<p>Not in the way you suggest: a sequence of letters with the property of being immutable by any type of permutation on its constituent bases. I would be interested if anything of the likes exists in mathematics.</p>
<p>Having said that, there are examples of sequences that seem to have such property but only in the light of evolution and the biological processes that come with it:</p>
<p><a href="https://en.wikipedia.org/wiki/Ultra-conserved_element" rel="nofollow noreferrer">Ultra-conserved regions</a> have been described as sequences of about 200 base pairs that appear to be exactly the same from humans to mice. They have not experience change in about ~300 million years of evolution (!) and exposure to the various forces of mutation.</p>
<p>The reason for this is not an underlying 'invariant to permutation' property, but rather strong negative selection that prevents individuals that acquire changes on the sequence from being able to pass the changes over to their progeny, thus effectively maintaining only the original version in the population.</p>
<p>The exact mechanisms, functions and properties of these regions are under research. You might want to see if the invariant properties you have in mind have anything to do with these interesting regions.</p>

CC BY-SA 4.0
2021-10-18T08:24:47.543Z
Enzymes' catalytic site(s) are also very often left unchanged for the same reason. If there happen to be a mutation there, the protein's function might be compromised. But sometimes it is  instead enhanced....
flavinsky
CC BY-SA 4.0
2021-10-18T20:08:24.060Z
Very interesting. Based on the criteria that their existence is due to very strong selective pressure, and not due to external mechanisms, I figure it is possible that, given they are relative few in number, the UCR sequences that are not completely essential could be something of this kind, were some to be actually inessential, but it is also possible that the UCR change with species, so it may actually take an enormous to prove/disprove.
Elkin Montoya
CC BY-SA 4.0
2021-10-19T07:42:06.950Z
Yes, I guess UCRs are specific to particular groups of species and/or have certain upper limits to the evolutionary time within which they remain conserved. The UCR shared by humans and mice for instance were present in their common ancestor, so therefore all species derived from this common ancestor have them too. As usual, proving a certain property in this or other UCR example might well lead to some degree of generalization,
JRodrigoF
CC BY-SA 4.0
2021-10-17T09:51:04.657Z
2021-10-17T15:08:44.577Z
2021-10-17T15:08:44.577Z
JRodrigoF
<p>This question is more on the theoretical-encoding side. Given the known kinds of genetic mutation, transposition, deletion, and such, what can be said about genes that would be left untouched by the mutation, left invariant by the permutation, if you will? Are there any such sequences? Would they be more common in a population, if not detrimental?</p>

CC BY-SA 4.0
2021-10-10T23:53:34.557Z
By definition, mutations are genetic variation, so a gene cannot be “left invariant by permutation”. Are you perhaps referring to variation in the proteins encoded by protein-coding genes or the downstream phenotypes?
acvill
CC BY-SA 4.0
2021-10-18T00:12:03.810Z
Have you looked up the chemical nature of mutations? Mixups like "swap the first base for the third" are not the most common form of mutation, not by a long shot.
swbarnes2
<genetics><molecular-genetics><phylogenetics>
Is there any genetic sequence, such that, for all the kinds of mutation, it still has a 100% probability to be passed on?
# Is there any genetic sequence, such that, for all the kinds of mutation, it still has a 100% probability to be passed on?

(Asked by: username_0 on 2021-10-10)

This question is more on the theoretical-encoding side. Given the known kinds of genetic mutation, transposition, deletion, and such, what can be said about genes that would be left untouched by the mutation, left invariant by the permutation, if you will? Are there any such sequences? Would they be more common in a population, if not detrimental?

**Tags:** genetics, molecular-genetics, phylogenetics
> **Comments:**
> **username_1**: By definition, mutations are genetic variation, so a gene cannot be “left invariant by permutation”. Are you perhaps referring to variation in the proteins encoded by protein-coding genes or the downstream phenotypes?  
> **username_2**: Have you looked up the chemical nature of mutations? Mixups like "swap the first base for the third" are not the most common form of mutation, not by a long shot.  

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## 1 answers

### Answer by username_3 on 2021-10-17. Score: 1

Not in the way you suggest: a sequence of letters with the property of being immutable by any type of permutation on its constituent bases. I would be interested if anything of the likes exists in mathematics.

Having said that, there are examples of sequences that seem to have such property but only in the light of evolution and the biological processes that come with it:

[Ultra-conserved regions](https://en.wikipedia.org/wiki/Ultra-conserved_element) have been described as sequences of about 200 base pairs that appear to be exactly the same from humans to mice. They have not experience change in about ~300 million years of evolution (!) and exposure to the various forces of mutation.

The reason for this is not an underlying 'invariant to permutation' property, but rather strong negative selection that prevents individuals that acquire changes on the sequence from being able to pass the changes over to their progeny, thus effectively maintaining only the original version in the population.

The exact mechanisms, functions and properties of these regions are under research. You might want to see if the invariant properties you have in mind have anything to do with these interesting regions.

> **Comments:**
> **username_4**: Enzymes' catalytic site(s) are also very often left unchanged for the same reason. If there happen to be a mutation there, the protein's function might be compromised. But sometimes it is  instead enhanced....  
> **username_0**: Very interesting. Based on the criteria that their existence is due to very strong selective pressure, and not due to external mechanisms, I figure it is possible that, given they are relative few in number, the UCR sequences that are not completely essential could be something of this kind, were some to be actually inessential, but it is also possible that the UCR change with species, so it may actually take an enormous to prove/disprove.  
> **username_3**: Yes, I guess UCRs are specific to particular groups of species and/or have certain upper limits to the evolutionary time within which they remain conserved. The UCR shared by humans and mice for instance were present in their common ancestor, so therefore all species derived from this common ancestor have them too. As usual, proving a certain property in this or other UCR example might well lead to some degree of generalization,  

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