Reaction A + B <-> C, mostly forward and with 1st-order kinetics for each species,¶

taken to equilibrium¶

Initial concentrations of A and B are spacially separated to the opposite ends of the system; as a result, no C is being generated.

But, as soon as A and B, from their respective distant originating points at the edges, diffuse into the middle - and into each other - the reaction starts, consuming both A and B (the forward reaction is much more substantial than the reverse one), until an equilibrium is reached in both diffusion and reactions.

A LOT of plots are sent to the log file from this experiment; the reason is to compare two graphic elements, "vue_curves_3" and "vue_curves_4"

In [1]:

LAST_REVISED = "Nov. 13, 2024"
LIFE123_VERSION = "1.0.0.rc.0"      # 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 BioSim1D, ChemData, GraphicLog, HtmlLog as log

import plotly.express as px

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_heatmap_11", "vue_curves_3", "vue_curves_4", "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 'rd_1.log.htm'

In [5]:

# Initialize the system
chem_data = ChemData(names=["A", "B", "C"], diffusion_rates=[50., 50., 1.])



# Reaction A + B <-> C , with 1st-order kinetics for each species; note that it's mostly in the forward direction
chem_data.add_reaction(reactants=["A", "B"], products=["C"], forward_rate=20., reverse_rate=2.)
bio = BioSim1D(n_bins=7, chem_data=chem_data)

In [6]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0:
     A    B    C
0  0.0  0.0  0.0
1  0.0  0.0  0.0
2  0.0  0.0  0.0
3  0.0  0.0  0.0
4  0.0  0.0  0.0
5  0.0  0.0  0.0
6  0.0  0.0  0.0

In [7]:

chem_data.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: A + B <-> C  (kF = 20 / kR = 2 / delta_G = -5,708 / K = 10) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {'A', 'B', 'C'}

In [8]:

# Send a header and a plot to the HTML log file
log.write("Reaction:  A + B <-> C",
          style=log.h2)
chem_data.plot_reaction_network("vue_cytoscape_2")

Reaction:  A + B  C
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

In [9]:

# Set the heatmap parameters
heatmap_pars = {"range": [0, 20],
                "outer_width": 850, "outer_height": 100,
                "margins": {"top": 30, "right": 30, "bottom": 30, "left": 55}
                }

# Set the parameters of the line plots (for now, same for single-curve and multiple-curves)
lineplot_pars = {"range": [0, 20],
                "outer_width": 850, "outer_height": 200,
                "margins": {"top": 30, "right": 30, "bottom": 30, "left": 55}
                }

Inject initial concentrations of A and B at opposite ends of the system¶

In [10]:

bio.set_bin_conc(bin_address=0, species_name="A", conc=20.)
bio.set_bin_conc(bin_address=6, species_name="B", conc=20.)

bio.describe_state()

SYSTEM STATE at Time t = 0:
7 bins and 3 species:
  Species 0 (A). Diff rate: 50.0. Conc: [20.  0.  0.  0.  0.  0.  0.]
  Species 1 (B). Diff rate: 50.0. Conc: [ 0.  0.  0.  0.  0.  0. 20.]
  Species 2 (C). Diff rate: 1.0. Conc: [0. 0. 0. 0. 0. 0. 0.]

In [11]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0:
      A     B    C
0  20.0   0.0  0.0
1   0.0   0.0  0.0
2   0.0   0.0  0.0
3   0.0   0.0  0.0
4   0.0   0.0  0.0
5   0.0   0.0  0.0
6   0.0  20.0  0.0

In [12]:

# Save the state of the concentrations of all species at the middle bin
bio.add_snapshot(bio.bin_snapshot(bin_address = 3))
bio.get_history()

Out[12]:

	SYSTEM TIME	A	B	C	caption
0	0	0.0	0.0	0.0

In [13]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A", "B", "C"], 
              title= f"A + B <-> C . System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red', 'orange', 'green'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"})
fig.show()

In [14]:

log.write(f"Initial system state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output to the log file a heatmap for each chemical species
for i in range(bio.n_species):
    log.write(f"{bio.chem_data.get_label(i)}:", also_print=False)
    bio.single_species_heatmap(species_index=i, heatmap_pars=heatmap_pars, graphic_component="vue_heatmap_11")

# Output to the log file a one-curve line plot for each chemical species
for i in range(bio.n_species):
    log.write(f"{bio.chem_data.get_label(i)}:", also_print=False)
    bio.single_species_line_plot(species_index=i, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

# Output to the log file a line plot for ALL the chemicals together (same color as used for plotly elsewhere)
bio.line_plot(plot_pars=lineplot_pars, graphic_component="vue_curves_4", color_mapping={0: 'red', 1: 'orange', 2: 'green'})


Initial system state at time t=0:
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

First step ¶

In [15]:

delta_t = 0.002   # This will be our time "quantum" for this experiment

In [16]:

# First step
bio.react_diffuse(time_step=delta_t, n_steps=1)
bio.describe_state()

SYSTEM STATE at Time t = 0.002:
7 bins and 3 species:
  Species 0 (A). Diff rate: 50.0. Conc: [18.  2.  0.  0.  0.  0.  0.]
  Species 1 (B). Diff rate: 50.0. Conc: [ 0.  0.  0.  0.  0.  2. 18.]
  Species 2 (C). Diff rate: 1.0. Conc: [0. 0. 0. 0. 0. 0. 0.]

After the first delta_t time step:

Species 0 (A). Diff rate: 50.0. Conc: [18. 2. 0. 0. 0. 0. 0.]

Species 1 (B). Diff rate: 50.0. Conc: [ 0. 0. 0. 0. 0. 2. 18.]

Species 2 (C). Diff rate: 1.0. Conc: [0. 0. 0. 0. 0. 0. 0.]

In [17]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0.002:
      A     B    C
0  18.0   0.0  0.0
1   2.0   0.0  0.0
2   0.0   0.0  0.0
3   0.0   0.0  0.0
4   0.0   0.0  0.0
5   0.0   2.0  0.0
6   0.0  18.0  0.0

In [18]:

# Save the state of the concentrations of all species at the middle bin
bio.add_snapshot(bio.bin_snapshot(bin_address = 3))
bio.get_history()

Out[18]:

	SYSTEM TIME	A	B	C	caption
0	0.000	0.0	0.0	0.0
1	0.002	0.0	0.0	0.0

In [19]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A", "B", "C"], 
              title= f"A + B <-> C . System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red', 'orange', 'green'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"})
fig.show()

In [20]:

log.write(f"System state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output to the log file a heatmap for each chemical species
for i in range(bio.n_species):
    log.write(f"{bio.chem_data.get_label(i)}:", also_print=False)
    bio.single_species_heatmap(species_index=i, heatmap_pars=heatmap_pars, graphic_component="vue_heatmap_11")

# Output to the log file a one-curve line plot for each chemical species
for i in range(bio.n_species):
    log.write(f"{bio.chem_data.get_label(i)}:", also_print=False)
    bio.single_species_line_plot(species_index=i, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

# Output to the log file a line plot for ALL the chemicals together (same color as used for plotly elsewhere)
bio.line_plot(plot_pars=lineplot_pars, graphic_component="vue_curves_4", color_mapping={0: 'red', 1: 'orange', 2: 'green'})


System state at time t=0.002:
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

Several more steps ¶

In [21]:

# Continue with several delta_t steps
for _ in range(7):
    bio.react_diffuse(time_step=delta_t, n_steps=1)
    bio.describe_state(concise=True)

SYSTEM STATE at Time t = 0.004:
[[16.4  3.4  0.2  0.   0.   0.   0. ]
 [ 0.   0.   0.   0.   0.2  3.4 16.4]
 [ 0.   0.   0.   0.   0.   0.   0. ]]
SYSTEM STATE at Time t = 0.006:
[[15.1   4.38  0.5   0.02  0.    0.    0.  ]
 [ 0.    0.    0.    0.02  0.5   4.38 15.1 ]
 [ 0.    0.    0.    0.    0.    0.    0.  ]]
SYSTEM STATE at Time t = 0.008:
[[1.4028e+01 5.0640e+00 8.4000e-01 6.5984e-02 2.0000e-03 0.0000e+00
  0.0000e+00]
 [0.0000e+00 0.0000e+00 2.0000e-03 6.5984e-02 8.4000e-01 5.0640e+00
  1.4028e+01]
 [0.0000e+00 0.0000e+00 0.0000e+00 1.6000e-05 0.0000e+00 0.0000e+00
  0.0000e+00]]
SYSTEM STATE at Time t = 0.01:
[[1.31316000e+01 5.53800000e+00 1.18493120e+00 1.36813108e-01
  8.13120000e-03 2.00000000e-04 0.00000000e+00]
 [0.00000000e+00 2.00000000e-04 8.13120000e-03 1.36813108e-01
  1.18493120e+00 5.53800000e+00 1.31316000e+01]
 [0.00000000e+00 0.00000000e+00 6.72320000e-05 1.90027530e-04
  6.72320000e-05 0.00000000e+00 0.00000000e+00]]
SYSTEM STATE at Time t = 0.012:
[[1.23722400e+01 5.86200882e+00 1.51504114e+00 2.28008774e-01
  1.98211433e-02 9.28816000e-04 2.00000000e-05]
 [2.00000000e-05 9.28816000e-04 1.98211433e-02 2.28008774e-01
  1.51504114e+00 5.86200882e+00 1.23722400e+01]
 [0.00000000e+00 4.44384640e-05 4.52470702e-04 9.37489304e-04
  4.52470702e-04 4.44384640e-05 0.00000000e+00]]
SYSTEM STATE at Time t = 0.014:
[[1.17212070e+01 6.07811756e+00 1.81983529e+00 3.33817478e-01
  3.75512896e-02 2.50955578e-03 1.00983808e-04]
 [1.00983808e-04 2.50955578e-03 3.75512896e-02 3.33817478e-01
  1.81983529e+00 6.07811756e+00 1.17212070e+01]
 [9.98666893e-06 2.62777001e-04 1.65200869e-03 3.01131931e-03
  1.65200869e-03 2.62777001e-04 9.98666893e-06]]
SYSTEM STATE at Time t = 0.016:
[[1.11568507e+01 6.21598919e+00 2.09433486e+00 4.48347321e-01
  6.09468566e-02 5.16378807e-03 2.94534867e-04]
 [2.94534867e-04 5.16378807e-03 6.09468566e-02 4.48347321e-01
  2.09433486e+00 6.21598919e+00 1.11568507e+01]
 [5.77983875e-05 8.74133777e-04 4.37882730e-03 7.45120113e-03
  4.37882730e-03 8.74133777e-04 5.77983875e-05]]

In [22]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0.016:
           A          B         C
0  11.156851   0.000295  0.000058
1   6.215989   0.005164  0.000874
2   2.094335   0.060947  0.004379
3   0.448347   0.448347  0.007451
4   0.060947   2.094335  0.004379
5   0.005164   6.215989  0.000874
6   0.000295  11.156851  0.000058

In [23]:

# Save the state of the concentrations of all species at the middle bin
bio.add_snapshot(bio.bin_snapshot(bin_address = 3))
bio.get_history()

Out[23]:

	SYSTEM TIME	A	B	C
0	0.000	0.000000	0.000000	0.000000
1	0.002	0.000000	0.000000	0.000000
2	0.016	0.448347	0.448347	0.007451

In [24]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A", "B", "C"], 
              title= f"A + B <-> C . System snapshot (interpolated) at time t={bio.system_time}",
              color_discrete_sequence = ['red', 'orange', 'green'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"},
              line_shape="spline")
fig.show()

A is continuing to diffuse from the left.
B is continuing to diffuse from the right.
They're finally beginning to overlap in the middle bin

In [25]:

log.write(f"System state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output to the log file a heatmap for each chemical species
for i in range(bio.n_species):
    log.write(f"{bio.chem_data.get_label(i)}:", also_print=False)
    bio.single_species_heatmap(species_index=i, heatmap_pars=heatmap_pars, graphic_component="vue_heatmap_11")

# Output to the log file a one-curve line plot for each chemical species
for i in range(bio.n_species):
    log.write(f"{bio.chem_data.get_label(i)}:", also_print=False)
    bio.single_species_line_plot(species_index=i, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

# Output to the log file a line plot for ALL the chemicals together (same color as used for plotly elsewhere)
bio.line_plot(plot_pars=lineplot_pars, graphic_component="vue_curves_4", color_mapping={0: 'red', 1: 'orange', 2: 'green'})


System state at time t=0.016:
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

Several group of longer runs ¶

In [26]:

# Now, do several group of longer runs
for _ in range(4):
    print("\n\n+ 10 steps later:")
    bio.react_diffuse(time_step=delta_t, n_steps=10)
    bio.describe_state(concise=True)


+ 10 steps later:
SYSTEM STATE at Time t = 0.036:
[[7.92576526 5.95824446 3.31917619 1.31581241 0.35918764 0.07038175
  0.01251229]
 [0.01251229 0.07038175 0.35918764 1.31581241 3.31917619 5.95824446
  7.92576526]
 [0.01555131 0.07914514 0.24409632 0.36133444 0.24409632 0.07914514
  0.01555131]]


+ 10 steps later:
SYSTEM STATE at Time t = 0.056:
[[6.29600683 5.06118233 3.15970431 1.44600532 0.47532616 0.12019317
  0.03045075]
 [0.03045075 0.12019317 0.47532616 1.44600532 3.15970431 5.06118233
  6.29600683]
 [0.07498099 0.28735559 0.78250579 1.12144639 0.78250579 0.28735559
  0.07498099]]


+ 10 steps later:
SYSTEM STATE at Time t = 0.076:
[[5.13609493 4.21433746 2.7454954  1.35328847 0.4992179  0.14748071
  0.04559633]
 [0.04559633 0.14748071 0.4992179  1.35328847 2.7454954  4.21433746
  5.13609493]
 [0.1615343  0.52706799 1.31954666 1.8421909  1.31954666 0.52706799
  0.1615343 ]]


+ 10 steps later:
SYSTEM STATE at Time t = 0.096:
[[4.2209458  3.50170661 2.34873485 1.23042685 0.50075376 0.16821567
  0.0606064 ]
 [0.0606064  0.16821567 0.50075376 1.23042685 2.34873485 3.50170661
  4.2209458 ]
 [0.25982593 0.75464804 1.76534285 2.40897641 1.76534285 0.75464804
  0.25982593]]

In [27]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0.09600000000000007:
          A         B         C
0  4.220946  0.060606  0.259826
1  3.501707  0.168216  0.754648
2  2.348735  0.500754  1.765343
3  1.230427  1.230427  2.408976
4  0.500754  2.348735  1.765343
5  0.168216  3.501707  0.754648
6  0.060606  4.220946  0.259826

In [28]:

# Save the state of the concentrations of all species at the middle bin
bio.add_snapshot(bio.bin_snapshot(bin_address = 3))
bio.get_history()

Out[28]:

	SYSTEM TIME	A	B	C
0	0.000	0.000000	0.000000	0.000000
1	0.002	0.000000	0.000000	0.000000
2	0.016	0.448347	0.448347	0.007451
3	0.096	1.230427	1.230427	2.408976

In [29]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A", "B", "C"], 
              title= f"A + B <-> C . System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red', 'orange', 'green'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"},
              line_shape="spline")
fig.show()

A is continuing to diffuse from the left.
B is continuing to diffuse from the right.
By now, they're overlapping in the middle bin sufficiently to react and generate C

In [30]:

log.write(f"System state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output to the log file a heatmap for each chemical species
for i in range(bio.n_species):
    log.write(f"{bio.chem_data.get_label(i)}:", also_print=False)
    bio.single_species_heatmap(species_index=i, heatmap_pars=heatmap_pars, graphic_component="vue_heatmap_11")

# Output to the log file a one-curve line plot for each chemical species
for i in range(bio.n_species):
    log.write(f"{bio.chem_data.get_label(i)}:", also_print=False)
    bio.single_species_line_plot(species_index=i, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

# Output to the log file a line plot for ALL the chemicals together (same color as used for plotly elsewhere)
bio.line_plot(plot_pars=lineplot_pars, graphic_component="vue_curves_4", color_mapping={0: 'red', 1: 'orange', 2: 'green'})


System state at time t=0.09600000000000007:
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

In [31]:

# Continue the simulation
for _ in range(4):
    print("\n\n+++ 30 steps later:")
    bio.react_diffuse(time_step=delta_t, n_steps=30)
    bio.describe_state(concise=True)


+++ 30 steps later:
SYSTEM STATE at Time t = 0.156:
[[2.39736516 2.05453684 1.50075745 0.92781069 0.48529917 0.22472198
  0.11560109]
 [0.11560109 0.22472198 0.48529917 0.92781069 1.50075745 2.05453684
  2.39736516]
 [0.57202182 1.29674075 2.59761288 3.36115673 2.59761288 1.29674075
  0.57202182]]


+++ 30 steps later:
SYSTEM STATE at Time t = 0.216:
[[1.43652347 1.28435794 1.02979899 0.73906751 0.47257834 0.28028088
  0.18445971]
 [0.18445971 0.28028088 0.47257834 0.73906751 1.02979899 1.28435794
  1.43652347]
 [0.8597085  1.64384498 2.94653088 3.67276444 2.94653088 1.64384498
  0.8597085 ]]


+++ 30 steps later:
SYSTEM STATE at Time t = 0.276:
[[0.94369275 0.88396666 0.77535511 0.63019458 0.46959173 0.33300009
  0.25664867]
 [0.25664867 0.33300009 0.46959173 0.63019458 0.77535511 0.88396666
  0.94369275]
 [1.09382006 1.85282552 3.05530325 3.70365274 3.05530325 1.85282552
  1.09382006]]


+++ 30 steps later:
SYSTEM STATE at Time t = 0.336:
[[0.69798039 0.68111864 0.64213556 0.57196145 0.47435422 0.37878712
  0.32097915]
 [0.32097915 0.37878712 0.47435422 0.57196145 0.64213556 0.68111864
  0.69798039]
 [1.27482053 1.97696102 3.05404907 3.62102222 3.05404907 1.97696102
  1.27482053]]

In [32]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0.33600000000000024:
          A         B         C
0  0.697980  0.320979  1.274821
1  0.681119  0.378787  1.976961
2  0.642136  0.474354  3.054049
3  0.571961  0.571961  3.621022
4  0.474354  0.642136  3.054049
5  0.378787  0.681119  1.976961
6  0.320979  0.697980  1.274821

In [33]:

# Save the state of the concentrations of all species at the middle bin
bio.add_snapshot(bio.bin_snapshot(bin_address = 3))
bio.get_history()

Out[33]:

	SYSTEM TIME	A	B	C
0	0.000	0.000000	0.000000	0.000000
1	0.002	0.000000	0.000000	0.000000
2	0.016	0.448347	0.448347	0.007451
3	0.096	1.230427	1.230427	2.408976
4	0.336	0.571961	0.571961	3.621022

In [34]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A", "B", "C"], 
              title= f"A + B <-> C . System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red', 'orange', 'green'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"},
              line_shape="spline")
fig.show()

In [35]:

log.write(f"System state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output to the log file a heatmap for each chemical species
for i in range(3):
    bio.single_species_heatmap(species_index=i, heatmap_pars=heatmap_pars, graphic_component="vue_heatmap_11")

# Output to the log file a one-curve line plot for each chemical species
for i in range(3):
    bio.single_species_line_plot(species_index=i, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

# Output to the log file a line plot for ALL the chemicals together (same color as used for plotly elsewhere)
bio.line_plot(plot_pars=lineplot_pars, graphic_component="vue_curves_4", color_mapping={0: 'red', 1: 'orange', 2: 'green'})


System state at time t=0.33600000000000024:
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

In [36]:

# Continue the simulation
for _ in range(4):
    print("\n+++++ 50 steps later:")
    bio.react_diffuse(time_step=delta_t, n_steps=50)
    bio.describe_state(concise=True)

+++++ 50 steps later:
SYSTEM STATE at Time t = 0.436:
[[0.53513401 0.5437576  0.54867719 0.53174198 0.48696931 0.43256384
  0.39647767]
 [0.39647767 0.43256384 0.48696931 0.53174198 0.54867719 0.5437576
  0.53513401]
 [1.49508439 2.09028492 2.96849022 3.41695934 2.96849022 2.09028492
  1.49508439]]

+++++ 50 steps later:
SYSTEM STATE at Time t = 0.536:
[[0.48751897 0.50165856 0.51768297 0.51798994 0.49498758 0.46076288
  0.4365229 ]
 [0.4365229  0.46076288 0.49498758 0.51798994 0.51768297 0.50165856
  0.48751897]
 [1.65797359 2.15520413 2.86719131 3.22213812 2.86719131 2.15520413
  1.65797359]]

+++++ 50 steps later:
SYSTEM STATE at Time t = 0.636:
[[0.47470241 0.48869324 0.50591479 0.51120986 0.49756771 0.47365233
  0.45594669]
 [0.45594669 0.47365233 0.49756771 0.51120986 0.50591479 0.48869324
  0.47470241]
 [1.78774781 2.20070508 2.77778668 3.05983384 2.77778668 2.20070508
  1.78774781]]

+++++ 50 steps later:
SYSTEM STATE at Time t = 0.736:
[[0.47257504 0.48488523 0.50040062 0.50652836 0.49733067 0.47935337
  0.46567693]
 [0.46567693 0.47935337 0.49733067 0.50652836 0.50040062 0.48488523
  0.47257504]
 [1.89367665 2.23536347 2.70338342 2.9284027  2.70338342 2.23536347
  1.89367665]]

In [37]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0.7360000000000005:
          A         B         C
0  0.472575  0.465677  1.893677
1  0.484885  0.479353  2.235363
2  0.500401  0.497331  2.703383
3  0.506528  0.506528  2.928403
4  0.497331  0.500401  2.703383
5  0.479353  0.484885  2.235363
6  0.465677  0.472575  1.893677

In [38]:

# Save the state of the concentrations of all species at the middle bin
bio.add_snapshot(bio.bin_snapshot(bin_address = 3))
bio.get_history()

Out[38]:

	SYSTEM TIME	A	B	C
0	0.000	0.000000	0.000000	0.000000
1	0.002	0.000000	0.000000	0.000000
2	0.016	0.448347	0.448347	0.007451
3	0.096	1.230427	1.230427	2.408976
4	0.336	0.571961	0.571961	3.621022
5	0.736	0.506528	0.506528	2.928403

In [39]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A", "B", "C"], 
              title= f"A + B <-> C . System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red', 'orange', 'green'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"},
              line_shape="spline")
fig.show()

In [40]:

log.write(f"System state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output to the log file a heatmap for each chemical species
for i in range(3):
    bio.single_species_heatmap(species_index=i, heatmap_pars=heatmap_pars, graphic_component="vue_heatmap_11")

# Output to the log file a one-curve line plot for each chemical species
for i in range(3):
    bio.single_species_line_plot(species_index=i, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

# Output to the log file a line plot for ALL the chemicals together (same color as used for plotly elsewhere)
bio.line_plot(plot_pars=lineplot_pars, graphic_component="vue_curves_4", color_mapping={0: 'red', 1: 'orange', 2: 'green'})


System state at time t=0.7360000000000005:
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

In [41]:

# Continue the simulation
for _ in range(4):
    print("\n+++++++++++++++ 150 steps later:")
    bio.react_diffuse(time_step=delta_t, n_steps=150)
    bio.describe_state(concise=True)

+++++++++++++++ 150 steps later:
SYSTEM STATE at Time t = 1.036:
[[0.47744061 0.4845086  0.49346999 0.49747162 0.49331726 0.48423339
  0.47709743]
 [0.47709743 0.48423339 0.49331726 0.49747162 0.49346999 0.4845086
  0.47744061]
 [2.11014111 2.3007984  2.55138084 2.66782039 2.55138084 2.3007984
  2.11014111]]

+++++++++++++++ 150 steps later:
SYSTEM STATE at Time t = 1.336:
[[0.48168804 0.48554921 0.49041386 0.49259511 0.49040626 0.48553552
  0.48167096]
 [0.48167096 0.48553552 0.49040626 0.49259511 0.49041386 0.48554921
  0.48168804]
 [2.2288825  2.33377315 2.46847456 2.52988061 2.46847456 2.33377315
  2.2288825 ]]

+++++++++++++++ 150 steps later:
SYSTEM STATE at Time t = 1.636:
[[0.48405962 0.48615505 0.48878337 0.48995858 0.48878299 0.48615437
  0.48405877]
 [0.48405877 0.48615437 0.48878299 0.48995858 0.48878337 0.48615505
  0.48405962]
 [2.29360822 2.350868   2.42345244 2.45618991 2.42345244 2.350868
  2.29360822]]

+++++++++++++++ 150 steps later:
SYSTEM STATE at Time t = 1.936:
[[0.48534444 0.4864795  0.48789956 0.48853323 0.48789955 0.48647947
  0.4853444 ]
 [0.4853444  0.48647947 0.48789955 0.48853323 0.48789956 0.4864795
  0.48534444]
 [2.32876222 2.35988613 2.39905402 2.4166151  2.39905402 2.35988613
  2.32876222]]

In [42]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 1.9360000000000015:
          A         B         C
0  0.485344  0.485344  2.328762
1  0.486480  0.486479  2.359886
2  0.487900  0.487900  2.399054
3  0.488533  0.488533  2.416615
4  0.487900  0.487900  2.399054
5  0.486479  0.486480  2.359886
6  0.485344  0.485344  2.328762

In [43]:

# Save the state of the concentrations of all species at the middle bin
bio.add_snapshot(bio.bin_snapshot(bin_address = 3))
bio.get_history()

Out[43]:

	SYSTEM TIME	A	B	C
0	0.000	0.000000	0.000000	0.000000
1	0.002	0.000000	0.000000	0.000000
2	0.016	0.448347	0.448347	0.007451
3	0.096	1.230427	1.230427	2.408976
4	0.336	0.571961	0.571961	3.621022
5	0.736	0.506528	0.506528	2.928403
6	1.936	0.488533	0.488533	2.416615

In [44]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A", "B", "C"], 
              title= f"A + B <-> C . System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red', 'orange', 'green'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"},
              line_shape="spline")
fig.show()

In [45]:

log.write(f"System state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output to the log file a heatmap for each chemical species
for i in range(3):
    bio.single_species_heatmap(species_index=i, heatmap_pars=heatmap_pars, graphic_component="vue_heatmap_11")

# Output to the log file a one-curve line plot for each chemical species
for i in range(3):
    bio.single_species_line_plot(species_index=i, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

# Output to the log file a line plot for ALL the chemicals together (same color as used for plotly elsewhere)
bio.line_plot(plot_pars=lineplot_pars, graphic_component="vue_curves_4", color_mapping={0: 'red', 1: 'orange', 2: 'green'})


System state at time t=1.9360000000000015:
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

In [46]:

# Continue the simulation
for _ in range(2):
    print("\n++++++++++ ... ++++++++++ 1,000 steps later:")
    bio.react_diffuse(time_step=delta_t, n_steps=1000)
    bio.describe_state(concise=True)

++++++++++ ... ++++++++++ 1,000 steps later:
SYSTEM STATE at Time t = 3.936:
[[0.48683089 0.48684974 0.48687325 0.48688372 0.48687325 0.48684974
  0.48683089]
 [0.48683089 0.48684974 0.48687325 0.48688372 0.48687325 0.48684974
  0.48683089]
 [2.36959744 2.37011659 2.37076408 2.37105229 2.37076408 2.37011659
  2.36959744]]

++++++++++ ... ++++++++++ 1,000 steps later:
SYSTEM STATE at Time t = 5.936:
[[0.48685551 0.48685582 0.48685621 0.48685639 0.48685621 0.48685582
  0.48685551]
 [0.48685551 0.48685582 0.48685621 0.48685639 0.48685621 0.48685582
  0.48685551]
 [2.37027551 2.37028411 2.37029484 2.37029961 2.37029484 2.37028411
  2.37027551]]

In [47]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 5.935999999999568:
          A         B         C
0  0.486856  0.486856  2.370276
1  0.486856  0.486856  2.370284
2  0.486856  0.486856  2.370295
3  0.486856  0.486856  2.370300
4  0.486856  0.486856  2.370295
5  0.486856  0.486856  2.370284
6  0.486856  0.486856  2.370276

In [48]:

# Save the state of the concentrations of all species at the middle bin
bio.add_snapshot(bio.bin_snapshot(bin_address = 3))
bio.get_history()

Out[48]:

	SYSTEM TIME	A	B	C
0	0.000	0.000000	0.000000	0.000000
1	0.002	0.000000	0.000000	0.000000
2	0.016	0.448347	0.448347	0.007451
3	0.096	1.230427	1.230427	2.408976
4	0.336	0.571961	0.571961	3.621022
5	0.736	0.506528	0.506528	2.928403
6	1.936	0.488533	0.488533	2.416615
7	5.936	0.486856	0.486856	2.370300

In [49]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A", "B", "C"], 
              title= f"A + B <-> C . System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red', 'orange', 'green'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"},
              line_shape="spline")
fig.show()

In [50]:

log.write(f"System state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output to the log file a heatmap for each chemical species
for i in range(3):
    bio.single_species_heatmap(species_index=i, heatmap_pars=heatmap_pars, graphic_component="vue_heatmap_11")

# Output to the log file a one-curve line plot for each chemical species
for i in range(3):
    bio.single_species_line_plot(species_index=i, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

# Output to the log file a line plot for ALL the chemicals together (same color as used for plotly elsewhere)
bio.line_plot(plot_pars=lineplot_pars, graphic_component="vue_curves_4", color_mapping={0: 'red', 1: 'orange', 2: 'green'})


System state at time t=5.935999999999568:
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `rd_1.log.htm`]

Equilibrium ¶

In [51]:

# Verify equilibrium concentrations (sampled in the 1st bin; at this point, all bins have equilibrated)
A_eq = bio.bin_concentration(0, 0)
B_eq = bio.bin_concentration(0, 1)
C_eq = bio.bin_concentration(0, 2)
print(f"\nRatio of equilibrium concentrations ((C_eq) / (A_eq * B_eq)) : {(C_eq) / (A_eq * B_eq)}")
print(f"Ratio of forward/reverse rates: {chem_data.get_forward_rate(0) / chem_data.get_reverse_rate(0)}")
# Both are essentially equal, as expected

Ratio of equilibrium concentrations ((C_eq) / (A_eq * B_eq)) : 9.999968840509963
Ratio of forward/reverse rates: 10.0

Plots of changes of concentration with time¶

In [52]:

fig = px.line(data_frame=bio.get_history(), x="SYSTEM TIME", y=["A", "B", "C"], 
              title="Reactions:  A + B <-> C . Changes in concentrations in the MIDDLE bin",
              color_discrete_sequence = ['navy', 'cyan', 'red'],
              labels={"value":"concentration", "variable":"Chemical"})
fig.show()

A and B overlap on the plot, due to the symmetry of the system.
Initially, in the middle bin, neither A nor B are present; over time they diffuse there... but then they react and get consumed (producing C), to an equilibrium value. C gradually diffuses away.

In [ ]:

Reaction A + B <-> C, mostly forward and with 1st-order kinetics for each species,¶

taken to equilibrium¶

Inject initial concentrations of A and B at opposite ends of the system¶

First step¶

Several more steps¶

Several group of longer runs¶

Equilibrium¶

Plots of changes of concentration with time¶

First step ¶

Several more steps ¶

Several group of longer runs ¶

Equilibrium ¶