 Good morning. So welcome to today's class. We were discussing polarization transfer. So in this concept we have seen that if two spins are coupled say spin A and spin X coupled by dipolar coupling then if you perturb one of the spin or saturate the population between two states of spin A the effect of that will be seen on the other spin which is called nuclear overhauser effect. So resonance line intensity change can be caused by this dipolar relaxation from the neighboring spin and with the perturb energy level of one spin. So here we have seen spin A and spin X. So if you are perturbing spin A the effect of that perturbation will be seen on spin X. So for this effect to be seen they have to be interacting through space and since it is interacting through space so there is a distance dependent phenomena. So if say R is the distance between these two spins so if distance increases the dipolar interaction between them will increases and therefore the effect will be becoming lesser and lesser. So because dipolar interaction drops with a distance and so this actually varies 1 to the power R by 6 that we have seen. So as we move it falls rapidly. So NO effect can occur only up to 5 to 6 angstrom and after that there will be NO effect seen in general. We have also seen that effect of like NO enhancement depends upon a factor that is called mixing time. So this mixing time we had seen if we are doing a transient NOE where we apply a selective pulse on one of the spin and then we mix it for say time Tm and then we record a spectrum. So this mixing time actually dictates how much NOE effect will be seen and for short mixing time this is linear. So here one can see that there is a linear but if you have like longer mixing time after a certain time it falls rapidly and this falls of NOE enhancement or decrease in the NOE enhancement is due to a phenomena which is called a spin diffusion. That means in a simple term spin loses out its magnetization to other spin and then you do not see that much enhancement. So in short time regime like short Tm it is a linear and that is typically used for measuring the distance in molecules, micromolecules or biomolecules. So nonlinearity in decay of the NOE at higher mixing time is a consequence of leakage to the lattice. So spin is leaking to the surrounding and that contribution can vary according to cross relaxation rate and this is called spin diffusion. Spin diffusion spin is diffusing to the other spins or lattice they are just losing out. So we had seen that this NOE concept is very very important in a structural biology. So you can actually do the same concept and you can take that in a 2D spectrum where you just this is the mixing time that we discussed in the previous slide. So you can measure here in 2D fashion this is the pulse sequence. This we will deal in detail when we go to 2D experiment but at the moment just understand that much that depending upon what Tm we can mix the spins and actually this magnetization transfer or NOE effect can be seen from the neighboring spins. So here you can see if this spin is closer to this spin, this spin is closer to this spin and all those they will be shown in the cross peak. Now each cross peak is essentially reflecting the distance between two spins and somehow if you quantify the intensity of these peaks we can get to know the distance between these two spins. So this NOE concept is generally used in the structural biology for measuring the inter proton distances. Now we had seen that earlier that for small molecules actually rho g is a better experiment, rho g is basically rotating frame rho g and we had also seen that for large molecule actually negative NOE we obtained for small molecule we can obtain positive NOE. So for small molecules rho g is a better experiment and rho g you do not do anything extra but you have a essentially a block which is called isotropic mixing block. So it is like you are putting that those spins in z direction and let them mix but these are through a space connected. So if that happens you get actual distance constraints in a small molecule and that cross peak sign comes negative. So why it comes negative we will discuss later when we go to like rho g and rho g in detail but here to remember that for bigger molecules we use NOG for measuring the distance between two protons. For smaller molecules like small organic molecules we can use rho g for measuring the distances and both of these has common phenomena that is actually enhancement of the signal by polarization transfer where we part of one of the spin and look at the effect on the other spin. Now up to this point we had done earlier. So now let us look move ahead this also actually we had done population distribution happens because of NOG effect. So we see because of relaxation population redistribute and we have seen previously that these are the population at different level. So for a x transition like x has a two transition x1 and x2 and for a you have two transition a1 and a2. So difference between these population is the signal that comes for a and these are the two distances that signal comes from x. So we had seen this different population distribution and how it changes because of relaxation. So now let us move to interesting concept of selective population inversion and how we can enhance signal of one of the spin by doing this. Now here these two spins that we are considering have two gamma right. They are not proton-proton but they are they can be carbon-proton or nitrogen-proton. So let us consider this as AX spin system. AX means the weakly coupled spin system like proton and carbon proton say on 600 megahertz resonates at 600 megahertz and carbon will resonate at say 150. And their J is typically around 140 or 120 hertz. So in that case they are weakly coupled spin system. So let us consider that and X is insensitive because it is gamma say gamma of 13 C we know that actually it is a four time less than gamma of proton. So this is four. So this nuclei is insensitive nuclei. So suppose we have a weakly coupled spin system AX where A is proton and X is nuclei like carbon or nitrogen which is insensitive. So in that case here is the energy level diagram for this spin system. So we have four states state 1, state 2, 3 and 4. Now the population of these states is suppose we have a delta plus delta. Here we have minus delta plus delta and here we have minus delta minus delta fourth and here we have delta minus delta. So now two transition that is happening for AX spin is this one and this one A1 and A2. So now A1 and A2 and for X it is happening X1 and X2. X is our insensitive nuclei. So the intensity of each of the peak will depend upon the difference in the population. So for A1 the difference is from here to here so that is plus 2 delta. So this minus this that is plus 2 delta and for A2 this minus this. So like here delta minus delta minus minus delta minus delta. So that is actually 2 delta. That is how A1 and A2 have intensity equivalent to 2 delta and they are sensitive nuclei so they have higher intensity. For X nuclei which is insensitive nuclei so similarly we can take for X1 and X2. So this minus this so big delta cancelled out and a small delta adds up that is 2 delta and for again for X it is 2 delta. So these are intensity for 2 insensitive nuclei that is 13 C suppose and this is say proton. Now that is typically case we have for a proton carbon spectrum and this difference in the intensity is because of the population distribution. So X is less insensitive nuclei therefore signal is less and population is also less. Now suppose we do a trick. So what we are doing? Now the two transition that we had is essentially A1 and A2 and then for X we had X1 and X2. So intensity for A1 and A2 that is what we looked is 2 big delta and for intensity for X transition is 2 small delta. So let us do a trick. The trick is that now we selectively apply a pulse on A1 this transition. So selectively apply a pulse 180 degrees. So 180 degree pulse is for inverting the population. So we are now inverting the population in this A1 transition. So what is the effect of happening because of this inversion pulse? So now take the difference for A1. So this minus this is essentially A1. A1 intensity will be state 1 minus state 2. So that will be minus delta plus delta minus delta plus delta. So that will be minus 2 delta and for A2 it will be as usual plus 2 delta. So this is for this and this is for this. Now A1 because we applied a selective 180 degree pulse so it inverted and A2 remained unchanged. So because of this inversion something happens to X transition. Now that is very very interesting. So what is happening to X transition? So now as we said we applied pulse on A1. So population level of state 1 and state 2 changed and intensity of X1 and X2 becomes now actually 2 big delta minus 2 small delta sorry 2 big delta plus 2 small delta. Now we can just go back and have this. So 1 minus 3 is for X1. So intensity for X1 is minus delta plus delta minus delta minus delta. So if you see this, this is actually minus 2 delta. So that is what intensity we have for X transition that is substantial change in the X transition. So change in the intensity of this transition from equilibrium state that is what we calculated is now plus 2 delta and minus 2 delta that is a substantial change in the intensity for X spin. So now what we did by doing this? So earlier we had an intensity for X that was small 2 delta. Now if you look at from the equilibrium it is big 2 delta. So that is a significant enhancement in the signal for X spin. So by potterbing A spin we are getting enhancement in the signal for X spin and that enhancement is substantial. So how much enhancement we are getting? So now because of perturbation we got it essentially 2 delta and earlier we had 2 small delta. So big delta and earlier we had now and earlier we had this. So essentially we are getting enhancement of big delta divided by small delta. Here you can see if we have potterbed A spin we are getting enhancement in X spin. So X1 and X2 and that enhancement is in tune of big delta divided by small delta. So that is equivalent to ratio of the gyromagnetic of the stimuli. So gamma A divided by gamma X and gamma A divided by gamma X is 4 times. So for a 13 C H coupled system we get enhancement factor is up to 4. So although these 2 spins are of opposite sign but enhancement is 4 times. So if you take for NH system where gamma of H divided by gamma of N is essentially 10. So for NH system we will get 10 times enhancement. This is huge. Potterbing A spin we are getting enhancement for X spin 4 times for a C H system and 10 times for a NH system. So selective inversion provided us a significant advantage for sensitivity enhancement. Where potterbed one spin we are getting 4 folds or 10 folds enhancement. But there is a problem. Problem is what that like here as you look at I potterbed only one transition in A spin. So that means our inversion pulse has to be transition selective so that it only potters A1 spin. Getting that clean pulse 180 degree is little difficult task. So and especially when it is a crowded spectrum where you do not have a transition very clearly defined like where resolution are poor in a crowded spectrum getting a transition selective pulse which will selectively invert one of the transition is difficult. Therefore in those case it can mix up and the enhancement that we are getting may not be that clean. So to circumvent such problem actually a method was developed and this method is called inept. What inept means insensitive nuclei enhancement by polarization transfer. So let me explain each of these term one by one insensitive nuclei. Insensitive means low gamma nuclei. Low gamma what we mean? So generally proton has a high gamma low gamma is like where population levels are not too far apart. So like carbon 13 and 15 phosphorus many other nuclei are low gamma nuclei and they are essentially insensitive nuclei. So we want to enhance the signal of this low gamma or insensitive nuclei by transferring the polarization from high gamma nuclei which is proton. So if you transfer the polarization from proton which is high gamma nuclei to carbon 13 or nitrogen 15 which is low gamma nuclei that method is called inept. Insensitive nuclei enhancement by polarization transfer that is a inept. So what actually it is? So it is a set of pulse that I am going to explain you in a moment and this is this pulse sequence actually helps to circumvent the issue related to selective inversion because as we see if the transitions are not far apart then getting 180 degree selective pulse is difficult. So in those case in in inept case we do not need that transition selective pulse. One can use non-selective pulse and which is called hard pulse like symbol for hard pulse is like a square shape and soft pulse are something like this. So hard pulse means their bandwidth is quite high and soft pulse that bandwidth is low that is how they call it hard pulse and soft pulse. So duration is short that means like duration of these hard pulse can be of few microsecond. So bandwidth is in going to be in like 1 by microsecond that will be in tune of say kilohertz or even megahertz. So few microsecond this megahertz tune and the soft pulse will be larger duration like 200 millisecond or 500 millisecond therefore actually their bandwidth is in kilohertz. Even if you look at so to selectively excite one of the transition in these pulse you need a bandwidth of few hertz and that means pulse has to be very long. Long pulse has its own problem. One problem that can be even non-selective like it cannot be very precisely selective that can leak out. So to circumvent such problem this method was developed where we can use hard pulse and you do not need to selectively like use transition selective pulse. So what this pulse sequence is let me explain you. It says that we have two spins. So here is our spin number one which is A spin and spin number two is X spin that is why these are two channels. So channels that means a frequency channel. If you are doing experiment at say 14.7 Tesla which roughly corresponds to 600 megahertz so that means proton channel will be around 600 megahertz and carbon channel will be around 150 megahertz. That is why they are two different channels. So the RF synthesizer will work in different regime and that is how they are two channels. So now on A channel we are applying a first 90 degree pulse in X direction. Then we are waiting for certain time which is tau. Then next step we are doing applying a 180 degree pulse on both channel A channel and X channel. Next we are waiting for same time period which is tau and next we are applying a 90 degree Y pulse on A channel followed by a 90 degree X pulse on X channel and then we are detecting now my resonance should be in XY plane which can be detected. So that is a simple pulse sequence for inept. We are applying with a 190 degree X pulse then waiting for a tau period, tau period I will just explain you a minute what actually it is. Then waiting for tau period then applying a simultaneous pulse 180 degree X pulse on A spin and X spin. Again waiting for a tau time period then apply a 90 degree Y pulse on A spin followed by a 90 degree X pulse on X spin and detecting it. So what happens because of this polarization? So this is the vector diagram let us understand. If I go back first thing we did we applied a 90 degree pulse on A channel. So A means proton. So suppose we are always discussing two transitions two vectors here. Two vectors we applied a pulse 90 degree pulse on A so that means they will go to minus Y. So just a thumb up rule now here I have drawn a circle I have written Z XY. First thing we are doing applying a 90 degree pulse on A channel 90 degree X pulse. So initially magnetization was in Z direction we applied an X pulse. So you apply X pulse on Z it will go to minus. So if it is moving anticlockwise it is a minus. If it moves clockwise that is a plus. So X pulse applied on Z magnetization it will lead to minus Y direction. So that is why we have here these spins are minus Y direction. And two spins because we have a it is the AX coupled system. So we have two transitions one vector shows one of one of the transition. So A1 and A2 both now are in minus Y direction. Then I said I have to wait for some period which is tau period. Now what is this tau period that is very important. So tau is basically will be dictated by what is the coupling constant between these two spins. And we will see in coming classes that if you keep your tau which is equivalent to 1 by 4 J, J is the coupling constant between like 13 C and proton. If you keep that now that will help you in transferring the magnetization from one spin to another spin when they are coupled through bond. So that is the tau period tau is equal to 1 by 4 J. So if you wait for that spin and we are not doing anything. So we have started like this then we are waiting for tau period. So now in that wait period spins will start moving in opposite direction from like minus Y axis. So here is minus Y axis and both of these spins in the second case they started moving. Second case what I mean by so here both of spins are in minus Y direction and then during this tau period they are like started from here and they are now moving like this moving like this. So that is what is shown here. So now though both of these vectors are moving in opposite direction. Then we had applied 180 degree pulse on A and 180 degree pulse on X. So let us look what is happening here. So we had applied 180 degree X pulse on A. So 180 degree pulse will create inversion. So now these two guys were moving like this here. Now it will create inversion so they will move like this and that is what actually it is shown. So here 180 degree pulse now they change the direction and they will be going in this direction. They will be coming along plus Y direction. Simultaneously we had applied 180 degree pulse on X. So that actually changes the direction of the precision. So then they will start going in opposite direction A1 and A2. Now next after this these two pulses we are waiting for after this pulse we are waiting again for tau period. So if you look at the vector diagram we started like this then during tau period they were like this and then like we inverted like this but they were coming like this. So we applied 180 degree pulse on X. So they changes the direction and they again are going further. Now after again time period tau which is again 1 by 4 J they will align along X axis. So one will be minus X and another will be X. So now then we are applying a Y pulse. The magnetization in X direction we are applying a Y pulse on A spin. So what we are doing 90 degree Y pulse. So if you apply here if you apply a Y pulse when magnetization is in X so it will go to Z direction. So now my magnetization for A spin will be along plus Z and minus Z. Now my magnetization is in Z direction. A spin it is in Z direction. So next we applied here a 90 degree X pulse. So 90 degree X pulse here population inversion happens. We have started both this transition in Z direction but at this stage what we have done? We inverted one of this spin if you look at. So then we apply a 90 degree X pulse on X spin and that transfer the selective polarization enhancement happens on X spin. So that is why we have now enhanced signal for X spin but only caveat here is that both of these transition will have opposite sign but their signal has been enhanced. That is how in in-app you enhance this signal for X spin by application of this pulse sequence which is nothing but couple of pulses which can be given by 90 tau 180 tau 1990. So we achieve the enhancement in the signal of of these spins. So that is what we have done. So finally we get an enhancement and this enhancement is actually equivalent to selective inversion of a transition here and consequent of that enhancement we are getting in X transition and that will be essentially governed by gamma A divided by gamma X. So for if you are doing this experiment or carbon proton coupled system we get 4 times enhancement and for nitrogen proton coupled system we get for N15 we get 10 times enhancement. So like selective population inversion we achieve enhancement but of course will be of opposite direction. But in-app has some disadvantage. One disadvantage we found it that both the signal for X spin are coming in opposite direction and there can be intensity abnormally. So incorrect relative intensity can occur because of different spin multiplications. So for simplicity we considered only two transitions one was like this and another was like this and we found that if we involve one of these X transition one was like this and another was like this. But what happens if there is a spin multiplied? So then we have a problem because then again we cannot get a clean enhancement. The another thing that we looked at one of the parameter that was there 1 by 4j. So now this j is playing important role because that dictates how much tau we are keeping. So if the strength of heteronuclear j coupling is different then transfer of magnetization of population inversion can be different. So this dictates how much transfer it is happening. So two thing j coupling and spin multiplicity actually dictates the transfer efficiency in case of in-app. So to get rid of that what we need to do we will look at this in next class. Based on today's lecture if you have any question do not hesitate to ask us we will try to resolve it. Thank you very much.