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Chirality, From Chemical Supply Houses to Life as We Know It

I wrote here a few years ago about the Mysterious Sparteine Shortage, and it’s a problem that hasn’t gone away. Sparteine, for those who collect neither alkaloids nor asymmetric organic chemistry routes, is a naturally occurring compound (found in a South American species of lupine, among other places), and it’s also an interesting reagent. Its rigid ring structure and placement of two basic tertiary amines make it able to form asymmetric anionic complexes in solution, especially with organolithium reagents. This can allow some some really useful reactions that form only one enantiomeric product (a mirror image isomer), a feature that synthetic organic chemists are always on the lookout for.

The problem, as mentioned in that blog post, is that the asymmetric reagent needs to be available. An imbalance of chirality doesn’t just appear. If you have a compound that’s a single enantiomer, you had to make it or purify it via something else that was a single enantiomer. Things that aren’t capable of being mirror-image isomers (like plain water) or are fifty-fifty mixtures of such isomers aren’t able to separate or synthesize pure enantiomers themselves. If someone drops a shoe down a straight metal tube (a symmetric item), you’re not going to be able to tell if it’s a left-hand or right-hand shoe that’s rattling down the thing, but if you reach out with your (asymmetric) left or right hand and touch said shoe after it comes out, you can tell even with the lights off.

We have the lupine to thank for making asymmetric sparteine for us, but someone has to go to the trouble of isolating it or synthesizing it from a more available “chiral pool” precursor (for sparteine, that would be another alkaloid, cytisine). There was some sort of major hiccup in the supply several years ago, though, which was not the first time this had happened. This makes large-scale attempts to use the synthetic methods based on the compound risky – here, for example, is the process group at Vertex opting to go via another route rather than take the chance. They were also looking at “sparteine surrogate”, a very similar compound that can perform the same types of chemistry, but that one is also derived from cytisine and doesn’t necessarily get around the supply problems, especially for production work.

The O’Brien group at York that developed the surrogate now reports a gram-scale synthetic route to it, which might help. This one doesn’t require a plant to make you a single alkaloid enantiomer at all – instead, the asymmetry comes from the use of a bacterial lipase enzyme (from a Burkholderia species) to deliver a single enantiomer at a key step during the synthesis. That’s another good example of “chirality’s gotta come from somewhere” – trace any preparation of a single enantiomer back far enough, and you’ll almost certainly find something derived from a living creature, since biochemistry is by far the most ready source of asymmetric molecules.

All proteins and all carbohydrates in living organisms on Earth have the same “handedness”, which is a powerful argument for a single origin of life (or at the very least, a single surviving lineage of such origins). How we all ended up that way is a deeply controversial topic – is there something about one enantiomeric series that’s intrinsically better? That should be impossible, actually – chemically, the two are identical. Is there some way that an imbalance of two mirror isomer amino acids or sugar percursors could have developed before life got going? That takes us back to “chirality’s gotta come from somewhere” and all kinds of weirdo explanations that go back to subtle asymmetries in basic physical laws and the like (a topic I wrote about on this blog in 2002 – man, have I written a lot of blog posts). If our sorts of life is relatively easy to develop in the universe (which after all is swimming in water, amino acids, and so on), will we run into a fifty-fifty mix of isomeric life forms as we start to explore? I have no idea, and neither does anyone else – it’s one of the major open questions, and looks to remain so for a good time to come.

One more philosophical topic, since it’s Friday, after all: how do we ourselves recognize asymmetry? In other words, how do we know right from left? The question sounds ridiculous, but improves on inspection. Humans are (mostly) bilaterally symmetric, but the two hemispheres of the brain are a strong exception. I cannot mention that exception without sending people down the rabbit hole that is the Jaynes “bicameral mind” hypothesis – Ash Jogalekar has pointed out to me that Richard Dawkins once called that one “either complete rubbish or a work of consummate genius, nothing in between“, and I can’t disagree. How embryos develop such asymmetries in the first place is another unexpectedly deep question, and might come down to the direction that cilia are beating, which might well come down to the proteins involved in their construction, and we’re back to chirality-of-biochemistry again.

Recall as well that our eyes are wired separately into each hemisphere (which has led to a few spectacularly weird reports in the literature after the desperate surgical expedient of corpus callosotomy in severe cases of epilepsy. Severing the main neural connections between the two hemispheres in such a fashion has a number of side effects, and among these can be that a patient (at least at first) gives different answers to the same questions when they’re read by the left eye versus the right one (the different verbal fluencies of each hemisphere are a factor, too). So my hypothesis is that on a macroscopic level, our chirality-recognition system is based on asymmetries in our conscious processing of the world via our left and right eyes, and thus our left and right brain hemispheres. I will be happy to see people poke holes in this idea in the comments.


62 comments on “Chirality, From Chemical Supply Houses to Life as We Know It”

  1. GladToMoveToProcess says:

    Regarding how we recognize asymmetry: many years ago, I had a sophomore organic student who could not do so – she didn’t understand the difference between left and right, clockwise and counterclockwise, and so on. She knew which was her left hand, as she put her watch on the left wrist (“It felt right when I put it there.”) Wow, did she struggle with R/S and the like. Interestingly, she did very well with all the rest of organic!

    1. UudonRock says:

      Yikes. I hope you strongly suggested pharmacology might not be the right field for her…

    2. Crap grad student says:

      Its going to be hilarious, when grad schools have to explain why the tuition waiver was total BS to attract ‘students’. People think republicans are some kind of evil anti science zombies. What they want to do is stop the manipulation of students and bring back some legitimacy to the institution. If you are a school, act like it, if your a slave driver bent on world domination, admit it. The students that are really dedicated, will only be too happy to take out a loan

      1. steve says:

        What an amazingly on point response!

        1. Crapgradstudent says:

          Oh, cant discuss things that were discussed 3 whole days ago on this blog and were being debated last night in the US congress, and 140k grad students formally submitted protests in regards to. No that would be too much. Wouldnt want to draw attention to manipulative grad schools, you might have to earn the respect of ypur students, instead of quietly encouraging them not to go into pharmacology.

          1. Scott says:

            You can discuss the grad student tuition waiver *in the blog post&comments* about it. *This* post and comments are talking about Chirality, and how inability to recognize the difference between things might make someone unsuited for a career in the field. You know, like how being red-green color blind might make someone unsuited for a career as an electronics repair tech, where being able to read the colors on a resistor matters. Black Brown Red Orange Yellow Green Blue Violet Gray White (better known by a vulgar mnemonic that I’m not going to inflict on people here). Is that a red band (2) or a green band (5)? Is that a blue band (6) or a yellow (4)?

            Or how being allergic to shellfish makes one unsuited to military service, because the military uses an iodine-based sanitizer on emergency air breathing masks. Having your face swell up while wearing a forced-air respirator is no fun for anyone involved!

  2. Me says:

    I would poke a hole, but i don’t know which hand to use, it may end up being the enantiomer of a poke which will rotate the plane of my meaning in an opposite direction.

  3. Curious Wavefunction says:

    You may be on to something. Consider that birds don’t have a corpus callosum, so weirdly enough, what the left eye of a pigeon sees is remembered only when the left eye is open. There seems to be no information transfer between the hemispheres in birds, which is what partly accounts for the ‘weaving’ motions hens make when they approach an object, alternately exposing each eye to it. Something similar has been observed for octuposes, although there’s at least some information transfer in them (and octopuses are just weird because of their “distributed” nervous systems). It’s very likely, therefore, that chirality recognition evolved when our ancestors lacked a corpus callosum and then got passed on as a useful adaptation into human beings.

  4. MP says:

    “a left-hand or right-hand shoe” made my laugh much more than it should have.

  5. anon says:

    “in our conscious processing of the world via our left and right eyes”
    So someone with only one eye wouldn’t be able to recognize chirality?

    1. AF says:

      Presumably one needs 3D vision – hence the 2 eyes with 6 degree angle or so (if I remember correctly)

    2. Peter S. Shenkin says:

      The blind can tell the difference between a left and right shoe. Not even a single eye is needed.

    3. OldLabRat says:

      From personal experience, I can say that persons without binocular vision have no trouble distinguishing chirality. 🙂 (assuming the corpus callosum is intact from birth).

  6. weak chiral says:

    I’d always wondered whether the only chiral force in nature, the weak nuclear force, was connected to our biological chirality in some way. And indeed, there’s an emerging body of literature that suggests the dice were loaded during abiogenesis.

    1. AF says:

      Why not the Earth magnetic field or the Coriolis force?

      1. Peter Shenkin says:

        The earth’s magnetic field has shifted several times on the geological time scale.

      2. Victor says:

        You can do asymmetric grignard reactions if you run them in an NMR

        1. Anonymous says:

          “You can do asymmetric grignard reactions if you run them in an NMR” sounds like a reference to the fraudulent claims of G. Zadel, C. Eisenbraun, G.-J. Wolff, and E. Breitmaier, Angew. Chem. Int. Ed. Engl. 1994, 33, 454. Although it got past the referees and editors of Angew, it was quickly recognized by others that it violates physical theory and was quickly exposed when the grad student admitted to spiking his samples with chiral products.

          Don’t put your hopes in the Mother Earth’s rotation, either. Dougherty claimed to achieve “Asymmetric Synthesis in a Confined Vortex: Gravitational Fields Can Cause Asymmetric Synthesis” which also seems to violate physical theory and could not be reproduced.

          Here’s a review that also covers the concepts: “Absolute Asymmetric Synthesis under Physical Fields: Facts and Fictions”, Avalos, et al., Chem Rev, 1998, 98(7), 2391. (PAYWALL)

    2. Red Agent says:

      The discussion of the origins of chirality in life on earth is reminiscent of the discussion of the preponderance of matter v. antimatter in the universe. Is there some inherent advantage or energy level preference for one over the other? Could the roll of the dice (flip of the coin more like) just has easily have gone the other way? Was some minor, random disproportion in the beginning magnified over time? And, really big grand unifying question, is there a connection between the two asymmetries? Hmmm….

    3. Kent G. Budge says:

      The weak force is so, well, weak, that it has an utterly negligible effect on chemistry (except nuclear chemistry). I suspect the chirality of life is a good example of spontaneous symmetry breaking, where the more stable configuration of nature is for one chirality to overwhelmingly predominate — no preference which, but one emerges during the process of evolution.

    4. Anonymous says:

      Even achiral substances, e.g., NaClO3, can spontaneously form chiral crystals. In 1854 (a few years after Pasteur), Marbach observed crystals of NaClO3, some of which were L-rotatory and some of which were R-rotatory.

      More recently (late 1900s), it was shown that you could get enantiomerically pure crystals by grinding or stirring. (Imagine one random crystal taking over the mixture and then driving the equilibrium to crystals all of one chirality.)

      One “origin of chiral life forms” model is that spontaneously chiralized minerals formed a chiral substrate for the formation and selection of chiral organics, and then chiral life.

  7. Uncle Al says:

    Gene-gineer tall pretty nitrogen-fixing annual legume Lupinus mutabilis for large alkaloid content. Furiously grow it US down South. Seeds are 42% protein and 18% fat. Sparteine, animal feed, biofuel. Hat trick!

    “All proteins and all carbohydrates in living organisms on Earth have the same “handedness” L-Chiral protein amino acids (achiral glycine, D-serine neurotransmitter, CIP notation freak cysteine), D-reducing sugars. Racemate spontaneous chiral resolution is not common re Viedma deracemization (DOI:10.1002/cphc.201300699)

    That life is resolved chiral is unremarkable. That life might be universally homochiral is an interesting question. Geometric chirality cannot be measured

    but it can be calculated from a structure file (HyperChem *.hin works well) with QCM software on scale from 0 (perfect sock) to 1 (perfect shoe), DOI:10.1063/1.1484559 Complicated, but good in any number of dimensions. It has not been a royal road to pharma.

  8. Icexcellence says:

    I’m pretty sure a few of the people I met in grad school were racemic

    1. agsone says:

      Reminds me of the scene in Orphan Black* where the main protagonist shoots her evil clone in the heart. The evil clone survives because she is actually a diastereomeric identical twin whose heart is on the right … she also transpires to be misguided rather than evil.

      *(BBC America, streams on Amazon, worth watching)

      1. aairfccha says:

        *tilt* Chirality has has nothing to do with situs inversus…

  9. Design Monkey says:

    Hmm, I would suppose that chiral stuff recognition in humans is located wholly in that spatial thingy hemisphere, and the other, speech one is not necessary for that and possibly is not even capable to distinguish those. It would be easily testable with those split brain human lab rats, and it might be that brain guys have already done that and its already is written up in papers out there.

  10. JSM says:

    Chirality can also occur via natural selection. Imagine a primordial ooze consisting of racemic amino acids (or nucleotides, etc). At key positions (active sites) within an evolving biopolymer, one enantiomer cannot substitute for another. So, given a racemic pool, only one enantiomer would be used.
    The global preference for one enatiomeric set (ie all L-amino acids) can thus be explained by evolutionary efficiency: it would be wasteful to evolve orthogonal biochemical pathways for processing both enantiomers of otherwise identical molecules.
    Likewise, once the machinery to process one enantiomer evolves, it is easier for that machinery to further evolve to process a similar chemical series (ie once an L-leucine processing biopolymer evolves, it is easier for it to mutate to an L-isoleucine processing biopolymer than it would be for it to mutate to process D-isoleucine).
    Taken together, chiral selection from an racemic pool seems reasonable as an early step in the evolution of life.

  11. executiveMBA says:

    Another question: why isn’t life racemic?

    1. Istvan Ujvary says:

      It is racemic!
      Just to reiterate (inIn case you have not seen it):

  12. PapaFrancesco says:

    Chirality exists because God has chosen a set of rules that you sanctimonious Nimrods haven’t discovered yet. Lika the reason RNA breaks down and da DNA remains sacrosanct. It is not for you to judge but to be judged on.

    So Love All Molecules-Not just the L ones.

    And God told me to tell you – Stop Picking His Lupines! They are for all of his Animals to enjoy, not just the Nimrods!

    1. Uncle Al says:

      ” Lika the reason RNA breaks down and da DNA remains sacrosanct”

      Ribose and deoxyribose, respectively, versus the adjacent phosphate center. For the latter, no nucleophilic oxygen, no chain disruption. Religion is like climatology, economics, psychology, and the Democrat Party: It can always voluminously explain what it can never succinctly predict.

  13. Barry says:

    Turns out, sparteine can also be extracted from scotch broom (as well as from lupines).Scotch broom is a notorious invasive non-native species, currently taking over huge tracts of Northern California (the closely related French Broom is rampant, too)
    If someone seriously wanted to undertake the extractions, kilotons of material are available.

    1. Derek Lowe says:

      I’ve seen that stuff blooming all over NW Washington state, too. It’s like some kind of yellow-blooming kudzu bush out there.

      1. Barry says:

        at least cows will eat kudzu. Even deer won’t touch Scotch Broom. Only goats (and fire) seem to stop it. Maybe it has a pest in its native environment that we’ll have to import.

        1. A Different Barry says:

          Hmmmm, now, is this where someone from Australia gets to mention introducing cane toads as seeming like a great idea l, so they could eat those pesky cane beetles?

  14. Gradschooltip says:

    ‘External’ advisers are supposed to be there to check your schools influence, or fill in if your prof decided he cant support your for whatever reason. This, like much of the grad school model, is a sham. My PI got into a dispute with me post-thesis, decided to pull the plug on me. Without options, i called my external adviser, who had reacted well to my thesis, and asked for 1 paragraph rec letter. He initially acted positive, then called my PI, and then said no letter would be forthcoming. They are just pawns for your PI.

  15. gippgig says:

    “you had to make it or purify it via something else that was a single enantiomer” – wrong! The first resolution of an optically active compound was done by individually sorting mirror image crystals that spontaneously formed when the racemic compound crystallized (at least that’s the story I’ve read – has this been properly verified?).

    1. Old Pump Kicker says:

      Louis Pasteur did the sorting scut-work for his doctoral dissertation. See the Wikipedia articles on tartaric acid and on Pasteur for the details.

    2. Iain says:

      Sorting mirror image crystals comes back to how we recognize asymmetry. The enantiomers could have been isolated via the chirality of amino acids in the brain

    3. Process guy says:

      Spontaneous resolution of organic molecule racemates is actually not so uncommon, as you say. Around 10% of all racemic mixtures form enantiopure conglomerates spontaneously (1).

      (1) Srisanga, S.; ter Horst, J. H. Cryst. Growth Des. 2010, 10, 1808–1812.

  16. I read somewhere (can’t remember quite when) that the eye wiring is even more intricate than that: the right of each retina is wired to the right brain, because it sees the left-field-of-view, so the mechanics there have to be dealt with by the right brain…. and so forth

    1. tangent says:

      This is correct. Classic brain-damage symptom is to lose one half of your visual field (and usually to lose awareness of it).

  17. Qedlin Saltum says:

    I was searching for elaboration of the most critical life-related chirality, i.e., amino acids and sugars, left and right, 100%, only produced with organisms, and never resulting from any naturalistic processes, not chemical, extraterrestrial, radiational, nuclear or electromagnetic. This exposes any naturalistic origin of life hypothesis, making all the follow-on discussion of brains, eyes, and the rest of any macro-level cellular or organism function as interesting but only relevant because of homochirality at the nucleotide, protein chain level.

  18. Chris Phoenix says:

    If I understand right, the visual symbols “b” and “d” are chiral equivalents. Your hypothesis seems to be that special chiral brain properties are necessary to distinguish them. However, fairly simple and apparently non-chiral artificial neural nets can distinguish them easily.

    1. Canman says:

      Just because they are mirror images does not mean they are chiral. The letters b and d are superimposable on one another, and thus not chiral.

      1. Kent Kemmish says:

        I think b is not superimposable on its mirror image d, and therefore b and d are chiral.

        1. Canman says:

          They are superimposable. Quite easily by flipping one over they will stack nicely on each other.

          1. Kent Kemmish says:

            As someone with topological dyslexia I might completely miss the point, but I think “b” is chiral. Everything assymetrical is chiral, right?

          2. Design Monkey says:

            Letter b has a plane of symmetry.

          3. Druid says:

            When b is on paper, the view from the other side is paper. When it is on a screen, the view is the back of the screen. If you take a marker pen and write a b on a pane of glass, from the other side it looks like d, but unlike the b you can’t rub it out. So in any practical situation b and d are enantiomers. They can be rotated to p and q but then most of the other letters such as e are upside down. If you can tell up from down from front from back, you are either chiral or pro-chiral.

          4. Design Monkey says:

            Nope, druid. You are talking about chirality of system of letter b and glass, on which you wrote it. That’s not the letter b alone. Take sheet metal , cut the letter b from it, and that’s it – perfectly superimposable with d.

            Actually AVS-600 already wrote about importance of number of dimensions. Perhaps that was the source of your misunderstanding. Letter b is chiral in 2 dimension space, and not chiral in 3 dimansions.

          5. Druid says:

            Dear Design Monkey, thank you for suggesting cutting the letters out of sheet metal – I never thought of that! It took me a while and a short visit to A&E but I bib it in the enb and bang me you were right – d’s and b’s are iqentical. I must puy you a brink, pecause you earneq it!

      2. AVS-600 says:

        *Every* chiral object in N dimensions becomes achiral if it’s transformed into a “flat” object in N+1 dimensions (it gains a plane of symmetry in every case). Clearly though, in the two-dimensional context that we concern ourselves with when we’re thinking about written words, b and d are non-superimposable.

        1. Canman says:

          You are just so wrong!

          1. DH says:

            Nope. Create a “b” and a “d” on small pieces of paper, and lay them on a larger piece of paper. Try to superimpose them *without removing them from the plane of the paper*. It is not possible. The letters are chiral in 2D, though not in 3D.

  19. TWolfgangR says:

    There’s some brilliant work on asymmetric amplification achieved by Soai’s autocatalytic reaction. Although he’s not creating a biologically relevant product, the concept is eye opening and might explain how homochirality might have occured. Blackmond’s work is also quite impressive, such as the synergistic kinetic resolution towards optically enriched RNA precursors. There are other interesting options that show how enantioenrichement of biologically-relevant compounds may have occurred (ex. sublimation, interstellar circular polarized radiation).

    Check out these papers below, or reviews related to them, to learn more: (Soai) (Blackmond)

  20. anon says:

    Our hands are not small molecules that are uncontrollably rotating in solution – the fact that they are chiral is not the important aspect that allows us to feel the difference between right and left shoes. Even if our hands were symmetric and had two thumbs, one on each side, the way our fingers are wired to our brain would tell us which thumb is which, and would still easily tell right shoes from left shoes.

    A drawing of a chiral molecule does not have to involve any chiral chemicals, nor do chiral chemicals need to be involved in sensing the image (CCD camera), or processing it (CMOS chips). We understand chirality as a learned geometrical concept (can’t superimpose mirror image), not because chiral chemistry has magically imbued a chiral instinct upon our brains. It would not be entirely surprising if geometry was mostly understood on one side of the brain (language areas are mostly concentrated in one hemisphere), but the way you phrased the question seemed to be asking for a more simplistic, chemical-like interpretation of the brain.

  21. chiz says:

    People with object orientation agnosia lose the ability to determine the orientation of objects.

    People with Gerstmann syndrome can’t tell left from right, but they also suffer from dysgraphia and dyscalculia and finger agnosia so this wouldn’t explain the first commenter’s student. But maybe there is a more specific form of brain damage that can cause L/R problems without the other three symptoms. In the last decade or so we’ve discovered that there are significant sub-populations of people with impairments that were once thought to be rare, or that we didn’t even know about – faceblindness, aphantasia, musical anhedonia, topographagnosia, etc so it wouldn’t surprise me if there was a sub-population of people with L/R-blindness.

    Just to be pedantic I will note that D-amino acids do occur in living organisms. The wikipedia says that this happens through post-translational modification but, as I understand it, they can also occur in non-ribosomally synthesized polypeptides and polyketides. In humans, D-serine shows up in our brains as a gliotransmitter/neurotansmitter.

    1. Uncle Al says:

      Autists are often L/R-blind, and common in speakers of Arabic, Aramaic, Azeri, Dhivehi/Maldivian, Hebrew, Kurdish (Sorani), Pashto, Persian/Farsim, Syriac, Urdu, and Yiddish, written and read right-to-left. Not A Good Idea. Where there is bad there is worse – bostrophonic languages that snake back and fourth in alternate lines.

      The tellurium crystal formula unit is one atom. The unit cell is three atoms, A given crystal is perfectly geometrically chiral, enantiomorphic space groups either P3(1)21 (right-handed) or P3(2)21 (left-handed). Three atoms can only form a flat triangle, achiral in 3D. Tricky stuff this chirality – there’s a geometric footnote.

  22. David Edwards says:

    Hmm, I’ve been thinking … aren’t ‘b’ and ‘d’ topologically equivalent?

    As in, you can deform one to form the other, in a continuous manner, without cutting and pasting?

    Only in 3D, a doughnut is topologically equivalent to a coffee cup, and it strikes me that similar concepts apply here.

    Which leads me to ask, at what point does the topology of a space make chirality possible?

    1. Anonymous says:

      Thinking of the letters of the alphabet as solid objects in 2D, any letter with an open hole is topologically equivalent to any other: a A b (but not B) d D g (but not G) o O p P q Q R (but not r). You can “shmush” the protruding bits back into the donut without tearing, cutting, or breaking the surface (and the reverse).

    2. Anonymous says:

      “Which leads me to ask, at what point does the topology of a space make chirality possible?” I’m not sure what that means. Topology defines the relationships of sets of points in a space. Chemists usually think of points as atoms, not as a lattice or network of coordinates in space that may or may not be occupied by atoms. Furthermore, chemical structure is about connectivity and geometry and the relative positions of points (atoms) in 3D-space. Topology is substantially non-metric and non-geometric. (Topology doesn’t care how long the connections (bonds or chains of atoms) are or the position of points (atoms) in space or on a surface. You can shmush things around and still have the same topology but a different molecular architecture. But this reminds me of some stories about topology …

      There is an interesting book on “Topological Methods in Chemistry” by Merrifield and Simmons. As a grad student with Roberts, Simmons proved the intermediacy (hence, the existence) of benzyne. He is the same Simmons as the Simmons-Smith Reaction. He also came up with the idea of longicyclic aromaticity (a topological variant of aromaticity), inside-out stereoisomerism and other brilliant ideas. The story goes that it was Simmons who conceived the idea of making the topologically non-planar molecules such as K5. The actual synthesis was carried out by his son in 1981. By a remarkable, even unbelievable coincidence, Paquette also synthesized K5 by almost the exact same route and the papers were published back-to-back in TL. (Some people believe that Paquette stole the idea. Maybe he was practicing for taxol.) (Walba synthesized a chemical Moebius strip, the first K3,3 non-planar molecule, in 1982. To your question: Walba’s 3-rung Moebius strip is chiral but I think the 4-rung Moebius strip is achiral [not sure, must check]. And other criteria have been explored.)

      A large ring of atoms has one topology (a ring). Benzene, cycloheXane, and cycloheCtane have the same topology. Snip a large ring, tie it into a trefoil knot and reconnect the ends and you have a different toplogy (a knot) even though the connectivity is the same. Trefoil knots are chiral. Take two rings, snip one, intercalate, and reconnect the snipped ends and you have catenane topology (first proposed by Willstatter in the early 1900s).

      I’m thinking of other papers on chemical topology but w/o literature access it’s impossible to look things up for checking things out.

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