Reversible (Diffusion-limited)

This is for an integrated test of E-Cell4. Here, we test a simple reversible association/dissociation model in volume.



In [1]:

    
%matplotlib inline
import numpy
from ecell4 import *
from ecell4.extra.ensemble import ensemble_simulations
from ecell4_base.core import GSLRandomNumberGenerator, Integer3

Parameters are given as follows. D, radius, N_A, U, and ka_factor mean a diffusion constant, a radius of molecules, an initial number of molecules of A and B, a ratio of dissociated form of A at the steady state, and a ratio between an intrinsic association rate and collision rate defined as ka andkD below, respectively. Dimensions of length and time are assumed to be micro-meter and second.



In [2]:

    
D = 1
radius = 0.005
N_A = 60
U = 0.5
ka_factor = 10  # 10 is for diffusion-limited



In [3]:

    
N = 20  # a number of samples
rng = GSLRandomNumberGenerator()
rng.seed(0)

Calculating optimal reaction rates. ka and kd are intrinsic, kon and koff are effective reaction rates.



In [4]:

    
kD = 4 * numpy.pi * (radius * 2) * (D * 2)
ka = kD * ka_factor
kd = ka * N_A * U * U / (1 - U)
kon = ka * kD / (ka + kD)
koff = kd * kon / ka

Start with no C molecules, and simulate 3 seconds.



In [5]:

    
y0 = {'A': N_A, 'B': N_A}
duration = 0.35
T = numpy.linspace(0, duration, 21)

Make a model with effective rates. This model is for macroscopic simulation algorithms.



In [6]:

    
with species_attributes():
    A | B | C | {'radius': radius, 'D': D}

with reaction_rules():
    A + B == C | (kon, koff)

m = get_model()

Save a result with ode as obs, and plot it:



In [7]:

    
obs = run_simulation(numpy.linspace(0, duration, 101), y0, model=m,
                     return_type='observer', solver='ode')
viz.plot_number_observer(obs)

Make a model with intrinsic rates. This model is for microscopic (particle) simulation algorithms.



In [8]:

    
with species_attributes():
    A | B | C | {'radius': radius, 'D': D}

with reaction_rules():
    A + B == C | (ka, kd)

m = get_model()

Simulating with spatiocyte. voxel_radius is given as radius. Use alpha enough less than 1.0 for a diffusion-limited case (Bars represent standard error of the mean):



In [9]:

    
alpha = 0.03
ensemble_simulations(T, y0, model=m, opt_args=('o', obs, '-'),
                     solver=('spatiocyte', radius), n=N)

Simulating with egfrd:



In [10]:

    
ensemble_simulations(T, y0, model=m, opt_args=('o', obs, '-'),
                     solver=('egfrd', Integer3(4, 4, 4)), n=N)