Title: Quantum biology, water and living cells
1Quantum biology, water and living cells
 Eugen A. Preoteasa
 HHNIPNE, 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 disclike cells
the erythrocyte  Cylindrical potential gap and rodlike cells
typical bacilli  The semipenetrable spherical well The toxic
effect of heavy water in eukaryotic cells  Conclusions
4Introductionand backgroundBiology from
classical to quantum
5Life is a phenomenon strikingly different of the
nonliving systems. Some distinctive traits
 Metabolism
 Homeostasis
 Replication
 Stability of descendents
 Spontaneous, lowrate 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
6Biological 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 XVIIXIX 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, ).
7Molecular biology a new reductionism
 DNA (or RNA) encodes all genetic information
(Crick Watson 1950) devastating effect on
biology.  Two images since 1967
 integrative (Jacob) vs.
 reductionist, (Monod)
 Recently, phenotypic plasticity and
selforganization 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 feedback?
 The main ideas of molecular biology
 All biological phenomena reduced to information
stored in some (privileged) molecules.  Only shortrange specific interactions.
 Classical (BolzmannGibs), 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.
9Cells, 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.
10Limits of molecular biology
 Complexity, integrality pointing to nonlinear,
optimal, selforganized systems , to longrange
correlations.  Molecular biology sticks and balls picture
isolated classical particles, shortrange
interactions.  Success of molecular biology at the roots of
its limits.  Origin of life unexplained probability of first
cell 1040,000 , of man 1024,000,000 in 4.109
yr.  Chance is not enough (Jacob 1967).
 Metabolic coordination 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 readonly memory) where the rest
comes from?  Unexplained brain activity, biological
chirality, etc.
11Features 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 longrange correlations and
interactions.  Living organisms are open, irreversible,
disipative systems.  They are selforganized, optimal systems
(gthomeostasis), with cooperative interactions.  Nonlinear interactions, highly integrated
dynamics.  Such features to some degree in various complex
nonliving systems but only organisms join them
altogether.
12Molecular 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?
13Correlations, functions and soft matter
 Organisms evolve by functions spacetime
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)aggregations and conformational changes.
Flexible geometic structure, conservative
topological correlations of freedom deg.s.
Dynamical organization.  Cells condensed matter facilitate longrange
correlations and information transfer.  Either correlations and information admit both
classical and quantum support.
14Classical and quantum correlations long range
interactions between (quasi)particles
 Long range correlations selfcorrelation
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 selfcorrelation 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.
 Welldefined sequence message, precise code,
maximum useful information, comands an unique
function.  Biological systems informational syst.
adressable both C/Q.
16Information 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
wavefunctions may play a role in transmission,
storage, processing, and control of information.
17Alternatives 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.
18Irreversibility, 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 nonliving much
more probable.
BelousovZhabotinsky reaction Heterogeneous
(order) out of homogeneous (disorder).
19Integral properties without molecular biology. I.
The fur of mammals by partial derivative equations
Diffusionreaction of melanin
Results
20Integral properties of cells without molecular
biology. II. Flickering modes of erythrocyte
membrane by Fourier / correlation analysis
21Quantum 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  Quantumlike phenomenology QM without H and/or
h.  Nonrelativistic QM.
 Biophoton (ultraweak emission) statistics.
 Solitons (Davydov), phonons, conformons,
plasmons, etc.  Decoherence, entanglement, quantum computation.
 Longrange coherent excitations Frohlich.
 QED coherence in cellular water Preparata, Del
Giudice.
22Decoherence, entanglement, quantum computation
Quantumlike phenomenology
 Consciousness, Psyche Orlov Piotrowski
Sladkowski  Embriogenesis Goodwin
Nonrelativistic QM
 Protein folding Bohr et al.
 Scaling laws and the size of organisms Demetrius
 Origin of life Davies AlKhalili 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, selfreplication Pati Bashford
Jarvis Patel  Quantum cellular automata Flitney Abbot
 Evolutionary stability Iqbal Cheon
23Embriogenesis 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
24Consciousness 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 
25Protein topology and folding by quanta of
torsion(Bohr, Bohr, Brunak)
 Heat consumed both for disorderorder and
orderdisorder transitions.  Spinglass type Hamiltonian
 Topology White theorem
 writhings twists const.
 Quantified longrange excitations
 of the chain, wringons.
 Explain heat consumption both in disorderorder
and orderdisorder transitions of some proteins
in aqueous solution.
26Fröhlichs longrange 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. nonliving difference.
Assumptions  (1) pumping of metabolic energy above a critical
threshold  (2) presence of thermal noise due to physiologic
temperature  (3) a nonlinear 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
Bosetype condensate.  Coherent oscillations of 10111012 Hz of electric
dipoles arise.  Intense electric fields allow longrange 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.
27Aims and evidences of Fröhlichs theory
 Applications theoretical models
 Biomembranes, biopolymers, enzymatic reactions,
metabolism (stability far from equilibrium),
cell division, intercellular signaling, contact
inhibition, cerebral waves.  Examples of experimental confirmations
 Cellcycle dependent Raman spectra in E. coli
(Webb)  Microwaves accelerated growth of yeast
(Grundler)  Cellcycle 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).
28Liquid 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.  OHO hydrogen bond, H2OHOH, L(OHO) 2,76 Å,
E(OHO) 20 kJ/mol gt E(Van der Waals) 0.4
4 kJ/mol kBT 2.6 kJ/mol.
 Angle 104,5o between OH bonds in H2O
Tetrahedral structure formation.  Intuitive explanation twophase phenomenological
model (Röntgen, Pauling).
29 Twophase model of water Hbond flickering
icelike clusters in dynamical equilibrium with
a dense gastype fluid with unbound molecules.  Near polar interfaces and intracellular surfaces
altered longrange interactions.
 Interfacial water bound w. (lt 5 nm), vicinal w.
1550 nm (DrostHansen), gel w. 110 mm
(Pollack).  The nonrepeating structure of proteins / nucleic
acids and shortrange forces may not explain a
concerted collective dynamics in the cell.  Water possible vehicle for longrange specific
interactions.
Water physical state changes in cell cycle.
 Hypothesis water converts positionspace
correlations to momentumspace correlations,
emergence of cellular order.
30QED 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,
inphase.  The water CDs are elementary excitations with a
low effective mass (excitation energy) meff
12.713.6 eV (me 511000 eV).  CDs are bosons (S 0), obey BoseEinstein
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 chainlike
proteins and some are free.  Around water filaments appear specific,
nonlinear forces.
31Experimental 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.
32New models of collective dynamics for liquid
water and the living cell
33Density 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 plasmonlike
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 longrange Coulomb potentials
in addition to shortrange potentials.  This leads to a Hz O2z twospecies ionic
stable plasma.  As a result, two branches of eigenfrequencies
appear, one corresponding to plasmonic
oscillations and another to soundlike 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 shortrange interaction c
 The plasma oscillations can be quantized in a
model for the local, collective vibrations of
particles in liquids with a twodimensional 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).
37The 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 biochemical
/ 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.
39Bosetype 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
Bosetype condensation of CDs where a coherent
state arise might exceed the usual temperature
of organisms (310 K).  A Bosetype 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, CDcorrelated, 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 coordinated by
interactions between enzymes and water CDs (Del
Giudices hypothesis).  The maximum dynamical order in cell life
reached when a Bosetype condensation of the
water CDs free in the cytoplasm occurs
supercoherence (D.G.).
41For 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
BoseEinstein 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 1035 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.
42Basic 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.
43Water coherent domains in a spherical potential
well maximum volume of typical prokaryotic cells
A water CD a quasiparticle 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
(Tdependent)  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
Bosetype 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 15 mm3.  Seemingly not confirmed to eukaryotic cells,
102104 mm3.
 But Eukaryotic cells  highly compartmentalized,
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.
46Interactions 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 selffocusing, selftrapping
of dipoles, filamentation (Preparata, Del
Giudice) nonlinear optics phenomena discovered
by G. Askaryan (SovietArmenian physicist, 1928 
1997).  Therefore CDs are supposed to have filament
shape.  Around water filaments strong electric field
gradients appear, developing frequencydependent,
specific, longrange, nonlinear 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 nondiffusively 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 (
noncentral component) of dipolar molecule vs.
CD.  Neglect the explicit dependence of the
noncentral 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 longrange (110 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 .1011
erg),  Forces due to tetrahedral structure of water
(1013 erg)  Quadrupolar interactions (2 .1012 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 acidbase 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) (rre) ½ U(re) (rre)2
...  k/2 (rre)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
1014 erg.  Assume water CD oscillator remains in ground
state during cell lifecycle, define a minimum
eigenfrequency  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 (rre)2  kmin wmin2 m 4.7 105 dyn/cm
 k from U ½k (rre)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 / (R15)4 5 105 / (R15)3
(0.021, 5 105 param.s)  Re 582 nm 0.6 mm ok, comparable to cell
size  k 2.7 104 dyn/cm gt 4.7 105 dyn/cm k min
ok
 U(Re) 7.1 1014 erg gt 6.45 1014 erg 3/2
KBT ok, not thermally dissociated  n 2.4 1013 s1 gt 1013 s1 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.
52Two 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.
55The 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 (rb/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,  bluegreen alga Prochlorococcus of Cyanobacteria
genre (V 0.10.3 µm3),  Mycoplasma (V 0.35 mm3).
60The cylindrical potential well and the shape and
size of discoidal cells the erythrocyte
 A disclike 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
coordinates 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 nonspherical cell,
neglecting biconcave shape, rounded margins.
Erythrocyte
 Biological implications The model neglects
nucleus / the erythrocyte is an eukaryotic
enucleated, nonreplicating 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, nonreplicating, but metabolically
active erythrocyte is a living cell indeed.  This sustains the general hypothesis of the
metabolism first, replication after origin of
life (Dyson).
63The cylindrical potential well and the shape and
size of rodlike cells typical bacilli
 Model of cylindrical gap with impenetrable walls
rodlike 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 rodlike 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, lifeforbidden
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 0.50.7 0.61.5 0.50.8
Francisella tularensis 0.2 0.30.7 0.30.7
Yersinia pestis 0.51.0 1.02.0 0.5
Escherichia coli 0.51.0 2.02.5 0.250.4
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 rodlike
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.
66The 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 waterfilled 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 D2Ofilled 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 D2Ofilled cells the first energy level is
higher than the height of potential well in
contrast to the H2Ofilled 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
D2Ofilled eukaryotic cells.  Contrarywise, CDs are bound in H2Ofilled
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.
71A last hour finding in rodlike bacteria a
possible proof of longrange interactions inside
living cells
 A new mechanism in bacteria support CDs
longrange 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 rodlike 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.
72Longrange hypothesis for rodlike 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
longrange 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 proteincell
longrange forces.
73Conclusions and final remarks
74 Quantum biology is one among several approaches
aiming of coming close to the collective,
nonlinear, 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.  Longrange coherence and Bosetype condensation
postulated in Fröhlichs theory as essential
features of living systems, explain many
biological phenomena.  Longrange 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 (1100 mm) between classical and
quantum a spatial scale for a specific
dynamics.  A quantum model size vs. metabolic rate
(Demetrius).  We propose new, metabolismindependent, quantum
models for cell size, based on CDs low mass
(1213.6 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 Bosetype 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.  Axiallysymmetric wells (disklike, rodlike)
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 waterbased
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.
77Acknowledgements
 Marian Apostol, for his crucial contribution to
our models, his longtime 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 longrange 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.
78References
 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, arXiv0812.0275v2  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 16