Cytoprotective Effect of Elf-Emf120hz on Early Chemical
Hepatocarcinogenesis through Quantum Measurements on
Enzymatic Interaction
Juan José Godina Nava
1,3
, Eduardo López Sandoval
2
, Arturo Rodolfo Samana
2
,
Paulo Eduardo Ambrosio
1
and Dany Sanchez Dominguez
1
1
Programa de Pós-Graduação em Modelagem Computacional, Departamento de Ciências Exatas e Tecnológicas, UESC,
Universidade Estadual de Santa Cruz, km 16 Rodovia Ilhéus-Itabuna, Salobrinho 45662-900 - Ilhéus, BA – Brazil
2
Departamento de Ciências Exatas e Tecnológicas, UESC, Universidade Estadual de Santa Cruz, km 16 Rodovia Ilhéus-
Itabuna, Salobrinho 45662-900 - Ilhéus, BA – Brazil
3
Departamento de Física, CINVESTAV-IPN, Ap. Postal 14-740, CdMex, C.P. 07000, México
Keywords: Extremely-Low Frequency Electromagnetic Fields, Radical Pair Mechanism, Hepatocarcinogenesis.
Abstract: Using the concept of quantum measures, we depict the mechanism in which the cytoprotective effect of ELF-
EMF-120Hz on early hepatocarcinogenesis chemically induced in rats matches with the theory. We used the
traditional Haberkorn approximation to evaluate the quantum yields at the rate of recombination production
of singlet spin state populations, assessing with this information, the magnetic field effect. In this work, we
study the system RP-Hepatocyte simply applying dynamic mapping.
1 INTRODUCTION
Nowadays, for all, it is known that both permanent
magnetic field (MF) and extremely low-frequency
electromagnetic field (ELF-EMF) interact with
biological systems (BS) at all levels (Paunesku,
2007). However, there still not exist a precise
molecular mechanism for which the ELF-EMF or MF
can characterize their therapeutic use, although much
research has been performed and reported several
effects on BS. The most common report is that an
external MF can significantly affect the rates of
chemical reactions in BS involving free radicals,
impacting the probability of transition between the
singlet to the triplet spin state , , in the
radical pair (RP) largely (Sagdeev, 1973; Maeda,
2011). The hyperfine interaction (HyI) is the
responsible for the control of the spin-flip conversion
spin states of the RP permitting to modify it
by the application of an external MF. The magnetic
energy compared with the chemical energy is 10-100
times smaller, in fact, the newest effect is the
magnetoreception in birds (Rodgers, 2008). The RP
recombination probability changes in a periodic way
whose frequency is determined by the HyI. The origin
of the oscillations is the interaction between the one
nuclear RP (spin 1/2) and two electrons. In fact, if we
start with a singlet correlated-spin state, when HyI
produces the oscillations , at the same time
determines that be precisely this spin singlet state
who through recombination probability oscillate in
time (Anisimov, 1983; Maeda, 2011). In a real
system, RP has many nonequivalent magnetic nuclei,
and in this case, the interaction between RP is
management in ensembles by harmonic oscillations,
but in this case, the regulation of the system is carried
on by a set of complex frequencies that interfere itself
and vanishes due to the superposition. The opposite
effect, which appears when the magnetic nuclei are
equivalent, i.e., the oscillation between and states
between differents RP are drafted in a variety of
frequencies, whose superpositions appears as beats of
the reaction probability. The only condition for their
observation is that the ensemble is prepared in a
different defined initial spin state and stimulated by
light, ionizing radiation or MF.
Facing our limited knowledge and using the
available information, we reported the cytoprotective
effect of ELF-EMF120Hz on early chemical
hepatocarcinogenesis during the enzymatic
procarcinogen activation of the Cytochrome P450
(CYP450) by quantum measurements. In the
Godina-Nava, J., Sandoval, E., Samana, A., Ambrosio, P. and Dominguez, D.
Cytoprotective Effect of Elf-Emf120hz on Early Chemical Hepatocarcinogenesis through Quantum Measurements on Enzymatic Interaction.
DOI: 10.5220/0006546401190126
In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 4: BIOSIGNALS, pages 119-126
ISBN: 978-989-758-279-0
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
119
experimental setup, we implementing the modified
resistant hepatocyte model with Male Fisher-344 rats
exposed them daily to 4.5 mT-120 Hz ELF-EMF
during 50 minutes. We analyze the effects
performing several biological tests concerning
apoptosis, proliferation and cell cycle progression.
We found that daily application of ELF-EMF inhibits
preneoplastic lesions in both size (56%) and number
(58%).
It appears when after formation of oxidation state,
the electron transfer is involved, and the MF
modulates those in the current Haberkorn approach
(Jones, 2011; Godina, 2017). The allowed
electrophilic reactions that appear in the enzymatic
reactions do not require a change of spin because the
spin total is zero. Those spin-forbidden reactions,
involving paramagnetic participants, can combine
their spins freely in any electronic configuration, but
it does not mean that all configurations have a
chemical reaction. The electron spin is who gives
origin to the MF effect (MFE), the magnetic isotope
effect and induced nuclear chemical polarization.
From all four possible combinations of quantum spin
states, only one is useful combining two radicals to
become a diamagnetic molecule (Buchachenko,
1995-a; Buchachenko, 2017; Godina, 2017).
The proposal is that when CYP450 metabolizes
the xenobiotics used in the experimental setup to
induce the chemical hepatocarcinogenesis, such
enzymatic proteins act as a molecular motor
providing a catalyzing electron that interacts with the
RP formed during the oxidative stress generated when
the substrate of the enzyme is oxygenated. Since the
metabolization is carry on in the liver, the hepatocytes
are in contact with the enzymatic protein like in a
thermal bath and with a Gibbsian distribution,
interacting with the RP like a harmonic oscillator.
Employing quantum measurements concepts, we
argue the way in which the MF modulates the singlet
spin population to diminish the preneoplastic lesion
observed during the experimental setup (Jimenez-
Garcia, 2010) and theoretically explained in (Lopez-
Riquelme, 2015; Godina, 2017). The complete
system between RP and electronic configuration of
hepatocytes interacting through the hyperfine
coupling constant, alter that the quantum spin state
removes spin prohibition giving rise to the
appearance of new reaction products. Such products
in our case, result of the spin selectivity plus HyI
action affecting the magnetic properties that impact in
the so-called initiated hepatocytes that become later
the preneoplastic lesion.
2 RADICAL PAIRS
The main protagonist in this approach is the so-called
radical pair (RP), short-lived intermediates that
participate in almost all reactions in solution in a
correlated way. The RP can recombine or participate
in other chemical reactions. They are the responsible
for a few phenomena like chemical polarization of
electrons and nuclei, and the influence of static and
pulsating MF. An RP can decay by recombination, or
put apart the radical by diffusion, or react with other
radicals. One of the properties of the RP is that
recombination probability depends on the spin
multiplicity, and it varies during RP lifetime. An
interesting detail is that are manifested such
variations as dynamic quantum oscillations, the so-
called quantum beats between (, ) spin states of the
RP. The quantum beats modulate the probability of
appearance of some reaction channels of the RP that
at time affect the MF Effect (MFE). By studying these
quantum beats, one can reveal valuable information
concern the structure, reactions, molecular and spin
dynamics of RP (Molin, 1999; Maeda, 2017; Godina,
2017). The RP spin-correlated is formed in the
coherent state which oscillates between and spin
state, an oscillation that depends on of the spin
Hamiltonian operator parameters, in particular of the
hyperfine coupling constant. The period of the
oscillation on organic radicals is in the range of
nanoseconds.
3 MAGNETIC FIELD EFFECT
In the first instance, in laboratory conditions, it is
possible that we can have significant magnetic field
effect (MFE) at low temperatures. There exist other
situations where the MFE are essential. In fact, the
most exciting possibilities appear when we study the
nonequilibrium situation. Thus, when we apart from
the equilibrium for a specific quantity, would be
involucrated some transport properties, related with
the nonequilibrium parameters like electric
conductivity, the Hall constant, the thermal
conductivity, and the diffusion coefficient
(Zeldovich, 1998; Maeda, 2017). The MFE of a
magnetic moment of the nuclei is similar to that of an
external MF. Other places where we can observe the
influence of the weak MF is at the rate of precession
of paramagnetic particles like radicals, or electrons,
participating in chemical reactions. The main
fundament of these effects is the so-called principle
of spin selectivity, i.e., that the chemical reactions are
BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing
120
only allowed starting from a definite spin state. For
example, the case that happens when is formed an
intermediates RP, the radicals in their formation can
adopt the singlet or triplet spin state, but the
recombination of the RP into a molecule only is
allowed through the singlet state, due that the reaction
by triplet state is spin-forbidden. When an oxygen
molecule meets with the RP, the Hausdorff space
spanned by the system of RP-oxygen is formed by
two doublets and one quartet state. However, in the
doublet is where is constituted the interaction
between the radical and oxygen molecule. The central
detail into an MFE is that although the MF
interactions of spins with external and internal
nuclear fields have negligible energies, their effect on
chemical reactions is of much strength since those
change the spin of the reacting participants promoting
new channels of interaction for the spin selection
(Zeldovich, 1998; Buchachenko, 2017; Godina,
2017).
The key is that those radicals are MF-dependent
quantities, and they are controlled by a weak MF (
) precisely by their spin correlation, taken as far
away from their equilibrium position. Thus, the
radical pair mechanism (RPM) is the only plausible
theory used to explain the MFE over the reactivity of
chemical reactions in BS (Rodgers, 2008; Maeda,
2017; Buchachenko, 2017).
Their importance appears because
phosphorylation is the most significant phenomenon
for living organisms. For every enzyme or molecular
machine, at low energy, appears electron transfer with
a high energy nucleophilic reaction. A consensus in
the several dissertations is that a weak, steady and
pulsating MF can affect the radical concentration
affecting the population distribution of nuclear and
electronic states, with side effects like interactions on
the rate of singlet state decay, affecting the BS.
4 THE MODEL
The MFE is used as a diagnostic tool in search of
chemical mechanism of the reaction since they
indicate the prominent participation of particular
reactants that signal some important chemical
transformations of particular radicals. The MFE
appear when we have an intermediate RP of
paramagnetic particles in a nonequilibrium
population of spin states. Can be seen a chemical
reaction as a physical process where there are
involved a set of regrouping of atoms with the
rearrangement of electronic shells of reacting
participants, giving place to the generation of new
molecular structures called reaction product. The new
ways to control chemical reactions have their basis on
the selectivity of a process where are involved the
spins of molecules, electrons, and nuclei of the
reacting participants. For this reason, the rate of spin-
selective processes is dependent of MF, whose alter
the spins of the participants changing partial or
wholly the spin selectivity (Zeldovich, 1998;
Buchachenko, 2017; Godina, 2017). Thus, revealed
the interaction to explain the cytoprotective effect of
ELF-EMF in CYP450, we must define the conditions
where is performed the quantum measurement. The
first condition is that all quantum states participating
in the system RP-hepatocytes in the enzymatic
reaction are singlets, for their high reactivity. The
second condition is during the enzymatic
procarcinogen activation of CYP450 when are
metabolized the xenobiotics, in which appear the RP
when is generated the oxidative stress. Are produced
the intermediaries in this step, and they are the
responsible of the insult to hepatocytes and, who will
become the future preneoplastic lesions after to finish
the chemical induction of hepatic cancer. The third
phase is the daily MF stimulation during all chemical
process. On the other hand, the spin evolution of RP
is driven by the MF through the HyI; is controlled
their reactivity by the spin dynamics converting non-
reactive triplet into reactive singlets and through
quantum measurement. We show the way in which
the MF modulates the charges in migration evaluating
the recombination probability. At this respect, when
the RP interact with another spin electron, this
interaction acts as a catalyst increasing the
recombination probability accelerating the
interconversion (Buchachenko, 1998; Buchachenko,
2017; Godina, 2017).
4.1 Spin Selectivity
We will use the basic principle of the chemical
reactions that those are spin selective. We satisfied
the spin angular momentum conservation between
reagents and products. The RP acts when there exist
interconversion, and this interaction will
generate the MFE (Buchachenko, 1995;
Buchachenko, 2017). Also, we use the fact that the
spin catalysis consists of changing the spin state of
the reactants in a chemical reaction.
In this spin catalysis, those spin states prohibited
are stimulated to appear, opening channels that
usually do not are open, promoted by the interaction
between the RP and the third spin. Such catalytic
effect due to the third spin is similar to that of the
Cytoprotective Effect of Elf-Emf120hz on Early Chemical Hepatocarcinogenesis through Quantum Measurements on Enzymatic Interaction
121
interconversion mechanism by the magnetic nuclei
of the RP (Gorbunov, 2011).
4.2 Haberkorn Approach
Thus, to study the results, involving the information
of all parameters employed in the evaluation of MFE,
the recombination yield, and the singlet population, is
needed the Haberkorn approach; which is the most
common theory used for spin dynamics studies. The
Haberkorn approach is obtained using the spin
density matrix in the framework of the Liouville-von
Neumann equation involving the rate at which
singlets disappear, and we named
; involved in a
unnormalized wave function (Jones, 2011; Godina,
2017)
(1)
here the amplitudes for the singlet disappears at the
rate
, provoked by the interaction between RP
and a third electron coming for the electron
configuration of the hepatocytes. With this approach,
can be written the standard density matrix (without
the third electron) as
(2)
moreover, to satisfied the unicity of the trace in the
density matrix, we include the third electron. The so-
called reaction products, according to with the rule of
conservation of the number of entities participating,
i.e., the generation of some product population
corresponds to the disappearance of some singlet
reactant population (Jones, 2011)
,
(3)
where
is a null vector.
4.2.1 Quantum Measurements
When we have a chemical reaction involving only
singlet spin state as in our case, we can consider it as
a quantum measurement (Jones, 2011), where the
amplitudes for the singlet disappears at the rate
provoked by the interaction of the third spin
electron that can be studied.
During the lifetime of the RP, their spin multiplicity
can change. Can be seen such changes by electron
spin resonance spectroscopy (ESR) studies. The name
for such changes in the spin is simply beats, which
means, the dynamical quantum oscillation between
the and spin states of the RP. They are
used to study the behavior of the spin dynamics of RP,
for example, the rate constants of reaction or the
fraction of singlet-correlated pairs, among others.
One crucial issue is that RP appears in the coherent
state, which permits the oscillations between
and spin states of the RP, commanding of HyI.
At a quantum level, these beats represent the
manifestation of the RP. They in ESR studies during
the recombination of spin-correlated ion RP were
measured. Tacitly, the beats correspond to
spin-flip transitions generated by HyI. The behavior
of a unpaired electron under MF, or without MF,
determines the influence of HyI so we can measure
the MFE.
Eq. 3 express the way at which singlet disappear at
desired rate
. On the other hand, the off-diagonal
terms, represent the coherent superposition terms
only decay at a rate
. The corresponding
equation of motion for the density matrix with
as
the interaction Hamiltonian operator is expressed as
(Jones, 2011; Godina, 2017)
(4)
where
is the projection operator
onto the singlet state.
The yield of recombination calculated from the
singlet state of the RP can be evaluated by
(5)
once that Eq. 4 is solved. Indeed, with this quantity,
the MFE is evaluated on the yields of the diamagnetic
products involved, and in those RP that does not
participate in the recombination process.
Furthermore, in the exponential approach, the
represents, the effect of all re-encounter times for the
reencounter probability of a diffusive geminate RP
when it is described the time evolution after their
formation, and
is the average re-encounter
time when
(Godina, 2017).
We use as an initial condition the fact that the
population is born in singlet state
BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing
122
, then the evolution time wave
function reads
(6)
With this sense, the quantum measurements
(Kominis, 2009) give us the formation of products
and then the effect of singlets into the hepatocytes
with an intensity
.
4.2.2 Dynamical Maps
Since the purpose is to analyze the influence of the
ELF-EMF on early hepatocarcinogenesis, in
particular, the effect of the singlet-triplet coherent
spin-flit conversion of the RP provoked by HyI on
hepatocytes by an enzymatic reaction in the liver. We
use a quantum mechanical model spin-based with the
goal that once is performed the calculation of singlet
spin population and determined the MFE, evaluating
the quantum yield for the intermediaries RP in the
system substrate product of the CYP450, to depict the
cytoprotective mechanism.
To study the spin population behavior of the system
was applied the Lanczos method to diagonalize the
interaction spin Hamiltonian. It was previously
rewritten the Hamiltonian in the superstate
representation (Godina, 2017). Beyond of the
mathematical model, the biology of the problem
concerns with the action of the EMF on RP affecting
the Hepatocytes during the enzymatic procarcinogen
activation of the CYP450, precisely modulating the
charges that are in migration during the electron
transfer reactions generated by the CYP450 in their
substrate producing electrophilic and reactive
oxidative species. The intermediaries generated
during this process are the source of the first insult to
hepatocytes in their way to become preneoplastic
lesions in a chemically induced cancer protocol. Are
used three assumptions: i) the chemical reactions are
spin selective, ii) chemical reactions present nuclear
spin selective, iii) chemical reactions are selective
with the spin of the electron. Under such
circumstances, only the reactions with singlets
favored the formation of standard molecules. The
reactions with triplet RP are forbidden. Under this
outline, the spin of the electron is who controls the
generation of the magnetic-spin effects (Godina,
2017). One of the keys of the model is to consider the
role for the enzymatic protein as a molecular motor.
Their function is supplying catalyzing electrons to the
reaction, where take action the RP generated into the
substrate of CYP450 when it is metabolizing the
xenobiotics used in the hepatocarcinogenic model.
Since it is in the liver where the metabolization is
performed employing the enzymatic protein, we
consider to the hepatocytes harmonically interacting
with a thermal bath in a Gibbsian distribution with the
RP. Dynamical maps are used to characterize, in a
general way, the form in which the interaction affect
both the reactive enzymatic system and the
hepatocytes (Godina, 2017).
Thus, we study the RP-third electron system,
considering that the hepatocytes coupled to the
enzymatic reaction system start with some healthy
initial cell configuration,
, and choose a
spontaneous decay process (there exist other
possibilities) in the recombination dynamics. The
system can be described by the following dynamical
mapping (Tiersch, 2012; Godina, 2017)
(7)
Figure 1: Evolution of the singlet spin population. Here, we
note that increasing the hyperfine coupling constant, A, the
singlet population is diminishing.
However, we need recover the evolution equation
for because the trace should take into account the
hepatocytes degree of freedom
. The
trace is evaluated keeping in mind the detailed
principle balance.
During the process appears an effective singlet
state
describing the degree of freedom of
Cytoprotective Effect of Elf-Emf120hz on Early Chemical Hepatocarcinogenesis through Quantum Measurements on Enzymatic Interaction
123
the hepatocytes, that appears with a probability
. The triplet state, that appears with a
probability
, does not interact. In
fact, both states do not evolve with the interaction
Hamiltonian operator
, but these probabilities
depend on time duration of the interaction because
they are matrix elements of the time-evolution
operator (Tiersch, 2012; Godina, 2017), defining
,
,
(8)
we can express such amplitudes of probabilities in the
form
,
(9)
generated by the interaction Hamiltonian (Tiersch,
2012; Godina, 2017)
(10)
where
represent the time evolution
operator. A projection over the
subsystem is
precise to obtain the effect on the hepatocytes, but this
step leaves without normalization to
. To recover
the evolution equation is needed to use an arbitrary
pure state
,
(11)
thus,
, and evolving with
as
(12)
+
4.2.3 Effect on Hepatocytes
When is done the normalization, the measurement of
the generation of some reaction product on the
hepatocytes is represented according to
(Tiersch, 2012; Godina, 2017)
(13)
where
(14)
with
(15)
The result expresses that hepatocytes can measure the
spin nature of the RP that is participating. The spin
state of the hepatocyte changes according to the spin
nature of the RP that is interacting. During the
measurement process, the and
components do
not change, but the hepatocytes change their spin
states according to the RP spin character following
the dynamical mapping (Tiersch, 2012; Godina,
2017)
(16)
instituted by the interaction (Tiersch, 2012; Godina,
2017)
BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing
124
(17)
here,
and
give us the strength of the interaction
of the hepatocytes with RP spin character, appearing
the new term,
, without
states.
In this case, the probabilities
or
express the appearance of a or
spin
states, represented by and (Godina,
2017). They measure the fraction of singlets
transformed into a reaction product or transformed
cell. It is precisely this kind of product formation
which change the electronic configuration of the
hepatocytes, as we claim. The result is evident from
Figure 1, where we note that increasing the hyperfine
coupling constant, A, the singlet population is
diminished. Thus, once the hepatocytes interact
during with the CYP450 by the enzymatic reaction,
they change their spin states by the effect of the
application of the selective spin operator. For each
time interval will be applied the dynamical
mapping to each new healthy hepatocyte in the tissue
incorporating them into the enzymatic
reaction which provides of catalyzing electrons
during the metabolization of xenobiotics (Godina,
2017)
(18)
Also, neglecting the memory effects due to the
previous results with other singlets, which are
diminishing as is evidenced by the quantum
measurement
, changing the electronic
configuration of the hepatocytes when it converted
the RP in a reaction product by the recombination
kinetics.
5 CONCLUSIONS
In this work, we studied a simple quantum mechanic
model to describe the interaction RP-Hepatocytes
following the typical Haberkorn approach for spin
dynamics. Was taken the quantum yields, MFE and
spin population from previous theoretical studies
(Lopez-Riquelme, 2015; Godina, 2017) to explain the
experimental one (Jimenez-Garcia, 2010).
In (Godina, 2017) is investigated in details the
calculations regarding the spin relaxation effects, and
also other forms of coupling to hepatocytes.
We evaluated the MFE due this is the diagnostic tool
for measure the efficiency in the conversion of triplet
spin state in reactive singlet spin state interacting with
hepatocytes. We evaluated it employing the Eq. (5),
subtracting the corresponding contribution
from that part of the magnetic field and
establishing the rate dividing by the contribution
without the field, and multiplying all by 100%. The
calculated MFE is an acceptable result compared with
the experimentally obtained value (61% compared
with 56% (size) - 59% (number) of preneoplastic
lesions) (Godina, 2017). The idea of this research
note is to obtain an explanation of the way in which
hepatocytes can modify their electronic structure
when is in interaction with the RP which come from
the enzymatic reaction. Our proposal includes the use
of the CYP450 as a molecular motor of electron spin
catalysis when is oxygenated during the electron
transit by the enzyme substrate during the process of
metabolization of the xenobiotics employed in
hepatic cancer induced chemically. The result gives
us a more knowledge respect the way in which MF
modulate the electrons which come from the
oxidative stress (cytoprotective effect) generated in
the reactive system RP-Hepatocyte in the liver, with
the finality of understanding carcinogenesis.
ACKNOWLEDGEMENTS
One of the authors (J.J.G.N.) would like to
acknowledge the financial support to Universidad
Estadual de Santa Cruz, UESC-BA-Brazil (Programa
Nacional de Pós-Doutorado PNPS/CAPES).
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