NMR Nuclear Magnetic Resonance

NMR Nuclear Magnetic Resonance Nuclear magnetic resonance (NMR) is an effect whereby magnetic nuclei in a magnetic field absorb and re-emit electromagnetic (EM) energy. This energy is at a specific resonance frequency which depends on the strength of the magnetic field and other factors. This allows the observation of specific quantum mechanical magnetic properties of an atomic nucleus.

NMR Gives dynamic information on a protein that a crystal doesn t Certain nuclei possess a property known as spin Spin refers to the nuclear spin angular momentum which is purely quantum mechanical property that has no classical analog. It s represented by I = spin quantum number. DO NOT PANIC WE ARE NOT GOING TO DO ANY QUANTUM MECHANICS

3 classes of nuclei: 1.Nuclei with odd mass number have ½integral spin (I=1/2) 2.Nuclei with even mass numbers and an even charge have no spin (I=0). 12 C, NMR inactive why Is this a problem? 3.Nuclei with even mass numbers and odd charge have integral spin. 14 N, broad lines..why is this a problem? Category 1 is the most used in NMR because I = ½and can use 1 H, 13 C, 15 N (we ll talk more about this later)

What does I = ½mean? Well, a nucleus can orient itself in 2I + 1 ways when placed in a magnetic field 2I + 1, I = ½= 2 2 nuclear orientations so 2 possible nuclear energy states If we represent these orientations as vectors what we can say is that in the absence of any external force or field, these 2 orientations are identical and have the same energy you can t tell them apart. But what happens if you introduce an external magnetic field? Of size B o? E E β α Energy states separate out with introduction of external magnetic field No field

The energy difference E = h ν (normal spectroscopy) can flip between states at different energy levels We can see that the stronger B o (ext field) then the further apart these energy levels so E α B o. The larger the field the larger the separation. h = planck s constant E = h γ Bo γ = some constant B o = magnetic field γ = magnetogyric ratio tells you how receptive a nucleus is to doing NMR

So essentially if we could cause a transition between the states this would be some sort of spectroscopy The frequency required to induce such transitions is in the MHz range radiofrequency referred to as RF From a basic standpoint if you put in RF at the appropriate MHz frequency then you will induce such a transition E E β α This is the basic unit of NMR phenomenon

γ H = 4 γ C γ H = 10 γ N Sensitivity also depends on natural abundance 1 H vs. 13 C = 100:1 So you would imagine H vs. 13 C is 400 (4x100)times better at natural abundance and 2700 (10x99.98/0.37)times better than 15 N

It turns out for a variety of complex reasons that NMR is not like other types of spectroscopy (eg. UV) If you fire in a photon with the right RF frequency to cause a transition from α to β β α then this states lifetime is so short that we can t see it The upshot of this is that we can t get an NMR signal from just one nucleus. We need BILLIONS of nuclei to get an NMR signal. We measure something called coherence.

The billions of nuclei all act together when we put in a radiofrequency (RF) pulse Setting up what is essentially a COHERENT effect between the α and β states. β Billions this coherence (like constructive interference) α oscillates at the frequency between the 2 levels and last for seconds So we put a billion nuclei into a magnetic field, separate the nuclear energy states and cause a coherence to be set up that we can detect at the specific frequency between those 2 levels. Any problem? YES of course there is, isn t there always?

The levels are very close in energy ~ 1 in 10 5 nuclei prefer to go in α rather than β β E α The distribution of population between the α and β states is given by the Boltzmann equation. E α B o Therefore, more go into α state as the external field gets bigger. Makes experiment more sensitive. But it s still small very sensitive technique

Make our protein express, purify, search for conditions Then put it in a magnet

Place current in coil and then cool. The electrons move forever because made a super conductive wire by keeping temperature at 4 Kelvin. There is no resistance in the wire.

Here s another problem: So, RF gets delivered and hits the nuclei coherence is set up and detected If there was only 1 nuclear type then 1 signal at one frequency easy to see

Here s another problem: So, RF gets delivered and hits the nuclei coherence is set up and detected If there was only 1 nuclear type then 1 signal at one frequency easy to see H2 hydrophobic core H3 cavity environments H1 outside 3 types different electronic The different electronic environments shield them to different extents from the main B o field.

So, if they have different B o responses then they have different E s and so different frequencies 3 different frequencies from 3 different environments All superimposed not easy to see 30 Hz 10 Hz H 1 = 10Hz H 2 = 20 Hz H 3 = 30 Hz 20 Hz All superimposed not easy to see More shielded proton the lower the frequency

Take the oscillating waves Fourier transform them get their frequencies 30 20 10 Chemical Shift Differences So each 1 H in a different environment has a different chemical shift property a nucleus possesses which is dependent on its electron environment. More electrons the more shielded from main field so will have different chemical shift then a lesser shielded electron. Normally measured in PPM We also notice some fine structure here. What s that?

Fine structure H A H B electrons C C Electrons from H A H B and vice versa so H A knows about H B and knows if it s in it s α or β state can be either so H A sees H α B and H β B Produces 2 lines at H A frequency Similarly H B sees H αa and H βa 2 lines at H B The two lines split by same amount and next to each in protein structure J J J = Scalar Coupling in Hz H A H B Why lines are split Thru bond interactions

The big point: we can connect nuclei that are adjacent in the structure via interactions involving electrons. We will find out shortly that we can perform experiments that essentially take magnetization from one nucleus and are able to pass it to an adjacent nucleus (connected through bonds/electrons). By doing this, we can connect the two structurally adjacent nuclei.

Scalar Coupling is through bond interaction So if we see scalar coupling we know that 2 nuclei are next to each other through bonds. Chemical shift structure info different positions on a molecule Scalar coupling structure info through bond connections There is one other type of interaction that is very, very important Not close in bonds (no H A H B scalar coupling) But close in space < 5A They can sense each other s presence as the molecule tumbles. Their dipoles are coupled Dipolar coupling through space interaction less than 5 Angstroms apart

This through space dipolar coupling interaction produces an effect known as the Nuclear Overhauser Enhancement (NOE) used to accurately determine distance Which allows us to very accurately monitor and calculate thru space distances. H H NOE @ a fixed distance. Use this as a reference More often we classify them as Weak Medium Strong ~5A 4 3/2 A 1 2 A

Helix (cis) H J / NOE H J small close in space and attached by bonds NOE Sheet (trans) C H C Use NOE and J to determine H structural positions in protein J big distance >5A Attached by bonds NO NOE C J / No NOE C H

Sequential NOE s will have unique scalar coupling 1 amino acid Peptide backbone No J between neighboring amino acids because no through bond protons present

So we can see different environments from chemical shifts, adjacent thru bond connections from scalar couplings and thru space interactions from dipolar couplings/ NOE Depending on the structure look @ all these possible thru space connections For a helix

What about helices next to each other? i i + 4 / 3 What about β strands / sheets? interhelix NOE between N H and N H across strand d NN No NOE between adjacent residues because too far NOE between adjacent reidues H H d α No d αn s on same residue No sequential d NN s if you see, there are interstrand

And turns. Adjacent residues Cross strand

So we can connect things accurately thru space to define different strands, sheets, helices and turns and their 3D position with respect to each other. Thru BOND scalar coupling connections are used to identify different amino acids. Each has a pretty unique coupling network. Will generate clearly different patterns So 1. identify amino acids using chemical shifts and scalar coupling patterns 2. (i) sequentially and (ii) 3 dimensionally arrange those amino acids by using NOE s This is called (i) sequential assignment (ii) structure generation

Sequential NOE s will have unique scalar coupling 1 amino acid Peptide backbone No J between neighboring amino acids because no through bond protons present

So if you say link 3 together you can find that run in the primary sequence and assign each resonance / peak to a specific proton in the protein. Ex. Amide of ALA32 βh of Leu 86 etc. If you have every peak assigned, then you can connect them all via NOE s 3D structure Scalar coupling use to ID the amino acids NOE s use for sequential ordering Problem The bigger the protein the more protons OVERLAP

One dimensional NMR: Do an RF pulse, collect data, Fourier Transform get spectrum Lotsofwordsalljumbledtogetherinonelineitsaproblemreadingthissohowtofixit Lots of words All jumbled together In one line It s a problem reading this So how to fix it

We have a lot of overlap in 1D spectra only one dimension to disperse info into H A C H B C Wouldn t it be great if we could transfer the magnetization of one nucleus, H A to H B (and vice verse)? So that in a spectrum we would have a peak H A and a peak H B But also a peak H A a peak H B > H B > H A Use the scalar coupling to transfer magnetization can we do this? Yes we can there are NMR experiments that can do this. Take magnetization on one nucleus and push some of it to the adjacent nucleus THROUGH BONDS.

Disperse the information into 2 dimensions. Do a special kind of experiment pulse the nuclei more than once collect lots of data. During the experiment we have some magnetization on HA and we push some onto HB. So magnetization is on BOTH nuclei during the experiment. Fourier Transform twice. Movement of frequencies goes both ways H A H B H B C C Establishes connectivities through bonds H A 2D Correlated Spectroscopy = COSY experiment Connects scalar coupled, through bond connected nuclei in 2 frequency dimensions. H A H B

2 dimensions gives you more resolution Each cross peak represents a connection thru bonds 2D Cosy Can t jump over C O bond (must have neighboring amino acids) because no protons to go thru

Examples of COSY patterns for amino acids. The strong resonances of the diagonal (large circles) give chemical shifts of indicated H atoms. Cross peaks give thru bond interactions.

Can you do this with dipolar thru space couplings? Send magnetization from one proton to another thru space? 2D NOESY Each cross peak represents a thru space connections from one proton to another (< 5A) Amount of peaks in line tells amount of stuff in a shell around a proton Closer to the stronger 1A Furthere apart the weaker 5A

We talked about only protons In proteins 12 C is dominant (99%) and 14 N too (approx 99.9%) Both these are INACTIVE NMR WISE useless 13 C and 15 N have I = ½ but have very low natural abundance can we do anything about that? Yes when you grow your proteins introduce 15 N via ammonium sulphate/chloride via glucose In growth medium 100% incorporation of 13 C and/or 15 N O H H O H 13 C 13 C 15 N 13 C 13 C 15 N 13 R 13 R Isotopically labeled and now NMR active except O We can pass magnetization anywhere via scalar coupling

NH correlation spectrum

No calcium With calcium

Methyl So in a C H group we can pass magnetization H C β α Looks fabulous but bigger proteins even make there 2D spectra look messy and overcrowded with peaks because more nuclei present 1D 2D 2D 3D?

We can combine experiments. NH Correlation spectrum + NOESY Pass magnetization from N to H(N) through bond and then from H(N) to all other H s within 5 angstroms. Do 3 FT s get a cube.think of it like pages in a book, each page with different information on it.

A peak belongs to what? The amide proton shifts about the same. But what if Nitrogens had different shifts? Could pull it apart. Step 3. Pull apart Step 2. Proton N chemical shift Step 1. NOSY Grey, black, and white dots 3 separate residue peaks

Proton NOSY spectrum Thru Bond Thru space

3D HNCA 1 peak that connect every NH and α C group Eventual goal using all these 3D experiments is to H N α C Assign every peak in every spectrum to a specific atom in the protein Know which peak is which proton 1 H ex. β proton of Ser 38 NH proton of Leu 94 etc. The use NOE s between pairs, to determine distance input this data in a program 3D Structure