On Left and Right Chirality from molecules to

On Left and Right: Chirality from molecules to galaxies to Rembrandt David Avnir Institute of Chemistry The Hebrew University of Jerusalem WSCI, Jerusalem, 20. 8. 15 1

1. Properties of chirality and its origin 2

Kelvin's definition: "I call any geometrical figure, or group of points, chiral, and say it has chirality, if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself. ” (Lord Kelvin, 1904, The Baltimore Lectures) “Chiral”, from Greek χειρ (kheir), "hand", 3

A positive definition Chirality: The property of having for the same object a left-form and a right-form This left and right forms are mirror-images of each other; they are termed enantiomers 4

* Enantiomers are different objects, but they look very similar The similarity is because they are mirror-images of each other The difference is that they cannot coincide with each other 5

Pairs of chiral helical enantiomers which cannot coincide 6

Chiral crystals - quartz 32 - Left Helix 31 - Right Helix Si. O 4 7

Labeling the left and right enantiomers Common labels: Left – Right S - R L - D The enantiomers of amino acids On our planet only L exists naturally – why? 8

The enantiomeric pair of the same design Left Alexander Mc. Queen Right 9

The two enantiomers of the Guggenheim Museum, Bilbao, Frank Gehry Which one is the left enantiomer and which one is the right one? While chirality is an inherent structural property, handedness is an arbitrary label 10

Molecules and crystals that are not chiral - achiral 11

These achiral structures have a common feature: reflection symmetry or mirror symmetry, or bilateral symmetry Zeolite 12

If there is mirror symmetry, the object coincides with its mirror image (no enantiomers): the object is achiral No pair of enantiomers 13

So why is it that for chirality we need to avoid mirror symmetry, while for achirality we need that symmetry? To understand it, let us first see why is this symmetry called “mirror symmetry”: Objects with that symmetry are built by reflection Combining an object with its mirror reflection produces mirror symmetry 14

Another example: Building an achiral object from (chiral) components in 2 D: a mirror line An object Its enantiomer The combined pair 15

So why does the reflection of an achiral object results in the same? Because reflection of mirror symmetry preserves itself. 2 D chirality – a mirror line Slide one picture over the other 16

2. Diastereomeric interactions DS Interactions 17

In general: For chirality to be expressed the chiral object must interact with another chiral object If the other object is achiral – the chirality is not expressed. Example: Adsorption of the chiral enantiomers of a chiral molecule on an achiral gold nanoparticle 18

Chirality is expressed when a chiral object interacts with another chiral object: Example - A right hand is detecting the difference between a right glove and a left glove The two different interactions: Rh-Rg Rh-Lg Comfortable vs. Very awkward This difference is called diastereomerism (DS) 19

Extreme case of DS: Bolts and nuts 20

In the life-sciences chiral DS interactions are highly important Reason: All biological receptors are chiral – they are built from left-handed amino acids only!; therefore: The interaction: Left-molecule receptor and the interaction: Right-molecule receptor are different 21

Therefore: left-handed and right-handed molecules: * Taste differently * Smell differently * Can heal or kill (Thalidomide) Carvone (R): Spearmint (S): Caraway 22 (kummel)

Left-handed and right-handed molecules: * Can heal or kill (Thalidomide) (R) – teratogenic (S) - sedative * Or can have different pharmaceutical indications 23

“How would you like to live in a Lookingglass House, Kitty? I wonder if they'd give you milk, there? Perhaps Looking-glass milk isn't good to drink“ “Through the Looking Glasss, and What Alice Found There”, Lewis Carrol (1871) 24

Chiral perception interactions with the brain * The left and right hemispheres of the brain are very unequal * Therefore, no mirror symmetry – the brain is chiral Specifically: the brain is a • chiral information receptor Therefore, left and right objects must be perceived differently by the brain 25

Psychology of aesthetic perception “When some pictures are mirror reversed, aesthetic evaluations of them change dramatically. ” “When a painting is viewed in a mirror… even the meaning can change…” “ The first major finding… was that paintings containing left-toright directional cues were preferred…” A. M. Mead and J. P. Mc. Laughlin, Brain and Cognition, 20, 300 (1992) 26

Rembrandt’s 2 D-chiral preferences N. Konstom, “Rembrandt’s use of models and mirrors”, Burlington Magazine, 99, 94 (1977) Saskia van Uylenburgh 27

The big question: Why does biology avoid DS interactions and works with only ONE enantiomer building blocks (homochirality)? Life is based only on left-handed amino acids. Why, and why not the opposite? And, when we make contact with aliens on distant planets, will they have the same handedness? 28

Temporary answers: Answer 1. Life can select its handedness (either left or right), but it must be homochiral because of efficiency of lifeinvolved operations – DS adds complexity 29

Temporary answer 2. The observed handedness on Earth is a chance-event which selected one option by a positive feedback loop mechanism of initial fluctuations One starts with a racemic mixture A process of partial right -handed enrichment Racemic mixture of gloves Homochiral 30

Temporary answer 3. The observed handedness on Earth is the result of a chiral influence on the synthesis of the building blocks Right-handed and left-handed light Neutron star Black-hole 31

3. Chirality and randomness 32

A chiral object with random features * What is its enantiomer? * What is the handedness of that tree? 33

Diffusion limited aggregates (DLAs) A random walker (drunken walker) 34

DLAs are chiral (in 2 D) New concepts are needed to treat this type of chirality 35

The chirality of a DLA is incidental Nothing in its construction is associated with left or right handedness Inherent chirality 36

The enantiomer of a DLA is virtual It can never be constructed by repeating the process The original DLA and its virtual enantiomer Real enantiomers 37

Assignment of handedness: The functional chirality solution (a)“Right” and (b) “left” DLAs Based on the differences in the diastereomeric interactions with a small L and the mirror image-L 38

Incidental and inherent chiralities can appear in the same object: Spiral chiral DLAs 39

The concept of real near enantiomers Left Right (real) Right (virtual) Right (real) Two(!) real right-handed near enantiomers 40

A chiral object may have an infinite number of near counter-enantiomers 41

4. The measurement of chirality 42

Different degrees of chirality Low degree and higher degree of chirality 43

Different degree of chirality in design

Various degrees of chirality: 45

Gradual changing 2 D chirality in aggregates O. Katzenelson 46

How do you build a measurement tool? The continuous symmetry measure : The original structure : The nearest G-symmetric srtucture N : Number of vertices d : Size normalization factor * The scale is 0 - 1 (0 - 100): The larger S(G) is, the higher is the deviation from G-symmetry H. Zabrodsky Hel-Or 47

The Continuous Chirality Measure 48

Is there a relation between the degree of chirality of a molecule and its ability to interact with a receptor? 49

Inhibition of acetylcholine esterase by chiral organophosphates S. Keinan 50

Symmetry of handaxes of early man 51

Symmetry of handaxes of early man S(s) = 1. 84 S(s) = 0. 77 S(s) = 0. 29 I. Saragusti 52

Conclusion Where does it all leave us? 53

Be careful: One day you may encounter your own enantiomer, and she/he may claim to be the real thing! 54

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