 So, till now we considered two dimensional NMR experiments of different times, J correlated spectroscopy. We discussed a couple of those examples, COSY, double quantum filtered COSY, TOXY, J scaling, omega 1 decoupled COSY or also called constant time COSY. All of them were based on transfer of information on the basis of J coupling. The mixing used the J coupling information to transfer information from one spin to another spin. So, now we will look at another kind of transfer process which is based on the dipolar interaction. The dipolar interaction leads to what we call as nuclear overhouser effect and that is the NOE, NOE correlated spectroscopy or briefly this is written as NOZ. It is also called as exchange spectroscopy, it is also called as exchange spectroscopy because the mechanism of transfer although it is through exchange the appearance of the peaks will be the same, exchange spectroscopy and this is called as XC. The spectra appear in the same manner, the pulse sequence is the same for both and you can both kinds of information in this spectra. By and large it is the NOZE which is used for structural purposes, for large molecules or even small molecules, for identification and exchange spectroscopy is limited to those situations where there is actually chemical exchange. Chemical exchange between two confirmations that happens and you will see peaks occurring because of the exchange process. Now, so how does this work? This is a pulse sequence indicated here. You have the first a 90 degree pulse here, another 90 and a third 90. There are three 90 degree pulses here just like in the COSY we had two 90 degree pulses 90 beta or something, double quantum filtered COSY also has three pulses but now we have a particular time period called as the mixing period. You start the pulse sequence with a 90 degree pulse which creates a transverse magnetization and after the transverse magnetization evolves during the period T1. It is frequency labeled with the particular frequency whatever is the frequency that is present. So for example, if I want to trans start with the magnetization of the K-spin with the IKZ so then if I apply 90 degree pulse I will generate transverse magnetization of the K-spin here and this will be I will call it as IKY or something and then this will evolve during the period T1 with this characteristic frequency which is omega K. Now the second 90 degree pulse what it does it is adjusted in such a way that you select from the various kinds of coherences that will come. We discussed the various types of coherences in the last class previous classes that we had the Z magnetization, double quantum filtered coherences, transverse magnetization, single quantum coherences all of those things we discussed but what we will do here is we will adjust these two 90 degree pulses their phases in such a way that at this point I will have the IKZ back again but with a negative sign. So it is an inverted Z magnetization of the K-spin. We start with the equilibrium magnetization of the K-spin and now I will at the end of this I will second 90 degree pulse I will have the Z magnetization of the K-spin but now it carries with it the frequency label because of the evolution during the period T1. Now during this period tau mix there is relaxation happening. The relaxation what does it do it transfers magnetization between two spins. Now if there is a L-spin which is close to the K-spin in space so that it can interact through dipolar interactions between the spins then it will transfer part of the magnetization here to the L-spin. So we will get some amount of L-spin here to the Z component I will get little bit of the LZ so Z magnetization of the L-spin I will get. So therefore during the mixing time what happens I will have IKZ transferred to ILZ partly not entirely partly it is transferred there will also be little bit of the IKZ left. So then when I apply the last 90 degree pulse then both is IKZ and ILZ will get converted into transfers magnetization. So I will get after the last 90 degree pulse I will have both IKY plus ILY both the transfer magnetization components will be present and these ones this will evolve in T2 with the characteristic frequency omega L this will evolve with the characteristic frequency omega K during the T2 period. Therefore IKZ in the T1 period I have the frequency omega K therefore what I will have in the T1 period I have omega K and in the T2 period I have mixture of omega K plus omega L and this transfer has happened through the dipolar interaction or the exchange process. So therefore the two dimensional spectrum therefore will represent the transfer process. So here this is indicated in a more explicit manner so we have the nosy you start with the relaxation delay here so you may do something saturation whatever something here that is for proton saturation or whatever something in the preparation period. So you have this 90 T1 90 and this mixing time tau m is indicated by D8 and the third 90 degree pulse and after that you collect the data as a function of time T2 therefore two dimensional Fourier transformation will produce peaks with diagonal this is the diagonal here in this spectrum and we have this cross peaks here these are the cross peaks and these ones will appear either because of the dipolar interaction or because of the exchange process between the two sides. So suppose these two sides are A and B suppose this where this site is called as A and this site is called as B and if there is an exchange between A and B then you will see a cross peak between these two you have the diagonal and also you will have the cross peak. Now depending upon whether the motion inside the solution is fast or slow this kind of a NOE which is there will have a positive and negative signs this we have seen before the NOE can be positive or negative when it is positive when omega tau c is much smaller than 1 when omega tau c is much smaller than 1 then I will have a positive NOE and when it is much larger than 1 that will be negative NOE and what is omega? Omega is the spectrometer frequency and tau c is the correlation time. So notice this is tau c here okay tau c this is correlation time if this is very very large which is the case in case of large molecules then you will have omega tau c much larger than 1 but in small molecules where the tau c is very small of the order of 10 to the minus 10 to 10 to the minus 12 whereas in large molecules it is of the order of 10 to the minus 8, 10 to the minus 9 in such situations you will have two different signs for the NOEs this we have seen okay. So here you will have positive NOEs positive NOE and here we will have negative NOE and how does this reflect in the 2D spectrum in the 2D spectrum you see here you will have both the cross peaks and the diagonal peaks appear within the same sign. So they will appear on both they are like this is up this is also up on the same side of the plane whereas if this is positive NOE you will see that these ones are appearing on the negative side these are going down they are going below the plane these peaks are going below the plane that is why it is looking like this these are the diagonal peaks and these ones going down the plane and those that is an indication that whether it a molecule is small molecule or a large molecule this is extremely important because directly you can distinguish whether it is very rapid motion in a small molecule or in the large molecule also there is a certain segment which is extremely rapidly moving almost behaving like a small molecule then you can distinguish these different kinds of NOEs in the same spectrum. So this is an extremely important parameter and now what does this intensity of the cross peak depend upon here the intensity of the cross peak first of all depends on the mixing time here intensity will depend upon is proportional to 1 mixing time which is the tau m and it will depend upon the T1 which is the spin lattice relaxation time longitude and relaxation time of the molecule of the particular spin which you are considering and then it will also depend upon the spectrometer frequency omega naught because omega naught tau c can be larger or smaller depending upon the spectrometer frequency as well and then in the case of exchange then you will have the exchange phenomena exchange rates exchange rates dipolar interaction will be will be the driving factor for the NOE and for the in the where there is exchange happening it is a transfer of magnetization through the exchange process which results in the cross peaks. So from the point of view of structural biology both are important and by and large for structure determination of large molecules it is the NOE which is extremely useful. Here I will give a little bit of an example of taking a small dipeptide segment what do we have here? So I have here a peptide this is NH C alpha CO this is one residue called as a residue I and this is the residue valine see here CH alpha CH beta and the two gamma mythiles. So this is the valine residue and then the next residue starts here this is the NH of the next residue then the C alpha of the I plus 1 and CO. So NH C alpha CO this is the residue I plus 1 NH C alpha CO this is the residue I. Now the dipolar interaction as we said that depends upon the in or the NOE NOE is proportional to NOE is proportional to 1 over Rij to the power 6. So this is Rij is the distance between the two protons. So wherever the distance is small you expect to see a cross peak that is indicated here. So if you see here you see this is a short distance from one residue to the previous residue alpha alpha proton and the amide proton to the beta proton of the previous residue and also from the amide proton to the CH3 protons of the previous residue in the case of this is the valine and these ones are less than 5 angstroms. So you will see NOE if the distance is less than 5 angstroms. So therefore less than 5 angstroms is typically what one observes. If the distance is 2.5 angstroms of course NOE will be stronger because of the transfer process will be more and the interaction will be more and therefore the intensity will be more. Therefore the intensity is proportional to the inverse 6 power of the distance which means the shorter the distance stronger is the peak. Now of course it cannot go beyond below 2.4 angstroms or something like that because why then there is a steric clash. No 2 atoms can come closer than 2.4, 2.5 angstroms depending upon the atom times. If you are taking protons of course you cannot have it less than 2.3, 2.4 if that is because there will be a steric clash such confirmations will not occur. So and then you start calculating which are the distances which are small in the given particular dipeptide segment. Of course you will have the short distances between here as well this NH proton to this alpha this NH proton to this beta also you will see but these ones you will see in the cosy spectrum as well. In the cosy spectrum these are all J couple therefore we will see NH to the H alpha. Of course you do not see NH to the H beta in the cosy spectrum. You will see H alpha to the H beta and H beta to the CH3 and CH3 this CH3 will see in the cosy spectrum. In the nosy spectrum you will see from NH to this C alpha H this is also a short distance. So approximately 3 through 3.5 angstroms you will see this. Now if you look at these distances calculate these distances of course it will depend upon the dihedral angles various dihedral angles in the dipeptide. So you will have the helical protein or beta sheet protein these dihedral angles can be different. So but there is a certain range of variation of all these distances. In every case this distance no matter what the dihedral angle combinations are dihedral angles are the phi and the psi of the Ramachandran plot. Phi psi are the Ramachandran plots and those ones are responsible for the variations in the conformations of the peptides or the dipeptide. So that can range from 3.5 to 5 angstroms these distances can vary. So therefore this you will always see these peaks but with more or more intensity or less intensity depending upon whether it is alpha kind of a structure or the beta kind of a structure you will see these peaks. And there will be intensity variations which will be extremely useful for structure calculations. Let me see how this can be used for your sequence specific assignments of the individual protons. This is an extremely important experiment. You use the COSY and the NOZI together or the rubble counter filtered COSY and the NOZI together to obtain resonance assignments in proteins. This is a segment which will continue like this. The COSY let me repeat here COSY will show you cross peak from the NH to the alpha and then from alpha to the beta and beta to the 2 methyl's. And the COSY will also and the NOZI will show you from the NH to this it may show from here to here it may also show from here to here it can show those. In addition all these are all within the same residue all these are within the same residue. Now in addition in the NOZI you will also see correlations from the NH of I plus 1 residue to the alpha to the beta and the gamma methyl's of the ith residue the previous residue. Notice you do not see it to the next residue not to the I plus 2 therefore there is a directionality involved here. So you will always go residue to the previous residue NH amide proton to the alpha beta and also NH NH this also will be seen. This distance also will be available that is typically in the alpha helices you will see that distance as well. So you have all these distance is available in the NOZI spectrum therefore if you look at this spectrum schematic spectrum here I have here the diagonal the diagonal has the NH proton of residue I and the NH of residue I plus 1 at this point. And then have here the alpha proton of residue I because you look at the color look at the colors. So I am talking about this valine residue this cyan color is reflecting the valine residue. So all these cyan ones are the correlations from the valine residue. So you will see the NH proton of residue I to the alpha proton of residue I that is this peak here. This will also be seen in the COSY. Now from this NH proton you will see to this proton which is the beta of the same residue and also to the two methyl of the same residue those ones are this to this and this to these two you will see those peak they are all filled cyan peaks. Now let us see from the NH of I plus 1 NH of I plus 1 I see to this same fellow here that is this to this that is this peak here and I will also see to this one here you see from this to this and then to the two methyl from these to these two methyl gamma 1 and gamma 2. So these are extremely useful sequential information sequential connectivity we call the sequential connectivity. Now what are these here? Now you also have some other things here what are these here unfilled peaks these obviously we belong to the alpha beta of the NH of I plus 1 residue of I plus 1 these ones belong to the alpha of the I plus 1 residue these ones belong to the betas of the I plus 1 residue they will also show up and what are this green ones here these green ones are the sequential peaks from the residue I to residue I minus 1 they will go to residue I minus 1 this is the alpha of I minus 1 and these are the beta or the gamma or whatever of residue I minus 1. Therefore you see you can start from the NH of I plus 1 you go to the alpha and then you come to the NH of I then from this NH of I you go to the alpha of I minus 1 go horizontal find out where its own self peak is present therefore you can walk along the polypeptide chain in this manner. You can do that using the alpha proton or you can also do that using the beta protons from the NH of I plus 1 you go here you go to the beta proton of residue I I from the NH of I plus 1 to residue I that is the beta then you go here so it is the self peak we call this as the self peak of residue NH I to its own beta then from here you come down to the beta of residue I minus 1 either here or the top then from here you can go further to the residue I minus I minus 1 either it will be this way or this way wherever that NH proton of I minus 1 is present. So therefore in this manner you will see sequential connectivities from the NH of I to all of those you also will see here the alpha to the beta which is the peak which is present in the cosy this peak is present in the cosy and now you will see in addition to this peak you will also see alpha to the gamma and the gamma 1 and gamma 2. Therefore the nosy has lot more information than the cosy however the cosy helps you to figure out which are the piece which are belonging to the same amino acid residue and which are not sequential residues you can go from one residue to another residue using the nosy you cannot go from one residue to another residue using the cosy spectrum. So therefore this is an extremely important experiment for from the structural biology point of view. So this is so far as the near neighbor interaction let us look at a typical spectrum of a protein but this is one of the very early experiment of on a protein this is not was such a wonderful great experiment but nevertheless it is such a very early experiment and therefore it is extremely important to show this one and today spectra of course they are much more crowded we will see some of those examples as you go further. Now what you see here this is a spectrum of a protein and you see here the diagonal which is the one dimensional spectrum and you see whole lot of peaks all around and these ones belong to those some of those examples which are explained to you i to i minus 1 i minus i plus 1 to i i to i minus 1 and so the sequential peaks but in addition you will also see some peaks which are not sequential sequential means not the near neighbor why does that happen consider a polypeptide chain which is like this suppose you have a polypeptide chain which is like this and you are considering the protons A B C and D . The A proton has a diagonal peak here the B proton has a diagonal peak there the C proton has a diagonal peak here and the D proton has a diagonal peak here ok. Now suppose the polypeptide chain this is a big polypeptide chain. Suppose the polypeptide chain force like this if the polypeptide folds like this. What happens now? You see the two end ones have come close. That is the A and the D have come close here. This is a short distance. Therefore then I will see a cross peak between A and D. Between A and D I will see a cross peak. These are long range peaks. Suppose the polypropane chain folds like this. Then which ones are coming close? Let us say this is A, B, C and D. Now C and D are coming close. If C and D are coming close less than 5 angstroms then you will see a cross peak between these two. That is the C and D. C and D you may see a cross peak between these two. On the other hand if it folds like this then it is the two central ones the B and C are coming close and that will show up in this here as a peak. Therefore you see in not only the sequential peaks from one residue to the neighbouring residue you will also see long range peaks depending upon the nature of the fold of the polypropane chain. This is an enormously important information. So therefore the nosy spectrum is called as the fingerprint of the structure of the molecule. So therefore this is called fingerprint of the structure. And now all of these peaks which you are seeing here these ones do not have the same intensities as you can see. These ones having different intensities. Some are weak and some are strong and why does that happen? Because the distances between the various pairs of protons are varying. Some are 2.5 angstroms, some are 3.5 angstroms, some are 4, 5, 6 things like that and then you will see strong peaks when the distance is short and you will see weak peak when the distance is large. Therefore now you can use this information. You can use this information quantitatively. You give a certain range of the distance. Let us say a particular peak on the basis of the intensity you classify the intensity here the distance range to be 2.5 to 3.5 or 3.5 to 4.5 or 4 to 5. So you can classify the peak intensities and in terms of the distances and then you try to build a model. Build a model of the protein and see that you get a structure which is consistent with all those peak intensities which you are giving. This has been the basis of structure determination of biological macromolecules whether it is protein or nucleic acids or carbohydrates or whatever it is it does not matter. So in every case you will see such kind of peaks. Of course the information is quite enormous. Not easy to extract all of this information because there are things which are very close to the diagonal and they are not easy to extract. Once which are far away from the diagonal and this typically will happen when you are considering from the amide protons to the aliphatic protons. Also from the aromatic protons. You also have the aromatic protons in this area. From 6 to 7.5 you will have the aromatic protons. Aromatic ring protons will show cross peaks to so many other protons along the polypeptide chain and you will see those cross peaks at well. So typically you may get like 1000 to 2000 such kind of peaks in the protein spectrum and you will be able to calculate the structure of the molecule on the basis of this distance information. So that is so far as proton-proton correlations are concerned. We talked about proton-proton correlations. We have the diagonal and we have the cross peaks. Now we go over to a further class of experiments which are called as heteronuclear experiments. Heteronuclear experiments let me write here. Heteronuclear correlations. Heteronuclear correlations Why are these important? These are important because the proton spectra can become very crowded. When the proton spectra are very crowded, proton spectra are very crowded. And secondly we have strong diagonal peaks in proton spectra, in proton-proton spectra. But information which you are using is only the cross peak information. The cross peak information is what we want. So therefore can we limit this only to the cross peaks? Surely you can limit it. In the proton-proton spectroscopy also it is possible to do it. But it is much more easier to do it in the case of heteronuclear correlations because you have information between proton and some ex-nucleus correlation. And this is one of the most important experiment which is called as heteronuclear single quantum coherence. There are several other methods, several other possibilities. But the most commonly used is the heteronuclear single quantum coherence. And this can have the heteronucleus can be the carbon-13 or the nitrogen-15, whatever. So depending upon the need one can do these different kinds of experiments. Of course if you are working with proteins, typically it may require the enrichment of this ex-nucleus. Typically you have C12. Now if you want to get a spectrum of such kind of correlations, you need to produce C13-labeled proteins or N15-labeled proteins. And fortunately this thing is now easily possible thanks to molecular biologists. So we have possibilities of producing the proteins and other things inside the cells where the cell itself will incorporate C13 and nitrogen-15 in your protein chains. So this bacteria can do this job for you and then you actually isolate the protein and do the correlation experiments using proton and ex-nucleus. So we will continue this in the next class.