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

taken to equilibrium¶

Diffusion not applicable (just 1 bin)

First Step
Numerous more steps
Equilibrium

TAGS : "reactions 1D"¶

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

In [ ]:

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_2.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 A <-> 3B , with 1st-order kinetics in both directions
reactions.add_reaction(reactants="A", products=[(3,"B",1)], forward_rate=5., reverse_rate=2.)

reactions.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: 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_2.log.htm`]

In [ ]:

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

In [ ]:

First step ¶

In [11]:

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

System Time is now: 0.1
SYSTEM STATE at Time t = 0.1:
1 bins and 2 chemical species:

Out[11]:

	Species	Diff rate	Bin 0
0	A	None	15.0
1	B	None	35.0

In [12]:

bio.get_bin_history(bin_address=0)

Out[12]:

	SYSTEM TIME	A	B	caption
0	0.0	10.0	50.0	Initial state
1	0.1	15.0	35.0

In [ ]:

Numerous more steps ¶

In [13]:

# Numerous more steps
bio.react(time_step=0.1, n_steps=10)

bio.describe_state()

System Time is now: 1.1
SYSTEM STATE at Time t = 1.1:
1 bins and 2 chemical species:

Out[13]:

	Species	Diff rate	Bin 0
0	A	None	14.545455
1	B	None	36.363636

Equilibrium ¶

Consistent with the 5/2 ratio of forward/reverse rates (and the 1st order reactions), the systems settles in the equilibrium: [A] = 14.54545455 , [B] = 36.36363636

In [14]:

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

0: A <-> 3 B
Current concentrations: [A] = 14.55 ; [B] = 36.36
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: 6.875e-10 %
Reaction IS in equilibrium (within 1% tolerance)

Out[14]:

True

In [15]:

bio.get_bin_history(bin_address=0)

Out[15]:

	SYSTEM TIME	A	B	caption
0	0.0	10.000000	50.000000	Initial state
1	0.1	15.000000	35.000000
2	0.2	14.500000	36.500000
3	0.3	14.550000	36.350000
4	0.4	14.545000	36.365000
5	0.5	14.545500	36.363500
6	0.6	14.545450	36.363650
7	0.7	14.545455	36.363635
8	0.8	14.545454	36.363637
9	0.9	14.545455	36.363636
10	1.0	14.545455	36.363636
11	1.1	14.545455	36.363636

Note how the simulation initially OVERSHOT the equilibrium values; the first step was too large!

Plots of changes of concentration with time¶

In [16]:

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

In [17]:

# Same plot, but with smooth line
bio.plot_history_single_bin(bin_address=0, 
                            title="Reaction  A <-> B . Concentrations at bin 0",
                            smoothed=True)

The early OVERSHOOTING of the equilibrium values shows prominently in the last plot!

In [ ]:

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

taken to equilibrium¶

TAGS : "reactions 1D"¶

First step¶

Numerous more steps¶

Equilibrium¶

Plots of changes of concentration with time¶

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

First step ¶

Numerous more steps ¶

Equilibrium ¶