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

Both mostly forward. 1st-order kinetics throughout.

Same as variable_steps_1, but with FIXED TIME STEPS: a lot of TINY steps - as a proxy for the "exact value"

TAGS : "uniform compartment"¶

In [1]:

LAST_REVISED = "Oct. 11, 2024"
LIFE123_VERSION = "1.0.0.beta.39"   # 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 ChemData as chem
from life123 import UniformCompartment

from life123 import 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 'variable_steps_2.log.htm'

Initialize the system¶

In [5]:

# Initialize the system
chem_data = chem()

# Reaction 2 S <-> U , with 1st-order kinetics for all species (mostly forward)
chem_data.add_reaction(reactants=[(2, "S", 1)], 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
chem_data.plot_reaction_network("vue_cytoscape_2")

Number of reactions: 2 (at temp. 25 C)
0: 2 S <-> U  (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products
1: S <-> X  (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: {'U', 'X', 'S'}
[GRAPHIC ELEMENT SENT TO LOG FILE `variable_steps_2.log.htm`]

Set the initial concentrations of all the chemicals¶

In [6]:

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

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

In [7]:

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

dynamics.single_compartment_react(initial_step=0.0001, target_end_time=0.35, 
                                  variable_steps=False)

df = dynamics.get_history()
df

3500 total step(s) taken

Out[7]:

	SYSTEM TIME	S	U	X	caption
0	0.0000	0.000000	50.000000	100.000000	Initialized state
1	0.0001	0.050000	49.990000	99.970000	1st reaction step
2	0.0002	0.099877	49.980042	99.940039
3	0.0003	0.149631	49.970126	99.910117
4	0.0004	0.199263	49.960252	99.880234
...	...	...	...	...	...
3496	0.3496	19.226544	61.042146	58.689164
3497	0.3497	19.226269	61.045319	58.683094
3498	0.3498	19.225995	61.048490	58.677024
3499	0.3499	19.225720	61.051662	58.670957
3500	0.3500	19.225445	61.054832	58.664891	last reaction step

3501 rows × 5 columns

In [8]:

dynamics.get_diagnostics().explain_time_advance()

From time 0 to 0.35, in 3500 steps of 0.0001
(3500 steps total)

Look up some values¶

In [9]:

df.iloc[400]

Out[9]:

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

In [10]:

df.iloc[1850]

Out[10]:

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

Plots of changes of concentration with time¶

In [11]:

dynamics.plot_history(colors=['darkturquoise', 'green', 'orange'])

In [12]:

dynamics.curve_intersect("U", "X", t_start=0.3, t_end=0.35)

Out[12]:

(0.3249894990583167, 60.23478689917821)

In [ ]:

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