One-bin `A <-> 3B` reaction, with 1st-order kinetics in both directions,¶

taken to equilibrium¶

Diffusion not applicable (just 1 bin)

LAST REVISED: May 6, 2024

First Step
Numerous more steps
Equilibrium

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.chemicals.chem_data import ChemData as chem
from src.life_1D.bio_sim_1d import BioSim1D

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_2"],
                  extra_js="https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js")

-> Output will be LOGGED into the file 'reaction_2.log.htm'

In [4]:

# Initialize the system
chem_data = chem(names=["A", "B"])     # NOTE: Diffusion not applicable (just 1 bin)

# Reaction A <-> 3B , with 1st-order kinetics in both directions
chem_data.add_reaction(reactants=["A"], products=[(3,"B",1)], forward_rate=5., reverse_rate=2.)

bio = BioSim1D(n_bins=1, chem_data=chem_data)

bio.set_uniform_concentration(species_index=0, conc=10.)
bio.set_uniform_concentration(species_index=1, conc=50.)

bio.describe_state()

SYSTEM STATE at Time t = 0:
1 bins and 2 species:
  Species 0 (A). Diff rate: None. Conc: [10.]
  Species 1 (B). Diff rate: None. Conc: [50.]

In [5]:

chem_data.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: A <-> 3 B  (kF = 5 / kR = 2 / delta_G = -2,271.4 / K = 2.5) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {'B', 'A'}

In [6]:

# Save the state of the concentrations of all species at bin 0
bio.add_snapshot(bio.bin_snapshot(bin_address = 0), caption="Initial state")
bio.get_history()

Out[6]:

	SYSTEM TIME	A	B	caption
0	0	10.0	50.0	Initial state

In [7]:

# Send the plot to the HTML log file
chem_data.plot_reaction_network("vue_cytoscape_2")

[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_2.log.htm`]

First step ¶

In [8]:

# First step
bio.react(time_step=0.1, n_steps=1, snapshots={"sample_bin": 0})
bio.describe_state()

SYSTEM STATE at Time t = 0.1:
1 bins and 2 species:
  Species 0 (A). Diff rate: None. Conc: [15.]
  Species 1 (B). Diff rate: None. Conc: [35.]

Early in the reaction :
[A] = 15. [B] = 35.

In [9]:

bio.get_history()

Out[9]:

	SYSTEM TIME	A	B	caption
0	0.0	10.0	50.0	Initial state
1	0.1	15.0	35.0

Numerous more steps ¶

In [10]:

# Numerous more steps
bio.react(time_step=0.1, n_steps=10, snapshots={"sample_bin": 0})

bio.describe_state()

SYSTEM STATE at Time t = 1.1:
1 bins and 2 species:
  Species 0 (A). Diff rate: None. Conc: [14.54545455]
  Species 1 (B). Diff rate: None. Conc: [36.36363636]

Equilibrium ¶

Consistent with the 5/2 ratio of forward/reverse rates (and the 1st order reactions), the systems settles in the equilibrium: [A] = 14.54545455 , [B] = 36.36363636

In [11]:

# Verify that the reaction has reached equilibrium
bio.reaction_dynamics.is_in_equilibrium(conc=bio.bin_snapshot(bin_address = 0))

0: A <-> 3 B
Final concentrations: [A] = 14.55 ; [B] = 36.36
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.5
    Formula used:  [B] / [A]
2. Ratio of forward/reverse reaction rates: 2.5
Discrepancy between the two values: 6.875e-10 %
Reaction IS in equilibrium (within 1% tolerance)

Out[11]:

True

In [12]:

bio.get_history()

Out[12]:

	SYSTEM TIME	A	B	caption
0	0.0	10.000000	50.000000	Initial state
1	0.1	15.000000	35.000000
2	0.2	14.500000	36.500000
3	0.3	14.550000	36.350000
4	0.4	14.545000	36.365000
5	0.5	14.545500	36.363500
6	0.6	14.545450	36.363650
7	0.7	14.545455	36.363635
8	0.8	14.545454	36.363637
9	0.9	14.545455	36.363636
10	1.0	14.545455	36.363636
11	1.1	14.545455	36.363636

Note how the simulation initially OVERSHOT the equilibrium values; the first step was too large!

Plots of changes of concentration with time¶

In [13]:

fig = px.line(data_frame=bio.get_history(), x="SYSTEM TIME", y=["A", "B"], 
              title="Changes in concentrations with time",
              color_discrete_sequence = ['navy', 'darkorange'],
              labels={"value":"concentration", "variable":"Chemical"})
fig.show()

In [14]:

# Same plot, but with smooth line
fig = px.line(data_frame=bio.get_history(), x="SYSTEM TIME", y=["A", "B"], 
              title="Changes in concentrations with time (smoothed)",
              color_discrete_sequence = ['navy', 'darkorange'],
              labels={"value":"concentration", "variable":"Chemical"},
              line_shape="spline")
fig.show()

The early OVERSHOOTING of the equilibrium values shows prominently in the last plot!

In [ ]:

One-bin A <-> 3B reaction, with 1st-order kinetics in both directions,¶

taken to equilibrium¶

First step¶

Numerous more steps¶

Equilibrium¶

Plots of changes of concentration with time¶

One-bin `A <-> 3B` reaction, with 1st-order kinetics in both directions,¶

First step ¶

Numerous more steps ¶

Equilibrium ¶