quantum criticality in biomolecules
TRANSCRIPT
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Quantum Criticality in Biomolecules
Gábor VattayDepartment of Physics of Complex Systems
Eötvös University Budapest
WIVACE 2016, Salerno October 4, 2016
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Much before life…
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electrons and protons
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Why electrons and protons can live forever?
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carbon synthesis
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why carbon exists in the Universe?
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QM and life
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Erwin Schrödinger
What is Life? (1944)
prediction of DNAand free will
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Albert Szent-Györgyi Nobel Prize 1937
energy transportFrenkel excitonlight harvesting
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Roger PenroseThe Emperor’s New Mind: Concerning Computers, Minds and Laws of Physics (1989)
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Stuart Hameroff
Quantum coherence in microtubules
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Stuart Kauffman
The Poised Realm
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Just before life …
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primordial soup
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The LEGO problem
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Combinatorial complexity of evolution
4n nucleotide sequences
20n amino acid sequences
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Quantum Superposition
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DecoherenceOpen quantum systems lose coherence and become classical FAPPIn 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.
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Quantum Biology
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green sulfur bacteria
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FMO complex
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FMO is searching the energy minimum
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FMO as a little quantum computer
Fleming and Engel (Nature, 2007)
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Environment Assisted Quantum Transport (2009)
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The Poised Realm
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Revisiting the chemical LEGO
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Articles of Faith1. 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.
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Fighting decoherenceDecoherence is fast for extended quantum statesDecoherence is slow for strongly localized statesSystems with strongly localized states are fragmentedSystems which are at the border of localization-delocalization survive decoherence the mostGraph of the molecule should resemble the gigantic component of a random graph at criticality
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Purity decay (Pattanayak 1999)
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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.
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Early evolved biosynthesized compounds have critical graphs
Erdös Rényi GC Vitamin D3
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Level 2.0
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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
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Quantum chaos (O.Bohigas 1984, M. Berry 1977)
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Metal-insulator transition
Disordered conductorsRandom hopping between sites: GOE statistics, fully connected quantum graph (gigantic component), delocalized states, conductor, short coherence timeHigh 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
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Critical quantum chaos:appears only in the critical point
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Articles of Faith 2.01. Critical quantum chaotic systems avoid decoherence the
best 2. Critical molecules don’t arise randomly, they require fine
tuning of parameters of the Hamiltonian3. 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
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Theophylline
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Nicotine
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Glucose
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Omega-6
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Picrotoxin
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Benzoanthracene
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Ooops! Benzoepyrene
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Testosterone
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Evidence of Quantum Criticality
in small and large molecules
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Wave functions in proteins
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Multifractal dimension of wavefunctions
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Level spacing in proteins
Gábor Vattay Dennis Salahub, István Csabai1, Ali Nassimi and Stuart A Kauffman 2015 J. Phys.: Conf. Ser. 626 012023
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Level statistics of various biomolecules
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Receptors, signaling and drugssex, drugs and rock-and-roll
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Adenosine1 O( 1) 2s2 O( 1) 2px3 O( 1) 2py4 O( 1) 2pz5 C( 2) 2s6 C( 2) 2px7 C( 2) 2py8 C( 2) 2pz9 C( 3) 2s10 C( 3) 2px11 C( 3) 2py12 C( 3) 2pz13 O( 4) 2s14 O( 4) 2px15 O( 4) 2py16 O( 4) 2pz17 C( 5) 2s18 C( 5) 2px19 C( 5) 2py20 C( 5) 2pz21 N( 6) 2s22 N( 6) 2px23 N( 6) 2py24 N( 6) 2pz25 C( 7) 2s26 C( 7) 2px27 C( 7) 2py28 C( 7) 2pz29 N( 8) 2s
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O(1) --- O(17)
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Adenosine1 O( 1) 2s2 O( 1) 2px3 O( 1) 2py4 O( 1) 2pz5 C( 2) 2s6 C( 2) 2px7 C( 2) 2py8 C( 2) 2pz9 C( 3) 2s10 C( 3) 2px11 C( 3) 2py12 C( 3) 2pz13 O( 4) 2s14 O( 4) 2px15 O( 4) 2py16 O( 4) 2pz17 C( 5) 2s18 C( 5) 2px19 C( 5) 2py20 C( 5) 2pz21 N( 6) 2s22 N( 6) 2px23 N( 6) 2py24 N( 6) 2pz25 C( 7) 2s26 C( 7) 2px27 C( 7) 2py28 C( 7) 2pz29 N( 8) 2s
O(1) O(17)
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Adenosine in the receptor
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Amino acid charges
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Adenosine in the receptor
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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)
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Adenosine1 O( 1) 2s2 O( 1) 2px3 O( 1) 2py4 O( 1) 2pz5 C( 2) 2s6 C( 2) 2px7 C( 2) 2py8 C( 2) 2pz9 C( 3) 2s10 C( 3) 2px11 C( 3) 2py12 C( 3) 2pz13 O( 4) 2s14 O( 4) 2px15 O( 4) 2py16 O( 4) 2pz17 C( 5) 2s18 C( 5) 2px19 C( 5) 2py20 C( 5) 2pz21 N( 6) 2s22 N( 6) 2px23 N( 6) 2py24 N( 6) 2pz25 C( 7) 2s26 C( 7) 2px27 C( 7) 2py28 C( 7) 2pz29 N( 8) 2s
O(1) O(17)
C(7)C(12)C(18)C(3) C(5) N(15
)
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Adenosine in the receptor
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Testosterone in the receptor
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Testosterone
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O(8) --- H(31)
O(19) --- C(18)
O(8) --- C(9)
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Plug and socket model
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Molecular level statistics is a relic of the prebiotic evolution
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Thank you!