# There is a lot physicists don’t know about living cells, but we do know some things, such as you don’t have hot mitochondria

Last year, Chrétien  et al. published a paper in PLOS Biology on mitochondria. Two mitochondria are shown above, they are structures inside our cells where a key part of our energy metabolism take place. I don’t want to be harsh, but the central claim of their work is clearly wrong. This claim is that the mitochondria inside cells are at a temperature of around 50 C, more than 10 C higher than the rest of the cell which is about 37 C. This really cannot be right, the mitochondria inside your body are at the same 37 C that the rest of you is, and with a little physics it is easy to see why.

A 10 C, or 10 K, difference in temperature between a structure about 1 micrometre across* [1], and its surroundings, is very 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** 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/m2, i.e., 10 million Watts per square metre!

To give you a rough idea how much that is, at the time of writing the cost of electricity is roughly 10 p per kWh. If say you lived in a flat with a total of 10 m2 of windows and you wanted to heat the flat but were losing heat at this rate, your heating bill would be £1000 per hour. This adds up to an almost £9 million a year bill!  Ten million Watts per square metre is serious heat loss.

Returning to mitochondria: If we assume that the surface area of a mitochondrion is roughly 1 square micrometre, sustaining this thermal flux requires the mitochondrion to burn energy at a rate of 10-5 W = 10 μW, because it will lose energy to its surroundings at approximately this rate.

The adult human body has about 10 trillion cells and a power consumption of about 100 W***. But if each cell had even one (our cells typically have many more than this) mitochondrion burning 10 μW, our power consumption would not be 100 W but 100 million Watts. Note this is just a rough estimate (sometimes called a Fermi estimate), that is accurate to at best an order of magnitude. However, unless it is off by a factor of a million, and I don’t think it is, the claims of mitochondria at 50 C look implausible.

So it seems very unlikely that our mitochondria are consistently more than 10 C hotter than the rest of the cell. Now, I have been wrong about some basic fact of biology before, and I am sure I will again, so I can’t realise criticise these biologists, but this is a good example of how a knowledge of basic physics, can save you from problems.

* Sizes of mitochondria and a lot else are discussed in the really useful and fascinating book Cell Biology by the Numbers. The book is available online and the relevant part here is at: http://book.bionumbers.org/how-big-are-mitochondria/
** Thermal conductivity of water: https://en.wikipedia.org/wiki/List_of_thermal_conductivities
*** Power consumption of cells is also discussed Cell Biology by the Numbers, and is at: http://book.bionumbers.org/what-is-the-power-consumption-of-a-cell/