A <-> B
,¶with 1st-order kinetics in both directions, taken to equilibrium.
This is a repeat of the experiment "react_2_a" , but with adaptive variable time steps and the use of diagnostic tools for insight into the details of the simulation.
Background: please see experiment react_2_a
LAST_REVISED = "July 24, 2024"
LIFE123_VERSION = "1.0.0.beta.37" # Version this experiment is based on
#import set_path # Using MyBinder? Uncomment this before running the next cell!
#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
import ipynbname
from life123 import check_version, UniformCompartment, GraphicLog, PlotlyHelper
check_version(LIFE123_VERSION)
OK
# Initialize the HTML logging (for the graphics)
log_file = ipynbname.name() + ".log.htm" # Use the notebook base filename for the log file
# IN CASE OF PROBLEMS, set manually to any desired name
# 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 'react_2_b.log.htm'
# Instantiate the simulator and specify the chemicals
dynamics = UniformCompartment(names=["A", "B"], preset="mid")
# 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'}
# Send a plot of the network of reactions to the HTML log file
dynamics.plot_reaction_network("vue_cytoscape_2")
[GRAPHIC ELEMENT SENT TO LOG FILE `react_2_b.log.htm`]
# Set the initial concentrations of all the chemicals, in their index order
dynamics.set_conc([10., 50.])
dynamics.describe_state()
SYSTEM STATE at Time t = 0: 2 species: Species 0 (A). Conc: 10.0 Species 1 (B). Conc: 50.0 Set of chemicals involved in reactions: {'B', 'A'}
dynamics.get_history()
SYSTEM TIME | A | B | caption | |
---|---|---|---|---|
0 | 0.0 | 10.0 | 50.0 | Initialized state |
dynamics.enable_diagnostics() # To save diagnostic information about the call to single_compartment_react()
# Useful for insight into the inner workings of the simulation
# For experiment repeatability, we specified, when instantiating the "UniformCompartment" class,
# a particular preset applicable to the adaptive time steps;
# that preset assigned the following values
dynamics.adaptive_steps.show_adaptive_parameters()
Parameters used for the automated adaptive time step sizes - THRESHOLDS: [{'norm': 'norm_A', 'low': 0.5, 'high': 0.8, 'abort': 1.44}, {'norm': 'norm_B', 'low': 0.08, 'high': 0.5, 'abort': 1.5}] STEP FACTORS: {'upshift': 1.2, 'downshift': 0.5, 'abort': 0.4, 'error': 0.25}
dynamics.single_compartment_react(initial_step=0.1, target_end_time=1.2,
variable_steps=True,
snapshots={"initial_caption": "1st reaction step",
"final_caption": "last reaction step"}
)
Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes 19 total step(s) taken Number of step re-do's because of elective soft aborts: 2 Norm usage: {'norm_A': 17, 'norm_B': 15, 'norm_C': 15, 'norm_D': 15}
history = dynamics.get_history() # The system's history, saved during the run of single_compartment_react()
history
SYSTEM TIME | A | B | caption | |
---|---|---|---|---|
0 | 0.000000 | 10.000000 | 50.000000 | Initialized state |
1 | 0.016000 | 11.120000 | 48.880000 | 1st reaction step |
2 | 0.032000 | 12.150400 | 47.849600 | |
3 | 0.048000 | 13.098368 | 46.901632 | |
4 | 0.067200 | 14.144925 | 45.855075 | |
5 | 0.086400 | 15.091012 | 44.908988 | |
6 | 0.109440 | 16.117327 | 43.882673 | |
7 | 0.132480 | 17.025411 | 42.974589 | |
8 | 0.160128 | 17.989578 | 42.010422 | |
9 | 0.193306 | 18.986635 | 41.013365 | |
10 | 0.233119 | 19.984624 | 40.015376 | |
11 | 0.280894 | 20.943812 | 39.056188 | |
12 | 0.338225 | 21.819882 | 38.180118 | |
13 | 0.407022 | 22.569810 | 37.430190 | |
14 | 0.489579 | 23.160168 | 36.839832 | |
15 | 0.588647 | 23.576169 | 36.423831 | |
16 | 0.707528 | 23.828097 | 36.171903 | |
17 | 0.850186 | 23.950713 | 36.049287 | |
18 | 1.021375 | 23.992900 | 36.007100 | |
19 | 1.226802 | 24.000193 | 35.999807 | last reaction step |
# Verify that the reaction has reached equilibrium
dynamics.is_in_equilibrium()
0: A <-> B Final concentrations: [A] = 24 ; [B] = 36 1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.49998 Formula used: [B] / [A] 2. Ratio of forward/reverse reaction rates: 1.5 Discrepancy between the two values: 0.001338 % Reaction IS in equilibrium (within 1% tolerance)
True
dynamics.plot_history(colors=['darkturquoise', 'orange'], show_intervals=True)
react_2_a
, where no adaptive time steps were used!¶react_2_a
¶To see the sizes of the steps taken:
dynamics.plot_step_sizes(show_intervals=True)
NOTE: this part is NOT meant for typically end users. It's for debugging, and for anyone interested in taking an "under the hood" look
diagnostics = dynamics.diagnostics # Available because we turned on diagnostics
The "Diagnostics" object contains a treasure trove of data and methods yo get insights into the inner workings of the simulation.
Diagnostic data was saved because of the call to enable_diagnostics()
prior to running the reaction
type(diagnostics)
life123.diagnostics.Diagnostics
# Let's revisit the variables steps taken
dynamics.diagnostics.explain_time_advance()
From time 0 to 0.048, in 3 steps of 0.016 From time 0.048 to 0.0864, in 2 steps of 0.0192 From time 0.0864 to 0.1325, in 2 steps of 0.023 From time 0.1325 to 0.1601, in 1 step of 0.0276 From time 0.1601 to 0.1933, in 1 step of 0.0332 From time 0.1933 to 0.2331, in 1 step of 0.0398 From time 0.2331 to 0.2809, in 1 step of 0.0478 From time 0.2809 to 0.3382, in 1 step of 0.0573 From time 0.3382 to 0.407, in 1 step of 0.0688 From time 0.407 to 0.4896, in 1 step of 0.0826 From time 0.4896 to 0.5886, in 1 step of 0.0991 From time 0.5886 to 0.7075, in 1 step of 0.119 From time 0.7075 to 0.8502, in 1 step of 0.143 From time 0.8502 to 1.021, in 1 step of 0.171 From time 1.021 to 1.227, in 1 step of 0.205 (19 steps total)
diagnostics.get_diagnostic_rxn_data(rxn_index=0) # For the 0-th reaction (the only reaction in our case)
Reaction: A <-> B
START_TIME | time_step | Delta A | Delta B | rate | caption | |
---|---|---|---|---|---|---|
0 | 0.000000 | 0.100000 | 7.000000 | -7.000000 | -70.000000 | aborted: excessive norm value(s) |
1 | 0.000000 | 0.040000 | 2.800000 | -2.800000 | -70.000000 | aborted: excessive norm value(s) |
2 | 0.000000 | 0.016000 | 1.120000 | -1.120000 | -70.000000 | |
3 | 0.016000 | 0.016000 | 1.030400 | -1.030400 | -64.400000 | |
4 | 0.032000 | 0.016000 | 0.947968 | -0.947968 | -59.248000 | |
5 | 0.048000 | 0.019200 | 1.046557 | -1.046557 | -54.508160 | |
6 | 0.067200 | 0.019200 | 0.946087 | -0.946087 | -49.275377 | |
7 | 0.086400 | 0.023040 | 1.026315 | -1.026315 | -44.544940 | |
8 | 0.109440 | 0.023040 | 0.908084 | -0.908084 | -39.413363 | |
9 | 0.132480 | 0.027648 | 0.964167 | -0.964167 | -34.872944 | |
10 | 0.160128 | 0.033178 | 0.997057 | -0.997057 | -30.052108 | |
11 | 0.193306 | 0.039813 | 0.997988 | -0.997988 | -25.066824 | |
12 | 0.233119 | 0.047776 | 0.959188 | -0.959188 | -20.076882 | |
13 | 0.280894 | 0.057331 | 0.876070 | -0.876070 | -15.280942 | |
14 | 0.338225 | 0.068797 | 0.749929 | -0.749929 | -10.900592 | |
15 | 0.407022 | 0.082556 | 0.590357 | -0.590357 | -7.150948 | |
16 | 0.489579 | 0.099068 | 0.416002 | -0.416002 | -4.199162 | |
17 | 0.588647 | 0.118881 | 0.251928 | -0.251928 | -2.119154 | |
18 | 0.707528 | 0.142658 | 0.122616 | -0.122616 | -0.859515 | |
19 | 0.850186 | 0.171189 | 0.042187 | -0.042187 | -0.246433 | |
20 | 1.021375 | 0.205427 | 0.007293 | -0.007293 | -0.035500 |
Line 2, above, shows that the concentration of the product [B], which was set by us to an initial value of 50, gets affected by a rate of change of -70, sustained over a delta_time of 0.016 .
The reaction rate is negative because the product is decreasing.
The new value for [B] is:
50. - 70. * 0.016
48.88
That's indeed the value we saw in the history of the product [B] at time t=0.016 :
dynamics.get_history(t=0.016)
search_value | SYSTEM TIME | A | B | caption | |
---|---|---|---|---|---|
1 | 0.016 | 0.016 | 11.12 | 48.88 | 1st reaction step |
In the examples below, we'll re-compute Delta values for individual steps, directly from the system history.
history[1:4]
SYSTEM TIME | A | B | caption | |
---|---|---|---|---|
1 | 0.016 | 11.120000 | 48.880000 | 1st reaction step |
2 | 0.032 | 12.150400 | 47.849600 | |
3 | 0.048 | 13.098368 | 46.901632 |
delta_concentrations = dynamics.extract_delta_concentrations(history, 1, 2, ['A', 'B'])
delta_concentrations
array([ 1.0304, -1.0304], dtype=float32)
As expected by the 1:1 stoichiometry, delta_A = - delta_B
# Get all the concentrations at the start of the above steps
baseline_conc = dynamics.get_historical_concentrations(row=1)
#dynamics.get_historical_concentrations(t=0.016) # Alternate way
baseline_conc
array([11.12, 48.88], dtype=float32)
# Computes some measures of how large delta_concentrations is, and propose a course of action
dynamics.adaptive_steps.adjust_timestep(delta_conc=delta_concentrations, baseline_conc=baseline_conc,
n_chems=2, indexes_of_active_chemicals=dynamics.chem_data.indexes_of_active_chemicals())
{'action': 'stay', 'step_factor': 1, 'norms': {'norm_A': 0.5308620929718018, 'norm_B': 0.09266187}, 'applicable_norms': 'ALL'}
Indeed, the simulator maintains the same time step :
original_step = history["SYSTEM TIME"][2] - history["SYSTEM TIME"][1]
original_step
0.016000000000000004
next_step = history["SYSTEM TIME"][3] - history["SYSTEM TIME"][2]
next_step
0.016000000000000007
next_step / original_step
1.0000000000000002
history[17:20]
SYSTEM TIME | A | B | caption | |
---|---|---|---|---|
17 | 0.850186 | 23.950713 | 36.049287 | |
18 | 1.021375 | 23.992900 | 36.007100 | |
19 | 1.226802 | 24.000193 | 35.999807 | last reaction step |
delta_concentrations = dynamics.extract_delta_concentrations(history, 17, 18, ['A', 'B'])
delta_concentrations
array([ 0.04218667, -0.04218667], dtype=float32)
# Get all the concentrations at the start of the above steps
baseline_conc = dynamics.get_historical_concentrations(row=17)
#dynamics.get_historical_concentrations(t=0.850186) # Alternate way
baseline_conc
array([23.950714, 36.049286], dtype=float32)
# Computes a measure of how large delta_concentrations is, and propose a course of action
dynamics.adaptive_steps.adjust_timestep(delta_conc=delta_concentrations, baseline_conc=baseline_conc,
n_chems=2, indexes_of_active_chemicals=dynamics.chem_data.indexes_of_active_chemicals())
{'action': 'low', 'step_factor': 1.2, 'norms': {'norm_A': 0.0008898575906641781, 'norm_B': 0.0017613951}, 'applicable_norms': 'ALL'}
Indeed, the simulator increases the time step x1.2:
original_step = history["SYSTEM TIME"][18] - history["SYSTEM TIME"][17]
original_step
0.17118912860651525
next_step = history["SYSTEM TIME"][19] - history["SYSTEM TIME"][18]
next_step
0.2054269543278182
next_step / original_step
1.1999999999999995
Where does that x1.2 factor come from? It's one of the parameters that we passed to the simulator; they can be seen as follows:
dynamics.adaptive_steps.show_adaptive_parameters()
Parameters used for the automated adaptive time step sizes - THRESHOLDS: [{'norm': 'norm_A', 'low': 0.5, 'high': 0.8, 'abort': 1.44}, {'norm': 'norm_B', 'low': 0.08, 'high': 0.5, 'abort': 1.5}] STEP FACTORS: {'upshift': 1.2, 'downshift': 0.5, 'abort': 0.4, 'error': 0.25}
1.2 is stored as the "step factor" (for the time steps to take) in case an 'upshift' (in step size) is the decided course of action
(note - this is possible because we make a call to set_diagnostics() prior to running the simulation)
diagnostics.get_diagnostic_conc_data() # This will be complete, even if we only saved part of the history during the run
TIME | A | B | caption | |
---|---|---|---|---|
0 | 0.000000 | 10.000000 | 50.000000 | |
1 | 0.016000 | 11.120000 | 48.880000 | |
2 | 0.032000 | 12.150400 | 47.849600 | |
3 | 0.048000 | 13.098368 | 46.901632 | |
4 | 0.067200 | 14.144925 | 45.855075 | |
5 | 0.086400 | 15.091012 | 44.908988 | |
6 | 0.109440 | 16.117327 | 43.882673 | |
7 | 0.132480 | 17.025411 | 42.974589 | |
8 | 0.160128 | 17.989578 | 42.010422 | |
9 | 0.193306 | 18.986635 | 41.013365 | |
10 | 0.233119 | 19.984624 | 40.015376 | |
11 | 0.280894 | 20.943812 | 39.056188 | |
12 | 0.338225 | 21.819882 | 38.180118 | |
13 | 0.407022 | 22.569810 | 37.430190 | |
14 | 0.489579 | 23.160168 | 36.839832 | |
15 | 0.588647 | 23.576169 | 36.423831 | |
16 | 0.707528 | 23.828097 | 36.171903 | |
17 | 0.850186 | 23.950713 | 36.049287 | |
18 | 1.021375 | 23.992900 | 36.007100 | |
19 | 1.226802 | 24.000193 | 35.999807 |
diagnostics.get_diagnostic_decisions_data()
START_TIME | Delta A | Delta B | norm_A | norm_B | norm_C | norm_D | action | step_factor | time_step | caption | |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0.000000 | 7.000000 | -7.000000 | 24.500000 | NaN | None | None | ABORT | 0.4 | 0.100000 | excessive norm value(s) |
1 | 0.000000 | 2.800000 | -2.800000 | 3.920000 | NaN | None | None | ABORT | 0.4 | 0.040000 | excessive norm value(s) |
2 | 0.000000 | 1.120000 | -1.120000 | 0.627200 | 0.112000 | None | None | OK (stay) | 1.0 | 0.016000 | |
3 | 0.016000 | 1.030400 | -1.030400 | 0.530862 | 0.092662 | None | None | OK (stay) | 1.0 | 0.016000 | |
4 | 0.032000 | 0.947968 | -0.947968 | 0.449322 | 0.078019 | None | None | OK (low) | 1.2 | 0.016000 | |
5 | 0.048000 | 1.046557 | -1.046557 | 0.547640 | 0.079900 | None | None | OK (stay) | 1.0 | 0.019200 | |
6 | 0.067200 | 0.946087 | -0.946087 | 0.447541 | 0.066885 | None | None | OK (low) | 1.2 | 0.019200 | |
7 | 0.086400 | 1.026315 | -1.026315 | 0.526662 | 0.068008 | None | None | OK (stay) | 1.0 | 0.023040 | |
8 | 0.109440 | 0.908084 | -0.908084 | 0.412308 | 0.056342 | None | None | OK (low) | 1.2 | 0.023040 | |
9 | 0.132480 | 0.964167 | -0.964167 | 0.464809 | 0.056631 | None | None | OK (low) | 1.2 | 0.027648 | |
10 | 0.160128 | 0.997057 | -0.997057 | 0.497061 | 0.055424 | None | None | OK (low) | 1.2 | 0.033178 | |
11 | 0.193306 | 0.997988 | -0.997988 | 0.497990 | 0.052563 | None | None | OK (low) | 1.2 | 0.039813 | |
12 | 0.233119 | 0.959188 | -0.959188 | 0.460021 | 0.047996 | None | None | OK (low) | 1.2 | 0.047776 | |
13 | 0.280894 | 0.876070 | -0.876070 | 0.383749 | 0.041830 | None | None | OK (low) | 1.2 | 0.057331 | |
14 | 0.338225 | 0.749929 | -0.749929 | 0.281197 | 0.034369 | None | None | OK (low) | 1.2 | 0.068797 | |
15 | 0.407022 | 0.590357 | -0.590357 | 0.174261 | 0.026157 | None | None | OK (low) | 1.2 | 0.082556 | |
16 | 0.489579 | 0.416002 | -0.416002 | 0.086529 | 0.017962 | None | None | OK (low) | 1.2 | 0.099068 | |
17 | 0.588647 | 0.251928 | -0.251928 | 0.031734 | 0.010686 | None | None | OK (low) | 1.2 | 0.118881 | |
18 | 0.707528 | 0.122616 | -0.122616 | 0.007517 | 0.005146 | None | None | OK (low) | 1.2 | 0.142658 | |
19 | 0.850186 | 0.042187 | -0.042187 | 0.000890 | 0.001761 | None | None | OK (low) | 1.2 | 0.171189 | |
20 | 1.021375 | 0.007293 | -0.007293 | 0.000027 | 0.000304 | None | None | OK (low) | 1.2 | 0.205427 |
In experiment react_2_a
, the time derivative (rate of change) of [A] was obtained by numeric differentiation of A, i.e. the time values of [A]
But no need for that! The rates (at every time step) of each reaction are automatically stored with the diagnostics data, whenever diagnostics data is saved :)
Let's again look at the table for reaction 0 :
df = diagnostics.get_diagnostic_rxn_data(rxn_index=0) # For the 0-th reaction (the only reaction in our case)
df
Reaction: A <-> B
START_TIME | time_step | Delta A | Delta B | rate | caption | |
---|---|---|---|---|---|---|
0 | 0.000000 | 0.100000 | 7.000000 | -7.000000 | -70.000000 | aborted: excessive norm value(s) |
1 | 0.000000 | 0.040000 | 2.800000 | -2.800000 | -70.000000 | aborted: excessive norm value(s) |
2 | 0.000000 | 0.016000 | 1.120000 | -1.120000 | -70.000000 | |
3 | 0.016000 | 0.016000 | 1.030400 | -1.030400 | -64.400000 | |
4 | 0.032000 | 0.016000 | 0.947968 | -0.947968 | -59.248000 | |
5 | 0.048000 | 0.019200 | 1.046557 | -1.046557 | -54.508160 | |
6 | 0.067200 | 0.019200 | 0.946087 | -0.946087 | -49.275377 | |
7 | 0.086400 | 0.023040 | 1.026315 | -1.026315 | -44.544940 | |
8 | 0.109440 | 0.023040 | 0.908084 | -0.908084 | -39.413363 | |
9 | 0.132480 | 0.027648 | 0.964167 | -0.964167 | -34.872944 | |
10 | 0.160128 | 0.033178 | 0.997057 | -0.997057 | -30.052108 | |
11 | 0.193306 | 0.039813 | 0.997988 | -0.997988 | -25.066824 | |
12 | 0.233119 | 0.047776 | 0.959188 | -0.959188 | -20.076882 | |
13 | 0.280894 | 0.057331 | 0.876070 | -0.876070 | -15.280942 | |
14 | 0.338225 | 0.068797 | 0.749929 | -0.749929 | -10.900592 | |
15 | 0.407022 | 0.082556 | 0.590357 | -0.590357 | -7.150948 | |
16 | 0.489579 | 0.099068 | 0.416002 | -0.416002 | -4.199162 | |
17 | 0.588647 | 0.118881 | 0.251928 | -0.251928 | -2.119154 | |
18 | 0.707528 | 0.142658 | 0.122616 | -0.122616 | -0.859515 | |
19 | 0.850186 | 0.171189 | 0.042187 | -0.042187 | -0.246433 | |
20 | 1.021375 | 0.205427 | 0.007293 | -0.007293 | -0.035500 |
A
, a reactant, we must flip the sign; since the stoichiometry of A
is simply 1, no further adjustment needed.¶df["A_dot"] = -df["rate"]
df
START_TIME | time_step | Delta A | Delta B | rate | caption | A_dot | |
---|---|---|---|---|---|---|---|
0 | 0.000000 | 0.100000 | 7.000000 | -7.000000 | -70.000000 | aborted: excessive norm value(s) | 70.000000 |
1 | 0.000000 | 0.040000 | 2.800000 | -2.800000 | -70.000000 | aborted: excessive norm value(s) | 70.000000 |
2 | 0.000000 | 0.016000 | 1.120000 | -1.120000 | -70.000000 | 70.000000 | |
3 | 0.016000 | 0.016000 | 1.030400 | -1.030400 | -64.400000 | 64.400000 | |
4 | 0.032000 | 0.016000 | 0.947968 | -0.947968 | -59.248000 | 59.248000 | |
5 | 0.048000 | 0.019200 | 1.046557 | -1.046557 | -54.508160 | 54.508160 | |
6 | 0.067200 | 0.019200 | 0.946087 | -0.946087 | -49.275377 | 49.275377 | |
7 | 0.086400 | 0.023040 | 1.026315 | -1.026315 | -44.544940 | 44.544940 | |
8 | 0.109440 | 0.023040 | 0.908084 | -0.908084 | -39.413363 | 39.413363 | |
9 | 0.132480 | 0.027648 | 0.964167 | -0.964167 | -34.872944 | 34.872944 | |
10 | 0.160128 | 0.033178 | 0.997057 | -0.997057 | -30.052108 | 30.052108 | |
11 | 0.193306 | 0.039813 | 0.997988 | -0.997988 | -25.066824 | 25.066824 | |
12 | 0.233119 | 0.047776 | 0.959188 | -0.959188 | -20.076882 | 20.076882 | |
13 | 0.280894 | 0.057331 | 0.876070 | -0.876070 | -15.280942 | 15.280942 | |
14 | 0.338225 | 0.068797 | 0.749929 | -0.749929 | -10.900592 | 10.900592 | |
15 | 0.407022 | 0.082556 | 0.590357 | -0.590357 | -7.150948 | 7.150948 | |
16 | 0.489579 | 0.099068 | 0.416002 | -0.416002 | -4.199162 | 4.199162 | |
17 | 0.588647 | 0.118881 | 0.251928 | -0.251928 | -2.119154 | 2.119154 | |
18 | 0.707528 | 0.142658 | 0.122616 | -0.122616 | -0.859515 | 0.859515 | |
19 | 0.850186 | 0.171189 | 0.042187 | -0.042187 | -0.246433 | 0.246433 | |
20 | 1.021375 | 0.205427 | 0.007293 | -0.007293 | -0.035500 | 0.035500 |
df = df[2:] # Drop the aborted first 2 steps
df
START_TIME | time_step | Delta A | Delta B | rate | caption | A_dot | |
---|---|---|---|---|---|---|---|
2 | 0.000000 | 0.016000 | 1.120000 | -1.120000 | -70.000000 | 70.000000 | |
3 | 0.016000 | 0.016000 | 1.030400 | -1.030400 | -64.400000 | 64.400000 | |
4 | 0.032000 | 0.016000 | 0.947968 | -0.947968 | -59.248000 | 59.248000 | |
5 | 0.048000 | 0.019200 | 1.046557 | -1.046557 | -54.508160 | 54.508160 | |
6 | 0.067200 | 0.019200 | 0.946087 | -0.946087 | -49.275377 | 49.275377 | |
7 | 0.086400 | 0.023040 | 1.026315 | -1.026315 | -44.544940 | 44.544940 | |
8 | 0.109440 | 0.023040 | 0.908084 | -0.908084 | -39.413363 | 39.413363 | |
9 | 0.132480 | 0.027648 | 0.964167 | -0.964167 | -34.872944 | 34.872944 | |
10 | 0.160128 | 0.033178 | 0.997057 | -0.997057 | -30.052108 | 30.052108 | |
11 | 0.193306 | 0.039813 | 0.997988 | -0.997988 | -25.066824 | 25.066824 | |
12 | 0.233119 | 0.047776 | 0.959188 | -0.959188 | -20.076882 | 20.076882 | |
13 | 0.280894 | 0.057331 | 0.876070 | -0.876070 | -15.280942 | 15.280942 | |
14 | 0.338225 | 0.068797 | 0.749929 | -0.749929 | -10.900592 | 10.900592 | |
15 | 0.407022 | 0.082556 | 0.590357 | -0.590357 | -7.150948 | 7.150948 | |
16 | 0.489579 | 0.099068 | 0.416002 | -0.416002 | -4.199162 | 4.199162 | |
17 | 0.588647 | 0.118881 | 0.251928 | -0.251928 | -2.119154 | 2.119154 | |
18 | 0.707528 | 0.142658 | 0.122616 | -0.122616 | -0.859515 | 0.859515 | |
19 | 0.850186 | 0.171189 | 0.042187 | -0.042187 | -0.246433 | 0.246433 | |
20 | 1.021375 | 0.205427 | 0.007293 | -0.007293 | -0.035500 | 0.035500 |
p1 = dynamics.plot_data(df=df, x_var="START_TIME", fields=["A_dot"], colors=['brown'],
ylabel="concentration change/unit time",
title="Rate of change of of A with time")
p1
Let's create a combined plot like we had in experiment react_2_a
:
p2 = dynamics.plot_history(chemicals="A", colors='darkturquoise') # The plot of [A] vs. time that we saw earlier
PlotlyHelper.combine_plots([p1, p2],
xlabel="SYSTEM TIME",
ylabel="concentration (darkturquoise) /<br> concentration change per unit time (brown)",
curve_labels=["A", "A_dot"],
title="Concentration of A with time (darkturquoise), and its rate of change (brown)")
react_2_a
!¶