Accurate results in the simulation of the coupled reactions `2 S <-> U` and `S <-> X`¶

Both mostly forward. 1st-order kinetics throughout.

Same as substeps_1, but with fixed steps: a lot of tiny steps - as a proxy for the "exact value"

LAST REVISED: May 25, 2023

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.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 'substeps_2.log.htm'

Initialize the system¶

In [4]:

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

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

# Reaction S <-> X , with 1st-order kinetics for all species (mostly forward)
chem_data.add_reaction(reactants="S", products="X",
                       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: 2 S <-> U  (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products
1: S <-> X  (kF = 6 / kR = 3 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products
[GRAPHIC ELEMENT SENT TO LOG FILE `substeps_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., "S": 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 (S). Conc: 0.0

In [6]:

dynamics.set_diagnostics()       # To save diagnostic information about the call to single_compartment_react()

dynamics.single_compartment_react(initial_step=0.0001, target_end_time=0.3, 
                                  variable_steps=False)

df = dynamics.get_history()
df

3000 total step(s) taken

Out[6]:

	SYSTEM TIME	U	X	S	caption
0	0.0000	50.000000	100.000000	0.000000	Initial state
1	0.0001	49.990000	99.970000	0.050000
2	0.0002	49.980042	99.940039	0.099877
3	0.0003	49.970126	99.910117	0.149631
4	0.0004	49.960252	99.880234	0.199263
...	...	...	...	...	...
2996	0.2996	59.344280	61.942266	19.369175
2997	0.2997	59.347906	61.935304	19.368883
2998	0.2998	59.351532	61.928345	19.368592
2999	0.2999	59.355156	61.921388	19.368300
3000	0.3000	59.358780	61.914432	19.368008

3001 rows × 5 columns

In [7]:

df.iloc[400]

Out[7]:

SYSTEM TIME         0.04
U              48.449494
X              90.386964
S              12.714047
caption                 
Name: 400, dtype: object

In [8]:

df.iloc[1850]      # This data point is used in experiment `substeps_1`

Out[8]:

SYSTEM TIME        0.185
U              54.529071
X              71.351769
S              19.590088
caption                 
Name: 1850, dtype: object

In [9]:

(transition_times, step_sizes) = dynamics.explain_time_advance(return_times=True)

From time 0 to 0.3, in 3000 steps of 0.0001
(3000 steps total)

In [10]:

np.array(step_sizes)

Out[10]:

array([1.e-04])

In [11]:

np.array(transition_times)    # Note: there will be one more transition time (the end time) than step sizes

Out[11]:

array([0. , 0.3])

Plots of changes of concentration with time¶

In [12]:

dynamics.plot_curves(colors=['green', 'orange', 'blue'])

In [ ]:

Accurate results in the simulation of the coupled reactions 2 S <-> U and S <-> X¶

Initialize the system¶

Set the initial concentrations of all the chemicals¶

Plots of changes of concentration with time¶

Accurate results in the simulation of the coupled reactions `2 S <-> U` and `S <-> X`¶