2 COUPLED reactions: `A + B <-> C` and `C + D <-> E` ,¶

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

Both reactions are stronger in their respective forward rates. For the most part, "C" is produced by the 1st reaction, and consumed by the 2nd one.

Diffusion not applicable (just 1 bin)

TAGS : "reactions 1D"¶

In [1]:

LAST_REVISED = "Jan. 13, 2025"
LIFE123_VERSION = "1.0.0rc2"        # 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
#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

from life123 import GraphicLog, HtmlLog as log

In [4]:

# 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_8.log.htm'

In [ ]:

Initialize the System¶

In [5]:

# Initialize the system
chem_data = ChemData(names=["A", "B", "C", "D", "E"])     # NOTE: Diffusion not applicable (just 1 bin)
bio = BioSim1D(n_bins=1, chem_data=chem_data)  

In [6]:

# Specify the reactions
reactions = bio.get_reactions()

# Reactions A + B <-> C  and  C + D <-> E , with 1st-order kinetics for each species
reactions.add_reaction(reactants=["A", "B"], products="C", forward_rate=5., reverse_rate=2.)
reactions.add_reaction(reactants=["C", "D"], products="E", forward_rate=8., reverse_rate=4.)
reactions.describe_reactions()

Number of reactions: 2 (at temp. 25 C)
0: A + B <-> C  (kF = 5 / kR = 2 / delta_G = -2,271.4 / K = 2.5) | 1st order in all reactants & products
1: C + D <-> E  (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {'B', 'D', 'E', 'A', 'C'}

In [7]:

# Send a header and a plot to the HTML log file
log.write("2 COUPLED reactions:  A + B <-> C  and  C + D <-> E",
          style=log.h2)

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

2 COUPLED reactions:  A + B  C  and  C + D  E
[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_8.log.htm`]

In [ ]:

Enable History¶

In [8]:

# Let's enable history - by default for all chemicals and all bins (we just have 1 bin)
bio.enable_history()

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

In [ ]:

Set the initial state¶

In [9]:

bio.set_all_uniform_concentrations( [3., 5., 1., 0.4, 0.1] )  # In the order the chemicals were added

bio.describe_state()

SYSTEM STATE at Time t = 0:
1 bins and 5 chemical species:

Out[9]:

	Species	Diff rate	Bin 0
0	A	None	3.0
1	B	None	5.0
2	C	None	1.0
3	D	None	0.4
4	E	None	0.1

In [10]:

bio.get_bin_history(bin_address=0)

Out[10]:

	SYSTEM TIME	A	B	C	D	E
0	0.0	3.0	5.0	1.0	0.4	0.1

In [ ]:

Start the reaction¶

In [11]:

# First step
bio.react(time_step=0.01, n_steps=1)

System Time is now: 0.01

In [12]:

bio.describe_state()

SYSTEM STATE at Time t = 0.01:
1 bins and 5 chemical species:

Out[12]:

	Species	Diff rate	Bin 0
0	A	None	2.270
1	B	None	4.270
2	C	None	1.702
3	D	None	0.372
4	E	None	0.128

In [13]:

bio.get_bin_history(bin_address=0)

Out[13]:

	SYSTEM TIME	A	B	C	D	E
0	0.00	3.00	5.00	1.000	0.400	0.100
1	0.01	2.27	4.27	1.702	0.372	0.128

In [ ]:

In [14]:

# Identical 2nd step
bio.react(time_step=0.01, n_steps=1)

System Time is now: 0.02

In [15]:

bio.describe_state()

SYSTEM STATE at Time t = 0.02:
1 bins and 5 chemical species:

Out[15]:

	Species	Diff rate	Bin 0
0	A	None	1.819395
1	B	None	3.819395
2	C	None	2.107073
3	D	None	0.326468
4	E	None	0.173532

In [16]:

bio.get_bin_history(bin_address=0)

Out[16]:

	SYSTEM TIME	A	B	C	D	E
0	0.00	3.000000	5.000000	1.000000	0.400000	0.100000
1	0.01	2.270000	4.270000	1.702000	0.372000	0.128000
2	0.02	1.819395	3.819395	2.107073	0.326468	0.173532

In [ ]:

Numerous more steps ¶

In [17]:

# Numerous more identical steps, to equilibrium
bio.react(time_step=0.01, n_steps=200)

System Time is now: 2.02

In [18]:

bio.describe_state()

SYSTEM STATE at Time t = 2.02:
1 bins and 5 chemical species:

Out[18]:

	Species	Diff rate	Bin 0
0	A	None	0.505080
1	B	None	2.505080
2	C	None	3.163167
3	D	None	0.068247
4	E	None	0.431753

In [ ]:

Equilibrium ¶

In [19]:

# Verify that each 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: [A] = 0.5051 ; [B] = 2.505 ; [C] = 3.163
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.5
    Formula used:  [C] / ([A][B])
2. Ratio of forward/reverse reaction rates: 2.5
Discrepancy between the two values: 8.882e-14 %
Reaction IS in equilibrium (within 1% tolerance)

Out[19]:

True

In [20]:

bio.reaction_dynamics.is_in_equilibrium(rxn_index=1, conc=bio.bin_snapshot(bin_address = 0))

C + D <-> E
Final concentrations: [C] = 3.163 ; [D] = 0.06825 ; [E] = 0.4318
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2
    Formula used:  [E] / ([C][D])
2. Ratio of forward/reverse reaction rates: 2
Discrepancy between the two values: 3.331e-14 %
Reaction IS in equilibrium (within 1% tolerance)

Out[20]:

True

In [21]:

# Do a consistent check with the equilibrium concentrations:

A_eq = bio.bin_concentration(0, 0)
B_eq = bio.bin_concentration(0, 1)
C_eq = bio.bin_concentration(0, 2)
D_eq = bio.bin_concentration(0, 3)
E_eq = bio.bin_concentration(0, 4)

Rf0 = reactions.get_forward_rate(0)
Rb0 = reactions.get_reverse_rate(0)

Rf1 = reactions.get_forward_rate(1)
Rb1 = reactions.get_reverse_rate(1)

equil = -(Rf0 * A_eq * B_eq - Rf1 * C_eq * D_eq) + (Rb0 * C_eq - Rb1 * E_eq)

print("\nAt equilibrium: ", equil, " (this should be close to 0 at equilibrium)")

At equilibrium:  -4.440892098500626e-15  (this should be close to 0 at equilibrium)

In [ ]:

In [22]:

bio.get_bin_history(bin_address=0)

Out[22]:

	SYSTEM TIME	A	B	C	D	E
0	0.00	3.000000	5.000000	1.000000	0.400000	0.100000
1	0.01	2.270000	4.270000	1.702000	0.372000	0.128000
2	0.02	1.819395	3.819395	2.107073	0.326468	0.173532
3	0.03	1.514087	3.514087	2.364291	0.278378	0.221622
4	0.04	1.295341	3.295341	2.539249	0.234590	0.265410
...	...	...	...	...	...	...
198	1.98	0.505080	2.505080	3.163167	0.068247	0.431753
199	1.99	0.505080	2.505080	3.163167	0.068247	0.431753
200	2.00	0.505080	2.505080	3.163167	0.068247	0.431753
201	2.01	0.505080	2.505080	3.163167	0.068247	0.431753
202	2.02	0.505080	2.505080	3.163167	0.068247	0.431753

203 rows × 6 columns

In [ ]:

Plots of changes of concentration with time¶

In [23]:

bio.plot_history_single_bin(bin_address=0, 
                            title="2 COUPLED reactions:  A + B <-> C  and  C + D <-> E . Concentrations at bin 0")

A and B get consumed.
C gets produced by the 1st reaction more quickly than consumed by the 2nd one. D gets consumed, while E gets produced.

In [ ]:

2 COUPLED reactions: A + B <-> C and C + D <-> E ,¶

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

TAGS : "reactions 1D"¶

Initialize the System¶

Enable History¶

Set the initial state¶

Start the reaction¶

Numerous more steps¶

Equilibrium¶

Plots of changes of concentration with time¶

2 COUPLED reactions: `A + B <-> C` and `C + D <-> E` ,¶

Numerous more steps ¶

Equilibrium ¶