A transient concentration inside an organelle can "escape" from it by passive transport across the membranes, only it if diffuses quicky - before a reaction transforms it into a chemical unable to cross membranes.¶

The "window of opportunity to escape" closes fast!¶

SCENARIO 1 : `A`, the chemical injected into the organelle, diffuses slowly - and gets converted into `C` (which cannot cross the membranes) by the reaction `A + B <-> C` , before it has a chance to leave the organelle. Trapped!¶

SCENARIO 2 : `A` diffuses fast enough to "escape" out of the organelle before getting completely trapped there¶

Note: B is plentiful everywhere

Recommended background:

experiment 1D/diffusion/membrane_gradient_diffusion_1
experiment 1D/reaction_diffusion/transient_getting_mopped_up

TAGS : "reactions 1D", "diffusion 1D", "membranes 1D"¶

In [1]:

LAST_REVISED = "Aug. 28, 2025"
LIFE123_VERSION = "1.0.0rc6"       # 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 BioSim1D, ChemData, ReactionRegistry, PlotlyHelper, check_version

In [4]:

check_version(LIFE123_VERSION)

OK

In [ ]:

Initialize the Chemical Data and the Reactions. They will be re-used in both scenarios¶

In [5]:

# Initialize the chemical data
chem_data = ChemData(names=["A", "B", "C"], 
                     diffusion_rates=[100., 800., 500.],        # The diffusion rate of `A` will later be increased in scenario 2
                     plot_colors=["red", "turquoise", "green"]) 

rxns = ReactionRegistry(chem_data=chem_data)

# Reaction A + B <-> C , with 1st-order kinetics for each species; note that it's mostly in the forward direction
# The reaction is mostly in the forward direction
rxns.add_reaction(reactants=["A", "B"], products="C", kF=0.1, kR=0.02)
rxns.describe_reactions()

Number of reactions: 1
0: A + B  <-> C  (Elementary Synthesis reaction)  (kF = 0.1 / kR = 0.02 / K = 5)
Chemicals involved in the above reactions: {"A" (red), "B" (turquoise), "C" (green)}

In [ ]:

SCENARIO 1 - `A` diffuses slowly, relatively to the reaction `A + B <-> C`¶

Initialize the 1D System, including Membranes¶

In [6]:

bio = BioSim1D(n_bins=30, chem_data=chem_data, reactions=rxns)

In [7]:

bio.membranes().set_membranes(membranes=[ (2, 18) ])
bio.membranes().membrane_list

Out[7]:

[(2, 18)]

In [8]:

# We'll use 1/2 of the diffusion rate of `A` and `B` 
# as their respective membrane permeability (by passive transport)
# `C`, by constrast, keeps the default 0 permeability (i.e., can't cross membranes)
bio.membranes().change_permeability("A", 50.)
bio.membranes().change_permeability("B", 400.)

In [ ]:

Initialize the initial concentrations¶

In [9]:

# Set up the initial bell-shape concentration of `A`, with a narrow peak close to one end of the system,
# centered at 20% of the width of the system, i.e. at bin 6
bio.inject_bell_curve(chem_label="A", center=0.2, sd=0.05, max_amplitude=200., bias=0., clip=(2,17))

In [10]:

# Chemical `B`, by contrast, is uniformly distributed
bio.set_uniform_concentration(chem_label="B", conc=80.)

In [11]:

# Show as heatmap (including the membranes, shown in brown)
bio.system_heatmaps(title_prefix="Initial strong, localized transient of chemical `A` (membranes shown in brown)")

The initial transient of `A` is localized within the compartment (organelle) between bins 2 and 18¶

In [12]:

# Visualize the system state so far
bio.visualize_system(title_prefix=["Initial strong, localized transient of chemical `A` (membranes shown in brown).", 
                                   "Notice that `B` is plentiful everywhere"])

In [13]:

df = bio.describe_state()
df

SYSTEM STATE at Time t = 0:
30 bins and 3 chemical species
Membranes present:  [(2, 18)]

Out[13]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2	Bin 3	Bin 4	Bin 5	Bin 6	Bin 7	...	Bin 20	Bin 21	Bin 22	Bin 23	Bin 24	Bin 25	Bin 26	Bin 27	Bin 28	Bin 29
0	A	100.0	0.0	0.0	6.451484	30.996376	92.555278	171.763341	198.106523	142.0058	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1	B	800.0	80.0	80.0	80.000000	80.000000	80.000000	80.000000	80.000000	80.0000	...	80.0	80.0	80.0	80.0	80.0	80.0	80.0	80.0	80.0	80.0
2	C	500.0	0.0	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.0000	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

3 rows × 32 columns

In [14]:

df[df.columns[2:21]]  # Zoom in where the action is

Out[14]:

	Bin 0	Bin 1	Bin 2	Bin 3	Bin 4	Bin 5	Bin 6	Bin 7	Bin 8	Bin 9	Bin 10	Bin 11	Bin 12	Bin 13	Bin 14	Bin 15	Bin 16	Bin 17	Bin 18
0	0.0	0.0	6.451484	30.996376	92.555278	171.763341	198.106523	142.0058	63.263381	17.516112	3.014131	0.322348	0.021425	0.000885	0.000023	3.625508e-07	3.595235e-09	2.215770e-11	0.0
1	80.0	80.0	80.000000	80.000000	80.000000	80.000000	80.000000	80.0000	80.000000	80.000000	80.000000	80.000000	80.000000	80.000000	80.000000	8.000000e+01	8.000000e+01	8.000000e+01	80.0
2	0.0	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.0000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000e+00	0.000000e+00	0.000000e+00	0.0

In [ ]:

Request history-keeping for some bins¶

In [15]:

# Request to save the concentration history at the bins with the initial concentration injection, 
# and the bins at, or near, both ends of the system
bio.enable_history(bins=[0, 6, 29], frequency=15, take_snapshot=True)    

History enabled for bins [0, 6, 29], for ALL chemicals

In [ ]:

Start the simulation of the reaction-diffusion¶

In [16]:

# The first round of reaction-diffusion, over a small time duration
bio.react_diffuse(total_duration=0.025, fraction_max_step=0.5, show_status=True)
bio.visualize_system(title_prefix=["The localized transient `A` starts turning into `C` by `A + B <-> C`, ",
                                   "before it can diffuse away much.  Notice the production of `C`, which can't cross the membrane"])

{'steps': 121, 'system time': '0.025208', 'time_step': 0.00020833125}

In [17]:

# SAME IN HEATMAP VIEW
bio.system_heatmaps(title_prefix=["The localized transient `A` starts turning into `C` by `A + B <-> C`, ",
                                  "before it can diffuse away much.  Notice the production of `C`, which can't cross the membrane"])

In [ ]:

Let's continue the reaction-diffusion¶

In [18]:

bio.react_diffuse(total_duration=0.025, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 121, 'system time': '0.050416', 'time_step': 0.00020833125}

`A` is crossing to some extent the nearby left membrane, but not making it in time to reach the right membrane, before getting consumed¶

In [19]:

bio.react_diffuse(total_duration=0.025, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 121, 'system time': '0.075624', 'time_step': 0.00020833125}

In [20]:

bio.react_diffuse(total_duration=0.025, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 121, 'system time': '0.10083', 'time_step': 0.00020833125}

In [21]:

bio.react_diffuse(total_duration=0.05, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 241, 'system time': '0.15104', 'time_step': 0.00020833125}

In [22]:

bio.react_diffuse(total_duration=0.15, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 721, 'system time': '0.30125', 'time_step': 0.00020833125}

In [23]:

bio.react_diffuse(total_duration=1.2, fraction_max_step=0.9, show_status=True)
bio.visualize_system()

{'steps': 3201, 'system time': '1.5016', 'time_step': 0.00037499625000000003}

In [24]:

bio.system_heatmaps()

In [ ]:

Now, let's look at a few individual bins, and their concentration change with time¶

In [25]:

bio.plot_history_single_bin(title_prefix=["Diffusion, membrane passive transport, and reaction `A + B <-> C`",
                                          "Bin where the transient originates."], 
                             bin_address=6)

In [26]:

bio.plot_history_single_bin(title_prefix=["Diffusion, membrane passive transport, and reaction `A + B <-> C`",
                                          "At left-most edge of system."], 
                            bin_address=0)

Only a small amount of `A` reaches bin 0 early on, and later converts to `C`¶

In [27]:

# Save this plot, for later comparison with the counterpart from scenario 2
scenario_1 = bio.plot_history_single_bin(title_prefix=["Diffusion, membrane passive transport, and reaction `A + B <-> C`",
                                                       "Faraway bin."], 
                                         bin_address=29)
scenario_1 

Virtually no `A` ever reaches the faraway bins!¶

In [ ]:

SCENARIO 2 - `A` diffuses quickly¶

Let's repeat, starting like before, but with a much higher diffusion rate of A

In [28]:

# Initial conditioned just like before

bio = BioSim1D(n_bins=30, chem_data=chem_data, reactions=rxns)

bio.membranes().set_membranes(membranes=[ (2, 18) ])

bio.inject_bell_curve(chem_label="A", center=0.2, sd=0.05, max_amplitude=200., bias=0., clip=(2,17))
bio.set_uniform_concentration(chem_label="B", conc=80.)

In [29]:

# 15 times faster diffusion rate of 'A', and of its membrane permeability, than before

chem_data.set_diffusion_rate(chem_label="A", diff_rate = 1500)  # **** x15 from scenario 1

bio.membranes().change_permeability("A", 750.)  # **** x15 from scenario 1 
bio.membranes().change_permeability("B", 400.)  # Same as before
# `C` keeps the default 0 permeability (i.e., can't cross membranes)

In [30]:

# Request history-keeping for some bins
bio.enable_history(bins=[0, 6, 29], frequency=15, take_snapshot=True)   

History enabled for bins [0, 6, 29], for ALL chemicals

In [31]:

# Visualize the system state so far
bio.visualize_system(title_prefix=["Initial strong, localized transient of chemical `A` (membranes shown in brown)", 
                                   "Same as in the earlier scenario."])

In [ ]:

Repeat the simulation¶

In [32]:

# The first round of reaction-diffusion, over a small time duration
bio.react_diffuse(total_duration=0.025, fraction_max_step=0.5, show_status=True)
bio.visualize_system(title_prefix=["This time, the localized transient `A` diffuses more substantially across the membrane,",
                                   "before being converted into `C`, which can't cross the membrane"])

{'steps': 226, 'system time': '0.025111', 'time_step': 0.00011111}

In [33]:

bio.react_diffuse(total_duration=0.025, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 226, 'system time': '0.050222', 'time_step': 0.00011111}

In this scenario, `A` is managing to cross both membranes, to some extent, before getting consumed¶

In [34]:

bio.react_diffuse(total_duration=0.025, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 226, 'system time': '0.075333', 'time_step': 0.00011111}

In [35]:

bio.react_diffuse(total_duration=0.025, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 226, 'system time': '0.10044', 'time_step': 0.00011111}

In [36]:

bio.react_diffuse(total_duration=0.05, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 451, 'system time': '0.15055', 'time_step': 0.00011111}

In [37]:

bio.react_diffuse(total_duration=0.15, fraction_max_step=0.5, show_status=True)
bio.visualize_system()

{'steps': 1351, 'system time': '0.30066', 'time_step': 0.00011111}

The increasingly prominent `C` (green) on the right is from `A` that managed to cross the membrane, and then converted to `C`¶

In [38]:

bio.react_diffuse(total_duration=1.2, fraction_max_step=0.9, show_status=True)
bio.visualize_system()

{'steps': 6001, 'system time': '1.5009', 'time_step': 0.000199998}

In [ ]:

Now, let's look at the faraway bin 29, and it concentration change with time¶

In [39]:

scenario_2 = bio.plot_history_single_bin(title_prefix=["Diffusion, membrane passive transport, and reaction `A + B <-> C`",
                                                       "Faraway bin."], 
                                         bin_address=29)
scenario_2

A lot more `A` (eventually converted into `C`) reaches the faraway bins, compared to the earlier scenario!¶

In [40]:

PlotlyHelper.combine_plots(fig_list = [scenario_1, scenario_2], 
                           title="Diffusion, membrane passive transport, and reaction `A + B <-> C`<br>Concentrations in faraway bin 29<br>Comparison of scenario 1 (dotted) and 2 (solid)", 
                           layout_index=0, modify = {0: "dot"})

Magnify plot to separate the red and green dots (very close to each other)!

Side note: B eventually equilibrates to the same value under either scenario - since B diffuses freely across membranes, and is the excess reactant: it diffuses throughout to bind to A, wherever A might be...

In [ ]:

A transient concentration inside an organelle can "escape" from it by passive transport across the membranes, only it if diffuses quicky - before a reaction transforms it into a chemical unable to cross membranes.¶

The "window of opportunity to escape" closes fast!¶

SCENARIO 1 : A, the chemical injected into the organelle, diffuses slowly - and gets converted into C (which cannot cross the membranes) by the reaction A + B <-> C , before it has a chance to leave the organelle. Trapped!¶

SCENARIO 2 : A diffuses fast enough to "escape" out of the organelle before getting completely trapped there¶

TAGS : "reactions 1D", "diffusion 1D", "membranes 1D"¶

Initialize the Chemical Data and the Reactions. They will be re-used in both scenarios¶

SCENARIO 1 - A diffuses slowly, relatively to the reaction A + B <-> C¶

Initialize the 1D System, including Membranes¶

Initialize the initial concentrations¶

The initial transient of A is localized within the compartment (organelle) between bins 2 and 18¶

Request history-keeping for some bins¶

Start the simulation of the reaction-diffusion¶

Let's continue the reaction-diffusion¶

A is crossing to some extent the nearby left membrane, but not making it in time to reach the right membrane, before getting consumed¶

Now, let's look at a few individual bins, and their concentration change with time¶

Only a small amount of A reaches bin 0 early on, and later converts to C¶

Virtually no A ever reaches the faraway bins!¶

SCENARIO 2 - A diffuses quickly¶

Repeat the simulation¶

In this scenario, A is managing to cross both membranes, to some extent, before getting consumed¶

The increasingly prominent C (green) on the right is from A that managed to cross the membrane, and then converted to C¶

Now, let's look at the faraway bin 29, and it concentration change with time¶

A lot more A (eventually converted into C) reaches the faraway bins, compared to the earlier scenario!¶

SCENARIO 1 : `A`, the chemical injected into the organelle, diffuses slowly - and gets converted into `C` (which cannot cross the membranes) by the reaction `A + B <-> C` , before it has a chance to leave the organelle. Trapped!¶

SCENARIO 2 : `A` diffuses fast enough to "escape" out of the organelle before getting completely trapped there¶

SCENARIO 1 - `A` diffuses slowly, relatively to the reaction `A + B <-> C`¶

The initial transient of `A` is localized within the compartment (organelle) between bins 2 and 18¶

`A` is crossing to some extent the nearby left membrane, but not making it in time to reach the right membrane, before getting consumed¶

Only a small amount of `A` reaches bin 0 early on, and later converts to `C`¶

Virtually no `A` ever reaches the faraway bins!¶

SCENARIO 2 - `A` diffuses quickly¶

In this scenario, `A` is managing to cross both membranes, to some extent, before getting consumed¶

The increasingly prominent `C` (green) on the right is from `A` that managed to cross the membrane, and then converted to `C`¶

A lot more `A` (eventually converted into `C`) reaches the faraway bins, compared to the earlier scenario!¶