Electromagnetic waves and living cells: A kinetic thermodynamic approach

Physica A xx (xxxx) xxx–xxx

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Physica A journal homepage: www.elsevier.com/locate/physa

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Electromagnetic waves and living cells: A kinetic thermodynamic approach Umberto Lucia Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

highlights • • • • •

Cells transports phenomena can occur across the cells membranes. Cells can also actively modify their behaviours in relation to any change of their environment. Their wasted heat represents also a sort of information. Effects of electromagnetic fields modify the cell membrane behaviour. Cells change their energy management.

article

info

Article history: Received 6 April 2016 Available online xxxx Keywords: Bio-chemical thermodynamics Constructal law Entropy generation Membrane electric potential Membrane surface elastic properties Bioengineering thermodynamics

abstract Cells are complex thermodynamic systems. Their energy transfer, thermo-electro-chemical processes and transports phenomena can occur across the cells membranes, the border of the complex system. Moreover, cells can also actively modify their behaviours in relation to any change of their environment. All the living systems waste heat, which is no more than the result of their internal irreversibility. This heat is dissipated into their environment. But, this wasted heat represents also a sort of information, which outflows from the cell towards its environment, completely accessible to any observer. The analysis of irreversibility related to this wasted heat can represent a new useful approach to the study of the cells behaviour. This approach allows us to consider the living systems as black boxes and analyse only the inflows and outflows and their changes in relation to any environmental change. This analysis allows also the explanation of the effects of electromagnetic fields on the cell behaviour. © 2016 Elsevier B.V. All rights reserved.

1. Introduction During the last decades, a great number of experiments have been developed on the interactions between low frequency and low amplitude electromagnetic fields and the living systems. They highlighted some biophysical and biochemical consequences on the cells behaviour. Some of these experimental evidences can be summarized as follows: 1. in vitro studies: • HeLa (human cervical cancer) and PC-12 (rat pheochromocytoma) cells [1], continuously exposed for 72 h, to ELF–EMF of (1.2 ± 0.1) mT, at 60 Hz, decrease in proliferation 18.4% (HeLa) and 12.9% (PC-12); • HeLa cells exposed to PEMF [2] of 0.18 T, at 0.8 Hz, for 16 h: they decrease 15% in proliferation, as observed 24 h later; • PC-12 cells exposed to ELF–EMF [3] at 50 Hz of different intensities and durations: transient decrease of the proliferation rate and morphological differentiation has been observed;

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.physa.2016.06.079 0378-4371/© 2016 Elsevier B.V. All rights reserved.

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• Human colon adenocarcinoma cells exposed to ELF–EMF of 1.5 mT peak and 1 Hz, for 360 min: they decrease in cell

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growth [4];

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• HCA-2/1cch (human colon adenocarcinoma) cells exposed to 25 Hz, 1.5 mT, for 2 h and 45 min in presence of dexamethasone: they decrease (55.84 ± 7.35)% in the relative cells number [5]; • HTB 63 (melanoma), HTB 77 IP3 (ovarian carcinoma), and CCL 86 (lymphoma; Raji cells) cell lines: 64 h exposure [6] under a 7 T uniform static magnetic field leads to reduction of viable cell number by (19.04 ± 7.32)% for HTB 63, (22.06 ± 6.19)% for HTB 77 IP3, and (40.68 ± 8.31)% for CCL 86; • WiDr (human colon adenocarcinoma), MCF-7 (human breast adenocarcinoma), and MRC-5 (embryonal lung fibrob-

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last) have been exposed to 3 mT static MF, modulated in amplitude with 3 mT ELF-MF, at 50 Hz, with a superimposition of ELF magnetic field, for 20 min. Both WiDr and MCF-7 cells showed morphological evidence of increased apoptosis. MRC-5 cells remained intact and did not show any increase in apoptosis [7]; • HL-60 and ML-1 (Human Myeloblastic Leukaemia) cells undergo apoptosis (detected through ladder type-DNA fragmentation) after exposure [8] at 50 Hz, 45 mT ELF–EMF for time periods of 1 and 2.5 h; • SCL II (human squamous cell carcinoma) cells and AFC (human amniotic fluid) continuously exposed at 50 Hz, 0.8–1.0 mT EMF, for 48 h and 72 h: they increase in the frequency of micronucleus (MN) formation and the induction of apoptosis has been observed [9]; • SH-SY5Y (human neuroblastoma) cells continuously exposed to a 900 MHz radiofrequency radiation (SAR: 1 W kg−1 ), for 24 h: reduction in the viability of neuroblastoma cells [10]; 2. in vivo studies: • Antitumour and immunomodulatory effects of pulsed magnetic fields have been observed when the pulse width is 238 µs, the peak magnetic field is 0.25 T, the frequency 25 Hz, 1000 Hz and the magnetically induced eddy currents in B16-BL6 melanoma model mice is 0.79–1.54 A m−2 . Exposure of mice in pulsed magnetic fields lasted in 16 days. Anticancer and immunomodulatory properties of pulsed magnetic stimulation and decrease of tumour growth and elevated production of tumour necrosis factor (TNF-a) have been observed in mouse spleens [11]; • Extremely low-frequency pulsed-gradient magnetic field with the maximum intensity of 0.6–2.0 T, gradient of 10–100 T m−1 , pulse width of 20–200 ms and frequency of 0.16–1.34 Hz, presented antitumour and antiangiogenic properties, in exposed Kunming mice bearing murine tumour [12–14]; • Male Fischer-344 rats, subjected to the modified resistant hepatocyte model, were exposed to 4.5 mT–120 Hz ELF–EMF. The results showed a decrease of more than 50% of the number and the area of γ -glutamyl transpeptidase-positive preneoplastic lesions, glutathione S-transferase placental expression, a decrease of proliferating cell nuclear antigen, Ki-67, and cyclin D1 expression. These results showed inhibition of preneoplastic lesions, through antiproliferative activity of ELF–EMF [15]; • Nude mice, bearing a subcutaneous human breast tumour (MDA-MB-435), were exposed for 70 min daily, for six consecutive weeks, to modulated MF (static with a superimposition of extremely low frequency fields at 50 Hz), of total intensity of 5.5 mT. The anticancer activity of MF was compared to that of cyclophosphamide. The inhibition on spread and growth of lung metastases caused by MF was greater than that caused by cyclophosphamide [16]; 3. clinic studies: • A combination of tumour-specific frequencies may have a therapeutic effect. A total of 1524 frequencies, ranging from 0.1 to 114 kHz, were identified from 163 cancer patients, while a compassionate treatment was offered to 28 patients with advanced cancer (breast, ovarian pancreas, colon, prostate, sarcoma and other types of cancer). The patients received a total of 278.4 months of experimental treatment and the median treatment duration was 4.1 months per patient. None of the patients, who received experimental therapy, reported any side effects of significance. Two of the patients presented a complete and partial response to the treatment and four patients presented stable disease. A woman, with breast cancer, showed a complete disappearance of some lesions, according to PET-CT (Positron emission tomography-computed tomography), and significant improvement of the overall condition. Thus, the tumour-specific frequencies provide an effective and well tolerated treatment which may present antitumour properties in end-stage patients [17]; • Eleven patients with mean age of 60 years and with stage IV, locally advanced or metastatic disease (adenocarcinoma, duct carcinoma, squamous cell carcinoma and other types), were enrolled in a human pilot study conducted. Patients were exposed for 5 days/week, over 4 weeks, according to two different static magnetic fields schedules: 20 min daily (4 patients) and 70 min daily (7 patients). Results showed that MF-exposed patients present mild or no side effects. Moreover, this pilot study supports the evidence that human exposure to MF with specific physical characteristics is associated with a favourable safety profile and good tolerability [18]; • Ten patients with recurrent glioblastoma were treated by using a 100–300 kHz magnetic fields. No serious adverse events were observed in all patients, after >70 months of cumulative treatment. The median time of disease progression and median overall survival were more than double the reported medians of historical control patients. This type of fields can be used as a safe and effective treatment for cancer patients [19]; • In 2008, a pilot study was developed to investigate the safety and efficacy of low-intensity, intermediate-frequency electric fields in 6 patients (heavily pretreated with several lines of therapy) with metastatic solid tumours, while no additional standard treatment option was available to them. A device was used to emit the frequencies 100–200 kHz, at a field intensity of 0.7 V/cm. A patient presented 51% reduction in tumour size, after 4 weeks of fields’ treatment.

U. Lucia / Physica A xx (xxxx) xxx–xxx

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Also, an arrest of tumour growth was seen in three patients, during treatment. Despite the small number of patients, this study revealed that this type of electric fields presented lack of toxicity and significant efficacy in patients’ treatment [20]; • In a recent phase I/II clinical study, 41 patients with advanced hepatocellular carcinoma (HCC), were subjected to very low levels of electromagnetic fields modulated at HCC specific frequencies (410.2–20 365.3 Hz). Patients were being administered with three-daily 60 min outpatient treatments, till the disease progression or death. During treatment no NCI grade 2, 3 or 4 toxicities (grades based on National Cancer Institute Common Terminology Criteria (CTC) for adverse events), were observed, while most of the patients reported complete disappearance or decrease of pain shortly after treatment initiation. Four patients presented a partial response to the treatment, while 16 patients (39%) had a stable disease for more than 12 weeks. This type of EMFs provided a safe and well tolerated treatment, as well as evidence of anticancer effects in HCC-patients [21]. Some consideration must be developed on these experiments. Indeed, there exist some difficulties in the reproducibility of experimental findings, due to non clearly described protocols or non accurate application of them [22–25]. Moreover, the exposure of AFC cells did not reveal any significant differences, compared to control, at different EMF intensities and various exposure periods [9] and the static magnetic fields seem not to affect the proliferation of normal cell lines: MRC-5 cells exposed to 3 mT static MF, modulated in amplitude with 3 mT ELF-MF, at 50 Hz, with a superimposition of ELF magnetic field, for 20 min, remained intact and did not show any increase in apoptosis [7]. Furthermore, normal human peripheral blood leukocytes did not undergo DNA fragmentation, when exposed to ELF–EMF at 50 Hz, 45 mT ELF–EMF for time periods [8] of 1 and 2.5 h. But, these fails can be explained as the positive results, by using the thermodynamic approach here developed. Indeed, all the theoretical models have been developed to highlight the effect of electromagnetic fields on cells. They use a RC-circuit for the analysis. Some thermodynamic models have been introduced by using local entropy production, but they have the aim to describe the behaviour of the cell in relation to its internal biochemical reactions. Consequently, they have not analysed the different behaviours between normal and cancer cells [26–38], which is currently of great interest. In summary, in literature the evidence of the successful use of the electromagnetic interaction with living cells is evident in a great number of applications on different diseases such as hypertension, myocardial infarction, varicose ulcers, fractures, bronchial asthma, etc. [39]. These results are the effect of the application of constant and variable magnetic fields on biological membranes. So, the study of the biophysical and biochemical mechanisms of the interaction between the electromagnetic field and the living systems is fundamental in order to understand the bases of the bio-systems behaviour in relation to fundamental biophysics and biochemistry, bio-systems energy, magnetodiagnostics and magnetotherapy, and biotechnology. In order to obtain information to bio-systems properties, a physical approach to understand the bio-systems behaviours during external interaction is required [39]. Indeed, in order to explain the interaction between electromagnetic waves and living cells many models (magnetite’s role in magnetoreception [40,41], free radicals effects [42,43], cell membrane behaviour [44–51], cell nuclei contribution [43,52–56], heat shock proteins [57], resonant effects [49,50,58–60], spatial summation [61,62], electromagnetic and elastic field induction [63,64], energy [61], corona ions [65]) have been proposed, but none of them has obtained a full comprehension of these phenomena [39]. In this paper, we suggest a bioengineering thermodynamic theory based on the fluxes analysis (based on constructal law) and the irreversible analysis in order to explain the interaction between electromagnetic fields and living cells. This approach allows the description of the trans-membrane ions flows and the consequent effects on the biochemical and biophysical behaviours of the cells. 2. The method suggested

coutside = cinside exp

Ze φ m d

τdrift

Φoutside − Φinside RT

(1)

(2)

where Ze is the electric charge of the ion, m is the ion mass, φ is the electric potential across the membrane, d is the length of the membrane and τdrift is the mean time between two collisions [66,67]:

τdrift =

mσ n (Ze)2

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42 43



where c is the molar concentration of the chemical species, R is the universal constant of gas, T is the temperature and Φ is the electric potential energy. The ions (H+ , Na+ , K+ , Ca2+ , Cl− , Mg2+ , etc.) cross the cell membrane with an ion drift velocity vdrift obtained by using the classical kinetic theory as [66,67]:

vdrift =

2

41

To understand how the low intensity and low frequency magnetic field interact with the cells, we consider the ions fluxes across the membrane. To do so, we consider the concentration of the ions on the opposite sides of the membrane [66,67]:



1

(3)

44

45 46 47

48

49 50

51

4

1 2

U. Lucia / Physica A xx (xxxx) xxx–xxx

where σ is the electric conductivity and n is the density number of ions. The consequence of these fluxes causes a variation of the entropy: dS = di S + de S

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it always increases, as a consequence of the second law: dS is the elementary variation of the total entropy elementary, de S is the entropy variation for interaction between the open system considered and its environment, and di S is the entropy variation due to irreversibility. The ions requires a time τ to cross the membrane and to modify their concentrations; during this time the following entropy rate occurs:

     Q = −∇ · + s˙g dV

dS 8

9 10

dt

    Q dS = 0 ⇒ −∇ · + s˙g = 0

14 15

16

(6)

T

and

  13

(5)

T

V

where Q is the heat flow, T is the temperature, V is the volume, t is the time and s˙g is the density of the entropy generation rate. The system together with its environment is an adiabatic closed system, without work, so it follows:

11

12

(4)

∇·

Q

= s˙g .

T

(7)

Consequently, the flows between the open system and its environment cause the entropy generation rate density, which, considering that: s˙g =



Jk · Xk

(8)

k 17 18

where Jk is the flow of the kth quantity involved in the process considered and Xk is the related thermodynamic force, it follows: 1

19

20 21 22 23

T

∇ ·Q=

 

25

27 28 29 30 31

32

33

34

35

36

τ

Sg =





−

Ti

i

τ



 Qi

S˙g dt = 1S −

0



˙ in sin − m



˙ out sout m

dt

(10)

out

in

˙ is the mass flow and where Q is the heat exchanged, T is the temperature of the thermal source, s is the specific entropy, m τ is the lifetime of the process. We consider that the mass flow can be related to the drift velocities; indeed, the mass flow can be written as: ˙ = ρ v A = ρ A Ncoll vdrif m

(11)

where ρ is the mass density, A is the surface area of the cell membrane, Ncoll is the number of collisions of the ion when it crosses the cell membrane, which can be evaluated as the ratio between the time τ required to cross the membrane and the time of drift τdrift : Ncoll =

τ τdrift

=

n (Ze)2

τ.

mσ

(12)

Consequently, the mass flow can be written as:

˙ = ρvA = ρ A m

Ze φ

τ

m d

(13)

so, Eq. (10) becomes: Sg = 1S −

 Qi i

37

(9)

T

in agreement with Le Chatelier’s principle [68], 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 [68]. Now, we consider the second law for the open systems:

0

26

1

Jk · Xk − Q · ∇

k

 24



= 1S −

Ti

 Qi i

Ti

τ

 − 0

−

φ d

A



ρi A

i

 i

1ρi

Zi e φ mi d Zi e mi

τi si dt

τ i si

(14)

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where i = H+ , Na+ , K+ , Ca2+ , Cl− , Mg2+ , . . . and the entropy generation has been evaluated as [66,67]: τ1

  dV −

 Sg =

o

V

τ4

 − 0

v T

v

τ2



Jq T2

· ∇ T dt −

Jj A˜ j +

v



o

τ5



T

0

j

v

 Jk · ∇

k

µ ˜k T



τ3

 dt − 0

v T

1

5 : ∇ x˙ B dt

2

 Jk · Fk

3

k

= Sg ,tf + Sg ,dc + Sg ,vg + Sg ,cr + Sg ,de

(15)

where:

5

1. Sg ,tf is the entropy generation due to the thermal flux driven by temperature difference; 2. Sg ,dc is the entropy generation due to the diffusion current driven by chemical potential gradients, with µ ˜ = µ + Zφ electrochemical potential, µ chemical potential; 3. Sg ,vg is the entropy generation due to the velocity gradient coupled with viscous stress; 4. Sg ,cr is the entropy generation due to the chemical reaction rate driven by affinity, always positive; 5. Sg ,de is the entropy generation due to the dissipation due to work by interaction with the environment; 6. Jk = ρk (˙xi − x˙ B ) is the diffusion flows and Fk are the forces, Jj is the chemical reaction rate of the jth chemical reaction and νij are quantities such that if they are divided by the molecular mass of the ith component they are proportional to the stoichiometric coefficients. Now, introducing the electro-chemical affinity A˜ = A + Z 1φ related also to pH variation and the electric field variation, with Aj = Σk νkj µj , Z the electric charge per unit mass, φ the electrostatic potential; and τi , i ∈ [1, 5], are the lifetimes of any process and:

Now, considering that the cell can be considered as an optimized system, the entropy generation becomes an extremum [69], it follows:

δ Sg = 0 ⇒

Ae  Zi d

i

mi

τi si (dρi + dφ) = dS −

 δ Qi i

Ti

.

(16)

This result highlights that any variation of the membrane potential or of the mass density of any ion causes a variation in entropy with the consequence of inducing a modification of the biological behaviour of the cell. Now, we consider the magnetic field: B = BDC + BAC exp (iωt )

(17)

where BDC is a static magnetic field and BAC is the intensity of an alternating magnetic field with frequency ω/2π and parallel to the static field. If an ion moves across a membrane when this field is applied, the interaction is described by the Lorentz equation of which the solution results [58]: ∞ Ze φ 

Jκ2



m d κ=1 1 + iω τdrift

q BAC m ω



6 7 8 9 10 11 12 13 14 15 16

1. the chemical potential gradient can be approximated through the ratio between the mean value of the chemical potential µ = 1.20 × 10−9 J kg−1 and the mean density is considered as ρ = 1000 kg m−3 ; 2. τ1 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 ≈ ρ cV /(hA) with ρ ≈ 1000 kg m−3 density, V the cell volume, A the external cell surface, c ≈ 4186 J kg−1 K−1 specific heath, and h the convection heat transfer coefficient evaluated as h ≈ 0.023Re0.8 Pr 0.35 λ/L, where λ ≈ 0.6 W m−1 K−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 2τcv < τ1 < 4τcv ; 3. τ2 is the time related to the diffusion current driven by chemical potential gradients. It can be evaluated as τ2 ≈ d/D, with d the length of the membrane, and D being the diffusion coefficient; 4. τ3 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 ≈ 2πc r , with c ∼ 1540 m s−1 the sound velocity, considered to be the same in biological tissue; 5. τ4 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−1 l−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; 6. τ5 is the time related to the dissipation due to work by interaction with the external forces. It depends on the interaction considered; 7. L is a characteristic length, introduced as usually done in transport phenomena.

vdrift =

4

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

38

39 40 41 42 43 44 45



q BDC m ω

−κ



(18)

46

6

1 2

U. Lucia / Physica A xx (xxxx) xxx–xxx

where Jκ is the Bessel function of κ order. Now, we remember that the definition of drift velocity was introduced by Eq. (2), which can be obtained by the relation (18) by the following conditions:

κ= 3

∞  κ=1

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

28 29 30 31 32 33 34 35 36 37 38 39 40 41

42

43 44 45 46 47 48 49 50 51

q BDC m 2

Jκ



ω q BAC m ω

(19)

 =1

which allows us to state that the interaction between electromagnetic waves and cell is no more than an ions resonance across the cell membrane. So, the interaction between the electromagnetic waves and the cell membrane is a resonant effect of the ions fluxes. Considering that any process presents a characteristic lifetime. The consequence is that different frequencies cause different effects (thermal flux tf, diffusion current driven by chemical potential gradients dc, velocity gradient coupled with viscous stress vg, chemical reaction rate driven by affinity cr, dissipation due to work by interaction with the environment de). As a consequence of the previous results [66,67], the low frequency electromagnetic waves generate a resonant ion flux such that it generates a variation in the entropy generation due to thermal fluxes, which causes a redistribution of energy in the cell, as theoretically hypothesized and experimentally verified [70–72]. The other frequencies cause the other phenomena. In order to evaluate the results here obtained, we highlight that, up to today, no experiments have been developed in order to verify the variation of entropy in relation to the behaviour of the cells. Consequently, now, we develop the analysis of an experiment, recently published [73], and designed to point out the effects of the low frequency electromagnetic fields on mitochondria metabolism. In this paper, the effects of ELF–EMF on cancer growth have been investigated by crystal violet assay, the modulation of mitochondrial activity was assessed by cytofluorimetric evaluation of membrane potential and by real-time quantification of mitochondrial transcription. The electromagnetic frequency used is 50 Hz. Here, we consider the same two cell lines, experimentally analysed in Ref. [73]:

• The gastric carcinoma cell line (GTL16): its volume is 1.20 × 10−15 m3 , its membrane volume is 3.46 × 10−16 m3 ; • Breast adenocarcinoma cell line (SKBR3): its volume is 2.90 × 10−14 m3 , its membrane volume is 2.88 × 10−15 m3 . From the experimental results, it has been pointed out that the long-term exposure to ELF–EMF reduces the proliferation of several cancer cell lines and the effect is associated to an increased mitochondrial activity without evident changes in ATP levels. This result can be explained as a consequence of the biochemical and biophysical effects of the thermal flux across the membrane [70]: this approach has just been verified by an in vitro experiment [72]. But, the mitochondria behaviour in Q5 relation to the consumption of ATP is related to the oxidative phosphorylation [74]: ADP + Pi + H+ → ATP

(20)

where ADP is the Adenosine-di-phosphate, P is the Phosphorus atom, H+ the Hydrogen ion and ATP Adenosine-triphosphate. This reaction involves the Hydrogen ion which can outflow from the cell across the cell membrane by the V-ATPase [70]. In relation to the mitochondria activity this reaction produces a variation in pH equal to −1.4, in the membrane electric potential equal to 0.14 V with a Gibbs potential variation equal to 21.5 kJ mol−1 . In order to obtain the phosphorylation of 1 mol of ADP it is required 3 mol of H+ [74]. Now, in order to prove our results we must consider that the mitochondria behaviour induced by the electromagnetic field produces a variation in the entropy generation due to thermal flux [70,72] (first term of Eq. (15)), but also that the behaviour of the mitochondria can occur only as a consequence of a H+ flux across the cell membrane (Eq. (14) together with the condition (16)). Consequently, we evaluate the two values of the entropy generation and we must obtain the same −1 −1 Q6 result. It follows that the entropy generation due to H+ -ATPase results 34.7 J mol K , and

• The GTL16 entropy generation due to thermal flux results 33.9 J mol−1 K−1 , with an error of 2.3%; • The SKBR3 entropy generation due to thermal flux results 34.2 J mol−1 K−1 , with an error of 1.4%. These results confirm the previous theoretical approach. 3. Conclusions Here, we provide a biochemical and bioengineering thermodynamic theory that allows the comprehension of the effects of the electromagnetic waves on the energy, mass and ionic flows across cell membranes and, consequently, the related cell behaviour. Living cells are separated from their environment by the lipid bilayer membrane, which presents a different concentration of specific ion species on both sides, maintained across the cell membrane by the electro-diffusion of ions down their electrochemical gradient. These ions move into an inside cell negative membrane potential (−70 to −100 mV). The cell function is regulated by the membrane proteins, sensitive to electric field, so, any change in the electric field is transduced into a conformational change that accomplishes the function of the membrane protein with consequences for the regulation of cell functions. This is why the interaction between electromagnetic waves and the membrane flows is interesting,

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with particular interest for possible future therapeutic support to some actual therapies for a great number of diseases, cancer included. The charged species, their arrangements, the local field strength, charges, spin and dipoles disposition and movements can vary with the result of changing the electric field which is transduced into a conformational change related to the protein functions themselves. Consequently, considering the role of the electrostatic potential in regulating normal migration, differentiation, and proliferation, its control is fundamental for the development of cancer as well. This result can be obtained simply by the control of the ion fluxes. Indeed, the voltage-responsive transduction mechanisms on the cell membrane allow bioelectric signals to regulate cell polarity. Cells can be modelled as an adaptive thermal and chemical engines which convert energy in one form to another by coupling metabolic and chemical reactions with transport processes, by consuming irreversibly free energy for thermal and chemical processes, transport of matter, energy and ions. So, life results an organizational thermodynamic process that tends towards the maximum conversion of available energy. To do so, the cell must exchange energy and matter through its membrane. The bioengineering thermodynamic approach here developed is based on the following considerations:

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1. The energy lost by a system is gained by the environment, consequently, the information lost by the system is gained by the environment: here the problem is to codify this information; 2. The environment is completely accessible by any observer, so it is easy to collect data on the lost energy of any system; 3. The flows cause entropy generation variations, consequently we can evaluate the entropy generation to obtain information to the flows, even when we are unable to evaluate the flows themselves; 4. The entropy generation is a global quantity, so we can obtain global information on the cells, but, in relation to life, just the global cells behaviour represents the useful information.

15 16 17 18 19 20 21

Biological systems are very interesting because they are able to adapt to the variation of environmental conditions; indeed, cells attain their ‘‘optimal’’ performance by a selection process driven by their environmental interactions. The resultant effect is a redistribution of energy, ions and mass flows in their metabolic network, by using regulatory proteins. As a consequence of these considerations, the bioengineering thermodynamics analysis can be developed just by using the fluxes analysis, and the irreversible and non equilibrium thermodynamics. The result allows us to highlight how the different ions have different effects on the behaviour of the cell. Moreover, the electromagnetic wave interaction with the cell results is frequency dependent because it is a resonant effect. Indeed, it was highlighted that transepithelial electric fields regulate cell migration, orientation and growth [75,76]. Recently, bio-electricity has been related to the regulation of individual cell function, embryogenesis and regenerative repair of complex structures [77–79] in non-neural cells and cancer. Moreover, in human mesenchymal stem cells [80], cardiomyocytes [81], vascular muscle [82], embryonic stem cells [83], myoblasts [84], the control of precursor differentiation [85] in the developing nervous system and heart, etc., it was shown that differentiation and proliferation are controlled by changes in the membrane’s electrostatic potential. Consequently, the thermodynamic approach to ion flux regulation could represent a new and interesting topic of investigation in order to obtain new bio-medical approaches [86]. Authors’ contributions U.L. has developed the bioengineering thermodynamics theory and the application to the bio-systems. He wrote the whole paper.

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