Exploring "Spin" in Molecular Biology and Physics

[CYP450]

So my main area of research is molecular biology and biochemistry, but nuclear and particle physics frequently manages to find its way in it and it's always baffling to me.

I've been participating in research on bacterial Cytochrome P450 enzymes; they catalyze the oxidation of organic substrates. There are a lot of redox partners, cofactors and sometimes secondary substrates involved, but the overall reaction is...

RH + O₂ + 2H⁺ + 2^e-→ ROH + H₂O

They're identified by the change in their absorbance spectra when CO binds to them. The reason that this happens, according to a lot of research journals I've read, is because Cytochrome P450's contain a ferrous heme group (like blood hemoglobin). When the iron is unbound, it is in a "high spin state" and absorbs light at 420 nm. When CO is bound to the iron, it goes into a "low spin state" and absorbs light at 450 nm.

I get the principles of absorbance spectra but "spin states" is beyond my understanding.

Anyway, you can also identify the reaction products by their Proton Nuclear Magnetic Resonance spectra. You store the reaction product in extremely cold temperatures, apply a strong magnetic field and the protons adjust their "spin" either parallel or antiparellel. Then you apply radio waves and all the protons "spin-flip" and send back an echo of lower frequency. Each chemical has a unique profile for the signals you get back.

I can read NMR spectra and interpret chemical structures from them, but I really don't understand the principles of "spin" and "spin flips." My orgo and biochem books don't really explain. They just say that "spin" has no real analogue in familiar, everyday mechanics or classical physics; that the closest concept is angular momentum, but that even that is a far cry.

Can someone please explain what "spin" is? Why does an iron atom have a "high spin state" when it's unbound to CO but a "low spin state" when CO is bound? Why do protons' spins align parallel or antiparallel in a B-field but "spin-flip" and echo when radiowaves are applied?

 

[kurros]

Phew, well there is quite a lot in there to talk about so we will have to keep it simple due to time constraints :).

First, spin. You are doing biochemistry so surely that involves regular chemistry and surely someone explained some basic things about spin to you in the course of that, otherwise the periodic table could not make any sense to you. So I will assume that you know about the Pauli exclusion principle, and that electrons are spin 1/2 particles and so they only have two allowed spin states (relative some specified measurement direction), and that in an atom you are therefore allowed to have two electrons in every orbital (where each orbital is characterised by a principle quantum number and an orbital angular momentum quantum number), and that you therefore understand what I mean if I say that the shell structure of an isolated, neutral iron atom is [Ar] 3d6 4s2. We will then be in a position to tackle this question:

When the iron is unbound, it is in a "high spin state" and absorbs light at 420 nm. When CO is bound to the iron, it goes into a "low spin state" and absorbs light at 450 nm.

I do not know the specifics of the compound you are talking about, but I think I understand the general phenomenon you speak of. It has to do with the relative energy levels of the 3d6 and 4s2 sub-shells and a phenomenon called "crystal field splitting", at least in the context I know it. The idea is this: the 3d sub-shell contains 5 orbitals (because the d subshell has orbital angular mometum L=2 and, well this is quantum mechanics so let's skip it for now) and so is allowed up to 10 electrons, however we can see from the configuration [Ar] 3d6 4s2 that it seems to have stopped at 6 and started filling up the 4s shell instead. This is because the 3d and 4s sub-shells are very close in energy. Now, if you recall that we can fit 10 electrons in 5 orbitals because we stick one of each allowed spin state into each orbital, and you consider that there is an energy cost associated with sticking two electrons in the one orbital, then you will accept that a half-filled 3d shell is a particularly stable sort of thing (because we have one electron in each orbital, and no pairing). It so happens that, even though the 4s shell is a higher energy shell than the 3d, the cost of pairing up electrons in the 3d shell is actually more than filling the 4s shell, so the next two electrons go there. 4p is higher energy still, so the final electron needed to make a neutral iron atom goes into the 3d shell, giving the final 3d6 4s2 structure. If I remember correctly anyway. At least the story is something close to that.

Now, if you have all these un-paired electrons floating about in the neutral iron atom (there would be 4 there, since one of the 5 3d orbitals was forced to pair up) then you have a "high-spin" state, because the spins of all those un-paired electrons don't cancel out with any spins pointing in the opposite direction as with the paired electrons. So the total spin would be 2 in this case (4 * 1/2).

Next things get trickier. When you bind your iron into some compound, the energy of the outer orbitals get all screwed up because of the presence of the nearby electrons in the other atoms of your compound. So the way the electrons are spread about in the 3d and 4s orbitals changes (aside from whatever ones you gain or lose or share due to chemical bonding), because suddenly some of the 3d subshells take more energy to fill than others and also the 4s subshell. The details of this vary greatly between compounds. So your starting compound will have its outer electrons arranged one way, and the final compound will have them arranged some different way. If the final compound has more of its electrons paired up than the inital compound then it will have a lower total spin, i.e. your "low spin" state.

The details of whether you get a low or high spin state depend on how much of an energy difference is induced between the various subshells of the 3d orbital. I think you generally get a low spin state if this gap is large so that it is favourable to pair up the electrons rather than try to fill the higher energy sub-shells, and conversly high spin if all the 3d orbitals are close enough in energy that it is favourable to keep the electrons un-paired as much as possible.

Of course all this messing about with the shell structure of your iron atom is going to mess with its absorbance spectra, so this is why you get a difference. Anyway, here is a wikipedia link to some of this: http://en.wikipedia.org/wiki/Crystal_field_theory#High-spin_and_low-spin

As for the NMR, this is related to the spins of the nuclei in your compound, not the spins of the electrons, but I have already written too much so perhaps we'll get back to that another time.

 

[CYP450]

Phew, well there is quite a lot in there to talk about so we will have to keep it simple due to time constraints :).

First, spin. You are doing biochemistry so surely that involves regular chemistry and surely someone explained some basic things about spin to you in the course of that, otherwise the periodic table could not make any sense to you.

We only learned the periodic table in terms of the number of protons, neutrons and electrons in each element; spin was never really discussed.

The first and only time spin was brought up in my entire curriculum was in Organic Chemistry, when bonding was described as electron pairing in orbitals with each having a "spin up" e^- and a "spin down" e^-.

But like I said, this was hard to grasp; how can you say a particle is spinning "up" or "down" if all frames of reference in the universe are valid? For example, why can't I take a "spin up" e^-, flip it over and call it "spin down?" If I were looking at an e^- out in space with no frames of reference around me, how could I possibly know it's spin direction?

Then again, I suspect "up" and "down" are figurative terms. Or are they?

 

[Mike H]

"Spin-up" and "spin-down" are conventions intended to reference the energetics of adding an electron to an orbital. If you have an electron and an empty orbital, that electron is "spin-up" since it's the first in and there is no electron already occupying that orbital. If you need to put another electron in that orbital, it's "spin-down."

Fortunately (or unfortunately), I happen to know a bit about NMR and cytochrome P450. The typically accepted P450 catalytic cycle starts with the enzyme in a "resting state" - the heme iron is in a ferric (Fe³⁺) state, it is axially coordinated by a water molecule (its other coordination sites are the nitrogens from the porphyrin group and the ligating cysteine from the protein), and no substrate is bound. This is a low-spin state - the effect of the coordination environment is such that there is a very large gap between the d-orbital energies, and they will pair up before going to the higher-energy orbitals. So of the five d electrons, four are paired and you have one unpaired electron. This is observed by the Soret peak at ~ 420 nm in a spectrophotometric experiment. The conventional wisdom is when the substrate binds, the iron remains in a ferric state, the water molecule is displaced and expunged, and it switches to a high-spin state. This change in its coordination environment - losing its water molecule - makes the gap between d orbitals smaller in the heme iron, and it becomes energetically favorable for the electrons to break up. Now, all five electrons are unpaired. This is indicated by the shift of the Soret peak to ~ 390 nm. Upon the initial one-electron reduction, the heme iron is now a ferrous (Fe²⁺) high-spin complex. The addition of CO creates the ferrous diamagnetic complex which has its Soret peak at 450 nm (giving rise to the P450 name). In essence, all we're doing is keeping track whether or not the electrons are pairing up depending on the coordination environment of the heme iron.

Insofar as NMR, what one is looking at are the magnetic moments caused by the intrinsic nuclear angular momentum, aka its "spin." For the purposes of NMR, we can pretend that they are little bar magnets, and our job is to make them dance so we can figure out structure and dynamics at a molecular level. For protons, it's pretty straightforward - you put them in a magnetic field, and the large static magnetic field "splits" them - they can either align parallel or antiparallel to the magnetic field. The ones that align parallel are the "spin-up" protons and the ones that align antiparallel are "spin-down." (This idea only really works this cleanly for protons and other spin-1/2 nuclei - there are nuclei which, when you put them in a magnetic field, will split into multiple energy levels. This straightforward picture does not work for them, and dealing with them quantitatively can be fairly laborious.)

In both cases, one is dealing with a particle's intrinsic angular momentum. For the coordination chemistry aspect, one is dealing with electrons and whether or not they pair up depending on the metal's coordination environment. For the NMR aspect, one is dealing with atomic nuclei and the associated magnetic moments. I don't know how much additional detail you need, but I can recommend certain reviews which are probably more appropriate than trying to rehash their arguments in an overly truncated form here.