Diffusion of a single chemical gradient, in the presence of membranes in its path (passive transport)¶

Three scenarios:

no membranes
membranes with permeability to that chemical equal its diffusion rate
membranes with much smaller permeability value

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

In [1]:

LAST_REVISED = "Aug. 18, 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, check_version

In [4]:

check_version(LIFE123_VERSION)

OK

In [ ]:

Part 1¶

No membranes; a simple diffusion¶

In [5]:

# Initialize the system
chem_data = ChemData(names="A", 
                     diffusion_rates=600.)

bio = BioSim1D(n_bins=100, chem_data=chem_data)

In [6]:

# Adding a gradient slanting to the left
bio.inject_gradient("A", conc_left = 10., conc_right = 60.)
bio.describe_state()

SYSTEM STATE at Time t = 0:
100 bins and 1 chemical species

Out[6]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2	Bin 3	Bin 4	Bin 5	Bin 6	Bin 7	...	Bin 90	Bin 91	Bin 92	Bin 93	Bin 94	Bin 95	Bin 96	Bin 97	Bin 98	Bin 99
0	A	600.0	10.0	10.505051	11.010101	11.515152	12.020202	12.525253	13.030303	13.535354	...	55.454545	55.959596	56.464646	56.969697	57.474747	57.979798	58.484848	58.989899	59.494949	60.0

1 rows × 102 columns

In [7]:

# Visualize the complete initial state
bio.visualize_system(title_prefix="Initial concentration gradient.  NO membranes present")

In [ ]:

In [8]:

# The first round of diffusion
bio.diffuse(total_duration=2.5, fraction_max_step=0.5, show_status=True) 
bio.visualize_system()

{'steps': 9001, 'system time': '2.5003', 'time_step': 0.000277775}

In [9]:

# Continue the diffusion
bio.diffuse(total_duration=5, fraction_max_step=0.5, show_status=True) 
bio.visualize_system()

{'steps': 18001, 'system time': '7.5005', 'time_step': 0.000277775}

Let's save the complete state of the system, to contrast it with the simulation state at the same time in Part 2¶

In [10]:

saved_state_no_membranes = bio.snapshot_system()
saved_state_no_membranes

Out[10]:

{'system_time': 7.500480549996486,
 'concentrations': array([[34.75897705, 34.75921491, 34.75969039, 34.76040304, 34.76135213,
         34.76253675, 34.76395571, 34.76560761, 34.76749084, 34.76960352,
         34.77194358, 34.7745087 , 34.77729635, 34.78030379, 34.78352804,
         34.78696592, 34.79061404, 34.79446879, 34.79852639, 34.80278281,
         34.80723386, 34.81187515, 34.8167021 , 34.82170993, 34.82689372,
         34.83224835, 34.83776852, 34.8434488 , 34.84928358, 34.85526709,
         34.86139344, 34.86765657, 34.87405032, 34.88056835, 34.88720426,
         34.89395148, 34.90080336, 34.90775313, 34.91479394, 34.92191883,
         34.92912079, 34.93639269, 34.94372737, 34.95111758, 34.95855603,
         34.96603538, 34.97354825, 34.98108722, 34.98864486, 34.99621371,
         35.00378629, 35.01135514, 35.01891278, 35.02645175, 35.03396462,
         35.04144397, 35.04888242, 35.05627263, 35.06360731, 35.07087921,
         35.07808117, 35.08520606, 35.09224687, 35.09919664, 35.10604852,
         35.11279574, 35.11943165, 35.12594968, 35.13234343, 35.13860656,
         35.14473291, 35.15071642, 35.1565512 , 35.16223148, 35.16775165,
         35.17310628, 35.17829007, 35.1832979 , 35.18812485, 35.19276614,
         35.19721719, 35.20147361, 35.20553121, 35.20938596, 35.21303408,
         35.21647196, 35.21969621, 35.22270365, 35.2254913 , 35.22805642,
         35.23039648, 35.23250916, 35.23439239, 35.23604429, 35.23746325,
         35.23864787, 35.23959696, 35.24030961, 35.24078509, 35.24102295]])}

In [11]:

# Further continue the diffusion
bio.diffuse(total_duration=12.5, fraction_max_step=0.9, show_status=True)     # we'll take bigger steps now
bio.visualize_system()

{'steps': 25001, 'system time': '20.001', 'time_step': 0.000499995}

Almost completely equilibrated...¶

In [ ]:

Part 2¶

With membranes.¶

The permeability of `A` across the membranes (passive transport) is EQUAL to its diffusion rate in water¶

In [12]:

# Initialize the system
chem_data = ChemData(names="A", 
                     diffusion_rates=600.)

bio = BioSim1D(n_bins=100, chem_data=chem_data)

bio.membranes().set_membranes(membranes=[ (20, 40) ])
bio.membranes().change_permeability("A", 600.)  # *********  We'll use the same value as the diffusion rate in water

In [13]:

# Adding a gradient slanting to the left
bio.inject_gradient("A", conc_left = 10., conc_right = 60.)
bio.describe_state()

SYSTEM STATE at Time t = 0:
100 bins and 1 chemical species
Membranes present:  [(20, 40)]

Out[13]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2	Bin 3	Bin 4	Bin 5	Bin 6	Bin 7	...	Bin 90	Bin 91	Bin 92	Bin 93	Bin 94	Bin 95	Bin 96	Bin 97	Bin 98	Bin 99
0	A	600.0	10.0	10.505051	11.010101	11.515152	12.020202	12.525253	13.030303	13.535354	...	55.454545	55.959596	56.464646	56.969697	57.474747	57.979798	58.484848	58.989899	59.494949	60.0

1 rows × 102 columns

In [14]:

# Visualize the complete initial state
bio.visualize_system(title_prefix="Initial concentration gradient.  Membranes shown in brown")

In [ ]:

In [15]:

# The first round of diffusion
bio.diffuse(total_duration=2.5, fraction_max_step=0.5, show_status=True) 
bio.visualize_system()

{'steps': 9001, 'system time': '2.5003', 'time_step': 0.000277775}

In [16]:

# Continue the diffusion
bio.diffuse(total_duration=5, fraction_max_step=0.5, show_status=True) 
bio.visualize_system()

{'steps': 18001, 'system time': '7.5005', 'time_step': 0.000277775}

Does that turquoise curve (the concentrations of `A` across the length of the system) look familiar??¶

It's absolutely identical to what we had in part 1 (with no membranes) - as if the membranes weren't there!
We can can verify below that they're indeed identical, from the previously-saved system snapshot at the same time in the simulation:

In [17]:

bio.snapshot_system()["system_time"] - saved_state_no_membranes["system_time"]   # Indeed, the snapshots were taken at the same times

Out[17]:

0.0

In [18]:

bio.snapshot_system()["concentrations"] - saved_state_no_membranes["concentrations"]

Out[18]:

array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
        0., 0., 0., 0.]])

In [ ]:

In [19]:

# Further continue the diffusion
bio.diffuse(total_duration=12.5, fraction_max_step=0.9, show_status=True)    # we'll take bigger steps now
bio.visualize_system()

{'steps': 25001, 'system time': '20.001', 'time_step': 0.000499995}

Almost completely equilibrated...¶

In [ ]:

Part 3¶

Identical re-run of Part 2, EXCEPT that the permeability of `A` across the membranes (passive transport) is now MUCH LESS than its diffusion rate in water¶

In [20]:

# Initialize the system
chem_data = ChemData(names="A", 
                     diffusion_rates=600.)

bio = BioSim1D(n_bins=100, chem_data=chem_data)

bio.membranes().set_membranes(membranes=[ (20, 40) ])
bio.membranes().change_permeability("A", 30.)  # ******** This time, MUCH smaller than before (1/20-th)

In [21]:

# Adding a gradient slanting to the left
bio.inject_gradient("A", conc_left = 10., conc_right = 60.)
bio.describe_state()

SYSTEM STATE at Time t = 0:
100 bins and 1 chemical species
Membranes present:  [(20, 40)]

Out[21]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2	Bin 3	Bin 4	Bin 5	Bin 6	Bin 7	...	Bin 90	Bin 91	Bin 92	Bin 93	Bin 94	Bin 95	Bin 96	Bin 97	Bin 98	Bin 99
0	A	600.0	10.0	10.505051	11.010101	11.515152	12.020202	12.525253	13.030303	13.535354	...	55.454545	55.959596	56.464646	56.969697	57.474747	57.979798	58.484848	58.989899	59.494949	60.0

1 rows × 102 columns

In [22]:

# Visualize the complete initial state
bio.visualize_system(title_prefix="Initial concentration gradient.  Membranes shown in brown")

In [ ]:

In [23]:

# The first round of diffusion
bio.diffuse(total_duration=2.5, fraction_max_step=0.5, show_status=True) 
bio.visualize_system()

{'steps': 9001, 'system time': '2.5003', 'time_step': 0.000277775}

Notice the "slowdown" across the membranes, because (passive) transport across them is much slower that diffusion across the system¶

In [24]:

# Continue the diffusion
bio.diffuse(total_duration=5, fraction_max_step=0.5, show_status=True) 
bio.visualize_system()

{'steps': 18001, 'system time': '7.5005', 'time_step': 0.000277775}

In [25]:

# Further continue the diffusion
bio.diffuse(total_duration=12.5, fraction_max_step=0.9, show_status=True)   # we'll take bigger steps now
bio.visualize_system()

{'steps': 25001, 'system time': '20.001', 'time_step': 0.000499995}

The system is almost completely equilibrated, but that process continues to happen at a slower rate across the membranes¶

In [ ]:

Diffusion of a single chemical gradient, in the presence of membranes in its path (passive transport)¶

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

Part 1¶

No membranes; a simple diffusion¶

Let's save the complete state of the system, to contrast it with the simulation state at the same time in Part 2¶

Almost completely equilibrated...¶

Part 2¶

With membranes.¶

The permeability of A across the membranes (passive transport) is EQUAL to its diffusion rate in water¶

Does that turquoise curve (the concentrations of A across the length of the system) look familiar??¶

Almost completely equilibrated...¶

Part 3¶

Identical re-run of Part 2, EXCEPT that the permeability of A across the membranes (passive transport) is now MUCH LESS than its diffusion rate in water¶

Notice the "slowdown" across the membranes, because (passive) transport across them is much slower that diffusion across the system¶

The system is almost completely equilibrated, but that process continues to happen at a slower rate across the membranes¶

The permeability of `A` across the membranes (passive transport) is EQUAL to its diffusion rate in water¶

Does that turquoise curve (the concentrations of `A` across the length of the system) look familiar??¶

Identical re-run of Part 2, EXCEPT that the permeability of `A` across the membranes (passive transport) is now MUCH LESS than its diffusion rate in water¶