`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: Feb. 11, 2023

In [1]:

# Extend the sys.path variable, to contain the project's root directory
import set_path
set_path.add_ancestor_dir_to_syspath(2)  # The number of levels to go up 
                                         # to reach the project's home, from the folder containing this notebook

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.reactions.reaction_data import ReactionData as chem
from src.modules.reactions.reaction_dynamics import ReactionDynamics

import numpy as np
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_1"],
                  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")],
                       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
graph_data = chem_data.prepare_graph_network()
GraphicLog.export_plot(graph_data, "vue_cytoscape_1")

Number of reactions: 2 (at temp. 25 C)
0: U <-> 2 D  (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products
1: X <-> D  (kF = 6 / kR = 3 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products
[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_2.log.htm`]

Set the initial concentrations of all the chemicals¶

In [5]:

dynamics = ReactionDynamics(reaction_data=chem_data)
dynamics.set_conc(conc={"U": 50., "X": 100., "D": 0.})
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

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(time_step=0.03, stop_time=0.5,
                                  dynamic_substeps=2, rel_fast_threshold=50)

df = dynamics.get_history()
df

single_compartment_react(): setting abs_fast_threshold to 16.666666666666668
17 total step(s) taken

Out[6]:

	SYSTEM TIME	U	X	D	caption
0	0.015	44.000000	91.000000	21.000000	Interm. step, due to the fast rxns: [0, 1]
1	0.030	39.350000	83.755000	37.545000
2	0.045	35.754350	77.906575	50.584725	Interm. step, due to the fast rxns: [0, 1]
3	0.060	32.981370	73.171296	60.865965
4	0.075	30.849584	69.324848	68.975984	Interm. step, due to the fast rxns: [0, 1]
5	0.090	29.216914	66.189531	75.376642
6	0.105	27.972183	63.624422	80.431212	Interm. step, due to the fast rxns: [0, 1]
7	0.120	27.028458	61.517628	84.425456
8	0.135	26.317806	59.780187	87.584200	Interm. step, due to the fast rxns: [0, 1]
9	0.150	25.787196	58.341259	90.084349
10	0.165	25.395263	57.144342	92.065133	Interm. step, due to the fast rxns: [0, 1]
11	0.180	25.109785	56.144282	93.636148
12	0.195	24.905695	55.304923	94.883686	Interm. step, due to the fast rxns: [0, 1]
13	0.210	24.763522	54.597246	95.875709
14	0.225	24.668171	53.997901	96.665757	Interm. step, due to the fast rxns: [0, 1]
15	0.240	24.607963	53.488049	97.296025
16	0.255	24.573888	53.052446	97.799778	Interm. step, due to the fast rxns: [1]
17	0.270	24.539814	52.678715	98.241657
18	0.285	24.542286	52.358506	98.556923	Interm. step, due to the fast rxns: [1]
19	0.300	24.544758	52.081302	98.829183
20	0.315	24.564262	51.841298	99.030178	Interm. step, due to the fast rxns: [1]
21	0.330	24.583767	51.631939	99.200527
22	0.360	24.635694	51.266237	99.462374
23	0.390	24.690870	50.989928	99.628331
24	0.420	24.742761	50.778291	99.736187
25	0.450	24.788670	50.614455	99.808205
26	0.480	24.827881	50.486592	99.857645
27	0.510	24.860649	50.386193	99.892510

In [7]:

dynamics.explain_time_advance()

From time 0 to 0.33, in 22 substeps of 0.015 (each 1/2 of full step)
From time 0.33 to 0.51, in 6 FULL steps of 0.03
(for a grand total of 17 full steps)

Plots of changes of concentration with time¶

In [8]:

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

Equilibrium ¶

In [9]:

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

U <-> 2 D
Final concentrations:  [D] = 99.89 ; [U] = 24.86
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.0181
    Formula used:  [D] / [U]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.4524 %
Reaction IS in equilibrium (within 1% tolerance)

X <-> D
Final concentrations:  [D] = 99.89 ; [X] = 50.39
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.98254
    Formula used:  [D] / [X]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 0.8731 %
Reaction IS in equilibrium (within 1% tolerance)

Out[9]:

True

2. Now, let's suddenly increase [U]¶

In [10]:

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

SYSTEM STATE at Time t = 0.51:
3 species:
  Species 0 (U). Conc: 70.0
  Species 1 (X). Conc: 50.38619345748053
  Species 2 (D). Conc: 99.89250950608736

In [11]:

dynamics.get_history(tail=3)

Out[11]:

	SYSTEM TIME	U	X	D	caption
26	0.48	24.827881	50.486592	99.857645
27	0.51	24.860649	50.386193	99.892510
28	0.51	70.000000	50.386193	99.892510	Set concentration of `U`

Again, take the system to equilibrium¶

In [12]:

dynamics.single_compartment_react(time_step=0.03, stop_time=1,
                                  dynamic_substeps=2, rel_fast_threshold=50)

df = dynamics.get_history()
df

single_compartment_react(): setting abs_fast_threshold to 16.666666666666668
17 total step(s) taken

Out[12]:

	SYSTEM TIME	U	X	D	caption
0	0.015	44.000000	91.000000	21.000000	Interm. step, due to the fast rxns: [0, 1]
1	0.030	39.350000	83.755000	37.545000
2	0.045	35.754350	77.906575	50.584725	Interm. step, due to the fast rxns: [0, 1]
3	0.060	32.981370	73.171296	60.865965
4	0.075	30.849584	69.324848	68.975984	Interm. step, due to the fast rxns: [0, 1]
5	0.090	29.216914	66.189531	75.376642
6	0.105	27.972183	63.624422	80.431212	Interm. step, due to the fast rxns: [0, 1]
7	0.120	27.028458	61.517628	84.425456
8	0.135	26.317806	59.780187	87.584200	Interm. step, due to the fast rxns: [0, 1]
9	0.150	25.787196	58.341259	90.084349
10	0.165	25.395263	57.144342	92.065133	Interm. step, due to the fast rxns: [0, 1]
11	0.180	25.109785	56.144282	93.636148
12	0.195	24.905695	55.304923	94.883686	Interm. step, due to the fast rxns: [0, 1]
13	0.210	24.763522	54.597246	95.875709
14	0.225	24.668171	53.997901	96.665757	Interm. step, due to the fast rxns: [0, 1]
15	0.240	24.607963	53.488049	97.296025
16	0.255	24.573888	53.052446	97.799778	Interm. step, due to the fast rxns: [1]
17	0.270	24.539814	52.678715	98.241657
18	0.285	24.542286	52.358506	98.556923	Interm. step, due to the fast rxns: [1]
19	0.300	24.544758	52.081302	98.829183
20	0.315	24.564262	51.841298	99.030178	Interm. step, due to the fast rxns: [1]
21	0.330	24.583767	51.631939	99.200527
22	0.360	24.635694	51.266237	99.462374
23	0.390	24.690870	50.989928	99.628331
24	0.420	24.742761	50.778291	99.736187
25	0.450	24.788670	50.614455	99.808205
26	0.480	24.827881	50.486592	99.857645
27	0.510	24.860649	50.386193	99.892510
28	0.510	70.000000	50.386193	99.892510	Set concentration of `U`
29	0.525	64.596775	50.346599	110.738553	Interm. step, due to the fast rxns: [0, 1]
30	0.540	60.167319	50.798640	119.145425
31	0.555	56.521603	51.588307	125.647190	Interm. step, due to the fast rxns: [0, 1]
32	0.570	53.508427	52.599482	130.662367
33	0.585	51.007286	53.745336	134.518794	Interm. step, due to the fast rxns: [0, 1]
34	0.600	48.921976	54.961601	137.473150
35	0.615	47.175533	56.201349	139.726288	Interm. step, due to the fast rxns: [0, 1]
36	0.630	45.706258	57.430910	141.435277
37	0.645	44.464565	58.626716	142.722857	Interm. step, due to the fast rxns: [0, 1]
38	0.660	43.410503	59.772840	143.684857
39	0.675	42.511788	60.859103	144.396023	Interm. step, due to the fast rxns: [0, 1]
40	0.690	41.742255	61.879605	144.914589
41	0.705	41.080622	62.831597	145.285863	Interm. step, due to the fast rxns: [0, 1]
42	0.720	40.509523	63.714617	145.545040
43	0.735	40.014731	64.529828	145.719412	Interm. step, due to the fast rxns: [0, 1]
44	0.750	39.584546	65.279517	145.830094
45	0.765	39.209303	65.966715	145.893382	Interm. step, due to the fast rxns: [0, 1]
46	0.780	38.880988	66.594913	145.921814
47	0.795	38.592924	67.167852	145.925003	Interm. step, due to the fast rxns: [0, 1]
48	0.810	38.339523	67.689371	145.910286
49	0.825	38.116089	68.163290	145.883235	Interm. step, due to the fast rxns: [0, 1]
50	0.840	37.918655	68.593340	145.848053
51	0.855	37.743858	68.983101	145.807885	Interm. step, due to the fast rxns: [0, 1]
52	0.870	37.588832	69.335977	145.765062
53	0.885	37.451124	69.655167	145.721288	Interm. step, due to the fast rxns: [0, 1]
54	0.900	37.328628	69.943660	145.677788
55	0.915	37.219526	70.204231	145.635420	Interm. step, due to the fast rxns: [1]
56	0.930	37.110424	70.439444	145.618410
57	0.960	36.941027	70.866001	145.530648
58	0.990	36.807019	71.207879	145.456785
59	1.020	36.700742	71.481572	145.395648

In [13]:

dynamics.explain_time_advance()

From time 0 to 0.33, in 22 substeps of 0.015 (each 1/2 of full step)
From time 0.33 to 0.51, in 6 FULL steps of 0.03
From time 0.51 to 0.93, in 28 substeps of 0.015 (each 1/2 of full step)
From time 0.93 to 1.02, in 3 FULL steps of 0.03
(for a grand total of 34 full steps)

In [14]:

dynamics.plot_curves(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)

U <-> 2 D
Final concentrations:  [D] = 145.4 ; [U] = 36.7
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.96165
    Formula used:  [D] / [U]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.9586 %
Reaction IS in equilibrium (within 2% tolerance)

X <-> D
Final concentrations:  [D] = 145.4 ; [X] = 71.48
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.03403
    Formula used:  [D] / [X]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 1.701 %
Reaction IS in equilibrium (within 2% tolerance)

Out[15]:

True

3. Let's again suddenly increase [U]¶

In [16]:

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

SYSTEM STATE at Time t = 1.02:
3 species:
  Species 0 (U). Conc: 100.0
  Species 1 (X). Conc: 71.48157153405576
  Species 2 (D). Conc: 145.39564765746923

In [17]:

dynamics.get_history(tail=3)

Out[17]:

	SYSTEM TIME	U	X	D	caption
58	0.99	36.807019	71.207879	145.456785
59	1.02	36.700742	71.481572	145.395648
60	1.02	100.000000	71.481572	145.395648	Set concentration of `U`

Yet again, take the system to equilibrium¶

In [18]:

dynamics.single_compartment_react(time_step=0.03, stop_time=1.6,
                                  dynamic_substeps=2, rel_fast_threshold=120)

df = dynamics.history.get()
df

single_compartment_react(): setting abs_fast_threshold to 40.0
20 total step(s) taken

Out[18]:

	SYSTEM TIME	U	X	D	caption
0	0.015	44.000000	91.000000	21.000000	Interm. step, due to the fast rxns: [0, 1]
1	0.030	39.350000	83.755000	37.545000
2	0.045	35.754350	77.906575	50.584725	Interm. step, due to the fast rxns: [0, 1]
3	0.060	32.981370	73.171296	60.865965
4	0.075	30.849584	69.324848	68.975984	Interm. step, due to the fast rxns: [0, 1]
...	...	...	...	...	...
88	1.500	52.843169	102.307495	208.883386
89	1.530	52.693812	102.691651	208.797945
90	1.560	52.575174	102.998969	208.727903
91	1.590	52.480806	103.244666	208.670941
92	1.620	52.405669	103.441011	208.624870

93 rows × 5 columns

In [19]:

dynamics.explain_time_advance()

From time 0 to 0.33, in 22 substeps of 0.015 (each 1/2 of full step)
From time 0.33 to 0.51, in 6 FULL steps of 0.03
From time 0.51 to 0.93, in 28 substeps of 0.015 (each 1/2 of full step)
From time 0.93 to 1.02, in 3 FULL steps of 0.03
From time 1.02 to 1.38, in 24 substeps of 0.015 (each 1/2 of full step)
From time 1.38 to 1.62, in 8 FULL steps of 0.03
(for a grand total of 54 full steps)

In [20]:

dynamics.plot_curves(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(explain=False)

Out[21]:

True

4. Now, instead, let's DECREASE [U]¶

In [22]:

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

SYSTEM STATE at Time t = 1.62:
3 species:
  Species 0 (U). Conc: 5.0
  Species 1 (X). Conc: 103.44101051057498
  Species 2 (D). Conc: 208.62487039926754

In [23]:

dynamics.get_history(tail=3)

Out[23]:

	SYSTEM TIME	U	X	D	caption
91	1.59	52.480806	103.244666	208.670941
92	1.62	52.405669	103.441011	208.624870
93	1.62	5.000000	103.441011	208.624870	Set concentration of `U`

Take the system to equilibrium¶

In [24]:

dynamics.single_compartment_react(time_step=0.03, stop_time=2.3,
                                  dynamic_substeps=2, rel_fast_threshold=80)

df = dynamics.history.get()
df

single_compartment_react(): setting abs_fast_threshold to 26.666666666666668
23 total step(s) taken

Out[24]:

	SYSTEM TIME	U	X	D	caption
0	0.015	44.000000	91.000000	21.000000	Interm. step, due to the fast rxns: [0, 1]
1	0.030	39.350000	83.755000	37.545000
2	0.045	35.754350	77.906575	50.584725	Interm. step, due to the fast rxns: [0, 1]
3	0.060	32.981370	73.171296	60.865965
4	0.075	30.849584	69.324848	68.975984	Interm. step, due to the fast rxns: [0, 1]
...	...	...	...	...	...
124	2.190	39.988395	81.223853	160.865238
125	2.220	40.043094	81.081431	160.898261
126	2.250	40.086647	80.967617	160.924969
127	2.280	40.121350	80.876693	160.946487
128	2.310	40.149015	80.804072	160.963778

129 rows × 5 columns

In [25]:

dynamics.explain_time_advance()

From time 0 to 0.33, in 22 substeps of 0.015 (each 1/2 of full step)
From time 0.33 to 0.51, in 6 FULL steps of 0.03
From time 0.51 to 0.93, in 28 substeps of 0.015 (each 1/2 of full step)
From time 0.93 to 1.02, in 3 FULL steps of 0.03
From time 1.02 to 1.38, in 24 substeps of 0.015 (each 1/2 of full step)
From time 1.38 to 1.62, in 8 FULL steps of 0.03
From time 1.62 to 1.98, in 24 substeps of 0.015 (each 1/2 of full step)
From time 1.98 to 2.31, in 11 FULL steps of 0.03
(for a grand total of 77 full steps)

In [26]:

dynamics.plot_curves(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)¶