Quantum biology, water and living cells

1
Quantum biology, water and living cells

• Eugen A. Preoteasa
• HH-NIPNE, LEPD (DFVM)

2

• nature is not sparing as for its structures,
  but only for its universally applicable
  principles.
• Abdus Salam

3

• Introduction and background
• Biology from classical to quantum
• New models of collective dynamics for liquid
  water and living cell
• Ionic plasma in water
• The cell dimensions problem
• Free water coherent domains Bose condensation
  The minimum volume of the cell
• Water coherent domains in an impenetrable
  spherical well The maximum cell volume of small
  prokaryotic cells
• Plausible interaction potential between coherence
  domains
• Two coupled water coherent domains as a harmonic
  oscillator and the maximum cell volume
• Isotropic oscillator in a potential gap and the
  spherical cells larger prokaryotes and small
  eukaryotes
• Cylindrical potential gap and disc-like cells
  the erythrocyte
• Cylindrical potential gap and rod-like cells
  typical bacilli
• The semipenetrable spherical well The toxic
  effect of heavy water in eukaryotic cells
• Conclusions

4
Introductionand backgroundBiology from
classical to quantum
5
Life is a phenomenon strikingly different of the
non-living systems. Some distinctive traits

• Metabolism
• Homeostasis
• Replication
• Stability of descendents
• Spontaneous, low-rate random mutations
• Diversity by evolution 8.000.000 species
• Adaptation (e.g., bacteria eating vanadium,
  bacteria living in nuclear reactor water, life in
  desert and permafrost)
• Damage repair (e.g., wound healing)
• Integrality / indivisibility

6
Biological phenomenology and evolution

• The phenomenology and evolution of the living
  world are described by classical biology.
• Classsical biology started with the optical
  microscope and developed in XVII-XIX centuries
  (by people like Leeuwenhoek, Maupertuis, Linne,
  Lamarck, Cuvier, Haeckel, Virchow, Darwin,
  Wallace, Mendel, Pasteur, Cl. Bernard, etc.).

Tree of life

• The main ideas of biology were influenced by
  classical physics (Newton, Pascal, Bernoulli,
  Carnot, Clausius, Bolzmann, Gibbs, Helmholtz,
  Maxwell, Faraday, Ostwald, Perrin, ) and
  chemistry (Lavoisier, Berzelius, Woehler,
  Berthelot, ).

7
Molecular biology a new reductionism

• DNA (or RNA) encodes all genetic infor-mation
  (Crick Watson 1950) devastating effect on
  biology.
• Two images since 1967
• integrative (Jacob) vs.
• reductionist, (Monod)

• Recently, phenotypic plasticity and
  self-organization re- vealed limits of the
  central dogma of molecular biology
• DNA RNA Enzymes
• Genome (DNA from the ovocite of a species
  individual) Phenotype (particular individual
  organism of a species)

8

• The central dogma raises questions, e.g.
• Is all information contained in DNA, RNA?
• Are mutations purely random?
• Is the environment only selecting mutations?
• No feed-back?
• The main ideas of molecular biology
• All biological phenomena reduced to information
  stored in some (privileged) molecules.
• Only short-range specific interactions.
• Classical (Bolzmann-Gibs), equilibrium
  statistics.
• Water mainly a passive solvent.
• The cell a bag filled with a solution of
  molecules.
• This picture rooted in XIX century thinking
  is disputable. It fails to seize complexity,
  integrality of living organisms.

9
Cells, complexity, integrality

• The cell basic unit of life / at the origin of
  any organism.
• Cells an unparalleled complexity, a singular,
  unique type of order. Integrality cells are
  killed by splitting .
• Biological complexity order (almost) without
  repetition different of the physical complexity
  ( nonintegrable, 3 bodies).
• A bacterial cell 4.1010 molecules H2O, and
  5.108 various organic molecules. An eukaryotic
  cell x105 more molecules.
• Huge complexity of metabolic network. Shown above
  only 5.

10
Limits of molecular biology

• Complexity, integrality pointing to nonlinear,
  optimal, self-organized systems , to long-range
  correlations.
• Molecular biology sticks and balls picture
  isolated classical particles, short-range
  interactions.
• Success of molecular biology at the roots of
  its limits.
• Origin of life unexplained probability of first
  cell 10-40,000 , of man 10-24,000,000 in 4.109
  yr.
• Chance is not enough (Jacob 1967).
• Metabolic co-ordination How a huge number of
  specific chemical reactions occur in a cell at
  the right place / time?
• Information content in the cell much larger than
  in DNA (a read-only memory) where the rest
  comes from?
• Unexplained brain activity, biological
  chirality, etc.

11
Features of life unsolved by molecular biology

• Collective dynamics of many freedom degrees.
• Life a metastable state.
• Various types of local and global order.
• Structural and dynamic hierarchy, successive
  levels.
• Biological complexity order without repetition.
• Short- and long-range correlations and
  interactions.
• Living organisms are open, irreversible,
  disipative systems.
• They are self-organized, optimal systems
  (-gthomeostasis), with cooperative interactions.
• Nonlinear interactions, highly integrated
  dynamics.
• Such features to some degree in various complex
  non-living systems but only organisms join them
  altogether.

12
Molecular biology, biophysics, quantum mechanics

• What is the usual place of biophysics
• and QM in molecular biology?

• A) Physical methods for special materials
  studies.
• B) Molecular structure and properties quantum
  chemistry integrated in the balls and sticks
  picture of molecular biology.
• Though A), B) based on QM ancillary / trivial
  role for QM .
• Could QM yield insight on the essence of life?

13
Correlations, functions and soft matter

• Organisms evolve by functions space-time
  correlations between freedom degrees.
• Functions are controlled by specific messages.
• Messages express biological complexity. Both
  imply order without repetition convey
  information.
• Cells soft matter facilitate functions by
  (re)aggrega-tions and conformational changes.
  Flexible geometic structure, conservative
  topological correlations of freedom deg.s.
  Dynamical organization.
• Cells condensed matter facilitate long-range
  correlations and information transfer.
• Either correlations and information admit both
  classical and quantum support.

14
Classical and quantum correlations long range
interactions between (quasi)particles

• Long range correlations self-correlation
  functions in biological, chemical and physical
  systems formally similar for
• a classical observable z(r) G(D) ltz(r)
  z(rD)gt
• a wavefunction Y(r) G(D) lt Y(r) Y(rD)gt
• The self-correlation or coherence function is
  connected to interference of waves associated
  with a (quasi)particule
• I(D) Y1(r) Y2(rD)2 1 G(D)cos Dk
• Necessary condition long range interactions
  between particles or quasiparticles.

15

• Biological order and information
• Biological order order without repetition. Such
  order - aperiodic and specific (Orgel 1973)
  conveys information.
• Periodic nonspecific order minimal information
  
• AAAAAAAAAAAA
• Periodic specific order useful information
  overwhelmed in redundance
• CRYSTAL CRYSTAL CRYSTAL
• Complexity aperiodic nonspecifica order
  maximal total information, minimal useful
  information
• AGDCBFE GBCAFED ACEDFBG
• Complexity aperiodic and specific order
• THIS IS A MESSAGE.
• Well-defined sequence message, precise code,
  maximum useful information, comands an unique
  function.
• Biological systems informational syst.
  adressable both C/Q.

16
Information and quantum mechanics

• Quantity of information (Shannon, Weaver 1949)
• H S pi log2 pi p ?2 Ex. H(Xe)
  136 bit.
• Information gain between 2 probability distrib.s
  P, W
• I (PW) S pi log2 (pi / wi)
• Information gain in a quantum transition mgt ?
  lgt (Majernik 1967)
• I ( fm fl ) ? fm fm log2 ( fm fm / fl fl)
  dv
• Ex. Potential gap, I(u2u1) 3,8 bit. Hydrogen
  atom, I(u2u1) 83,1 bit.
• Hypothesis In biological systems, certain
  wave-functions may play a role in transmission,
  storage, processing, and control of information.

17
Alternatives to molecular biology

• Postulate Living organisms contain both
  classical and quantum (sub)systems.
• Alternatives to describe biological complexity
  and integral properties of organisms
• Far from equilibrium dynamics, dissipative
  structures (classical or quantum)
• Models of periodic phenomena based on equations
  with eigenfunctions and eigenvalues (classical or
  quantum)
• Quantum biology.

18
Irreversibility, far from equilibrium dynamics,
dissipative structures (Prigogine, Nicolis,
Balescu)
Spontaneous synchronization of oscillations in
glycolysis (glucose consumption) in yeast cells
(Bier)

• Limit cycle (strange attractor) All
  trajectories, whatever their initial state, lead
  finally to the cycle.
• Makes the origin of life from non-living much
  more probable.

Belousov-Zhabotinsky reaction Heterogeneous
(order) out of homogeneous (disorder).
19
Integral properties without molecular biology. I.
The fur of mammals by partial derivative equations
Diffusion-reaction of melanin
Results
20
Integral properties of cells without molecular
biology. II. Flickering modes of erythrocyte
membrane by Fourier / correlation analysis
21
Quantum biology

• Bohr, Heisenberg, Schrodinger, John von Neumann,
  C. von Weizsacker, W. Elsasser, V. Weisskopf, E.
  Wigner, F. Dyson, A. Kastler, and others QM
  essential for understanding life.
• Quantum biology (QB) speculative
  interdisciplinary field that links quantum
  physics and the life sciences (Wikipedia) runs
  the first phase, inductive synthesis, of every
  science. Some directions
• Quantum-like phenomenology QM without H and/or
  h.
• Non-relativistic QM.
• Biophoton (ultraweak emission) statistics.
• Solitons (Davydov), phonons, conformons,
  plasmons, etc.
• Decoherence, entanglement, quantum computation.
• Long-range coherent excitations Frohlich.
• QED coherence in cellular water Preparata, Del
  Giudice.

22
Decoherence, entanglement, quantum computation
Quantum-like phenomenology

• Consciousness, Psyche Orlov Piotrowski
  Sladkowski
• Embriogenesis Goodwin

Non-relativistic QM

• Protein folding Bohr et al.
• Scaling laws and the size of organisms Demetrius

• Origin of life Davies Al-Khalili McFadden
• Photosynthesis Castro et al coherence found
  experimentally.
• Decoherence in proteins, tunelling in enzymes
  Bothema et al
• Protein biosynthesis and molecular evolution
  Goel
• Cytoskeleton, decoherence, memory Nanopoulos
  Hameroff
• Genetic code, self-replication Pati Bashford
  Jarvis Patel
• Quantum cellular automata Flitney Abbot
• Evolutionary stability Iqbal Cheon

23
Embriogenesis by variational principle (Goodwin)
2 4 8 16 32

• Introduce a field function u (q, j) i.e., a
  morphogenetic field
• Its nodal lines lines of least resistance
• Define the surface energy density
• The cleavage planes given by the minima of the
  integral
• Eigenfunctions spherical harmonics Ylm (q, j)
• Biological constraint / selection rule the
  number of cells 2p

24
Consciousness by spinor algebra (Orlov)

• Yuri Orlov (Soviet physicist and disident).
• Consciousness states cannot be reduced to the QM
  states of brain molecules.
• Consciousness is a system that observes itself,
  being aware of doing so. No physical analogue
  exists. Partly true for life (?)
• Consciousness state described by a spinor. Let
  a proposition
• Every elementary logical proposition can be
  represented by the 3rd component of Pauli spin
• Hamlets dilemma
• 
  and
• 
  

25
Protein topology and folding by quanta of
torsion(Bohr, Bohr, Brunak)

• Heat consumed both for disorder-order and
  order-disorder transitions.
• Spin-glass type Hamiltonian
• Topology White theorem
• writhings twists const.
• Quantified long-range excitations
• of the chain, wringons.
• Explain heat consumption both in disorder-order
  and order-disorder transitions of some proteins
  in aqueous solution.

26
Fröhlichs long-range coherence in living systems

• Herbert Fröhlich postulated a dynamical order
  based on correlations in momentum space, the
  single coherently excited polar mode, as the
  basic living vs. non-living difference.
  Assumptions
• (1) pumping of metabolic energy above a critical
  threshold
• (2) presence of thermal noise due to physiologic
  temperature
• (3) a non-linear interaction between the freedom
  degrees.
• Physical image and biological implications
• A single collective dynamic mode excited far from
  equilibrium.
• Collective excitations have features of a
  Bose-type condensate.
• Coherent oscillations of 1011-1012 Hz of electric
  dipoles arise.
• Intense electric fields allow long-range Coulomb
  interactions.
• The living system reaches a metastable minimum of
  energy.
• This is a terminal state for all initial
  conditions (e.g. Duffield 1985) thus the genesis
  of life may be much more probable.

27
Aims and evidences of Fröhlichs theory

• Applications theoretical models
• Biomembranes, biopolymers, enzymatic reactions,
  metabo-lism (stability far from equilibrium),
  cell division, inter-cellular signaling, contact
  inhibition, cerebral waves.
• Examples of experimental confirmations
• Cell-cycle dependent Raman spectra in E. coli
  (Webb)
• Micro-waves accelerated growth of yeast
  (Grundler)
• Cell-cycle effects on dielectric grains
  dielectrophoresis (Pohl)
• Optical effects at 5 mm in yeast (Mircea Bercu)
• Erythrocyte rouleaux formation 5 mm forces
  (Rowlands).
• Other models consistent to Fröhlichs theory
• 1) Water dynamical structure coherence domains
  (Preparata, Del Giudice), 2) cell models based on
  water coherence domains (Preoteasa,Apostol), 3)
  ionic plasma water (Apostol,Preoteasa).

28
Liquid and cellular water

• Water an unique liquid with remarkable
  anomalies (density, compresibily, viscosity,
  dielectric constant, etc.).
• Water remarkable properties
• The dipole moment d 1,84 D would yield a
  dielectric constant er10, while experimental
  value er 78,5.
• Dissociation, H2OHOH H3O OH H3O(H2O)3
  OH.
• O-HO hydrogen bond, H2OHOH, L(O-HO) 2,76 Å,
  E(O-HO) 20 kJ/mol gt E(Van der Waals) 0.4
  4 kJ/mol kBT 2.6 kJ/mol.

• Angle 104,5o between O-H bonds in H2O
  Tetrahedral structure formation.
• Intuitive explanation two-phase phenomenological

model (Röntgen, Pauling).
29

• Two-phase model of water H-bond flickering
  ice-like clusters in dynamical equilibrium with
  a dense gas-type fluid with unbound molecules.
• Near polar interfaces and intracellular surfaces
  altered long-range interactions.

• Interfacial water bound w. (lt 5 nm), vicinal w.
  15-50 nm (Drost-Hansen), gel w. 1-10 mm
  (Pollack).
• The non-repeating structure of proteins / nucleic
  acids and short-range forces may not explain a
  concerted collective dynamics in the cell.
• Water possible vehicle for long-range specific
  interactions.

Water physical state changes in cell cycle.

• Hypothesis water converts position-space
  correlations to momentum-space correlations,
  emergence of cellular order.

30
QED theory of water coherence domains in living
cell (of the Milano group)

• New models based on the concept of coherence
  domains (CD) of water from the QED theory of
  Preparata, DelGiudice.
• Water forms polarization coherence domains (CDs)
  where the water dipoles oscillate coherently,
  in-phase.
• The water CDs are elementary excitations with a
  low effective mass (excitation energy) meff
  12.7-13.6 eV (me 511000 eV).
• CDs are bosons (S 0), obey Bose-Einstein
  statistics below a critical temperature Tc.
• Due to low effective mass, much longer de Broglie
  wavelength l h/meffn enhaced wavelike
  properties high Tc.
• The coherence domains are shaped as filaments,
  R15 - 100 nm, L100 - 500 nm. In cells some
  water filaments are located around chain-like
  proteins and some are free.
• Around water filaments appear specific,
  non-linear forces.

31
Experimental proofs of water QED model
Density anomaly Specific heat at 4 oC
at constant pressure

• QED model predicts water anomal properties.
• QED model predicts expelling of H ions CDs
  external electric field dialysis DpH between
  compartments.
• Biological proof Ionic Cyclotron Resonance
  Zhadin effect.

32
New models of collective dynamics for liquid
water and the living cell
33
Density oscillations in water and other similar
liquids (M. Apostol and E. PreoteasaPhys Chem
Liquids 466,653 668, http//arXiv.org/abs/0803
.2949v1 20 March 2008)

• A model for liquid water by plasmon-like
  excitations.
• The dynamics of water has a component consisting
  of O2z anions and Hz cations, where z is a
  (small) effective charge.
• Due to this small charge transfer, the H and O
  atoms interact by long-range Coulomb potentials
  in addition to short-range potentials.
• This leads to a Hz O2z two-species ionic
  stable plasma.
• As a result, two branches of eigenfrequencies
  appear, one corresponding to plasmonic
  oscillations and another to sound-like waves.

34

• Calculating the spectrum given by the eq. of
  motion without neglecting terms in q2 gives

For vanishing Coulomb coupling, z -gt 0, this
asymptotic frequency looks like an anomalous
sound with velocity
35

• Hydrodynamic sound velocity vo 1500 m/s.
• Anomalous sound velocity vs
• Hence we get the short-range interaction c
• The plasma oscillations can be quantized in a
  model for the local, collective vibrations of
  particles in liquids with a two-dimensional boson
  statistics.
• The energy levels of the elementary excitations
• This allowed an estimate of the correlation
  energy per particle and cohesion energy
  (vaporization heat) of water
• ecorr 102 K at room temperature.
• Similar results for OH- H or OH- H3O
  dissociation forms.

36

• In the living cell, the ionic plasma oscillations
  of water and their fields may interact with
  various electric fields associated to
  biomembranes, biopolymers and water polarization
  coherence domains may play a certain role in
  intra- and intercellular communications.
• The water ionic plasmons should have a very low
  excitation energy (effective mass), of 200z
  meV, and are almost dispersionless the
  associated de Broglie wavelength may be very
  large entanglement of their wavefunctions is
  possible support for intercellular correlations
  at very long distance, of major interest for
  phenomena such as embrio-, angio-, and
  morphogenesis, malign proliferation, contact
  inhibition, tissue repair, etc.
• The model is consistent to the general Fröhlich
  theory.
• Ionic plasma model of brain activity postulated
  (Zon 2005).

37
The cell size problem

• Cells are objects of dimensions of typically 1
  100 µm specific dynamical scale.
• Smaller biological objects are not alive.
• Biological explanations
• Lower limit min. 5.102 5.103 different types
  of enzymes necessary for life.
• Upper limit due to metabolism efficiency
  (prokaryotes), surface / volume ratio (animal
  eukaryotic cells), and large vacuoles (plant
  eukaryotic cells).
• The explanation relies on empirical bio-chemical
  / biological data it only displaces the
  problem.
• Systems biology starting not from isolated
  genes but from particular whole genome network
  (Bonneau 2007, Feist 2009) classical dynamics,
  is it sufficient?

38

• Physical explanations
• Schrödinger (1944) a minimum volume
  cooperation of a sufficient number of molecules
  against thermal agitation.
• Dissipative structures (Prigogine) cell as a
  giant density fluctuation cell size must exceed
  the Brownian diffusion during the lifetime.
• Empirical allometric relationship P aWb P
  metabolism, W size both in uni- / multicellular
  organisms. Mechanistic / fractal models fail
  for unicellular organisms.
• Quantum model (Demetrius) electron/proton
  oscillations in cell respiration and oxidative
  phosphorilation applies Plancks quantization
  rule and statistics deduces P aWb for both
  uni- and multicellular organisms.
• Demetrius QM model depends on metabolism a
  purely physical basis for cell size is
  possible?
• We propose a new quantum model for the cell size
  and shape based on coherence domains of water,
  without explicit reference to metabolism.

39
Bose-type condensation of water coherent
domains the minimum cell volume

• The assemble of water CDs in cell - a boson ideal
  gas in a spherical cavity.
• The wavefunctions of the water CDs boson gas
  reflect totally on the membrane.
• The cell a resonant cavity of volume V limited
  by membrane containing N CDs.

• At a critical density and temperature, the
  wavefunctions of CDs overlap and collapse
  common wavefunction, single phase.
• Water CDs low effective mass temperature Tc of
  Bose-type condensation of CDs where a coherent
  state arise might exceed the usual temperature
  of organisms (310 K).
• A Bose-type condensate of CDs in whole cells at
  310 K.

40

• For T lt Tc, a coherent state of CDs in the whole
  cell emerges. The dynamical states of all CDs
  correlated supercoherence (Del Giudice).
• The collective wavefunction of CDs an unified
  system for transmission, storage and processing
  of information, maximizing correlation of
  molecular dynamics in the cell.
• High order, CD-correlated, coherent dynamics
  supercoherence new macroscopic dynamical
  properties essential for life .
• Postulates enhancing the role of water CDs
• The living state is defined in the essence by
  metabolism, and not by replication (Dysons
  metabolism first, replication after
  hypothesis).
• The metabolism is dinamically co-ordinated by
  interactions between enzymes and water CDs (Del
  Giudices hypothesis).
• The maximum dynamical order in cell life
  reached when a Bose-type condensation of the
  water CDs free in the cytoplasm occurs
  supercoherence (D.G.).

41
For a critical density of CDs wavefunctions
overlap and collapse in a common wavefunction a
coherent state arises. The temperature Tc where
the coherent state arise given by the
Bose-Einstein equation of a boson gas
condensation

• Tc (N/V) / z(3/2) 2/3 2p h2/ meffkB
• For Tc 310 K, meff 13.6 eV 2.4 10-35 kg,
  imposing N gt 2
• (Nc 2 the smallest possible number of
  condensing CDs),
• V gt Vmin 1.02 mm3
• Correct as magnitude order or better !
• The smallest cell known, Mycoplasma, V 0.35 mm3
  
• Typical prokaryotic cells e.g. E. coli, V
  1.57 mm3
• Eukaryotic cells RBC, V 85 mm3
• Typical volumes for eukaryotic cells 103 104
  mm3.

42
Basic postulates for models giving cells maximum
volume and shape

• In the following models new basic postulates
• Water CDs in the cell bound quantum systems.
• Quantized dynamics of water CDs (translation in
  potential gaps, harmonic oscillations).
• Biological constraints certain levels / certain
  transitions between the quantized energy levels
  forbidden for biological stability thermally
  inaccessible energy levels / forbidden
  transitions.
• Cell size and shape selected in evolution fit
  the QM potentials and wavefunctions of CDs.

43
Water coherent domains in a spherical potential
well maximum volume of typical prokaryotic cells
A water CD a quasi-particle of meff 13.6 eV in
a potential well.
In addition to coherent internal oscillations, a
CD may have translation, rotation, deformation,
etc. freedom degrees. The cell a spherical
well of radius a with impenetrable walls
(infinite potential barrier, Uo ). The orbital
movement is neglected (l 0). The translation
energy of the CD inside the spherical well is
quantized on an infinite number of discrete
levels E1, E2, E3, En p2 h2/2meffa2 n2
9.87 u n2 (n 1, 2, ...) Notation u h2/2meffa2
44

• For a spherical well with semipenetrable walls,
  i.e. finite potential barrier, e.g. Uo 4 u 4
  h2/2meffa2 ,
• En 1,155 h2/2mBa2 n2 1,155 u n2 (n 1, 2,
  ...)
• For a spherical cell of 2 mm diameter, a 1 mm,
  the energy/frequency of the first level, in these
  two cases, is
• - impenetrable wall E1 3.5 1012 Hz,
• - semipenetrable wall E1 4.0 1011 Hz,
• in agreement as order of magnitude to the
  frequencies of coherent oscillations predicted by
  Fröhlich.
• To estimate the maximum volume of a cell, we
  postulate
• The metastable living state requires that the
  second level E2 to be thermally inaccessible from
  the first level E1.
• Thus the energy difference E2 E1 should exceed
  thermal energy at physiological
  T, 37 oC 310 K.
• Hence for the spherical well with impenetrable
  walls
• p2 h2/2mBa2 (22 12) gt 3kT/2

Staphylo- coccus
45

• The maximum radius of the spherical impenetrable
  cell defining also a basic biological length ao
  (T-dependent)
• a(T) lt amax(T) ao hp / (mB kT)1/2 1.02 mm
  for T 310 K
• The cell maximum volume Vmax 4.45 mm3.
• Together with the minimum volume estimated by
  Bose-type condensation, we have the limits of the
  cell volume
• 1.02 mm3 Vmin lt Vcell lt Vmax 4.45 mm3
• Satisfactorily confirmed for typical prokaryotic
  cells, e.g. E. coli 1,57 mm3, Eubacteria,
  Myxobacteria 1-5 mm3.
• Seemingly not confirmed to eukaryotic cells,
  102104 mm3.

• But Eukaryotic cells - highly compartmenta-lized,
  organelles divide cell in small spaces.
• These spaces obey the above volume limits.
• This sustains the evolutionary internalization of
  organelles as small foreign cells.
• The dimensions of the first protocells may have
  been similar to the prokaryotic cells.

46
Interactions between water CDs the possibility
of a harmonic potential

• The previous models do not assume interactions
  involving CDs and neglects their nature and
  structure.
• Water CDs form by interaction between H2O dipoles
  and radiation by self-focusing, self-trapping
  of dipoles, filamenta-tion (Preparata, Del
  Giudice) nonlinear optics phenomena disco-vered
  by G. Askaryan (Soviet-Armenian physicist, 1928 -
  1997).
• Therefore CDs are supposed to have filament
  shape.
• Around water filaments strong electric field
  gradients appear, developing frequency-dependent,
  specific, long-range, non-linear forces to
  dipolar biomolecules (Askaryan forces)
• F (??2 - ?2) / (??2 - ?2) 2 G2 Ñ?2
• They have the same form as the dielectrophoresis
  forces of an oscillating e.m. gradient field on a
  dielectric body (Pohl).

47

• Depending on the ? to ?o ratio, they can be
  attractive or repulsive.
• Askaryan force is higher when ? is close to ?o in
  a narrow frequency band resonant and selective
  character.

• They can bring non-diffusively into contact
  dipolar specific biomolecules, controlling thus
  cell metabolism (Del Giudice).
• The Askaryan force derives from a Fröhlich
  potential UA(r)
• FA - UA/r
• The potential depends on distance ( central
  component) and on relative orientation (
  non-central component) of dipolar molecule vs.
  CD.
• Neglect the explicit dependence of the
  non-central part
• UA(r ) UA(r ) ltA(q, f)gt, A geometric
  factor

47
48

• Central part of Fröhlich potential 2 terms
  (Tuszinsky)
• U(r ) F/r 6 E/r 3
• F/r 6 Van der Waals
• E/r 3 Fröhlich potential water CD dipole
  molecule.
• At resonance long-range (1-10 mm) potential
  between a CD and a dipolar molecule. At
  sufficient long distance U r -3.
• P1 The potential between two water CDs is
  similar to the potential between a CD and a
  permanent dipole molecule.
• P2 At sufficiently short distance, the potential
  will have always a repulsive term at least.
• Repulsive forces in water
• Pauli forces, A/r 12 repulsion between
  electron clouds of H2O in the two CDs (3 .10-11
  erg),
• Forces due to tetrahedral structure of water
  (10-13 erg)
• Quadrupolar interactions (2 .10-12 erg)

49

• Interactions due to the CDs surface electric
  field polarization of the cavity created in the
  dielectric medium following the displacement of
  solvent water by the CD Polarization pushes
  cavity toward lower field Spheres, potential r
  - 4.
• Solvent cosphere free energy potential -
  repulsive or attractive, depending on the
  relative volumes of solute and solvent species.
• Lewis acid-base interactions attractive or
  repulsive (v.Oss).
• Qualitative account of potential 1. repulsion
  due to the cavity created in the dielectric (r
  4) Fröhlich attraction (r3)
• U(r ) G/r 4 E/r 3
• Neglect Pauli repulsion (r -12), Van der Waals
  attraction (-r -6).
• The potential U(r) minimum/gap equilibrium
  distance re between the two CDs a diatomic
  molecule of 2 water CDs.
• Expand U(r) to 2nd degree approx. harmonic
  potential
• U(r) U(re) U(re) (r-re) ½ U(re) (r-re)2
  ...
• k/2 (r-re)2 U(re), k U(re)

50

• The interaction potential between two CDs
  approx. around re as a harmonic potential, the
  two CDs form a harmonic oscillator, with
  eigenfrequency
• w (k/m)1/2
• m effective mass of the oscillator.
• Gap depth U(re) exceed thermal
• energy, avoid dissociation

• U(re) gt 3/2 kBT
• At pysiol. T, 37 oC 310 K 3/2 kBT 6.45
  10-14 erg.
• Assume water CD oscillator remains in ground
  state during cell lifecycle, define a minimum
  eigen-frequency
• T 310 K, wmin 3kBT/2h, nmin 0.97 1012 Hz
  1013 Hz very close to the Fröhlich band
  upper limit.

51

• Min. frequency k min in the harmonic potential
  ½k (r-re)2
• kmin wmin2 m 4.7 10-5 dyn/cm
• k from U ½k (r-re)2 G/r 4 E/r 3 must
  satisfy k gt kmin.
• An example a possible potential of a CD of 15
  nm radius
• U 0.021 / (R-15)4 5 10-5 / (R-15)3
  (0.021, 5 10-5 param.s)
• Re 582 nm 0.6 mm ok, comparable to cell
  size
• k 2.7 10-4 dyn/cm gt 4.7 10-5 dyn/cm k min
  ok

• U(Re) 7.1 10-14 erg gt 6.45 10-14 erg 3/2
  KBT ok, not thermally dissociated
• n 2.4 1013 s-1 gt 1013 s-1 nmin ok, slightly
  above Froehlich band
• hw 1.6 1013 erg gt 6.45 1014 erg 3/2 KBT
  ok, oscillator excitation produces dissociation
  forbidden.
• Postulated potential realistic.

52
Two water coherent domains coupled in a spherical
harmonic oscillator maximum cell volume of small
prokaryotic cells

• Two CDs a spherical harmonic oscillator, in the
  center of mass coordinate system, distance d,
  reduced mass m
• Harmonic potential
•  
• In the ground state, nr 0 (n 1), l 0 (no
  orbital motion), m 0, Gaussian wavefunction, of
  halfwidth do

d0 sd (ltdgt2 ltd2gt)1/2
53

• The diameter 2a of a spherical cell equals the
  sum of equilibrium distance re between CDs and a
  length proportional to halfwidth d0
• c gt 1 c 4 for 4s probab. gt 99.99 for
  oscillator inside cell.
• In the ground state we take re, for instance
• re ltd2gt1/2 3 h / meff w½
• Cell radius a as a function of eigenfrequency w
• a (3½ / 2 2 . 2½ ) h / meff w½
• Postulate In the living cell, the oscillator is
  in the ground state of energy E000 3hw/2. For
  stability, the thermal energy must be lower than
  the energy quantum hw E100 E000 to first
  excited level

54

• Maximum radius of a spherical cell
• a lt 0,987 µm, maximum volume V lt 4,03 µm3.
• Comparison of harmonic oscillator and spherical
  gap
• æ 4,03 µm3 harmonic spherical
• 0,42 µm3 Vmin lt Vcell lt Vmax í oscillator
• è 4,45 µm3 impenetrable sphe- rical
  potential gap
• Concordance of radius better than 3 the two
  models are consistent with, and sustain, each
  other.
• Experimental confirmation typical prokariotes
  Eubacteria, Myxobacteria 1 -5 µm3, E. Coli 0.39
  1.57 µm3, small Cyanobacteria.
• Confirmation sustains a harmonic potential
  between CDs.

55
The isotropic oscillator in a spherical potential
well maximum volume of larger prokaryotes and
small eukaryotes

• Excellent agreement of a by spherical well and
  isotropic oscillator models both realistic no
  discrimination make a combined model
  isotropic harmonic oscillator enclosed in a
  spherical box with impenetrable walls larger than
  that required to accommodate only the oscillator.
  
• Centre of mass of the oscillator independent
  translation system with two freedom degrees.
• Cell spherical well of radius a one particle
  of mass 2meff translate in a smaller well of
  radius b oscillator of reduced mass meff / 2 in
  virtual sphere of radius recd0
• a b re cd0
• Perturbation treatment Unperturbed energy levels
  in box
• En p2 h2 n2 / 4 meff b2

56

• Energy difference between first two unperturbed
  levels
• DE21(0) E2(0) E1(0) (3/4) p2 h2 /4meff b2
• En levels of unperturbed Hamiltonian of the
  potential well. Wave functions
• Yn(r) (2/b)1/2 sin (n p r / b)
• The harmonic potential V(r) - centred at the half
  b/2 of radius
• V(r) k/2 (r-b/2)2
• Harmonic potential V a small perturbation on
  the unperturbed functions. The shifts of the
  first two unperturbed energy levels,
• b
• V11 k/b ?(r b/2) sin2 pb/r dr k b2/4 (1/6
  1/p2)
• 0
• b
• V22 k/b ? (r b/2) sin2 2pb/r dr k b2/4
  (1/6 1/4p2)
• 0
• Their difference
• V22 - V11 3/16p2 k b2
• adds to the difference DE21(0) between the
  unperturbed levels of the spherical gap.

57

• Difference between the perturbed first two levels
  DE21(1), assumed higher than thermal energy
• DE21(1) (3/4) p2 h2/4meff b2 3/16p2 k b2 gt
  3/2 kBT
• For the minimum oscillator frequency w wmin
  3kBT/2h ? kmin
• kmin (3/2 kBT/h)2 meff/2
• Obtained ? 4th degree equation in b (b ? 0)
• 9meff2kB2T2b4 64 p2 h2meffkBTb2 32p4h4 0
• with one real positive solution
• b ph/(meffkBT)1/2 2/3 (4 461/2)1/2
• 2/3 (4 461/2)1/2 a0 2,1891 a0 2,23 mm
• Total maximum radius of the spherical cell
  obtained
• a 2/3 (4 461/2)1/2 a0 1/p (2/3)1/2
  (31/2/2 2 21/2) a0
• 3,1493 a0 3.21 µm
• where a0 a0(T) ph/(meffkBT)1/2 1.02 mm for
  T 310 K.
• Maximum cell volume 138.6 µm3.

58

• Vmax 138.6 µm3 experimental confirmation
  biological data
• Larger prokariotes
• Taxa Myxobacteria including extremes (V 0.5
  20 µm3)
• Sphaerotilus natans (V 6 240 µm3)
• Bacillus megaterium (V 7 38 µm3).

• The smallest eukayotic cells
• Beakers yeast Saccharomyces cerevisiae
  (V 14 34 µm3, a 1,5 2 µm),
• Unicellular fungi and algae (V 20 50 µm3),
• Erythrocyte, enucleated eukaryotic cell
  (V 85 µm3),
• Close to the lymphocyte (V 270 µm3).

Yeast
59

• Correction of minimum cell volume/radius
  estimated on the basis of the Bose condensation,
  due to meff (single free CD) 2meff (two CDs in
  harmonic oscillator)
• Vmin decrease by a factor of 23/2 0,3536 to
  0.15 µm3,
• amin decrease by 21/2 0.7071, from 0.46 to
  0.33 µm.
• Biological implication included the smallest
  known cells,
• blue-green alga Prochlorococcus of Cyanobacteria
  genre (V 0.10.3 µm3),
• Mycoplasma (V 0.35 mm3).

60
The cylindrical potential well and the shape and
size of discoidal cells the erythrocyte

• A disc-like cell a cylindrical well, of finite
  thickness a, radius ro.
• Along the rotational axis the problem reduces to
  a linear gap with impenetrable walls and the
  length a energy levels En.

• In the circular section of the disk polar
  co-ordinates solution of the form Y(r, f)
  f(r) g(f) radial part Bessel functions of the
  first degree and integer index, f(r) Jl(r).
• Probability density vanish on the walls of the
  cylinder, Jl(aro) 0, radius given by the
  roots xlm of the function Jl(ar), with energy
  eigenvalues Elm.

61

• No immediate restriction to the values of l, m
  (radial movement) with respect to n (axial
  movement).
• Total energy - sum of the two energies
• Enlm En Elm
• The only restriction for l and m due to the
  obvious rule
• En lt En Elm lt En1.
• Total energy of an arbitrary quantified level
• Enlm h2/2meff (p2n2/a2 xlm2/ro2)
• Choose E110 as the ground level, E221 higher
  level.
• Impose E221 E110 as a thermally inaccessible
  transition
• E221 E110 h2/2meff (4p2/a2 x212/ro2 - p2/a2
  x102/ro2) 3/2 kBT
• x10 0, x21 5.32 first roots of J1(r) and
  J2(r) Bessel functions.
• We are lead to a second degree inequality, with
  the solution
• ro x21 ao a / p (a2 ao2)1/2, for a ? 0, a gt
  ao,
• where ao p h / (meff kBT)1/2 1,02 µm.

62

• Radius ro of discoidal cell monotonously
  decreases with thickness a. Thickness a ? radius
  ro.
• The ratio ro/a determines the cell shape.
• For a 1.15 µm, ro 3.8 µm. Red blood cell 2
  µm thickness, 3.75 µm radius.
• The model describes a non-spherical cell,
  neglecting biconcave shape, rounded margins.

Erythrocyte

• Biological implications The model neglects
  nucleus / the erythrocyte is an eukaryotic
  enucleated, non-replicating cell.
• The experimental confirmation of predicted shape
  and size - sustains water CDs dynamics in
  erythrocyte.
• According to our basic assumption that water CDs
  dynamics is essential for living state the
  enucleated, non-replicating, but metabolically
  active erythrocyte is a living cell indeed.
• This sustains the general hypothesis of the
  metabolism first, replication after origin of
  life (Dyson).

63
The cylindrical potential well and the shape and
size of rod-like cells typical bacilli

• Model of cylindrical gap with impenetrable walls
  rod-like bacilli of typical size.
• Advantage used liberty in choosing the l and m
  values of xlm roots of the Bessel functions
  Jl(r).
• Approximate roots of Bessel functions for l m gt
  2
• xlm ¾ p l p/2 m p
• Specific postulate in the rod-like cell
  biologically relevant transitions leave unchanged
  the axial translation energy En,
• Dn 0
• Some radial levels Elm fall between the En levels
  close of each other the lowest thermally
  occupied.

E. coli

• Other radial levels Elm thermally inccessible
  biologically forbidden transitions between such
  levels.

64

• For n 1 and Dn 0, a thermally inaccessible
  state 1lmgt defines a biologically forbidden
  transition 1lmgt ? 1lmgt. Thus
• E1lm E1lm h2/2meff (xlm2 xlm2)/ro2 gt
  3/2 kBT
• ro lt 1/p (xlm2 xlm2)/31/2 ph/(meff kBT)1/2
• ro lt 1/p (xlm2 xlm2)/31/2 ao ,
  with ao 1,02 µm.
• Postulate ground state 102gt, life-forbidden
  transition 102gt ? 121gt. Substitute x02 5.52
  and x21 5.32 roots of the J0 and J2 Bessel
  functions. radius ro lt 0.28 µm or diameter 2ro
  lt 0.55 µm axial length ao 1,02 µm form ratio
  2ro/ ao 0.54.

Species 2ro (µm) ao (µm) 2ro/ao
Calculated 0.55 1,02 0.54
Brucella melitensis 0.5-0.7 0.6-1.5 0.5-0.8
Francisella tularensis 0.2 0.3-0.7 0.3-0.7
Yersinia pestis 0.5-1.0 1.0-2.0 0.5
Escherichia coli 0.5-1.0 2.0-2.5 0.25-0.4
65

• Other biologically forbidden couple of states
  103gt ? 122gt, 2ro 0.41 µm, ao 1,02 µm.
• Similar results with the pairs of states 113gt ?
  104gt, 124gt ? 105gt, 125gt ? 106gt, ... . Some
  of these levels may be unoccupied at 310 K.
• Empirical selection rule emerges for
  biologically forbidden transitions in
  relatively small, typical bacilli, with diameters
  close to half of a 1.02 µm length.
• D(l m) ¹ 0, 1
• The model neglects rounded ends of rod-like
  bacteria and possible influence of
  inhomogeneous distribution of DNA inside.
• The model size and shape of axially symmetric
  cells there are no intermediate cell shape
  between erythrocyte and bacilli.
• Some of the above assumptions still need
  sufficient rationales they are postulates,
  justified so far only by results.
• Further studies needed to describe larger
  bacilli.

66
The toxic effect of heavy water and water
coherent domains in a spherical well

• D2O and H2O chemical properties - almost
  identical most physical properties difer by 5
  10 ,
• However, D2O induces severe, even mortal
  biological effects. Complete substitution with
  isotopes 13C, 15N, 18O well tolerated.
• Effects - irreversible and much worse to
  eukaryotes than procaryotes.
• Looking for an explanation
• in the cell
• in the physical properties of D2O vs. H2O.
• 1) Eukaryotes divided by organelles,
  prokaryotes not.
• 2) D2O vs. H2O substantial physical differences
  H ion mobility (-28.5), OH- ion mobility
  (-39.8), Ionization constant, Ionic product
  (-84,0), Inertia moment (100).

67

• The unique twofold different physical property of
  D2O vs. H2O - inertia momentum of water
  molecule (mD _at_ 2 mH)
• I(D2O) S mDd2 _at_ 2 S mHd2 2 I(H2O)
• Doubling of inertia momentum implies radically
  different physical properties of CDs in D2O and
  H2O, as evidenced in QED theory (Del Giudice et
  al 1986, 1988).
• Rotation frequecy wo of water molecule
• Size d of a water CD

68

• Effective mass meff of CDs
• Consequence Substitution of H2O by D2O
  reduction to a half of water CD effective mass
• The eukaryotic cell approximated as an
  aggregate of small water-filled spheres of radius
  a closed by membranes.
• CDs confined in spherical wells with finite
  potential walls.

• Postulate The CDs potential barrier heigth
  admitted the same in H2O- and D2O-filled cells
• U0 4 h2/2meffa2 4 u const.
• (4u arbitrary)

69

• Constant Uo by compensation of opposed D2O
  effects due to lower ionization constant, ionic
  product, D and OD- ions mobility, and of higher
  CD mobility due to lower meff.
• For the spherical well of finite height there is
  a minimal heigth Umin for the occurrence of the
  first quantified energy level
• With meff meff(H2O) and meff(D2O) _at_
  meff(H2O)/2 the minimal height of well is
  double for D2O vs. H2O.
• The relation of Umin vs. Uo is thus fundamentally
  changed
• Umin(H2O) 2.5 u lt 4 u Uo
• Umin(D2O) 5 u gt 4 u Uo

70

• Umin(H2O) lt Uo
• Umin(D2O) gt Uo
• In D2O-filled cells the first energy level is
  higher than the height of potential well in
  contrast to the H2O-filled cells.
• Therefore the D2O coherence domains will not be
  in a bound state in the cell compartments the
  CDs will move freely in the whole volume of
  D2O-filled eukaryotic cells.
• Contrarywise, CDs are bound in H2O-filled
  compartments of eukaryotic cells.
• This qualitative difference a totally perturbed
  dynamics of heavy water may explain D2O
  toxicity in eukaryotes.
• Eukaryotes internal membranes high D2O
  toxicity.
• Prokaryotes no internal membranes no
  qualitative CD dynamics difference of D2O vs.
  H2O low D2O toxicity.

71
A last hour finding in rod-like bacteria a
possible proof of long-range interactions inside
living cells

• A new mechanism in bacteria support CDs
  long-range interactions.
• Some proteins navigate in the cell sensing the
  membranes curvature.
• Proteins recognize geometric shape rather than
  specific chemical groups. Bacillus subtillis
  DivIVA protein convex SpoVM concave
  curvatures, i.e. poles of rod-like bacteria
  (Ramamurthi, Losick 2009).
• Protein adsorption model explanation limited to
  highly concave membrane curvatures of protein
  and cell are very different a single protein
  could not sense the curved surface cooperative
  adsorption of small clusters of proteins once a
  protein located on the curved membrane, may
  attract others.

72
Long-range hypothesis for rod-like cells effect

• Limits of cooperative adsorption model How is
  directed the first protein? Difficulty proteins
  which recognize convex surface.
• Alternative explanation Proteins are carried by
  long-range forces derived from strong potential
  gradients as expected from our cylindrical well
  model and oscillating electromagnetic fields
  generated by CDs (Del Giudice).
• Attraction to the cell extermities superimposes a
  deterministic dielectrophoretic (Askaryan) force
  on Brownian motion.
• Probability of transport to curved cell ends much
  enhanced.
• Because the Askaryan dielectrophoretic forces can
  be attractive / repulsive specific proteins
  attracted by negatively / positively curved
  surfaces.
• Suggested test different electrical
  characteristics of SpoVM (concave), DivIVA
  (convex), and of proteins not attracted.
• The effect first evidence of protein-cell
  long-range forces.

73
Conclusions and final remarks
74

• Quantum biology is one among several approaches
  aiming of coming close to the collective,
  non-linear, holistic phenomena of the living
  cell, beyond the reductionist view of life given
  by molecular biology.
• A large variety of models based on different
  assumptions already succeeded to deal with
  biological facts unexplained by molecular
  biology.
• Long-range coherence and Bose-type condensation
  postulated in Fröhlichs theory as essential
  features of living systems, explain many
  biological phenomena.
• Long-range interactions in cells - experimentally
  proved. Coherence proved in photosynthesis.
• Models of water consistent to Fröhlichs theory
  explain its remarkable properties and its key
  role in living cells.

75

• A ionic plasma model explains the second sound
  and more usual properties of water (Apostol
  Preoteasa).
• The QED model of water CDs explains water
  anomalies, dynamical order in cell, cell activity
  effects, Zhadin effect and ICR, etc. (Preparata,
  Del Giudice).
• The cell size (1-100 mm) between classical and
  quantum a spatial scale for a specific
  dynamics.
• A quantum model size vs. metabolic rate
  (Demetrius).
• We propose new, metabolism-independent, quantum
  models for cell size, based on CDs low mass
  (12-13.6 eV) dynamics (Preoteasa and Apostol).
• The models suggest that cell size and shape
  selected in evolution, fit the size and shape of
  potentials and QM wavefunctions describing water
  CDs dynamics.

76

• Bose-type condensation may explain lower size
  limit.
• Impenetrable spherical well, isotropic
  oscillator, isotropic oscillator in spherical
  well, explain upper size limits of cocci, yeast,
  algae, fungi.
• Axially-symmetric wells (disk-like, rod-like)
  explain size / shape of erythrocyte and typical
  bacilli.
• Cell shape sensing by proteins in bacilli backs
  model.
• A model of spherical well with semipenetrable
  walls explains the toxic effects of D2O, much
  stronger in eukaryotic than in prokaryotic cells.
  
• Explanation of D2O toxicity sustains water-based
  QM models! The same model connects D2O toxicity
  and cell size/shape two very different
  phenomena.
• QM water dynamics models still provide a vast
  potential for further explaining other cellular
  facts.

77
Acknowledgements

• Marian Apostol, for his crucial contribution to
  our models, his long-time interest and his
  decisive participation.
• Dan Galeriu, Andrei Dorobantu and Serban
  Moldoveanu (Reynolds Labs.) for essential
  literature and for stimulating discussions.
• Mircea Bercu (Fac. Phys., Buc.), for new
  experimental confirmation of long-range cellular
  interactions.
• Emilio Del Giudice (Milano), for generous
  encouragement.
• Carmen Negoita (Fac. Vet. Medicine, Buc.) and
  Vladimir Gheordunescu (Inst. Biochem., Buc.), for
  highly interesting data and discussions on living
  cells.
• Cristina Bordeianu, Vasile Tripadus, Dan Gurban,
  Mihai Radu, Ileana Petcu, Adriana Acasandrei, and
  Anca Melintescu for stimulating discussions,
  observations and comments.

78
References

• Eugen A. Preoteasa and Marian V. Apostol,
  Collective Dynamics of Water in the Living Cell
  and in Bulk Liquid. New Physical Models and
  Biological Inferences, arXiv-0812.0275v2
• M. Apostol and E. Preoteasa, Density oscillations
  in a model of water and other similar liquids,
  Physics and Chemistry of Liquids 466 (2008) 653
  668
• M. Apostol, Coherence domains in matter
  interacting with radiation, Physics Letters A
  (2008), 18445 1-6