?>

# Department of Science, Math, & Technology

E = mc²
Mitosis and meiosis equivalents with odd numbers of parents
Posted: Posted September 2nd, 2016 by bloodb4roses
 So, the processes of mitosis and meiosis in species that are diploid are comparatively simple, since having polar bodies on opposite ends of the cell is pretty easy. (I'd posit that any ploidy that is a power of 2 would be relatively straight forward. Though the higher the ploidy in general the more complex things get.) How would analogous processes work in species that have genetics in odd numbered sets? I suppose mitosis could work as normal: A cell duplicates all of its genetics and splits in half, each daughter cell receives the same three copies of each chromosome that the original cell had (assuming everything goes right, which it should most of the time). But how do you get a process like meiosis without a large number of mistakes? I could see, if the cells split and split again, then there'd be a good likelihood that some gametes would get some copies of some chromosomes, but not others. I don't think it would be impossible, but maybe unlikely for the cells to just split three ways directly.
There are 11 Replies
Page: settingsSettings

I'm not sure I can figure out the logic why there would be, or wouldn't be, difficulty.

With diploidy, there are still mistakes exactly as you're talking about. (FAIK there are also other mechanisms leading to various aneuploidies or dysnumerics.)
The question is, how many is "a lot of mistakes"?

I don't really understand how ordinary meiosis works in real life.
For instance, why does meiosis require the cell to divide twice? First, it replicates all the chromosomes and divides, (at least prima facie) as it does in mitosis; then each of those cells re-divides without replication.

I think, for our purposes, we're best served (at least at present) by invoking the process of handwavification.

Any theory that somebody (smarter than me) eventually comes up with, will still be pretty damn'd provisional, until they can actually create a triploid cell that can both mitote and meiote correctly at least more often than not.

For purposes of creating a fictional conworld, it's not necessary that we know how it works, because it's not necessary that our con-people know how it works.
OTOH, if we want to just pick a mechanism and declare by fiat that that's it in our conworld, we're allowed to do so.

------------------------------------------------

It's a good question.

Sorry that this non-answer is the best I could come up with in 42 minutes!

Posted September 3rd, 2016 by chiarizio

I'm not sure I can figure out the logic why there would be, or wouldn't be, difficulty.

With diploidy, there are still mistakes exactly as you're talking about. (FAIK there are also other mechanisms leading to various aneuploidies or dysnumerics.)
The question is, how many is "a lot of mistakes"?

Well, in diploid creatures, it's a simple matter of pairs lining up and being pulled away from each other to opposite ends of the cell. This is true whether it's mitosis or meiosis. There are mistakes sometimes, but it's rare. With an odd number, you either need a way for the cell to split equally N number of ways (where N of course equals the ploidy) OR split in two however many times so that you have (N-1)/2 of all chromosome sets on one side and (N+1)/2 on the other, and then have any cells with multiple copies of chromosomes splitting again until they all have one copy of each.

For example, using three as a sample:

/ XXX \
O - XXX - O
\ XXX /

There's our cell ready to divide for "meiosis". The chromosomes are all doubled so some of them can cross over with their neighbors, but that's not what we're looking at today. Let's say it first splits like this if things are going correctly:

/ X - - XX \
O - X - - XX - O
\ X - - XX /

Which then ends up like this:

/ X \ / XX \
O - X - O O - XX - O
\ X / \ XX /

The cell on the left can just split again separating the chromosomes into "normal" chromosomes, waiting to match up with analogous ones in other gametes. And the one on the right would just split a couple more times I guess.

But if it split wrong more like this:

/ X - - XX \
O - X X - - X - O
\ X - - XX /

Then of course things would just be difficult whether either side split once or twice more. And it would be more likely the more chromosome sets there are and the more chromosomes there are in a "normal" set.

I don't really understand how ordinary meiosis works in real life.
For instance, why does meiosis require the cell to divide twice? First, it replicates all the chromosomes and divides, (at least prima facie) as it does in mitosis; then each of those cells re-divides without replication.

I'm not sure if it's known specifically but AFAIK it has something to do with recombining the DNA within pairs of chromosomes, AKA cross over.

I think, for our purposes, we're best served (at least at present) by invoking the process of handwavification.

True but it's good to know what issues would exist even if you can't say how those issues are answered.

ETA: That's what i get for not checking if things line up right but hopefully you know what i'm getting at with those.

Posted September 6th, 2016 by bloodb4roses

….
For example, using three as a sample:
….
The cell on the left can just split again separating the chromosomes into "normal" chromosomes, waiting to match up with analogous ones in other gametes. And the one on the right would just split a couple more times I guess.

But if it split wrong more like this:
….
Then of course things would just be difficult whether either side split once or twice more. And it would be more likely the more chromosome sets there are and the more chromosomes there are in a "normal" set.
….
ETA: That's what i get for not checking if things line up right but hopefully you know what i'm getting at with those.

Thanks! I think I got it.
Having the example helped a lot!

+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

I had instead envisioned a three-poled process (really, two different three-poled processes, one for mitosis and one for meiosis).
I am reluctant to try to illustrate them with ASCII-art; it would probably take me several tries and a lot of time, and so I might be better-advised to save it for later.

For pentaploidy etc. it might be even harder to illustrate.

_____________________________________________________________

…. in diploid creatures, it's a simple matter of pairs lining up and being pulled away from each other to opposite ends of the cell.

"Simple"?
Maybe so; but might it not also be possible that you are "misunderestimating" how complex it is?
Also, it'll "be easier" (won't it?) with an asexually-reproducing, mitosis-only one-celled species; and (perhaps independently) among a one-chromosome species.

…. And it would be more likely the more chromosome sets there are and the more chromosomes there are in a "normal" set.

IRL Drosophila melanogaster fruit flies have IIANM four pairs of chromosomes (counting sex-chromosomes).
Mendel's peas (Pisum sativum) have IIANM 7 pairs of chromosomes.
Humans have 23 pairs of chromosomes (counting the XX or XY pair).*
Dogs (Canis familiaris) OTOH have IIANM 39 pairs of chromosomes (including sex-chromosomes).
Are errors more common in peas than in fruit flies, and more common in humans than in peas, and more common in dogs than in humans?

*(Bonobos, chimpanzees, gorillas, orangutans, and other great apes, have 24 pairs. But two of their chromosomes fused into one of ours.)

TTBOMK the biggest effect of having more chromosomes is that genes freely re-associate when they're on different chromosomes, but they can't re-associate if they're on the same chromosome without a comparatively rare (i.e. significantly less likely than 50% -- e.g. 25%?) cross-over event. If they're on the same chromosome, the closer together they are the less likely they are to re-associate; to put it another way, the further apart they are the more likely they are to re-associate.

This means that, it's easier to recombine traits among dogs than among any other of those species I mentioned above; next-easiest among any non-human great-ape species; middling-difficult among humans; a bit more difficult among peas; and most difficult among fruit-flies.

At first glance, it does seem that, the more chromosome-pairs there are, the more chances for aneuploidies to occur. And maybe it's so. But I don't know if that's really significant. In any case, with the kind of selective pressure we've recently been discussing (in other recent threads, if not this one), freely re-associating traits would be heavily favored, so the species would push "more chromosome-sets" (whether that's "chromosome-triples" or other numbers-per-set) as far as it could, until the difficulties (whatever they are) due to having too many chromosome-sets (if there are any) overwhelm the advantage of freely re-combining traits.

-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --

Does any of that make sense to you?

I admit I'm not an expert, and am hypothesizing.

Posted September 7th, 2016 by chiarizio

Well, I'm no expert either, and I don't think any actual experts have triploidy species to look at. :D So I think best guesses and reasoning are as close as we'll get. It could be possible that there would be several ways to tackle this situation. Heck, you brought up a good question about why meiosis starts with doubling.

I also wonder if beings with anything like this might have extra double checks and repair mechanisms.

Posted September 8th, 2016 by bloodb4roses

[color=#804000](edited 2016/09/09 12:23 Fri Sep 9 12:23 PM EDT)

When euploid means "even-ploid", let's call that "artioploidy".
When euploid means "odd-ploid", let's call that "perissoploidy".
See this search.

I also wonder if beings with anything like this might have extra double checks and repair mechanisms.

___________________________________________________________________________________________________________

Relevant to that comment, but perhaps not to perissoploidy (euploid n-ploidy where n is odd):

In my four-base-pair-per-codon genetic code (totaling 4^4 = 256 types of codons), I made a few (around three? or four?) other differences from real-life that weren't logically required by the switch from 3bp codons to 4bp codons.

First: There isn't even one of my 96 amino-acids in my fictional code that isn't coded for by more than one codon. And 20 of them are encoded by more than two codons.
Four are encoded by three codons each; two are encoded by four codons each; thirteen are encoded by five codons each; and one is encoded by six codons.
By contrast, in the real-life genetic code, of the 20 amino-acids coded for, two (Met and Trp) are encoded by only one codon each. Nine are encoded by two codons each (two encodings per amino acid are typical); one (Ile) is encoded by three codons; five (Ala, Gly, Pro, Thr, Val) are encoded by four codons each (providing evidence that originally only the first two bases of a codon mattered); and three (Arg, Leu, Ser) are encoded by six codons each.

In real life, the middle base is invariant for each amino-acid. The first base usually also has only one choice, but for three amino-acids (Arg, Leu, Ser) has two. The third base has two choices for around half the amino-acids, doesn't matter at all for around a quarter of them, and has three choices for one of them; it has to be just one value to encode for a particular amino-acid, only in the cases of Met and Trp.

But in my fictional code, for each of the fourteen amino-acids encoded in at least five ways, any one of the four bases in the codon can be changed without changing the codon's translation. (And for any of the sixteen (including the fourteen aforementioned) A-As with at least four encodings, two of the bases can be changed simultaneously without changing the translation.)

In my mind, this was in response to a high likelihood of point-mutations. The genetic code was evolved in a way to prevent the more-frequent point-mutations from causing the more-damaging substitutions of amino-acids.

Second: In real-life there are only three STOP codons; TAA and two others very similar to it, namely TAG and TGA.
But in my fictional code, there are thirteen STOP codons; GGGN and GGNG and GNGG and NGGG, where G represents guanine and N represents any nucleotide-base.
Also; IRL, each gene that encodes for a protein, ends with two consecutive STOP codons.
But, in my fictional code, each gene that encodes for a protein ends with three consecutive STOP codons.

I was thinking the first of those just-mentioned features (thirteen highly-similar STOP codons) was, to not only make it less likely that a mutation could change a STOP to a non-STOP, but also make it less likely that a mutation could change a non-STOP to a STOP (thus truncating the translated protein).
The codons at risk for being mutated into a STOP codon are those that could be represented (in "compressed" form) by GGHH, or GHGH, or GHHG, or HGGH, or HGHG, or HHGG, where H represents any base other than guanine. Of the 37(?) amino-acids thus encoded, only five do not have other encodings. (Possibly problematically one of those five is the one with six different encodings; the other four have only two encodings each.)

The second of those just-mentioned features (three consecutive STOP codons at the end of every protein-encoding gene), I thought, would be evolved in response to a strong selective pressure against translation-run-on. To mutate GGGG-GGGG-GGGG into three consecutive non-STOP codons would require six point-mutations; two among the first four bases, two among the last four, and two among the middle four. I'm assuming that's pretty damn'd unlikely. But what if two among the middle four, together with two among either the first four or the last four, is insufficiently unlikely? Then having three STOP codons in a row would still rescue the translation from running-on.

In order to handle the problem of STOP-to-non-STOP mutations, I thought of introducing an enzyme system that would edit certain non-STOP codons, when preceded by and followed by certain combinations of certain STOP codons, back into STOP codons.
And in order to handle the problem of nonSTOP-to-STOP mutations, I thought of introducing an enzyme system that would edit certain STOP codons, when preceded by and followed by certain combinations of certain nonSTOP codons, back into nonSTOP codons. Obviously one couldn't be certain one had changed it back to the "correct", original nonSTOP codon; but perhaps one could just pick the likeliest candidate.
But I didn't finish working either of those out, so that they wouldn't get into trouble in case they mistook the reading-frame. There's probably a way to do it, especially since it doesn't have to be perfect nor comprehensive; it just has to make the end result be less likely to be deleterious, or likely to be less deleterious, than doing nothing.

[color=#804000](edit): edited 2016/09/09 12:23 Fri Sep 9 12:23 PM EDT)
The RL STOP codes of TAA, TAG, and TGA, and the RL "always end a protein-encoding gene with two STOP codons", don't protect against reading-frame errors.
If there were four (instead of three) RL STOP codes, and they were (for instance) AAA and AAT and ATA and TAA, then ending every protein-encoding gene with two STOP codons would protect against reading-frame shifts. No matter how the frame is shifted, the "double-STOP-code" will contain at least one three-base triple that will get read as a STOP.
Indeed, even if a point-mutation were to convert one of the two consecutive STOP codons into a non-STOP codon, and there were also a reading-frame shift, there would still be a good chance -- (around 58.9285714%, maybe? i.e. 66 out of 112?) -- that there'd still be a three-base-pair sequence recognizable as a STOP codon among those six base-pairs, even with the frame-shift and after the one-base mutation.

--- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- ---

In my fictional genetic code, with GGGN, GGNG, GNGG, and NGGG as STOP codons, if only one point-mutation converts one of the STOP codons to a non-STOP codon and there's a reading-frame shift, still, a STOP codon will be read (if it's clear what I mean?).
Even if two of the three consecutive STOP codons are "spoiled" by single-point mutations, and there's a reading-frame shift, there seems to be about a 96% chance that at least one STOP codon will still be read, and even about a 54% chance that two STOP codons will still be read.
(/edit)

Third: IRL the "START" sequence (the "Shine-Delgado sequence" in some organisms) is eight ( 8 ) base-pairs long, always ending with the three-base codon for Met (methionine). And in fact the first amino-acid of any protein, at least when first translated, is always N-formyl-methionine -- a special form of methionine that only occurs as the first amino-acid in a protein. Certain positions in the "START" sequence can be filled by alternate bases (sometimes only by one alternate, sometimes by two, etc.); I think of this as "mistakes are allowed, up to a certain number".
But in my fictional code, the START-sequence is 32 bp long.
(The "START" sequence includes one (or two non-consecutive) "STOP" sequence(s). (Reminiscent of the WINDOWS "SHUTDOWN" button showing up only on the "START" menu.) That way translation of a gene can't start without translation of the previous gene stopping.)

I chose the START sequence such that, if the gene-translation mechanism starts "reading" at the wrong place, it would have to tolerate up to eleven errors in the START sequence to continue translating.
Likewise, if it should begin reading and trying to translate the complement strand (the "non-sense" strand as opposed to the "sense" strand) of the DNA, it would need to tolerate around eleven or so errors to continue translating.

IRL reading-frame errors are very rare, except in certain viruses with such small genomes that they actually depend on varying the reading-frames to get all of their proteins encoded (they're a kind of gene-code poets, IMO; and btw some computer "viruses" have plagiarized this trick).
One mechanism to prevent such errors involves the fact that beginning translation is faster with any given START sequence the more "correct" it is; and once translation has begun with a certain reading-frame it is very difficult for any other translation to start, since ordinarily one copy after another is translated right on the heels of the previous copy.

I figured on requiring that, before translation could start, the START sequence had to occur at least two-thirds correct. It would begin very quickly if there were no "errors". Since point-mutations are so (relatively to RL) common in my fictional biome, I wanted the slow-down due to a single "error" to be insignificant, undetectable, and immeasurable. The slow-down due to two errors, I thought, should be (barely?) detectable, but translation should still happen pretty fast if there were two, but only two, "errors". The slow-down due to three errors should be more significant -- enough so that if there were some other reading frame whose START sequence had no errors or only one, it would pre-empt the three-error translation-process -- but translations should nevertheless "take-off" in time, in such cases, not to impact the health of the organism. Delays due to four, five, …, nine, or ten errors, could be progressively slower; slow enough to impact the health of the organism if those were the only reading-frames that had effective START-sequences, but also slow enough that if there were any reading-frame with a START-sequence with fewer (say, at least three fewer) errors in the START sequence, the less-erroneous translation-process would "bump" the more-erroneous one.

Translation should be impossible if the "START-sequence" "has" twelve or more errors.

I was thinking that there ought to be a "START-sequence repair" process that would "correct" a sequence that was recognizably probably a mutated START-sequence to one that was "less erroneous". Perhaps translation could be allowed to begin with a START-sequence that has eleven errors in it, provided that would be slower than the "repair" mechanism.

Anyway: I was thinking this was evolved in response to a selective pressure to really, really, really, REALLY avoid reading-frame errors.

___________________________________________________________________________________________________________

How much, if any, of that, inspires you for ideas about what you mentioned in your "extra double checks and repair mechanisms" post?

___________________________________________________________________________________________________________

BTW: In real-life DNA-replication, there is an enzyme floating around whose job is just to remove the last nucleotide-base that was added to the currently-forming new strand -- regardless of whether it was correct or incorrect.
It so happens that adding the correct complement to the new strand is faster than this enzyme's action, while adding an incorrect (non-)"complement" is slower than this enzyme's action.
Since this enzyme can't remove a base once the next base has been put in place, this means that, just by chance!, odds are that it will remove an incorrect "complement" but will not remove a correct one; and if it removes a base, the removed base is likelier to be replaced by the correct complement than by an incorrect complement.

There's an example of a RL double-check and repair mechanism. You see that it's statistically likely to improve matters, but not guaranteed to; and statistically unlikely to make matters worse, but not guaranteed not to.

Does that help, even if none of "my own, original" ideas did?

[color=#804000](edited 2016/09/09 12:23 Fri Sep 9 12:23 PM EDT)

Posted September 8th, 2016 by chiarizio

@bb4r:
Have you heard of "amitosis"?
Also see https://www.google.com/search?q=one-celled+eukaryotes+amitosis+meiosis+mitosis; especially the hits that are not "missing 'amitosis'".

_______________________________________________________________

IRL it looks like myriaploid* (10000-ploid to 99999-ploid), chiliaploid* (1000-ploid to 9999-ploid), and hektaploid* (100-ploid to 999-ploid) species's cells just skip mitosis, and reproduce by amitosis instead. Resulting errors in "ploidy" are (at least sometimes) repaired by some mechanism involving RNA; I get the idea that there are RNA-"enzymes", and/or maybe organelles made out of RNA (the way ribosomes, and IIANM nucleoli, are made out of RNA), that carry out the repairs.

*[color=#404040](I just made these words up.)

The "repairs" may only restore the ploidy from not-close-enough-to-euploid to close-enough-to-euploid; I doubt that they can, for instance, restore any lost variant alleles, or restore any lost "heterozygosity" (if any word related to "zygote" is even appropriate here).

Many of these organisms also mate. There are mating classes; two conspecific organisms can't mate if it happens that their mating-classes are not compatible. I don't know that all the classes in every species are totally-out-crossing (same-class mating disallowed). And I don't know that all the species have just two mating-classes. I think in most species, most, if not all, classes are totally-outcrossing; and I think in some species there are more than two mating-classes.

But there aren't mothers-and-fathers, and so there aren't males-and-females.

In some of them, the mates merge into a single cell, then split again. A single act of splitting can be into two, or three, or four cells. If division is into two cells, and mating involves merging, then after mating they have to divide at least twice, in order for it to count as "reproduction".

If mating involves merging, it means that each of the parents contribute roughly half of their respective cytoplasmic genes to each of the offspring.

Mating may -- I think, usually does -- involve meiosis.

Many of these organisms have two nuclei; a macronucleus and a micronucleus.
The micronucleus has longer chromosomes, and lower ploidy -- e.g. diploid, or FAIK tetraploid or hexaploid, or at least something significantly fewer than hektaploid. It is the only nucleus that undergoes mitosis in asexual reproduction, and the only nucleus that undergoes meiosis in sexual reproduction.

The macronucleus is the only nucleus involved in gene-expression; in particular, in translating DNA into proteins. The macronucleus has shorter "nano-chromosomes", and very high "ploidy". Its chromosomes may be constructed by cutting up copies of those in the micronucleus and then re-assembling them, possibly in a different sequence and possibly with different numbers of copies, and possibly reversing some of them so that what functions as the "sense" strand in the macronucleus's chromosome is what functioned as the "complement" strand in the micronucleus. I haven't been told so, but I strongly suspect the pieces of the copies don't necessarily all consist of a multiple of three base-pairs; in that case, no reading-frame for the macronucleus's chromosome can consistently match the reading-frame in the micronucleus's chromosome.

--- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- ---

Do you think that could inspire some thoughts regarding your conspecies?

[/end edit]

Posted September 17th, 2016 by chiarizio

I read the Wikipedia article on Polyploidy; and here is my summary of what it says that is pertinent to this thread.

In Real Life:

Among multicellular eukaryotes other than Protista, polyploidy is particularly common among plants.
Artioploid (even-ploid) specimen are often fertile, and/or interfertile with each other; so they can create a new variety of their species, or a new subspecies.

Polyploidy is often induced artificially during hybridization, especially of plants that are related enough to have almost-homologous genomes, but not related enough for the offspring to be naturally fertile.
This usually involves having a diploid set from one parent species and a diploid set from the other, in every cell of the adult organism.
(Possibly consequentially to the above), such hybrids are usually artiploid.
For example, some cotton is tetraploid; some wheat and some kiwifruit is hexaploid; some dahlias are octaploid; and some strawberries are decaploid.

Many cultivars (cultivated varieties) of various crop species, OTOH, are perissoploid (odd-ploid); for instance, triploid (watermelon) or pentaploid (kenai birch).

-------------------------------------------------------------------------------------

Perissoploid individuals frequently can't reproduce, or have a lot of trouble reproducing.
Many are seedless.
Many can reproduce only by cuttings assisted by the cultivators.
Some can reproduce without assistance, but only parthenogenetically.
Some can reproduce sexually, but only with an artioploid mate.**

• (see e.g. [quote:0e5c3b8c50="Wikipedia"
• )
(Originally I thought they said there was a pentaploid variety of watermelon that could be fertilized by an ordinary watermelon; but I can't find that now, so maybe I misread or misremembered.)

Mostly, fertile perissoploid individuals are monoploid (not polyploid) members of a species among whom one sex is monoploid and the other is diploid.

-------------------------------------------------------------------------------------

Many fungi and animal groups are also prone to natural polyploidy.
Among animals, these are mostly invertebrates.
Among vertebrates, these are mostly fish and amphibians.
Examples in reptiles, birds, and mammals, seem to be either artificially-induced in laboratories, or to be very rare and perhaps unstable in nature.
OTOH there's some evidence that there has been some polyploidy in the past of some mammal species. Was any of it perissoploidy? (probably not).

Posted September 28th, 2016 by chiarizio

Anyone have anything further to add to any of this? Or does any of it inspire anyone to say anything, maybe in a different direction?

Posted December 25th, 2017 by chiarizio

More?
Also: Merry Christmas and Happy Holidays!

Posted December 24th, 2018 by chiarizio

More?
Also: Merry Christmas and Happy Holidays!

We might want to just keep this as an archive thread or add some of the things we've considered to other genetics threads.

Then again, at least for my part, I'm leaning toward a 3 sex system that either uses paired chromosomes instead of triplets, so this might not be useful except as thought fodder.

Also a late happy winter solstice and an early happy new year

Posted December 25th, 2018 by bloodb4roses

You’re right.
While I can see this being of interest to others sometime, up ‘til now you and I seem to have been practically the only contributors.
So, I want this to be saved; but I should calmly and patiently await someone* having more use for it.
*That could be me, if inspiration strikes!

Posted December 25th, 2018 by chiarizio
Reply to: Mitosis and meiosis equivalents with odd numbers of parents