Quantum Evolution, Johnjoe McFadden. Chapter 11

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Quantum Evolution - Chapter 11 - The quantum cell

‘…The first target in our search for the quantum-classical border inside the cell will be a proton that is part of one of the cell’s many proteins: a single molecule of the enzyme called beta-galactosidase. The enzyme looks rather like any other protein inside the cell: a tightly knotted bundle of amino acid rope made up of about 1000 amino acids. But this enzyme is currently inactive. Its job, when it is active, is to hydrolyse (react with water) the disaccharide milk sugar lactose, breaking into its two component bits: glucose and galactose. However, the human host to our E. coli cell has not drunk any milk since breakfast and it is now the middle of the night. The enzyme has nothing to do until the next batch of lactose arrives, along with the breakfast cereal, the next morning. Our cell has been without food for some time now and has exhausted its reserves. To conserve energy, it switches itself into a kind of hibernation state called dormancy, until the lactose arrives.

Our information is that within the beta-galactosidase enzyme lies our target proton on one of the protein’s amino acids. This proton (remember, a hydrogen nucleus) is attached to an oxygen atom within the amino acid molecule, by a covalent bond. Our sources also tell us that nearby lies a nitrogen atom which like the oxygen atom, is relatively electron rich and would like to capture our target proton. We will imagine that if our proton is supplied with enough energy then it might escape the pull of the oxygen atom’s electrons and hop onto the nitrogen atom. In fact, we will suppose that calculations indicate that at body temperature the surrounding thermal energy gives the proton a 50% chance of hopping from one atom to another. If at some later time we were to use some ultra-powerful electron microscope to locate the proton we would find it still attached to the oxygen atom about 50% of the times that we looked, and attached to the nitrogen atoms the remainder. Our task is then to discover: does the proton inhabit the quantum or classical realm? Or, to put the question another way: is the proton’s position real?

The first point to make absolutely clear is that our target proton is a quantum particle that will exist in a quantum superposition of states until it is measured. We will eschew the Copenhagenist interpretation that our presence as observers is necessary to collapse the wave function describing the particle. Instead we will be looking for evidence of our target proton interacting with a complex environment to cause decoherence and thereby observer-free measurement. But what level of interaction will be sufficient to cause decoherence of protons inside living cells? Does our target proton live above or below the quantum/classical border?

The quantum borderland

In his 1944 book, “What is Life?” Erwin Schrödinger postulated that ‘The living organism seems to be a macroscopic system which in part of its behaviour approaches purely mechanical (as contrasted to thermodynamical) behaviour to which all systems tend, as the temperature approaches the absolute zero and the molecular disorder is removed.’ As we discussed above, absolute zero is the temperature at which decoherence is completely suppressed and all matter falls under the sway of quantum rules. Schrödinger was therefore suggesting that decoherence is somehow suppressed inside living organisms, allowing them to obey quantum rules at high temperatures. Regrettably however, we cannot rely upon even as eminent an authority as Schrödinger to find the quantum/classical border inside living cells. We must instead look towards estimates of decoherence times.

Unfortunately, we cannot use Zurek’s equation directly to come up with a decoherence time for a proton inside a living cell. There are too many unknowns. We can however use the equation to give us a few pointers towards those factors that are likely to be important. Clearly mass and temperature will be working against quantum coherence. A typical protein has a mass many thousands of times bigger than a single proton so its decoherence time will be correspondingly reduced. On the other hand, displacement distances will be small within a protein so this factor will tend to work towards maintaining coherence. Flexibility is also very restricted in biological systems due to the high density of electrostatic forces. Some measure of the limited freedom of intracellular protons can be obtained by a technique called nuclear magnetic resonance (NMR) which perturbs a proton in a magnetic field and then allows it to relax. The time it takes for the proton to fall back into its original state gives a rough measure of the flexibility of protons. The protons in a bucket of warm water have very rapid relaxation times but those inside living cells take much longer to relax – from milliseconds to tens of seconds – indicating that the intracellular matrix is far more rigid than might be expected from its chemical composition alone. And proton NMR measures only the relaxation time for the majority of protons which are attached to water molecules inside cells. Protons buried within biomolecules such as proteins or DNA are likely to have much longer (though harder to measure) relaxation times and correspondingly lengthy decoherence times.

Another factor that will interact with this reduced flexibility of biological molecules is the energy flux through the system. The physicist Herbert Frölich proposed that if metabolic energy was supplied to biological molecules inside living cells at a high enough rate, then they may be forced to oscillate at a single coherent frequency. This kind of metabolic energy pumping is somewhat analogous to the energy pumping that gives rise to pulses of coherent photons inside lasers. There is so far no convincing evidence for these high frequency coherent oscillations inside living cells but the possibility of energy pumping does emphasise the considerable level of uncertainty in our understanding of the quantum dynamics inside living cells. There have been a number of reports of quantum-coherent phenomena in biological systems, suggesting that decoherence times may be lengthy. S. Gider from the University of California detected quantum magnetic phenomena in the iron-carrying protein called ferritin. Electron tunnelling (which is of course a quantum phenomenon) is widely assumed to play a role in electron transport in respiration, photosynthesis and in many enzyme mechanisms. Weak electromagnetic fields have been shown to have surprising effects on biological systems – from making nematode worms grow faster to changing genes expression levels or preventing cell apoptosis (a kind of cell suicide). It is very hard to account for how these low strength fields exert their influence by any conventional electromagnetic induction effects. However, phase coherence is exquisitely sensitive to electromagnetic perturbations and it is therefore possible that it is coherent oscillations inside living cells that are the targets of these low strength fields.

You may remember from Chapter 9 that another useful way to consider decoherence is as a measure of leakage of information concerning the state of a quantum system into a complex environment. In the two slit experiment it was ‘which way?’ information that leaked into the environment to cause decoherence. For our protons, it will similarly be ‘which way?’ information that will cause decoherence; only now it is which way has the proton gone: to the oxygen or nitrogen atom?

Imagine first that the position of our target proton has no significance to the protein or its surrounding cell (there are likely to be very many protons in this situation inside living cells). The proton will be buried within the globular structure of the protein molecule in some out of the way stretch of the amino acid chain that plays no role in the enzyme’s catalytic activity. Although the proton shift may cause changes in the enzyme’s structure due to the shift in our target proton’s position and the subsequent reshaping of its electric field, these are likely to be very small, insufficient to cause decoherence on their own. The proton’s position will not become entangled with the external environment. We could stare as long as we like at the target protein from the cockpit of our miniaturised submarine but we will not spot any information that correlates with the particle’s position in the environment of the cell. With no leakage of information, decoherence will be retarded and the proton will remain as a quantum superposition indefinitely.

But the position of many protons in the cell will not be so inconsequential. Remember that enzymes are proteins that catalyse reactions by mobilising the electrons and protons in their substrates. They do so by attacking the substrates with their own particles: the electrons and protons attached to their amino acids. So the precise location of their electrons and protons is crucial for their enzymatic activity. Now imagine that our target proton is bound to an oxygen atom on the 461th amino acid of the beta galactosidase enzyme: a glutamine. This proton is in fact particularly critical for enzyme activity since the breakdown of lactose is initiated by it being fired into the heart of the lactose molecule where it destabilises chemical bonds. If the proton has however taken a jaunt over to the adjacent nitrogen atom then it cannot be fired into the substrate and the enzyme will not work. So the enzyme can measure its own proton’s position, if lactose is available as a substrate.

But how will we see the breakdown of lactose. Fortunately, it will be easy since the breakdown of lactose does not stop with the generation of glucose and galactose. The products are instead drawn into a complex web of metabolic pathways, where they will be broken down further and their electrons harvested and fed into the respiratory chain that makes ATP (as I described in Chapter 5). The ATP energy may then be utilised in a variety of ways by the cell. It may wake the cell out of its dormancy. It might be used to provide energy to power up the flagella motor in the cell. The energy could equally be used for cell division or to supply the power for biosynthesis of new proteins. Each of these possibilities will cause massive changes to the positions and energies of billions of particles both inside and outside the cell that we will be able to easily spot. If we witnessed any of these classical level events then we could be sure the target proton was attached to the oxygen atom. Equally, the absence of these phenomena would constitute a null measurement of the particle’s position; in which case we would know that it is attached to the nitrogen atom.

In fact we don’t even need to be miniaturised to witness these classical signals. A full-sized microscopist could detect the cell’s motility or a molecular biologist could detect its DNA replication. The host to our E. coli cell could even suffer a bout of urgently classical diarrhoea from an infection initiated by the revived bacterium. Just as a Geiger counter can generate a classical signal that betrays whether or not a radioactive atom has decayed, so a living cell can generate a classical signal that betrays proton position. However, unlike a Geiger counter, the living cell is turned in upon itself to perform measurements on its own particles and thereby perform internal quantum measurement.

An important point to note is that our target proton will only be measurable when lactose is available in the cell. If there is no lactose then the position of our proton will make no difference to the cell and no information correlating with particle position will leak into the surrounding cell. We could stare at the cell as hard as we like but we will be unable to discern whether the proton is attached to the oxygen or nitrogen atom. Under these circumstance, decoherence will be suppressed and the proton will remain as a quantum superposition. Quantum measurement will be conditional upon the state of the cell.

There is of course nothing special about beta-galactosidase enzyme’s role as the target of internal quantum measurement. The average bacterial cell is capable of producing more than one thousand different proteins and each of them will have fundamental particles poised within their active sites, subject to quantum measurement by the cell. For our target enzyme, internal quantum measurement was conditional upon the presence of lactose in the cell. For other components, it might be different substrates, temperature, light, brightness or any other physical parameter that could affect the cell’s ability to perform internal quantum measurement. Measurement will also not be confined to particle position. Real values for energy, momentum, spin or indeed any quantum property will be similarly conditional upon quantum measurement. The chain of entanglement between the particles inside cells and their environment ensures that living cells are uniquely sensitive to all kinds of quantum events taking place within their interior.

Our mission was to find the border between the quantum and classical realm inside living cells. What we have discovered is that there is no fixed border inside living cells but one that shifts up and down the hierarchy of cell function, depending on the state of the cell and the resources it has available. In starved, inactive cells, most of fundamental particles will be sunk into the quantum world of superpositions and interference. But give the cell some food and its quantum measuring apparatus will be armed with substrates that allow it to perform densely spaced measurements on critical particles, forcing them to take on real values and inhabit the classical world. The quantum-classical border will thereby be pushed down into the bowels of the cell where only non-critical particles, shielded from environmental interactions, will continue to persist as quantum entities.’