Talmudic Question #89

Of the ~10³⁰ prokaryotic cells on Earth, what proportion would you guess are viable (using your favorite criterion for viability)?

Comments

[qetzal]

I like Jason' steady-state analysis, too, except I think there's another factor to consider. How long does a dead cell persist?

I think the percentage of live cells will depend on the degradation half-life of the dead cells (i.e. the time it takes a dead cell to degrade to the point that it no longer counts as a cell at all).

If the degradation half-life is the same as the generation time, then there should be 50% live cells. If the degradation time is longer (shorter), the percentage of live cells should be lower (higher) than 50%.

[Doug]

What is "viability" - the ability of the whole organism to reproduce or the survival of a genome (with adequate potential to be transmitted to another organism)? I admit it is a bit of a stretch to argue that a chunk of DNA large enough to be considered as representing a specific organism would be able to subvert a pasing microbe. However, a passing microbiologist could facilitate that event. Hence the argument can be reduced to that of what % of a genome is required to define an organism. Then one wonders how long that %age would remain once self-replication of an organism has been inactivated. In this argument, the total number of "viable" microorganisms is >10e30 by a factor which I chose to argue is 5x but with no basis for that number whatsoever (other than a specious guestimate of the minimum genome size of a bacterium).
In the end, the answer to the question must be 100% since the measurement of total numbers will include a definition of what constitutes an organism. This definition must be based in DNA and such DNA can be recovered, amplified, and restored to a self-replicating condition.

[Doug]

Where viable means "not dead", the proportion is probably 100%. Where viable means "contains intact DNA", the proportion is arguably around 500%. Might just as well ask "How long is a piece of string?"

Elio replies: That's the idea behind Talmudic Questions, they allow you to set your own definitions. So, assume whatever length you want for the piece of string. By 500% what do you mean? What's the denominator? Shouldn't that be 100%?

[Jason]

If we assume that the population of cells is constant (10^30) and each cell can divide into two cells, then one of those two must die or the population of cells will rise. Conversely, one of those two must live or the population of cells will lower.

So, I would guess that about 50% of cells are viable if ability to replicate in the given environment is the measure of viability.

If a cell is considered viable if it will replicate given adequate nutrients, then 99% or more are viable, since per replication mutation rates are said to be somewhere from 1 in 100 to 1 in 1000.

Elio replies: Nice arguments. Thanks a lot.