Kleiber’s Law has basal metabolism for constant temperature animals Y vary as M^3/4 for animal mass M. This 3/4 metabolic scaling keeps cellular temperature constant because the 4/3 scaling of the rate of energy supply is counterbalanced by the 3/4 scaling of the rate of energy use: Metabolism’s plot twists,. Thus metabolic scaling results in intracellular energy balance. Sarrus and Rameaux in 1838 proposed on theoretical grounds a surface law: Preprint Sarrus and Rameaux, 1838, translated into English
. The surface law is discounted by Kleiber’s empirical work and Kleiber’s reasoning about the role of the circulatory system: There are also logical inconsistencies in the surface law:Preprint Metabolic scaling's exponent
. Sarrus and Rameaux in 1838 observed that the constant temperature animals must be in heat balance: animal body heat production must be balanced by animal body heat emission. Heat production is proportional to 3 dimensions; heat emission is proportional to 2 dimensions. If that is so, then even if there is intracellular energy balance, it seems there may be a problem of how to account for overall animal body heat balance:Preprint Metabolic scaling and heat dissipation
. Perhaps if there is intracellular energy balance the heat imbalance question does not arise: if cells have energy balance there would be no surplus heat. On the other hand, perhaps the two issues are related but distinct: heat generated in 3 dimensions can only leave via 2 dimensions so there is a question of how heat balance is achieved. Perhaps the heat balance question can be addressed by supposing that cells convert part of the energy they receive to uses (motion, neuron activity) that consume energy that does not contribute to the creation of heat so that animal body heat is in balance. The perspectives above are mainly based on physics. Are there biological perspectives that can reconcile energy balance and heat balance? And is this a valid question: For metabolic scaling, can energy balance and heat balance be reconciled?
Check this paper:
https://www.nature.com/articles/s41598-018-19853-6
Fernando Ballesteros:
Many thanks for your February 28, 2020 reply and for linking to the open 2018 article by you and your colleagues in Nature On the thermodynamic origins of metabolic scaling. From my initial superficial reading, it appears the article among other things looks at heat balance as factor affecting metabolic scaling. (Speakman and Krol in 2010 wrote on maximal heat dissipation for endotherms with heat balance a controlling metabolism, if I recall.) This seems possible. One reason: a mammal has body heat which is dissipated in part. That heat must be fueled by energy generated by cells. So some energy goes to heat production. Second reason: one may reasonably question whether heat used by a cell is used perfectly efficiently.
I am unsure about the cellular efficiency argument. Perhaps it is possible that cellular mechanisms are maximally efficient and that heat waste is incidental to a maximally efficient process. On ResearchGate I posted an article in October 2018, Metabolic scaling and heat dissipation, after your article’s date. Preprint Metabolic scaling and heat dissipation
Unfortunately, I did not know about your article then, or until today, which led me to ask in my article why the question raised by Sarrus and Rameaux in 1838 about heat balance had not been addressed.
The gist of my approach is that energy supply via the animal circulatory system scales by exponent 4, while tissue use of that energy scales by exponent 3. Hence relative to energy use, energy supply scales by 4/3. The 4/3 scaling of energy supply is itself scaled by 3/4, the exponent for supply 4/3 is multiplied by the exponent for use 3/4 giving constant 1. In that way animal cells are kept in energy balance and incidentally (perhaps) heat balance, enabling cellular processes to proceed at approximately the same temperature. Otherwise animal cells would over heat.
Suppose part of the 4/3 scaling of energy supply diverts to create some heat. Then the ratio 4/3 would be very slightly lower, and the metabolic scaling would be very slightly higher than 3/4. I don’t know if that works, but that is about as far as I got.
I have a project on RG on metabolic scaling. The articles on The Kozlowski Konarzewski - West Brown Enquist Debate and Metabolism’s marvelous plot twists might be of interest, as well as my English translation of Sarrus and Rameaux 1838.
Best regards.
The following article relates to this question.
Allometric scaling of heat and water exchanges in the mammals' lung
by Sobac, Karamaoun, Haut, Mauroy. December 15, 2019 on arXiv.
"Our study derives, for the first time, with an analytical, highly tractable and validated model, how a universal number G drives the heat and water exchanges amongst mammals."
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