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Original post:

Imagine a world in which both left- and right-handed chirality appeared and evolved into a variety of complex organisms comparable to post-Cambrian Explosion Earth (both plant and animals).

As on Earth, chirality would apply to amino acids, sugars, enzymes, and potentially other essential biochemicals. A biochemical with the correct chirality will taste or smell a particular way to an organism with matching chirality, and be digestible/usable by their body, while a biochemical with opposite chirality will lack flavour or smell differently, and their body may be unable to digest it.

Is it plausible for both forms of chirality to not only arise but thrive, without one driving the other to extinction very early on?

For clarification:

As stated in the comments below, assume the following:

  • In primordial conditions the likelihood of a given biochemical molecule developing left- or right-handedness is 50/50.

  • The conditions that give rise to such a molecule are, at least in the immediate area at the time of its formation, stable and/or repeatable enough that opposite-handed molecules will also form.

  • If nearly identical conditions can be found elsewhere, the same processes there may give rise to opposite-handed molecules as well.

So in reading the question above, emphasis should be placed on the second half:

Is it plausible for both forms of chirality to not only arise but thrive, without one driving the other to extinction very early on?

"Early on" should be understood as any point prior to the emergence of multicellular life.

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    $\begingroup$ Don't believe it is, but can't find scientific reference. But think like that: we know life to occur once. You require it to start twice, independently, and at the same time, so the second one wouldn't find a world already occupied. $\endgroup$ – Mołot Oct 26 '16 at 16:11
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    $\begingroup$ It's not necessary for it to start twice. Conceivably the earliest replicating biochemical compounds to form have a 50/50 chance of going right or left; I am speculating that populations of both survive. $\endgroup$ – rek Oct 26 '16 at 16:14
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    $\begingroup$ they may have had a 50/50 chance to appear, but once the coin fell what puts it in the air again? The left handed life-ish stuff would have to appear before the right handed stuff had filled the pool or experienced much Darwinian action. Maybe it's a reeeally big pool or lots of similar pools that don't mix. $\endgroup$ – user25818 Oct 26 '16 at 17:16
  • $\begingroup$ @notstoreboughtdirt Presumably the conditions that allows for a single biochemical to form allows for others to form in the immediate area under identical conditions simultaneously. $\endgroup$ – rek Oct 27 '16 at 16:45
  • $\begingroup$ I read Deavin's answer to mean that I was wrong about 50/50. As the last ingredient mix life precipitates with a handedness predictable from concentrations and temperature. Maybe that mixing could happen in a non-uniform place though. $\endgroup$ – user25818 Oct 27 '16 at 17:13
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In the primordial ocean the first compounds were synthesized essentially by random chance using available energy sources, including radiation and lightening; here chirality was 50/50.

From this "soup" the first, very rough, self-replicating "things" emerged.

These thrived consuming the large amount of available organic material.

As soon as these materials become less abundant a strong evolution push appeared: the ability to produce needed complex (rare!) compounds from relatively abundant "simpler" ones.

This lead to first enzymes acting as catalysts for chemical reactions.

This is the point where symmetry was broken. Most (if not all) enzymes catalyze a single chirality.

This means (relatively) shortly after first "true" living proto-cells started colonizing the ocean (much before fitoplancton started changing atmosphere composition) the vast majority of organic compounds available were produced by "living" cells... and thus with a specific chirality.

It is conceivable two non-communicating primordial oceans could have given birth to unrelated bio(emi)spheres with partially (or completely) different compounds, possibly with different chirality. As a very special case it would be possible the two bio(emi)spheres could include the same compound with different chirality.

Probability of something like this happening in practice is anyone guess, but I regard it as rather low. Rationale being a very long and complex chain of unlikely events was needed to produce living cells in the first place and chance this chain could happen twice in the time span needed for first one to fill all "likely" environments is quite low.

Complex reactions are very difficult to set-up and replicate; as an example mitochondria (who learned how to produce energy from sugar and Oxygen) were never replicated, but accepted as symbiotic "partners" inside other cells, being so successful there's virtually no cell not hosting them (and they are all closely related; no "parallel evolution").

Bottom line: it is conceivable to have different and unrelated biospheres on the same planet, given suitable morphology. It is also conceivable these two biosphere could come in contact much later (perhaps because of a tectonic movement removing the barrier). In this case, however, it's extremely unlikely the biota would be anywhere near "similar". Chirality would be the least of the problems.

UPDATE:

O.P. asked: At some point the progeny of these two incubators – whether two oceans a world apart or two tide pools metres apart – have to come in contact. Then what happens?

It (as always) depends on specifics. I'll attempt a speculation.

In general there will be an initial stage where the two different populations will simply ignore each other and compete on an equal basis for the available resources. Compounds produced by the "other world" would be useless or even toxic (because the enzymatic set isn't able to handle them) and thus no direct interaction will happen.

From this moment, as said, the two populations will be in competition for resources, this means if one has a significant edge over the other then it will slowly drive the "less efficient" "half world" toward extinction (it may resist in some sheltered niche). This is what happened to anaerobic bacteria in our world when more efficient aerobic metabolism appeared.

OTOH, if efficiency (even if based on different chemical processes) is about the same then some kind of "mutual recognition" is going to take place.

There will be a push to:

  • avoid poisoning from the "other"
  • find ways to metabolize "alien" compounds.

Each step in this direction risks breaking the above-mentioned equilibrium and will push to develop "counter-measures". Something similar to "invention" of lignin by trees which took million years to bacteria to find out a way to cope with.

Here you can imagine two divergent results:

  • war: competition to death and thus one of the two "halves" prevailing sooner or later and driving the other to extinction (or to some biological enclave).

  • cooperation: development of one or many symbiotic arrangements where complex biological interactions will include species from both "halves".

In any case it would be extremely unlikely "parallel evolution" of any kind.

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  • $\begingroup$ I agree that having two primordial oceans is the key. The second key would be for the two oceans to connect before multicellular life evolves but the question assumes that so it is fine. I am also kind of curious how mitochondria and chloroplasts would work in this scenario. Bacteria without either did not go extinct though so parallel evolution should be possible if the chirality is a real barrier. Which it might not be if bacteria evolve the ability to consume either chirality. $\endgroup$ – Ville Niemi Jan 18 '18 at 4:05
  • $\begingroup$ @VilleNiemi: fact I'm trying to stress is: given two separate "incubators" they are bound to generate two completely different life forms, based on completely different molecules. It is highly likely they would be based on some kind of long polymers, but either of them being what we call "protein" is unlikely at best; having both of them sharing the same basic structure would imply some contingency we're not currently aware of. Having two independent "worlds" evolving basically the same kind of biology (possibly but for chirality) is something from the Star Trek Universe. $\endgroup$ – ZioByte Jan 18 '18 at 8:59
  • $\begingroup$ Good point but bit off topic for the question as it is about the possibility not probability. And it isn't really that unreasonable to assume such contingency. The number of possible chemistries likely is fairly limited and the two oceans would probably be fairly similar in chemical composition as they are not actually separate worlds. But yeah, good point anyway. $\endgroup$ – Ville Niemi Jan 18 '18 at 14:27
  • $\begingroup$ At some point the progeny of these two incubators – whether two oceans a world apart or two tide pools metres apart – have to come in contact. Then what happens? $\endgroup$ – rek Jan 24 '18 at 4:15
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    $\begingroup$ @rek: I updated the Answer. Please have a look. $\endgroup$ – ZioByte Jan 24 '18 at 10:49
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Sure. In How can orientation-discriminating people keep their views when it turns out they live on a non-orientable surface?, I posit a world on a real projective plane (see the 5th note). In particular, it is non-orientable.

In this world, although chirality exists locally, it does not exist as a global property of any object (chemical, organism, etc...). This means that as life spreads across the world, and wraps around it, it will essentially reverse its chirality automatically, like a mobius band (indeed, a projective plane is basically a mobius band without a boundary).

I suspect that many organisms would become partially achiral (even locally) in such a world though, so as to be able to eat more things.

Note that your world doesn't necessarily need to be a real projective plane for this to work. Any nonorientable surface will due (just remember that it has to be embeddable in a suitable 3D space, unless you want your world to be another Flatland).

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    $\begingroup$ I'm a bit confused by this answer, as it does not seem applicable to a physical planet of the sort we know to exist. $\endgroup$ – rek Jan 24 '18 at 3:59
  • $\begingroup$ @rek sorry, I thought we the question was about fictional worlds. Was it supposed to be Earth like? $\endgroup$ – PyRulez Jan 24 '18 at 4:01
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    $\begingroup$ @py It never occurred to me I'd have to specify that it is a physical, spherical, matter-based world in three dimensional space, comparable in all facets to planets we know to exist. But yes, call it Earth-like. $\endgroup$ – rek Jan 24 '18 at 4:19
  • $\begingroup$ @rek Okay. Than this answer definitely does not work. $\endgroup$ – PyRulez Jan 24 '18 at 4:23
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    $\begingroup$ @rek (Also, non-orientable wormholes might exist, which would also allow this to work.) $\endgroup$ – PyRulez Jan 24 '18 at 4:30
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We can delve into levels of chemistry that would astound you, just from this question alone.

Keeping it short and non-technical (relatively so), it would be theoretically possible, though, as pointed on in comments on the question, it's unknown about what the chances would be.

The best place to start would be finding out how chirality is determined (I don't mean how we determine a chemical's chirality, but how the synthesis of the chemical determines the chirality). This published 'theoretical' study shows an attempt at predicting chirality:

Results for a variety of TADDOL [...] derivatives show good agreement with experimental findings for the sign, magnitude, and the temperature dependence of the helical twisting power (HTP). [...] We discuss the temperature and solvent dependence of the helical twisting power and argue that in all the systems studied here, preferential selection of certain molecular conformations at different temperatures and in different solvents are able to explain the observed experimental behavior of the HTP.

So it's theoretically possible to predict chirality. Awesome.

Next we need to know the processes the biochemicals that started life underwent to be created. Then the same for the biochemicals early life needed to survive. This goes on until you have an accounting of all the chemicals, and their synthesis conditions.

In other words, likely impossible to discover.

That being said, if we make the assumption that life of both chiralities arose in the same biosphere, then it's really a matter of "could they co-habitate?" Probably, but not in direct association. Almost all animals are territorial, and would likely force the other out of their territories. A lot of plant life relies on animal life to aid in pollination/spreading seeds, so that chirality of plant life would flourish there while there other may not (specifically ones that require digestion interactions for spreading seeds, like bird-poop).

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    $\begingroup$ "Probably, but not in direct association" I disagree. There are more examples of mutualism, for example, between different species than we can count. Any two species could have such a relationship without caring for each other's chirality. $\endgroup$ – Renan Jan 17 '18 at 21:00
  • $\begingroup$ The question presupposes these biochemicals arise more or less equally, so I don't think much of this answer is applicable. As to the last paragraph, complex organisms of incompatible chirality are, arguably, not competing for the same resources and in turn are not "resources" (prey), so I can imagine left-lions cohabitating with right-zebras, or a herd of right-zebra and left-zebra-look-alikes (each an inedible decoy for the other), but whether it could get to that state is the question. $\endgroup$ – rek Jan 24 '18 at 4:12
  • $\begingroup$ @Renan any form of imbalance in the delicate ecosystem would cause the scale to tip. Say there are 20 of both chiralities of Plant, 21 d-Bird and 19 l-Bird. Since there is 1 more d-Bird, they will eat d-Plants faster, l-Plants will have more opportunity to spread, l-Birds will have more food and pop-grow, forcing d-Birds out through either territorialism or reduced food availability. That's what I was getting at. Perhaps oversimplified, but it's just an example. Regardless, OP's edit 3 months after this answer was posted renders it moot. $\endgroup$ – Daevin Jan 24 '18 at 15:57
  • $\begingroup$ @rek this answer presupposes the little detail in the original question, 3 months ago when I answered it. Also, take plants for example; plants of any chirality must compete for basic things like water, nitrogen, carbon dioxide, and sunlight. So the base of the ecosystem is very much in competition for resources, and any specific chirality that gets an advantage will have repercussions going up the food chain. That doesn't matter know, based on your edit... but I'm curious: what is this for? Are you building a world/lore based on this? Why not just assume it can, with your other assumptions? $\endgroup$ – Daevin Jan 24 '18 at 17:18
  • $\begingroup$ @rek if you're syaing "let's assume molecules will form in 50:50 chirality", then why not "let's assume life has thrived with 50:50 chirality"? $\endgroup$ – Daevin Jan 24 '18 at 17:19

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