A NOTE ON THE CONSEQUENCES OF A HOT MITOCHONDRION: SOME RECENT DEVELOPMENTS AND OPEN QUESTIONS

Peyman Fahimi, Mohamed A. Nasr, Lázaro A. M. Castanedo, Youji Cheng, Cyrus A. Toussi, Chérif F. Matta* Department of Chemistry and Physics, Mount Saint Vincent University, Halifax, Nova Scotia, Canada B3M2J6 Département de chimie, Université Laval, Québec, Québec, Canada G1V 0A6 Center of Excellence for Stem Cells and Regenerative Medicine (CESC), Zewail City of Science and Technology, 6th of October City 12588, Egypt Department of Chemistry, Saint Mary's University, Halifax, Nova Scotia, Canada B3H3C3 Department of Biomedical Engineering, Hakim Sabzevari University, Sabzevar, Iran Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H4J3 * Tel.: +1-(902)-457-6142; Fax: +1-(902)-457-6134; E-mail: cherif.matta@msvu.ca Submitted November 14, 2019 Accepted January 16, 2020


PROBLEM FORMULATION
Other concerns have been raised against the used MTY by Arai et al. who suggested that MTY fluorescence signal can be affected by several parameters that include pH, oxygen species, membrane potential, viscosity, and ionic strength [4]. Moreover, MTY dye has showed different sensitivity depending on the tissue type. Another concern is the possibility of MTY dye leakage from mitochondria which may give false positive results of increased mitochondrial temperature. This leakage has been attributed to the non-covalent bonding of MTY to the mitochondrial aldehyde dehydrogenase [4]. Although it is known that MTY dye binds to mitochondrial aldehyde dehydrogenase, its precise location inside the mitochondrial matrix is not exactly known [7]. Other possible caveats have been discussed by Lane such as the possibility of MTY fluorescence quenching at high concentrations [6].
The experimental design by Chrétien et al. has tackled most of the previously mentioned concerns showing, for example, that the decrease in fluorescence was specific to the increased mitochondrial temperature [5]. Other conceptual and theoretical concerns can be raised not against the increase in the mitochondria temperature but against the extent of this increase. Baffou et al. have previously shown that that the maximal temperature increase by endogenous thermogenesis in cells cannot exceed 10 -5 K for the entire cell and 10 -4 K for mitochondria, later known as the 10 5 gap, as a critique for reported temperature elevations measured by thermosensitive probes [8]. However, other authors have criticized some points that were overlooked by Baffou et al. and which may make the 10 5 gap unnecessarily true under realistic biological conditions and approximations [9,10].
Lane applied the 10 5 gap criticism of endogenous thermogenesis to the 10°C increase in mitochondrial temperature, doubting the correctness of the 10 5 gap calculations and at the same time doubting the 10°C increase value [6]. Finally, a conceptual problem was raised by Lane about what the meaning of temperature measurement in mitochondria if a steep temperature gradient (10°C) exists since -by definition -temperature is the average kinetic energy [6].
Much more dramatically, and based on an order of magnitude estimation of the power consumption of a growing bacterial cell and the thermal conductivity of water, Sear challenges the Chrétien et al.'s finding and arrives at a maximum estimated energy flux of 1 W/m 2 which translates into a temperature gradient of a maximum of 1 K/m, that is, a maximum gradient of the order of a μK across the dimensions of the cell [11]. Sear's challenge is to essentially falsify the proposition of any notable temperature difference between cell compartments since at the most these would be in the micro-Kelvin range.
However, the fact remains as to how can one explain away Chrétien et al.'s results? And also the fact that other experimenters have come to similar conclusions, albeit not as dramatic as Chrétien et al.'s 10°C gradient. For instance, Shen et al. use rhodamine B methyl ester dye as a mitochondrial thermometer to establish that the natural anti-inflammatory autacoid prostaglandin E 2 (PGE 2 ) can decrease the intracellular temperature of hepatocytes [12]. These workers argue that Chrétien et al.'s findings are consistent with theirs since PGE 2 downregulates metabolism and, hence, heat production in the hepatocites [12]. Using fluorescent thermometry, Okabe et al. report a 1°C gradient between the cell nucleus and the cytosol [13,14]. The presumed existence of (significant) intracellular temperature gradients motivated researchers to develop molecular thermometers that can penetrate mammalian cells and yeast (see for example Ref. [15]).

DISCUSSION
If indeed the mitochondrion is hotter than its surroundings, even by a few degrees, then some of our understanding of mitochondrial biochemistry and biophysics may possibly need to be slightly revisited. We insist on the adjective "slight" since even in the most extreme case of ~ 10 o C temperature gradient, this would translates through Eq. (1) into a theoretical maximum of only ~ 4% revision of the efficiency, while this number drops to a maximum of ~ 0.3% for a 1°C gradient which is, at best, a perturbation that is much less than any hopedfor precision of intracellular conditions. One has also to consider the local random fluctuation of temperature in very small confined spaces in the spatial dimensions [16] as well as in the temporal dimension [17].
Hence, and more explicitly, such a revision may include a reconsideration of the explicit dependence of the first term (ΔG chem. ) in the Gibbs energy expression of the chemiosmotic energy (Eq. (1)) on T and also the indirect effect of the temperature on the second electric term (ΔG elec. ): elec. chem.  where mol here refers to a mole of protons. Now if we assume a temperature of 320 K (i.e., 47°C, ten degrees higher than normal body temperature), and focusing only on the chemical term (ignoring the potential term since we do not know the functional dependence of the potential on the temperature at this point), the change in G Δ per proton would be then:

pH +
for a ΔpH of one unit, which is a very small correction of the order of 3% of the chemical (minor) term. At this point we have no estimates of the effect of temperature on the dominant electrical term. As for temperature, pH, and concentrations, and in view of the small physical space of the mitochondrial "capacitor", one must also account for the local and temporal fluctuation of the voltage and its associated electric field across the inner mitochondrial membrane [18,19]. Furthermore, the obligatory energy dissipation by ATP synthase, a Maxwell demon as it acts as a molecular sorting machine [20][21][22], should be mildly revised as well whereby the minimum energy of k B Tln2 per proton crossing it should be increased by 10 k B Tln2 (which represents a correction of ~ 3% at the most). Finally, perhaps one can also consider a minor aspect of a "heat engine" operation in the mitochondrion whereby one can add an energy term proportional to cold hot . None of the above considerations touch upon another crucial aspect that would be far more (exponentially) sensitive to a temperature difference and that is kinetics aspects. In fact, just from simple Arrhenius law, for a reaction with an activation energy of say 50 kJ/mol, the ratios of the rate constants' in the two extreme cases of 1°C temperature gradient (37°С → 38°C) and 10°C gradient (37°С → 47 o C) would be bracketed by: implying an almost doubling of reactions (with E a = 50 kJ/mol) in the mitochondrion at the higher end of the temperature gradient scale, and a 6% rise in the rate of this reaction for a 1 o C gradient. Nasr et al. have recently examined some of the biological consequences of a possible "hot mitochondrion" [3]. Among the problems that such a higher temperature mitochondrion is representing is that of the instability of mitochondrial macromolecules, particularly proteins and nucleic acids, at elevated temperatures as they can approach or reach their melting temperatures. This is further complicated by the known increase in reactive oxygen species (ROS) production at these higher temperatures (see Ref. [3] and references therein). Nasr et al. suggest that heat shock proteins (Hsps), abundant in the mitochondria and primarily thought to act as molecular chaperones to ensure the proper folding of imported proteins, may also act according to their conventional role as stabilizers of protein structures at higher temperatures. These Hsps can also have a secondary role as protectants against the temperature-dependent increase in ROS levels. These propositions are corroborated by the presence of other compatible solutes (known thermoprotectants and stabilizers of protein structures) such as di-myo-inoitol-1,1'-phosphate, and also by the richness of at least some mitochondrial nucleic acids encoding for Hsps in purine tracks compared to their cytosolic counterparts [3].
Purine tracks are long segments of a nucleic acid that have purine bases stacked one on the top of the next, and -given the larger aromatic rings of purines compared to pyrimidinesthis imparts added stability to these nucleic acids presumably to confront the hotter mitochondrial environment [3]. The very presence of these Hsps and their proposed role as structural stabilizers against the insults of the higher temperature argues in favor of the proposition that the mitochondrion could be indeed "hotter" than its surroundings, but the open question appears to be "by how much?" Hotter or not, the fact remains that temperature must be maintained within a range that allows for the proper functioning of the mitochondrion. So the next question enquires on how the mitochondrion is capable of maintaining its thermal homeostasis? How does it regulate its temperature within an acceptable range? The authors are proposing a feedback mechanism for the regulation of the temperature of the mitochondrion [23].
The proposed control loop is based on the realization that the rate limiting step of the electron transport chain (ETC) is the lateral diffusion of ubiquinone/ol (in its various oxidation states, collectively referred to as "UQ" species) within the inner mitochondrial membrane [24,25]. An increase in the rate of heat production will be associated with a rise in the temperature of the mitochondrion, the higher temperature will decrease the viscosity of the membrane which, in turn, increases the diffusion coefficients of UQ. The faster mobility of UQ accelerates the electron transport chain, and as a result enhances the rate of proton pumping into the inter-membrane gap. The higher gradient created as a result will be associated with a stronger (chemiosmotic) electric field perpendicular to the membrane (and larger voltage across the inner mitochondrial membrane). As any capacitor, this electric field exerts a pressure P over the capacitor dielectric medium (here the phospholipid membrane itself) according to: where ε is the dielectric constant of the membrane and E is the magnitude of the electric field normal to the membrane. This increase in the pressure on the membrane liquid crystal, in turn, increases its viscosity which reduces the diffusion coefficient of UQ putting the breaks on the further pumping of protons and of heat generation. The loop can operate in the opposite mode if the heat production is lower than optimal. This positive/negative feedback mechanism provides an explanation for the thermal homeostasis needed to maintain the mitochondrial temperature within working bounds.

CONCLUSION
Whether the mitochondrion is hotter than its surrounding remains debated. The literature appears to point to a hotter mitochondrion but with probably a lesser temperature gradient than suggested by Chrétien et al. The implications on the thermodynamic efficiency of the mitochondrion are, at best, a small perturbation and probably negligible within the biological context. However, and due to the exponential nature of Arrhenius equation, a small rise in temperature can have a considerable effect on the kinetics of the reactions of the Krebs cycle and of the electron transport chain.