction X <-> D , with 1st-order kinetics for all species
chem_data.add_reaction(reactants="X", products="D",
                       forward_rate=6., reverse_rate=3.)

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: 2 (at temp. 25 C)
0: U <-> 2 D  (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products
1: X <-> D  (kF = 6 / kR = 3 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {'X', 'U', 'D'}
[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_2.log.htm`]

Set the initial concentrations of all the chemicals¶

In [5]:

dynamics = UniformCompartment(chem_data=chem_data, preset = "fast")
dynamics.set_conc(conc={"U": 50., "X": 100.})
dynamics.describe_state()

SYSTEM STATE at Time t = 0:
3 species:
  Species 0 (U). Conc: 50.0
  Species 1 (X). Conc: 100.0
  Species 2 (D). Conc: 0.0
Set of chemicals involved in reactions: {'X', 'U', 'D'}

In [ ]:

1. 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(initial_step=0.03, target_end_time=0.5,
                                  variable_steps=True, explain_variable_steps=False)

dynamics.get_history()

Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
42 total step(s) taken
Number of step re-do's because of negative concentrations: 0
Number of step re-do's because of elective soft aborts: 5
Norm usage: {'norm_A': 32, 'norm_B': 17, 'norm_C': 17, 'norm_D': 17}

Out[6]:

	SYSTEM TIME	U	X	D	caption
0	0.000000	50.000000	100.000000	0.000000	Initialized state
1	0.002333	49.066880	98.600320	3.265920
2	0.004199	48.346505	97.514534	5.792455
3	0.006065	47.646316	96.455051	8.252317
4	0.007932	46.965762	95.421204	10.647272
5	0.009798	46.304308	94.412342	12.979043
6	0.011664	45.661432	93.427831	15.249305
7	0.013530	45.036628	92.467055	17.459688
8	0.016330	44.125790	91.060592	20.687828
9	0.018569	43.427897	89.976007	23.168198
10	0.020809	42.753617	88.922661	25.570105
11	0.023048	42.102175	87.899605	27.896044
12	0.026407	41.158146	86.409082	31.274626
13	0.029095	40.441377	85.267936	33.849309
14	0.031782	39.753857	84.165948	36.326338
15	0.034469	39.094431	83.101698	38.709439
16	0.037157	38.461991	82.073822	41.002196
17	0.041188	37.552211	80.584595	44.310983
18	0.044413	36.869199	79.454040	46.807562
19	0.047638	36.219910	78.369514	49.190667
20	0.050863	35.602742	77.329027	51.465488
21	0.055700	34.722882	75.831509	54.722726
22	0.059570	34.071443	74.706080	57.151033
23	0.063439	33.458967	73.634974	59.447093
24	0.069244	32.595350	72.105604	62.703696
25	0.073888	31.966786	70.970090	65.096338
26	0.078532	31.383796	69.899547	67.332862
27	0.085498	30.572955	68.385212	70.468877
28	0.091070	29.995382	67.276804	72.732432
29	0.099429	29.205486	65.726543	75.862484
30	0.106116	28.657688	64.611327	78.073296
31	0.116147	27.924301	63.072149	81.079249
32	0.124171	27.432914	61.987277	83.146895
33	0.136208	26.792927	60.512982	85.901165
34	0.148245	26.280871	59.244618	88.193640
35	0.166300	25.669531	57.603648	91.057291
36	0.180744	25.333826	56.557174	92.775174
37	0.202410	24.962896	55.235160	94.839047
38	0.234909	24.637090	53.711149	97.014671
39	0.283658	24.487559	52.189072	98.835810
40	0.356781	24.617071	50.973253	99.792605
41	0.466466	24.907587	50.264503	99.920324
42	0.630993	25.003005	49.964069	100.029921

In [7]:

dynamics.explain_time_advance()

From time 0 to 0.002333, in 1 step of 0.00233
From time 0.002333 to 0.01353, in 6 steps of 0.00187
From time 0.01353 to 0.01633, in 1 step of 0.0028
From time 0.01633 to 0.02305, in 3 steps of 0.00224
From time 0.02305 to 0.02641, in 1 step of 0.00336
From time 0.02641 to 0.03716, in 4 steps of 0.00269
From time 0.03716 to 0.04119, in 1 step of 0.00403
From time 0.04119 to 0.05086, in 3 steps of 0.00322
From time 0.05086 to 0.0557, in 1 step of 0.00484
From time 0.0557 to 0.06344, in 2 steps of 0.00387
From time 0.06344 to 0.06924, in 1 step of 0.0058
From time 0.06924 to 0.07853, in 2 steps of 0.00464
From time 0.07853 to 0.0855, in 1 step of 0.00697
From time 0.0855 to 0.09107, in 1 step of 0.00557
From time 0.09107 to 0.09943, in 1 step of 0.00836
From time 0.09943 to 0.1061, in 1 step of 0.00669
From time 0.1061 to 0.1161, in 1 step of 0.01
From time 0.1161 to 0.1242, in 1 step of 0.00802
From time 0.1242 to 0.1482, in 2 steps of 0.012
From time 0.1482 to 0.1663, in 1 step of 0.0181
From time 0.1663 to 0.1807, in 1 step of 0.0144
From time 0.1807 to 0.2024, in 1 step of 0.0217
From time 0.2024 to 0.2349, in 1 step of 0.0325
From time 0.2349 to 0.2837, in 1 step of 0.0487
From time 0.2837 to 0.3568, in 1 step of 0.0731
From time 0.3568 to 0.4665, in 1 step of 0.11
From time 0.4665 to 0.631, in 1 step of 0.165
(42 steps total)

Plots of changes of concentration with time¶

In [8]:

dynamics.plot_history(colors=['red', 'green', 'gray'])

Equilibrium ¶

In [9]:

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

0: U <-> 2 D
Final concentrations: [U] = 25 ; [D] = 100
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00072
    Formula used:  [D] / [U]
2. Ratio of forward/reverse reaction rates: 4
Discrepancy between the two values: 0.0179 %
Reaction IS in equilibrium (within 1% tolerance)

1: X <-> D
Final concentrations: [X] = 49.96 ; [D] = 100
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00204
    Formula used:  [D] / [X]
2. Ratio of forward/reverse reaction rates: 2
Discrepancy between the two values: 0.1019 %
Reaction IS in equilibrium (within 1% tolerance)

Out[9]:

True

In [ ]:

2. Now, let's suddenly increase [U]¶

In [10]:

dynamics.set_single_conc(species_name="U", conc=70., snapshot=True)
dynamics.describe_state()

SYSTEM STATE at Time t = 0.63099291:
3 species:
  Species 0 (U). Conc: 70.0
  Species 1 (X). Conc: 49.96406885180444
  Species 2 (D). Conc: 100.02992131107243
Set of chemicals involved in reactions: {'X', 'U', 'D'}

In [11]:

dynamics.get_history(tail=3)

Out[11]:

	SYSTEM TIME	U	X	D	caption
41	0.466466	24.907587	50.264503	99.920324
42	0.630993	25.003005	49.964069	100.029921
43	0.630993	70.000000	49.964069	100.029921	Set concentration of `U`

Again, take the system to equilibrium¶

In [12]:

dynamics.single_compartment_react(initial_step=0.03, target_end_time=1,
                                  variable_steps=True)

Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
24 total step(s) taken
Number of step re-do's because of negative concentrations: 0
Number of step re-do's because of elective soft aborts: 9
Norm usage: {'norm_A': 51, 'norm_B': 28, 'norm_C': 28, 'norm_D': 28}

In [13]:

#dynamics.get_history()
#dynamics.explain_time_advance()

In [14]:

dynamics.plot_history(colors=['red', 'green', 'gray'])

The (transiently) high value of [U] led to an increase in [X]¶

In [15]:

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

0: U <-> 2 D
Final concentrations: [U] = 36.7 ; [D] = 145.3
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.9596
    Formula used:  [D] / [U]
2. Ratio of forward/reverse reaction rates: 4
Discrepancy between the two values: 1.01 %
Reaction IS in equilibrium (within 2% tolerance)

1: X <-> D
Final concentrations: [X] = 71.31 ; [D] = 145.3
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.03768
    Formula used:  [D] / [X]
2. Ratio of forward/reverse reaction rates: 2
Discrepancy between the two values: 1.884 %
Reaction IS in equilibrium (within 2% tolerance)

Out[15]:

True

In [ ]:

3. Let's again suddenly increase [U]¶

In [16]:

dynamics.set_single_conc(species_name="U", conc=100., snapshot=True)
dynamics.describe_state()

SYSTEM STATE at Time t = 1.0692249:
3 species:
  Species 0 (U). Conc: 100.0
  Species 1 (X). Conc: 71.30574896594584
  Species 2 (D). Conc: 145.29798215919604
Set of chemicals involved in reactions: {'X', 'U', 'D'}

In [17]:

dynamics.get_history(tail=3)

Out[17]:

	SYSTEM TIME	U	X	D	caption
66	0.977392	37.441093	69.408954	145.702851
67	1.069225	36.695130	71.305749	145.297982
68	1.069225	100.000000	71.305749	145.297982	Set concentration of `U`

Yet again, take the system to equilibrium¶

In [18]:

dynamics.single_compartment_react(initial_step=0.03, target_end_time=1.6,
                                  variable_steps=True)

Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
34 total step(s) taken
Number of step re-do's because of negative concentrations: 0
Number of step re-do's because of elective soft aborts: 14
Norm usage: {'norm_A': 81, 'norm_B': 44, 'norm_C': 44, 'norm_D': 44}

In [19]:

#dynamics.get_history()
#dynamics.explain_time_advance()

In [20]:

dynamics.plot_history(colors=['red', 'green', 'gray'])

The (transiently) high value of [U] again led to an increase in [X]¶

In [21]:

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

0: U <-> 2 D
Final concentrations: [U] = 52.11 ; [D] = 208.3
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99727
    Formula used:  [D] / [U]
2. Ratio of forward/reverse reaction rates: 4
Discrepancy between the two values: 0.06828 %
Reaction IS in equilibrium (within 1% tolerance)

1: X <-> D
Final concentrations: [X] = 104.1 ; [D] = 208.3
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00191
    Formula used:  [D] / [X]
2. Ratio of forward/reverse reaction rates: 2
Discrepancy between the two values: 0.09565 %
Reaction IS in equilibrium (within 1% tolerance)

Out[21]:

True

In [ ]:

4. Now, instead, let's DECREASE [U]¶

In [22]:

dynamics.set_single_conc(species_name="U", conc=5., snapshot=True)
dynamics.describe_state()

SYSTEM STATE at Time t = 1.6922388:
3 species:
  Species 0 (U). Conc: 5.0
  Species 1 (X). Conc: 104.05849412376946
  Species 2 (D). Conc: 208.31604776017218
Set of chemicals involved in reactions: {'X', 'U', 'D'}

In [23]:

dynamics.get_history(tail=3)

Out[23]:

	SYSTEM TIME	U	X	D	caption
101	1.555133	52.537879	102.920098	208.607876
102	1.692239	52.114595	104.058494	208.316048
103	1.692239	5.000000	104.058494	208.316048	Set concentration of `U`

Take the system to equilibrium¶

In [24]:

dynamics.single_compartment_react(initial_step=0.03, target_end_time=2.3,
                                  variable_steps=True)

Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
27 total step(s) taken
Number of step re-do's because of negative concentrations: 0
Number of step re-do's because of elective soft aborts: 18
Norm usage: {'norm_A': 102, 'norm_B': 57, 'norm_C': 57, 'norm_D': 57}

In [25]:

#dynamics.get_history()
#dynamics.explain_time_advance()

In [26]:

dynamics.plot_history(colors=['red', 'green', 'gray'])

The (transiently) LOW value of [U] led to an DECREASE in [X]¶

In [27]:

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

Out[27]:

True

In [ ]:

U ("Up-regulator") up-regulates X , by sharing a reaction product D ("Drain") across 2 separate reactions:¶

U <-> 2 D and X <-> D (both mostly forward)¶

Initialize the system¶

Set the initial concentrations of all the chemicals¶

1. Take the initial system to equilibrium¶

Plots of changes of concentration with time¶

Equilibrium¶

2. Now, let's suddenly increase [U]¶

Again, take the system to equilibrium¶

The (transiently) high value of [U] led to an increase in [X]¶

3. Let's again suddenly increase [U]¶

Yet again, take the system to equilibrium¶

The (transiently) high value of [U] again led to an increase in [X]¶

4. Now, instead, let's DECREASE [U]¶

Take the system to equilibrium¶

The (transiently) LOW value of [U] led to an DECREASE in [X]¶

`U` ("Up-regulator") up-regulates `X` , by sharing a reaction product `D` ("Drain") across 2 separate reactions:¶

`U <-> 2 D` and `X <-> D` (both mostly forward)¶

Equilibrium ¶