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

In [1]:

```
%matplotlib inline
from ecell4.prelude import *
```

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`

and`kD`

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
```

Calculating optimal reaction rates. `ka`

and `kd`

are intrinsic, `kon`

and `koff`

are effective reaction rates.

In [4]:

```
import numpy
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
opt_kwargs = {'legend': True}
```

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]:

```
ret1 = run_simulation(duration, y0=y0, model=m)
ret1.plot(**opt_kwargs)
```

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
ret2 = ensemble_simulations(duration, ndiv=20, y0=y0, model=m, solver=('spatiocyte', radius), repeat=N)
ret2.plot('o', ret1, '-', **opt_kwargs)
```

Simulating with `egfrd`

:

In [10]:

```
ret2 = ensemble_simulations(duration, ndiv=20, y0=y0, model=m, solver=('egfrd', Integer3(4, 4, 4)), repeat=N)
ret2.plot('o', ret1, '-', **opt_kwargs)
```