Pythonic Evolution – Part 1

This post is in different parts. The fact is that it requires quite a lot of time investment, something I really don’t have in this period.

A long time ago I wanted to play with the concept of genetic code, and how it represents nothing but a language to code for molecular machines. As the Jacquard loom, it’s nothing but a chemical punchcard who gets executed by the ribosome loom, and loomed into a protein. The fact behind evolution at this level is that if a small mutation happen in the punchcard by accident, and the resulting protein turns out to provide a competitive advantage for survival and reproduction, then this wrong punchcard will naturally exploit this advantage by becoming the predominant form. Even a very tiny advantage is sufficient, in the span of million of years, to reach fixation (the old code is completely replaced by the new one).

The math is simple. Here is a program that does it

normal = 500
mutated = 1

normal_survive_prob = 0.90
mutated_survive_prob = 0.91

for generation in xrange(1,1000):
    normal -= int(normal * (1-normal_survive_prob))
    mutated -= int(mutated*(1-mutated_survive_prob))

    normal *= 2
    mutated *= 2

    total = normal + mutated
    print "Generation %d -- normal : %d %%  mutated : %d %% " % \ 
          (generation, 100*normal/total, 100*mutated/total)

In this program (which has some simplifications, but the concept is there), we have a population of bacteria. We start with 500 normal bacteria, and only one mutant. This mutant has an advantage: its mutation makes him more likely to survive (for example, to an antibiotic, or to UV light from the Sun, or to oxygen). In this case the probability that the standard bacterium can survive is 90 %. In other words, if you have a large quantity of bacteria, some of these will die due to UV light. If you divide the number of survived bacteria by the number of bacteria you had, you will find out that 90 out of 100 survived, and the other 10 out of 100 died. The remaining 90 % do what bacteria do all the time: reproduce by splitting in two, meaning that if 40 bacteria survived the UV light and they reproduce, you will get 80 bacteria. In turn, some of them will die, and other will survive, and reproduce, and this goes on and on.The mutated bacteria has an advantage: its mutation makes it more resistent to UV light, so it has a slightly higher probability of surviving: 91 %

If you run the program, you will find out thatat generation 1, almost everything is made out of normal bacteria

Generation 1 -- normal : 99 %  mutated : 0 %

At generation 100, you see that the mutated ones start to be visible

Generation 107 -- normal : 99 %  mutated : 1 %

At generation 365, the mutated ones can start a political party

Generation 365 -- normal : 85 %  mutated : 14 %

After 525 generations, they are fifty/fifty:

Generation 525 -- normal : 49 %  mutated : 50 %

At generation 700, the mutated ones are the large majority

Generation 700 -- normal : 12 %  mutated : 87 %

And finally, at generation 1000 the normal ones are basically disappeared, and the mutated ones conquered their environmental niche:

Generation 1000 -- normal : 0 %  mutated : 99 %

Now, if you consider that a bacterial generation happens in days, or even hours, you see how it does not take much for bacteria to evolve. If our bacterium here divided every day, we would have a total fixation after just three years. If you assume that the difference in probability is 0.01 % (instead of 1% as in this example)  you will get the same result, it will just take more time (and even million of years is a blink of an eye against the age of the Earth).

The best part about evolution is that it works for everything behaving with the same modality. What you need is:

  1. An imperfect replicator, an entity able to produce a copy of itself, for example the DNA of our bacteria in the example above. The replication mechanism must have a certain degree of imperfection, so that some chance for occasional mutation must be possible, and consequently variability.
  2. Action of the replicator on the environment. For example, The DNA molecule, through a complex biological setup is able to produce proteins which, according to the laws of chemistry, influence the external world by digesting a metabolite and obtaining energy, or fighting an aggression to survive (to UV light, in our example) and reproduce.
  3. Variability of the replicator “phenotype” (which means the “final visible result” of the replicator). Small modifications (accidental or not) to the replicator will change its interaction with the external environment (for example, by granting him to survive better under UV light)
  4. Environmental conditions: the environment will propose conditions, for example availabe metabolites, temperature, pressure, UV light irradiation and these conditions could also change as time passes..
  5. Selective pressure: the interaction between the environmental conditions and the replicator phenotype will create a differentiation between replicators. Those better coping with the conditions will have higher reproductive chance than the others, producing a drift toward better replicators (in our case, the bacteria were under selective pressure because the UV light was killing them, but the mutated ones were more likely to survive)

A famous example of evolution at work is antibiotic resistance. The selective pressure of a poisonous substance (an antibiotic) kills the organisms not able to neutralize it, while those less sensitive to it survive and reproduce, creating more copies of so-called antibiotic resistant bacteria. Very soon, the antibiotic becomes ineffective against this new breed, and a new one must be invented. This is also the reason why antibiotics should be used sparingly, and always up to the end of the treatment, so to be sure that even those bacteria that are more resistant received a lethal dose and are therefore unable to start a resistant strain.

But the funny part of the evolutive setup is that it works no matter what the replicator and environment are….

Continued!

Comments are closed.