Substantia. An International Journal of the History of Chemistry 6(1): 25-36, 2022 Firenze University Press www.fupress.com/substantia ISSN 2532-3997 (online) | DOI: 10.36253/Substantia-1451 Citation: Henry M., Radman M., Ben- ichou L., Alfarouk K.O., Schwartz L. (2022) Singlet Dioxygen 1O2, its Generation, Physico-chemical Properties and its Possible Hormetic Behavior in Cancer Therapy. Substantia 6(1): 25-36. doi: 10.36253/Substantia-1451 Received: Nov 08, 2021 Revised: Jan 22, 2022 Just Accepted Online: Jan 22, 2022 Published: Mar 07, 2022 Copyright: © 2022 Henry M., Rad- man M., Benichou L., Alfarouk K.O., Schwartz L. This is an open access, peer-reviewed article published by Firenze University Press (http://www. fupress.com/substantia) and distributed under the terms of the Creative Com- mons Attribution License, which per- mits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All rel- evant data are within the paper and its Supporting Information files. Competing Interests: The Author(s) declare(s) no conflict of interest. Research Articles Singlet Dioxygen 1O2, its Generation, Physico- chemical Properties and its Possible Hormetic Behavior in Cancer Therapy Marc Henry1,  Miro Radman2, Luc Benichou3, Khalid O. Alfarouk4, Laurent Schwartz5,* 1 Institut Le Bel, Université de Strasbourg/CNRS, UMR 7140, 4 rue Blaise Pascal, 67070 Strasbourg 2 Mediterranean Institute for Life Sciences (MedILS), Split, Croatia 3 Paris-Est Créteil University (UPEC) School of Medicine. Créteil, France 4 Zamzam University College, Khartoum, Sudan 5 Assistance Publique des Hôpitaux de Paris, Paris France *Corresponding author. Email: dr.laurentschwartz@gmail.com Abstract. Singlet dioxygen 1O2 is one excited state among the three other possible spectroscopic states of molecular oxygen. Here, we first describe the use of published spectroscopic data and thermodynamic modeling based on irreversible entropy pro- duction. Such concepts are further applied to the synthesis of singlet dioxygen and its reactions with crucial biological molecules. In a last section, we suggest that sin- glet dioxygen and ozone may be responsible for the success of radiation therapy, that has been used to treat cancer successfully for over 120 years. Its precise mechanism of action remains controversial. We thus aim to clarify the role of singlet oxygen in radiotherapy and chemotherapy. A partial conversion of ionizing radiation in the body into thermal photons could be assumed. The antitumor effect may involve these thermal photons, such as the one delivered by red/infrared sources. Thermal photons (wavelengths of 635 nm and 1270 nm) convert triplet dioxygen into singlet dioxygen by changing the spin of its outer electrons. Despite its short half-life, Singlet dioxygen is responsible for the activation of multiple free radicals (such as hydrogen peroxide), which may target proteins and DNA, induce either apoptosis or oxidative phospho- rylation. At moderate concentrations, thermodynamic data suggests that singlet diox- ygen may readily react with water to form a potent pro-apoptotic molecule (ozone), thus decreasing cancer growth. However, at high concentration cytotoxic effects against all kind of cells occurs. This strongly suggests a non-linear hormetic behavior of singlet dioxygen. It is also proposed that cytotoxic chemotherapy induces the same free radicals that singlet dioxygen does. There are also other ways to enhance the pro- duction of singlet dioxygen, such as phototherapy using Methylene Blue for instance. As a source of reactive oxygen species (ROS), singlet oxygen could thus be a common agent active both in radiotherapy and chemotherapy. It is probable that the activity of radiation therapy and chemotherapy may be mediated by the conversion of triplet to singlet oxygen. This may explain the oxygen effect such as described in radiotherapy and chemotherapy. Keywords: cancer, phototherapy, Warburg’s effect, radiation therapy, singlet oxygen, chemotherapy, oxygen effect. http://www.fupress.com/substantia http://www.fupress.com/substantia http://www.fupress.com/substantia 26 Marc Henry et al. INTRODUCTION Less than two months after the discovery of X-rays by Wilhelm Röntgen in 1895, Leopold Freund treated, successfully, a child with a large nevus, a benign skin lesion[1]. In the following months, there were multiple reports of the efficacy of radiation therapy in the treat- ment of both benign and malignant lesions. Radiation therapy (RT) is a therapy using ionizing radiation to control or kill  inflammatory and cancer cells. RT has been extensively used for the treatment of inflamma- tion, but this indication is slowly disappearing because of the risk of radiation-induced malignancies[2]. RT may be curative in several types of cancer if they are local- ized to one limited area of the body. Several shaped radiation beams coming from several angles of exposure intersect at the tumor to spare normal tissues (such as skin or organs that radiation must pass through to treat the tumor). This provides a much higher absorbed dose there than in the surrounding healthy tissue. RT kills normal cells, and every radiation oncologist knows the dose not to trespass to the normal tissues. Ionizing radiation has been published to target the DNA  leading to cell death. In the laboratory setting, the damage caused by ionizing radiation to the DNA is immediate and consists of single or double-strand breaks and mutations[3]. A correlation exists between the toxicity of RT to the normal cells and the damage to the DNA[4]. Unlike the laboratory setting, there is no immediate sign of death for cancer cells in clinical practice. In the minutes following a cardiac infarct, there is an increased level of cardiac enzymes, such as troponin, in the blood plasma[5]. Assessment of the treatment response after RT occurs, not minutes or even days but weeks after the inception of treatment[6]. Recently, Radman demonstrated that the prime tar- get of radiation is not the DNA as previously thought but the proteasome. The cell dies because of oxidative damage to its proteins[7]. The polymerases may repair the concomitant damage to the DNA. This paper aims to suggest existence of a link between RT and production of singlet dioxygen medi- ated by thermal photons. Radiation may also affect the activity of water around proteins or DNA and change mitochondria activity. Herein, we will not try reviewing the past 50 years in mechanistic, spectroscopic, compu- tational, and biological studies of singlet oxygen. This topic is covered in great details in a recent textbook[8]. Our interest is rather to work in an historical perspective with focus on rather old concepts that will be revisited through the lens of the entropy concept[9-11]. Moreover, we are perfectly aware that singlet dioxygen reacts by two distinctive pathways (Type I and Type II mechanisms), and causes damage to biomolecules, materials such as polymers, food, paints etc. Amino acids, nucleic acids, unsaturated molecules (e.g.; membranes) also react with singlet oxygen to yield decomposed products and con- sequently to cause cell death. But, all these important properties, which rationalize the toxic and fatal behav- ior of 1O2 to organisms completely neglects the fact that many biological processes, display a biphasic or triphasic response to exposure to increasing amounts of a sub- stance or condition such as radiation. Even if this horme- sis model of dose response is still vigorously debated[12], it seems worth investigating if it could apply to the biologi- cal response of singlet dioxygen. Moreover, in the spirit of putting more physics in biological or medical think- ing, part of the article will be devoted to a reminder of the electronic structure and spectroscopic properties of these species deriving from molecular oxygen. Finally, we will focus mainly on healing cancer, even if the ideas exposed here could be extended to other diseases. THERMAL PHOTONS ARE EFFECTIVE AGAINST CANCER AND INFLAMMATION The metabolism of the cancer cells has been exten- sively studied since the seminal work of the German sci- entist Otto Warburg[13]. Warburg’s effect is, in fact, the cause of every hallmark of cancer, such as the prolifera- tion of cells, angiogenesis, or immortality[14]. Cancer is not the only disease involving Warburg’s effect, as this effect is also crucial in inflammation[15] or Alzheimer’s disease[16]. Alleviating Warburg’s effect decreases cell proliferation[14]. Non-ionizing radiation has been developed success- fully in the treatment of both benign and malignant tumors. Delivery of hyperthermia is possible using non- ionizing radiation such as ultrasound, microwave, or most commonly infrared (thermal) photons. Red and infra-red photons have also been used in the treatment of inflammation. It is a well-accepted fact that a practice does not need total mechanism clarity to operate. More than 6500 publications registered on PubMed from LLLT keyword (Low-Level Light Therapies) covering cancer[17] wound healing[18], inf lammation and pain management[19], muscles and joints injuries[20] as well as nerve regenera- tion[21], traumatic brain injuries[22], depression and anxi- ety[23] and more recently neurodegenerative such as Alz- heimer and Parkinson diseases[24] as well as Age-Related Macular Degeneration[25]. 27Singlet dioxygen 1O2, its generation, physico-chemical properties and its possible hormetic behavior in cancer therapy THE THREE FORMS OF MOLECULAR DIOXYGEN Dioxygen is a very peculiar molecule whose chemi- cal behavior cannot be explained using conventional octet’s rule[26]. Such rule generally applies to any mol- ecule built from atoms belonging to the second period of the periodic table of the elements. Let N be the total number of atoms, E, the total number of valence elec- trons, Q the number of atoms other than hydrogen, and C, the number of cycles. It then mathematically follows that the number of single bonds should be S = N + C – 1, the number of lone pairs should be L = E – 3×Q – N, and the number of multiple bonds should be M = 3×Q – E/2 – C + 1 – E%2[27]. Here E%2 = 0 or 1 if E is respec- tively even or odd. For dioxygen O2 characterized by E = 6 + 6 = 12, N = Q = 1 + 1 = 2, C = 0, the rule predicts that S = 2 + 0 – 1 = 1 (one single bond), L = 12 – 3×2 – 2 = 4 (four lone pairs) and M = 3×2 – 12/2 – 0 + 1 = 1 (one double bond). This corresponds to the classical notation :O:=:O: found in every elementary chemistry textbook. The trouble is that such a formula is utterly wrong as it predicts that dioxygen, having an even num- ber of electrons, should be a diamagnetic molecule in its ground state. Experiments, on the other hand, show that dioxygen is rather a paramagnetic molecule in its ground state, diamagnetic states corresponding to excit- ed states. Such a deep mystery could be resolved by writing Lewis’s structures after the removal of two electrons (O22⊕ ion with E = 10) or the addition of two electrons (O22⊝ ion with E = 14)[28]. For the dication, Langmuir’s rules predicts that the number of single bonds does not change (S = 1), but that L = 10 – 3×2 – 2 = 2 (two lone pairs) and M = 3×2 – 10/2 – 0 + 1 = 2 (one triple bond). This corresponds to the classical notation, ⊕:O≡O:⊕, meaning that the two electrons in the highest occupied energy level are of anti-bonding character, as removing them leads to the apparition of an additional chemical bond. Concerning, the dianion, the same rules predicts that L = 14 – 3×2 – 2 = 6 (six lone pairs) and M = 3×2 – 14/2 – 0 + 1 = 0 (no multiple bond, i.e. ⊝:Ö:–:Ö:⊝). This means that the lowest unoccupied energy level is also of anti-bonding character, as adding 2 electrons there leads to the transformation of the double bond into two lone-pairs and a single bond. So, using just the well- established octet’s rule, it could be anticipated that the states of the highest energy (occupied and unoccupied) in dioxygen are of similar nature (anti-bonding charac- ter). This strongly suggests that these two states have the same energy (degeneracy) with a single unpaired elec- tron in each state, •:O: —:O:•. This explains the observed paramagnetism of dioxygen in its ground state. Further development of quantum mechanics and group theory has confirmed the validity of such a pic- ture. Accordingly, owing to its high symmetry (D∞h cylindrical symmetry), molecular orbital (MO) theory predicts that dioxygen has a doubly degenerated HOMO (highest occupied molecular orbital) or LUMO (lowest unoccupied molecular orbital). In other words, writing structures obeying the octet’s rule is an easy graphical way to get good solutions for Schrödinger’s equation. From MO-theory, we also learn that, owing to the phenomenon of resonance, obeying octet’s rule can be of a dynamic nature. Thus, starting from the static solution (S = 1, L = 4, M = 2), we get the dynamic solution (S = 1, L = 5, M = 1), after transformation of the double bond into a delocalized lone pair: :Ö:⊝—:O:⊕ ↔ ⊕:O: —:Ö:⊝ Here, violation of the octet’s rule occurs at a given time. However, after averaging in time, there is no pos- sibility of distinguishing between the two oxygen atoms owing to the D∞h cylindrical symmetry. This restores octet’s rule, but in a dynamic sense. Consequently, for a good understanding of dioxygen chemistry, it appears necessary to consider three main forms for this molecule: One apolar resonant paramagnetic bi-radical (triplet dioxygen): 3O2 (3Σg-): •a:O: —:O:•b ↔ •b:O: —:O:•a One polar resonant diamagnetic molecule (singlet dioxygen) 1O2 (1∆g): :Ö:⊝—:O:⊕ ↔ ⊕:O: —:Ö:⊝ One apolar static diamagnetic molecule (singlet dioxygen) 1O2 (1Σg+): :O:=:O: The Greek symbols in brackets are the rigorous notation using labels derived from the symbols of the irreducible representations of D∞h point group sym- metry. Without such a notation, it would be impossible to distinguish between the two different forms of sin- glet dioxygen 1O2. This is a crucial point, as these three forms do not have the same energy. Solving Schrödinger’s equation thus shows that the ground state is 3O2 (3Σg-) followed by the first excited state 1O2 (1∆g) located at an energy ∆E = 153 zJ (1 zJ = 10-21 J) above the ground state. To reach this state, the dioxy- 28 Marc Henry et al. gen molecule should absorb a photon of wavelength λ = h·c/∆E, where h is Planck’s constant and c the celerity of light in the vacuum. With h·c = 198 645 nm·zJ, the 1O2 (1∆g) state could be reached with a photon of wavelength λ = 198 645/153 = 1298 nm (infrared light). Reaching the second state 1O2 (1Σg+), located at an energy ∆E = 259 zJ above the ground state, will involve a photon of wave- length λ = 198 645/259 = 767 nm (red light). It is then quite unfortunate that most biology text- books treat dioxygen as a single species, generally writ- ten as :O:=:O: or O2 in short, which is not the ground state formulation. The fact that the spin state (upper left digit before the chemical symbol) is usually not even mentioned is also quite unfortunate. Accordingly, it is worth recalling that spin conservation is one of the most fundamental laws of physics expressed by Witmer-Wign- er for chemical transformation[29]. These rules state that if SA is the spin of reactant A and SB the spin of reactant B, a reaction will be spin-allowed if the total spin of the products is included in the series: |SA + SB|, |SA + SB - 1|, |SA + SB - 2|,…, |SA - SB|. Let us consider, for instance, one of the most exo- thermic reactions known in chemistry: 2 1H2 (g) + 3O2 (g) → 2 1H2O (l) ∆rG° = -2×237 = -474 kJ·mol-1 As indicated by the superscripts showing spin mul- tiplicities, such a direct reaction is spin-forbidden, as we have S(1H2) = ½(1 – 1) = 0 and S(3O2) = ½(3 – 1) = 1. It then follows that the total spin of the reactants is S = 2×0 + 1 = 1. For the products, we have S(1H2O) = ½(1 – 1) = 0, meaning that the total spin of the reactants is S = 2×0 = 0. There is thus a violation of spin conservation in water synthesis from dihydrogen and dioxygen taken in their ground state. This is the reason why nothing happens upon mixing a powerful reductant (H2) with a powerful oxidant (O2). However, it is a well-known fact that the reaction is immediate and explosive after the introduction of sparkle in the mixture. The role of spar- kle is to bring enough energy to transform triplet oxygen 3O2 (3Σg-) into singlet oxygen 1O2 (1∆g). The reaction then becoming: 2 1H2 (g) + 1O2 (g) → 2 1H2O (l) ∆rG° = -2×237 - 95 = -569 kJ·mol-1 As now ∆S = 0, the reaction can proceed eas- ily without any catalyst. It is worth recalling here that water synthesis is at the heart of complex-IV (CcO). This complex of the electron transport chain (ETC) in mitochondria has a catalytic site allowing direct reduc- tion of triplet dioxygen into the water using separated fluxes of protons and electrons. The separation of pro- tons from electrons is thus mandatory, as upon mixing them together, we would obtain singlet dihydrogen that is unable to react with triplet dioxygen to form water. This means that quantum chemistry should be at the heart of biological thinking. The fact that it does not have deleterious consequences, particularly for medicine, as prevention of water synthesis from triplet dioxygen in mitochondria leads to Warburg’s effect, a common source for many kinds of diseases[14]. SPECTROSCOPIC PROPERTIES OF SINGLET DIOXYGEN As explained above, thermal photons may inter- act with triplet dioxygen (3O2) to form singlet dioxygen (1O2). Switch from triplet to singlet state necessitates energy. The most common way to switch to the singlet form is irradiation by visible photon (red at 635 nm), allowing reaching the 1O2 (1Σg+) state or infrared ones at 1270 nm, leading to the 1O2 (1∆g) state. The average life- time of singlet oxygen is 1-50 µs in aqueous systems[30]. In the gas phase, both singlet states may relax towards the triplet state 3O2 (3Σg-) by two different mechanisms. The 1O2 (1∆g) state may use collisions with other mole- cules M according to: 1O2(1∆g) + n M → 3O2 (3Σg-) + n M* + heat The notation M* means that, after the collision, the molecules M are left in a rotating state of higher energy. The intrinsic electronic spin has thus been transformed into an extrinsic spin (rotations), ensuring spin-conser- vation. The generated heat corresponds to the energy difference ∆E = 153 zJ existing between the first excited state and the ground state. The following relationship allows estimating the expected temperature increase ∆T after dissipation of an energy ∆W into heat: Here, we have used the equipartition theorem of sta- tistical physics ∆W = ½kB×∆T×Σ(df ), where kB is Boltz- mann’s constant and Σ(df ), the total number of degrees of freedom concerned by the relaxation process. Now, for a non-linear molecule made of n atoms, one may expect three degrees for the translation of the center of mass, three degrees for the rotation around the center of mass, and 2×(3n – 6) degrees for the normal modes of 29Singlet dioxygen 1O2, its generation, physico-chemical properties and its possible hormetic behavior in cancer therapy vibration. Factor 2 considers that each vibration mode has two degrees, one associated with the position and the second one to speed. Each non-linear molecule will then contribute 6×½kB + (3n-6)×(½kB + ½kB) = ½kB×(6n - 6). For a linear molecule, the rotation around the molecular axis cannot be used to store energy and thus corresponds to a vibration mode. Each linear molecule will then contribute to ½kB×(6n -5). It then follows that if nL stands for the number of linear molecules and nC for the number of non-linear ones and if N is the total number of atoms, we have Σ(df) = 6×(N – nC) – 5×nL. Water being the most abundant molecule in a cell, we have N = 3×nW, nL = 0 and nC = nW, leading to ∆T(K) = 12×∆W(zJ)/nW. Consequently, in order reaching a tem- perature T = 310 K (or 37°C) from a temperature T = 288 K (or 15°C, the average temperature of the earth), the total number of concerned water molecules involved in the relaxation of one 1O2(1∆g) molecule characterized by ∆W = 153 zJ is estimated as nW = 1849/(310 – 288) = 84 molecules. Furthermore, the average volume v of a molecule having a molecular weight M (Da) in a liquid of density ρ (g·cm-3), assuming a random packing effi- ciency ξ = 0.6366, is given by: For water (M = 18 Da, ρ ≈ 1 g·cm-3, i.e. v = 19 Å3), the thermal relaxation volume around one 1O2(1∆g) molecule is about 19×84 = 1598 Å3, corresponding to a sphere of radius R = 7.3 Å. As the average diameter of isolated water is a molecule is D = (19×6/π)⅓ ≈ 3.3 Å, this corresponds to 2 shells of water molecules. This shows how we may relate a biological number, the aver- age body temperature, to a molecular quantum process relaxation of 1O2(1∆g) towards the 3O2 (3Σg-) ground state through heating, using well-known physical laws. Besides this thermal relaxation process involving water molecules, there is a radiative mechanism involv- ing infrared photons: 1O2(1∆g) → 3O2 (3Σg-) + 3γIR Here, nature uses the fact that a photon is a parti- cle of spin S = 1, allowing photonic relaxation with the emission of a photon spinning in one direction (mS = +1), leaving the dioxygen molecule in its ground state with the two electrons spinning in the same direction opposite to that of the photon (mS = –1/2 – ½ = –1) to conserve the initial null spin (0 = 1 – 1). Heisenberg’s uncertainty relationship drives the timescale associat- ed with such photonic relaxation. It allows relating the intrinsic lifetime τ of the excited state having energy ∆E to the reduced Planck’s constant ħ ≈ 106 zJ·fs: ∆E×τ ≈ ħ. Consequently, with ∆E = 153 zJ, it comes that τ ≈ 106/153 = 0.7 fs. This lifetime should be compared with the average rotation time τc of a water molecule at a giv- en temperature, needed for allowing thermal non-radi- ative relaxation. Stokes-Einstein relationship gives this correlation time that depends on absolute temperature T, viscosity η and molecular volume v: τc = η×v/(kB×T), i.e. τc(ps) = 72.4×η(mPa·s)×v(Å3)/T(K)[31]. For liquid water (v = 19 Å3) at T = 310 K, we have η = 0.69 mPa·s, meaning that τc ≈ 3 ps. This shows that for one molecule under- going thermal relaxation from the excited state to the ground state, about 5,000 molecules undergo photonic relaxation in the near-IR part of the electromagnetic spectrum. As the second excited state 1O2 (1Σg+) is much higher in energy (∆E = 259 zJ), its thermal relaxation towards the ground state will mobilize a much more number of water molecules, typically nW = 3128/(310 – 288) = 142 molecules. This forms a relaxation volume of 2,702 Å3, corresponding to a sphere of radius R = 8.6 Å, i.e., near- ly 3 shells of water molecules around one 1O2 (1Σg+) mol- ecule. The average lifetime of this second excited state being shorter, τ ≈ 106/259 = 0.4 fs, about 7,300 mol- ecules undergo photonic relaxation as a characteristic, red-colored visible light when one relaxes using the ther- mal channel. FORMATION OF SINGLET DIOXYGEN Singlet dioxygen cannot be formed by direct optical excitation of triplet dioxygen by infrared or red photons. Accordingly, from Fermi’s Golden rule and group the- ory, such transitions are both spin-forbidden and orbit- al-forbidden. This is the reason why a photosensitizer should be used[30]. Another completely different way of forming singlet dioxygen is to use a chemical reaction releasing a large amount of entropy. Reasons for using entropy and not Gibbs’ free energies have been analyzed elsewhere[9-11]. Shortly, a single criterion of spontane- ous evolution in nature is that entropy of the universe should always increase in any kind of transformation, whether chemical or biological. In other words, biologi- cal systems are fully compliant with the second law of thermodynamics with no need to introduce alternate notions such as negentropy, for instance. The observed complexity of biological systems is a consequence of large entropy f lux towards the universe, in compli- ance with the laws of irreversible, far from equilibrium, thermodynamics. From a technical viewpoint to each 30 Marc Henry et al. transformation of matter corresponds to a change in the standard irreversibility potential ∆πi° (T = 25°C, p = 1 atm) that cannot be negative. Rules for computing an irreversibility potential πi° for each substance involved in the transformation have been presented elsewhere[10]. For biological systems, such standard irreversibility potentials are transformed to π’i° values considering that biology occurs in water (pH = 7) in the presence of ionic species (ionic strength I ≈ 250 mM). We have used gen- eralized Legendre’s transformation, a mathematically straightforward procedure[32]. All the computational details are available as supplementary information (SI). Irreversibility potentials (IrPs) are useful for com- paring two substances according to their entropy con- tent relative to the whole universe. Basically, substances that have strongly negative IrPs are reducing substances. They present a spontaneous tendency to be irreversibly transformed through oxidation into substances having a strongly positive IrP. One may thus notice that singlet dioxygen has a significantly more negative IrP than tri- plet dioxygen. This automatically means that combus- tion with 1O2 leads to larger entropy production than combustion with 3O2. Moreover, the burning of a com- bustible substance existing in a singlet spin-state with 1O2 is spin-allowed, whereas its combustion with 3O2 is spin-forbidden, needing the presence of a catalyst. In biology, singlet dioxygen plays a key role in pho- tosynthesis. Generation of 1O2 from water molecule has been widely reported during photosynthesis in plants, using energy from the sunlight. Photosensitizers are generally necessary for producing singlet through light absorption. This is particularly true in plants where 1O2 is generated by chlorophyll and other cofactors of the photosystem[33]. In plants exposed to excess light, the increased pro- duction of singlet dioxygen can result in cell death[34]. Various substances such as quinones, carotenoids, and tocopherols contained in chloroplasts quench singlet dioxygen and protect against its toxic effects. In humans, transportation of the dioxygen mol- ecule to the target cell occurs through the triplet state. It is used in the mitochondria together with electrons and protons at the level of the complex IV of the mito- chondria, producing water as a non-toxic waste togeth- er with some heat and biomolecules with very negative IrPs such as NADH (πi’° = -6.23829 zJ·K-1) or NADPH (πi’° = -1.32422 zJ·K-1) for instance. It is worth noticing the large difference in irreversibility potentials between NADH and NADPH. However, when considering oxi- dized forms NAD⊕ (πi’° = -5.89863 zJ·K-1) and NADP⊕ (πi’° = -0.98399 zJ·K-1), we get almost the same standard oxidation potential: NAD⊕ + H⊕ + 2 e⊝ = NADH ⟹ ∆πi’° = -0.34534 zJ·K-1 ⟺ E’° = -321 mV NADP⊕ + H⊕ + 2 e⊝ = NADPH ⟹ ∆πi’° = -0.34534 zJ·K- 1 ⟺ E’° = -321 mV Therefore, IrPs are much more useful for biological thinking than oxidation potentials. Accordingly, NADH appears in catabolism for glycolysis, for β-oxidation, by pyruvate dehydrogenase (PDH), by tricarboxylic acid cycle (TCA), in the electron transport chain (ETC), and by nicotinamide nucleotide transhydrogenase (NNT) (35). This simply stems from its negative IrP much lower than any of the non-metallic species. Accordingly, biosynthe- sis of NADH needs absorption of a large positive entropy flux, such as the one generated at the level of the TCA or the ETC. In deep contrast, NADPH is used in anabo- lism for performing reductive biosynthesis, in the pentose phosphate pathway (PPP), by isocitrate dehydrogenase (IDP), by the malic enzyme (ME), by aldehyde dehydro- genase (ALDH), and by NADPH-oxidase (36). Owing to its much lower IrP, biosynthesis of NADPH needs a much smaller positive entropy flux than the one required for NADH. It follows that NADPH is more able to drive biosynthetic pathways and is also involved in redox sens- ing and as a substrate of NADPH oxidases for generating reactive oxygen species. So, we have here a good example of two remarkably similar reductants having quite con- trasted entropy content, explaining the observed strong compartmentalization of redox functions in a living cell. It is also worth noticing that at the mitochondrion level, there is the orientation of the positive entropy flux towards the synthesis of biomolecules displaying large positive IrPs. Such molecules play the role of “canned entropy” for driving molecular machines, just like bat- teries act as “canned electricity” for driving electrical motors. The best candidates are polyphosphates such as adenosine diphosphate (ADP with πi’° = +7.93486 zJ·K- 1) or adenosine triphosphate (ATP with πi’° = +12.76803 zJ·K-1). Accordingly, the positive entropy flux for making ATP from ADP appears too small relative to their entro- py content: ADP + Pi = ATP + H2O ⟹ ∆πi’° = -0.2007 zJ·K-1 ⟺ pK = 6.3 At a temperature T = 298.15 K, such a pK-value cor- responds to a free energy change ∆G’ = +36.0 kJ·mol-1 = 60 zJ. Conversely, this is just the amount of heat that would be generated upon the hydrolysis of ATP into ADP. Here, it is worth using our relationship ∆T(K) ≈ 12×W(zJ)/nW allowing converting an amount of heat W into a temperature change ∆T after spreading such heat 31Singlet dioxygen 1O2, its generation, physico-chemical properties and its possible hormetic behavior in cancer therapy among nW water molecules. Choosing ∆T = 1 K for W = 60 zJ leads to nW = 720 or RW = 1.66×nW⅓ = 14.9 Å, in terms of radius of the hydration shell surrounding the spatial location of the reaction. Now, on average, four shells of water molecules surround each biomolecule in a living cell[37]. This translates into a radius of hydration Rh = 4×3.3 = 13.2 Å, a value close to the radius of con- version of entropy into heat RW. As explained in previ- ous papers (9,10), the main role of ATP in a living cell is not to provide energy but rather to play the role of a powerful hydrotrope[35]. ATP has thus the crucial dou- ble role of being both an entropy sink and avoids by its presence the irreversible coagulation of proteins. There is obviously not enough entropy liberated through hydrolysis of a single ATP molecule to convert triplet dioxygen into singlet dioxygen. From the relative IrPs of 1O2 and 3O2 and with ∆πi’° = 0.2007 zJ·K-1 for ATP hydrolysis, the formation of singlet dioxygen from tri- plet dioxygen would require the simultaneous hydrolysis of at least n(ATP) = sup(0.53256/0.2007) = 3 molecules. As this is very unlikely on the statistical ground or as it would involve a huge protein, it may seem that singlet dioxygen would have a negligible role to play in a living cell favoring triplet dioxygen. This is, of course, the con- ventional biological thinking putting the exclusive focus on the ground state 3O2 (3Σg-) with very few references to the first excited state 1O2(1∆g). Owing to its quite negative IrP, very few substances can create singlet dioxygen as a waste. Among them, we have, for instance, ozone 1O3. It is easy checking that water has entropy high enough to resist oxidation into hydrogen peroxide by ozone: 1O3 + 1H2O = 1O2 + 1H2O2 ∆πi’° = -0.22868 zJ·K-1 ⟺ pK = 7.2 This is not the case of hydrogen peroxide that is eas- ily reduced into the water by ozone with singlet dioxy- gen as a by-product: 1O3 + 1H2O2 = 2 1O2 + 1H2O ∆πi’° = +0.29663 zJ·K-1 ⟺ pK = -9.3 Suppose the reaction leading to triplet dioxygen is much more favorable, it is, however, spin-forbidden, allowing singlet dioxygen to be the main kinetic product in the absence of a catalyst. The trouble is that if ozone is an important compound in the atmosphere owing to its irradiation by the sun, its occurrence in a living cell is not so obvious. Singlet dioxygen may also be produced in a living cell subjected to an oxidative stress upon annihilation of oxygen-based radicals: 2O2•⊝ + 2OH• = 1O2 + 1OH⊝ ∆πi’° = +0.80038 zJ·K-1 ⟺ pK = -25 2HO2• + 2HO2• = 1O2 + 1H2O2 ∆πi’° = +0.03602 zJ·K-1 ⟺ pK = -1.1 However, such reactions are in competition with formation of triplet dioxygen and a much larger entropy release: 2O2•⊝ + 2OH• = 3O2 + 1OH⊝ ∆πi’° = +1.33282 zJ·K-1 ⟺ pK = -42 2HO2• + 2HO2• = 3O2 + 1H2O2 ∆πi’° = 0.56846 zJ·K-1 ⟺ pK = -18 Catalysis of this last reaction in vivo involves the well-studied enzyme superoxide dismutase (SOD) that is not affected by the presence of singlet oxygen[35]. As triplet dioxygen has higher irreversibility poten- tial than singlet dioxygen, it will always play the role of the thermodynamically favored species. This means that the production of singlet dioxygen using the annihila- tion of inorganic radicals is, as a rule, quite difficult to control. This is no more the case by using singlet species, as even if the formation of triplet dioxygen is still more favorable, it becomes slow as the reaction is now spin- forbidden. Here is a good example that readily occurs in neutrophils, for instance: 1ClO⊝ + 1ClO⊝ = 1O2 + 2 1Cl⊝ ∆πi’° = +0.39840 zJ·K-1 ⟺ pK = -12.5 However, such a reaction requires a high concen- tration of the rather unstable hypochlorous ion. This is the reason for the extensive use of phagosomes by neu- trophils. Under diluted conditions, there is the possibil- ity of using hydrogen peroxide, forming as by-products water and chloride ions: 1H2O2 + 1ClO⊝ = 1O2 + 1Cl⊝ + 1H2O ∆πi’° = +0.46186 zJ·K-1 ⟺ pK = -14.5 It is worth noting that use of the hypochlorous ion is mandatory, as the entropy difference between the chlorous and hypochlorous species is not high enough for allowing the production of singlet dioxygen: 1H2O2 + 1ClO3⊝ = 1O2 + 1ClO2⊝ + 1H2O ∆πi’° = -0.09802 zJ·K-1 ⟺ pK = 3.1 32 Marc Henry et al. TRAPPING OF SINGLET DIOXYGEN Singlet dioxygen could be very harmful to normal cells. The first reason stems from the fact that there is no spin restriction for reacting with other singlet molecules. A second reason is that it has a quite negative IrP. It is worth recalling here its Lewis’ structure: :Ö:⊝—:O:⊕ ↔ ⊕:O: —:Ö:⊝ A most prominent feature is the formal positive charge on one of the two oxygen atoms, meaning that singlet dioxygen has a high affinity for any electron-rich centers. Among them, carbon atoms engaged in a C=C double bond are sites for preferential attack owing to their complementary dynamic Lewis’ structure: >C=C< ↔ >C:⊝—C⊕< ↔ >⊕C —C:⊝< The reaction of singlet dioxygen with C=C double bonds often leads to the formation of endoperoxides (fig- ure 1). For a single C=C double bond, the resulting endop- eroxides have a quite strained four-membered ring, lead- ing to a highly unstable addition compound. This is not the case when oxidation leads to a rather stable six- membered ring, a situation encountered in any molecule containing at least two conjugated C=C double bonds. Singlet dioxygen may react rapidly with other sin- glet molecules forming species such as hydroxyl radical (•OH), hydrogen peroxide (H2O2) or superoxide radical (•O2−). These reactive oxygen species will oxidize DNA (mutation and DNA breaks), proteins and lipids. Here is a list of favorable reactions with ubiquinol (H2CoQ10), ascorbic acid (vitamin C, AscH2), reduced cytochrome-c, dihydrolipoic acid (DHLA), reduced glutathione (GSH) and free iron (II): 1O2 + 1H2CoQ10 = 1H2O2 + 1CoQ10 ∆πi’° = +0.850 zJ·K-1 ⟺ pK = -27 1O2 + 1AscH2 = 2 2HO• + 1DHA ∆πi’° = +0.680 zJ·K-1 ⟺ pK = -21 1O2 + 1AscH2 = 1H2O2 + 1DHA ∆πi’° = +1.719 zJ·K-1 ⟺ pK = -54 1O2 + cytc-1Fe2⊕ = 2O2•⊝ + cytc-2Fe3⊕ ∆πi’° = +0.326 zJ·K-1 ⟺ pK = -10 1O2 + 1DHLA = 2 2HO• + 1ALA ∆πi’° = +0.195 zJ·K-1 ⟺ pK = -6 1O2 + 2 1GSH = 2 2HO• + 1GSSG ∆πi’° = +0.173 zJ·K-1 ⟺ pK = -5 1O2 + Fe2⊕ + = 2O2•⊝ + 2Fe3⊕ ∆πi’° = +0.049 zJ·K-1 ⟺ pK = -2 It is worth noticing the mandatory generation of hydrogen peroxide with ubiquinol, as there is, in this case, not enough entropy for generating two hydroxyl radicals: 1O2 + 1H2CoQ10 = 2 2HO• + 1CoQ10 ∆πi’° = -0.190 zJ·K-1 ⟺ pK = 6 SINGLET DIOXYGEN, OZONE, AND RADIATION THERAPY The above reactions explain why singlet oxygen (1O2) is widely used in photodynamic therapy of cancer.  Dur- ing photodynamic therapy, photosensitizers excited by light react with ground state oxygen  3O2, which leads to the generation of this major cytotoxic agent. After generation, singlet dioxygen oxidizes all the molecules responsible for the redox homeostasis of the cell rapidly, killing the surrounding tissues and cells[38]. It has been more than 60 years since the discov- ery of the  oxygen effect  that empirically demonstrates the direct association between cell radiosensitivity and oxygen tension, important parameters in radiotherapy. However, no real understanding of the mechanisms underlying this principle tenet of radiobiology is yet available[39]. Figure 1. Affinity of singlet dioxygen for conjugated double bonds leading to the formation of an endoperoxide bridge. Endoperox- ides may also be formed from triplet dioxygen in the presence of a photosensitizer. One may speak of endoperoxides as “canned singlet dioxygen” owing to their ability to release 1O2 upon heating. 33Singlet dioxygen 1O2, its generation, physico-chemical properties and its possible hormetic behavior in cancer therapy Photons react with water to form free radicals, including singlet oxygen. Singlet oxygen interacts with the mitochondria to cause the permeabilization of the mitochondrial outer membrane, leading to the cytosolic release of pro-apoptotic proteins and to the impairment of the bioenergetic functions of mitochondria and result- ing apoptosis[40]. About twenty years ago, it was shown by Wentworth et al. that antibodies catalyze the generation of ozone by a water oxidation pathway[41]. It was first postulated that dihydrogen trioxide [H2O3] was a key intermediate. However the direct formation of this intermediate is not thermodynamically favorable: 1O2 + 1H2O = 1H2O3 ∆πi’° = -0.509 zJ·K-1 ⟺ pK = 16 It is worth noticing that adding another singlet dioxygen cannot oxidize water into ozone O3 according to: 2 1O2 + 1H2O = 1O3 + 1H2O2 ∆πi’° = -0.297 zJ·K-1 ⟺ pK = 9 However, upon generation of at least three singlet dioxygen molecules, water oxidation becomes possible with the release of triplet dioxygen as waste: 3 1O2 + 1H2O = 1O3 + 1H2O2 + 3O2(aq) ∆πi’° = +0.236 zJ·K-1 ⟺ pK = -7 However, such a reaction is spin-forbidden. Hence, we propose this final scheme, which is spin-allowed: 4 1O2 + 1H2O = 1O3 + 1H2O2 + 2 3O2(aq) ∆πi’° = +0.768 zJ·K-1 ⟺ pK = -24 Owing to the liberation of ozone, any tumor would be burnt with the generation of only gases as wastes. Moreover, one of the reactants is the water molecule, the most abundant chemical species in a living cell. The crucial point is that water no more acts here as a solvent whose activity is equal to one, owing to its huge abun- dance. It is a well-established fact that the status of water in tumors is quite different from that of water in a nor- mal cell. In thermodynamics language, this translates into the fact that water activity cannot be the same in a tumor and in a normal cell[42–46]. As the above equilib- rium is sensitive to water activity, one may expect dif- ferent yields of ozone according to the status of water in the cell exposed to radiations able to generate singlet dioxygen in the large amount. In other words, there is a possibility of targeting any 1O2-treatment towards cancer cells, leaving normal cells relatively unaffected. The radiation therapist knows that soft tumors like lymphomas and seminoma are more sensitive to radia- tion than harder ones. Accordingly, doses needed to eradicate seminoma and lymphoma is smaller, and the treatment is shorter than the treatment of squamous cell carcinoma or adenocarcinoma. The earlier sign of tumor response during radiation therapy is the change of con- sistency (harshness) of the tumor. This is in line with a change in the activity of water (see above). CONCLUSION It is possible that ionizing radiation such as pro- duced by modern linear accelerators act at the cellular level by the mean of thermal photons. These photons will induce, in turn, the synthesis of singlet dioxygen. In such a scheme of thought, high-energy photons are just a way to deliver thermal photons to deep-seated tumors. Infrared photons are not powerful enough to reach these lesions. Absorption of over 90% of the dose occurs in the first cm[47]. Cytotoxic chemotherapy activates the concentra- tion of free radicals such as the ones induced by singlet dioxygen or radiation therapy. This is evident by the elevation of lipid peroxidation products; the reduction in plasma levels of antioxidants such as vitamin E, vita- min C, and β-carotene; and the marked reduction of tis- sue glutathione levels that occurs during chemotherapy. Those agents that generate high levels of ROS include the anthracyclines (e.g., Doxorubicin, Epirubicin, and Daunorubicin), alkylating agents, platinum coordination complexes (e.g., Cisplatin, Carboplatin, and Oxaliplatin), epipodophyllotoxins (e.g., Etoposide and Teniposide), and the Camptothecins (e.g., Topotecan and Irinotecan) [48]. One other option to improve the efficacy of infrared photons is to activate a photosensitizer such as methyl- ene blue[49]. Moreover, an often-overlooked fact is that water activity is higher in cancer cells than in normal cells. As demonstrated just above this could mean that in a can- cer cell, singlet dioxygen may react with water yielding ozone, a powerful oxidant. Such a possibility opens the road to a non-linear hormetic behavior of singlet diox- ygen. Typically, we expect a harmful increase of oxida- tive stress at low concentration, a healing effect against cancer at moderate concentration (due to selective in- situ formation of ozone) and a well-documented cyto- toxic effect towards any kind of cell at high concentra- tion. Future experimental research is needed to confirm 34 Marc Henry et al. or reject such a putative behavior suggested by available thermodynamic data. FUNDING We acknowledge the help of the “Fondation Guérir du cancer”. REFERENCES 1. Feeund L. Elements of General Radiotherapy for Practitioners. Arch. Roentgen Ray. 1904; 9: 33–34. 2. Calabrese EJ, Calabrese V. Low dose radiation thera- py (LD-RT) is effective in the treatment of arthritis: Animal model findings. Int. J. Radiat. Biol. 2013; 89: 287–294. 3. Prise KM, Pinto M, Newman HC, et al. A review of studies of ionizing radiation-induced double-strand break clustering. In: Radiation Research.Vol 156. Radiation Research Society; 2001: 572–576. 4. Rieger KE, Hong WJ, Tusher VG, et al. Toxicity from radiation therapy associated with abnormal tran- scriptional responses to DNA damage. Proc. Natl. Acad. Sci. U. S. A. 2004; 101: 6635–6640. 5. Wu AHB, Feng YJ, Moore R, et al. Characteriza- tion of cardiac-troponin subunit release into serum after acute myocardial infarction and comparison of assays for troponin T and I. Clin. Chem. 1998; 44: 1198–1208. 6. Sahani D V., Kalva SP, Hamberg LM, et al. Assess- ing tumor perfusion and treatment response in rec- tal cancer with multisection CT: Initial observations. Radiology. 2005; 234: 785–792. 7. Radman M. Protein damage, radiation sensitivity and aging. DNA Repair (Amst). 2016; 44: 186–192. 8. Sies H. (editor), “Oxidative Stress, 1st Edition : Eus- tress and Distress”, Academic Press (2019). 9. Henry M, Schwartz L. Entropy export as the driv- ing force of evolution. Substantia. 2019; 3(2) suppl. 3: 29–56. 10. Schwartz L, Devin A, Bouillaud F, et al. Entropy as the Driving Force of Pathogenesis: an Attempt of Diseases Classification Based on the Laws of Physics. Substantia. 2020; 4(2): 7-13. 11. Henry M. Thermodynamics of Life. Substantia. 2021; 5(1): 43-71. 12. Mattson M. P., Hormesis defined, Ageing Res Rev. (2008); 7(1): 1–7. 13. Warburg O. On the origin of cancer cells. Science. 1956; 123: 309–14. 14. Schwartz L, Supuran CT, Alfarouk KO. The War- burg effect and the Hallmarks of Cancer. Anticancer. Agents Med. Chem. 2017; 17: 164–170. 15. Wen H, Ting JPY, O’Neill LAJ. A role for the NLRP3 inflammasome in metabolic diseases - Did Warburg miss inflammation? Nat. Immunol. 2012; 13: 352– 357. 16. Schwartz L, Peres S, Jolicoeur M, et al. Cancer and Alzheimer’s disease: intracellular pH scales the meta- bolic disorders. Biogerontology. 2020. 17. Hamblin MR, Nelson ST, Strahan JR. Photobiomod- ulation and Cancer: What Is the Truth? Photomed. Laser Surg. 2018; 36: 241–245. 18. Kajagar BM, Godhi AS, Pandit A, et al. Efficacy of Low Level Laser Therapy on Wound Healing in Patients with Chronic Diabetic Foot Ulcers-A Randomised Control Trial. Indian J. Surg. 2012; 74: 359–363. 19. De Oliveira Chami V, Maracci LM, Tomazoni F, et al. Rapid LLLT protocol for myofascial pain and mouth opening limitation treatment in the clinical practice: An RCT. Cranio - J. Craniomandib. Pract. 2020. 20. Silveira PCL, Scheffer DDL, Glaser V, et al. Low- level laser therapy attenuates the acute inflammatory response induced by muscle traumatic injury. Free Radic. Res. 2016; 50: 503–513. 21. Tezcan S, Ozturk FU, Uslu N, et al. Carpal tunnel syndrome: Evaluation of the effects of low-level laser therapy with ultrasound strain imaging. J. Ultrasound Med. 2019; 38: 113–122. 22. Poiani G da CR, Zaninotto AL, Carneiro AMC, et al. Photobiomodulation using low-level laser thera- py (LLLT) for patients with chronic traumatic brain injury: A randomized controlled trial study protocol. Trials. 2018; 19. 23. Schiffer F, Johnston AL, Ravichandran C, et al. Psy- chological benefits 2 and 4 weeks after a single treat- ment with near infrared light to the forehead: a pilot study of 10 patients with major depression and anxi- ety. Behav. Brain Funct. 2009; 5: 46. 24. Salehpour F, Gholipour-Khalili S, Farajdokht F, et al. Therapeutic potential of intranasal photobiomodula- tion therapy for neurological and neuropsychiatric disorders: A narrative review. Rev. Neurosci. 2020; 31: 269–286. 25. Merry GF, Munk MR, Dotson RS, et al. Photobio- modulation reduces drusen volume and improves visual acuity and contrast sensitivity in dry age-relat- ed macular degeneration. Acta Ophthalmol. 2017; 95: e270–e277. 26. Lewis GN. The atom and the molecule. J. Am. Chem. Soc. 1916; 38: 762–785. 27. Langmuir I. Types of valence. Science. 1921; 54: 59–67. 35Singlet dioxygen 1O2, its generation, physico-chemical properties and its possible hormetic behavior in cancer therapy 28. Reed J. L. The lewis structure: An expanded perspec- tive. J. Chem. Educ. 1994; 71: 98–100. 29. Allen RC. Role of oxygen in phagocyte microbicidal action. In: Environmental Health Perspectives. Vol 102. Public Health Services, US Dept of Health and Human Services; 1994: 201–208. 30. Devasagayam TPA, Kamat JP. Biological significance of singlet oxygen. In: Indian Journal of Experimental Biology. Vol 40; 2002: 680–692. 31. O’Reilly DE, Peterson EM. Rotational correlation times and coefficients of viscosity of electrolytic solu- tions. J. Phys. Chem. 1970; 74: 3280–3285. 32. Alberty RA. Thermodynamics of Biochemical Reac- tions. Hoboken, NJ, USA: John Wiley & Sons, Inc.; 2003. 33. Krieger-Liszkay A. Singlet oxygen production in pho- tosynthesis. In: Journal of Experimental Botany. Vol 56. J Exp Bot; 2005: 337–346. 34. Laloi C, Havaux M. Key players of singlet oxygen- induced cell death in plants. Front. Plant Sci. 2015;6. 35. Patel A, Malinovska L, Saha S, et al. ATP as a biologi- cal hydrotrope. Science. 2017; 356: 753–756. 36. Agledal L, Niere M, Ziegler M. The phosphate makes a difference: Cellular functions of NADP. Redox Rep. 2010; 15: 2–10. 37. Henry M., «The topological and quantum structure of zoemorphic water», in Aqua Incognita: Why Ice Floats on Water and Galileo 400 Years on, P. Lo Nostro & B. W. Ninham Eds, Connor Court Pub., Ballarat (2014), chap IX, 197-239. 38. Liang X, Wang KK, Zhu TC. Singlet oxygen dosim- etry modeling for photodynamic therapy. In: Kessel DH, Hasan T, eds. Optical Methods for Tumor Treat- ment and Detection: Mechanisms and Techniques in Photodynamic Therapy XXI. Vol 8210. SPIE; 2012: 82100T. 39. Richardson RB, Harper ME. Mitochondrial stress controls the radiosensitivity of the oxygen effect: Implications for radiotherapy. Oncotarget. 2016; 7: 21469–21483. 40. Berneburg M, Grether-Beck S, Kürten V, et al. Singlet oxygen mediates the UVA-induced generation of the photoaging- associated mitochondrial common dele- tion. J. Biol. Chem. 1999; 274: 15345–15349. 41. Wentworth Jr. P, Wentworth AD, Zhu Xueyong, Wil- son IA, Janda KD, Eschenmoser A, Lerner RA. Evi- dence for the production of trioxygen species during antibody-catalyzed chemical modification of antigens. Proc. Natl. Acad Sci. USA, 2003; 100: 1490-1493. 42. Beall PT, Hazlewood CF, Rao PN. Nuclear magnetic resonance patterns of intracellular water as a function of HeLa cell cycle. Science. 1976; 192: 904–907. 43. Beall PT, Brinkley BR, Chang DC, et al. Microtubule Complexes Correlated with Growth Relaxation Times in Human Breast Cancer Cells. Cancer Res. 1982; 42. 44. Gniadecka M, Nielsen OF, Wulf HC. Water content and structure in malignant and benign skin tumours. J. Mol. Struct. 2003; 661–662: 405–410. 45. McIntyre GI. Cell hydration as the primary factor in carcinogenesis: A unifying concept. Med. Hypotheses. 2006; 66: 518–526. 46. Davidson R, Lauritzen A, Seneff S. Biological Water Dynamics and Entropy: A Biophysical Origin of Can- cer and Other Diseases. Entropy. 2013; 15: 3822–3876. 47. Arslan H, Doluğan YB, Ay AN. Measurement of the Penetration Depth in Biological Tissue for Different Optical Powers. 2017. 48. Conklin KA. Chemotherapy-associated oxidative stress: Impact on chemotherapeutic effectiveness. Integr. Cancer Ther. 2004; 3: 294–300. 49. Tardivo JP, Del Giglio A, De Oliveira CS, et al. Meth- ylene blue in photodynamic therapy: From basic mechanisms to clinical applications. Photodiagnosis Photodyn. Ther. 2005; 2: 175–191. ANNEX Table 1 gives irreversibility potentials (IrPs or πi’°) values in ascending order for species discussed in this work. As the whole universe is by definition a closed sys- tem, this allows, in compliance with the second law, to identify three kinds of processes in nature: i) Irreversible processes that are spontaneous being such that ∆π’i° > 0. ii) Fully reversible processes are characterizing equilib- rium situations as ∆π’i° = 0. iii) Non-spontaneous processes, such that ∆π’i° < 0, thus requiring to be coupled with another spontaneous process characterized by ∆Πi’° > -∆π’i° > 0. Moreover, owing to their definition, irreversibility potentials changes may be related to equilibrium con- stants K, or to standard oxidation potentials E’°, using the following conversion relationships (T = 298.15 K): Conversion into standard oxidant potentials are for transformations involving electrons and requires the knowledge of the number of electrons n that should be added to an oxidant to transform such species into its conjugated reduced form. 36 Marc Henry et al. Let us consider for instance the two-electrons reduc- tion of protons into dihydrogen (2 H⊕ + 2 e⊝ = H2) or the four-electrons reduction of dioxygen into water (3O2 + 4 H⊕ + 4 e⊝ = 2 H2O). From table 1, we evaluate that: This allows classifying dihydrogen as a reductant (E’° < 0) and dihydrogen as an oxidant (E’° > 0). But, one may also consider reacting dihydrogen with dioxy- gen in order to produce water (2 H2 + O2 = 2 H2O). Electrons being eliminated, the irreversibility potential change is now expressed as equilibrium constant K: pK = -31.456 × [2 × (0.8667 + 0.55218) + 0.09135) = -92.1 As at T = 298.15K, we have ∆G’°(kJ·mol-1) = RT·ln(10)×pK = 5.708×pK, the highly positive ∆πi’° = 2.92943 zJ·K-1 variation responsible to the quite nega- tive pK, corresponds to a large negative change of the so-called “Gibbs’ free energy,” viz. ∆G’° = -526 kJ·mol-1. With such a pK value, one may conclude that water syn- thesis is a spontaneous quasi-quantitative process. The reason for such a huge release of entropy is obvious after noticing that on the right of the equation, a substance with a large positive irreversibility potential appears, whereas, on the left, two substances with negative irre- versibility potentials disappear. Leading the left column, we find species with large negative potentials (reductants), thus providing the larg- est entropy production upon their transformation into species located on the right column (oxidized forms). Consequently, such species are to be considered as use- ful low entropy “food.” Reciprocally, species at the bot- tom of the right column are generally end products in a chemical transformation, owing to their high entropy content. Consequently, they may be qualified as “waste” that will be eliminated in order to maintain the largest entropy gradient in the living organism. Another cru- cial point is that we find in both columns radical species holding unpaired electrons. This means that some radi- cals should be considered as food and others as waste. Moreover, some radicals may be strong reductants, such as atomic hydrogen: H⊕ + e⊝ = H•(aq) ⟹ ∆πi’° = -1.46898 zJ·K-1 ⟺ E’° = -2.31 V On the other hand, the hydroxyl radical HO• behaves as a strong oxidant: HO• + H⊕ + e⊝ = H2O ⟹ ∆πi’° = +1.24046 zJ·K-1 ⟺ E’° = +2.73 V Table 1. Irreversibility potentials πi’° and corresponding standard free energies of formation ∆fG’° for chemical species considered in this work. Values computed at T = 398.15 K, pH = 7 for an ionic strength I = 0.25 M. Species πi’0/zJ·K-1 ∆fG’°/zJ ∆fG’°/kJ·mol-1 CoQ10 -25.28740 7539 4540.36 CoQ10H2 -25.22108 7520 4528.45 DHLA -1.77480 529 318.67 H•(aq) -1.46898 438 263.75 ALA -1.45613 434 261.45 O3 -0.96965 289 174.10 1O2 -0.62378 186 112.00 H2(aq) -0.55211 165 99.13 1O2(g) -0.52665 157 94.56 H2(g) -0.45409 135 81.53 HO• -0.37352 111 67.07 H2O3 (C2-symmetry) -0.26618 79 47.79 HO2•/O2•⊝ -0.18370 55 32.98 3O2(aq) -0.09134 27 16.40 3O2(g) -0.00000 0 0.00 Cytc-[Fe3⊕] 0.04059 -12 -7.29 [ClO3]⊝ 0.04879 -15 -8.76 Fe3⊕(aq) 0.06676 -20 -11.99 Cytc-[Fe3⊕] 0.15455 -46 -27.75 HOCl/ClO⊝ 0.22429 -67 -40.27 H2O2 0.29239 -87 -52.50 Fe2⊕(aq) 0.45747 -136 -82.14 Cl⊝ 0.73538 -219 -132.04 H2O 0.86694 -258 -155.66 GSH 1.52051 -453 -273.01 AscH2 3.03142 -904 -544.29 GSSG 3.33710 -995 -599.18 DHA 3.83413 -1143 -688.42 Pi 5.90080 -1759 -1059.49 NADH 6.10589 -1820 -1096.31 NAD⊕ 6.44221 -1921 -1156.70 ADP 7.93486 -2366 -1424.71 NADPH 11.08026 -3304 -1989.46 NADP⊕ 11.40756 -3401 -2048.23 ATP 12.76803 -3807 -2292.50 Substantia An International Journal of the History of Chemistry Vol. 6, n. 1 - 2022 Firenze University Press To Print or not to Print? Preprints and publication: how the Covid-19 pandemic affected the quality of scientific production Pierandrea Lo Nostro Faraday’s Dogma Stephen T. Hyde Creativity in the Art, Literature, Music, Science, and Inventions Singlet Dioxygen 1O2, its Generation, Physico-chemical Properties and its Possible Hormetic Behavior in Cancer Therapy Marc Henry1, Miro Radman2, Luc Benichou3, Khalid O. Alfarouk4, Laurent Schwartz5,* Is the Second Law of Thermodynamics Able to Classify Drugs? Laurent Schwartz1,*, Luc Benichou2, Jules Schwartz1, Maxime Pontié3, Marc Henry4 History of Research on Phospholipid Metabolism and Applications to the Detection, Diagnosis, and Treatment of Cancer Peter F. Daly1, Jack S. Cohen2,* Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3. 1840s –1900ca. The First CE of Ions in 1861. Transference Numbers, Migration Velocity, Conductivity, Mobility Ernst Kenndler The Early History of Polyaniline II: Elucidation of Structure and Redox States† Seth C. Rasmussen Path to the Synthesis of Polyacetylene Films with Metallic Luster: In Response to Rasmussen’s Article Hideki Shirakawa Comments on Shirakawa’s Response Seth C. Rasmussen Lipids, Chloroform, and Their Intertwined Histories Carlos A. Ramírez Professor Alexander Kessenikh (1932-2021) Andrey V. Andreev1, Vadim A. Atsarkin2, Konstantin V. Ivanov1, Gennady E. Kurtik1, Pierandrea Lo Nostro3, Vasily V. Ptushenko4,5, Konstantin A. Tomilin1, Natalia V. Vdovichenko1, Vladimir P. Vizgin1