A geeky post which is sure to not stir controversy among anyone reading this blog

In late 2021, Fields and Levin published an article hypothesizing that cells are entangled quantum entities, and their membranes isolate them from a decohering classical environment. As evidence for this, they observe that cells from all taxa use much less energy to do their stuff than would be predicted by classical computation theory, which says that the minimum power dissipated is roughly Ln(2) N kT f, where Ln is the natural logarithm, N is the number of bits to be flipped in the computation, k is Boltzmann’s constant and T is the temperature in Kelvin. My initial reaction is that this hypothesis might be incorrect and they would get a similar answer if they studied a dead cell, which requires even less energy than a live one, but takes just as much energy to simulate. And they (rightly) claim that quantum computation requires no energy at all, except for communicating with the classical world, which tends to decohere it.

I am particularly interested in this topic because I have a different, competing hypothesis as to the function of membranes: they are necessary to keep resources mostly inside, and to provide informational abstraction in order to keep costs, mostly of free riding monitoring (inside the membrane), and environmental prediction (outside the membrane) low.

It’s not like there is a mystery in cell metabolism, the energetics and kinetics of enzymes are pretty well understood, e.g. from one of the foundational papers cited in Levin and Fields’ article. There is quantum mechanics involved in figuring out bond energies, but the dynamics are classical (there is nothing known like entanglement of mesoscopic classical states that would allow Bell correlations to be measured) at time scales larger than the so-called decoherence time (femtoseconds). The energy cost of building proteins or DNA is known to be about 20-100 kT per amino acid or nucleotide inserted or removed, and it comes from sugars or other nutrients which are obtained from the environment, fed to mitochondria, which excrete ATP, which supplies the energy needed for these functions, as well as all other cellular functions.

I think what the paper claims is that the timescales for decoherence should be on the order of 10^(-15) to 10^(-6) seconds, whereas based on power consumption of cells, they would be on the order of 10^11 to 10^15 seconds. But why should the decoherence time be similar to the time it takes cells to metabolize? It should be much smaller, and it is, whether the cell is alive or dead (and not metabolizing).

Another conceptual issue in the paper is that for live cells, metabolism (and also catabolism) only happens for some small fraction of all the motions of proteins and DNA (the ones that decrease entropy like a Maxwell Demon and require metabolic energy), and for a small fraction of the time. This means N is much smaller than their estimate, which means f can be larger, and the timescale for irreversible bit flips can be smaller, (more on the order of microseconds to seconds, still much larger than the decoherence time). This much smaller subset of computational “bit flips” is what distinguishes live from dead cells and why cellular metabolism requires much less energy than Fields and Levin estimate with classical computation theory.

Additionally, I am skeptical that cell membranes insulate cell components enough to prevent quantum decoherence at femtosecond scales because cells (dead or alive) have an aqueous environment inside at an equilibrated temperature which is usually pretty high (a bit higher for live endotherms than ectotherms) compared to the kinds of low temperatures where macroscopic quantum effects are typically observed. Typical cell membranes are not good enough thermal insulators to keep the insides of cells near absolute zero. And if they were, enzymes would not be very good at doing their jobs, which require relatively high temperatures.