 So, far we discussed the two-dimensional experiments which correlated same kind of spins or which we call them as homonuclear correlation experiments. So, we are now going to go into another class of experiments which are called as heteronuclear correlation experiments. Coherence transfer can be effected between two different types of nuclear species, I and S, I can be a proton, S can be something else, carbon, nitrogen, whatever. Such experiments are referred to as heteronuclear correlation experiments. Now, you can design a variety of heteronuclear experiments because the RF pulses can be applied selectively to either species because proton and carbon they are very widely separated in terms of the frequencies therefore application of the pulses is not a problem and you can also do heteronuclear broadband decoupling can be incorporated without any constraints. So, during the indirect detection period or the evolution period where there is no acquisition going on you can also do various kinds of decoupling tricks and even during the acquisition when you are doing if one particular kind of nucleus is being detected the other nucleus can be decoupled because those pulses can be applied without interfering with the detection of the signal. So, therefore these are particularly useful and these have actually revolutionized the applications in biology. Structural biology came to a long way with the application of heteronuclear experiments and some of those experiments we will show in the coming classes. Now, what are the specific advantages? See increase sensitivity of indirect detection as evidenced in the inept pulse sequence. See in the inept gave a significant advantage to the insensitive nucleus because you transferred polarization from the most sensitive nucleus like the proton you transfer from proton to the carbon or you can do transfer from the proton to the nitrogen so which are insensitive. So, nitrogen is insensitive it is garamagranic ratio is one-tenth of that of proton and carbon's garamagranic ratio is one-fourth of that of proton therefore if you transfer polarization from the proton to the carbon or the nitrogen the ex nucleus will have a much greater sensitivity and that is one particular significant advantage. Secondly, possibility of unraveling overlapping eye resonances by exploiting the chemical shifts of the S suspense and vice versa. So since you are using two different kinds of nuclei here so in the correlation experiments the overlap of chemical shifts of a particular type of protons in the case of protons for example can be resolved by making use of the chemical shifts of the S suspense, the carbon spins of the nitrogen spins and therefore this is a specifically important from in complex molecules where there are large number of protons or large number of signals of a particular species and there are invariably they will overlap and therefore you need a second nucleus to separate these into multiple distinct peaks. Then correlation of chemical shifts of different nuclear species would facilitate assignments in complex systems and this is because you improve the sensitivity on one hand and improve the resolution or the separation of the peaks on the other. And this is typically used for proton carbon correlations proton nitrogen correlations or sometimes proton F19 correlations and all of these are particularly useful in many complex systems. Let us look at some of the standard correlation experiments here heteronuclear cosy to understand their principles and how do they work. Now this is the simplest correlation experiment this is a heteronuclear cosy by direct detection here. So this is very similar to the cosy homonuclear cosy what we have studied earlier okay except that we have two separate channels here this is the X channel and this is the proton channel and we can apply pulses selectively to this channel or to this channel and that is the big advantage as I mentioned to you before. So in this case we apply a pulse to the proton therefore I create here only the transverse magnetization of the protons at this point okay and the proton magnetization then evolves during the T1 period and this is the 90 degree simultaneous pulses on both the proton as the X nucleus and then the transfer of magnetization from proton to the X nucleus happens as the result of this mixing this is a mixing pulse right. So this is a mixing sequence here so there will be transfer of magnetization from here proton to the carbon or to the nitrogen whatever the X nucleus is and then after that you detect the signal of this nucleus. So detect the X nucleus during the T2 period and let me repeat here so during the T1 period I have the proton magnetization evolving with its characteristic frequencies and with this a pair of 90 degree pulses applied simultaneously you transfer the magnetization transfer coherence from the protons to the X nucleus and the X nucleus is detected during the T2 period. So therefore what do you expect? You expect after the two dimensional Fourier transformation I should have the X frequencies along the F2 axis and the proton frequencies along the F1 axis. So a typical correlation spectrum will therefore look like this so this is the schematic here we have taken 4 peaks here. Now the each of these peaks will have the fine structure why do they have fine structure? Because there is also coupling evolution here the proton X nucleus coupling evolution happens here and during this period as well there is also the X nucleus coupling evolution happens with the proton. So because X is coupled to the proton therefore the structure will be very similar to that in the cosy cross peak. So in other words we are recording just the cross peaks here there are no diagonal peaks in such a kind of a spectrum where only recording the cross peaks there is a correlation peaks between the proton and the X nucleus and each of those cross peak has the fine structure as in the normal cosy. So it will have plus minus minus plus structure and the separation between them is the coupling constant as we have discussed before. So along both the axis we have this coupling information present and notice here by and large these are one bond couplings. So if I am talking about proton to carbon it is a proton attached directly to the carbon. So typically we are talking about one bond couplings and the transfer is happening on the basis of the one bond coupling. Then these coupling constants are usually very large so 140 hertz and they do not vary too much. So therefore one bond couplings are nearly same in all kinds of species. So this separation will always be the same in every molecule. So generally this information may not be required for you so that we will see separately later. Now let us look at some of the signal to noise considerations here typically the signal to noise in any experiment is dependent on the gyromagnetic ratios of the excited nucleus and the detected nucleus. It is proportional directly to the gamma of the excited nucleus with regard to the detected nucleus it is proportional to the 3 half power of the gyromagnetic ratio of that nucleus. Therefore in this case the signal to noise ratio will be proportional to gamma H into gamma X to the power 3 by 2. Now let us look at the an alternative sequence here is an indirect detection there it was carbon X magnetization as directly detected. In this case we will record the X magnetization in an indirect manner how do we do it? We start with the X magnetization here so we start with the X spin apply 90 X pulse to the X spin and the X magnetization evolves during the T1 period. So X magnetization evolved during the T1 period and with this pair of pulses here you transfer the polarization to the proton. The relevant density operators product operators are indicated here you have the XZ here and at this point you create proton magnetization which is anti phase to X and you have the 2HY XZ. In the previous case also it was the same you started with HZ here and you ended up with anti phase magnetization of the X spin to 2X, Y, HZ is a product operator term and that results in this anti phase nature of the fine structure in the cross peaks. So here also it is similar you start with X and you end up with 2HY XZ and now you detect the proton because it is anti phase proton magnetization you detect the proton therefore during the T2 period you will have the proton evolution going on and coupling evolution also will be going on. So therefore in the 2D spectrum you have here the proton along the F2 axis and the X nucleus along the F1 axis therefore we call it as indirect detection of the X nucleus. Once again the fine structure will be the same as in the previous case you will have the plus minus minus plus character in the individual cross peaks here the coupling constant appearing as a separation between the 2 peaks in the fine structure. Now the signal to noise will be different because we are exciting the X nucleus therefore it is proportional to the gamma of the X nucleus but we are detecting the H nucleus and now therefore it is proportional to the 3 half power of the proton. So it is gamma X into gamma H to the power 3 by 2. So it will appear therefore that this might have a better signal to noise in the spectrum because this is gamma H raised to the power 3 by 2. However when you are detecting X nucleus indirectly then along the F1 axis you have the spectral width of the X nucleus. Notice the spectral width of the X nucleus is very large especially if it is carbon you have a 200 ppm chemical shift range and therefore it will be very difficult to cover this entire spectral range with a good resolution therefore resolution along the F axis will suffer. So because you cannot give such a larger spectral width if you give a larger spectral width your increment will be very small you would not be able to excite all your frequencies by this pulses special tricks will have to be used but generally because of the larger spectral width here you suffer from the resolution problem in the indirect dimension. Now so what shall we do to remove this coupling constant because we say the coupling constant is the same in the all the molecules for all the carbons why do we need that information here we are looking for correlation between the two nuclei. So what we need is a correlation between the chemical shifts coupling constant is not necessarily required here because we are not going to since there is no variation in the coupling constant there is no need to measure it either here. So we simply want the correlation information so but we cannot remove it unless we can decouple them if you decouple the two species then only we can remove the coupling information. So what we will have to do for that so therefore let us look at the indirect detection experiment here so we started from here and we came to the proton at this point. Now this was anti-phase mechanization of the proton at this point now we have to refocus this into in phase mechanization of the proton then only we can decouple the X nucleus because if you decoupled here what happens the 2 plus minus components will merge and then they will cancel each other therefore the peak will vanish therefore we cannot afford to do a decoupling in the previous experiments because of the anti-phase nature of the cross peaks. So therefore we will have to refocus it so for refocusing we adopt this inept type of sequence you remember this is the inept sequence basically so you have 1 by 4j evolution for 1 by 4j 180 pulse again 1 by 4j so during this period the one bond coupling evolution happens and you can exactly match it with this delays taking this j you can exactly calculate how much this delay should be and you put that here then there will be complete transfer of anti-phase mechanization into in phase mechanization. So you have here at this point the only operated term will be Hx and you do not have anything from the anti-phase components at all here. So once it is Hx now then you can decouple this so this is a broadband decoupling across the entire spectral width you can do decoupling so all the protons all the X nuclei will be decoupled you are detecting the proton and every coupling with the proton X nucleus coupling will be removed. So therefore what happens the F2 axis and this is the F1 axis along the F2 axis the coupling has been removed right this is the F2 axis here detection here gives you the F2 frequencies and there we have decoupled it therefore the coupling along the F2 axis has been removed. However it still remains along the F1 axis because here we did not do anything to remove the coupling evolution so in the T1 period the coupling evolution still happens and therefore we do have the plitting due to this J coupling in the F1 dimension. The signal to noise remains the same as in the previous case. Now if you do that for the heteronuclear direct detection you start from here and you come to this anti-phase X magnetization here the X magnetization is anti-phase with respect to the proton now you do the same trick you put the same 1 by 4j 1 by 4j inept kind of a sequence here it is called the refocusing sequence refocusing element here so you need to apply 180 pulses simultaneously on both X nucleus as well as the proton so at this point you will have the in-phase magnetization of X nucleus. Now the X nucleus evolves during the T2 period therefore along so this is the decoupling has been affected along the T2 dimension therefore there will be no splitting along the F2 axis but there will be splitting along the F1 axis so this portion will remain the same as in the previous case okay notice this so this will be plus minus here along the F1 axis and not in this manner. So now we have here X here and proton here and this the coupling appears along the T1 axis and along the T2 axis there is no coupling evolution therefore in the F2 axis there will be no splitting there will be splitting only along the F1 axis okay. So therefore we want to remove this as well and that leads us to the so called heteronuclear single quantum coherence and typically known as HSQC and this goes in the following manner. So you have 2 channels once more proton and X first of all there is an inept sequence here you start with the proton magnetization here at this point and you do an inept sequence here this inept sequence is 90 tau 180 tau 90 here and there is a 180 here and a 90 here these are 90 degree pulses okay and if this is the X pulse this has to be a y pulse and this can be anything X or Y does not matter. So we start here we select tau is equal to 1 by 4 J when we do that this is an exact inept sequence therefore there will be total transfer of magnetization from the proton to the X nucleus at this point. So here I will have anti phase magnetization of the X and then during this next T1 period I have the evolution of the X spins and there is in the middle I have put a 180 degree pulse and at the end of the T1 period there is magnetization which transfer back to the proton here and then during the next refocusing period this is a tau 180 tau coupling evolution happens and there is a refocusing here and then you generate in phase now we look at the product operators little bit more explicitly here and then you decouple you can now you can decouple with the detecting proton you detect the X nucleus now I have proton along the F2 axis and X along the F1 axis. How does this work? Let us look at this little bit more explicitly using product operator terms rho 1 is HZ proton magnetization Z magnetization of the proton and rho 2 is X magnetization anti phase to the proton therefore I have here 2 HZ XY between the time points 2 and 3 the following things happen X chemical shift evolves for the period T1 proton chemical shifts are refocused because I apply 180 degree pulse on the proton you recall whether there is a 180 pulse applied on the thing therefore there is no proton chemical shift evolution happening in the T1 period H chemical shifts are refocused HX coupling is removed. Now HX coupling is removed why? Because I have applied a 180 pulse to only proton I have not applied to the X nucleus therefore when you apply a 180 degree pulse to only one of the species you have we have seen before that it refocuses the coupling evolution as well therefore there is no coupling evolution during this period T1 therefore there is only chemical shift evolution of the X nucleus therefore at the point rho 3 which is rho 3 at this point at this point rho 3 I have 2 HZ XY F of T1 the F T1 is a function of T1 because this has happened as a result of the chemical shift evolution of the X spin so this will contain coefficients arising from the evolution of the X chemical shift. Now when I apply next 90 degree pulse on both the X as well as the proton I convert this X magnetization into proton magnetization now this will be 2 HX XZ which is proton magnetization anti phase to X and this of course remains the same. During this next refocusing period that is the here during this period here tau 180 tau and then I come to the density operator term time point 5 here when at that time point I have the in phase magnetization these 2 HX XZ evolves under the coupling to produce HY and this F T1 of course remains the same. Now you see this is in phase magnetization of proton and which can be detected with X nucleus decoupling. So this represents in phase proton magnetization X can be decoupled during the detection period thus there will be no fine structure in the cross peaks. So you see during the T1 period there was no coupling evolution and therefore there is no coupling along the F1 axis and during the T2 period your decoupled the X nucleus therefore again there is no coupling in the F2 axis therefore finally you will only have one peak you will not have any fine structure in the cross peaks at all. Now since here I have excited the proton and I also detected the proton therefore the signal to noise will be now proportional to gamma H by gamma X to the power 5 by 2 compared to standard X detection. You apply an anti pulse on carbon and detect the carbon or anti oxygen X nucleus detect X nucleus and decoupling the proton compared to that you have a gamma H by gamma X to the power 5 by 2 and this is a quite a substantial enhancement in the sensitivity. So you look at for example if this were proton and nitrogen this is a factor of 10 10 to the power 5 by 2 so this is huge 10 to the power 5 is 100,000 and the square root of that is almost like 330. So you gain a signal to noise of 330 in the case of proton nitrogen and that is a substantial saving in the experimental time and sensitivity enhancement is therefore a big big big advantage in this HSQC experiment. So let me show you some examples here. So here is the typical proton nitrogen correlation spectrum obtain a large molecule this shows the advantage which I mentioned in the very beginning. So in a complex molecule you will have the protons chemical shifts overlapping and then you will not be able to resolve them in the normal spectrum. Now you see you make use of the N15 chemical shift and you see you separate those peaks along the N15 axis and you get a cross peak structure which is like this. These are all cross peaks and therefore in complex molecule such as proteins you can resolve these peaks in the two dimensional correlation spectrum heteronuclear correlation spectrum in fact you can count the peaks here you can count the peaks and say how many residues are there in your protein. Each amino acid produces one protein which has one amide group. So one amide proton to its own nitrogen you will appear a correlation peak. So you will count the number of peaks here and say okay this has so many residues in my protein therefore this is typically called as the fingerprint of a protein. Now similarly this is the proton carbon correlation spectrum you see here so many peaks are present in the carbon proton correlation spectrum and these are pretty well resolved here compared and you could not have achieved this in the normal one-dimensional spectrum at all. Any separation of the chemical shifts here would be impossible in the normal one-dimensional spectrum of proton. In any proton-proton correlation spectrum you would not be able to resolve this and this advantage of S nucleus chemical shift. The X nucleus chemical shift is a significant feature of this heteronuclear correlation experiments which I mentioned to you earlier. So therefore to repeat you have a significant signal to noise enhancement by this indirect detection schemes. The X nucleus is detected along the indirect dimension and you detect the protons. You also excite the protons and detect the protons you have a significant advantage of the sensitivity in the spectrum. However of course when you decouple the X nucleus and it is also very demanding because X nucleus chemical shift range is quite large therefore you need special tricks to decouple X nuclei and that is the broadband decoupling sequences. There are many such broadband decoupling sequences designed to cover a wider range of spectral width along the in the T2 dimension for the decoupling purposes. So I think with that I will stop here and we will continue with the heteronuclear correlations in the next class.