A <-> B
, with and without an enzyme¶LAST REVISED: June 23, 2024 (using v. 1.0 beta36)
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
from life123 import ChemData
from life123 import UniformCompartment
# Initialize the system
chem_data = ChemData(names=["A", "B"])
# Reaction A <-> B , with 1st-order kinetics, favorable thermodynamics in the forward direction,
# and a forward rate that is much slower than it would be with the enzyme - as seen in part 2, below
chem_data.add_reaction(reactants="A", products="B",
forward_rate=1., delta_G=-3989.73)
chem_data.describe_reactions()
Number of reactions: 1 (at temp. 25 C) 0: A <-> B (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products Set of chemicals involved in the above reactions: {'A', 'B'}
dynamics = UniformCompartment(chem_data=chem_data, preset="fast")
dynamics.set_conc(conc={"A": 20.},
snapshot=True)
dynamics.describe_state()
SYSTEM STATE at Time t = 0: 2 species: Species 0 (A). Conc: 20.0 Species 1 (B). Conc: 0.0 Set of chemicals involved in reactions: {'A', 'B'}
dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()
dynamics.single_compartment_react(duration=3.0,
initial_step=0.1, variable_steps=True)
16 total step(s) taken Number of step re-do's because of negative concentrations: 0 Number of step re-do's because of elective soft aborts: 1 Norm usage: {'norm_A': 10, 'norm_B': 9, 'norm_C': 8, 'norm_D': 8}
#dynamics.explain_time_advance()
dynamics.plot_history(colors=['darkorange', 'green'], show_intervals=True, title_prefix="WITHOUT enzyme")
dynamics.curve_intersect("A", "B", t_start=0, t_end=1.0)
(0.7243697199909254, 10.000000000000002)
# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium()
0: A <-> B Final concentrations: [A] = 3.337 ; [B] = 16.66 1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.99265 Formula used: [B] / [A] 2. Ratio of forward/reverse reaction rates: 5.00001 Discrepancy between the two values: 0.1471 % Reaction IS in equilibrium (within 1% tolerance)
True
This in an approximation that we'll drop in later experiments
# Initialize the system
chem_data = ChemData(names=["A", "B", "E"])
# Reaction A + E <-> B + E , with 1st-order kinetics, and a forward rate that is faster than it was without the enzyme
# Thermodynamically, there's no change from the reaction without the enzyme
chem_data.add_reaction(reactants=["A", "E"], products=["B", "E"],
forward_rate=10., delta_G=-3989.73)
chem_data.describe_reactions() # Notice how the enzyme `E` is noted in the printout below
Number of reactions: 1 (at temp. 25 C) 0: A + E <-> B + E (kF = 10 / kR = 2 / delta_G = -3,989.7 / K = 5) | Enzyme: E | 1st order in all reactants & products Set of chemicals involved in the above reactions (not counting enzymes): {'A', 'B'} Set of enzymes involved in the above reactions: {'E'}
dynamics = UniformCompartment(chem_data=chem_data, preset="mid")
dynamics.set_conc(conc={"A": 20., "B": 0., "E": 30.},
snapshot=True) # Plenty of enzyme `E`
dynamics.describe_state()
SYSTEM STATE at Time t = 0: 3 species: Species 0 (A). Conc: 20.0 Species 1 (B). Conc: 0.0 Species 2 (E). Conc: 30.0 Set of chemicals involved in reactions (not counting enzymes): {'A', 'B'} Set of enzymes involved in reactions: {'E'}
dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()
dynamics.single_compartment_react(duration=0.1,
initial_step=0.1, variable_steps=True)
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes 43 total step(s) taken Number of step re-do's because of negative concentrations: 3 Number of step re-do's because of elective soft aborts: 2 Norm usage: {'norm_A': 31, 'norm_B': 28, 'norm_C': 28, 'norm_D': 28}
#dynamics.explain_time_advance()
dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix="WITH enzyme")
dynamics.curve_intersect("A", "B", t_start=0, t_end=0.02)
(0.0024674107137523833, 10.000000000000002)
# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium()
0: A + E <-> B + E Final concentrations: [A] = 3.334 ; [E] = 30 ; [B] = 16.67 1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.99958 Formula used: ([B][E]) / ([A][E]) 2. Ratio of forward/reverse reaction rates: 5.00001 Discrepancy between the two values: 0.008546 % Reaction IS in equilibrium (within 1% tolerance)
True
The concentrations of A
and B
now become equal (cross-over) at t=0.00246 , rather than t=0.740
dynamics.get_history()
SYSTEM TIME | A | B | E | caption | |
---|---|---|---|---|---|
0 | 0.000000 | 20.000000 | 0.000000 | 30.0 | Initialized state |
1 | 0.000250 | 18.500000 | 1.500000 | 30.0 | |
2 | 0.000375 | 17.817500 | 2.182500 | 30.0 | |
3 | 0.000500 | 17.165712 | 2.834288 | 30.0 | |
4 | 0.000625 | 16.543255 | 3.456745 | 30.0 | |
5 | 0.000750 | 15.948809 | 4.051191 | 30.0 | |
6 | 0.000875 | 15.381112 | 4.618888 | 30.0 | |
7 | 0.001000 | 14.838962 | 5.161038 | 30.0 | |
8 | 0.001125 | 14.321209 | 5.678791 | 30.0 | |
9 | 0.001250 | 13.826755 | 6.173245 | 30.0 | |
10 | 0.001375 | 13.354551 | 6.645449 | 30.0 | |
11 | 0.001525 | 12.813405 | 7.186595 | 30.0 | |
12 | 0.001675 | 12.301481 | 7.698519 | 30.0 | |
13 | 0.001855 | 11.720345 | 8.279655 | 30.0 | |
14 | 0.002071 | 11.068171 | 8.931829 | 30.0 | |
15 | 0.002330 | 10.346417 | 9.653583 | 30.0 | |
16 | 0.002589 | 9.692012 | 10.307988 | 30.0 | |
17 | 0.002900 | 8.980003 | 11.019997 | 30.0 | |
18 | 0.003274 | 8.221264 | 11.778736 | 30.0 | |
19 | 0.003647 | 7.564476 | 12.435524 | 30.0 | |
20 | 0.004095 | 6.882233 | 13.117767 | 30.0 | |
21 | 0.004543 | 6.309997 | 13.690003 | 30.0 | |
22 | 0.004991 | 5.830030 | 14.169970 | 30.0 | |
23 | 0.005528 | 5.346939 | 14.653061 | 30.0 | |
24 | 0.006066 | 4.957322 | 15.042678 | 30.0 | |
25 | 0.006711 | 4.580248 | 15.419752 | 30.0 | |
26 | 0.007485 | 4.232821 | 15.767179 | 30.0 | |
27 | 0.008413 | 3.932073 | 16.067927 | 30.0 | |
28 | 0.009528 | 3.691843 | 16.308157 | 30.0 | |
29 | 0.010865 | 3.519230 | 16.480770 | 30.0 | |
30 | 0.012470 | 3.411824 | 16.588176 | 30.0 | |
31 | 0.014396 | 3.357403 | 16.642597 | 30.0 | |
32 | 0.016707 | 3.337375 | 16.662625 | 30.0 | |
33 | 0.019480 | 3.333337 | 16.666663 | 30.0 | |
34 | 0.022808 | 3.333329 | 16.666671 | 30.0 | |
35 | 0.026802 | 3.333331 | 16.666669 | 30.0 | |
36 | 0.031594 | 3.333330 | 16.666670 | 30.0 | |
37 | 0.037345 | 3.333331 | 16.666669 | 30.0 | |
38 | 0.044245 | 3.333330 | 16.666670 | 30.0 | |
39 | 0.052526 | 3.333332 | 16.666668 | 30.0 | |
40 | 0.062463 | 3.333327 | 16.666673 | 30.0 | |
41 | 0.074388 | 3.333341 | 16.666659 | 30.0 | |
42 | 0.088697 | 3.333285 | 16.666715 | 30.0 | |
43 | 0.105869 | 3.333568 | 16.666432 | 30.0 |