10 ms·

Something that I always found fascinating is how DNA is a base 4 information format. There's this thing called radix economy, which is basically an expression o

Something that I always found fascinating is how DNA is a base 4 information format. There's this thing called radix economy, which is basically an expression of how efficient a number system is. Base e is the theoretical maximum, and so base 3 is the closest integer. Obviously if you have a special use case, then that may dominate your radix economy (like hex, b64, etc...), but for general purpose information purposes, the order base 3, base 4, then base 2. This present a lot of interesting questions to me. Like, why didn't DNA end up as base 3? (probably because 4 naturally lends itself to pairs of 2). Also, this idea of radix economy goes beyond just the encoding of information and is represented in logical economy as well. So for example, ternary logic is (much) more efficient than binary logic. Having that 3rd state just makes problem solving much more elegant. To that end, I have always wondered how nature has exploited this 4-state number system logically. Like, are there all sorts of exotic logic gates that come from a 4 state system?

go_elmo 3y ago
Might error-correction play a role? Having a lightly inefficient base 4 system might provide capacity for the surplus error correcting code information capacity?
- Faaak 3y ago
  One mutation in a base pair can lead a totally different amino acid (c.f the genetic code), so I doubt it ?
  - go_elmo 3y ago
    True, iff the error persists correction cycles which are present, how exactly they work / if theyre comparable with eccs I dont know.
  - toufka 3y ago
    BUT, if you look at the codon table, precisely because it's base-4 and not base-3, many base flips are silent when coded. By using base-4, there's enough space to permit lossiness of the coding itself - given the number of amino acids and the 3-NT encoding. So you really aren't optimizing JUST for nucleotide encoding, but you're also optimizing in concert with 3-nt/AA, and 20AA codes. So if you have to optimize for information density and fidelity, given X-nucleotides, Y nucleotides/AA, and Z AAs, and sample as much chemical and physical diversity in those AAs life has settled upon: X=4, Y=3, Z=20. If we went with X=3, you might need Y=4 to get the same kind of fidelity, but that cranks up your energy costs by 30% (from 3 to 4 NT per AA).
- icoder 3y ago
  DNA mostly relies on the fact that there's 2 strands that are (logically speaking) a mirror copy of each other (a C is paired with a G and vice versa, an A to a T and vice versa), it's like RAID 3 with only 2 disks (one being parity). Apart from repairing structural damage such as missing bonds, the cell can even repair missing bases or non-straight breaks without loss. This mechanism is also used for replication: the entire strand is split and each half is completed with its mirror counterpart.
  - go_elmo 3y ago
    Im aware of that, but was rather thinking about ECCs like hamming-code, that are able to correct single sequences of info based on surplus info in that same string.
    - dekhn 3y ago
      Nothing algorithmically sophisticated, but DNA repair enzymes already do this.
icoder 3y ago
DNA is not really processed like that, afaik. Mostly, each 3 bases code for an amino acid, which are glued together to a string (protein), which folds in a 3D structure based on the characteristics of all amino acids. Some DNA is used to attract other proteins, or even interact with DNA elsewhere on the strand, or is translated to RNA (one-on-one) which can then have a function based on its sequence or the structure it folds into. Any 'logic' there is, is built _on top_ of this.
- jacquesm 3y ago
  Any logic that we are currently aware of. DNA contains many unsolved mysteries and I expect that gift to keep on giving for a long time to come.
usrbinbash 3y ago
> Like, why didn't DNA end up as base 3? Why did we end up with only 20 proteinogenic amino acids? Why are vertebrate neural architectures inverted (cell bodies on the inside, connections on the outside, even though the other way round way (eg. like a squids brain is organised) is easier and less inhibitive to growth? 2 Reasons: a) Because nature and evolution cannot engineer. Random mutation, recombination and natural selection are the only mechanisms available. Things get selected if they outcompete existing alternatives, they don't need to be the best solutions. b) All solutions have to be built by modifying what already exists. Evolution doesn't get to do greenfield projects, because anything that has to start from scratch is so disadvantaged in natural selection compared to already evolved complex life, it will fail. This leads to systems that, from an engineering point of view, don't always make a lot of sense. Eg. the architecture of the vertebrate neural system creates a lot of issues (eg. our light sensitive cells point in the wrong direction). The only way this makes any sense if when one looks at how the neural tube (the precursor to the backbone) is formed by the endodermis folding in on itself. This process is so deeply at the root of the Chordata, and so many other things depend on it, that it simply cannot change any more. Many many biological systems are "legacy systems" in the truest sense of the word: Solutions produced a long time ago that may have many problems, but are simply too deeply enmeshed with everything that came after, that they are now impossible to change.
- sparrowInHand 3y ago
  Short answer: Likelihood of noise (brownian motion) producing the element and keeping it interacting. Then once it gets going, likelihood of keeping state, while interacting.
- t_serpico 3y ago
  A classic armchair response. DNA has complementary nucleotides (AT,GC) that facilitates its pairing. Base 3 wouldn’t work in that sense. Also, you can’t forget about the genetic code. See https://arxiv.org/pdf/q-bio/0605036.pdf https://arxiv.org/pdf/q-bio/0605036.pdf for interesting thoughts. Remember, evolutionary biology is a field and people think about these questions!
  - 3y ago
jszymborski 3y ago
There's a lot of interesting things to consider. One, is that base 4 makes a lot of sense for the stability of DNA structures. You have two purines, two pyrimadines. Another is that partly because codons are degenerate, the distribution is way off a uniform distribution. For chemistry and mol bio reasons, the distribution of AGTC is very skewed. When i fully wake up, this might be a fun blog post to draft.
Llamamoe 3y ago
Radix is important for digit-efficiency, but in a biological system that's not necessarily related to molecule size efficiency.
- pythonguython 3y ago
  I’m also failing to see how digit efficiency would be important in DNA. In fact, it seems that a high base system would be more efficient. If you had 80 nucleobases instead of 4, each base pair would contain far more information
  - JumpCrisscross 3y ago
    > If you had 80 nucleobases instead of 4, each base pair would contain far more information Which is a problem given DNA is a lossy format.
    - Llamamoe 3y ago
      Strictly speaking, you could encode more error-correction bits into a higher nucleobase count but that'd pretty much require intelligent design, and wouldn't necessarily be viable for microorganisms to have that many proteins handling all the metabolic scaffolding.
  - asimpletune 3y ago
    The efficiency comes from the ratio of the alphabet to the number of character places needed to express them. Otherwise why not base a million? Or a billion? This ratio is what leads to base e being the theoretical maximum.
throwawaymaths 3y ago
It's probably not base four because you have to stretch out more pairs to match up four pairs and that's entropically disfavored. However ribosomes can accomodate a four pair matching, though at a very reduced yield (unless you think Schultz's postdoc fabricated those data)
PaulHoule 3y ago
DNA has the same limitation that many serial protocols have: if you repeat the same base pairs (e.g. "AAAAAAAAAAAAAAAAAAAAAA") you will have trouble w/ the DNA not spiraling correctly. Some sequences of 2-6 repeated base pairs seem to "deliberately" cause variant behavior in DNA and RNA, see https://en.wikipedia.org/wiki/Repeated_sequence_(DNA) https://en.wikipedia.org/wiki/Repeated_sequence_(DNA) Many real wire protocols have mechanisms to prevent repeated sequences entirely https://en.wikipedia.org/wiki/8b/10b_encoding https://en.wikipedia.org/wiki/8b/10b_encoding DNA coding for real proteins is unlikely to be too terribly repetitive but I image a long α helix could have a repetitive amino acid sequence. Many amino acids can be coded with variant codons, I guess if repetition were a problem in a particular gene natural selection could step in.
- deleted 3y ago
  [deleted]
- amateurCoder5 3y ago
  Repetitive DNA sequences do occur and do cause problems. https://en.m.wikipedia.org/wiki/Trinucleotide_repeat_expansion https://en.m.wikipedia.org/wiki/Trinucleotide_repeat_expansi... TLDR: DNA triplet repeat expansions cause diseases like Huntington's disease.
dylan604 3y ago
>So for example, ternary logic is (much) more efficient than binary logic. Having that 3rd state just makes problem solving much more elegant. Binary for electronics is obvious because there are 2 states in electric components: on or off. There is no 3rd option.
- nicoburns 3y ago
  I believe "on" and "off" in electronics typically correspond to different voltage levels. So you absolutely could have a third intermediate state if you wanted to. Flash memory does this (and even sometimes has 4 states). I guess designing switches (transistors) that could take advantage of and propagate these extra states could be tricky though.
  - ohwellhere 3y ago
    https://en.wikipedia.org/wiki/Ternary_computer https://en.wikipedia.org/wiki/Ternary_computer
toufka 3y ago
You (at least) have 3 systems that are optimized in concert in a (our) DNA/Protein world. DNA base set, Amino acid set, Translation layer between DNA/Proteins. Currently, we've got: 4 DNA bases, 3 bases/AA, 20 AAs; 4^3 => 20 If you change one of those numbers, you'll need to rejigger the rest, and you'd need to reoptimize. And there are competing goals which at least include: - maximize access to biophysical/chemical diversity - minimize energy expenditure to produce each component, chemically - minimize energy expenditure to both copy instructions & produce products - maximize information fidelity - minimize or at least degrade gracefully in the context of errors In the context of a 3-base system, you very well could throw off those optimizations given the consequences for the other 2 parameters (#AA & nt/AA). 3^3 = 27, which is very close to the maximum of 20 amino acids. Which means you'd probably need a 4nt->AA translation layer to keep the same number of AAs, and that alone would add 30% more energy expenditure. If you kept the 3nt->AA system you'd BOTH need to reduce the number of accessible amino acids AND you'd lose some of the error correction mechanisms of having degenerate codons code for the same amino acid.
dahfizz 3y ago
Why do my eyelashes, meant to protect my eyes, fall into my eyes? Why do my cheeks/tongue sometimes get in the way of my teeth so that I bite them? And why do they then get inflamed so that I continually byte them for the next few days? We are all a bunch of biological goop resulting from random processes. Don't expect optimal solutions from evolution. There is no "why".
- erenyeager 3y ago
  There is a why and reasons we find and insights we glean. The denial of a why is itself an anthropocentric take on biology, influenced by Darwinian thought. But any biological system we study we need a why, otherwise the corollary of your statement essentially leads to no learning or understanding, because everything becomes “arbitrary” and explained away by randomness. Ironic to say it’s not optimal, really we don’t have the full knowledge. Often when we learn more we learn how little we really know about biology.
guerrilla 3y ago
> (probably because 4 naturally lends itself to pairs of 2). Why would pairs of two be favorable? > So for example, ternary logic is (much) more efficient than binary logic. Having that 3rd state just makes problem solving much more elegant. What do you have in mind here? > Like, are there all sorts of exotic logic gates that come from a 4 state system? I don't know but you may be interested in this [1]. 1. https://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADi https://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADi
asdff 3y ago
On paper this might be an interesting game, but you have to think of things in terms of crystal structure, what is able to form hydrogen bonds, what ends up being sterically hindered and what that means for the molecule. This is why watson and crick and franklin's work was so seminal, it showed how genetic information was inherited through mechanical logic of these molecules alone. Before the structure of DNA was solved, there were a lot of competing theories over what molecule was the source of heritable information, and how this information was exactly passed down between generations.
lurknot 3y ago
https://en.wikipedia.org/wiki/Chargaff%27s_rules https://en.wikipedia.org/wiki/Chargaff%27s_rules
htss2013 3y ago
Maybe it has something to do with protein folding, since apparently scientists do not understand the physical mechanisms that translate a given DNA sequence into a given 3D shape. They best they can do is infer probabilistic patterns using ML to proxy a mechanistic of action. Maybe there's something quantum at work that means it will never be fully deterministic.

go_elmo 3y ago

Might error-correction play a role? Having a lightly inefficient base 4 system might provide capacity for the surplus error correcting code information capacity?

Faaak 3y ago
One mutation in a base pair can lead a totally different amino acid (c.f the genetic code), so I doubt it ?
- go_elmo 3y ago
  True, iff the error persists correction cycles which are present, how exactly they work / if theyre comparable with eccs I dont know.
- toufka 3y ago
  BUT, if you look at the codon table, precisely because it's base-4 and not base-3, many base flips are silent when coded. By using base-4, there's enough space to permit lossiness of the coding itself - given the number of amino acids and the 3-NT encoding. So you really aren't optimizing JUST for nucleotide encoding, but you're also optimizing in concert with 3-nt/AA, and 20AA codes. So if you have to optimize for information density and fidelity, given X-nucleotides, Y nucleotides/AA, and Z AAs, and sample as much chemical and physical diversity in those AAs life has settled upon: X=4, Y=3, Z=20. If we went with X=3, you might need Y=4 to get the same kind of fidelity, but that cranks up your energy costs by 30% (from 3 to 4 NT per AA).
icoder 3y ago
DNA mostly relies on the fact that there's 2 strands that are (logically speaking) a mirror copy of each other (a C is paired with a G and vice versa, an A to a T and vice versa), it's like RAID 3 with only 2 disks (one being parity). Apart from repairing structural damage such as missing bonds, the cell can even repair missing bases or non-straight breaks without loss. This mechanism is also used for replication: the entire strand is split and each half is completed with its mirror counterpart.
- go_elmo 3y ago
  Im aware of that, but was rather thinking about ECCs like hamming-code, that are able to correct single sequences of info based on surplus info in that same string.
  - dekhn 3y ago
    Nothing algorithmically sophisticated, but DNA repair enzymes already do this.

icoder 3y ago

DNA is not really processed like that, afaik. Mostly, each 3 bases code for an amino acid, which are glued together to a string (protein), which folds in a 3D structure based on the characteristics of all amino acids. Some DNA is used to attract other proteins, or even interact with DNA elsewhere on the strand, or is translated to RNA (one-on-one) which can then have a function based on its sequence or the structure it folds into. Any 'logic' there is, is built _on top_ of this.

jacquesm 3y ago
Any logic that we are currently aware of. DNA contains many unsolved mysteries and I expect that gift to keep on giving for a long time to come.

usrbinbash 3y ago

> Like, why didn't DNA end up as base 3? Why did we end up with only 20 proteinogenic amino acids? Why are vertebrate neural architectures inverted (cell bodies on the inside, connections on the outside, even though the other way round way (eg. like a squids brain is organised) is easier and less inhibitive to growth? 2 Reasons: a) Because nature and evolution cannot engineer. Random mutation, recombination and natural selection are the only mechanisms available. Things get selected if they outcompete existing alternatives, they don't need to be the best solutions. b) All solutions have to be built by modifying what already exists. Evolution doesn't get to do greenfield projects, because anything that has to start from scratch is so disadvantaged in natural selection compared to already evolved complex life, it will fail. This leads to systems that, from an engineering point of view, don't always make a lot of sense. Eg. the architecture of the vertebrate neural system creates a lot of issues (eg. our light sensitive cells point in the wrong direction). The only way this makes any sense if when one looks at how the neural tube (the precursor to the backbone) is formed by the endodermis folding in on itself. This process is so deeply at the root of the Chordata, and so many other things depend on it, that it simply cannot change any more. Many many biological systems are "legacy systems" in the truest sense of the word: Solutions produced a long time ago that may have many problems, but are simply too deeply enmeshed with everything that came after, that they are now impossible to change.

sparrowInHand 3y ago
Short answer: Likelihood of noise (brownian motion) producing the element and keeping it interacting. Then once it gets going, likelihood of keeping state, while interacting.
t_serpico 3y ago
A classic armchair response. DNA has complementary nucleotides (AT,GC) that facilitates its pairing. Base 3 wouldn’t work in that sense. Also, you can’t forget about the genetic code. See https://arxiv.org/pdf/q-bio/0605036.pdf https://arxiv.org/pdf/q-bio/0605036.pdf for interesting thoughts. Remember, evolutionary biology is a field and people think about these questions!
- 3y ago

jszymborski 3y ago

There's a lot of interesting things to consider. One, is that base 4 makes a lot of sense for the stability of DNA structures. You have two purines, two pyrimadines. Another is that partly because codons are degenerate, the distribution is way off a uniform distribution. For chemistry and mol bio reasons, the distribution of AGTC is very skewed. When i fully wake up, this might be a fun blog post to draft.

Llamamoe 3y ago

Radix is important for digit-efficiency, but in a biological system that's not necessarily related to molecule size efficiency.

pythonguython 3y ago
I’m also failing to see how digit efficiency would be important in DNA. In fact, it seems that a high base system would be more efficient. If you had 80 nucleobases instead of 4, each base pair would contain far more information
- JumpCrisscross 3y ago
  > If you had 80 nucleobases instead of 4, each base pair would contain far more information Which is a problem given DNA is a lossy format.
  - Llamamoe 3y ago
    Strictly speaking, you could encode more error-correction bits into a higher nucleobase count but that'd pretty much require intelligent design, and wouldn't necessarily be viable for microorganisms to have that many proteins handling all the metabolic scaffolding.
- asimpletune 3y ago
  The efficiency comes from the ratio of the alphabet to the number of character places needed to express them. Otherwise why not base a million? Or a billion? This ratio is what leads to base e being the theoretical maximum.

throwawaymaths 3y ago

It's probably not base four because you have to stretch out more pairs to match up four pairs and that's entropically disfavored. However ribosomes can accomodate a four pair matching, though at a very reduced yield (unless you think Schultz's postdoc fabricated those data)

PaulHoule 3y ago

DNA has the same limitation that many serial protocols have: if you repeat the same base pairs (e.g. "AAAAAAAAAAAAAAAAAAAAAA") you will have trouble w/ the DNA not spiraling correctly. Some sequences of 2-6 repeated base pairs seem to "deliberately" cause variant behavior in DNA and RNA, see https://en.wikipedia.org/wiki/Repeated_sequence_(DNA) https://en.wikipedia.org/wiki/Repeated_sequence_(DNA) Many real wire protocols have mechanisms to prevent repeated sequences entirely https://en.wikipedia.org/wiki/8b/10b_encoding https://en.wikipedia.org/wiki/8b/10b_encoding DNA coding for real proteins is unlikely to be too terribly repetitive but I image a long α helix could have a repetitive amino acid sequence. Many amino acids can be coded with variant codons, I guess if repetition were a problem in a particular gene natural selection could step in.

deleted 3y ago
[deleted]
amateurCoder5 3y ago
Repetitive DNA sequences do occur and do cause problems. https://en.m.wikipedia.org/wiki/Trinucleotide_repeat_expansion https://en.m.wikipedia.org/wiki/Trinucleotide_repeat_expansi... TLDR: DNA triplet repeat expansions cause diseases like Huntington's disease.

dylan604 3y ago

>So for example, ternary logic is (much) more efficient than binary logic. Having that 3rd state just makes problem solving much more elegant. Binary for electronics is obvious because there are 2 states in electric components: on or off. There is no 3rd option.

nicoburns 3y ago
I believe "on" and "off" in electronics typically correspond to different voltage levels. So you absolutely could have a third intermediate state if you wanted to. Flash memory does this (and even sometimes has 4 states). I guess designing switches (transistors) that could take advantage of and propagate these extra states could be tricky though.
- ohwellhere 3y ago
  https://en.wikipedia.org/wiki/Ternary_computer https://en.wikipedia.org/wiki/Ternary_computer

toufka 3y ago

You (at least) have 3 systems that are optimized in concert in a (our) DNA/Protein world. DNA base set, Amino acid set, Translation layer between DNA/Proteins. Currently, we've got: 4 DNA bases, 3 bases/AA, 20 AAs; 4^3 => 20 If you change one of those numbers, you'll need to rejigger the rest, and you'd need to reoptimize. And there are competing goals which at least include: - maximize access to biophysical/chemical diversity - minimize energy expenditure to produce each component, chemically - minimize energy expenditure to both copy instructions & produce products - maximize information fidelity - minimize or at least degrade gracefully in the context of errors In the context of a 3-base system, you very well could throw off those optimizations given the consequences for the other 2 parameters (#AA & nt/AA). 3^3 = 27, which is very close to the maximum of 20 amino acids. Which means you'd probably need a 4nt->AA translation layer to keep the same number of AAs, and that alone would add 30% more energy expenditure. If you kept the 3nt->AA system you'd BOTH need to reduce the number of accessible amino acids AND you'd lose some of the error correction mechanisms of having degenerate codons code for the same amino acid.

dahfizz 3y ago

Why do my eyelashes, meant to protect my eyes, fall into my eyes? Why do my cheeks/tongue sometimes get in the way of my teeth so that I bite them? And why do they then get inflamed so that I continually byte them for the next few days? We are all a bunch of biological goop resulting from random processes. Don't expect optimal solutions from evolution. There is no "why".

erenyeager 3y ago
There is a why and reasons we find and insights we glean. The denial of a why is itself an anthropocentric take on biology, influenced by Darwinian thought. But any biological system we study we need a why, otherwise the corollary of your statement essentially leads to no learning or understanding, because everything becomes “arbitrary” and explained away by randomness. Ironic to say it’s not optimal, really we don’t have the full knowledge. Often when we learn more we learn how little we really know about biology.

guerrilla 3y ago

> (probably because 4 naturally lends itself to pairs of 2). Why would pairs of two be favorable? > So for example, ternary logic is (much) more efficient than binary logic. Having that 3rd state just makes problem solving much more elegant. What do you have in mind here? > Like, are there all sorts of exotic logic gates that come from a 4 state system? I don't know but you may be interested in this [1]. 1. https://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADi https://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADi

asdff 3y ago

On paper this might be an interesting game, but you have to think of things in terms of crystal structure, what is able to form hydrogen bonds, what ends up being sterically hindered and what that means for the molecule. This is why watson and crick and franklin's work was so seminal, it showed how genetic information was inherited through mechanical logic of these molecules alone. Before the structure of DNA was solved, there were a lot of competing theories over what molecule was the source of heritable information, and how this information was exactly passed down between generations.

lurknot 3y ago

https://en.wikipedia.org/wiki/Chargaff%27s_rules https://en.wikipedia.org/wiki/Chargaff%27s_rules

htss2013 3y ago

Maybe it has something to do with protein folding, since apparently scientists do not understand the physical mechanisms that translate a given DNA sequence into a given 3D shape. They best they can do is infer probabilistic patterns using ML to proxy a mechanistic of action. Maybe there's something quantum at work that means it will never be fully deterministic.