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

taken to equilibrium¶

Diffusion not done

LAST REVISED: July 14, 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.chemicals.chem_data import ChemData as chem
from src.life_2D.bio_sim_2d import BioSim2D

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 'reaction_1.log.htm'

In [4]:

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



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

bio = BioSim2D(n_bins=(3,4), chem_data=chem_data)

bio.set_bin_conc_all_species(bin_x=0, bin_y=0, conc_list=[10.,50.])
bio.set_bin_conc_all_species(bin_x=0, bin_y=1, conc_list=[20.,35.])
bio.set_bin_conc_all_species(bin_x=2, bin_y=3, conc_list=[5.,100.])

bio.describe_state()

SYSTEM STATE at Time t = 0:
Species `A`:
      0     1    2    3
0  10.0  20.0  0.0  0.0
1   0.0   0.0  0.0  0.0
2   0.0   0.0  0.0  5.0
Species `B`:
      0     1    2      3
0  50.0  35.0  0.0    0.0
1   0.0   0.0  0.0    0.0
2   0.0   0.0  0.0  100.0

In [5]:

chem_data.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: A <-> B  (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products

In [6]:

# Send the plot to the HTML log file
graph_data = chem_data.prepare_graph_network()
GraphicLog.export_plot(graph_data, "vue_cytoscape_1")

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

First step¶

In [7]:

# First step (NOTE: here we're using a lower-level function that doesn't update the system state;
#                   it only computes the delta_reactions array)
bio.reaction_step(delta_time=0.1)
print("bio.delta_reactions:\n", bio.delta_reactions)

bio.delta_reactions:
 [[[  7.    1.    0.    0. ]
  [  0.    0.    0.    0. ]
  [  0.    0.    0.   18.5]]

 [[ -7.   -1.    0.    0. ]
  [  0.    0.    0.    0. ]
  [  0.    0.    0.  -18.5]]]

In [8]:

bio.system += bio.delta_reactions       # Matrix operation to update all the concentrations
bio.system_time += 0.1

bio.describe_state()

SYSTEM STATE at Time t = 0.1:
Species `A`:
      0     1    2     3
0  17.0  21.0  0.0   0.0
1   0.0   0.0  0.0   0.0
2   0.0   0.0  0.0  23.5
Species `B`:
      0     1    2     3
0  43.0  34.0  0.0   0.0
1   0.0   0.0  0.0   0.0
2   0.0   0.0  0.0  81.5

Second step¶

In [9]:

# NOTE: now, we're using a highel-level function that also updates the system state
bio.react(time_step=0.1, n_steps=1)
bio.describe_state()

SYSTEM STATE at Time t = 0.2:
Species `A`:
      0     1    2      3
0  20.5  21.5  0.0   0.00
1   0.0   0.0  0.0   0.00
2   0.0   0.0  0.0  32.75
Species `B`:
      0     1    2      3
0  39.5  33.5  0.0   0.00
1   0.0   0.0  0.0   0.00
2   0.0   0.0  0.0  72.25

Many more steps, to equilibrium¶

In [10]:

bio.react(time_step=0.1, n_steps=8)
bio.describe_state()

SYSTEM STATE at Time t = 0.9999999999999999:
Species `A`:
           0          1    2          3
0  23.986328  21.998047  0.0   0.000000
1   0.000000   0.000000  0.0   0.000000
2   0.000000   0.000000  0.0  41.963867
Species `B`:
           0          1    2          3
0  36.013672  33.001953  0.0   0.000000
1   0.000000   0.000000  0.0   0.000000
2   0.000000   0.000000  0.0  63.036133

In [11]:

bio.react(time_step=0.1, n_steps=10)
bio.describe_state()

SYSTEM STATE at Time t = 2.0000000000000004:
Species `A`:
           0          1    2          3
0  23.999987  21.999998  0.0   0.000000
1   0.000000   0.000000  0.0   0.000000
2   0.000000   0.000000  0.0  41.999965
Species `B`:
           0          1    2          3
0  36.000013  33.000002  0.0   0.000000
1   0.000000   0.000000  0.0   0.000000
2   0.000000   0.000000  0.0  63.000035

The system has now reached equilibrium¶

in individual bins, which remain separate because we're NOT doing diffusion in this experiment¶

Verify the equilibrium in each of the active bins

In [12]:

bio.reaction_dynamics.is_in_equilibrium(rxn_index=0, conc={"A": 23.99998665, "B": 36.00001335})

A <-> B
Final concentrations:  [B] = 36 ; [A] = 24
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.5
    Formula used:  [B] / [A]
2. Ratio of forward/reverse reaction rates: 1.5
Discrepancy between the two values: 9.271e-05 %
Reaction IS in equilibrium (within 1% tolerance)

Out[12]:

True

In [13]:

bio.reaction_dynamics.is_in_equilibrium(rxn_index=0, conc={"A": 21.99999809, "B": 33.00000191})

A <-> B
Final concentrations:  [B] = 33 ; [A] = 22
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.5
    Formula used:  [B] / [A]
2. Ratio of forward/reverse reaction rates: 1.5
Discrepancy between the two values: 1.447e-05 %
Reaction IS in equilibrium (within 1% tolerance)

Out[13]:

True

In [14]:

bio.reaction_dynamics.is_in_equilibrium(rxn_index=0, conc={"A": 41.99996471, "B": 63.00003529}, explain=False)

Out[14]:

True

In [ ]:

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