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!