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For the protein interactions that occur in our cells, do they "follow" classical mechanics or quantum mechanics when interacting?

I have zero knowledge about quantum mechanics, but I was wondering if the interactions could be mainly seen as "classical phenomenon" or "quantum phenomenon". For example, when two proteins touch each other to bind, are their interactions similar to how my hand interacts with my glove (except obviously polarity and charge, which makes a big difference for proteins)? Or is it much more complicated than classical mechanics?

I remember once reading that quantum effects sometimes play a significant role when you're at the scale of DNA, but since many of the proteins are much larger than DNA, I was wondering if the quantum effects become insignificant (like my hand in my glove). Sorry if this question might be unclear, I'm not quite sure how to word this well. Please let me know if I can improve it.

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Your question is a good one, though it's somewhat unclear. I think what you're asking, in essence, is whether one needs quantum mechanics to accurately model the activity of proteins, or whether classical physics is sufficient. If one takes the proteins as already existing, the answer, in the vast majority of cases, is that classical mechanics is sufficient. In fact, the standard "molecular dynamics" methods of computational simulations of proteins binding to one another, changing shape, etc., are all classical in nature. In a bit more detail:

The chemical bonds that hold atoms together in molecules, such as proteins, are inherently quantum mechanical in nature; classical physics is insufficient to explain them. But, once one "has" a molecule in hand and wants to think of this object as a whole, one needn't (in most cases) worry about the substructure. Very roughly, one can get a sense of how important quantum mechanics is by thinking about the de Broglie wavelength of an object, compared to its size. For a protein with ~$kT$ of energy, the thermal de Broglie wavelength is ~$ 10^{-12}$ m, much smaller than the size of the protein; its wave-like character is largely irrelevant. Modeling the protein, therefore, is a fine job for classical physics. As mentioned, this is, in fact, what is generally done, quite successfully.

There are exceptions, of course, but these tend to involve situations in which the motions of electrons are much more important, such as excitations in photosynthesis. (Electrons have much smaller mass, and so much greater wavelengths.)

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  • $\begingroup$ Thanks for the great response - that's exactly what I was trying to ask. So, for example, if one was to model a drug molecule interaction with a protein, it could be done using classical mechanics principles? (Since drug molecules are usually a lot smaller than the proteins, I wasn't sure if classical mechanics is still sufficient). $\endgroup$ – F16Falcon Oct 13 at 17:59
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Quantum mechanics as a theory was invented in order to explain why classical mechanics and classical electrodynamics did not work in certain situations: small scales, spectra of atoms , black body radiation. Classical mechanics and classical electrodynamics cannot explain or predict the behavior of atoms (their interactions) , neither that of molecules.

Thus the answer is proteins interact with quantum mechanics. It can be mathematically demonstrated that classical mechanics and electrodynamics emerges from the underlying quantum nature when dimensions are large.

Now this:

(like my hand in my glove).

Even this depends on quantum mechanics. Scattering experiments have shown that most of the space around atoms, so that means your glove also, is empty. If the quantum mechanical theory were not at work, we would all fall to the center of the earth drawn by gravity after some time, to join all the other matter there. It is the Pauli exclusion principle that does not allow this.

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  • $\begingroup$ Hmm, your explanation "Thus the answer is proteins interact with quantum mechanics." is interesting, and seems to contradict Cleonis's answer. You're right (it seems to me) that quantum physics plays a role in even macroscopic interactions, however, for example, if we drew a free body diagram of my hand in a glove, I'm sure quantum forces (is that what they're called?) would be negligible? Similarly, do you know if we drew free body diagrams for proteins, would we have to include quantum stuff? Or can they reasonably accurately (but not completely) be modeled using classical mechanics? $\endgroup$ – F16Falcon Oct 13 at 14:00
  • $\begingroup$ I guess "reasonably accurately" would be a subjective term, however, I'm interested in knowing if, lets say for example, if someone a computer model of two proteins' interactions using only classical mechanics principles, would it be fairly accurate enough to predict the interaction? $\endgroup$ – F16Falcon Oct 13 at 14:02
  • $\begingroup$ @F16Falcon If you are thinking of throwing a protein in the air, or like a particle in an accelerator, dimensions are such that classical mechanics would accurately give the trajectory. In interacting with other molecules or atoms, quantum mechanics has to enter to get a correct description of the interactions. Look up the Pauli exclusion principle to understand how necessary it is to keep us on the surface of the earth. and the chemistry of the world as it is. It is a quantum principle. $\endgroup$ – anna v Oct 13 at 14:20
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This is a partial answer.

There is a class of proteins called enzymes. Enzymes facilitate chemical reactions. Many enzymes facilitate in the following way: a particular small region of the enzyme has a high affinity for a particular molecule. That is, when that molecule comes in contact with that active region it tends to get stuck there. The fit is good, but the fit is slightly off in such a way that the molecule becomes deformed in a way that a particular chemical reaction occurs more readily. When that chemical reaction does occur the changed molecule has less affinity for the active region of the enzyme, and the molecule tends to float away. (This is of course a highly simplified account, for the purpose of this question.)

It has been proposed that there are classes of enzyme facilitated reactions that involve quantum tunneling.

This has been proposed, for instance, for forms of hydrogen transfer. In an experiment the hydrogen that the enzyme helps to transfer was replaced with deuterium, and then the reaction was seen to proceed a 100 times slower. If the enzymatic facilitation mechanism would be classical in nature you would not expect such a large difference, suggesting the facilitation mechanism was that the enzyme is actually creating favorable conditions for quantum tunneling.

Some general remarks:

The very fact that atoms form covalent bonds so that macromolecules such as proteins can exist cannot be accounted for in terms of classical mechanics.

But of course that is not the thrust of your question.
Many of the interactions between proteins and between proteins and other (smaller) molecules can be accounted for in terms of electrostatic force in one way or another, so all of that can be understood in terms of classical mechanics. That is, if you take as granted that atoms can bond to each other and form molecules, and you take the properties of those bonds as a given, then from that level on things can be accounted for in terms of classical mechanics

In that sense the usual form of enzymes facilitating chemical reactions can be understood in terms of classical mechanics. (But as I noted, it has been proposed that in some cases the reaction involves quantum tunneling.)

About size:
The size of the molecules is in itself not a factor. When molecules are in touch with each other then the areas of touch are small, the size of atoms, and it is at the areas of touch that anything chemical occurs


It has dawned on me that I misunderstood your question.

Given how I understand your question now I assert: the physics of quantum mechanics is a phenomenon in itself. The fact that atoms can exist arises from the nature of the phenomenon of quantum physics. The interactions of proteins with other molecules is quantummechanical in nature, just as anna v wrote.

To explain what I had in mind while writing the first version of my answer let me present a comparison.

Among the oldest scientific insights is Archimedes' principle. Archimedes principle is a forever principle because it does not depend on the nature of water on, say, the size scale of atoms.

Archimedes' principle holds good independent of whether fluids are a continuum or that fluids consist of separate molecules.

There are insights in the nature of things that remain valid even when there is a revolution in the scientific understanding.

The realisation that all matter consists of atoms was a revolution in physics understanding, but that revolution didn't affect the validity of Archimedes' principle.

Now let's take for example statistical mechanics. The development of statistical mechanics to a high level was before the introduction of quantum mechanics. Similar to the example of Archimides' principle: after the development of the science of quantum mechanics the understanding of Nature provided by the science of statistical mechanics remained as valid as before.

An example of before/after difference:
Statistical mechanics takes the sizes and interaction properties of the various atoms as a given, and takes it from there. In terms of quantum mechanics it is possible to account for the sizes and interaction properties of atoms in terms of the distribution of electrons around the nucleus.

So that is how I took your question while writing the first version of my answer

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  • $\begingroup$ Thanks for the reply. So, even if we go down to the scale of small molecules (let's say like ATP), the interactions between ATP and a protein can still be understood using classical mechanics, and quantum effects only play a significant role for some interactions (like the tunneling you mentioned)? $\endgroup$ – F16Falcon Oct 13 at 14:05
  • $\begingroup$ Your comment makes it clear that I had misunderstood your question. I have added a discussion, it starts with making the same assertion as in the answer by anna v. $\endgroup$ – Cleonis Oct 13 at 15:57

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