See also

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This is for an integrated test of E-Cell4. Here, we test homodimerization and annihilation.

```
[1]:
```

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

Parameters are given as follows. `D`

, `radius`

, `N_A`

, and `ka_factor`

mean a diffusion constant, a radius of molecules, an initial number of molecules of `A`

, 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.

```
[2]:
```

```
D = 1
radius = 0.005
N_A = 60
ka_factor = 0.1 # 0.1 is for reaction-limited
```

```
[3]:
```

```
N = 30 # a number of samples
```

Calculating optimal reaction rates. `ka`

is intrinsic, `kon`

is effective reaction rates. Be careful about the calculation of a effective rate for homo-dimerization. An intrinsic must be halved in the formula. This kind of parameter modification is not automatically done.

```
[4]:
```

```
import numpy
kD = 4 * numpy.pi * (radius * 2) * (D * 2)
ka = kD * ka_factor
kon = ka * kD / (ka + kD)
```

Start with `A`

molecules, and simulate 3 seconds.

```
[5]:
```

```
y0 = {'A': N_A}
duration = 3
opt_kwargs = {'xlim': (0, duration), 'ylim': (0, N_A)}
```

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

```
[6]:
```

```
with species_attributes():
A | {'radius': radius, 'D': D}
with reaction_rules():
A + A > ~A2 | kon * 0.5
m = get_model()
```

Save a result with `ode`

as `obs`

, and plot it:

```
[7]:
```

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

Simulating with `gillespie`

:

```
[8]:
```

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

Simulating with `meso`

:

```
[9]:
```

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

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

```
[10]:
```

```
with species_attributes():
A | {'radius': radius, 'D': D}
with reaction_rules():
A + A > ~A2 | ka
m = get_model()
```

Simulating with `spatiocyte`

:

```
[11]:
```

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

Simulating with `egfrd`

:

```
[12]:
```

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