# %% [markdown]
# # Chemostat
#
# A chemostat can maintain a concentration of nutrients in a container by flowing in and flowing out nutrients each at a constant rate.
# Here we will set up a simulatable chemostat with a clonal and unevolving unicellular organism, and adjust the flow rate to observe the effect on the growth rate of the cells.
# More specifically, we will assume that a cell `C` replicates following metabolism of three units of the nutrient `N`, and that cells die memorylessly at a constant stochastic rate.

# %%
from pykappa import System
import matplotlib.pyplot as plt

system = System.from_ka(
    """
    %init: 10 C(n{0})  // Start with a few cells

    %obs: 'C' |C()|

    %var: 'inflow' 1  // Nutrient inflow rate
    . -> N() @ 'inflow'
    N() -> . @ 0.1  // Nutrient outflow

    // Metabolism
    C(n{0}), N() -> C(n{1}), . @ 0.5
    C(n{1}), N() -> C(n{2}), . @ 0.5
    C(n{2}), N() -> C(n{3}), . @ 0.5

    C(n{3}), . -> C(n{0}), C(n{0}) @ 0.1 // Cell division
    C() -> . @ 0.01  // Cell death
    """,
    seed=42,
)

# %% [markdown]
# If we started with only, say, one cell, it would be reasonably likely that the population would die out before replicating sufficiently to virtually preclude extinction.

# %% [markdown]
# Let's start the chemostat and observe the population size:

# %%
while system.time < 10**3:
    system.update()
system.monitor.plot()
plt.show()

# %% [markdown]
# Now let's double inflow of the nutrient without changing outflow.
# The population size increases.

# %%
system["inflow"] = 2

while system.time < 5 * 10**3:
    system.update()
system.monitor.plot()
plt.show()