A simple `A <-> B` reaction between 2 species with initial uniform concentrations across 3 bins,¶

with 1st-order kinetics in both directions, taken to equilibrium

Diffusion NOT taken into account

See also the experiment "reactions_single_compartment/react_1"

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 (for the graphics)
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_1.log.htm'

Initialize the System¶

In [4]:

# Initialize the system
chem_data = chem(names=["A", "B"])              # Diffusion NOT taken into account
bio = BioSim1D(n_bins=3, chem_data=chem_data)   # We'll specify the reactions later

bio.set_uniform_concentration(species_name="A", conc=10.)
bio.set_uniform_concentration(species_name="B", conc=50.)

bio.describe_state()

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

In [6]:

bio.get_history()

Out[6]:

	SYSTEM TIME	A	B	caption
0	0	10.0	50.0	Initial state

In [7]:

# Specify the reaction

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

print("Number of reactions: ", chem_data.number_of_reactions())

Number of reactions:  1

In [8]:

chem_data.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: A <-> B  (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {'B', 'A'}

In [9]:

# Send a plot of the network of reactions to the HTML log file
chem_data.plot_reaction_network("vue_cytoscape_2")

[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_1.log.htm`]

First step ¶

In [10]:

# First step of reaction
bio.react(time_step=0.1, n_steps=1)
bio.describe_state()

SYSTEM STATE at Time t = 0.1:
3 bins and 2 species:
  Species 0 (A). Diff rate: None. Conc: [17. 17. 17.]
  Species 1 (B). Diff rate: None. Conc: [43. 43. 43.]

NOTE: the concentration of species A is increasing, while that of species B is decreasing. All bins have identical concentrations; so, there's no diffusion (and we're not attempting to compute it):
[[17. 17. 17.]
[43. 43. 43.]]

In [11]:

# 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[11]:

	SYSTEM TIME	A	B	caption
0	0.0	10.0	50.0	Initial state
1	0.1	17.0	43.0

Numerous more steps ¶

In [12]:

# 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:
3 bins and 2 species:
  Species 0 (A). Diff rate: None. Conc: [23.99316406 23.99316406 23.99316406]
  Species 1 (B). Diff rate: None. Conc: [36.00683594 36.00683594 36.00683594]

Equilibrium ¶

NOTE: Consistent with the 3/2 ratio of forward/reverse rates (and the 1st order reactions), the systems settles in the following equilibrium:

[A] = 23.99316406

[B] = 36.00683594

In [13]:

bio.bin_snapshot(bin_address = 0)

Out[13]:

{'A': 23.9931640625, 'B': 36.0068359375}

In [14]:

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

0: A <-> B
Final concentrations: [A] = 23.99 ; [B] = 36.01
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50071
    Formula used:  [B] / [A]
2. Ratio of forward/reverse reaction rates: 1.5
Discrepancy between the two values: 0.04749 %
Reaction IS in equilibrium (within 1% tolerance)

Out[14]:

True

In [15]:

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

Out[15]:

	SYSTEM TIME	A	B	caption
0	0.0	10.000000	50.000000	Initial state
1	0.1	17.000000	43.000000
2	0.2	20.500000	39.500000
3	0.3	22.250000	37.750000
4	0.4	23.125000	36.875000
5	0.5	23.562500	36.437500
6	0.6	23.781250	36.218750
7	0.7	23.890625	36.109375
8	0.8	23.945312	36.054688
9	0.9	23.972656	36.027344
10	1.0	23.986328	36.013672
11	1.1	23.993164	36.006836

Plots of changes of concentration with time¶

In [16]:

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 [17]:

# Same plot, but with a smoothed 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()

For more in-depth analysis of this reaction, see the experiment "reactions_single_compartment/react_1"¶

In [ ]:

A simple A <-> B reaction between 2 species with initial uniform concentrations across 3 bins,¶