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Kvantum Kritikus
Biológia
ELTE 2016
október 27.
From quarks to carbon
Erwin Schrödinger
What is Life? (1944)
prediction of DNA
and free will
Albert Szent-Györgyi
Nobel Prize 1937
energy transport
Frenkel exciton
light harvesting
Roger Penrose
The Emperor’s New Mind: Concerning Computers, Minds and Laws of Physics (1989)
Stuart HameroffQuantum coherence in microtubules
Stuart Kauffman
The Poised Realm
Just before life …
primordial soup
The LEGO problem
Combinatorial complexity of
evolution
4n
nucleotide sequences
20n
amino acid sequences
Quantum Superposition
DecoherenceOpen quantum systems lose coherence and become classical
FAPP
In physics:
low temperature (below mK)
separation from the environment
In biology:
high temperature (300 K)
strong coupling (water and dipole moments)
Verdict: On the mass and length scale of amino acids and
nucleotides coherence is too short lived to make any
difference.
Quantum Biology
green sulfur bacteria
FMO complex
FMO is searching the energy
minimum
FMO as a little quantum
computer
Fleming and Engel (Nature, 2007)
Environment Assisted
Quantum Transport (2009)
The Poised Realm
Revisiting the chemical LEGO
Articles of Faith
1. There is no such thing as classical, p and e stay
quantum: Molecules can hover between quantum and
classical all the time (The Poised Realm).
2. Without quantum parallelism evolution can’t beat
combinatorics.
3. Chemicals, which can stay coherent for a long time in a
hostile, coherence breaking environment (soup), have
more chance to try new combinatorial possibilities.
4. They are the ones which evolve into even larger
molecules.
5. Decoherence avoidance is a selectional advantage.
Fighting decoherence
Decoherence is fast for extended quantum states
Decoherence is slow for strongly localized states
Systems with strongly localized states are fragmented
Systems which are at the border of localization-
delocalization survive decoherence the most
Graph of the molecule should resemble the gigantic
component of a random graph at criticality
Purity decay (Pattanayak
1999)
Anderson transition
L
Critical states Localized states
Extended states
disorder VW /
Purity decay of the chromophore ring with 1D Harper hamiltonian.
Vattay G, Kauffman S, Niiranen S (2014) Quantum Biology on the Edge
of Quantum Chaos. PLoS ONE 9(3): e89017.
Early evolved biosynthesized
compounds have critical
graphsErdös Rényi GC Vitamin D3
Level 2.0
Random matrix theory
Wigner and Dirac
(1951)
Universal GOE level
spacing statistics
Random nuclear interaction
Hamiltonian
Statistical description of
energy levels
Semicircle law for DOS
Quantum chaos
(O.Bohigas 1984, M. Berry 1977)
Metal-insulator transitionDisordered conductors
Random hopping between sites: GOE statistics, fully
connected quantum graph (gigantic component), delocalized
states, conductor, short coherence time
High on site randomness: Poisson statistics, fragmented
quantum graph, localized states, insulator, long coherence time
Phase transition between conductor and insulator at a critical
level of on site randomness,
Critical quantum chaos: semi-Poissonian statistics, critical
quantum graph, fractal states, conductor and long
coherence time
Critical quantum chaos:
appears only in the critical point
Articles of Faith 2.0
1. Critical quantum chaotic systems avoid decoherence the best
2. Critical molecules don’t arise randomly, they require fine tuning of parameters of the Hamiltonian
3. Critical molecules should be rare exceptions among molecules in general
4. It is an evolutionary advantage for a molecule to be in the critical chaotic state
5. Naturally evolved molecules -- molecules with biological functions -- should be predominantly critical
Theophylline
Nicotine
Glucose
Omega-6
Picrotoxin
Benzoanthracene
Ooops! Benzoepyrene
Testosterone
Evidence of Quantum
Criticalityin small and large molecules
Wave functions in proteins
Multifractal dimension of
wavefunctions
Level spacing in proteins
Gábor Vattay Dennis Salahub, István Csabai1, Ali Nassimi and Stuart A Kauffman
2015 J. Phys.: Conf. Ser. 626 012023
Level statistics of various
biomolecules
Receptors, signaling and
drugssex, drugs and rock-and-roll
Adenosine1 O( 1) 2s
2 O( 1)
2px
3 O( 1)
2py
4 O( 1)
2pz
5 C( 2) 2s
6 C( 2)
2px
7 C( 2)
2py
8 C( 2)
2pz
9 C( 3) 2s
10 C( 3)
2px
11 C( 3)
2py
12 C( 3)
2pz
13 O( 4) 2s
14 O( 4)
2px
15 O( 4)
2py
16 O( 4)
2pz
17 C( 5) 2s
18 C( 5)
2px
O(1) --- O(17)
Adenosine1 O( 1) 2s
2 O( 1) 2px
3 O( 1) 2py
4 O( 1) 2pz
5 C( 2) 2s
6 C( 2) 2px
7 C( 2) 2py
8 C( 2) 2pz
9 C( 3) 2s
10 C( 3) 2px
11 C( 3) 2py
12 C( 3) 2pz
13 O( 4) 2s
14 O( 4) 2px
15 O( 4) 2py
16 O( 4) 2pz
17 C( 5) 2s
18 C( 5) 2px
19 C( 5) 2py
20 C( 5) 2pz
21 N( 6) 2s
22 N( 6) 2px
23 N( 6) 2py
24 N( 6) 2pz
25 C( 7) 2s
26 C( 7) 2px
27 C( 7) 2py
28 C( 7) 2pz
29 N( 8) 2s
O(1) O(17)
Adenosine in the receptor
Amino
acid
charges
Adenosine in the receptor
O(1) --- O(17)
C(7) --- C(12)
C(18) --- H(30),H(31)
C(3) --- C(5)
C(3) --- C(16)O(17)O(19)
N(15)
Adenosine1 O( 1) 2s
2 O( 1)
2px
3 O( 1)
2py
4 O( 1)
2pz
5 C( 2) 2s
6 C( 2)
2px
7 C( 2)
2py
8 C( 2)
2pz
9 C( 3) 2s
10 C( 3)
2px
11 C( 3)
2py
12 C( 3)
2pz
13 O( 4) 2s
14 O( 4)
2px
15 O( 4)
2py
16 O( 4)
2pz
17 C( 5) 2s
18 C( 5)
2px
O(1) O(17)
C(7)C(12)
C(18)C(3) C(5) N(15)
Adenosine in the receptor
Testosterone in the receptor
Testosterone
O(8) --- H(31)
O(19) --- C(18)
O(8) --- C(9)
Plug and socket model
Molecular level statistics is a
relic of the prebiotic evolution
Thank you!
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