 So we are now ready to go into the next class of two-dimensional experiments or in general multi-dimensional experiments and these are called as correlation experiments or correlation spectroscopy, 2D correlation spectroscopy. In fact this has been the most fundamental, most crucial experiments from the point of view of structural biology and this is the one which actually led to the Nobel Prize to the two persons, one is Richard Ernst and then other one is Kutvitrik and we will go along those ones. And the basic developments were made by Richard Ernst, we see here are Ernst, first was published in 1976 in Journal of Chemical Physics and then again in Journal of Chemical Physics 1979, two fundamental experiments which have been crucial in all applications in structural biology. So we prepared the ground to understand these experiments in the previous class because all of these involve very crucial magnetization transfers and that is the one which is the information carrier in these experiments. So what is this experiment look like, what is the correlation experiment? Correlation experiment is like this, schematically this is an experiment which is indicated like this. So we have the two dimensions here which are represented as omega 1 and omega 2. Of course we could have used F1 and F2. This is just taken a two spin system here, there are only single schematically indicated two lines there is one line here and the other one. So this is the A spin, this is the and this is the B spin, A spin and the B spin here. Now it is the two dimensional experiment the spectrum looks like this schematically, schematically it is looking like this. So you have the so called A peak here, this is the A peak which has the same frequency along the omega 1 axis and the omega 2 axis. You look here, this is omega A here and omega A here. And similarly this peak is omega B here and omega B here. So therefore these are called as the diagonal peaks. So we have diagonal peaks. So therefore the diagonal if you want to look at essentially it represents the one dimensional spectrum. This represents the 1D spectrum. Then you have the so called X, these ones here. Now along this axis we have the omega A here and this axis it is the omega B. So far as this peak is concerned. Similarly for this peak we have the omega A along this axis on the omega 2 axis and omega B along this axis. So these are called as cross peaks. Cross peaks are the correlation peaks. These are the information carriers. So the cross peaks are the information carriers. What do they tell you? This will tell you that the spins A and B are somehow correlated. What kind of a correlation? It can be very different. There can be different kinds of correlations, it can be J coupling correlation or dipolar coupling correlation whatever it is there can be different kinds of correlations possible accordingly you will have different kind of spectra. So therefore correlation peaks A and B and how do they arise? This depends on the pulse sequence. This depends on the way you design the pulse sequence in what are the pulses you use, what are your mixing sequences etc. And that is the important part of this. This is the schematic of the two dimensional correlated spectroscopy. You have two frequency axis and the diagonal of this correlated spectrum is basically a one dimensional spectrum and you have off diagonal peaks or also called as the cross peaks. The cross peaks actually are the correlation peaks and these are your information carriers. Therefore whatever information is present in the one dimensional spectrum, I mean if you take the one dimensional spectrum certainly there will be these correlations are present already. Suppose you are talking about the J correlation, J coupling. J coupling is present in your one dimensional spectrum but you do not know how to extract it. You do not know which spin is coupled to what, you do not know that. In a complex NMR spectrum of a protein for example, you do not know which peak is connected to what, which spin is connected to what spin, where do these appear in your NMR spectrum, you do not know that. But when you do a correlation experiment of this type then you will see that you get correlations which are off diagonal and you can connect them to the diagonal positions. Then this will tell you that spin A and spin B are correlated, they are coupled, there is a J correlation or some other correlation. Therefore these are called as the information carriers and the entire plane is available to you to display this correlation. That is why this became an extremely powerful, powerful tool for improving the resolution NMR spectra and the information content NMR spectra. Now this is the pulse sequence for the COSY, two dimensional COSY experiment. So we start with a 90 degree pulse here, this can be a 90 degree pulse and this can be a pulse of flip angle beta or it can also be a 90 degree pulse. So beta can vary from one value to another value but it can be a 90 degree pulse also. Here you have the T1 period which is called as the evolution, this is the evolution and this pulse which is the beta pulse, second pulse which is there, this also acts as the mixing. This pulse acts as the mixing and T2 is your detection period, FID is collected during the T2 period therefore you generate a two dimensional Fourier transformation, two dimensional spectrum after you do this. The evolution time as I described earlier is incremented systematically from one time, one FID to another FID. So therefore you generate a two dimensional information. Whatever is the frequency present in the T1 period will appear along the F1 dimension or the omega 1 dimension. Now what does this mixing do? The mixing do, it does, it transfers magnetization. For example if I have during this transfer, so here I let us say I have starting with the case pin Z magnetization to begin with. To begin with I have here at this point 1, suppose I have Z magnetization, Z magnetization of the case pin. When I apply the 90 degree pulse then I will generate the Y magnetization let us see because the 90 degree pulse rotates the Z magnetization into the transverse plane. So now the evolution period during this period, the K magnetization, the transverse magnetization evolves during this evolution period. So when this evolves, it evolves with the frequency omega K therefore you generate K magnetization and then it is frequency labeled. As your function of T1 it will be frequency labeled because you are systematically incrementing the T1 value therefore the evolution will follow this frequency. So therefore you acquire various kinds of phases. Now what happens during the beta period? During the mixing, mixing transfers part of K magnetization to say L spin to say L spin. So therefore I have initially I have a K then I transfer some of it to the L spin. Therefore what is present in the T2 period? So therefore in the T2 period I have both K, K and L magnetizations. And this is the basis of this scheme here. So during the T1 period, so what is present along the F1 axis, the omega 1 axis if I consider the omega A frequency, omega A frequency which is present during the T2 period because of the mixing I have both A magnetization and B magnetization or the K magnetization and the L magnetization. Therefore I will have both the frequencies present and because of that when I do Fourier transformation I will have the diagonal peak and the cross peak. What remained on the A spin remains as diagonal, what got transferred to the B spin appears as a B magnetization and that appears as the cross peak. So that is the philosophy of this experiment and let us see how this is useful. Let us take a particular molecule here and what is this molecule? This is a peptide, this is a dipeptide. So this is a dipeptide here, the NH, C alpha, CO, this is one amino acid, it is written as I, I, I, so I represents the magnetized of the residue in a polypeptide chain. So this is the polypeptide chain from N, C alpha, CO, this is residue I and the next residue is I plus 1 and the previous residue is of course I minus 1. So now you see let us consider this, the Kozy experiment is designed for J correlations. This will allow transfer due to J coupling, J coupling correlation. Now what are the J couplings present here? Let us examine this molecule. If we examine this molecule, let us say I have the NH, when we are talking about the protons here, we are talking about the protons. Which are the protons present? NH proton, alpha proton, the beta proton and the mythiles and the mythiles we call them as gamma protons, alpha, beta, gamma and so on and so forth. Now there is a 3-bond coupling from NH proton to the alpha proton and therefore there is a transfer between NH and alpha. NH and alpha transfer produces me this peak here, it produces this one peak. Similarly, alpha to the NH produces this corresponding peak on the other side, okay. Now from the alpha proton, I also have a coupling to the beta proton, this is a 3-bond coupling. So alpha to the beta, this is again a 3-bond coupling, so therefore I have a alpha to the beta cross peak. So this is the alpha to the beta cross peak and similarly this is beta to the alpha cross peak or either way one can say beta to the alpha cross peak and this is alpha to the beta cross peak because the flow is going like this, if I call this as omega 1 axis and if I call this as omega 2 axis, so this peak is coming from beta to the alpha transfer and this peak is coming from alpha to the beta transfer. This peak is coming from alpha to the NH transfer and this peak is lower, one is coming from NH to the alpha transfer, alright. So now what happens next? From the beta, do I have any other transfer? Now look here, the beta proton is coupled to the methyl groups, CH3 protons. So therefore there is a coupling there also. Therefore from beta, I will have a coupling to the gamma and there are 2 gammas and if these are non-equivalent, if these 2 CH3 groups are non-equivalent in terms of chemical shifts, I will have 2 peaks there. From the same beta, I will have 2 peaks. So therefore this is of 1 gamma to the beta, same beta, this is the second gamma to the same beta transfer and this is from beta to the 2 gammas. These peaks are appearing from beta to the 2 gammas and what is this residue? See those of you who remember this amino acid structures, this residue is valine NH, C alpha, C beta H, CH3, 2 CH3 groups and this is valine residue, okay. So therefore whatever is enclosed in the dotted box on the right hand side, all these are exhibiting J coupling, J coupling, there is a J coupling between them. Therefore the quasi-spectrum here is displaying a pattern, displaying a pattern of cross peaks which are very characteristic of the coupling network in this amino acid residue. So we have NH to the alpha, alpha to the beta, beta to the 2 gammas. Notice there is no gamma-gamma coupling, gamma-gamma coupling is 4 bond coupling, okay. This is 4 bond and you do not have that coupling, that coupling is very small. Therefore you do not see that, okay. So this is typically the kind of a structure what you will have at a low resolution spectrum, you will have a pattern like this. This is the very important information with respect to identifying the spin system. So this is called as the spin system, spin system of valine, okay. So this is we say the spin system of valine in 2D cozy, okay, alright. Now of course there is no coupling from any of these protons in a particular residue I to the next residue. Is there a coupling to the NH of I plus 1? NH of I plus 1 is far. See there is no coupling from here to here, okay. Of course this do not look at the thick arrows there now, that is related to the another experiment. But there is no coupling, J coupling from this proton to this proton. Likewise, there is no coupling from this proton to this proton or any of those ones. Therefore these cross peaks do not appear in this, do not appear in the cozy spectrum of this. If you are looking at the NH of this, there is only correlations appearing for within the same amino acid residue. There is no connection from one amino acid residue to the next amino acid residue, neither here, neither on the I minus 1 side. So therefore these are within the amino acid residue, you have the J coupling correlations. Therefore this cozy spectrum is extremely useful to identify the spin systems of individual amino acid residues, okay. Let us look into this in a more detail, a finer structure. I showed you that there is a, each one of them is a cross peak here, there is a cross peak. Let us consider this cross peak here, I said this is one full dot which is actually indicated. Is it just that, is it just a dot like this or it has any structure? If you look at the 1D spectrum of this NH, NH is coupled to this proton, right. So therefore NH will be doublet and this doublet going to be reflected in this or not, or in this or not, whether the doublet pattern of this NH, is it going to show up here or not. And it must show up because where it will go, you are not doing anything with respect to that, it must show up and similarly in this peak as well. So if I consider this as an AX spin system now, NH to the alpha, let us forget these ones which are, consider only those 2 spins. By considering a 2 spin, look at this cross peak. So I have here a 2 spin system for some molecule, this is 2, 3 di bromo thiophene. This is a simple 2 spin system. It has no other coupling available, no other, only one coupling available. So therefore the 2D Cauchy spectrum of this will have, now you see this is a 1D spectrum is a doublet and a doublet here. This is a doublet, this is a doublet, okay, that is the same thing here as well. Now I have the diagonal here, diagonal, these 2 peaks are the diagonal peaks and these 2 are the cross peaks. So there is a transfer from here to here and transfer from here to here. What else? This fine structure, how does it appear in the spectrum? What is done here is you take cross section through this spectrum, through this spectrum. At this point, at the next point, then at this point here and at this point here, you take cross sections and plant those cross sections here, these are the various cross sections. From the top to the bottom, these are the 4 different cross sections taken through the spectrum and what do you see? You see here positive or negative. If this is positive, the next one is negative or if this one is negative, the next one is positive, kind of an anti-phase term which I talked to you earlier and these are both absorptive signals, these negative, positive, absorptive signals. You continue in this one, you come here, see here, these are dispersive signals. These dispersive signals, it goes like this and then the R 1 gain goes like this. Therefore, these are in phase, so if I want to write here, these are in phase dispersive and what are these? These are anti-phase absorptive. So therefore, this is the cross peak has this feature and the diagonal peak has this kind of a feature and similarly, the next one if I see, the next line, if you take the next line here and what do you see? See positive or negative, earlier it was the top one was negative, positive and this one is positive-negative and this one is all positive again, all positive and this has dispersive line shapes again. So therefore, the diagonal has dispersive line shapes and the cross peak has absorptive line shape but the sign patterns are different. You come down to the third one here, now this is the diagonal once more. The diagonal is again have cross sections like this, dispersive in phase, absorptive anti-phase and you take the next one, the last one here, last one is again dispersive in phase and this is absorptive anti-phase but this sign pattern is different from this. What is negative here is positive here, what is positive here is negative here. So therefore, typically what we will say here is, if I wait to blow up, if I blow up this peak, if I blow up this peak, I show here this is what we get, this is what we have. So, if I draw on to draw the sign here, what is the sign here? This is negative, this is positive, this is positive, this is negative, absorptive line shape, these are positive-negative components and these ones, they are all positive but dispersive, this is positive, positive, positive and positive. All are in phase, that is why I say positive, positive, positive, positive but they have dispersive line shapes. This dispersive line shapes actually creates a very ugly shape here, what is plotted here? This is the contour plot, these are called as contour plot, these are the cross section, the top, what is plotted is a cross section but when you display a two dimensional spectrum, you represent it as a contour plot. So what you do? You have a spectrum like this at a cross section at various heights and plot the contours, how the things are going. So that is the contour plot. So therefore in the contour plot, it is usually easy to analyze a contour plot here like this. This is the contour spectrum and you see various contours drawn at different heights of the peaks and the center of the peak is of course the center of the line, the chemical shift, center of the chemical shift or it indicates the chemical shift. So therefore and you can measure the separation between these and the separation between these is what? It is the coupling constant. So therefore the coupling constant information is present in the fine structure of your cross peak. It is also present in the fine structure of the diagonal peak but you cannot extract from the diagonal peak because the line shapes are very ugly and this very difficult to find the center here. Therefore, the information carriers are the cross peaks which have absorptive line shapes and beautifully separated components here and you can see you can directly measure the coupling constant along both axes here as well as here it is the same coupling constant. J coupling constant is present here. Therefore in the correlated spectrum which is recorded with high resolution, a cosine spectrum recorded with high resolution you will be able to see such fine structure. If you do not do with high resolution then there can be possibilities of cancellations. This also that because of these intensity patterns, because you have the positive negative peaks here. Suppose you do not have enough resolution along this axis. Here I have clear resolution along this axis that these peaks are well separated. Therefore I do not have any cancellations here but suppose this resolution is not good sufficient then there is a possibility of cancellation of these intensities. This sum of this portion may cancel with some of these intensities. So that actually can be a problem that you do not get suppose the coupling constant is very small because what does it depend upon? This separation depends on the coupling constant. So if the resolution is not sufficient to resolve this coupling constant is not enough then there can be cancellation of the intensities then there can be some difficulties in identifying your cross. The peak may disappear. In that case that is why you do not see the 4 bond couplings. Why you do not see 4 bond couplings because coupling constant is very very small. If it is 0.1 hertz or 0.2 hertz or less than that then the positive negative are so close that you will not be able to separate them and they will cancel out the intensities. And that leads us to a new experiment which is called as a double quantum filtered cosy. Double quantum filtered cosy, this is the particular improvement over here. So without going into the theory of this one we will see what is the final result. What is the result that comes out here? So here is, this is the pulse sequence of the double quantum filtered cosy. So you have the 90 T1 90, of course here you can use the 90 degree pulse here. This is up till here it is the same portion as the cosy. But here we introduced a small time delay here, someone did some small time delay that is a very small time delay. So we call it as let us say delta, extremely small time, it is kind of order of a few 100 microseconds, it can be that much time delay or small time delay. Now what you do is you manipulate the transfer pathway, you transfer the magnetization transfer pathway. What you do here is manipulate the mixing, mixing and transfer pathway. So therefore what you get? You adjust it in such a way that at the end of the second 90 degree pulse here, at the end of the second 90 degree pulse here I will have double quantum coherences. I will have double quantum coherences here at this point. So let us say if you call this point as 1, I will have at 0.1, I will have double quantum coherences. This is the manipulation, we will not go into how it is done but this is the manipulation that is done. So that is why it is called as double quantum filter. So you, the process of mixing at creation of the first 90 degree pulse creates all of these pathways. It creates single quantum coherences, double quantum coherences, it will create all of those. These 90 degree pulse will create all of those. But then you do a kind of a filtering technique, by doing this filtering techniques we keep here the double quantum coherences here. And then the double quantum coherences as I mentioned are not directly observable. So therefore to observe that we need another pulse and this actually converts the double quantum coherences into single quantum coherences. And therefore after that you can measure it. Before that you cannot measure it. You measure it after this is second 90 degree, third 90 degree pulse and then you will be able to measure the signal. Before that you cannot because you have done a trick here during this 90 T 190 and you do a trick to filter out a particular kind of a coherence. The transfer pathway when I apply this second 90 degree pulse here it will the various kinds of components of magnetization will be present. There will be single quantum coherences, there will be double quantum coherences, there will be Z magnetization, all components will be present at this point. But to do a filtering technique which we will not go into the detail by which you only retain here the double quantum coherence pathways, double quantum coherences. And then when you apply the next 90 degree pulse, this will be converted into single quantum coherences and that is what you can measure. What is the advantage? What is the advantage of this? Here is a comparison of the COSY spectra and the double quantum filtered COSY spectra. See these are contour plots. You look at the again for the single two spin system here. This is the cross peak for the COSY and this is the diagonal peak in the COSY. This is looking very ugly. This COSY is looking very ugly here. This one is clean of course but this one is looking very ugly. Now look at the double quantum filtered COSY. This and this are identical. See I have here plus minus plus minus, I also have here plus minus plus minus but absorptive, absorptive line shapes. So therefore I have absorptive here and also absorptive there. So therefore if I want to call that as absorptive as A, this is also A. Absorptive A for absorptive, absorptive line shapes. So therefore all that information that was lost because of this kind of ugly line shape can be recovered. There is an example here. See this is the COSY, this is the diagonal. The diagonal showing you all kinds of tails and any peak which is under this here you cannot measure it at all. You cannot identify that at all. And in the double quantum filtered COSY you can see this clear resolution and peaks which are extremely close to the diagonal. See this cross peak here, this cross peak, this cross peak and another one which is very close to that all of them can be resolved. They can be identified and things which are close here they can be identified. These are all of these becomes a beautiful well resolved spectrum, better resolved spectrum. And secondly if there is any singlet in this spectrum, the singlet will appear in the COSY spectrum as a diagonal. It will not have any cross peak because the singlet has no coupling. Therefore the singlet will not produce a cross peak but it will produce a singlet along the diagonal. And that can be nuisance like the water. And it can be nuisance, it produce a huge line and it can mask all your peaks which are in the close vicinity of that. So that will be very destructive. And here in the double quantum filtered COSY the singlets will not appear. And this process of filtering technique here which eliminates the singlets. And therefore singlets will not appear and in the double quantum filtered COSY you have beautiful resolution and the fine structure is very clear. And that is the advantage of double quantum filtered COSY experiment. All of these are employed in application to all kinds of biomolecular system, peptides, proteins and you need this to identify the individual spin systems of the amino acids. Because many amino acids will have very complex coupling patterns and you should be able to identify all those coupling patterns, you should be able to identify the cross peaks in the individual amino acids. Then you can identify the spin system so that you can see the correlations in other spectra. So this is the power of the double quantum filtered COSY over the COSY. So I think we can stop here and we can continue in the next class.