A simple `A <-> B` reaction between 2 species with initial uniform concentrations across 3 bins,¶

with 1st-order kinetics in both directions, taken to equilibrium

Diffusion NOT taken into account

See also the experiment reactions_single_compartment/react_1

TAGS : "reactions 1D", "quick-start"¶

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 life123 import ChemData, BioSim1D

In [ ]:

Initialize the System¶

In [4]:

# Initialize the system
chem_data = ChemData(names=["A", "B"])              # Diffusion NOT taken into account
bio = BioSim1D(n_bins=3, chem_data=chem_data)       # We'll specify the reactions later

bio.set_uniform_concentration(species_name="A", conc=10.)   # Same across all bins
bio.set_uniform_concentration(species_name="B", conc=50.)   # Same across all bins

bio.describe_state()

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

Out[4]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2
0	A	None	10.0	10.0	10.0
1	B	None	50.0	50.0	50.0

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Enable History¶

In [5]:

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

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

In [6]:

bio.get_bin_history(bin_address=0)

Out[6]:

	SYSTEM TIME	A	B
0	0.0	10.0	50.0

In [7]:

bio.get_bin_history(bin_address=1)

Out[7]:

	SYSTEM TIME	A	B
0	0.0	10.0	50.0

In [8]:

bio.get_bin_history(bin_address=2)

Out[8]:

	SYSTEM TIME	A	B
0	0.0	10.0	50.0

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In [9]:

# Specify the reaction
reactions = bio.get_reactions()

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

reactions.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: A <-> B  (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {'B', 'A'}

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First Reaction Step¶

In [10]:

# First step of reaction
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:
3 bins and 2 chemical species:

Out[10]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2
0	A	None	17.0	17.0	17.0
1	B	None	43.0	43.0	43.0

NOTE: the concentration of the chemical species A is increasing, while that of B is decreasing. All bins have identical concentrations; so, there's no diffusion (and we're not attempting to compute it; didn't specify diffusion rates)

In [11]:

bio.get_bin_history(bin_address=0)

Out[11]:

	SYSTEM TIME	A	B
0	0.0	10.0	50.0
1	0.1	17.0	43.0

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Several more reaction steps¶

In [12]:

# Several 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:
3 bins and 2 chemical species:

Out[12]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2
0	A	None	23.993164	23.993164	23.993164
1	B	None	36.006836	36.006836	36.006836

In [13]:

bio.get_bin_history(bin_address=0)

Out[13]:

	SYSTEM TIME	A	B
0	0.0	10.000000	50.000000
1	0.1	17.000000	43.000000
2	0.2	20.500000	39.500000
3	0.3	22.250000	37.750000
4	0.4	23.125000	36.875000
5	0.5	23.562500	36.437500
6	0.6	23.781250	36.218750
7	0.7	23.890625	36.109375
8	0.8	23.945312	36.054688
9	0.9	23.972656	36.027344
10	1.0	23.986328	36.013672
11	1.1	23.993164	36.006836

In [14]:

bio.get_bin_history(bin_address=2)

Out[14]:

	SYSTEM TIME	A	B
0	0.0	10.000000	50.000000
1	0.1	17.000000	43.000000
2	0.2	20.500000	39.500000
3	0.3	22.250000	37.750000
4	0.4	23.125000	36.875000
5	0.5	23.562500	36.437500
6	0.6	23.781250	36.218750
7	0.7	23.890625	36.109375
8	0.8	23.945312	36.054688
9	0.9	23.972656	36.027344
10	1.0	23.986328	36.013672
11	1.1	23.993164	36.006836

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Equilibrium ¶

NOTE: Consistent with the 3/2 ratio of forward/reverse rates (and the 1st order reactions), the systems settles in the following equilibrium:

[A] = 23.99316406

[B] = 36.00683594

In [15]:

bio.bin_snapshot(bin_address=0)

Out[15]:

{'A': 23.9931640625, 'B': 36.0068359375}

In [16]:

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

0: A <-> B
Final concentrations: [A] = 23.99 ; [B] = 36.01
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50071
    Formula used:  [B] / [A]
2. Ratio of forward/reverse reaction rates: 1.5
Discrepancy between the two values: 0.04749 %
Reaction IS in equilibrium (within 1% tolerance)

Out[16]:

True

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Plots of changes of concentration with time¶

In [17]:

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

In [18]:

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

For more in-depth analysis of this reaction, see the experiment `reactions_single_compartment/react_1`¶

In [ ]:

A simple A <-> B reaction between 2 species with initial uniform concentrations across 3 bins,¶

TAGS : "reactions 1D", "quick-start"¶

Initialize the System¶

Enable History¶

First Reaction Step¶

Several more reaction steps¶

Equilibrium¶

Plots of changes of concentration with time¶

For more in-depth analysis of this reaction, see the experiment reactions_single_compartment/react_1¶

A simple `A <-> B` reaction between 2 species with initial uniform concentrations across 3 bins,¶

Equilibrium ¶

For more in-depth analysis of this reaction, see the experiment `reactions_single_compartment/react_1`¶