Attaining a Concentration Gradient¶

by continuosly injecting and draining, at opposite ends¶

The system starts out with a uniform concentration.
Then identical concentrations are repeatedly injected to the left and drained from the right

LAST REVISED: June 23, 2024 (using v. 1.0 beta34.1)

In [1]:

import set_path      # Importing this module will add the project's home directory to sys.path

Added 'D:\Docs\- MY CODE\BioSimulations\life123-Win7' to sys.path

In [2]:

from experiments.get_notebook_info import get_notebook_basename

from life123 import BioSim1D

import plotly.express as px

from life123 import ChemData as chem
from life123 import HtmlLog as log
from life123 import GraphicLog

In [3]:

# Initialize the HTML logging
log_file = get_notebook_basename() + ".log.htm"    # Use the notebook base filename for the log file
GraphicLog.config(filename=log_file,
                  components=["vue_heatmap_11", "vue_curves_3"])

-> Output will be LOGGED into the file 'gradient_1.log.htm'

In [4]:

# Set the heatmap parameters
heatmap_pars = {"range": [75, 125],
                "outer_width": 850, "outer_height": 150,
                "margins": {"top": 30, "right": 30, "bottom": 30, "left": 55}
                }

# Set the parameters of the line plots
lineplot_pars = {"range": [75, 125],
                "outer_width": 850, "outer_height": 250,
                "margins": {"top": 30, "right": 30, "bottom": 30, "left": 55}
                }

In [5]:

# Initialize the system with a uniform concentration (of the only species)
chem_data = chem(names=["A"], diffusion_rates=[0.6])
bio = BioSim1D(n_bins=9, chem_data=chem_data)

bio.set_uniform_concentration(species_index=0, conc=100.)

bio.describe_state()

SYSTEM STATE at Time t = 0:
9 bins and 1 species:
  Species 0 (A). Diff rate: 0.6. Conc: [100. 100. 100. 100. 100. 100. 100. 100. 100.]

In [6]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0:
       A
0  100.0
1  100.0
2  100.0
3  100.0
4  100.0
5  100.0
6  100.0
7  100.0
8  100.0

In [7]:

# Visualize the system's initial state
bio.visualize_system(caption="Diffusion")

In [8]:

# Show as heatmap
fig = px.imshow(bio.system_snapshot().T, 
                title= f"Diffusion. System snapshot as a heatmap at time t={bio.system_time}", 
                labels=dict(x="Bin number", y="Chem. species", color="Concentration"),
                text_auto=True, color_continuous_scale="gray_r")         # text_auto='.2f'

fig.data[0].xgap=4
fig.data[0].ygap=4

fig.show()

In [9]:

# Output to the log file
log.write("Creation of a gradient", style=log.h3)

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

# Output a heatmap to the log file
bio.single_species_heatmap(species_index=0, heatmap_pars=heatmap_pars, header=f"Time {bio.system_time} :\n", graphic_component="vue_heatmap_11")
# Output a line plot the log file
bio.single_species_line_plot(species_index=0, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

Creation of a gradient


System state at time t=0:
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

Start the simulation steps¶

In [10]:

delta_time = 1.

In [11]:

for i in range(501):
    # Inject to the leftmost bin
    bio.inject_conc_to_bin(bin_address=0, species_index=0, delta_conc=4, zero_clip = False)
    
    # Drain from the rightmost bin
    bio.inject_conc_to_bin(bin_address=8, species_index=0, delta_conc=-4, zero_clip = False)
    
    # Note: the NET GAIN of moles of A in the system is zero!
    
    # Diffuse for the time span delta_time
    status = bio.diffuse(total_duration=delta_time, time_step=0.1)

    
    if (i <= 12 and i%3 == 0) or (i%100 == 0):   # Display more frequently initially
        print()
        bio.describe_state(concise=True)
        
        # Show the system state as a line plot
        bio.visualize_system(caption="Diffusion")
        
        # Show as heatmap
        fig = px.imshow(bio.system_snapshot().T, 
                        title= f"Diffusion. System snapshot as a heatmap at time t={bio.system_time}", 
                        labels=dict(x="Bin number", y="Chem. species", color="Concentration"),
                        text_auto='.2f', color_continuous_scale="gray_r")

        fig.data[0].xgap=4
        fig.data[0].ygap=4

        fig.show()

        # Output a heatmap the log file
        bio.single_species_heatmap(species_index=0, heatmap_pars=heatmap_pars, header=f"Time {bio.system_time}\n", graphic_component="vue_heatmap_11")
        # Output a line plot the log file
        bio.single_species_line_plot(species_index=0, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

SYSTEM STATE at Time t = 1:
[[102.50172719 101.14444998 100.29805415 100.04921258 100.
   99.95078742  99.70194585  98.85555002  97.49827281]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 4:
[[107.42285216 104.74375636 102.29241276 100.85388504 100.
   99.14611496  97.70758724  95.25624364  92.57714784]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 7:
[[110.88507422 107.69013213 104.36899081 101.90793997 100.
   98.09206003  95.63100919  92.30986787  89.11492578]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 10:
[[113.59743191 110.06014065 106.11080705 102.82666877 100.
   97.17333123  93.88919295  89.93985935  86.40256809]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 13:
[[115.76754    111.96612839 107.52278434 103.57670355 100.
   96.42329645  92.47721566  88.03387161  84.23246   ]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 101:
[[124.65573484 119.78183626 113.32331552 106.66286788 100.
   93.33713212  86.67668448  80.21816374  75.34426516]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 201:
[[124.67064114 119.79494464 113.33304492 106.66804479 100.
   93.33195521  86.66695508  80.20505536  75.32935886]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 301:
[[124.67065158 119.79495382 113.33305173 106.66804841 100.
   93.33195159  86.66694827  80.20504618  75.32934842]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 401:
[[124.67065159 119.79495383 113.33305174 106.66804842 100.
   93.33195158  86.66694826  80.20504617  75.32934841]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

SYSTEM STATE at Time t = 501:
[[124.67065159 119.79495383 113.33305174 106.66804842 100.
   93.33195158  86.66694826  80.20504617  75.32934841]]

[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `gradient_1.log.htm`]

By now, the gradient has stabilized with¶

[A] = 124.67065159 on the left and [A] = 75.32934841 on the right¶

Note: if the drain is too large, relative to the diffusion rate, the smaller concentration could "saturate" at zero

In [ ]: