Transcript Mirror symmetry - The Institute of Chemistry

On left and right:
Symmetry and Chirality in Molecules and Design
David Avnir
Institute of Chemistry
The Hebrew University of Jerusalem
Shenkar, 23/12/2014
1. Why is a chemist visiting Shenkar’s design
department?
Insulin
Haemoglobin
Quasi-crystals
Diffusion-reaction pattern
Symmetry - a universal language of shape and structure
Mirror symmetry
Rotational symmetry
Rotational and mirror
symmetries combined
Our focus: Mirror symmetry
Called also reflection symmetry, bilateral symmetry
Why is this symmetry called “mirror symmetry”?
Combining an object with its mirror
reflection produces that symmetry
Combining an object with its mirror reflection produces mirror symmetry
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2D mirror symmetry in chemistry
3D molecular mirror symmetry
Zeolite
Carbon
nanotube
Alexander McQueen
(1969 – 2010)
2D-Mirror symmetry, textile: scarves design
Alexander McQueen
The basic 3D mirror symmetry in textile design for fashion
3D mirror symmetry of the body preserved in textile design
2. Moving away from mirror symmetry - chirality
Near symmetry in chemistry
cyclohexane
HIV Protease
Near-symmetry in McQueen’s design
Bjork
Far-away from mirror symmetry
Far-away from mirror symmetry –
because of design
Far-away from mirror symmetry –
because of body posture
Far-away from mirror symmetry –
because of body posture and design
Chirality and handedness
When mirror symmetry is removed, a special property emerges:
The object may come in two forms:
a left-form and a right-form (handedness)
* These left and right forms are called enantiomers
* 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.
If there is mirror symmetry, the object coincides with its mirror
image, the object is achiral – and there is no pair of enantiomers
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Chirality is an extremely important property in
the natural sciences
Life is based on left-handed amino acids and
right-handed sugars
Why is it so important?
To understand it let us take the case of spiral chirality
Diastereomeric (DS) interactions
The hand-glove interactions
The interaction between a right-hand
(Rh) and a right-glove (Rg) is different
from the interaction of a right-hand (Rh)
with a left-glove (Lg)
Two different interactions:
Rh-Rg
Rh-Lg
Comfortable vs. Very awkward
In the life-sciences chiral interactions are highly
important
Reason: All biological receptors are chiral; therefore:
The interaction: Left-molecule
receptor
and the interaction: Right-molecule
receptor
are different
“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)
Left-handed and right-handed molecules:
* Taste differently
* Smell differently
* Can heal or kill (Thalidomide)
Carvone
(R): Spearmint
(S): Caraway
(kummel)
3. Relevance of chirality considerations to design
Many textile design patterns are chiral
But now we know that such designs can come in left or
right forms; here they are:
The enantiomeric pair of the same design
Why has McQueen selected the right spiral?
Is it an important question for design?
Our biological receptor at focus:
The chiral 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, if the information
– visual – is chiral, DS
interactions result between the
brain and the information
Therefore, left and right
objects must be
perceived differently by
the brain
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. McLaughlin, Brain and Cognition, 20, 300 (1992)
Rembrandt’s 2D-chiral preferences
N. Konstom,
“Rembrandt’s use
of models and
mirrors”,
Burlington
Magazine, 99, 94
(1977)
Are chirality considerations relevant/important to
textile design?
First answer:
Yes, the left enantiomer and the right
enantiomer of the same design may be
perceived aesthetically in a different way.
4. Additional considerations in brief
Induction of chirality: Accessories
Induction of chirality by 3D texture
Illumination induces chirality
Alexander McQueen
Randomness is always a source of chirality
Are these left- or right-handed?
The specific label is not important:
Handedness labeling is an agreed convention, not an
inherent property like chirality itself
Chirality has a degree
The environment strongly affects perception
Posture and design - The four possibilities:
# Left design –
Left posture
# Left design –
Right posture
# Right design –
Left posture
# Right design –
Right posture
Diastereomeric interactions with artificial chiral environments
Diastereomeric interactions with natural chiral environments
Conclusion
Are chirality considerations relevant to design?
First answer:
Yes, the left enantiomer and the right enantiomer of the same
design may be perceived aesthetically in a different way.
Second answer:
Yes - most environments are chiral, and therefore left- and
right versions of the same design, interact with it differently.