Lecture was given on October 4, 2016, on Wivace/Bionam, Salerno, Italy

1. Quantum Criticality in
Biomolecules
Gábor Vattay
Department of Physics of Complex Systems
Eötvös University Budapest
WIVACE 2016, Salerno October

2. Much before life…

3. electrons and protons

4. Why electrons and protons can
live forever?

5. carbon synthesis

6. why carbon exists in the
Universe?

7. QM and life

8. Erwin Schrödinger
What is Life? (1944)
prediction of DNA
and
free will

9. Albert Szent-Györgyi
Nobel Prize 1937
energy transport
Frenkel exciton
light harvesting

10. Roger Penrose
The Emperor’s New Mind: Concerning Computers,
Minds and Laws of Physics (1989)

11. Stuart Hameroff
Quantum coherence in microtubules

12. Stuart Kauffman
The Poised Realm

13. Just before life …

14. primordial soup

15. The LEGO problem

16. Combinatorial complexity of
evolution
4n
nucleotide sequences
20n
amino acid sequences

17. Quantum Superposition

18. Decoherence
Open 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.

19. Quantum Biology

20. green sulfur bacteria

22. FMO complex

25. FMO is searching the energy
minimum

26. FMO as a little quantum
computer
Fleming and Engel (Nature, 2007

27. Environment Assisted
Quantum Transport (2009)

28. The Poised Realm

29. Revisiting the chemical LEGO

30. 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.

31. 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

32. Purity decay (Pattanayak
1999)

33. Anderson transition
L
Critical states Localized
states
Extended states
disorderVW /

35. 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.

36. Early evolved biosynthesized
compounds have critical
graphs
Erdös Rényi GC Vitamin D3

37. Level 2.0

38. 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

39. Quantum chaos
(O.Bohigas 1984, M. Berry 1977)

40. Metal-insulator transition
Disordered 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

41. Critical quantum chaos:
appears only in the critical point

42. 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

43. Theophylline

44. Nicotine

45. Glucose

46. Omega-6

47. Picrotoxin

48. Benzoanthracene

49. Ooops! Benzoepyrene

50. Testosterone

51. Evidence of Quantum
Criticality
in small and large molecules

52. Wave functions in proteins

53. Multifractal dimension of
wavefunctions

55. Level spacing in proteins
Gábor Vattay Dennis Salahub, István Csabai1, Ali Nassimi and Stuart A Kauffman
2015 J. Phys.: Conf. Ser. 626 012023

57. Level statistics of various
biomolecules

58. Receptors, signaling and
drugs
sex, drugs and rock-and-roll

62. Adenosine
1 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)

63. O(1) --- O(17)

64. Adenosine
1 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)

65. Adenosine in the receptor

66. Amino
acid
charges

67. Adenosine in the receptor

68. 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)

69. Adenosine
1 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)
O(1) O(17)
C(7)
C(12)
C(18)
C(3) C(5) N(15)

70. Adenosine in the receptor

71. Testosterone in the receptor

72. Testosterone

73. O(8) --- H(31)
O(19) --- C(18)
O(8) --- C(9)

74. Plug and socket model

75. Molecular level statistics is a
relic of the prebiotic evolution

76. Thank you!