Quantum Criticality in Biomolecules

Quantum Criticality in Biomolecules

Gábor VattayDepartment of Physics of Complex Systems

Eötvös University Budapest

WIVACE 2016, Salerno October 4, 2016

Much before life…

electrons and protons

Why electrons and protons can live forever?

carbon synthesis

why carbon exists in the Universe?

QM and life

Erwin Schrödinger

What is Life? (1944)

prediction of DNAand free will

Albert Szent-Györgyi Nobel Prize 1937

energy transportFrenkel excitonlight harvesting

Roger PenroseThe Emperor’s New Mind: Concerning Computers, Minds and Laws of Physics (1989)

Stuart Hameroff

Quantum 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 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.

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 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.

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

Purity decay (Pattanayak 1999)

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 graphs

Erdös 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 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

Critical quantum chaos:appears only in the critical point

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

Theophylline

Nicotine

Glucose

Omega-6

Picrotoxin

Benzoanthracene

Ooops! Benzoepyrene

Testosterone

Evidence of Quantum Criticality

in 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) 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)

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)

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) 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

)

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!