 So, we were discussing about the various aspects of FTNMR. We discussed about the water suppression and we have discussed about the spin echo and I want to show you here how a spin echo based water suppression scheme which we discussed last time as a water gate, how it will achieve the water suppression. So, here is an experimental spectrum. We can see here, this is the normal experimental spectrum recorded in water. The sample is phenylalanine, dissolved in water, phenylalanine in water with a small concentration. This is the normal spectrum without doing anything, the top stress is the normal thing without doing anything. You can only see water, nothing else, this is water. Now, you just blow it up, just scale it up here somewhat more. Then you start seeing little this tiny signals which are already present here but then of course they are not seen clearly because of the huge water signal. You adjusted the scale such a way that the water signal completely comes in the screen here, then you do not see the other signals. Now you scale this up, so if the water gets saturated here, saturated meaning actually this is cut off here and you start seeing little tiny signals here of this phenylalanine. So, this again the same spectrum as this except that it is just scaled up. Now you do an experiment with the water gate. Now you suppress the water and now you see where is the water? This is the water signal. Water signal is much less than your actual sample signals. So these are your sample signals, the phenylalanine signals and this is also all these are belonging to the phenylalanine. Now you see those ones are stronger than the water itself. So this is what is achieved by the water gate pulse sequence which I described to you last time. And this is taken from this source here, University of Ottawa NMR facility and you will find many of such works in the Google search if you do of course you will find many examples of water gate suppression and also many other pulse techniques which are there for water suppression and I have taken one simple example here to illustrate how the water gate is useful for recording good spectra. So that was just a continuation of the last slide, last topic. So now we move on to another topic which is called as dynamic NMR. In the sense that the NMR spectra are very sensitive to the dynamic effects in your system. If the molecule is undergoing conformational exchange or chemical exchange between two different conformations or multiple conformations whatever then it will show up in the NMR spectra and this is illustrated here as a by simulation I will also show the experimental spectra. So here you consider for instance a simple two site exchange, a chemical exchange, a proton exchange is between two sites A and B and these ones have different chemical shifts. So these chemical shifts are here you can see this one is these are the two chemical shifts signed in terms of the frequencies here and if the exchange is happening and now it depends upon what is the exchange rate and what is the population of these individual states. So what does the population depend upon? It depends on the energy difference between these two. Suppose they are of similar energy they may have similar populations but there can be barrier in between and the barrier will result in different exchange rates different forward rates and backward rates and the exchange rate is defined as the sum of these two rates. So suppose I want to write suppose I write here the two exchange rates here as the forward exchange I write it as K1 and the backward exchange I write it as K minus 1 then I have the exchange rate is defined as K exchange is equal to K1 plus K minus 1. So one single time constant describes the two the process of exchange and that is defined as a K exchange or this is the same as the K here which is written here this is the same as this K exchange here. This is the simulation which has been done assuming the following parameters assumed here that the populations of the two states are identical PA is equal to PB is equal to half that means that is these are the probabilities. The probabilities of meaning one the populations are the same in both cases and the tau A and tau B these are the lifetimes these are the lifetimes of the individual states. So lifetimes if both are equal so if I say tau A is equal to tau B is equal to 2 tau so that is the lifetime and the lifetime is related to the exchange rate. So the K the K1 is equal to 1 by tau A and K minus 1 is equal to 1 by tau B and now if you put tau A is equal to tau B is equal to 2 tau then we define one rate which is the K K exchange or K K exchange is the same as the K is equal to 1 by tau A plus 1 by tau B a single time constant is defined this is equal to 1 by tau. Now we can substitute here 1 by yeah so this is K minus 1 plus K so if you substitute tau A is equal to tau B is equal to 2 tau then what you will get you will get 1 by tau. So tau is the single time constant which describes the exchange phenomena how the spectra will change as a result of this exchange happening of course how does one change the exchange rate you can change the exchange rate by changing the conditions like you can change the temperature you can change the viscosity by adding different things and so on so forth. And then it also depends upon the relaxation times of the individual states how much is the relaxation time of the spin in the two sides. So here are the two relaxation times here but those become individually assumed here that they are infinitely long that in the sense that the 1 by tau A is equal to 1 by tau B is equal to 0 that means they are extremely slowly relaxing therefore we do not include here the effect of this relaxation but we include here the changes that are happening as a result of the exchange process only. So that is why to show the effect of the exchange we are doing the stimulations here. So you see when the exchange is very very slow k is equal to 10 hertz you see two clear lines see you see two clear lines here and use and of course the intensities are also high and increase it to 100 hertz the lines have broadened and therefore the intensity has come down okay the height has come down increase it further you give even less then you reach a state when it is like almost you are not able to distinguish between these two and you start getting a broad line very broad line this is known as coalescence. The two lines tend to merge the two lines tend to merge when that happens the tau is equal to tau is equal to or tau into omega A minus omega B is equal to 1.414 when this condition is satisfied then you will see coalescence you will start getting a single line. Now what happens after that if the exchange rate increase is further then the lines start narrowing narrowing further okay now we start becoming sharper and sharper okay and where it will appear this line will appear at the average of the weighted average of the two individual chemical shifts okay the final position the final position what you will observe in this situation will be omega observed will be P A or P A omega A plus P B omega B where P A and P B are the populations okay so omega A and omega B are the individual frequencies and this average will appear at the weighted average position when the exchange rate is far, far larger than the separation between those two and what is the meaning of fast this is called as fast exchange. Fast exchange meaning K is much, much larger than omega A minus omega B and this one is a slow exchange here this is slow exchange here K is much less than omega A minus omega B this is called as slow exchange okay so therefore you can see by monitoring this changes in the spectra as a function of some temperature or something like that or whatever you can actually try and measure the exchange you can study the dynamics of molecules inside your in the system and by simple examination at this point you can actually find out what should be the exchange rate of course you should know the omega A and omega B omega omega B these will present only when there is a slow exchange when you do it as a function of temperature at very low temperature you will see these two separate lines you take them as omega A and omega B okay and then you substitute that here then at the coalescence temperature or coalescence condition you can find out what is tau and once you know what is tau can calculate what is the exchange rate okay so let me show you an experimental spectrum of this here is a molecule so this is what we are seeing here are the two lines of these two methyl NCH3 CH3 these are the two methyl groups which have separate positions okay these are two separate lines and this is the spectrum recorded at 223 degree Kelvin and of this molecule in some solvent okay this is taken from this resource here okay so that is annual reports and annual spectroscopy so these two methyl groups are non-equivalent because the double bond character in this NC bond here therefore there is no free rotation around this bond therefore these two methyl groups are non-equivalent and then you will see two separate lines now as you start increasing the temperature there will be free rotation around this bond the rotation around this bond happens okay so when there is a rotation around this bond okay so therefore the exchange is happening the lines will start getting seeing the exchange between these two lines the lines start getting broadening broadened here and then at some intermediate value you see the lines have become so broad that is almost they are overlapping they are there is a small dip here that the depth of this one is decreasing and you get a coalescence condition here at 263 degree Kelvin see there is only one line the broad line here you see this is the coalescence condition and at this happens at 200 so now from here you can estimate what is the exchange rate and because you know this omega a and omega b here of these two positions and then you know you can therefore you can calculate here what is the exchange rate you can calculate tau and you can calculate the exchange rate and this happens at 263 degree Kelvin and if you increase the temperature further this will start narrowing down again and you will see this peak at an average position notice here that this is not quite in the middle of this line this is not here this is not quite in the middle so it is slightly shifted on to this side this is because the two populations of these are not necessarily the same they can be slightly different as a consequence of that you will see a line which is slightly at one side or rather okay this is an experimental spectrum and I will show you another experimental spectrum and this is of a molecule which is undergoing equilibrium like this so here you have a molecule so and we are talking about these two protons here so these two protons this is a bridge here and the bridge there are these two protons which are there and then you see this undergoes conformational equilibrium the trotomerism here between these two positions okay these two conformations okay so and therefore you see the signals which are presented this is the signal at slow time scale and you see the separately these signals here okay all of them are separately seen and you start increasing the temperature to minus 138 degree centigrade here okay you see this is extremely at a very very low temperature okay and as you start increasing the temperature exchange rate starts increasing and you see here at this point at this point this is become broad and this is sort of vanished here and then actually it is started appearing again the broadening has happened already here okay this is already broadened here this is the coalescence has already happened here and this happens differently for different groups you see it is not the same for this group and for this group it is different for the different groups therefore the exchange positions in the groups itself there can be different rates in the given molecule as because barriers can be different for the different rotations and therefore for this group you have a coalescence temperature at one point for this group there is a coalescence temperature at another point okay so therefore you can measure these exchange rates for the two things at different so at this point here this is the final thing at K is equal to infinity these extremely fast motions then you start seeing only these two lines here right this happens at minus 65 degree centigrade and you measure the exchange rate as 5880 seconds inverse okay so this provides a useful technique to measure the exchange rates and will also show you how you can use this phenomena to understand dynamics in proteins because in proteins there are all kinds of dynamics present there are the conformational exchanges domain motions and these are microsecond time scale motions the millisecond time scale motions nanosecond time scale motions so in proteins you have all kinds of motions on these various kinds of motions will show up in your NMR spectra how to extract that that is an important point there are other methods this is the very simple method of obtaining the information from looking at the one dimensional spectra but when you go into the proteins this spectra may not be so well resolved you may have to do other techniques and then of course the principles remain the same of course you are the slow exchange intermediate exchange fast exchange so the appearance in the spectra will change and you can use those data to estimate the conformational dynamics in proteins okay now there can be other effect of the exchange phenomena so there is let us say there are two conformations of a particular molecule suppose I have a molecule which is in conformation A and these exchanges with a another conformation B and here I have one coupling constant there is a particular proton pair let us say I have a coupling constant here and this is another coupling constant here J2 and I represent here the two spectra like this so I will have a line splitting here and I will have a line splitting here and this is J1 and this is J2 okay separation between these two and that is what is shown in this here so for the A side so I will have two lines here I will have two lines because of the splitting the separation between them is the coupling constant for the B side again I will have two lines and the separation between them is the coupling constant okay so now if there is a exchange here the coupling constant also will get averaged out the coupling constant will get averaged out and then you will get a J average J average is equal to PA J1 plus PB J2 okay and that shows up that is what you will see in the bottom spectrum here this is the bottom spectrum see where does it appear you see it is neither here nor it is in between if you draw a vertical line from there to here down so this line is lying in between this position and this position it is somewhere in the average position between these two lines and similarly this is also present at the average position between these two lines okay so therefore what you will measure is this coupling constant you will measure this coupling constant because of the conformational averaging so when this happens if you try to interpret this coupling constant in terms of the structure as one one common leaders because the coupling constants are related to dihedral angles in molecules so you have suppose I have a situation like this a three bond coupling so there is a J here then I measure here the J then I try to interpret the torsion angle this as a consequence we use the car plus relationship and things like that now you should be careful that if there is a conformational averaging what you will directly interpret may be wrong because of the average coupling constant will give you a certain value here fine but that may not be the actual structural value it be the it is the result of an averaging between these two positions therefore you must look at the stable conditions change the temperature change the conditions and find out the individual coupling constants there and then you will be able to figure out from this what are the populations of the individual individual conformations this is an important application also in structural biology this typically happens in proteins there are rapid rotations in the phi psi torsion angles in proteins this we will see as we go along okay that is the I am preparing the ground for understanding the phenomena in proteins and nucleic acids which will be your focus in the area of structural biology okay so now so this is the so far as the dynamism in the in the spectra and now we move on to another important concept in in NMR and that is the so called polarization transfer or NOE or polarization transfer is a very general term polarization transfer meaning that we transfer magnetization from one spin to another spin that means we transfer magnetization from one spin to another and this is an extremely useful structural tool or it can also be an assignment tool among these there is one important thing which is called as NOE this is nuclear overhouser effect okay now what is what is NOE new overhouser is the name of the person who invented it and of course there was initially it was the electron nuclear overhouser effect and subsequently this is the overhouser this is the nuclear nuclear overhouser effect that has become extremely useful for structure determination in proteins I will tell you what this means this is application I am just writing straight away structure determination in macromolecules okay so what is NOE let us say I have a spectrum so there are so many lines there okay when there are so many lines they of course have different chemical environments and therefore you have different lines now what I do is I do a perturbation here perturb this line what is the meaning of perturbation either I can do a saturation there apply a RF another RF which is exactly on line of that one and what is the consequence of this perturbation so you have a molecule something like that let us say we have a proton here and a proton there and a proton here a proton there so and so forth and this line let us say belongs to let us say this call this line as A let us this line be A and there are various other ones B, C, D and so on so many protons are there they are all giving you signals at various places now if you perturb this proton A will the perturbation remain there will it always remain there or it does it go to somewhere else can it transfer this perturbation to some other proton so if it has to transfer the perturbation there has to be an interaction between them if there is an interaction between them this can put it is like you know pack of cards so you have cards put one behind the other you perturb one fellow in the front and then all other fellows will fall down so it is a relay so the relay can happen see if a perturb this proton perturb it can relay its perturbation to another one so it can relay it here it can relay it here and so on so forth relay the perturbation and for this what is required there has to be coupling for this there is in coupling and that is the dipolar coupling and these are magnetic dipoles all the protons are magnetic dipoles therefore there is a magnetic dipolar coupling so if you perturb one of those so what it means when I perturb as I said suppose I have the energy levels for the spin A and these are the populations here so let us say I have this N1 here and N2 there when I perturb it meaning I change its populations so I have it here like this okay there was something like this so when I perturb it here then I may make it both of them equal I can make them equal or this is one perturbation or I can also do I can make it this one here and this one down there this is the number one number two so both kinds of perturbations are possible so essentially what we are doing is both are contributing to changes in the populations changed in the populations of the states okay so that is like a relaxation phenomena after you change the populations the system will have to recover okay and the system will have to recover how does it recover it has to give away its perturbation to somebody else okay so the perturbed populations have to recover and this happens by spin lattice relaxation so because of the spin lattice relaxation there is a relay of the perturbation from one spin to another spin and then it will show up in the intensity of this of this proton okay so let us say as a result of this I get a new spectrum whenever so what I do is I do two spectra so I do two spectra I have the same lines here this is the unperturbed spectrum well unperturbed is so for this I do a perturbation somewhere far away this is called the off resonance perturbation there is no line there I put a perturbation somewhere there so this is just as a control of resonance perturbation so I get a spectrum like this okay so this happens as a control just to see that the RF irradiation which I am doing and this is by RF irradiation and then I do another spectrum where I do the same thing and I have perturbed this this line this is perturbed okay so what do we do now this is the perturbed spectrum okay so this is x-ray let us say I call this as experiment number one this is experiment number two then what I do is I take one minus two different spectrum I take a difference so what do I get when I perturb this I will transfer the perturbation to those protons which are dipolarly coupled those which are not coupled they will not be perturbed at all there will be no difference in that so then what I will when I do this I will get a spectrum which may be like this there is a line here there is a line there and all others are gone to zero and here I will get something which is negative because you have perturbed this is made it zero here or saturated made it zero then I take this minus this or this minus this so I get a negative one here I have written one minus two but it could be two minus one also it does not matter so you have here a some change happening in this particular line some change happening in this particular line because these are the ones which are dipolarly coupled okay to the perturbed line so these are the enhancements or there can be decrease also and depending upon that we will have some perturbations in these areas okay so these are the so these are the relate and this effect is known as NOE okay and we can quantitatively define this as NOE is defined as n i let us say s is equal to i i minus i naught divided by i naught and what is i i i i is the perturbed intensity of spin i due to do the perturbation at spin s at spin s and i naught is the equilibrium intensity of spin i in the control that means in the absence of perturbation at spin s okay so when you do this you will measure this n i s and you say this will be this will be dependent on on various factors various factors the important thing being the gammas the gammas of the individual residues and the relaxation times the t ones relaxation times and the dipolar coupling dipolar coupling means distance because the dipolar coupling is proportional to inverse cube of the distance of course the NOE is proportional to inverse a sixth power of the distance so this here it is inverse sixth power of the distance distance between what and what between i and s these are the two spins which are considering we are saturating or perturbing the spin s and monitoring spin i okay and what I have here this is the i i minus i naught and these both refer to the spin i because the spin s we are not looking at we are looking at the spin i we are perturbed the spin s we are looking at the spin i so i i minus i naught divided by i naught so this is the with respect to the unperturbed intensity what is the change in the intensity that we are measuring so the effect of that is what is useful in a quantitative estimations of distances which in turn is a structural parameter okay so we can we can stop here