One-bin `2A <-> 3B` reaction, with 1st-order kinetics in both directions, taken to equilibrium¶

Diffusion not applicable (just 1 bin)

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 BioSim1D

import plotly.express as px
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 'reaction_3.log.htm'

In [4]:

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

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

# 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[5]:

	SYSTEM TIME	A	B	caption
0	0	10.0	50.0	Initial state

In [6]:

chem_data.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: 2 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 [7]:

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

[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_3.log.htm`]

First step ¶

In [8]:

# First step
bio.react(time_step=0.05, n_steps=1)
bio.describe_state()

SYSTEM STATE at Time t = 0.05:
1 bins and 2 species:
  Species 0 (A). Diff rate: None. Conc: [15.]
  Species 1 (B). Diff rate: None. Conc: [42.5]

Early in the reaction : [A] = 15. [B] = 42.5

We're taking a smaller first step than in experimetn "reaction_2", to avoid over-shooting the equilibrium value with too large a step!

In [9]:

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

Out[9]:

	SYSTEM TIME	A	B	caption
0	0.00	10.0	50.0	Initial state
1	0.05	15.0	42.5

Numerous more steps ¶

In [10]:

# Numerous more steps
bio.react(time_step=0.1, n_steps=100, snapshots={"sample_bin": 0})

bio.describe_state()

SYSTEM STATE at Time t = 10.05:
1 bins and 2 species:
  Species 0 (A). Diff rate: None. Conc: [16.25]
  Species 1 (B). Diff rate: None. Conc: [40.625]

Equilibrium ¶

Consistent with the 5/2 ratio of forward/reverse rates (and the 1st order reactions), the systems settles in the following equilibrium: [A] = 16.25 , [B] = 40.625

In [11]:

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

2 A <-> 3 B
Final concentrations: [A] = 16.25 ; [B] = 40.63
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: 1.776e-14 %
Reaction IS in equilibrium (within 1% tolerance)

Out[11]:

True

In [12]:

bio.get_history()

Out[12]:

	SYSTEM TIME	A	B	caption
0	0.00	10.00	50.000	Initial state
1	0.05	15.00	42.500
2	0.15	17.00	39.500
3	0.25	15.80	41.300
4	0.35	16.52	40.220
...	...	...	...	...
97	9.65	16.25	40.625
98	9.75	16.25	40.625
99	9.85	16.25	40.625
100	9.95	16.25	40.625
101	10.05	16.25	40.625

102 rows × 4 columns

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",
              color_discrete_sequence = ['navy', 'darkorange'],
              labels={"value":"concentration", "variable":"Chemical"})
fig.show()

Notice the early overshoots (the time step is too large early in the simulation!)¶

Variable, adaptive time steps are explored at length in the "reactions_single_compartment" experiments

In [ ]:

One-bin 2A <-> 3B reaction, with 1st-order kinetics in both directions, taken to equilibrium¶

First step¶

Numerous more steps¶

Equilibrium¶