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

Diffusion not applicable (just 1 bin)

TAGS : "reactions 1D", "basic"¶

In [1]:

LAST_REVISED = "May 4, 2025"
LIFE123_VERSION = "1.0.0rc3"        # Library version this experiment is based on

In [2]:

#import set_path                    # Using MyBinder?  Uncomment this before running the next cell!

In [3]:

#import sys, os
#os.getcwd()
#sys.path.append("C:/some_path/my_env_or_install")   # CHANGE to the folder containing your venv or libraries installation!
# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try:  import set_path

from experiments.get_notebook_info import get_notebook_basename

from life123 import ChemData, BioSim1D, check_version

from life123 import GraphicLog

In [4]:

check_version(LIFE123_VERSION)

OK

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In [5]:

# 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 [6]:

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

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

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

bio.describe_state()

SYSTEM STATE at Time t = 0:
1 bins and 2 chemical species:

Out[6]:

	Species	Diff rate	Bin 0
0	A	None	10.0
1	B	None	50.0

In [7]:

# Specify the reaction
reactions = bio.get_reactions()

# Reaction 2A <-> 3B , with 1st-order kinetics in both directions
reactions.add_reaction(reactants=[(2,"A",1)], products=[(3,"B",1)], forward_rate=5., reverse_rate=2.)
reactions.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 [8]:

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

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

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In [9]:

# Let's enable history - by default for all chemicals and all bins
bio.enable_history(take_snapshot=True, caption="Initial state")

History enabled for bins None and chemicals None (None means 'all')

In [10]:

bio.get_bin_history(bin_address=0)

Out[10]:

	SYSTEM TIME	A	B	caption
0	0.0	10.0	50.0	Initial state

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First step ¶

In [11]:

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

System Time is now: 0.05
SYSTEM STATE at Time t = 0.05:
1 bins and 2 chemical species:

Out[11]:

	Species	Diff rate	Bin 0
0	A	None	15.0
1	B	None	42.5

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

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Numerous more steps ¶

In [12]:

# Numerous more steps
bio.react(time_step=0.1, n_steps=100)

bio.describe_state()

System Time is now: 10.05
SYSTEM STATE at Time t = 10.05:
1 bins and 2 chemical species:

Out[12]:

	Species	Diff rate	Bin 0
0	A	None	16.250
1	B	None	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 [13]:

# 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
Current 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[13]:

True

In [14]:

bio.get_bin_history(bin_address=0)

Out[14]:

	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 [15]:

bio.plot_history_single_bin(bin_address=0, 
                            title="Reaction  2A <-> 3B . Concentrations at bin 0")

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¶

TAGS : "reactions 1D", "basic"¶

First step¶

Numerous more steps¶

Equilibrium¶

Plots of changes of concentration with time¶

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

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

First step ¶

Numerous more steps ¶

Equilibrium ¶