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The doubling rate of the cell is defined as t=ln(2)/u_net (can be how fast the cell grows)
If the u_net is negative, then the cell is dying.

The energy available to the cell can be u_net/u_mm (might need to change this)

where u_mm is the maximum growth for the "best" substrate or food source.

So obviously this only accounts for one
type of food source at a time, S. And cells sometimes need more than one
type of nutrient source to survive. (sugars, amino acids, etc. ) Or the
cell might be able to consume multiple nutrient subsets I.E. glucose,
lactose, fructose for simple sugars. I'm still working on how to
account for multiple foods for growth. (it may just end up being
something like S1/(k_s1+S1)*S2/(k_s2+S2) but I'm not sure if that is
scientifically accurate. But since cells tend to favor one type of food
source over another almost completely, (they will consume it until it is
gone) we can use this to get a pretty decent model. By having the
method just move down a list of preferred substrates and pick the one
that has the greatest k_m and the amount of S is not zero, or a critical
minimum.

So kd is not a single term but rather a collection, and it would be collectively: kd=sum(k_di)
where k_di is a death rate associated with a particular cause (temperature, toxins, maintenance etc)
Examples:

Temperature: kd=A*e^(-kdt/T) where Ed is activation energy for thermal death

Toxins: kd = kd_toxin*C_toxin.

Cell maintenance (the amount of nutrients required to sustain a cell) can also be accounted for here as

kd = kd_m (this is a necessary value otherwise the cells would be able to live with no food, which is not realistic)

So
oxygen is actually pretty easy to model, each cell species has a
critical oxygen level, DO_crit, where if the oxygen falls below this
point it inhibits cell growth.

This effect is actually linear and can be modeled as u_m=u_m*min(1 , DO/DO_crit)

Class
structure for each cellular 'species' would need a u_m and K_s or kd
for every compound it can interact with at the cellular level, as well
as Ea, Ed, kd_m, and DO_crit.

An auto_evolution function can
take a copy of a species profile, and modify it in a random but
restricted way. (there must be both a benefit, and a cost. ) I.E. maybe
increasing the u_m of one substrate or food source, but decreasing
another, or increasing maintenance costs.

The temperature energies must be linked in some way, so that each species has a small preferred range of temperatures.

This
will change how the cell is conditioned to live in each specific
environment, and eventually cells with a better fit will outgrow the
competition.

There would definitely have to be restrictions on what mutations are possible, (a food source should not also be a toxin).

The
other thing is that this relies on diverging, and converging
limitations. I.E. if there is always enough food, the system will keep
generating mutations. In order to put a survival of the fittest
situation there needs to be some type of stress on the biome. I.E.
sudden loss of a substrate, dramatic temperature change, increase in
toxins)

Biome
splitting. By assuming the conditions (T,S,Toxins) in each biome are
relatively constant per update, the u_net calculation only needs to be
done once per cell species, per biome per update. A major improvement
over doing it with each and every cell.

Species Extinction: If
the amount of cells of a species falls below a certain minimum
threshold, it should be declared extinct, instances of it should be
removed, and it should be cleared from further updates.

Exceptions:
The player's cells should always go through the u_net so that it
provides a more realistic experience for local environment.

First
and foremost, this equation does not account for how much substrate, S
is being consumed. I'm looking into that, and there is a solution, but
it requires experimental data which won't be available for theoretical
mutations. I'll keep looking or hash together a reasonable model.

What
happens on cell death? I'd imagine it would increase certain substrate
concentrations locally, but how would the breakdown of complex
molecules, back to simple substrates take place?