A quantitative bound on motional narrowing in the radical-pair nuclear register: the neural band requires $S^2\lesssim0.07$

The human brain is a wet, warm, and chaotic place, a environment where delicate signals usually dissolve into noise almost instantly. For decades, scientists have wondered if the brain could harness the strange rules of quantum mechanics to process information, a field of inquiry known as quantum biology. One specific idea suggests that tiny, short-lived pairs of molecules called radical pairs, found in enzymes within the brain, could act as a storage system for quantum information. The hope is that the nuclei of atoms within these molecules could hold onto a memory long enough to influence how a neuron fires, a process that takes about ten milliseconds. However, the heat and movement of the brain usually destroy such delicate quantum states in a fraction of a second. To make this work, the theory relies on a mechanism called motional narrowing, where the rapid, jittery movement of atoms inside the molecule somehow averages out the noise and extends the life of the memory.

A new study by researchers Hikaru Wakaura and Taiki Tanimae puts this specific hope to a rigorous test. They did not simply ask if the idea was possible in theory; they built a precise mathematical model to see if the numbers actually add up for a real biological system. Their work focuses on a specific enzyme called cryptochrome, which contains a pair of molecules that can form a radical pair. The researchers examined whether the internal motion of atoms within this enzyme could shorten the time it takes for the quantum memory to fade, thereby extending it to the required ten milliseconds. By running detailed simulations based on established physics, they found that the natural movements inside the protein are not fast or chaotic enough to save the memory. The quantum state fades away in less than half the time needed for a neuron to integrate a signal, effectively ruling out the idea that this specific biological mechanism can support quantum processing in the brain as currently proposed.

The researchers began by defining exactly what "enough" time means for this system. They used a standard measure of how much information a system can hold and process, known as memory capacity, to set a hard limit. For the brain's quantum memory to be useful, it must survive for at least ten milliseconds. The team calculated how long the memory would last in a radical pair formed by a flavin molecule and a tryptophan molecule, which are known to exist in the brain. In a calm, still environment, this memory would vanish in less than two milliseconds. The only way to extend this life is through motional narrowing, where the internal parts of the molecule spin and vibrate so quickly that they blur out the magnetic interactions that cause the memory to decay. The researchers tested whether the natural rotation of a small part of the molecule, specifically a methyl group attached to the flavin, could provide this necessary blur.

The results were clear and quantitative. The rotation of this methyl group does happen, but it is not chaotic enough to fully average out the magnetic noise. The study calculated that for the memory to last the full ten milliseconds, the internal motion would need to leave less than seven percent of the original magnetic order intact. However, the actual rotation of the methyl group leaves about twenty-five percent of that order untouched. Because the motion is too restricted, the memory only lasts for about seven milliseconds. This falls short of the ten-millisecond window required for neural computation. The researchers checked their work against various uncertainties, such as how much water surrounds the protein or how dense the surrounding fluid is, and in every scenario, the memory still faded too quickly. The margin is narrow enough to matter: the result is best read as a sharp quantitative boundary rather than a categorical exclusion, as a register on the methyl C–H vector rather than the proton–proton pair would sit marginally inside the band.

The paper also examined other ideas that had been proposed to save this quantum memory. One suggestion was that a special quantum state, known as a long-lived singlet, could protect the information. The authors found that this state protects a different kind of property than the one the brain would need to use for memory, so it does not help. Another idea involved using different types of atoms, such as replacing hydrogen with carbon or phosphorus, to slow down the decay. While the simulations showed that these substitutions could extend the memory life to over twenty-eight milliseconds or even ninety-one milliseconds, these atoms are not naturally found in the brain's radical pairs. Therefore, while these methods work in a laboratory setting, they do not apply to the biological system in question. The study concludes that the only way to make the quantum memory last long enough is to change the fundamental atoms of the system, which is not possible in a living human brain.

To prove their conclusion is correct, the authors propose a specific experiment that could be done in a lab. They suggest creating a series of solutions with different thicknesses, or viscosities, to slow down the movement of the enzyme molecules. By measuring how long the quantum memory lasts in these different conditions, scientists could see if the memory lifetime scales exactly as their model predicts. If a natural, unmodified protein is ever found that can hold the memory for ten milliseconds, their conclusion would be wrong. However, based on current data and simulations, the evidence points to a definitive limit. The internal motions of the proteins in the brain are simply too slow and too ordered to clear the noise fast enough. The quantum memory fades away before the neuron has a chance to use it, suggesting that the brain does not rely on this particular quantum mechanism for its processing power.