Transcript Slide 1

Quantum biology, water
and living cells
Eugen A. Preoteasa
HH-NIPNE, LEPD (DFVM)
… nature is not sparing as for its structures,
but only for its universally applicable
principles. –
Abdus Salam
I.
Introduction and background
– Biology from classical to quantum
II. 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
III. Conclusions
Introduction
and background
Biology
from classical to quantum
Life is a phenomenon strikingly different of the
non-living systems. Some distinctive traits
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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
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, …).
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 revealed 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)
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.
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%.
Limits of molecular biology
• Complexity, integrality – pointing to nonlinear, optimal, selforganized 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 readonly memory) – where the rest comes from?
• Unexplained: brain activity, biological chirality, etc.
Features of life unsolved by molecular biology
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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 (->homeostasis), 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.
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?
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)aggregations 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.
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) = <z(r) z(r+D)>
• a wavefunction Y(r):
G(D) = < Y*(r) Y(r+D)>
• The self-correlation or coherence function is connected to
interference of waves associated with a (quasi)particule:
I(D) ~ |Y1(r) + Y2(r+D)|2 ~ 1 + |G(D)|cos Dk
• Necessary condition – long range interactions between
particles or quasiparticles.
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.
Information and quantum mechanics
• Quantity of information (Shannon, Weaver 1949):
H = – Σ pi log2 pi ; p = |ψ|2 ; Ex. H(Xe) = 136 bit.
• Information gain between 2 probability distrib.s P, W:
I (P|W) = Σ pi log2 (pi / wi)
• Information gain in a quantum transition |m> → |l>
(Majernik 1967):
I ( φm | φl ) =
∫ φm φm *
log2 ( φm φm* / φl φl*) dv
• Ex.: Potential gap, I(u2|u1) = 3,8 bit. Hydrogen atom, I(u2|u1)
= 83,1 bit.
• Hypothesis: In biological systems, certain wave-
functions may play a role in transmission, storage,
processing, and control of information.
Alternatives to molecular biology
• Postulate: Living organisms contain both classical and
quantum (sub)systems.
• Alternatives to describe biological complexity and integral
properties of organisms:
1. Far from equilibrium dynamics, dissipative structures
(classical or quantum);
2. Models of periodic phenomena based on equations
with eigenfunctions and eigenvalues (classical or
quantum);
3. Quantum biology.
Irreversibility, far from equilibrium dynamics,
dissipative structures (Prigogine, Nicolis, Balescu)
Spontaneous
synchronization of
oscillations in
glycolysis (glucose
consumption) in
yeast cells (Bier)
Belousov-Zhabotinsky
reaction: Heterogeneous
(order) out of homogeneous
(disorder).
• 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.
Integral properties without molecular biology. I. The
fur of mammals by partial derivative equations
Diffusion-reaction of melanin:
Results:
Integral properties of cells without molecular
biology. II. Flickering modes of erythrocyte
membrane by Fourier / correlation analysis
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.
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
Decoherence, entanglement, quantum computation
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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
Embriogenesis by variational principle (Goodwin)
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• 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:
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:
• Hamlet’s dilemma:
and
Protein topology and
folding by quanta of
torsion
(Bohr, Bohr, Brunak)
• Heat consumed both for disorder-order and orderdisorder 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.
Fröhlich’s 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.
Aims and evidences of Fröhlich’s 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 Fröhlich’s 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).
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 er~10, while experimental value er = 78,5.
• Dissociation, H2O…HOH  H3O+ + OH–  H3O(H2O)3+ + OH–.
• O-H…O hydrogen bond, H2O…HOH, L(O-H…O) = 2,76 Å,
E(O-H…O) = 20 kJ/mol > 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: twophase phenomenological
model (Röntgen, Pauling).
• 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. (< 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 physical state
changes in cell cycle. • Water – possible vehicle for long-range
specific interactions.
• Hypothesis: water converts position-space correlations to
momentum-space correlations, – emergence of cellular order.
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, R~15 - 100 nm,
L~100 - 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.
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.
New models of collective
dynamics for liquid water
and the living cell
Density oscillations in water and other similar liquids
(M. Apostol and E. Preoteasa
Phys Chem Liquids 46:6,653 — 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 O–2z anions and
H+z 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 short-range potentials.
• This leads to a H+z – O–2z two-species ionic stable plasma.
• As a result, two branches of eigenfrequencies appear, one
corresponding to plasmonic oscillations and another to sound-like
waves.
• Calculating the spectrum given by the eq. of motion without
neglecting terms in q2 gives:
For vanishing Coulomb
coupling, z -> 0, this
asymptotic frequency looks
like an anomalous sound
with velocity:
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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 twodimensional boson statistics.
The energy levels of the elementary excitations:
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This allowed an estimate of the correlation energy per particle
and cohesion energy (vaporization heat) of water:
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ecorr ~ 102 K at room temperature.
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Similar results – for OH-– H+ or OH-– H3O+ dissociation forms.
• 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).
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 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?
• 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 Planck’s
quantization rule and statistics  deduces P = aWb  for both uniand 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.
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.
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At a critical density and temperature, the wavefunctions of CDs
overlap and collapse  common wavefunction, single phase.
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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).
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A Bose-type condensate of CDs  in whole cells at ~310 K.
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For T < 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
1. The living state is defined in the essence by
metabolism, and not by replication (Dyson’s
“metabolism first, replication after” hypothesis).
2. The metabolism is dinamically co-ordinated by
interactions between enzymes and water CDs (Del
Giudice’s hypothesis).
3. 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.).
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ħ2/ meffkB
• For Tc = 310 K, meff = 13.6 eV = 2.4 10-35 kg, imposing N > 2
(Nc = 2 – the smallest possible number of condensing CDs),
V > Vmin = 1.02 mm3
• Correct as magnitude order – or better !
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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.
Basic postulates for models giving
cell’s 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.
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 ħ2/2meffa2 n2 = 9.87 u n2 (n = 1, 2, ...)
Notation: u = ħ2/2meffa2
• For a spherical well with semipenetrable walls, i.e. finite potential
barrier, e.g. Uo = 4 u = 4 ħ2/2meffa2 ,
En = 1,155 ħ2/2mBa2 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:
Staphylococcus
p2 ħ2/2mBa2 (22 – 12) > 3kT/2
The maximum radius of the spherical impenetrable cell – defining
also a basic biological length ao (T-dependent):
a(T) < amax(T) = ao = ħp / (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 < Vcell < 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, ~102–104 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.
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 ~ { (ωο2 − ω2) / [ (ωο2 − ω2) 2 + Γ2] } Ε2
• They have the same form as the dielectrophoresis forces of an
oscillating e.m. gradient field on a dielectric body (Pohl).
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20
2
2
(4 -  )/(4 -  -1,2)
F
10
0
-10
-20
0
1
2
3
4
• Depending on the ω to ωo ratio, they
can be attractive or repulsive.
• Askaryan force is higher when ω is close
to ωo 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 ) |<A(q, f)>|,
A – geometric factor
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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.
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P1: The potential between two water CDs is similar to the potential
between a CD and a permanent dipole molecule.
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P2: At sufficiently short distance, the potential will have always a
repulsive term at least.
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Repulsive forces in water :
1. “Pauli forces”, +A/r 12 – repulsion between electron clouds of
H2O in the two CDs (~3 .10-11 erg),
2. Forces due to tetrahedral structure of water (~10-13 erg);
3. Quadrupolar interactions (2 .10-12 erg);
3. Interactions due to the CD’s 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.
4. Solvent cosphere free energy potential - repulsive or attractive,
depending on the relative volumes of solute and solvent species.
5. 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 (–r–3):
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)
• The interaction potential between two CDs  approx.
around re as a harmonic potential, the two CDs form a
harmonic oscillator, with eigenfrequency:
 = (k/m)1/2
U = G/(R-Re)4 - E /(R-Re)3
• m – effective mass of the oscillator.
• Gap depth U(re)  exceed thermal
• energy, avoid dissociation:
|U(re)| > 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:
2,0
1,5
1,0
U(x)
0,5
0,0
-0,5
-1,0
-1,5
-2,0
0,8
1,0
1,2
1,4
1,6
1,8
x
3
  k B T 12
•T = 310 K, min = 3kBT/2ħ, nmin = 2
0.97 × 10 Hz ~ 1013 Hz –
very close to the Fröhlich band upper limit.
2,0
• Min. frequency k min in the harmonic potential ½k(r-re)2 :
kmin = min2 m = 4.7 10-5 dyn/cm
• k from U = ½k(r-re)2  G/r 4 – E/r 3 must satisfy k > 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 > 4.7 10-5 dyn/cm = k min  ok ;
• |U(Re)| = 7.1 10-14 erg > 6.45 10-14
erg = 3/2 KBT  ok, not thermally
dissociated;
• n = 2.4 1013 s-1 > 1013 s-1 = nmin 
ok, slightly above Froehlich band;
• ħ = 1.6 10–13 erg > 6.45 10–14 erg
= 3/2 KBT  ok, oscillator excitation
produces dissociation  forbidden.
• Postulated potential – realistic.
Model
Adj. R-Square
-6,50E-014
E
-6,60E-014
E
E
0,00E+000
E (erg)
-6,70E-014
-6,80E-014
Adj. R-Square
E
-6,90E-014
E
-7,00E-014
E
-7,10E-014
-2,00E-014
-7,20E-014
520
E (erg)
Model
540
560
580
600
620
640
R (nm)
-4,00E-014
-6,00E-014
-8,00E-014
350 400 450 500 550 600 650 700 750 800 850 900 950 1000
R (nm)
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:
d  r1  r 2
meff
m1 m2
m 

2
m1  m2
• Harmonic potential:
•
1
1
2
2
2
V (d )  m  (d  re)  k (d  re)
2
2
• In the ground state, nr = 0 (n = 1), l = 0 (no orbital motion), m = 0,
Gaussian wavefunction, of halfwidth do:
d0 = sd = (<d>2 – <d2>)1/2
d 0   m  2   meff 
• The diameter 2a of a spherical cell equals the sum of equilibrium
distance re between CDs and a length proportional to halfwidth d0:
2a  re  cd 0  re  c  m  re  c 2   meff 
• c > 1; c = 4 for 4s; probab. > 99.99 % for oscillator inside cell.
• In the ground state we take re, for instance:
re ~ <d2>1/2 = [3 ħ / meff ]½
• Cell radius a as a function of eigenfrequency :
a = (3½ / 2 + 2 . 2½ ) [ħ / meff ]½
• Postulate: In the living cell, the oscillator is in the ground state of
energy E000 = 3ħ/2. For stability, the thermal energy must be lower
than the energy quantum ħ = E100 – E000 to first excited level:

3

kBT
2
• Maximum radius of a spherical cell:
 2
4 

a

 2

3



meff k B T
• a < 0,987 µm, maximum volume V < 4,03 µm3.
• Comparison of harmonic oscillator and spherical gap:
 4,03 µm3
0,42 µm3 = Vmin < Vcell < Vmax = 
harmonic spherical
oscillator
 4,45 µm3 impenetrable spherical 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.
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 re+cd0 :
a = b + re + cd0
• Perturbation treatment: Unperturbed energy levels in box :
En = p2 ħ2 n2 / 4 meff b2
• Energy difference between first two unperturbed levels :
DE21(0) = E2(0) – E1(0) = (3/4) p2 ħ2 /4meff b2
• En levels of unperturbed Hamiltonian of the potential well. Wave
functions:
Yn(r) = (2/b)1/2 sin (npr/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
V’11 = k/b ∫(r – b/2) sin2 pb/r dr = k b2/4 (1/6 – 1/p2)
0
b
V’22 = k/b ∫ (r – b/2) sin2 2pb/r dr = k b2/4 (1/6 – 1/4p2)
0
• Their difference:
V’22 - V’11 = 3/16p2 k b2
adds to the difference DE21(0) between the unperturbed levels of the
spherical gap.
• Difference between the perturbed first two levels DE21(1), assumed
higher than thermal energy:
DE21(1) = (3/4) p2 ħ2/4meff b2 + 3/16p2 kb2 > 3/2 kBT
• For the minimum oscillator frequency  = min = 3kBT/2ħ → kmin:
kmin = (3/2 kBT/ħ)2 meff/2
• Obtained → 4th degree equation in b (b ≠ 0) :
9meff2kB2T2b4 – 64 p2 ħ2meffkBTb2 + 32p4ħ4 = 0
with one real positive solution:
b = pħ/(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) = pħ/(meffkBT)1/2 = 1.02 mm for T = 310 K.
• Maximum cell volume = 138.6 μm3.
• 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:
Beaker’s yeast Saccharomyces
cerevisiae Yeast
(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).
• 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 2–3/2 = 0,3536 to
0.15 µm3,
amin decrease by 2–1/2 = 0.7071, from 0.46 to
0.33 µm.
Biological implication: included the smallest
known cells,
• blue-green alga Prochlorococcus of
Cyanobacteria genre (V = 0.1–0.3 μm3),
• Mycoplasma (V = 0.35 mm3).
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.
• 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 < En + Elm < En+1.
• Total energy of an arbitrary quantified level:
Enlm = ħ2/2meff (p2n2/a2 + xlm2/ro2)
• Choose E110 as the ground level, E221 higher level.
• Impose E221 – E110 as a thermally inaccessible transition :
E221 – E110 = ħ2/2meff (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 > ao,
where ao = p ħ / (meff kBT)1/2 = 1,02 µm.
• 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).
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 > 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.
• Other radial levels El’m’ – thermally inccessible  biologically
forbidden transitions between such levels.
E. coli
• For n = 1 and Dn = 0, a thermally inaccessible state |1l’m’> defines a
biologically forbidden transition |1lm> ↔ |1l’m’>. Thus:
E1l’m’ – E1lm = ħ2/2meff (xl’m’2 – xlm2)/ro2 > 3/2 kBT
ro < 1/p [(xl’m’2 – xlm2)/3]1/2 pħ/(meff kBT)1/2
ro < 1/p [(xl’m’2 – xlm2)/3]1/2 ao ,
with ao = 1,02 µm.
• Postulate: ground state |102>, „life-forbidden” transition |102> ↔
|121>. Substitute x02 = 5.52 and x21 = 5.32 roots of the J0 and J2 Bessel
functions. radius ro < 0.28 µm or diameter 2ro < 0.55 µm; axial
length ao = 1,02 µm; form ratio 2ro/ ao = 0.54.
Species
Calculated
2ro (µm)
0.55
ao (µm)
1,02
2ro/ao
0.54
Brucella melitensis
0.5-0.7
0.6-1.5
0.5-0.8
Francisella tularensis
Yersinia pestis
Escherichia coli
0.2
0.5-1.0
0.5-1.0
0.3-0.7
1.0-2.0
2.0-2.5
0.3-0.7
~ 0.5
0.25-0.4
• Other biologically forbidden couple of states: |103> ↔ |122>, 2ro =
0.41 µm, ao = 1,02 µm.
• Similar results with the pairs of states |113> ↔ |104>, |124> ↔
|105>, |125> ↔ |106>, ... . 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) 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.
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:
1) in the cell;
2) 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%).
• The unique twofold different physical property of D2O vs. H2O inertia momentum of water molecule (mD @ 2 mH):
I(D2O) = S mDd2 @ 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:

0 
2I
~
2p
0
67
• Effective mass meff of CDs:
meff


c
• Consequence: Substitution of H2O by D2O  reduction to a half of
water CD effective mass:
meff H 2 O 
meff D2 O  @
2
• 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 D2O-filled cells:
U0 = 4 ħ2/2meffa2 = 4 u = const.
(4u – arbitrary)
68
• 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:
U min 
p    2.47 u
4 2 meff a2
2
2
• With meff = meff(H2O) and meff(D2O) @ 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 < 4 u = Uo
Umin(D2O) ~ 5 u > 4 u = Uo
Umin(H2O) < Uo
Umin(D2O) > 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.
70
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 membrane’s 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.
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.
Conclusions and final remarks
• 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 Fröhlich’s 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 Fröhlich’s theory explain its
remarkable properties and its key role in living cells.
• 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.
• 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.
Acknowledgements
• 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
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.
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 46:6 (2008) 653 — 668
• M. Apostol, Coherence domains in matter interacting
with radiation, Physics Letters A (2008), 18445: 1-6