 So, this week we are discussing about protein dynamics which can be proved by NMR spectroscopy. So, in last lectures I discussed why dynamics, why dynamics is important, what all methods are there to measure dynamics and why NMR based dynamics. So, we will continue our discussion for the NMR based dynamics how we can do the experiments. So, typically we discussed that we measure the spin dynamics spin relaxation rate by carrying out two dimensional heteronuclear experiments such as HSQC heteronuclear single quantum coherence or heteronuclear multiple quantum coherence experiment. And then we can like measure the 13C or N15 relaxation, proton relaxation are rather complicated. So, they are not directly measured in protein NMR. So, typical scheme for 2D heteronuclear relaxation measurement is something like this. We have to start with a preparation state where we start preparing a desirable coherence like we start with a proton transfer to N15. And there we introduce the variable delay of various length which actually captures the auto cross relaxation rate. After this we introduce a T1 period which indirectly encodes the frequency such as N15 or 13C. So, that is a T1 period after T1 period we transfer the magnetization to proton because we are going to detect on proton. So, finally, transferring the magnetization back to proton and acquiring on proton while decoupling the heteronuclear like a 13C or N15. And then after acquisition there is a delay period that D1 period and this D1 period ensures that our magnetization are again back to the Z direction before we start the next scan. So, that then we go back and start the next scan. So, typically this is the experiment that is done preparation T1 delay here we are encoding that like a in case of say T1 experiment we will be encoding here longitudinal relaxation rate. So, delay T then followed by a T1 period indirectly frequency encoding transferring the magnetization on proton and finally, acquiring it. That is a typical acquisition period that we have in the 2D. So, if you look at the pulse sequence of a longitudinal relaxation which is like a T1 relaxation T1 or R1 relaxation rate longitudinal relaxation. This is the kind of pulse sequence that we used this is water flip back sensitivity enhanced T1 HSQC experiment. So, like water flip back is required for suppressing water as you know in protein the concentration of protein is typical of few hundred micromolar or maximum 1 or 2 millimolar, but the water concentration is very high. So, we need to kill the water water is general 55 molar. So, we have to kill the water and that is how all the protein experiments in encodes like has this water flip back or water suppression schemes here is also water flip back experiment. So, if you look at typically we are starting here with a inept transfer we are coming on the nitrogen then here we are encoding the T1 right that is a T1 variable and here is frequency encoding and after that we are transferring back to proton and then we are doing the sensitivity enhanced finally, we are acquiring on proton while decoupling on nitrogen. These are a gradient pulse for coherence selection as well as killing the undesired magnetization. So, this is the T1 period this is being introduced to measure the trans longitudinal relaxation rate in T1 pulse sequence. So, what we have typically 180 degree inversion pulse right. So, that inverts the magnetization from SZ direction to minus SZ direction SZ direction to minus SZ that is a inversion pulse right and then this T period is allowed that is given magnetization to come back to the Z direction. So, we first we invert it and then allow magnetization. So, once we invert like this it does the precessional motion come back to Z direction. So, this T period is basically varied and that is what measures. So, you start with a minus Z direction and then with a different T period we are measuring how the intensity changing and coming back to equilibrium. So, that is what you measured MZ at any point T is equal to MZ of equilibrium 1 minus 2 into e to the power T divided by T1. So, this is the rate and this T which was there if I use the eraser here. So, if you look at here we have a T period that T period essentially this T period is the time period that we are giving and T1 rate is the rate like this is the T time delay and T1 is the rate right. So, a 90 degree pulse creates the observable transverse magnetization for detection that is why we apply a 90 degree and then 41 measurement this relaxation block is inserted in the sensitivity enhance sensitivity enhance HSQC experiment ok. So, so that is that is how we do the experiment. So, let me summarize again we start with proton magnetization transfer to nitrogen then we invert it and then allow a T1 period then T1 period to create an observer sorry to spin to relax and then we apply a 90 degree pulse which creates the observable transfer magnetization transfer back to proton detect the proton that is what essentially we are doing in this T1 experiment. So, in terms of product operator if you look at we start with a z direction H z which with a 90 degree pulse converted to H minus H y then we are evolving under coupling and finally, transferring back magnetization to the nitrogen n y. Then we introduce the T1 time period here and finally, it goes to some eta of n z. Now, this factor eta is a T dependent time dependent of magnetization signal amplitude. So, you can write this factor is equal to 1 minus 2 e to the power T that time we are giving and T1 rate right or in simplified version 1 minus 2 e to the power minus T r 1. So, 1 by T1 1 by T1 is r 1 that is the rate and this is the time ok. So, this gives is so, the intensity that has decayed essentially gives us how much the magnetization is changing and that is how we measure it. So, this is the conceptual framework for doing the T1 experiment. Let us go how we set up the experiment and how we process the data in this case. So, we start with a usual stuff right we take a protein sample whatever concentration you can afford take it about 500 microlitre at 10 percent of D2O this is for locking. Then you do the sample height adjustment. So, like in a typical NMR to you, you have to have something around 2.1 cm or around 20 or 21 mm height adjustment. Then you tune the magnet, shim the magnet, set the one frequency one setting that usually stop in any protein NMR experiment that we do we are going to do it. Then we determine the 90 degree pulse there we calibrate it for transmitter and decoupler and we choose the spectral window how much we want to keep for our typical protein that we have. So, here generally you want to 0 to 12 ppm and here say 100 to 130 ppm should be fine for recording an N15 HSQC experiment. Now, important point because we are doing relaxation experiment, so typically we have to set a D1 which will be 5 times of T1. So, typically setup of D1 is recycle delay should be 1.5 to 2 second and generally we have to signal average good right. So, we have like a certainly number of a scan should be 4 or 8. So, in the experiment different T point we are recording right different time where the spin is relaxing. So, we need typically of 8 to 12 T delay which you can range from 5 millisecond to 1.5 second for N15. So, first 2D experiment we do with 5 millisecond, then 50 millisecond, 100 millisecond, 500 millisecond, 800 millisecond something like that at least 8 to 12 we need to do. And since these are inept based sequence, so we have to also look at what is the typical inept sequence. So, you can say you have set the time delay which is here tau it is at 2.7 millisecond right. So, that is what we set essentially and then we set the carrier frequency. So, in proton dimension it should be set at 4.7 ppm or something around that at water. The N15 dimension you have to set it somewhere in between. So, if you are doing that 100, 230 we typically set at 115 or something like that, 118, 115. Now you acquire the data, so like minimum should be 128 complex point in T1 and for proton it can be 1 k like 1024 T2 points. You can also record with this as a 256, here you can record at 256 and this is fine or you can record at 2 k right. So, that is a typical parameters that we are using. So, as we said we are recording 8 to 12 2D points. So, here is a representation of 2D, we are recording and with a different time point different T1 delay the signal is going to change right. So, essentially we start with a minus inverted signal then little bit less, little bit less and that is how it is in 1D that is what we see right, it goes something like this. But in 2D the signal is going to decay as we increase the T1 point. So, we record this data the 2D data and then do the two Fourier transform for each of these 2D data. And before doing Fourier transform we just do the usual stop like multiplying with a 90 degree shift square, sine bell function or cosine bell function or Gaussian whatever you fit it, then you 0 field at least twice of the digital resolution. So, you can 0 field up to 2 k and 1 k or 512 and 2 k, 2 k in in direct dimension 512. So, that digital resolution is typically of 2 hertz per point and then you can apply a 90 degree pulse on proton dimension or nitrogen dimension, 0 field is required before Fourier transform. If required you can do linear prediction that improves the digital resolution, but all the time it may not be required. So, you can take a call whether you want to have a linear prediction or not. So, these are cosmetics or processing data processing. Once you have processed data, remember all 2D like whatever 8 or 10 2D we are recording they should be identically processed right. So, for measuring the intensity, so once we process identically using these stops right. So, typically if you open a broker top spin that is what I have taken from this is the 0 filling you can do up to 5 to 48, 512. This is the frequency that you can for like spectrometer frequency, the SR values, then window function what we want cosine or sine, line broadening what is the SSV, you can choose all of these parameter that you need, phase correction value, now BC mode right all of these you can choose it whatever is needed for data processing getting a nicer well separated peaks. So, because you cannot measure confidently intensity of the peaks which are merged something like this right. So, you need to process so that all peaks are very well separated and one can only take well separated peak for data analysis right. So, we create this series of 8 or 10 or 12 2D, then for each peak now we are going to measure the intensity. So, series of the each series of the spectra is phase corrected right and then proton dimension adjusted according to the first FID, phase or dimension like a phase of the N15 phase is here that phase is corrected here. So, phase you have to correct for the both dimension, phase is corrected. Now essentially we are measuring the amplitude of cross peaks or we can measure the volume integral of each peaks and signal should not be a overlap right. So, you need to have that is what I was mentioning, you need to have all separated signal in the 2D for the data analysis. We measure the volume integral or intensity integral say ij at any point any t point right say 2 millisecond, 5 millisecond, 500 millisecond so all those intensity are measured and that is fitted in a equation to measure the longitudinal relaxation time constant by fitting the equation. So, what is the equation that we are fitting essentially this is the equation that we had discussed earlier right. So, this equation essentially we are fitting to get the T 1 parameter. So, this equation 1 minus 2 e to the power t divided by T 1 or multiplied with R 1. So, rate or time we can measure it. So, if you measure it for say various amino acid that I am showing from one of the protein work. So, here for leucine sorry leucine 24 phenylalanine 36 lysine 46 you see with the T 1 time which is varying from 0 100 to say 1.2 millisecond intensity is plotted and you can see with a time this intensity decrease. And that is what we are going to fit into this equation that we were saying T by T 1. So, we fit this equation and find the T 1 time or the R 1 rate that is coming right. So, this fitting we can do residue a specific manner all non-overlapping residues should be used for this fitting. Once we fit it we can get the T 1 relaxation rate for each of the gemino acid and now one can plot it in a residue a specific manner. So, here I am showing you a protein which is called human sumo that I had worked on. Now, this protein has a globular domain which is here it has a similar fold like a ubiquitin beta beta alpha beta beta alpha fold and it has a long end terminal stale of about 20 amino acid and short C terminal stale of about 4 to 5 amino acid there are loops here. So, now, we are like I am going to discuss the T 1 data that we have recorded for this protein. So, here is the residue a specific manner plotting of this data. What we see here right so, initially the T 1 of these 20 amino acid shows higher value. Now, for all the well folded region alpha helix beta sheet or so, we are seeing the sorry this is the R 1 value 1 by T 1 so, 1 by T 1 is R 1. So, relaxation rate for the flexible domain is higher for well folded domain is lower that means, the T 1 value for this is going to be shorter and for this is going to be longer. So, T 1 and R 1 has an inverse relation. If you look at all the flexible portion has a high relaxation rate longitudinal relaxation rate again loops here which connects the 2 beta from here and some of the C terminal again have high here loops are high. So, all the loops you can see shows high longitudinal relaxation rate and all well structured domain in this protein whether it is alpha helix or beta sheet shows relatively less relaxation like longitudinal relaxation rate. Now, suppose I put this protein in urea where all measure of the secondary structure is removed. So, suppose I am doing the same experiment in 8 molar urea which denatures the protein. So, now the typically alpha helix beta sheets all the are all of those are gone and now you see what the rates are changing. So, if you look at here residue specific manner 0 to 100 what we see here that more or less it becomes flat. So, whatever you see sequence wise variation here when the protein is folded if you denature the relaxation rate is gone. So, if we measure the T 1 relaxation rate of a protein it tells the motion in a residue specific manner the longitudinal relaxation rate in a residue specific manner and you see if we remove the structural elements from the protein this T 1 relaxation rate becomes majorally flat. That means, all the relaxation sequence wise variation that we were getting is becoming absolutely similar. Good. So, that was about longitudinal relaxation rate which is called spin lattice relaxation rate. Now, coming back to another relaxation rate which is called transverse relaxation rate the T 2 relaxation rate T 2 or T 1 row the T 1 in a rotating frame are more or less similar I will just discuss the T 1. So, what is how we can measure the sorry we will just discuss the T 2 how we measure the transverse relaxation rate ok. So, the sequence of T 2 was initially developed by Faroe et al that I am going to show you in the next slide. So, it is similar to T 1 essentially it is a similar to T 1 instead of creating a minus z direction right by applying of 180 degree pulse here we create a coherence. So, here we inversion scheme is replaced by a CPMG or spin lock sequence CPMG in case of R 2 and spin lock in case of T 1 row. So, this rather than like here in T 1 what we saw our magnetization started with minus z direction and it went back to the plus z direction. Now, in this case we are starting with a transverse relaxation rate. So, rather than decaying along the longitudinal relaxation the heteronuclear magnetization relax in the transverse plane during this time T in the T 2 pulse sequence. So, here we are not going like this here just by applying a 90 degree pulse or CPMG pulse we are coming in the transverse plane and from here now our spin is going back to the equilibrium state right. So, what contributes so, in your addition to spin-spin interaction why because this is transverse relaxation rate is spin-spin relaxation rate. So, other than the spin-spin interaction the field homogeneity magnetic field in homogeneity also contributes to transverse relaxation rate. So, to remove this contribution coming from field homogeneity the CPMG spin echo sequence which was developed by Karl, Pulsall, Meeboom and Gill was introduced in the T 2 scheme. So, CPMG scheme of heteronuclear magnetization what happens here we started with a S z and by applying a 90 degree pulse we came to S x. So, S x evolved during this period of say epsilon under the interaction of chemical shift and field in homogeneity. Then we apply a 90 degree pulse which reverse the direction of process. So, we started with here we went back here and now it is slowly diffusing and then we apply a 180 degree pulse. So, it goes like this and then slowly it defuses and then finally, it refocussed during the second period of eta right. So, first it defuses then you apply it and then it come back. So, the provided the spin being refocused remain in the identical magnetic field during this both period of epsilon right. So, then we can measure the rate. So, resulting transfers magnetization at the end of the even echo period of the CPMG CPMG pulse strain has an amplitude something like this I is a intensity at any time point and I 0 is the initial intensity. Now, T is the time period with which we have like waited for and R2 is the spin relaxation rate ok. So, that is what we measure basically for the T. So, now T is 2n 2 eta that time that we are discussing pulse width of 180 degree pulse. So, that is a CPMG pulse strain that we are measuring and essentially we are measuring again intensity during the T2 period. So, this is our pulse sequence that we are using we have started in a with a inept block we are coming back to here nitrogen then you can see here we are introducing this CPMG pulse and during this the T2 relaxation is happening then we are frequency encoding going back to proton detecting on proton while decoupling the nitrogen. So, this is the T period during which transfers relaxation is happening and that is happening on nitrogen nuclei. So, that is what we measure. So, again we record from 8 to 12 of 2D with different T2 time the Fourier transform them process them and then we measure the intensity in a residue specific manner as we did for T1 and you can get the T2 rate. So, here typically the duration that we keep is 0 to about 200 millisecond. So, here you can see for different residue like Q53, 25 K that lysine and K25 that is lysine and I solution 88 here the signal intensity decay are measured ok. So, now each of this fitting gives us a rate of a particular N15 nuclei. So, data processing is done in a similar manner typically 8 to 12 relaxation delay ranging from 5 millisecond to 150 millisecond is recorded and data processing similar like T1. So, if you do that and plot in a residue specific manner. Now, what we get is this one. So, here this is the again rate. So, here the for the flexible portion we are getting the less R2 value whereas, all the structured portion we are getting more R2 value this you remember this is spin-spin relaxation. Now, this was slightly different in case of T1 here if you look at this is reverse here for the flexible portion we are getting the higher R1 rate lower R2 value. For the structured portion we are getting typically lower R1 value, but higher R2 value. So, this is the typical signature we get again at the end you see the lower R2 values are there. Now, some of these peaks are also showing the high value. The one contribution because R2 consist of R2 intrinsic plus rex. Now, this is exchange phenomena. So, R2 also encodes the exchange chemical exchange that is happening for doing that you require like a relaxation dispersion experiment, but looking at this you can say that this protein is geared to show some chemical exchange which needs to be further probed. So, I am not going in detail of the rex at the moment, but that information is hidden there. Now, similarly if you look at the denatured protein again if you put this sumo protein in it molar urea you can see similar like R1 the R2 becomes also flat. So, all exchange are suppressed all the sequence wise variation is suppressed. So, here is the folded protein in zero molar urea R2 and for ready reference I am also showing in denatured state. So, everything is suppressed now protein behaves quite uniformly because earlier it was quite folded and when you put in 8 molar urea it become like a disorder right. So, 8 molar is zero molar. So, just to show that the dynamics that we are measuring also tells a lot about structural compaction where is the flexibility where is the rigidity. So, not only structure, but also NMR can probe dynamic in a residue specific manner. Now, you can even use this concept for protein folding study. So, here I show you how like a urea concentration wise R2 changing. So, 8 molar urea you have more or less flat, but when you reduce the urea you see some central portion is coming up like it has a this profile if you go to 5 molar it has this profile. So, all the central portion where a structure was supposed to be there basically building up and that is how measuring the R2 dynamics also tells about what is the folding hot spot where the structure is forming and that is what you can measure it in a residue specific manner to understand the protein folding. So, with this I just want to summarize today R1 and R2 are two basic experiment that are done for the protein NMR. Next class I am also going to discuss about heteronuclear NOE, R1 measures the longitudinal relaxation rate, R2 measures the spin relaxation rate and they are for the folded region and there is a like for the folded region there will be low R1 high R2 for like a disordered region or the flexible portion it will have a high R1 low R2 right. So, and R2 can be used to monitor the structure that could be formed during the protein folding that is what I am showing you here. So, with this I am going to close it today and in next class we can take heteronuclear NOE and how we can combine all these basic experiment of protein NMR, T1, T2 and NOE, R1, R2 or NOE to reduce spectral density function or even modal free ok. So, with this I am closing it here for today see you in the next class. Thank you very much.