An engineering thermodynamic approach to select the electromagnetic wave effective on cell growth
Umberto Lucia1,a,*, Giulia Grisolia1,b, Antonio Ponzetto2,c, Francesca Silvagno3,d
1 Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2 Dipartimento di Scienze Mediche, Università di Torino, corso A.M. Dogliotti 14, 10126 Torino,
Italy
3 Dipartimento di Oncologia, Università di Torino, Via Santena 5 bis, 10126 Torino, Italy
1 umberto.lucia@polito.it
b giulia.grisolia@studenti.polito.it c antonio.ponzetto@unito.it
d francesca.silvagno@unito.it
* Corresponding author: Dr. Umberto Lucia, Dipartimento Energia, Politecnico di Torino, Corso Duca
degli Abruzzi 24, 10129 Torino, Italy, E-mail: umberto.lucia@polito.it; Phone: +39 011 090 4558; Fax: +39 011 090 7114
Abstract
To date, the choice of the characteristics of the extremely low-frequency electromagnetic field beneficial in proliferative disorders is still empirical. In order to make the ELF interaction selective, we applied the thermodynamic and biochemical principles to the analysis of the thermo-chemical output generated by the cell in the environment. The theoretical approach applied an engineering bio-thermodynamic approach recently developed in order to obtain a physical-mathematical model that calculated the frequency of the field able to maximize the mean entropy changes as a function of cellular parameters. The combined biochemical approach envisioned the changes of entropy as a metabolic shift leading to a reduction of cell growth. The proliferation of six human cancer cell lines was evaluated as the output signal able to confirm the correctness of the mathematical model. By considering the cell as a reactive system able to respond to the unbalancing external stimuli, for the first time we could calculate and validate the frequencies of the field specifically effective on distinct cells.
Keywords: Extremely low-frequency electromagnetic field, thermodynamic approach, biochemical
Introduction
The living systems are exposed to a broad spectrum of natural electromagnetic waves (mostly from the sun and the earth itself) and take advantage of this energy by absorbing selected quanta. To achieve this, specialized molecular structures or mechanisms have evolved so that the biological systems adapt their components to optimize energy absorption from the electromagnetic wave reaching their niche. The most common example of such evolutionary adaptation is the photosynthetic apparatus of photoautotrophic organisms, including chlorophylls of reaction centers and antenna pigments of light-harvesting complexes. These structures collect and utilize light energy, each molecule being selective for specific wavelengths, to generate a proton-motive force and the high energy bonds of ATP; the electrons liberated in the process are used to reduce inorganic carbon to form organic molecules necessary to build cellular components. Therefore photosynthetic organisms are able to select specific wavelengths and transform their energy in chemical energy. The ability to adapt to specific wavelengths or to the intensity of light has been reported also for yeasts (Robertson et al. 2013) and some fungi (Marsh et al. 1959; Bahn et al. 2007) .
The most exploited frequencies of electromagnetic wave are those of visible light; however the earth also has a natural electromagnetic field (EMF) detected by animals and used to navigate and orient themselves, particularly during migrations. It is believed that animals sense the electromagnetic wave through either crystals of magnetite (Kirschvink et al. 2001), or photoreceptors acting with a radical pair mechanism (Rodgers et al. 2009). Among the latter, the blue-light photoreceptor cryptochrome responds to extremely low frequency and static EMFs, as demonstrated in Drosophila melanogaster (Fedele et al. 2014).
The extremely low frequency electromagnetic fields (ELF-EMF) affect many organisms, as well documented by several studies carried out on plants, animals and men (Belyaev and Alipov 2001; Cosarrizza et al. 1989; Gaetani et al. 2009; Galland and Pazur 2005; Goodman and Henderson 1988; Novikov and Fesenko 2008; Smith et al. 1987; Zhadin et al. 1999). Several
molecular mechanisms have been proposed to explain the effects of ELF-EMF, however the effects and the reported molecular events are numerous, depending on the cellular model studied and the selected electromagnetic field. A general theory explaining why and how different cells respond to the distinct frequencies and intensities of ELF electromagnetic waves has not been formulated yet. Nevertheless, several hypotheses have been put forward and reviewed in Liboff 2014, Funk et al. 2009. Many biological effects of ELF-EMF are believed to be mediated by changes in intracellular Ca2+ signaling and homeostasis, although the evidences of modulation of calcium channels are still controversial (Karabakhtsian et al. 1994; Zhou et al. 2002; Manikonda et al. 2007; Lisi et al 2006; Carson et al. 1990; Pessina et al 2001; Lindstrom et al. 1995). In human tissues and clinical applications, the effects of ELF-EMF have been tested within a standard range of frequencies, namely those of electric power that reaches every household and working place of about 50 and 60 Hertz, and those of cellular phones in the MHz range; the former were tested at intensities around 0.001-10 mT, which are the values found in a human-made electromagnetic environment. In medical field, the impact of these selected electromagnetic waves has been investigated with the aim of ameliorating pathological conditions. For example the exposition to ELF-EMF has been proposed in cancer diagnosis and containment at 50 Hz in humans (Ronchetto et al. 2004); other treatments were aimed at ameliorating side effects of chemotherapy (Rossi et al. 2007), or at improving the well-being of terminally sick cancer patients (Sun et al. 2012). Moreover the effects of ELF-EMF have been investigated in association with standard therapies (Artacho-Cordón et al. 2013; Omote et al 1990). Notwithstanding the vast number of studies, no one ever presented a rationale for the chosen frequencies or the intensities of the applied electromagnetic field; therefore our aim was to determine the optimal parameters of the electromagnetic wave affecting different cell types.
In this study we test the hypothesis that the ELF-electromagnetic wave induces a response that requires a shift in cellular energy conversion, and the consequent metabolic perturbation produces an increase in entropy coupled to a decrease in cell growth. We consider the effects of
ELF-EMF from a thermodynamic perspective; indeed cells obey to the thermodynamic laws by transforming and dissipating energy into work and disorder. In heterotrophs the transformation step ensures that the energy stored in nutrients can be used both in oxidative phosphorylation process originating ATP and in biosynthetic pathways consuming such ATP. The partial dissipation of the assimilated energy causes entropy changes, often mediated by heat produced by metabolism.
Here we use a thermodynamic approach to predict the characteristics of the electromagnetic wave able to induce the entropy changes in the cell-environment system. To this purpose, a mathematical model is formulated, which accounts for cellular parameters and calculates wave frequency and intensity adequate to augment cellular entropy. While the thermodynamic analysis provides the basis for the mathematical model, alone it could not predict the biological response to the field. Thus in complementarity with the thermodynamic analysis we put forth a biochemical model that illustrates the metabolic switch driven by ELF-EMF and explains why the increment of entropy is translated in cell growth reduction. Finally, we measure cell proliferation as a read-out system to verify the soundness of the proposed biochemical-thermodynamic model.
Results
The biochemical model: biochemical basis for the thermodynamic approach
Cells can be modeled as small systems that permanently dissipate energy, so they operate in a nonequilibrium steady-state condition where heat is continuously produced and transferred to the environment. The irreversible loss of energy from the system to the environment leads to entropy generation. If the system does not grow in space but evolves only in time, it changes its internal configuration, disperses energy as heat and the entropy generation of the cell-environment system results maximum. If the system evolves in space the energy is converted into work and the entropy generation results minimum.
The former case, where entropy generation is maximum, describes a differentiated cell in which the metabolic work is aimed at maintaining the molecular gradients. Here the energy from
nutrients is converted in protonmotive force driving ATP synthesis, necessary to transport molecules against gradient, and a substantial dispersion of energy as heat occurs in mitochondrial respiratory chain and oxidative phosphorylation. The latter case, where entropy generation of the cell-environment system results minimum, can be applied to a proliferating cell that in order to duplicate its biological material (proteins, lipids, nucleic acids) forces energy utilization toward biosynthesis. The resulting conversion of energy in biosynthetic intermediates dissipates less heat than the mitochondrial respiration (Prusiner and Poe 1968; Rolfe and Brown 1997).
In this context, the steady-state condition in which the cell is operative ensures that the external perturbation changing the equilibrium must be balanced by an additional energy-consuming work. We consider the ELF electromagnetic wave as an external perturbation able to affect cellular fluxes, forcing the cell to react and restore the gradients. To do so, the cellular energy is channeled into respiratory activity and heat dispersion, at the expense of biosynthetic activities, hence the proliferation is curtailed. We propose that by eliciting this cellular response the ELF-EMF maximizes the mean entropy changes. The model that illustrates the biochemical thermodynamic approach and presents a possible effect of ELF-EMF is depicted in Figure 1.
As it will be shown later in this paper, it is possible that only a few specific frequencies of the wave will be optimal to maximize the entropy generation of the cell-environment system and hamper cell growth. For each cell type, the parameters of the most effective electromagnetic wave can be calculated by the thermodynamic model.
The biochemical engineering thermodynamic model
Cells are adaptive biochemical engines, able to convert energy from one form to another by coupling metabolic and chemical reactions with transport processes (Lucia 2014a); cells irreversibly consume free energy to maintain thermal and chemical processes and to sustain the transport of matter, energy and ions (Lucia 2012). Consequently, life results in an organisational process, in which the maximum conversion of available energy occurs.
The fluxes across the cell membrane represent a fundamental quantity for any physical analysis; an irreversible biochemical thermodynamic approach can be introduced in the study of these fluxes and their biochemical effects. To develop this approach, some considerations must be introduced (Lucia 2015a;Lucia 2015b):
1. The energy lost by cells is gained by the environment. The exchange of energy is a form of communication between cells and environment. If we were able to codify this flow we could increase our knowledge of cell behaviour;
2. The environment is always completely accessible by any observer. Consequently, we can always observe and collect data on this communication between cells and their environment; 3. The flows cause changes in entropy generation. Entropy generation is a measure of the
irreversibility related to the flows across the cells membrane and an indication of the interactions between cells and environment; in fact, different cells manage energy in different ways due to their own nature, with different dissipations and consequent related different entropy generation.
4. The entropy generation of the cell-environment system is a global quantity. Consequently, by analyzing entropy we can obtain information on the behaviour of the whole cells, thus we can consider the cooperative effect of the different biochemical and bio-energetic processes inside the cells.
The cells reach their optimal asset by a selective process of interactions with their environment, with the consequent effect of the redistribution of energy and mass flows in their metabolic network, enabled by regulatory proteins.
In this paper, in order to study the interaction cell-environment and the related processes, we develop the irreversible biochemical thermodynamic analysis of living cells. The thermodynamic theory is based on the constructal law. The use of this theory requires us to consider a defined control volume with continuous matter and energy fluxes, which occur in the least time useful to adapt to any environmental changes. With this approach, we consider that heat spontaneously
exchanged by the cells is related to their biochemical and biophysical behaviour. Because cells are too complex to understand the contribution of each process to their biological behaviour, we introduce a black box model to simplify our analysis. As a result, we can consider only the inflow and outflow balances (Lucia 2014b). Our model is based on the following considerations (Lucia 2013a; Lucia 2013b ):
1. The cell is a non-linear and complex open system; 2. Each process inside the cell has a finite "lifetime" ;
3. What happens in each instant in the range [0,] isn't completely known, but what has happened after time (the result of the process) is well-known;
4. The equations related to the fluxes are balance equations of fluxes of energy, mass and ions; 5. Any process is irreversible; consequently the fundamental quantity for the irreversible
biochemical thermodynamic analysis is the entropy generation of the cell-environment system. 6. The cells environment can be considered a thermostat;
7. The cells together with their experimental environment tightly controlled can be considered an irreversible adiabatic closed system
Based on these assumptions, the total entropy change dS can be introduced considering that it is the result of the entropy change deS for interaction between the open system analysed and its environment, and the entropy change diS due to irreversibility (Denbigh 1989a; Denbigh 1989b):
dS=d
iS+d
eS
(1)Now, we can write the relation (1) as (de Groot and Mazur 1984): dS
dt=
∫
V[
−∇⋅(
QT
)
+ ˙sg]
dV(2) where Q is the heat flow, T is the temperature, V is the volume, t is the time and ´sg is the density of the entropy generation rate. Considering that the stationary states of the open system correspond
to the equilibrium states of the adiabatic closed system whose entropy change is maximum, it follows(Lucia 2016a):
dS=0 ⇒
[
−∇⋅(
Q T)
+ ˙sg]
=0 ⇒ ∇⋅(
Q T)
= ˙sg=∑
k Jk⋅Xk (3) where Jk is the flow of the k-th quantity involved in the process considered and Xk is the related thermodynamic force. It follows that the entropy generation of the cell-environment system is caused just by the flows between cells and their environment. Considering the relation (3), after some algebraic manipulation we can write:1
T ∇⋅Q=
∑
k Jk⋅Xk−Q⋅∇(
1
T
)
(4)in agreement with Le Chatelier's principle (Atkins 1993), for which any change in concentration, temperature, volume, or pressure generates a readjustment of the system in opposition to the effects of the applied changes in order to establish a new equilibrium, or stationary state. Consequently, any readjustment in the energy and mass distribution in a cell system is obtained by generating fluxes (Bejan2016) of free energy, which causes a change in entropy for irreversibility, evaluated by the entropy generation of the cell-environment system, defined as follows (Lucia 2016a ):
Sg=
∫
0 τ ˙ Sg dt=ΔS−∑
iQi Ti−∫
0 τ(
∑
in ˙ minsin−∑
out ˙ moutsout)
dt (5) where Q is the heat exchanged, T is the temperature of the thermal source, s is the specific entropy,˙m is the mass flow and is the lifetime of the process. Now, after some mathematical
manipulation it is possible to obtain (Lucia2013b; Lucia 2014c; Lucia2014d; Lucia2016b):
Sg=
∫
V dV(
−∫
o τ1 v T2Q⋅∇ Tdt−∫
o τ2 v∑
k Jk¿∇(
~μ k T)
dt −∫
0 τ3 v T Π : ∇ ˙xBdt−∫
0 τ4 v T∑
j Jj~Aj+∫
0 τ5 v T∑
k Jk¿Fk)
= =Sg ,tf+Sg , dc+Sg, vg+Sg , cr+Sg ,de (6)where v is the specific volume, Q is the heat flow, ´xi is the relative velocity in relation to the centre of mass reference, and ´xB is the centre of mass velocity, s is the specific entropy, u is the
internal specific energy, p is the pressure, T is the temperature, Fk are the forces, Jj is the chemical reaction rate of the j-th chemical reaction and ij are quantities such that if they are divided by the molecular mass of the i-th component they are proportional to the stoichiometric coefficients. Here we introduce the electro-chemical affinity à = A + Z related also to pH variation and the electric field variation, with Aj = k kjj, Z the electric charge per unit mass, the electrostatic potential; Sg,tf is the entropy generation due to the thermal flux driven by temperature difference,
Sg,dc is the entropy generation due to the diffusion current driven by chemical potential gradients, with ~μ = + Z electrochemical potential, with chemical potential, Sg,vg is the entropy generation due to the velocity gradient coupled with viscous stress, Sg,cr is the entropy generation due to the chemical reaction rate driven by affinity, always positive, Sg,de is the entropy generation due to the dissipation due to work by interaction with the environment, and i, i [1,5], are the lifetimes of any process.
The biochemical and thermodynamic quantities are evaluated as follows:
1. the volume of the cell is evaluated by a characteristic length, in transport phenomena usually the diameter of the cell is considered approximated as the diameter of a sphere
L=(6 V / π )1 /3=2 r , with r being the cell radius;
2. the mean environmental temperature can be assumed as T0 = 310 K and the mean cell temperature has been estimated to be T0 + T. The quantity T would be experimentally evaluated for different cells lines in relation to their metabolism;
3. the internal energy density results in u = 3.95×107 Jm-3, being calculated as the ratio between the ATP energy, U = 3×10-7 J and the mean value of the cell inside the human body, V = 7600 m3. It must be emphasized that this is an approximation because the cell volume inside the human body is in the range of 200-15000 m3;
4. the thermal molecular mean velocity inside the cytoplasm is considered to be xth= 5×10-5 m
5. the membrane volume is calculated with Vm=4 3π r 3 −4 3 π
(
r−de)
3 =4 3π r 3 −4 3π (r−0.2r ) 3 =0.992V being de = 0.2 r;6. the chemical potential gradient can be approximated through the ratio between the mean value of the chemical potential = 1.20×10-9 J kg-1 and the membrane length d
m = 0.01 m, with the mean density being = 1000 kg m-3;
7. the viscosity is taken to be 6.91×10-3 N s m-2; 8. 2.07×10-3 N s m-2 at 30°C;
9. ´xB is set as 3.0×10-6 m s-1;
10.1 is the time related to the thermal flow driven by temperature difference. It can be assessed considering that the time constant of the thermal transient for heat conduction is
τcv≈ ρcV /(hA) with 1000 kg m-3 density, V the cell volume, A the external cell surface, c 4186 J kg-1K-1 specific heat, and h the convection heat transfer coefficient evaluated as:
h ≈ 0.023 ℜ0.8Pr0.35λ /L ,where 0.6 W m-1K-1 of heat conductibility, L the characteristic dimension of the cell (here we have considered the diameter), Re 0.2 the Reynolds number and Pr 7 the Prandtl number. The process would have occurred in a time 1 5 cv. For human cells this value can be considered in the range 15-269 ms;
11.2 is the time related to the diffusion current driven by chemical potential gradients. It can be evaluated as τ2≈ d / D ,with d = 0.01 m, i.e., the length of the membrane, and D being the diffusion coefficient. Considering that the diffusion coefficient of glucose is approximately 10-9 m2s-1 it follows that 2 10 s;
12.3 is the time related to the velocity gradient coupled with viscous stress. This time can be evaluated as the propagating time of a mechanical wave on the surface of the cell
τ3≈2 πr
c , with c 1540 m s-1 the sound velocity, considered to be the same in biological
tissue;
13.4 is the time related to the chemical reaction rate driven by affinity and it can be evaluated considering the magnitude order of a chemical reaction in a cell ( 10-7 mol s-1l-1). Moreover, we consider that the moles number is proportional to the density of the chemical species (for glucose 1540 kg m-3) and the volume of the cell itself. It follows that this time is in the range 17-1283 ns;
14.5 is the time related to the dissipation due to work by interaction with the external forces. It depends on the interaction considered;
15. L is a characteristic length, introduced as usually done in transport phenomena.
In the relation (6) external fields are considered; in this study, we apply low frequency and low intensity electromagnetic fields and we seek to evaluate the frequency of the electromagnetic field that causes biochemical effects on the cells. The hypothesis here introduced is that the interaction is a resonant one, and we can assess the lifetime of the process we want to stimulate by evaluating both the entropy generation of the cell-environment system and the entropy generation rate. We consider that a readjustment of energy occurs in the cell. It is the result of the balance between the power generated by the cell and the heat lost by convection with the environmental fluids: this balance is directly related to entropy generation due to the thermal flux driven by temperature difference, consequently we can evaluate the lifetime
τ
tf of this process by the following relation:τtf=Sg,tf ˙
where
S
˙
g,tf is the entropy generation rate due to thermal fluxes. The frequency of the electromagnetic wave must be such as to induce the thermal fluxes in a spontaneous way, which means at the same frequency of the occurring phenomenon, which is:f = 1
τtf (8)
This relation suggests that the interaction between electromagnetic waves and cell is no more than a resonance of the biomolecular structures of the cell membrane. In our model, the system is predicted to interact only with a specific frequency of the electromagnetic waves, related to the volume of the cell, and this is an indication that a resonance-like phenomenon occurs. In Figure 2 we highlight the relationship between the frequency and the volume of the cells. The dependence of frequency on cell volume can be explained by the thermo-mechanical properties of the cell membrane. Indeed, the surface tension of the membrane is proportional to its surface area. The greater is the volume the greater is its border area and the lower is the surface tension; consequently the energy required to obtain a vibration of the membrane becomes low for large volumes, with the related effects on the resonant behaviour of its molecular structure.
Experimental validation of biochemical thermodynamic principles
Six independent experiments have been carried out to test the biochemical thermodynamic model and in each case the results have been in agreement with prediction. We chose six different cell types originated from distinct tumors, different from each other in morphology, growth rate and oncogene expression. (Figure 3); we characterized some of their biophysical properties and we used them in the mathematical model to calculate the frequency most effective on each cell type. These parameters are shown in Table 1. In each experiment we exposed three different cell lines to the electromagnetic field, with a frequency and intensity chosen to be effective in maximizing the mean entropy changes of only one cell type out of three. The value of wave amplitude was less critical in our approach, representing simply the number of photons triggering the biological event. Because
we hypothesize that the electromagnetic field evokes a resonant response, the key parameter is the frequency and not the intensity of the wave; therefore we chose a value of intensity that we considered as sufficient to produce a statistically significant number of events in the analysis of the energy interaction. After four days of exposure, the proliferation of untreated and exposed cells was analyzed by a colorimetric assay. The results of six experimental sets are shown in Figure 4. In each experimental condition we found a reduced cell number only in the cell line for which the applied frequency was calculated as optimal. Therefore in every experiment the electromagnetic field was effective in inhibiting the growth of only one cell type, as predicted by the model.
Discussion
All the previous studies exploring the beneficial effects of electromagnetic waves on cell growth were focalized on dissecting the molecular pathways stimulated by ELF-EMF and on explaining the mechanisms through which the electromagnetic wave affects living matter; however, this approach has produced only theories that not always apply to all experimental models.
The novelty of this study lies in the evaluation of the homeostatic cellular response, in other words in the analysis of the thermo-chemical output of the cell in the environment (mean entropy changes), rather than the single pathway(s) affected. In this work we exploited the principle of action and reaction in terms of membrane flux variation and we calculated the frequency most effective to maximize the entropy generation of the cell-environment system in each cell type. Our biochemical model predicted the inhibition of cell growth as consequence of mean entropy changes, therefore we used the proliferation rate as the output signal able to confirm the correctness of the thermodynamic model. The biophysical parameters calculated for six different cell types were used in the mathematical model to calculate the optimal frequency for each cell line, and the analysis of proliferation confirmed the effectiveness and selectivity of the chosen field parameters in inhibiting cell growth.
In our biochemical model we hypothesize that ion fluxes triggered by resonant frequencies of ELF-EMF elicit a homeostatic response to compensate and minimize the perturbation. Ionic gradients are restored by mechanisms of primary or secondary active transport, both driven by ATP hydrolysis. The cell has thus the necessity of incrementing mitochondrial production of ATP through mitochondrial respiration. Mitochondrial oxidative metabolism feeds the respiratory chain; the energy of the electron flow is converted in proton gradient necessary to drive the synthesis of ATP but it is partly dissipated in the uncoupling process that converts energy in heat.
Mitochondrial activity, heat dispersion and the thermodynamic variable entropy are the parameters that we predict as modulated by ELF-electromagnetic wave. This model is supported by the fact that two out of three of these parameters have been verified in our previous work; in fact we have demonstrated that ELF-EMF induces mitochondrial activity and modulates mitochondrial protein expression (Destefanis et al. 2015) and our study of biochemical engineering thermodynamics has shown the increased heat dissipation of cells exposed to ELF-EMF (Lucia et al.2015). In this work we take in consideration the third parameter, which is the entropy change.
In our biochemical model the event that links entropy changes with proliferation is a metabolic shift induced by ELF-EMF. Electromagnetic wave is able to alter intracellular metabolism, as previously demonstrated in different cell types, such as yeast (Perez et al. 2007; Robertson et al. 2013 ) and mammalian cells (Destefanis et al. 2015), and in organisms such as
Caenorhabditis elegans (Shi et al. 2015). For example ELF magnetic field induces alterations in
ethanol production by Saccharomyces cerevisiae (Perez et al. 2007), by a postulated mechanism of alterations of ion transport (substrates) that results in stimulatory effects on cell metabolism. Moreover, in yeast the exposure to specific wavelengths of visible light significantly alters the respiratory oscillations through a mechanism of light absorption mediated by cytochromes (Robertson et al. 2013); the light-driven metabolic rhythmicity allows cells to perform anabolic and catabolic processes in a finely coordinated and efficient fashion, helping to minimize the occurrence of futile reactions. Here we propose a similar impact of electromagnetic wave, which supposedly
enhances the catabolic pathways to maintain gradients at the expenses of biosynthetic processes necessary to proliferation.
In previous work we have demonstrated that ELF-EMF exposure enhances respiratory activity and reduces growth rate of cancer cells (Destefanis et al. 2015); moreover recent reports (Consiglio
et al. 2014; Santidrian et al. 2013; Park et al. 2010)support the idea that increasing respiratory chain
activity inhibits growth in cancer cells. Therefore, the negative effects of electromagnetic fields on cancer cellular proliferation have been interpreted as a consequence of the intensified activity of the respiratory chain, which stimulates the oxidative catabolism, with a net disadvantage for biosynthetic pathways; thus the cancer cells are not supported in their demand of mitochondrial biosynthetic intermediates essential to proliferation. These considerations are reasonably based on our previous work (Destefanis et al. 2015; Lucia et al. 2015) and in this study have been used to predict the biological behavior of cells forced to entropy changes of the cell-environment system by the electromagnetic field; however the molecular events hypothesized by the model remain to be elucidated and will be the subject of future studies. Of course other physical phenomena could occur as consequence of ELF-EMF interaction with the living matter: for example in physical analysis of the interaction of ELF-EMF with liquid water it has been pointed out that the field can generate quantum coherent domains in which the water molecules can oscillate between the ground state and an excited state close to the ionizing potential of water. This can favour redox reactions affecting the energy metabolism in living organisms. Coherent domains can also activate specific biochemical reactions through resonance, a mechanism used for fine regulation of gene function (Ho 2014).
The novelty of our approach is also based on a general applicability of our theories, because we do not evaluate the metabolic peculiarities of cells, but instead the effect is based on the homeostatic response that changes energy utilization. With ELF-EMF we induce a perturbation of cellular equilibrium and we evoke a balancing response that requires a metabolic shift and generates entropy changes, therefore differences in basal metabolism are irrelevant.
Depending on the cellular characteristics, only few frequencies of the electromagnetic waves will be effective in perturbating energy homeostasis of the cell. Many studies have reported the existence of specific energy windows that enhance the effects of ELF-EMF on cells (Sadeghipour et al. 2012; Postow and Swicord 1996; Ubeda et al. 1983). The cell adsorbs energy of ELF-EMF at a resonant frequency and intensity adequate to trigger ion fluxes (Bawin and Adey1976; Blackman et al. 1982; Blackman et al. 1985). When the electromagnetic wave has a frequency resonant with oscillatory frequencies of biological molecules, a cellular response is evoked. To explain how resonance can affect cellular structures, different mechanisms have been proposed, as reviewed in Blank and Findl 1987; Cifra et al. 2011; Funk et al. 2009; Panagopoulos et al. 2002).
The specific effect of single frequencies has two important consequences:
1. In every cell type different parameters of ELF-EMF impact differently the energy utilization and proliferation. The proposed model allows to select the parameters most effective on inhibiting cell growth.
2. The same electromagnetic wave has distinct effects on different cells and tissue, with the proposed model we can predict the selectivity of the wave for a single tissue and exploit this possibility for medical purposes.
In summary, we propose a method to define which ELF-electromagnetic wave is most effective in reducing the proliferation of a specific cell line. We describe a biochemical thermodynamic approach to evaluate the thermochemical output of the cells exposed to ELF-EMF and to interpret the associated biological effect that is the reduction in proliferation. This work is innovative in its applicability to individual cells types and tissues, and creates a basis for challenging future biological and biochemical studies aimed at investigating at the molecular level the effects exerted by ELF-EMF on proliferation. The selection of specific field parameters would be most beneficial in contrasting the proliferative disorders, primarly cancer. The illustrated method offers promising avenue to solve the problem of selecting the optimal wavelength and intensity on different tissues and on different sub-population of the same altered tissue; the latter case is very
common in cancer. The results found in this study should benefit the large community of researchers that propose EMF as therapeutic tool in several pathological conditions.
Methods
Cell cultures
MCF7 and SKBR3 are two human breast cancer cell lines that differ in their dependency on estrogen stimulation, oncogene expression and show different cell size, although both grow in epithelial-like clusters. GTL16 is a human gastric cancer cell line overexpressing the MET oncogene, characterized by a rapid growth and a round-shaped morphology. HT29 is a human colorectal adenocarcinoma cell line, with epithelial morphology. A375P and SK-MEL-28 are two human melanoma cell lines that differ in their morphology, growth rate and malignancy. GTL-16 cells were a gift from Dr. Enzo Medico (Institute for Cancer Research and Treatment, Torino School of Medicine, Italy). MCF7, SKBR3, HT29, A375P and SK-Mel-28 cell lines were purchased from American Type Culture Collection (ATCC) (Manassas, VA, USA). The cells were cultured in Dulbecco's modified Eagle's medium (DMEM) or RPMI medium (HT29 cell line) that had been supplemented with 10% fetal bovine serum and 1% antibiotics (penicillin-streptomycin) at 37°C in a humidified atmosphere containing 5% CO2. All culture reagents were from Sigma-Aldrich(Sigma, St Louis, MO, USA).
Cell size was evaluated by photographs taken in different areas of the dish. For each cell type, cellular and nuclear size was calculated using an ImageJ software analysis on thirty images (Sun Microsystems Inc., Palo Alto, CA).
Proliferation assay
The effect of ELF-EMF on the growth of the different human cell lines was determined by colorimetric measurement of cell numbers by crystal violet staining. Different amounts of cells (2000, 1000 or 500) were seeded on 96-multiwell plates, taking into account their different
proliferation rate, and they were cultured for four days in standard conditions (control) or exposed to ELF-EMF. At the end of this period, the cells were fixed for 15 min with 11% glutaraldehyde and the plates were washed three times, air-dried and stained for 20 min with a 0.1% crystal violet solution. The plates were then extensively washed and air-dried prior to solubilization of the bound dye with a 10% acetic acid solution. The absorbance was determined at 595 nm. The data collected from twelve wells were averaged for each experimental condition, and each experiment was repeated three times.
ELF-EMF exposure system
The experimental setup has been described previously (Destefanis, M. et al 2015). A schematic drawing of the device can be found as Supplementary Figure S1. Briefly, the cell culture plate was placed in the central part of the apparatus for magnetic exposure, made of two independent couples of coaxial coilswound into aframe of cylindrical shape, with an outer radius of 8 cm and a distance between the two coaxial coil couples of 8 cm. The experimental setup was placed in the incubator inside a boxthat shielded the apparatus from the background magnetic field.The AC current signal was generated as a sine wave at the frequencies f, 2f, and 4f, in order to take into account the volume variability of the cells. The intensity of f was 70 T for all experiments, a value that was estimated sufficient to produce a statistically significant number of events in the analysis of the energy interaction. Because the amplitudes are proportional to the weight of the resonant frequency distribution in relation to the volume distribution, the intensity of 2f and 4f were 22 and 11T, respectively. The untreated cells (controls) were placed in the incubator without shielding, so that they were subjected to an electromagnetic background representative of the common electromagnetic exposure of everyday life. The cells exposed to ELF-EMF were shielded in order to isolate the effect of specific frequencies and intensity of the field.
The data are presented as the means ± S.D. Statistical analysis of the data was performed using an unpaired, two-tailed Student's t-test. P < 0.05 was considered to be significant.
Acknowledgements
This work was supported by Ministero dell’Istruzione Università e Ricerca
Author contributions
U.L. constructed the thermodynamic theory, the theoretical approach and wrote the paper. G.G. supported the numerical computation of the thermodynamic model by using the experimental data obtained. A.P. supervised the biomedical approach and reviewed the paper. F.S. proposed the biochemical model, performed the experiments and wrote the paper. All authors discussed the results at the all stages.
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Figure Legends
Figure 1. ELF-EMF changes the conversion of energy. (A)The different transformation of energy into work (W) keeps the cells in equilibrium between the quiescent status with the maximum entropy changes and the proliferating energy consuming condition. Heat production (Q) and entropy generationof the cell-environment system represent the thermochemical output analysed in the environment. (B) When the cells are exposed to ELF-EMF, the increased demand for ATP produces the maximum entropy generation of the cell-environment system, enhances heat dissipation and shifts the equilibrium at the expenses of duplication.
Figure 2. Correlation between ELF-EMF frequency and cell volume. The shape has been evaluated as 1/1. The plot highlights that to greater cell volumes correspond smaller frequencies.
Figure 3. Morphological analysis of selected cell lines. Six different human cell lines were photographed in order to evaluate their size. Bar: 200 m.
Figure 4. The effects of selected frequencies on proliferation. The influence of ELF-EMF on cell growth was evaluated using a crystal violet assay on cells that had been stained after four days of exposure (ELF) or left untreated (control, ctrl). Each experimental set was exposed to a single frequency of ELF-EMF predicted as effective on only one cell type. The staining was proportional to cell number and the values for the exposed cells were expressed as the percentage of their respective controls. The data represent the means ± SD of twelve samples and the experiments were repeated three times. * P<0.05 compared to the control.
Table 1. Cell parameters and calculated ELF-EMF frequencies.
For each cell line, thirty cells in different fields were evaluated in their size; three representative values are shown. Cell volumes were estimated and used in the mathematical model to calculate the most effective frequencies of ELF-EMF. The mean frequency was obtained for each cell line. The values of frequencies are expressed as the mean ± SD of thirty calculated frequencies.
cell line
mean nuclear
diameter cell size cell size cell volume
mean frequency [m] [m m] [m2] [m3] [Hz] 24.5 26.0 5.1 16,468 793 MCF7 12.3 0.1 12.0 28.0 4.0 17,303 1,040 5.0 0.7 16.0 52.0 6.8 42,284 2,068 16.5 20.0 3.7 1,795 97 SKBR3 14.5 0.1 20.0 33.0 5.3 29,048 1,301 8.0 2.0 16.0 49.0 6.5 47,594 2,168 18.0 18.5 3.7 1,300 80 GTL16 10.5 0.1 23.2 25.8 4.9 2,630 140 14.0 3.0 16.5 20.5 3.7 1,260 77 16.4 20.4 3.7 333 21 HT29 10.5 0.1 15.2 27.2 4,2 408 24 50.0 5.5 11.2 21.6 3.3 373 26 16.8 37.6 5.4 944 45 A375P 13.5 0.1 25.4 34.4 6.0 786 34 31.0 4.6 12.0 38.0 5.0 988 54 16.4 94.0 11.0 10,327 496 SK-Mel-28 11.3 0.1 13.6 145.6 15.9 9,119 462 7.0 1.5 24.0 89.2 11.3 14,789 627
