 During the last several lectures, we have discussed in great detail a variety of two-dimensional NMR experiments. Various kinds of correlations have been discussed and we have seen how they will be helpful in determining structures of molecules in solution. One of the major applications of NMR has been to proteins. So therefore we will take forward from there to discuss the applications of NMR to proteins and we will see how protein NMR applications have revolutionized NMR itself. It has led to further developments in NMR than what we have discussed so far and that has been a feedback mechanism for NMR spectroscopy developments. So here I show you first a one-dimensional NMR spectrum of a protein. This is the protein called Lysozyme which is molecular weight of 15 kilo Dalton. It is made up of 130 amino acid residues and this is the one-dimensional so proton spectrum at 500 megahertz and you can see here this has a very well spread out spectrum. Peaks are there all the way from minus 1 ppm to 11 ppm and there are a large number of peaks. This protein has nearly 500 protons. So therefore and you should expect the complexity of this spectrum to be as seen here. There are a large number of resonances and one can only say from this one-dimensional spectrum that these belong to the amide protons and here you have the amide protons and the aromatic protons on the basis of the chemical shifts and these ones belong to the alpha protons to the beta protons and then you have the methyl shear and so on. But more than that you cannot tell anything about what peak belongs to what amino acid residue and what proton in amino acid residue and so on. To circumvent such problems we had to record a two-dimensional spectrum and this is the so-called two-dimensional nosy spectrum which we have discussed earlier. But look here this has thousands of peaks here. This actually reflects correlations between the various protons which are close by in space less than 5 angstroms distance and there are some which are 3 angstroms 4 angstroms 5 angstroms and things like that and the intensities will depend upon this distance. But this spectrum is also extremely complicated. We have so much of overlap of the cross peaks here and it is almost impossible to analyze this spectrum in great detail to identify the peaks as belonging to individual protons in the protein. So therefore this again posed a challenge. So as we went from one dimension to two dimensions in case of smaller molecules to remove the ambiguities and obtain assignments with that even the two-dimensional spectrum here is not adequate to obtain full assignments of the individual protons. So what do we do? So we have to use other strategies as we went from 1D to 2D now we can go to 3D and 4D and so on. How does that help? Let us look at that in a schematic manner here. This is the proton-proton spectrum schematically and you have the amide protons and then you have the other protons, aliphatic protons, aromatic protons etc etc here and at this particular one chemical shift along the proton resonance in the amide region you are seeing 10 peaks here which are obviously belonging to multiple amide protons. Obviously there are more than one amide protons here because one amide proton cannot produce so many cross peaks. So therefore we try and see how many are present here then you try and look at the heteronuclear correlation if they are between amides and the nitrogen. Let us do a amide nitrogen correlation here the amide proton the N15 correlation spectrum which we also discussed earlier and this is producing at this particular amide proton chemical shift three peaks which means there are three nitrogen at least at this position. So now what we do is make use of this N15 chemical shift and disperse these peaks along the third dimension as per the N15 chemical shift. So one of these belongs to this N15 chemical shift this plane belongs to this N15 chemical shift and this plane belongs to this N15 chemical shift. So the corresponding peaks are now distributed in these respective planes. So there are three peaks here at this N15 four peaks here and three peaks here. Whether there is any degeneracy here can we identify this further as to belonging to the particular protons we can remove this further degeneracy using a carbon 13 chemical shift. Now use carbon 13 chemical shift to disperse these peaks for example these four peaks on four different planes according to their different carbon chemical shifts because they are attached to different carbons but they are producing peaks at the particular N15 and are correlated to the amide proton at that chemical shift. So therefore you are now able to resolve the various aliphatic protons of the individual amino acid residues at least three amino acid residues here and they are distributed like this the same will happen for this plane as well and also for this plane as well. So all the 10 peaks will have proton N15 carbon 13 and amide proton chemical shifts uniquely identified. So this is a schematic the idea is you want to get to this. So therefore how do we do this three dimensional experiments? How do we do four dimensional experiments? So we will take as an illustration the three dimensional experiments. The idea is very simple it follows the same strategy as we did when we went from one dimension to a two dimensions. So the schematic of three dimensional NMR spectroscopy is indicated here. So here you have a preparation period which is common as in the case of 2D as well and here you have the evolution time T1 which is an incrementable time which produces one of the time variables and then you have the mixing to transform magnetization from this one period to the next period. Now in the case of 2D here we had the detection period we collected the data as a function of time and we produced a two dimensional spectrum after two dimensional Fourier transformation. In this case we will not collect the data here but we will treat this as another evolution time with the label T2 then we add another mixing period here called mix 2 and then transfer the magnetization from here to here and finally we have the detection period which is T3. We collected data as a function of time here and therefore this data which is collected will be modulated by what happens here and what happens here in independent manner. You systematically increment this T1 period you also increment this T2 period and for every one of those you collected data. So let us say to be more explicit for a particular value of T2 you collect some let us say 256 FIDs and then you increment the T2 collect another 256 FIDs increment again collect another 256 FIDs therefore you will generate a cube of FIDs here. So T1 is one variable here T2 is another variable here and the T3 is the third variable here. So you collect FIDs for independent variation of T1 and T2. Therefore you generate a three dimensional time domain data which we write as ST1, T2, T3. Now if you do a three dimensional Fourier transformation and you will get a three dimensional frequency domain spectrum SF1, F2, F3. So here is an example of a particular three spin system. Suppose you have a three spin system here A, B and C and those three spin systems are here indicated here their corresponding chemical shifts are at this point and then you will have correlations between each one of those. So the mixing transfers magnetization between each one of those. So and then if you have a two dimensional corresponding spectrum for a three spin system you will have nine peaks in the 2D correlation spectrum. So now if you have a the second mixing time then you establish correlations once more with all these nine peaks in the two dimensional spectrum. In the 2D spectrum we had a nine peaks for a three spin system of this type. Now when you have another evolution period establish correlations with those once more with those nine peaks you generate 27 peaks therefore you have in this 27 peaks in this the three dimensional spectrum all of them are separated and then by analyzing this you can follow the magnetization transfer pathway. So you see here these three nine peaks here and each of these produces the correlation to the other two each peak produces the correlation to the other two and therefore you from each of the nine peaks you will have a total of 27 peaks in your spectrum. This is in this particular case and suppose you have a linear system in that case of course you will not have a correlation from A to C in the normal two dimensional spectrum. So therefore the number of peaks will be somewhat less and still it is quite substantial here the two mixing periods are assumed to be the same. M1 is equal to M2 the two mixing periods are the same if it is a j correlation it is a j correlation but in principle you need not have the two mixing periods the same one of them may be j correlation other one may be I mean in this example this can be a j correlation or this can be NOE correlation this can be j correlation this can also be j correlation or this can be NOE correlation this can also be NOE correlation. So like that you can have different combinations of mixing sequences and that will produce different number of peaks in the individual spectrum. So here you have when M1 is not equal to M2 you will see much greater reduction in the number of peaks and it will be of course easier to analyze. So this of course becomes quite complicated to analyze but this one will be relatively easier to analyze in the three dimensional spectrum. So following this strategy a large number of pulse sequences have been generated for example here I have here a three dimensional cozy cozy pulse sequence that means the first mixing sequence uses a j correlation mixing and the second mixing is also a j correlation mixing therefore you have a three pulse experiment here this is a T1 increment then you have the mixing here and they have T2 increment another mixing here then you have a small period for some adjustments and then you acquire the data here at this point. So this is a cozy cozy and this is also a cozy cozy experiment except that here you have a selective pulse applied here it was a hard pulse this was a selective pulse applied here for particular group of protons spins and then you transfer from those particular group of spins to selectively to another group of spins and by j correlation and then they evolve here period and then it is transferred back to these protons to acquire the data. This is also a cozy cozy but then this is of course selective cozy selectively some peaks are excited here and some peaks are excited here and you observe correlations between only those ones. So you can make all such combinations here so therefore you generate a whole lot of experiments here is an experiment called as nosy cozy and you selectively excite a certain number of protons here and you transfer the magnetization to the z axis here and do a nosy mixing this is the nosy mixing. So after the nosy mixing you apply selective pulse once more transfer the magnetization to some other protons and then you do a T2 evolution you frequency label those ones and then you transfer the protons once more do a second mixing and then this is the j correlation mixing so therefore this becomes a nosy cozy experiment. So you have here the nosy mixing period then this pulse acts as the j correlation mixing or the cozy mixing therefore you will have the nosy cozy three dimensional experiment. So likewise you can also have the nosy toxy here homonuclear experiment this is the T1 evolution for the particular group of protons which are excited and then you have the nosy experiment here you do the same thing as before magnetization is kept on the z axis and then you do a nosy mixing and after that this is converted into the transverse magnetization and then you frequency label those after the nosy mixing you do a frequency labeling and then you do a toxy mixing. So this is the second mixing period you have the frequency labeling here then you have the second mixing period here and therefore and then you collect the data so this produce you say nosy toxy correlation. So correlation between f1 and f2 will be nosy and f2 and f3 will be toxy so therefore this will go in that manner. So you can do such kind of experiments various combinations are possible so you have nosy toxy here you have the hetero cozy cozy because invoke the heteronuclease here transfer to the heteronuclease and then they do a kind of an H2C type of experiment here T1 evolution here and transfer back to this is a proton and then you carry through some mixing period here and then you do a decoupling and this is the cozy mixing here. So this is homonuclear cozy experiment that will here it is a hetero experiment this is a hetero correlation after that it is a homonuclear correlation during this T2 evolution there is a homonuclear transfer from one proton spin to another proton spin and these top periods are required to convert anti phase into in phase and things like that. So all of those is thing which already discussed and we will not go into the further detail theoretical calculations here but the principles are the same so it is easy to follow by actually working out the product operators at the individual steps what are the product operators at various places why do we need the delays at various certain points and how one can proceed with this. So a large number of experiments have thus been developed and one can use it as per the need. A rough calculation here of the experimental time you have the measuring time of a 3D experiment this is not true for of course all the experiments this is typical numbers which you have put here depending upon what numbers you of course your data the time factor will be different. Suppose you do 256 T1 experiments and you do 512 T2 increments and you collect 1024 data points along the T3 for each one of those and assume that the acquisition time the FID length is 0.2 seconds and relaxation delay which is 1 second then suppose you do minimum of 4 scans typically one needs this to do phase cycling as I indicated to you earlier. If you want to filter out certain pathways and select certain pathways some number of scans will be required minimum and then of course you will have that sort of a minimum number of scans and you also use some dummy scans for the spin system to reach a steady state initially. So therefore if we calculate this time this works out to be 11 days and this is a huge amount of time therefore for the information you gain by dispersing the peaks in the three dimensions you certainly pay a price in terms of the machine time here if you do experiment in this manner. So but generally one is not doing this strategies one is adopting certain kind of a combinations of nuclei so that you do not need to do these many increments in each of these dimensions and then you will be able to save time. This is a particular advantage of heteronuclear experiments where you can actually choose a small section of the spectrum and collect the data in a rather less time. So here is one of the heteronuclear three-dimensional experiment which is called proton N15 Toxy HSQC. So the first mixing here is a Toxy mixing and the second mixing is the HSQC mixing. So this is the heteronuclear transfer the Toxy means it is a proton proton homonuclear transfer that is indicated here the experiment goes like this you have the first 90 degree pulse on the proton and you evolve it during the period T1 but you apply 180 degree pulse in the middle of the T1 period on the N15 channel. So as a result of this there will be no proton N15 coupling evolution this will decouple this 180 pulse decouples proton from N15 and you will have only proton-proton coupling evolution going on. Therefore you do a Toxy mixing of the proton-proton here from here to here. The Dipsy 2 is a Toxy mixing sequence these pulses are applied to flank this Dipsy this is the whole thing is a part of the Dipsy 2 mixing. So then after that you have transferred the proton magnetization from one spin to another spin among the proton coupling network and now you do a HSQC experiment from here to here it is a inept transfer from proton to the nitrogen 15 here then of course you need 180 degree pulses on both the channels at this point and this magnetization is transferred to the N15. Now here the magnetization is on N15 and this will evolve with the its characteristic frequencies and this time label is now T2 at the middle of this you have 180 degree pulse as in the case of normal HSQC. So you have only frequency labeling of the N15 nuclei here and then from here you transfer the magnetization back to the proton at this point and therefore now it is anti-phase magnetization of proton which is anti-phase with respect to the nitrogen and then during this tau 180 tau period you allow this anti-phase magnetization to refocus and you can collect the proton data here. You collect proton FIDs and when you are collecting this you can decouple the nitrogen 15. So this is the Toxy HSQC experiment. Similarly you can also do a nosy HSQC experiment. The nosy HSQC goes in the same manner here you have the proton magnetization excited here and then you have the evolution for labeling the proton frequencies and this is done once again to remove the proton nitrogen coupling. So this is only proton frequencies here and this now whole block from here to here will be the nosy part. So you have the nosy mixing therefore the transfer of magnetization happens from one proton to another proton because of nosy mixing and then you start your inept sequence from here onwards you actually transfer the magnetization to the nitrogen 15. So from this is the inept sequence you transfer it from here to here and now the magnetization here is only a 15 and do a HSQC type of experiment. These pulses which are present here are some improvements so we will not go into those details. I mean of course compared to the standard HSQC what I have given you earlier there are some differences here but these ones are to improve the performances, remove some artifacts and things like that. So but let us not go into those details similarly of course this one pulse also which is applied for some removing some artifacts and imperfections and then you transfer the magnetization back to the proton at this point and then now you have to do a refocusing and there is also some other additional which is added here which we have not discussed this is to increase the sensitivity of the experiment and finally you collect the data here and do decouple the nitrogen frequencies. So therefore this is something which is additionally put for improving the sensitivity of the experiment. So this is called nosy HSQC basically you have in the first mixing it is nosy mixing period and in the second mixing you have the HSQC this is heteronuclear correlation that is the J correlation and then you collect the data as a function of proton frequencies. Now let us look at some experimental data. So here is an illustration application to a protein this is a 3D nosy HSQC spectrum. This is a 3D HSQC spectrum now on this side a two-dimensional HSQC spectrum is shown for ease of understanding. So on this axis in the HSQC of the protein you have the proton dimension here and on this axis you have the nitrogen 15. So you have the nitrogen 15 chemical shifts here and the proton chemical shifts along this axis. So these are amide proton chemical shifts. So as we said earlier this is actually fingerprint of your protein you will have one peak per residue and by actually counting the number of peaks here you can actually figure out how many amino acids are there in your protein. Now a three-dimensional spectrum a nosy HSQC will look like this. So on one of the axis you have the nitrogen 15 here as indicated you in the schematic and then you have other two axis have the proton or here and here. But this portion what is chosen here is the amide proton chemical shift because it is only the amide protons which will show correlation to nitrogen 15. No other proton shows a correlation to the nitrogen 15 through coupling. Therefore if you are actually passing the magnetization from the proton to the nitrogen it will only be from the amide proton to the nitrogen. Therefore we will only have in this case amide proton to nitrogen correlations here. Now after the nitrogen 15 it is transferred they are doing an HSQC experiment you label the nitrogen 15 and transfer it back to the amide proton and do the detection. So before you actually transferred you have done the proton proton nosy and then you are transferred to the nitrogen 15 and you have done the HSQC there and you generate a 3 dimensional spectrum. So therefore this is a 2 dimensional HSQC spectrum amide proton N15 correlation here. Now if I take a particular cross section here at the particular N15 chemical shift here and I plot that here in this and this is what we have got. So you see even though this is also complex but still it is much less than what you would have in a simple 2 dimensional spectrum all of them the peaks appearing in one place. So if you take a particular cross section means supposing I am taking a cross section at this point you can see here how many amide protons are there. So you can choose at least 10 so you can count more. So there is so much of amide proton degeneracy at this N15 chemical shift. So now all these amide protons will show NOE correlations to the respective aliphatic protons. So this is for example from here you show a correlation to the alpha proton to the beta proton the gamma proton the delta proton and so on. So likewise for this one you see this amide proton is showing a correlation to this alpha protons here and then the beta proton and perhaps the methyl protons here. So likewise all of these amide protons which are present here they are on this axis and they show correlations to various the other aliphatic protons and some of them show correlations to the aromatic protons as well. So all these which are present here these are amide amide correlations and amide aromatic correlations. Aromatic protons also appear in this region right. So they appear between 6 to 7 ppm 7.58 and all the amides are present in this area. Therefore amide amide correlations appear in this area and this area belongs to the amide aliphatic correlations. So therefore since the particular N15 chemical shift there are so many amide protons here you will have so many peaks present in this and this is analyzable because you can go plane by plane and look at the correlations between the various groups of protons. So and often one does to simplify the procedure one takes an area where there is not too much of degeneracy for example here and typically these ones belong to the glycines and then you will have a good starting point. Once you start from such unambiguous positions you will be able to establish correlations between the amino acid residues and then you will be able to walk along the polypeptide chain. So that is of course a combination of a lot of these experiments are used toxy HSQCs and nosy HSQCs are used to identify residences that belong into the individual protons. So let me show you here how does the actually the experiment the spectrum look at three dimensional spectrum the same nosy HSQC here now you see the three dimensional cube. So you have here the peaks on the various planes. So in principle you can take cross sections at various chemical shifts and analyze the individual peaks you can see now there are only a small number of peaks here and this plane also has a certain number of peaks this is behind that. So if you come forward then you will have some peaks here which belong to this particular proton. So you now you take a projection down this axis you produce a two dimensional spectrum here. So therefore essentially as I indicated to you in the schematic this three dimensional spectrum is now pulled apart along this but with the NOE correlations in this case the NOE correlations are not there this is the HSQC spectrum. Now NOE correlations are displayed along the third dimension here. So therefore this is the proton-proton axis. So you will have correlations from this particular amide proton at this particular N15 chemical shift to these many aliphatic protons here. And likewise this one will also show these many aliphatic correlations and therefore it becomes much easier to analyze a three dimensional spectrum. And this allowed to determine the structures of reasonably sized protein molecules something like 150 and sometimes even 200 amino acid residues have been analyzed. And of course it all depends upon what is the quality of your spectrum how well resolved are the peaks in the HSQC spectra if they are well resolved then the protein is well folded it indicates the protein is well folded. So once you have well folded proteins the peaks will be better resolved then you can go to larger and larger systems. So this has been a success story and for all of these developments you know this Professor Wietrich was awarded the Nobel Prize for protein structure determination using NMR. The methodology of two dimensional NMR and three dimensional was developed by Professor Richard Ernst who also invented the Fourier transform NMR technique and he was awarded the Nobel Prize in 1991 for this technique development. And the applications were elegantly done by Wietrich's group in Zurich incidentally both of them are in Zurich in the same institute ETH. And as it Wietrich won the Nobel Prize for these applications in 2002. And this is of course this was the beginning and now we have gone much further using more of N15 and heteronuclear experiments carbon 13 experiments which was which I mentioned to you and we do not have time to do all of that in this course probably one may have to do another course and then you have to develop triple resonance experiments where you use not only two nuclei at a time but three nuclei at a time you can use and disperse the peaks and these are called triple resonance experiments and hundreds of such experiments have been developed and this has allowed us to push the limits of molecular ways to several tens of kilodaltons. The ambition is to go as large as possible study large assemblies study intrinsically disordered proteins and so on so forth. I think that is well beyond the scope of this course and maybe one has to do this at a later stage. With that I will stop here and I hope you enjoyed the course.