We showed that the new metabolic rate relation13 can be directly linked to the total energy consumed in a lifespan if a constant number ({mathrm{N}}_{mathrm{r}}) of respiration cycles per lifespan is conjectured, and a corrected relation for the total energy consumed in a lifespan was found [Eq. (1)] that can explain the origin of variations in the ‘rate of living’ theory2,5 and unify them into a single formulation. It is important to note that Eq. (1) is a direct consequence of combining the two empirical relations mentioned (the new metabolic rate relation and the relation of the total number ({mathrm{N}}_{mathrm{r}}) of respiration cycles per lifespan) and is not an assumption (based on the lifespan energy expenditure per gram) as in the traditional ‘rate of living’ theory2,5. We test the validity and accuracy of the predicted relation [Eq. (1)] for the total energy consumed in a lifespan with (sim 300) species representing different classes of living organisms, and we find that the relation has an average scatter of only 0.3 dex, with 95% of the organisms having departures of less than a factor of (pi) from the relation, despite the difference of (sim 20) orders of magnitude in body mass.
Successful testing of predictions is crucial in any proposed theory according to Popper’s deductive method of falsification (27), which is the criterion for identifying a successful scientific theory. Therefore, the success of the predicted Eq. (1) that is displayed in Fig. 1 implies that the corrected metabolic rate relation13 has passed an initial test. This prediction also reduces any possible interclass variation in the relation, which has been considered the most persuasive evidence against the ‘rate of living’ theory, to only a geometrical factor and strongly supports the conjectured invariant number ({mathrm{N}}_{mathrm{r}} sim 10^8) of respiration cycles per lifespan in all living organisms.
Invariant quantities in physics traditionally reflect fundamental underlying constraints, a principle that has also been applied recently to life sciences such as ecology21,22. Figure 2 indicates the fact that, for a given temperature, the total lifespan energy consumption per gram per ‘generalized beat’ (({mathrm{N}}_{{mathrm{b}}}^{mathrm{G}} equiv mathrm{a} {mathrm{N}}_{{mathrm{r}}} = {mathrm{a}} ,1.62 times 10^8)) is remarkably constant (around ({mathrm{E}}_{2019})), a result that is also in agreement with previous expectations based on (lifespan) basal oxygen consumption at the molecular level38. This supports the idea that the overall energetics during the lifespan are the same for all the organisms studied, as it is predetermined by the basic energetics of respiration, and therefore, Rubner’s original picture is shown to be valid without systematic exceptions but in a more general form. Moreover, since the value determined from Fig. 2 is remarkably similar to ({mathrm{E}}_{2019} {mathrm{N}}_{mathrm{r}}), it can be considered an independent determination of ({mathrm{E}}_{2019}), suggesting that ({mathrm{E}}_{2019}) is a candidate for being a universal constant and not just a fitting parameter from the corrected metabolic relation13.
In addition, we showed here that the invariant total lifespan energy consumption per gram per ‘generalized beat’ comes directly from the existence of another invariant, the approximately constant total number ({mathrm{N}}_{mathrm{r}} sim 10^8) of respiration cycles per lifetime, effectively converting the ‘generalized beat’ into the characteristic clock during the lifespan. Therefore, the exact physical relation between (oxidative) free radical damage and the origin of aging is most likely related to the striking existence of a constant total number of respiration cycles ({mathrm{N}}_{{mathrm{r}}}) over the lifetime of all organisms, which predetermines the extension of life. Moreover, the relation ({mathrm{t}}_{{mathrm{life}}} = mathrm{N}_{mathrm{r}}/mathrm{f}_{{{mathrm{resp}}}}) quantifies the ideas of oxidative damage by the respiratory metabolism, which are motivated mainly by biomedical considerations, into a simple mathematical form that could be included in a broader life-history framework; this is needed to produce testable predictions for the ‘free-radical’ hypothesis in the life-history context28. Future theoretical and experimental studies that investigate the exact link between the constant number ({mathrm{N}}_{mathrm{r}} sim 10^8) of respiration cycles per lifespan and the production rates of free radicals (or alternatively, other byproducts of metabolism) should shed light on the origin of aging and the physical cause of natural mortality.
Although this relation ({mathrm{t}}_{{mathrm{life}}} = mathrm{N}_{mathrm{r}}/mathrm{f}_{{mathrm{resp}}}) has only been empirically examined for mammalian vertebrates, in terms of heartbeats per lifetime, there is evidence to believe that the relative constancy of the number of respiration cycles per lifetime is more widely distributed in the animal kingdom. For example, a reptile such as the Galapagos tortoise with a life expectancy of 177 years and a respiration rate of 3 breaths/min has (2.8 times 10^8) breaths per lifetime29, which is within a factor of 2 of the value determined for mammals. A more different case is that of birds, which have more heartbeats/lifetime by a factor of 330; this difference is reduced to a factor of 1.5 in terms of breaths/lifetime ((mathrm{N}_{mathrm{r}} = mathrm{N}_{mathrm{b}}/{mathrm{a}}), with (hbox {a}=9) for birds and 4.5 for mammals; 17). Among fish, the average number of heartbeats/lifetime tends to be an order of magnitude less than that in mammals ((mathrm{N}_{mathrm{b}} = 7.3 times 10^8);16), for example, (mathrm{N}_{mathrm{b}} = 6.7 times 10^7) for trout31, but in such cases, the parameter a can be as low as 0.5 (i.e., a heart frequency lower than the respiratory frequency; 32), again implying a similar ({mathrm{N}}_{mathrm{r}} ,(= mathrm{N}_{mathrm{b}}/{mathrm{a}} = 1.3 times 10^8)). A more extreme difference in terms of heartbeats is the tiny Daphnia, which uses up to (1.7 times 10^7) heartbeats (at 25 C) in a short lifespan of 30 days33. Simple invertebrates, such as Daphnia, do not have a complex respiratory system with lungs and obtain oxygen for respiration through diffusion, but a “breath frequency” can be estimated from its respiration rate ((sim mu {mathrm{l}} {mathrm{O}}_2 hbox {hr}^{-1});34) divided by ({mathrm{E}}_{2019} M) (with ({mathrm{M}} sim 100 mu {mathrm{g}});35), giving ({mathrm{N}}_{mathrm{r}} = 1.5 times 10^8) respiration cycles per lifetime. In summary, a difference of two orders of magnitude in total heartbeats (between Daphnia and birds) is reduced to less than a factor of 2 in breaths per lifetime, further supporting that all organisms seem to live for the same span in units of respiration cycles (({mathrm{N}}_{mathrm{r}} sim 10^8)).
It has also been suggested that an analogous invariant originates at the molecular level23, the number of ATP turnovers of the molecular respiratory complexes per cell in a lifetime, which, from an energy conservation model that extends metabolism to intracellular levels, is estimated to be (sim 1.5 times 10^{16})23. A similar number can be determined by taking into account that human cells require the synthase of approximately 100 moles of ATP daily, equivalent to (7 times 10^{20}) molecules per second. For (sim 3 times 10^{13}) cells in the human body and for a respiration rate of 15 breaths per minute, this gives (sim 9 times 10^{7}) ATP molecules synthesized per cell per breath, which for the invariant total number ({mathrm{N}}_{mathrm{r}}) of respiration cycles per lifetime found in this work, rises to the same number of (sim 1.5 times 10^{16}) ATP turnovers in a lifetime per cell, showing the equivalence between both invariants and linking ({mathrm{N}}_{mathrm{r}}) to the energetics of respiratory complexes at the cellular level.
The excellent agreement between the predicted relation [Eq. (1)] and the data across all types of organisms emphasizes the fact that lifespan indeed depends on multiple factors (B, a, M, T & (mathrm{T}_{mathrm{a}})) and strongly supports the methodology presented in this work of multifactorial testing, as shown in Fig. 1, since quantities in life sciences generally suffer from a confounding variable problem. An example of this problem, illustrated by individually testing each of the relevant factors, is given in24, which for a large (and noisy) sample test for ({mathrm{t}}_{{{mathrm{life}}}} propto 1/B) shows no clear correlation. From Eq. (1), it is clear that in an uncontrolled experiment, the dependence on the rest of the parameters (M, a, T, & ({mathrm{T}}_{mathrm{a}})) might eliminate the dependence on the metabolic rate B (in fact, this may be for the same reason that Rubner’s work7 focused on the mass-specific metabolic rate B/M instead of B). This work24 finds only a residual inverse dependence of ({mathrm{t}}_{{mathrm{life}}}) on the ambient temperature ({mathrm{T}}_{{mathrm{a}}}) for ectotherms, which is expected according to Eq. (1) (Big (mathrm{t}_{{mathrm{life}}} propto {mathrm{exp}}Big ({small frac{mathrm{E}_{mathrm{a}}}{mathrm{k} {mathrm{T}}_{mathrm{a}}}}Big ) Big )).
Finally, the empirical support in favor of Eq. (1) allows us to perform several estimations regarding how much the energy consumption will vary with changing physical conditions on Earth. For example, computing by how much the energy consumption will vary in biomass performing aerobic respiration as the Earth’s temperature increases is relevant in the current context of possible global warming. This is given by the factor ({mathrm{exp}}Big [{small frac{mathrm{E}_{mathrm{a}}}{{mathrm{k}}} Big (frac{1}{ {mathrm{T}}}} – {small frac{1}{ {mathrm{T}}+1}}Big ) Big ]), which for an activation energy of ({mathrm{E}}_{mathrm{a}} = 0.63 ,hbox {eV}) and a temperature of (30^{circ }hbox {C}) implies an increase of 8.3% in energy consumption per 1 degree increase in the average Earth temperature. This result can be straightforwardly applied in ectotherms since their body temperatures adapt to the environmental temperature (({mathrm{T}}={mathrm{T}}_{mathrm{a}})), but its implications for endothermic organisms are less clear. Another relevant estimation is to compute by how much B({mathrm{t}}_{{mathrm{life}}})/M would vary from Eq. (1) (i.e., the difference between Figs. 2 and 3) as a function of body temperature (T) and the ratio of heart rate to respiratory rate ((mathrm{a}= mathrm{f}_{mathrm{H}}/ {mathrm{f}}_{{mathrm{resp}}})). Variations in B({mathrm{t}}_{{mathrm{life}}})/M are relevant since this is a key quantity in the estimation of the energy allocation to fitness, which aims to explain in terms of trade offs the so-called ‘Equal Fitness Paradigm’39 that concerns why most organisms in the biosphere are more or less equally fit, other than the diversity seen in the size, form and function of living organisms on Earth.
In the near future, our plan is to generate a (metabolic) theory starting from the new metabolic rate relation13 by assuming that it is the controlling rate in ecology in order to explain a variety of ecological phenomena in a similar fashion as the metabolic theory of ecology18 does using Kleiber’s law. A first step in this direction looks very promising40, as it can show that ontogenetic growth can be described by a universal growth curve without the aid of fitting parameters, can explain the origin of several ‘Life History Invariants’21 and can show how the heart rate may actually set several biological times (i.e., lifespan and generation time) and even some ecological rates (i.e., The Malthusian parameter).
Source: Ecology - nature.com
