Complicated Patterns Result from Simple Rules but Only the Useful Patterns are Stable

As we had seen from Steven Wolfram's cellular automata complicated patterns can result from simple rules. Evolution does not need complicated rules to conduct complexity (see Figure 78). The simple fact that for each position only 4 different nucleotides are taken into account when constructing the genetic code leads to an incredible number of possible configurations for a sequence of hundred nucelotides (for 100 nucleotides 4100 configurations are thinkable which equals about 1025, i.e. the number of atoms in one pound of carbon). Some people believe that this enormous number is an indication for the fact that the world can not be a product by chance, however these interpretations often neglect a series of further details important to know when the real probability for random developments in evolutionary processes shall be correctly estimated.

The estimation of the possible configurations of a polypeptide chain in proteins and the comparison of this number with the time necessary to conduct the folding of a protein by chance lead to the Levinthal-paradox found by Cyrus Levinthal in 1969. Due to the very large number of degrees of freedom in an unfolded polypeptide chain a number of possible conformations in the order of 10100 has to be “tested” until the right configuration is found. Levinthal noted that the time necessary to “find” the right folding would exceed the age of the universe by far. (Levinthal, 1969).

Detail of the Mathematica® calculation of the “rule 30”

Figure 78. Detail of the Mathematica® calculation of the “rule 30” (see Figure 1 and Figure 2) of Steven Wolfram’s cellular automata (left side) in comparison to a pigmented seashell (right side) (Coombes 2009). Image reproduced with permission.

This is true even if conformations are sampled at rapid (nanosecond or picosecond) rates. The “paradox” is that most small proteins fold spontaneously on a millisecond or even microsecond time scale. Of course Levinthal was aware of this fact and he had already suggested favorized pathways for the folding process (Levinthal 1968). He suggested that the paradox can be resolved if “protein folding is sped up and guided by the rapid formation of local interactions which then determine the further folding of the peptide; this suggests local amino acid sequences which form stable interactions and serve as nucleation points in the folding process” (Levinthal, 1969). Today it is known that the protein folding follows an energetic landscape and that in case that a single configuration is stable it is kept in this stable position and a large majority of further configurations is not tested anymore because they become energetically disadvantaged due to the presence of the stable partial configuration that lead the protein into an energetic local minimum. The correct configuration of local interactions determines the further folding of the peptide. The local stable interactions serve as nucleation points. The process is comparable to a skier that has to test a ski slope. The skier could do that following a large number of pathways. However there is a small selection of all possible slopes in the beginning that clearly point to the energetic minimum, i.e. downhill direction. The skier will follow this route especially if he does not use his free will. As soon as he had started and finished already some part of the skiing slope he will not be able to return to the starting point again and test for another route. So the Levinthal paradox is similar to the assumption that a skier would never reach the valley as there are so many possible routes leading from the top to the bottom. But we know that in spite of the fact that such a large number of pathways is possible is possible he will quickly reach the valley. The skier just takes the right path - and we should be aware that the answer to the Levinthal-Paradox is similarly trivial somehow. The image of the “correctly chosen pathway” is representing a selection process: There is a constraint (the energetic landscape, for the skier the gravity) that choses the right path from all possible pathways. The paradox is resolved by a selection process that was unknown or underestimated when the paradox was formulated.

If we look at evolution the Levinthal-paradox is sometimes applied to genes. Some people argue that the age of the universe would not be large enough to develop something as complicated as a human being. However such an assumption is rather baseless and probably does not take into account some constraints evolution is facing. This might be even more true as genetics comprises features which are not mentioned up to now. One very important factor that drives the diversity of genes is reproduction. Each gene tends to reproduce itself due to the double helix character of the DNA. However reproduction can only occur if a minimum stability of the gene is guaranteed as a prerequisite and in consequence each gene which undergoes a mutation that delivers an advantage for the organism hosting that gene is reproduced.

It is a bit misleading to argue that any complex gene will be found at any future time by chance as this is underestimating the power of reproduction and selection that both work on the pool of genetic variation. Assuming an absolute random process that has to occur until the final gene configuration for a complex organism is found relies on the so called infinite monkey theorem. The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. This argument is surely true. However it can be abused arguing that the time needed to find only one of Shakespeare's great works might exceed the age of the universe. In an infinite number of time any finite text would be typed - but the time is not infinitely most probable.

The whole concept is misleading and also the actual variants of the theorem including multiple and even infinitely many typists, and the

According to the infinite monkey a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of Willia

Figure 79. According to the infinite monkey a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.

target text varying between an entire library and a single sentence do not respect the important mechanisms of reproduction and selection which are necessary to correctly understand evolution. To correlate the infinite monkey theorem with evolution we would have to introduce two significant variations that respect reproduction and selection in a correct way. Reproduction occurs if any of the mutations happening when the large number of typing monkeys (each single evolving organism and it means each individual of a population should be represented by a single monkey) just finds a short “correct” sequence by chance. This might be a single word or it can be half a page, any change in the text that is not contraproductive meaning that it does not lead to a disadvantage in reproduction will be copied many times. The importance of reproduction is even bigger if a mutation in the text leads to a reproduction advantage for the new mutant. In that case the new, meaningful mutation which, as we should keep in mind, is possibly just one correct word in the large text, will be reproduced in larger number than the other sequences. The new mutant will possibly quickly grow over the whole population. This effect might additionally be stronger if we keep in mind that next to the reproduction capability other selection rules exist like predators or the natural lifespan. If a new predator shows up he might be hungry for the monkey's texts and just eats them up, except one fragment that contains a specially long text sequence of Shakespeare's Romeo and Juliet and is therefore able to escape. As now there is much space for the diminished population to grow it might be possible that after a short time only this surviving text fragment is copied many times and present everywhere (all others are extinguished) and just in the next round all monkeys start to type on the text that has been largely worked over and contains the correct text sequence in all copies now.

Such a leap of evolution in all monkeys texts does not follow severe mutations but free space for the genetic diversity to grow together with selection pressure. A prominent example for such a leap of evolution is given in the next chapter 5.3.

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