One-bin Association/Dissociation reaction `A + B <-> C`¶

with 1st-order kinetics for each species, taken to equilibrium¶

Diffusion not applicable (just 1 bin)

See also the experiment "reactions_single_compartment/react_3"

LAST REVISED: May 28, 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.reactions.reaction_data import ReactionData as chem
from src.modules.reactions.reaction_dynamics import ReactionDynamics
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_1"],
                  extra_js="https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js")

-> Output will be LOGGED into the file 'reaction_4.log.htm'

In [4]:

# Specify the chemicals
chem_data = chem(names=["A", "B", "C"])     # NOTE: Diffusion not applicable (using just 1 bin)


# Reaction A + B <-> C , with 1st-order kinetics for each species
chem_data.add_reaction(reactants=["A" , "B"], products=["C"],
                       forward_rate=5., reverse_rate=2.)

chem_data.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: A + B <-> C  (kF = 5 / kR = 2 / Delta_G = -2,271.45 / K = 2.5) | 1st order in all reactants & products

In [5]:

# Initialize the system
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.set_uniform_concentration(species_index=2, conc=20.)

bio.describe_state()

SYSTEM STATE at Time t = 0:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [10.]
  Species 1 (B). Diff rate: None. Conc: [50.]
  Species 2 (C). Diff rate: None. Conc: [20.]

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	C	caption
0	0	10.0	50.0	20.0	Initial state

In [7]:

# 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_4.log.htm`]

First step ¶

In [8]:

# First step
bio.react(time_step=0.002, n_steps=1)
bio.describe_state()

SYSTEM STATE at Time t = 0.002:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [5.08]
  Species 1 (B). Diff rate: None. Conc: [45.08]
  Species 2 (C). Diff rate: None. Conc: [24.92]

Early in the reaction : [A] = 5.08 , [B] = 45.08 , [C] = [24.92]

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	C	caption
0	0.000	10.00	50.00	20.00	Initial state
1	0.002	5.08	45.08	24.92

Numerous more steps ¶

In [10]:

# Numerous more steps
bio.react(time_step=0.002, n_steps=29, snapshots={"sample_bin": 0})

bio.describe_state()

SYSTEM STATE at Time t = 0.06:
1 bins and 3 species:
  Species 0 (A). Diff rate: None. Conc: [0.29487831]
  Species 1 (B). Diff rate: None. Conc: [40.29487831]
  Species 2 (C). Diff rate: None. Conc: [29.70512169]

Equilibrium ¶

Consistent with the 5/2 ratio of forward/reverse rates (and the 1st order reactions), the systems settles in the following equilibrium:
[A] = 0.29487831 , [B] = 40.29487831 , [C] = 29.70512169

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))

A + B <-> C
Final concentrations:  [C] = 29.71 ; [A] = 0.2949 ; [B] = 40.29
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.49999
    Formula used:  [C] / ([A][B])
2. Ratio of forward/reverse reaction rates: 2.5
Discrepancy between the two values: 0.0003107 %
Reaction IS in equilibrium (within 1% tolerance)

Out[11]:

True

In [12]:

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

Out[12]:

	SYSTEM TIME	A	B	C	caption
0	0.000	10.000000	50.000000	20.000000	Initial state
1	0.002	5.080000	45.080000	24.920000
2	0.004	2.889616	42.889616	27.110384
3	0.006	1.758712	41.758712	28.241288
4	0.008	1.137262	41.137262	28.862738
5	0.010	0.784874	40.784874	29.215126
6	0.012	0.581625	40.581625	29.418375
7	0.014	0.463266	40.463266	29.536734
8	0.016	0.393960	40.393960	29.606040
9	0.018	0.353248	40.353248	29.646752
10	0.020	0.329288	40.329288	29.670712
11	0.022	0.315171	40.315171	29.684829
12	0.024	0.306849	40.306849	29.693151
13	0.026	0.301940	40.301940	29.698060
14	0.028	0.299045	40.299045	29.700955
15	0.030	0.297336	40.297336	29.702664
16	0.032	0.296328	40.296328	29.703672
17	0.034	0.295734	40.295734	29.704266
18	0.036	0.295383	40.295383	29.704617
19	0.038	0.295176	40.295176	29.704824
20	0.040	0.295053	40.295053	29.704947
21	0.042	0.294981	40.294981	29.705019
22	0.044	0.294939	40.294939	29.705061
23	0.046	0.294914	40.294914	29.705086
24	0.048	0.294899	40.294899	29.705101
25	0.050	0.294890	40.294890	29.705110
26	0.052	0.294885	40.294885	29.705115
27	0.054	0.294882	40.294882	29.705118
28	0.056	0.294880	40.294880	29.705120
29	0.058	0.294879	40.294879	29.705121
30	0.060	0.294878	40.294878	29.705122

Note: "A" (now largely depleted) is largely the limiting reagent¶

Plots of changes of concentration with time¶

In [13]:

fig = px.line(data_frame=bio.get_history(), x="SYSTEM TIME", y=["A", "B", "C"], 
              title="Reaction A + B <-> C .  Changes in concentrations with time",
              color_discrete_sequence = ['red', 'violet', 'green'],
              labels={"value":"concentration", "variable":"Chemical"})
fig.show()

For more in-depth analysis of this reaction, including variable time steps, see the experiment "reactions_single_compartment/react_3"¶

In [ ]:

One-bin Association/Dissociation reaction A + B <-> C¶