Membranes in 1D : Diffusion and Passive Transport across Membranes¶

Simple scenarios with 1 chemical¶

TAGS : "membranes 1D", "basic", "quick-start", "diffusion 1D", "under-the-hood"¶

In [1]:

LAST_REVISED = "May 19, 2025"
LIFE123_VERSION = "1.0.0rc3"        # 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, os
#os.getcwd()
#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 [ ]:

Prepare the initial system¶

with a single chemical A

In [5]:

chem_data = ChemData(diffusion_rates=10.)   # Name "A" automatically assigned to single chemical

bio = BioSim1D(n_bins=4, chem_data=chem_data)

In [6]:

initial_conc = [20, 50, 150, 250]

In [7]:

bio.set_species_conc(conc_list=initial_conc, chem_index=0) 

bio.describe_state()

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

Out[7]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2	Bin 3
0	A	10.0	20.0	50.0	150.0	250.0

In [8]:

bio.system_snapshot()

Out[8]:

	A
0	20.0
1	50.0
2	150.0
3	250.0

In [9]:

bio.visualize_system()   # Line curve view

In [10]:

bio.system_heatmaps()

In [ ]:

Add Membranes¶

The bins would normally mix up by diffusion, but we'll prevent that by inserting impermeable membranes¶

In [11]:

bio.set_membranes(membranes=[ (1,2) ])    # By default impermeable

In [12]:

bio.membranes_obj

Out[12]:

[(1, 2)]

In [13]:

bio.describe_state()

SYSTEM STATE at Time t = 0:
4 bins and 1 chemical species
Membranes present:  [(1, 2)]

Out[13]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2	Bin 3
0	A	10.0	20.0	50.0	150.0	250.0

In [14]:

bio.system_heatmaps()

In [ ]:

Now, let's start the diffusion¶

In [15]:

bio.diffuse(time_step=0.02, n_steps=1)

Out[15]:

{'steps': 1, 'system time': '0.02'}

In [16]:

bio.system_snapshot()

Out[16]:

	A
0	20.0
1	50.0
2	170.0
3	230.0

In [17]:

bio.system_heatmaps()

Nothing has changed in the 2 leftmost bins, as a result of the impermeable membranes¶

By contrast, diffusion is progressing between the 2 rightmost bins

Technical side note: since we're using, by default, simple 3-1 stencils for the diffusion step, the concentration increment in bin 3, and its corresponding decrement in bin 2, is:

In [18]:

0.02 * 100 * 10 / (1*1)    # (Time step) * (Delta concentration) * (Diffusion rate const) / (bin length squared)

Out[18]:

20.0

The 150 initial value in bin 2 increased by 20 to 170, and the 250 value in bin 3 correspondingly decreased to 230

In [ ]:

Let's further advance the diffusion, by many more steps¶

In [19]:

bio.diffuse(time_step=0.02, n_steps=14)

Out[19]:

{'steps': 14, 'system time': '0.3'}

In [20]:

bio.system_heatmaps()

In [ ]:

Now, let's assign a small permeability to our single chemical `A` to the membranes (by passive transport)¶

In [21]:

bio.change_permeability("A", 1.)

In [22]:

bio.diffuse(time_step=0.02, n_steps=1)

Out[22]:

{'steps': 1, 'system time': '0.32'}

In [23]:

bio.system_heatmaps()

Passive transport across membranes is now taking place both out of bin 1 (to its left neighbor) and into it (from its right neighbors)¶

Diffusion is continuing normally between the 2 rightmost bins

Technical side note - Passive membrane transport out of bin 1 (conc. 50) into bin 0 (conc. 20) in this single step was:

In [24]:

30 * 1 * 0.02   # (Delta conc) * Permeability * (Time step) , since all bin sizes are 1

Out[24]:

0.6

The concentration of bin 0 has increased from 20 to 20.6 during this single step.
The concentration of bin 1 is also increasing, because its loss to bin 0 is more than compensated by its gain from bin 2 (bigger conc. difference)

In [ ]:

Let's continue to advance the diffusion¶

In [25]:

bio.diffuse(time_step=0.02, n_steps=4)

Out[25]:

{'steps': 4, 'system time': '0.4'}

In [26]:

bio.system_heatmaps()

In [27]:

bio.diffuse(time_step=0.02, n_steps=45)

Out[27]:

{'steps': 45, 'system time': '1.3'}

In [28]:

bio.system_heatmaps()

In [29]:

bio.diffuse(time_step=0.02, n_steps=500)

Out[29]:

{'steps': 500, 'system time': '11.3'}

In [30]:

bio.system_heatmaps()

Verify that the total amount of our chemical present hasn't changed; it has simply shifted across bins¶

In [31]:

bio.check_mass_conservation(expected=sum(initial_conc), chem_index=0)

Out[31]:

True

In [ ]:

Membranes in 1D : Diffusion and Passive Transport across Membranes¶

Simple scenarios with 1 chemical¶

TAGS : "membranes 1D", "basic", "quick-start", "diffusion 1D", "under-the-hood"¶

Prepare the initial system¶

Add Membranes¶

The bins would normally mix up by diffusion, but we'll prevent that by inserting impermeable membranes¶

Now, let's start the diffusion¶

Nothing has changed in the 2 leftmost bins, as a result of the impermeable membranes¶

Let's further advance the diffusion, by many more steps¶

Now, let's assign a small permeability to our single chemical A to the membranes (by passive transport)¶

Passive transport across membranes is now taking place both out of bin 1 (to its left neighbor) and into it (from its right neighbors)¶

Let's continue to advance the diffusion¶

Verify that the total amount of our chemical present hasn't changed; it has simply shifted across bins¶

Now, let's assign a small permeability to our single chemical `A` to the membranes (by passive transport)¶