A minimalist demonstration for the reaction `A <-> B`,¶

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

"No frills!" For advanced graphics, analysis, diagnostics, fine-tuning, etc, please see other experiments.

LAST REVISED: Dec. 3, 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 src.modules.reactions.reaction_dynamics import ReactionDynamics

In [ ]:

Initialize the System¶

In [3]:

# Instantiate the simulator and specify the chemicals
dynamics = ReactionDynamics(names=["A", "B"])

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

dynamics.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'}

In [4]:

# Set the initial concentrations of all the chemicals, in their declared index order
dynamics.set_conc([80., 10.])

Run the reaction¶

In [5]:

dynamics.single_compartment_react(initial_step=0.1, target_end_time=1.)   # Using defaults for all other parameters

* INFO: the tentative time step (0.1) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.04) [Step started at t=0, and will rewind there]
* INFO: the tentative time step (0.04) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.016) [Step started at t=0, and will rewind there]
* INFO: the tentative time step (0.016) leads to a least one norm value > its ABORT threshold:
      -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0064) [Step started at t=0, and will rewind there]
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes
47 total step(s) taken

In [6]:

dynamics.get_history()   # The system's history, saved during the run of single_compartment_react()

Out[6]:

	SYSTEM TIME	A	B	caption
0	0.000000	80.000000	10.000000	Initial state
1	0.006400	78.592000	11.408000
2	0.009600	77.910528	12.089472
3	0.013440	77.105846	12.894154
4	0.018048	76.158767	13.841233
5	0.023578	75.048458	14.951542
6	0.029107	73.968846	16.031154
7	0.034637	72.919083	17.080917
8	0.040166	71.898344	18.101656
9	0.045696	70.905827	19.094173
10	0.052332	69.747735	20.252265
11	0.058967	68.628067	21.371933
12	0.065603	67.545546	22.454454
13	0.072238	66.498940	23.501060
14	0.078874	65.487058	24.512942
15	0.085509	64.508749	25.491251
16	0.093472	63.373726	26.626274
17	0.101434	62.283893	27.716107
18	0.109397	61.237449	28.762551
19	0.117360	60.232668	29.767332
20	0.125322	59.267889	30.732111
21	0.134877	58.156249	31.843751
22	0.144433	57.097717	32.902283
23	0.153988	56.089758	33.910242
24	0.163543	55.129955	34.870045
25	0.175009	54.033218	35.966782
26	0.186475	52.999357	37.000643
27	0.197941	52.024769	37.975231
28	0.211701	50.922312	39.077688
29	0.225460	49.895700	40.104300
30	0.239220	48.939717	41.060283
31	0.255731	47.871459	42.128541
32	0.272242	46.891393	43.108607
33	0.292056	45.812407	44.187593
34	0.311869	44.840314	45.159686
35	0.335646	43.789365	46.210635
36	0.359422	42.863355	47.136645
37	0.387953	41.884245	48.115755
38	0.422191	40.876927	49.123073
39	0.456429	40.042050	49.957950
40	0.497514	39.211704	50.788296
41	0.546817	38.419979	51.580021
42	0.605980	37.704113	52.295887
43	0.676975	37.099191	52.900809
44	0.762170	36.630965	53.369035
45	0.864404	36.308436	53.691564
46	0.987084	36.119241	53.880759
47	1.134300	36.031470	53.968530

Plots changes of concentration with time¶

Notice that adaptive variable time steps were automatically taken

In [7]:

dynamics.plot_history(colors=['red', 'green'], show_intervals=True)

In [8]:

# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium()

0: A <-> B
Final concentrations: [A] = 36.03 ; [B] = 53.97
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.49782
    Formula used:  [B] / [A]
2. Ratio of forward/reverse reaction rates: 1.5
Discrepancy between the two values: 0.1456 %
Reaction IS in equilibrium (within 1% tolerance)

Out[8]:

True

In [ ]:

A minimalist demonstration for the reaction A <-> B,¶

Initialize the System¶

Run the reaction¶

Plots changes of concentration with time¶

A minimalist demonstration for the reaction `A <-> B`,¶