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closeA 10 C difference requires an implausibly large power consumption by mitochondria
Posted by rsear on 24 Jul 2018 at 12:25 GMT
A 10 K (or 10 C) difference in temperature between a structure about 1 micrometre across [1], and its surroundings, is hard to maintain, in a good conductor of heat, which is what water and so living cells are. Living cells are mainly water. The thermal conductivity of water is roughly 1 W/K/m [2], so if there is a 10 K difference in temperature over a distance of 1 micrometre, there is a flux of heat energy of about 107 W/m^2, i.e., 10 million Watts per square metre. Assuming a surface area of a mitochondrion of 1 square micrometre, sustaining this thermal flux requires the mitochondrion to burn energy at a rate of 10-5 W, i.e., 10 micro-Watts, because it will lose energy to its surroundings at approximately this rate. This power consumption of a mitochondrion is unrealistically high.
The adult human body has about 10 trillion cells and a power consumption of about 100 W [3]. But if each cell had even one (our cells typically have many more than this) mitochondrion burning 10 micro-Watts, our power consumption would not be 100 W but 100 million Watts. Note this is just a rough (sometimes called a Fermi) estimate, that is accurate to at best an order of magnitude. But please note that this estimate, based on the reported 10 K temperature difference, is a factor of one million out from our known power consumption.
In conclusion, it seems unlikely that our mitochondria are consistently more than 10 C hotter than the rest of the cell. If I put numbers in that correspond to our actual power consumption, then temperature differences of maybe milli-Kelvin seem more likely. Two final points: 1) although I used human power consumption for the purposes of illustration, our power consumption is not much different from that of other organisms [3], so this argument applies to all cells, not just human. 2) Cells are not just water, but structures such as membranes are relatively thin, and not expected to have dramatically lower thermal conductivities than water, for example hydrocarbons (similar to the tails of lipids) have thermal conductivies of around 0.1 W/K/m [2].
References:
[1] Sizes of mitochondria are discussed in: http://book.bionumbers.or...
[2] Thermal conductivty of water: https://en.wikipedia.org/...
[3] Power consumption of cells is discussed at http://book.bionumbers.or...
RE: A 10 C difference requires an implausibly large power consumption by mitochondria
PRustin replied to rsear on 24 Jul 2018 at 14:26 GMT
See however : Theoretical model and characteristics of mitochondrial thermogenesis.
Kang JS. Biophys Rep. 2018;4(2):63-67. doi: 10.1007/s41048-018-0054-2.